University
stringclasses 19
values | Text
stringlengths 458
20.7k
|
|---|---|
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
2.3. A hydraulic balance using a hydraulic mixing-cell method
The hydraulic mixing-cell (HMC) method introduced in this paper allows the
streamflow generation mechanisms to be deconvoluted from the streamflow
hydrograph at any point along the stream. The method relies on standard
hydraulic output from numerical models only. It is based on the modified mixing
cell of Campana and Simpson (1984). Furthermore, it is assumed for the
simplicity of coding that the width of the stream does not change during the
simulation and additionally that the flow direction in the stream does not change.
This mass balance of the HMC method is verified by application to two numerical
test cases using HydroGeoSphere. The method can be generalised to any spatially
distributed surface water - groundwater code, as mentioned previously.
2.3.1. Theory
The numerical modelling of streamflow requires discretisation over space and
time of the relevant governing flow equation using a finite difference (FD), finite
volume (FV) or finite element (FE) scheme. The method developed herein is
designed to fit in accordingly with existing numerical models.
Consider the continuity of flow for a stream cell i of arbitrary shape. This can be
expressed in terms of the streamflow generation/depletion as:
dV
Q (cid:6)Q (cid:6)Q (cid:6)Q (cid:6)Q (cid:5)Q (cid:4)Q (cid:4)Q (cid:3) (2.1)
Up GW OF UF PF Rain Down Evap dt
Where Q [L3/T] is the upstream flow (generated from groundwater, overland
Up
flow, unsaturated flow and rainfall) into the stream cell; Q , Q , Q and Q
GW OF UF PF
[L3/T] are the groundwater, overland flow, unsaturated flow and preferential flow,
respectively, flowing into or out of the cell; Q [L3/T] is the rainfall contribution
Rain
to the stream cell, Q is the flow downstream (generated from groundwater,
Down
overland flow, unsaturated flow and rainfall) flowing out of the cell [L3/T]; Q
Evap
[L3/T] is the loss of water from storage (composed of groundwater, overland flow,
unsaturated flow and rainfall) due to evaporation; dV/dt [L3/T] is the rate of
change of storage within the cell.
19 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
For each component of streamflow the fraction is determined using the modified
mixing cell which approaches a perfectly mixed cell as the time step approaches
zero. A perfectly mixed cell will completely mix all contents across the entire cell
instantaneously and takes the form:
(cid:14) (cid:11)
(cid:7)m V N (cid:12)(cid:12) f N(cid:4)1(cid:5)(cid:7)n V N f N(cid:4)1 (cid:9)(cid:9) (cid:7)n V N f N(cid:4)1
f N (cid:3)V iN(cid:4)1 f N(cid:4)1(cid:4) j(cid:3)1 ij N(cid:4)1(cid:13) i(k) j(cid:3)1 ji N(cid:4)1 j(k) (cid:10) (cid:5) j(cid:3)1 ji N(cid:4)1 j(k) (2.10)
i(k) V iN i(k)
VN
(cid:5)(cid:7)n
V
N V iN
i ji N(cid:4)1
j(cid:3)1
It can be readily seen that Eq. 2.9 approaches Eq. 2.10 as the time step approaches
zero, as only the first term on the right hand side in both equations will remain.
In applying this method, volumes in and out need to be determined at the start and
end of each timestep. This requires reconstruction of the functions describing flux
in and out of each cell. The approach used in calculating volumes needs to be
consistent with the manner in which the fluid mass balance is calculated in the
particular model used. In this study, the HydroGeoSphere (HGS) (Therrien et al.,
2009) code is used in which the flux Q between two adjacent nodes is back
calculated at the end of the time step, giving rise to the following equation for
evaluating the volume in or out over each time step:
VN (cid:3)QN (cid:16)(cid:15)tN where (cid:15)tN (cid:3)(tN (cid:4)tN(cid:4)1) (2.11)
ij ij
Where Q N denotes the calculated flux from HGS from node i to j over (cid:15)t.
ij
The form of Eq. 2.11 will vary from code to code depending on how the fluid
mass balance is calculated. Furthermore, the choice of numerical approach, be it
finite difference, finite volume or finite element, is irrelevant as long as the
volumetric balance for each cell is formulated correctly and is mass conservative.
The latter requirement is due to the error in the mass balance at each time step
being cumulative in the HMC method. Stability of the HMC method is not
guaranteed for any flow solution as highlighted above. The use of suitable
convergence criteria within the flow solution is imperative in successful
application of the HMC method. A strict convergence criterion that is applied at
22 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
the nodal level is required. The nodal flow check tolerance in HGS, which is
derived in McLaren et al. (2000), was utilised to ensure the nodal volumetric
balances calculated in the HMC method were sufficient in preventing large
cumulative errors. The choice of timestep and cell size also plays an important
role in the stability of the HMC method because the volumetric balance at each
HMC cell over each timestep is directly related to timestep and cell size. The
proportion of volumes of water entering or leaving each cell over each time step
compared to the storage volume in the cell has a direct impact on the HMC
method’s stability. The use of small HMC cells and large timesteps can lead to the
volume entering or leaving a cell being greater than the storage and as such the
method will become unstable causing spurious oscillations. Hence it is necessary
to use suitable time steps for a fixed grid (i.e. fixed cell size) to ensure stability.
2.3.2. Implementation of the HMC method in HydroGeoSphere
The testing of the HMC method outlined in this paper was carried out by
considering two conceptual test cases using the HGS model. HGS solves the
diffusion wave approximation to the 2D St Venant equations in the surface
domain and solves a modified form of the 3D Richards equation for variably
saturated flow in the subsurface domain using a control volume finite element
approach (details of the model can be found in Therrien et al. (2009)). The surface
and subsurface are coupled using either continuity of head or (as in this study) a
conductance concept, with exchanges between the two domains given by:
k K
q (cid:3) r zz (h (cid:4)h ) (2.12)
exch l o pm
exch
Where q [L/T] is the exchange flux between the surface and subsurface
exch
domain; k [dimensionless] is the relative permeability; K [L/T] is the saturated
r zz
hydraulic conductivity of the porous medium; l [L] is the coupling length, h
exch o
[L] and h [L] are the heads of the surface and subsurface, respectively. HGS has
pm
been verified for both gaining (Therrien et al., 2009) and losing streams (Brunner
et al., 2009a, 2009b). The model solves the governing flow equations using the
finite element (FE) method, finite volume (FV) method or, alternatively, the finite
difference (FD) method applied on a node centred grid (Therrien et al., 2009).
23 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
Application of the HMC method requires specific HGS model outputs in order to
accurately construct the volumetric balances in each HMC cell. As HGS utilises a
node centred approach, the following HGS outputs are required for the volumetric
balance at any given node:
1.) Computed surface water depth at the node – for the storage at each time step.
2.) Contributing area, CA [L2] for the node determined from finite element basis
functions (1/4 of the area of each element adjacent to the node for both FD and FE
on a structured rectangular grid) – for the Storage ( = depth x CA) [L3] at each
time step.
3.) Exchange flux between the subsurface and surface node – for the volume (Eq.
2.11) exchanged between the subsurface and surface over each time step.
4.) Flux from upstream contributing nodes – for the upstream volume (Eq. 2.11).
5.) Flux to downstream nodes – for the downstream volume (Eq. 2.11).
1.) and 2.) are used to calculate V, 3.) used to calculate V for the exchange, 4.)
i ji
used to calculate V for upstream flow, 5.) used to calculate V for downstream
ji ij
flow. The initial values for the fractions of stream flow are subjective and so a
dummy (or undefined) fraction can be used until the streamwater is turned over at
which point the dummy fraction will be zero.
This output data provides all the information required to apply the HMC method
and determine the groundwater component of streamflow at each time step in each
cell of the stream. The partitioning of groundwater, overland flow and rainfall
entering the HMC cell is calculated from the upstream cell in the previous time
step. The fractions of streamflow components leaving a given cell over a given
time step are given by the cells’ fractions at the previous time step. In doing so,
water entering over a given time step remains in the given cell until the next time
step. The HMC method was coded in Visual Basic for Excel and is used as a post
processing tool on HGS outputs.
24 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
2.3.3. Verification of mass conservation in the HMC method
2.3.3.1. Test case 1
This test case is used to check that the flow components can be tracked accurately
and to explore the significance of grid discretisation. The surface domain of the
model is subjected to groundwater discharge (gaining conditions) across half of
the model surface. This groundwater discharge in the gaining region is equal to
the summed exfiltration obtained from the overall water balance, providing a
benchmark against which the method can be tested.
The model domain is 2 m x 1 m x 1 m, split into two evenly sized rectangular
cells (Figure 2.4). Two regions are highlighted in Figure 2.4, a gaining region in
one half and a non-gaining region in the other. The non-gaining region has
negligible interaction with the subsurface. With the soil fully saturated and an
initial surface water depth of 0.01 m across the surface domain, a square pulse of
groundwater (1.0 m3/day for 0.1 days) is injected into the subsurface cell
underlying the gaining region. No-flow boundaries are applied to all edges of the
model domain allowing the groundwater (GW) pulse to be the only forcing
function within the model. This simulation is run over a period of half a day with
the groundwater pulse applied at 0.1 days. The grid spacing is 1 m along the x, y
and z axes. For this HGS simulation, a control volume finite difference
formulation is used to solve the coupled surface and subsurface flow equations.
The nodal properties give rise to three ‘cells’ for the HMC method (see Figure
2.4). Note that rather than considering six nodes individually, the HMC ‘cells’
each consist of 2 adjacent nodes perpendicular to the flow direction. The HMC
cells are given the initial conditions of containing ‘surface water’ (SW) only and
hence f = 1 and f = 0 for all HMC cells at t = 0.
SW GW
In the surface domain, a high value of Manning’s n (1.5 x 10-5 day/m1/3) is used
in order to make the transient part of the simulation apparent. The aquifer
parameters are defined such that surface/subsurface interactions other than the
groundwater pulse are negligible. The porosity is 0.45 and a low value of
hydraulic conductivity (1 x 10-4 m/day) is used to effectively render the
subsurface inactive with regard to infiltration.
25 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
Figure 2.4: Test case 1: “two-region” model grid, and HMC cells for HGS
nodes in “two-region” model grid. In the right part of the figure the two
nodes at y = 0 belong to HMC cell 1, the two nodes at y = 1 belong to HMC
cell 2 and the nodes at y = 3 belong to HMC cell 3.
As the subsurface is fully saturated, infiltration is negligible, and the groundwater
injected to the system will directly result in a fluid flux from the subsurface to the
surface domain. The coupling length chosen (1 x 10-5 m) is sufficiently small to
achieve continuity of head between the surface and subsurface. A maximum
timestep of 1 x 10-3 days was used for the first simulations. As the diffusion wave
approximation to the Saint Venant Equations is used in HGS, inertial effects are
ignored and therefore water entering the gaining region will move to the non-
gaining region and not flow back as it would if inertial effects were included.
Figure 2.5 shows the volumetric balances of surface water and groundwater
calculated for each of the three HMC cells in the model, highlighting the subtle
complexities that can easily be overlooked when considering the dynamics of
such a system. It can be seen in cell 1 of Figure 2.5 that whilst the groundwater
pulse is applied to the subsurface, groundwater is entering the gaining region,
causing an increase in volume (and hence head) and a resultant flux from the
gaining to the non-gaining region. Moreover, the volume of surface water in the
gaining region decreases as the groundwater enters, which is due to the water in
the gaining region flowing to the non-gaining region. The volumes of
groundwater and surface water in cell 2 are collectively larger than those in cells 1
or 3 because the contributing area of cell 2 is twice that of cells 1 and 3 (see
Figure 2.4). The small lag between the surface water and groundwater curves in
the volumetric balance for cell 3 (Figure 2.5) indicates that surface water initially
26 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
contributes more to the flow from the gaining region to the non-gaining region, as
the surface water is displaced by the groundwater. The SW and GW balances for
each of the HMC cells in the top panel of Figure 2.5 are also shown with the total
cell volume. Clearly, the SW and GW balances sum to the total volume,
indicating that that the HMC method conserves mass. The SW and GW fractions
for each of the HMC cells in the bottom panel of Figure 2.5 are seen from the
average of the two fractions to be inversely proportional to each other, as
expected. As the balances are calculated independently, this further highlights the
accuracy within the HMC method.
The relative error ((cid:17)) in the balances is based on Eq. 2.7 and is determined using
the following equation:
(cid:7)k
(cid:17)(cid:3)1(cid:4) f N (2.13)
i(k)
j(cid:3)1
The relative error relates to the accuracy of the numerical methods for solving the
flow equations, which is determined by the convergence criteria used in the
numerical scheme. This error grows slightly due to round-off errors and imperfect
balances in the numerical scheme used to solve the flow equations (finite
difference in this case). Such imperfect balances will always exist due to error in
the numerical scheme adopted, however they can be minimised by use of a small
value for the convergence criterion. In this test case the maximum relative error in
the HMC method was 1.5 x 10-3% in cell 1.
To investigate the effect of discretisation, the grid spacing dy in the flow direction
(y axis) is reduced in HGS from 1 m to 10 cm. As a result, the number of
corresponding cells in the HMC method increases to 21 (see Figure 2.6). Three
different simulations are then run to test the impact of time discretisation, with
constant time steps equal to 10-2, 10-3 and 10-4 days, respectively.
27 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
Figure 2.5: HMC cell, SW and GW balances (top panel) and fractions
(bottom panel) for test case 1. The volumetric balance in the top row shows
the HMC calculated balances for SW and GW in the HMC cells as well as the
total volume in the cell which is calculated directly from the model outputs.
The HMC cell SW and GW fractions in the bottom panel are calculated
independently of each other.
The effects of temporal discretisation on the SW and GW fractions for the case of
dy = 10 cm are shown in Figure 2.7. In Figure 2.7, only the two end cells (1 and
21) and the middle cell (11) are shown. It can be seen that the finer timesteps
make little difference to the SW and GW fractions in cells 1 and 11, but that a
distinctly different solution of the SW and GW fractions arises in cell 21 for the
three timesteps used, with convergence at t = 10-3 and 10-4 days. It follows that it
is important to note that the timestep used in the model will dictate the SW and
GW fraction profiles in the HMC method. As highlighted in the theory, as dt
approaches zero, a perfectly mixed cell solution is approached. Variation in grid
size changes the representative area of the HMC cells. For example, halving the
grid size would result in the HMC cell area for the larger grid size being
represented by two HMC cells for the halved grid size. As the HMC cells are
representative of an area and not a point, results based on different grid
discretisations are not directly comparable. However, finer grids will give greater
spatial resolution of the SW and GW fractions along the surface. It follows that
28 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
smaller cell sizes in the model grid and hence in the HMC method, result in
greater spatial clarity of the solution, converging towards a point solution as dy
approaches zero. As dy approaches zero, the area of the cell approaches zero and
hence the volume in the cell approaches zero. Given that stability requires that the
volume in or out of the cell cannot be greater than the storage, the time step dt will
also have to decrease as dy decreases to ensure numerical stability.
Figure 2.6: The 21 HMC cells for the "two-region" model with dy = 10 cm.
Figure 2.7: Effect of temporal discretisation on the SW and GW fractions in
HMC cells 1, 11 and 21.
A second approach to testing the accuracy of the HMC method is to compare the
total volumes of surface water and groundwater resulting from summing these
components in each HMC cell at the end of the simulation with the overall water
balance in the model. By summing the final volumes of groundwater in each
HMC cell, and comparing these to the total volume that was exchanged from the
subsurface to the surface domain during the simulation, a global volume error
(GVE) can be defined as follows:
29 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
(cid:7)
f N VN
i(GW) i
GVE(%)(cid:3) 1(cid:4) (cid:18) (cid:7)i (cid:16)100 (2.14)
QN(cid:15)tN
SE
(cid:18)N
Where Q N [L3/T] is the summed exfiltration (SE) across the model domain at
SE
time N from the overall water balance of HGS.
This measure gives the error of the HMC method relative to the summed
exfiltration from the overall water balance. The cumulative error of the HMC
method (as opposed to the instantaneous nodal fluid mass balance error in HGS)
will grow according to the convergence criteria, number of time steps and number
of stream cells. As the GVE is based on the summed exfiltration from the overall
water balance, it can only be used along completely gaining sections. It also
requires that all water is retained in the model domain (i.e. no losses). The
maximum relative error and GVE are given in Table 2.1 for the different spatial
and temporal discretisation tested, highlighting both the reduced maximum
relative error and GVE as the spatial and temporal resolution is increased.
Table 2.1: Maximum relative error in the HMC method, and the global
volume error (GVE) for the HMC method.
HMC max.
GVE Timesteps
relative error
dy = 1m, t = 0.001 days 1.5 x 10-3% 1.97 x 10-4% 500
dy = 10cm, t = 0.01 days 1.8 x 10-4% 5.23 x 10-10% 50
dy = 10cm, t = 0.001 days 3.6 x 10-5% 1.17 x 10-10% 500
dy = 10cm, t = 0.0001 days 3.9 x 10-7% 2.81 x 10-11% 5000
In the HMC cells of Test case 1, the relative and absolute errors are relatively
small and consequently the HMC method can be used in larger and more complex
model scenarios provided that fluid mass conservation is fulfilled.
2.3.3.2. Test case 2
The model setup for Test case 2 mirrors the physical processes of the catchment
shown in Figure 2.1. This test case is used to test not only the theoretical effects of
time lags (seen in the hydrographs of Figure 2.2) and accurate attribution and
tracking of streamflow generation mechanisms, but also to test the HMC method
30 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
in a highly transient model scenario whilst comparing the HMC method’s
groundwater component of streamflow with the summed exfiltration from the
overall water balance of the model.
Test case 2 is loosely based on the tilted V-catchment by Panday and Huyakorn
(2004), which has been used in verification of surface/subsurface interaction in
fully integrated models such as MOD-HMS and HGS. A number of modifications
are carried out to the V-catchment to mirror the spatial and temporal distribution
of the catchment shown in Figure 2.1. In order to distribute the subsurface to
surface exchange to the stream over its entire length, the slopes are reduced,
resulting in a significantly flatter catchment. The model domain shown in Figure
2.8 is 1000 m along the y axis by 810 m along the x axis (catchment area of
810,000 m2), with a homogeneous soil layer thickness of 20 m at (x = 800 – 810
m, y = 0 m) increasing in thickness with a gentle surface slope of 5 x 10-4 m/m
along the y axis (from y = 0 m to y = 1000 m) and 0.02 m/m along the x axis
(from x = 800 m to x = 0 m). With the use of the gentle slopes, the head gradient
required in order to produce an exchange from the subsurface to the surface along
the entire stream is achieved by raising the adjacent plane 2 m over a 5 m length
above the streambed as shown in the cross section of Figure 2.9.
Figure 2.8: Test case 2 catchment model (modified version of the V-
catchment in Panday and Huyakorn (2004)). The contours correspond to the
elevation.
31 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
Figure 2.9: Part cross section of hypothetical catchment highlighting the
raised plane which is used to create a greater hydraulic gradient next to the
stream leading to constant subsurface to surface exchange along the entire
length (from x = 790 – 810 m, at y = 0 m and z = -4 to 2 m). The plane (left),
bank (middle) and streambed (right) are seen in the division of top cells.
Grid spacing along the x axis is 50 m from x = 0 – 750 m, 25 m from x = 750 –
775 m, 15 m from x = 775 – 790 m, 5 m from x = 790 - 800 and 10 m from x =
800 – 810 m. The grid spacing is 50 m along the y axis and 1 m along the z axis
for the first 10 m below the surface with a thickness of 10 m to 26.5 m, varying
with the slopes of the catchment for the bottom layer. Streamflow at the
downstream boundary is governed by a critical depth boundary condition at the
end of the stream, which acts at nodes (800,0,0) and (810,0,0). The critical depth
boundary in HGS specifies the surface head to be at critical depth at the nodes
which are set with this boundary condition.
Saturation-relative permeability and saturation-pressure relationships are
described by the van Genuchten (1980) equations. The soil is a homogeneous
sand with the soil parameters derived from Carsel and Parrish (1988). The
surface friction is described using Manning’s n, with a value representing a
straight uniform channel (Chow, 1959), and a rill storage height and obstruction
height (as defined in Panday and Huyakorn (2004)) of 1 mm and 0 mm,
respectively. The rill storage height provides a threshold to surface flow whilst the
obstruction height provides retardation to flow. The surface and subsurface
parameters are detailed in Table 2.2. The coupling length (Eq. 2.12) is chosen
such that continuity of pressure at the surface/subsurface interface is maintained,
without jeopardising the accuracy of the flow solution. The solution of continuous
32 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
pressure at the surface/subsurface interface leads to much larger run times for the
simulations in this study (see Ebel et al., 2009), however for small coupling
lengths, the solution approaches that of continuous pressure at the
surface/subsurface interface.
Table 2.2: Surface and subsurface parameters for test case 2.
Parameter Value
Surface
Manning’s roughness 0.015 s/m1/3
Rill storage height 0.001 m
Obstruction storage height 0.0 m
Subsurface
Porosity 0.1
Saturated hydraulic conductivity 8.25 x 10-5 m/s
Van Genuchten (cid:2) 14.5 m-1
Van Genuchten (cid:19) 2.68
Residual saturation (cid:20) 0.045
r
Surface/Subsurface coupling
Coupling length 0.5 m
The simulations for the hypothetical catchment are carried out in two phases:
1. Firstly, initial conditions are generated by running the model with a fully
saturated subsurface with only the critical depth forcing function in the surface
domain for approximately 40 days. This first simulation provides quasi steady-
state initial conditions for phase 2.
2. Based on these initial conditions the model is run for another 40 days with 3
rainfall events and constant groundwater pumping throughout the entire
simulation. The drawdown around the pump results in a losing section along a
part of the stream. Rainfall is applied across the entire catchment, starting at time t
= 0 seconds at a rate of 5.88 x 10-7 m/s (2.12 mm/hr) for a day at a time with three
recovery periods after each rainfall period of 10, 5 and 22 days, respectively for
each rainfall event. Pumping is applied at node (750,500,0) at a rate of -0.02 m3/s
throughout the simulation time. This extraction rate is sufficient to produce losses
over part of the stream. Over the length of the simulation there is a rainfall input
of 1.75 x 105 m3 and a loss through pumping of 6.84 x 104 m3. The maximum time
33 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
step used in the second phase of the simulation is 100 seconds. The rainfall and
pumping in the second phase create highly transient conditions. The length of the
stream that is losing is changing throughout the simulation. The nature of this
transience in the streamflow conditions allows for rigorous stability testing of the
HMC method because the stream cells are switching between gaining and losing
and are subject to sharp changes in volume and rate of change of volume in the
cell.
The rainfall events in the simulations provide recharge to the groundwater system,
sustaining flow to the stream. However, the gentle rainfall events and gentle
slopes in the catchment result in pure recharge with no overland flow on the
planes and hence no direct overland flow to the stream itself. Figure 2.10
highlights the changes in the subsurface to surface exchange, as well as the depth
and velocity along the stream at time = 1 second, 12 days and 40 days. At t =1
second in Figure 2.10, the initial stream is gaining along its entire length, before
groundwater abstraction has taken effect. At t = 12 days, there is an increased
discharge of groundwater at the top and bottom areas of the stream, which can be
attributed to the recharge resulting from rainfall as well as stream losses in the
middle section due to near stream groundwater extraction. The proportion of the
stream that is gaining and losing is varying throughout the entire simulation.
At t = 40 days, the subsurface to surface exchange to the stream has decreased
along the length of the stream due to the last rainfall event finishing 20 days
earlier. It also shows an increased loss from the stream over the middle losing
section due to reduced recharge in response to the groundwater extraction. This
loss rate from the stream in the middle causes the stream depth to drop over the
losing region, however streamflow is maintained through the entire simulation.
This qualitative analysis provides a reasonable understanding of the governing
processes in the system. For quantifying the groundwater component of
streamflow, the HMC method is required.
34 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
The HMC method is applied to each pair of adjacent nodes that are located at x =
800 m and x = 810 m and that lie in the stream perpendicular to the direction of
flow. HMC cells are numbered from upstream (y = 1000m) to downstream (y =
0m) and correspond perfectly to the HGS cells. This gives rise to 21 HMC cells,
with 20 surface cells (x = 800 – 810 m and y = 0 – 1000 m) defined as the stream.
As a node based approach is used, the contributing area of nodes lying along x =
800 m takes into account the surface cells lying between x = 795 – 800 m. The
HMC maximum relative error in the simulation was 8.7 x 10-3% in HMC cell 13
at around t = 12 days.
The use of the HMC method allows the quantification of the groundwater
component of streamflow at any cell along the stream. Since the simulation set up
does not produce overland flow, the streamflow in each HMC cell consists of the
groundwater component and the direct rainfall component of streamflow. The
resultant groundwater component and direct rainfall fractions before and after the
first rainfall event for the HMC cells located at y = 0, 600 and 1000 m are shown
in Figure 2.11. In Figure 2.11, the rise and fall of the direct rainfall fraction is
sharp and fast in cell 1 and slower and longer in cells 13 and 21. This can be
attributed to the time lags of upstream flow that are evident at the downstream
cells and to the streamflow velocity in each cell. In Figure 2.10, the stream flow
velocity is seen to increase from the top of the stream (y = 1000 m) to the bottom
of the stream (y = 0 m) as water keeps entering the stream, although this is only
seen in the gaining regions. At t = 12 and 40 days, the stream is losing over the
middle section which is clearly evident in Figure 2.10 at around y = 400 m where
the velocity drops off only to start increasing again at y = 500 m. As surface flow
velocity is faster at the bottom sections of the catchment, storage effects alone can
be ruled out as causing the slower recession of the rainfall fraction in cells 13 and
21. The rainfall fraction after the first rainfall event (t = 1 day) in cells 13 and 21
must be due to rainfall from upstream cells in which there is a significant time lag
of approximately 0.2 days. It is also apparent that the rainfall fraction in cell 13 is
greater than the fraction in cell 21, which can be attributed to the increase in the
groundwater entering when moving downstream of cell 13. As there are only two
streamflow generation mechanisms in this simulation, the same explanation leads
to the groundwater component of streamflow results shown in Figure 2.11.
36 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
Figure 2.11: HMC direct rainfall (RF) and groundwater (GW) component
fractions before and after the first rainfall event for cells 1, 13, and 21. Note
the time lags of rainfall in the downstream cells 13 and 21 (~3.5hrs).
The resulting partition of the groundwater component of streamflow is shown in
Figure 2.12. The HMC groundwater component of streamflow and direct rainfall
to the stream are calculated using the HMC fractions in HMC cell 21. It is
highlighted that the summed exfiltration from the overall water balance cannot be
used as a measure of the groundwater component of streamflow as it clearly leads
to an overestimation as the summed exfiltration is greater than the streamflow.
This is due to the losses occurring in the middle section of the stream, which is
not captured by the summed exfiltration upstream of this section where flows are
partially lost through the losing section of the stream. The infiltration in the
overall water balance cannot be utilised to account for the net change either, due
to the very large amount of infiltration over the planes resulting from the rainfall
events. Whilst the error in the groundwater component of streamflow as estimated
using the summed exfiltration along the stream may appear small, the volumetric
differences found by integrating the summed exfiltration and HMC groundwater
component of streamflow over the recession periods (t = 1 – 11 days, t = 12 – 17
days and t = 18 - 40 days) were found to be 1,620 m3 (1.62 Ml), 858 m3 (0.85 Ml)
and 5,420 m3 (5.42 Ml), respectively. This is a total of 7,340 m3 (7.34 Ml) during
the recession periods, a significant difference in response to a single hydrograph
event in a small catchment. Given the area of this catchment (0.81 km2), the
impacts on the difference/error that would be seen in a larger catchment are
significantly greater. However, it is not only the area of the catchment that will
37 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
make use of the HMC method critical in determining the groundwater component
of streamflow generation. The travel time within the streams also undermines the
application of the summed exfiltration as seen in Figure 2.11. As the streams
become longer, the streamflow travel time from upstream to downstream
increases, and as such the summed exfiltration can be much sharper and
completely out of phase with the total streamflow as hypothesised in Figure 2.2.
The proportion and distribution of both gaining and losing sections also have a
clear effect of leading to overestimation of the groundwater component of
streamflow at the outlet.
Figure 2.12: Hyetograph for catchment and Hydrograph at the catchment
outlet, showing separation of direct rainfall and groundwater components of
streamflow, as well as the summed exfiltration from the overall water
balance. The summed exfiltration (SE) from the water balance is clearly seen
to exceed the outflow in this hypothetical catchment. The HMC direct
rainfall and groundwater components of streamflow are calculated using the
HMC fractions in HMC cell 21.
2.4. Discussion and Conclusions
The hydraulic mixing-cell (HMC) method developed in this paper overcomes
many of the limitations that exist in current methods of quantifying streamflow
generation mechanisms based on fully integrated spatially distributed SW-GW
38 |
ADE | 2. A hydraulic mixing-cell method to quantify the groundwater component of
streamflow within spatially distributed fully integrated surface water -
groundwater flow models. (Paper 1)
interaction models. The HMC method accurately extracts streamflow generation
mechanisms using only hydraulic information. Streamflow generation
mechanisms at every HMC defined cell along the stream are extracted by post-
processing of the flow solution obtained from the numerical flow model. Because
the HMC method tracks the streamflow generation mechanisms along the stream,
temporal and spatial components that affect these mechanisms can be accounted
for. The HMC method correctly handles changing flow regimes (e.g. if a stream
changes from gaining to losing within the catchment), accounts for storage effects
within the channel and the time lags that occur within a catchment. These
attributes give the HMC method the ability to deal with the dynamic nature of
varying flow regimes in large and complex systems, such as the catchment
described in Figure 2.1. The only data requirements for the HMC method are the
fluxes at each cell and surface water depths, which are part of the flow solution.
By using this method, one does not have to make the commonly made
assumptions of negligible time lags in streamflow and exchanges being always
positive to the stream, in order to determine the streamflow generation
mechanisms.
In the current formulation, the HMC method is based on the modified mixing cell
(Campana and Simpson, 1984). Unless the mixing processes in the river are
explicitly simulated, the modified mixing rule has to be used. As highlighted in
the theory section, the HMC method is stable as long as the ratio of the volume of
water entering or leaving a HMC cell to the storage volume of the HMC cell is
less than unity. The assumption of constant river width and flow direction are
used in the coding of the HMC algorithm in this study. The initial formulation of
the HMC method presented here is based on the assumption of a constant river
width. In models such as HGS, the width of the stream can change in response to
a changing flowrate. In order to capture a changing river, the definition of the
river in the HMC algorithm must match the changes in the river. Further
development of the method is required to quantify streamflow generation
mechanisms in such systems. The HMC method presented is applicable (in
principle) to any spatially distributed flow modelling code, however the coding
requires generalisation to time varying river widths and lengths. The HMC
39 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
Abstract
Baseflow is often considered to be the groundwater discharge component of
streamflow. It is commonly estimated using conceptual models, recursive filters
or a combination of the two. However, it is difficult to validate these methods due
to the current challenges of measuring baseflow in the field. In this study,
simulation of a synthetic catchment’s response to rainfall is carried out using a
fully integrated surface water-groundwater flow model. A series of rainfall events
with differing recovery periods and varied antecedent moisture conditions is
considered to span a range of different streamflow generation dynamics. Baseflow
is estimated for the outlet hydrograph of the synthetic catchment using a selection
of commonly used automated baseflow separation methods. These estimates are
compared to the baseflow signal obtained from the numerical model, which serves
as the control experiment. Results from these comparisons show that depending
on the method used, automated baseflow separation underestimates the simulated
baseflow by as much as 28%, or overestimates it by up to 74%, during rainfall
events. No separation method is found to be clearly superior to the others, as the
performance of the various methods varies with different soil types, antecedent
moisture conditions and rainfall events. The differences between the various
approaches clearly demonstrate that the baseflow separation methods investigated
are not universally applicable.
3.1. Introduction
Quantifying baseflow contributions to streamflow is of great interest in the
understanding, identification and quantification of streamflow generation
processes, in particular where baseflow supports important ecosystems and/or
provides critical dry season water supply (e.g. Smakhtin, 2001; Werner et al.,
2006). The term baseflow is often referred to as the groundwater contribution to
streamflow (e.g. Freeze, 1972; Brutsaert and Nieber, 1977; Eckhardt, 2005),
although it is also referred to as the release from both groundwater and other
natural storages of water that sustain streamflow between rainfall events (e.g.
Hall, 1968; Smakhtin, 2001; Piggott et al., 2005). In this paper, the term baseflow
is used to describe groundwater discharge that reaches the stream, not including
interflow through the vadose zone.
45 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
Baseflow can be inferred through field measurements of temperature, artificial
and natural tracer concentrations, and flow in seepage meters installed in stream
beds (Becker et al., 2004; Cook et al., 2003; Cook et al., 2008). However, for
practical reasons, it is very difficult to apply these techniques over an entire
catchment. Furthermore, the required end members in chemical mass balance
approaches are difficult to characterise (McCallum et al., 2010), which
complicates baseflow estimates using measurement of tracers. Consequently, the
available field methods do not currently allow accurate determination of spatially
and temporally distributed baseflow. In the absence of detailed field data, but
where a streamflow hydrograph is available, baseflow is therefore often estimated
using simple baseflow separation methods.
Since the early twentieth century, a variety of methods has been developed to
estimate baseflow. The earliest methods and some of the more recent ones are
based on a linear storage-discharge relationship between aquifer and stream (e.g.
Maillet, 1905; Barnes, 1939; Hall, 1968; Boughton, 1993). More recently, non-
linear storage-discharge relationships have also been applied to baseflow
separation (e.g. Wittenberg, 1994; Wittenberg and Sivapalan, 1999; Wittenberg,
2003) following theoretical studies suggesting that non-linear recessions are
appropriate for some catchments. Also, other methods that use some form of
hydrological reasoning have been developed without a physically based
mathematical framework. Currently, the separation of baseflow from the
streamflow hydrograph can be carried out utilising methods that can be grouped
into the following four categories: 1) graphical separation (Sloto and Crouse,
1996), 2) recession analysis (Tallaksen, 1995), 3) conceptual models (Barnes,
1939; Singh and Stall, 1971; Furey and Gupta, 2001; Eckhardt, 2005; Huyck et
al., 2005) and 4) recursive digital filters (Nathan and McMahon, 1990; Arnold
and Allen, 1999).
The different categories of separation approaches as noted above have been
compared and reviewed in several previous studies (Hall, 1968; Nathan and
McMahon, 1990; Arnold et al., 1995; Chapman, 1999; Smakhtin, 2001; Schwartz,
2007; Eckhardt, 2008). The reviews of Hall (1968), Smakhtin (2001) and
Schwartz (2007) provide a history of methods for baseflow separation, and discuss
46 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
the problems related to the definition of baseflow, as well as the underlying
assumptions of the different separation methods. In the context of identifying
groundwater recharge from streamflow records, the underlying assumptions that
underpin many methods were examined by Halford and Mayer (2000). They
concluded that identifying the groundwater contribution from streamflow records
can be ambiguous due to drainage exponentially decreasing from other sources,
such as bank storage, wetlands and the unsaturated zone. Furthermore, they noted
that simple automated methods are highly subjective with respect to their
algorithmic structure, and affected by the same underlying assumptions as other
more complex methods.
The analyses used in comparative studies to evaluate baseflow separation methods
(e.g. Nathan and McMahon, 1990; Arnold et al., 1995; Mau and Winter, 1997;
Chapman, 1999; Halford and Mayer, 2000; Schwartz, 2007; Eckhardt, 2008) are
often based on subjective measures, such as the plausibility of hydrological
behaviour, rather than a quantitative comparison to a known and well-quantified
baseflow hydrograph. This point was emphasised by Mau and Winter (1997) who
highlighted the need to validate baseflow estimates to avoid issues related to
subjective measures and other shortcomings of simplified methods. Unfortunately,
to date, no measured baseflow hydrograph at the catchment scale is available.
Until comprehensive data and better observation techniques come into existence,
numerical models, although theoretical, provide the best independent
conceptualisation of baseflow dynamics in catchments under different forcing
functions and hydrological conditions.
Some studies (e.g. Szilagyi, 2004; Fenicia et al., 2006; Ferket et al., 2010) have
compared baseflow estimated by separation methods with simulated baseflow
from lumped and semi-distributed catchment models. However, a critical analysis
of separation methods is inhibited by the lack of a reliable estimate of baseflow,
as well as some simplifications in the lumped and semi-distributed models, such
as the aquifer storage-discharge relationship (linear reservoir in Fenicia et al.
(2006), the sum of multiple linear reservoirs in Szilagyi (2004), and the
Boussinesq-equation in Ferket et al. (2010)).
47 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
More recently, physically based separation methods have been developed based
on process-based formulations of fluid mass balance equations of an aquifer (e.g.
Furey and Gupta, 2001; Furey and Gupta, 2003; Huyck et al., 2005). They
constitute an important step in overcoming the subjective elements of earlier
simpler methods, and attempt to alleviate some of their simplifying assumptions.
As well as the development of two physically based baseflow separation methods,
Furey and Gupta (2003) evaluated their methods against a complex physically
based numerical model of a hill-slope. Their study appears to be the first to
critically compare baseflow separation methods with a physically based numerical
model. However, by considering only the discharge from a single 2D synthetic
hill-slope (rather than a catchment), Furey and Gupta (2003) neglected important
catchment-scale processes, such as channel routing (e.g. streamflow attenuation
and translation) and channel losses (through losing sections, abstraction and
evaporation).
Fully integrated surface and subsurface flow models, some examples of which are
HydroGeoSphere (HGS) (Therrien et al., 2009), MODHMS (Hydrogeologic Inc.,
2006) and Parflow (Kollet and Maxwell, 2006), are useful for evaluating simpler
models because they do not need to assume a functional relationship between
baseflow and streamflow, or simple empirical relations. These models typically
represent 3D variably saturated subsurface flow with Richard’s equation, and 1D
and 2D surface flow with the diffusion wave approximation to the St. Venant
equations. A unique feature of fully integrated models is that water that is derived
from rainfall is allowed to partition into overland flow, streamflow, evaporation,
infiltration and recharge, whilst subsurface discharge to surface water features,
such as lakes and streams, occurs in a physically based fashion (Therrien et al.,
2009). Therefore, physically based numerical models provide an excellent means
for comparison of baseflow separation methods if the modelled baseflow
component of streamflow can be extracted.
Using physically based numerical models of 3D systems to evaluate baseflow
separation methods is difficult because the baseflow component of streamflow is
not a standard output. For a 2D hill-slope model, the baseflow component of
outflow is simply groundwater discharge. However, in the extension beyond 2D
48 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
hill-slopes, the baseflow component of simulated streamflow must be calculated
in some other way. As highlighted by Partington et al. (2011), the available
integrated models do not explicitly report the groundwater contribution to
streamflow. This problem is of particular importance for catchments where the
flow regime between surface water and groundwater is changing (e.g. gaining to
losing sections of a stream and vice versa). To overcome these difficulties,
Partington et al. (2011) developed a hydraulic mixing-cell (HMC) approach that
allows extraction of the groundwater contribution to streamflow within integrated
surface and subsurface flow models. Combining the HMC approach with the
HydroGeoSphere model, they demonstrated that spatiotemporal fluxes into and
out of a stream can be translated to a point along the stream allowing for
meaningful hydrograph separation. The HMC method allows for theoretical
examination of baseflow dynamics within a 3D catchment model, thus providing a
platform for comparison to automated baseflow separation methods.
In the current study, the HMC method is used in conjunction with HGS in order to
compare the outputs from a series of commonly used automated baseflow
separation methods. A numerical control experiment is developed using the
integrated model to simulate hydrological processes within a synthetic catchment.
Multiple simulations are carried out using differing initial, hydrologic and forcing
conditions in order to generate a series of outflow and baseflow hydrographs.
Baseflow separation methods are then applied to the outflow hydrographs from
the simulations. This allows comparison of the baseflow obtained from the
separation methods to the simulated baseflow. The commonly used separation
methods are based on graphical, conceptual and digital filter methods. The
analysis is limited to automated methods that are readily available and that only
rely on streamflow discharge data and catchment area. This analysis does not
include an assessment of more complex physically based methods. However, it is
noteworthy that this approach could also be used to test physically based methods,
e.g. those developed by Furey and Gupta (2001).
3.2. Methodology
The HydroGeoSphere (HGS) model used here is a fully integrated, physically
based model that simultaneously simulates 3D variably saturated subsurface flow
49 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
and 2D surface flow (Therrien et al., 2009). Water is exchanged between the
surface and subsurface domains through a first-order leakage relation based on the
head difference between the domains. The model also accounts for
evapotranspiration as a function of the leaf area index, soil moisture and root
depth. For further details on the numerical formulation and a review of the code,
the reader is referred to Park et al. (2009), Therrien et al. (2009) and Brunner and
Simmons (2011).
3.2.1. The synthetic catchment
The geometry of the catchment is loosely based on the tilted V-catchment
employed by Panday and Huyakorn (2004). As in Panday and Huyakorn (2004),
the catchment is symmetrical and therefore only half of the catchment is modelled
(shown in Figure 3.1). This particular geometry is an ideal synthetic framework
for generating hydrographs, because a range of hydrological processes control the
catchment’s behaviour. These processes include 3D saturated/unsaturated
groundwater flow, infiltration/exfiltration, overland flow and streamflow. An
analysis of the Panday and Huyakorn (2004) synthetic catchment highlighting
some of the issues associated with their model setup was undertaken by
Gaukroger and Werner (2011), and in response to these, several modifications to
the original setup are adopted here. The steep slopes and initially horizontal water
table in the Panday and Huyakorn (2004) case cause all groundwater discharge to
be concentrated around the outlet. Reducing the slope of the catchment
(particularly along the stream) creates a greater spatial distribution of the surface-
subsurface exchanges throughout the catchment. Therefore, the slopes
perpendicular and parallel to the stream are decreased from 0.05 m/m and 0.02
m/m to 0.002 m/m and 0.0005 m/m, respectively. Furthermore, the horizontal
water table represents an unrealistic (overly dry) initial condition. To start the
model from more realistic initial conditions, the catchment is saturated and
allowed to drain for between 7 and 9 months without any precipitation events. The
original roughness coefficients used for the hill-slope and stream domains cause
overland flow to be dominant parallel and adjacent to the stream, rather than in
the stream (Gaukroger and Werner, 2011). In order to allow overland flow to
discharge into the stream as it reaches the banks (rather than flowing alongside the
50 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
stream), the same roughness (0.015 s/m1/3) is used in both the overland flow and
stream domains. Also, the plane adjacent to the stream is raised by 0.6 m over a 5
m length to promote direct discharge of groundwater to the stream as opposed to
upslope exfiltration or return flow. Finally, the areal extent of the catchment is
increased from 810,000 m2 to 3,220,000 m2 by doubling the original length and
width of the catchment (keeping the stream width at 10 m). This reduces boundary
effects and increases aquifer storage capacity, which promotes sustained baseflow
contributions to the stream. Given the modifications outlined above, a wide range
of hydrographs can be generated by changing the forcing functions (e.g. rainfall,
groundwater pumping and evapotranspiration).
Figure 3.1: Modified tilted V-catchment used for simulation of the synthetic
catchment’s rainfall response. Points 1 and 2 denote locations of
groundwater pumps. Note that due to the symmetry of the catchment, only
half of it is shown.
The bottom elevation of the model domain is set at -20 m relative to the 0 m
elevation of the streambed at the outlet. The aquifer properties are homogeneous
and isotropic. In separate model scenarios, two different sets of properties of the
aquifer material are considered (Table 3.1). Properties for evaporation and
transpiration are also included in Table 3.1.
The spatial discretisation in the catchment model is as follows: grid spacing along
the x axis is 50 m from x = 0 - 1550 m, 25 m from x = 1550 - 1575 m, 15 m from
x = 1575 - 1590 m, 5 m from x = 1590 - 1600 m and 10 m from x = 1600 - 1610
m. The grid spacing along the y axis is 50 m. The vertical grid discretisation
51 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
increases in thickness according to the slopes perpendicular and parallel to the
stream. Vertical discretisation along the z axis ranges from 0.25 m to 1 m for the
first 10 m below the surface. The time steps used in the model vary in accordance
with an adaptive time-stepping approach with a maximum step of 1000 seconds.
A no flow boundary is applied at the bottom and sides of the model domain. A
critical depth boundary is used at (x, y, z) = (1600 m, 0 m, 0 m) and (1610 m, 0 m,
0 m) to control the outflow at the stream outlet.
3.2.2. Baseflow calculation using the HMC method
The tracking of the streamflow generation mechanisms within a model simulation
requires the tracking of the spatiotemporal fluxes into, out of, and along the
stream. Parcels of groundwater discharging directly to the stream are “tracked”
using the HMC method (Partington et al., 2011) to allow determination of when
(and if) groundwater contributes to streamflow, as measured at the outlet (or at
any other location along the stream). The HMC method accounts for the travel
time along the stream and the spatiotemporal variation in the surface-subsurface
exchange fluxes, thereby separating the simulated streamflow hydrograph into
baseflow, overland flow and direct rainfall to the stream. A version of HGS that
has the HMC method incorporated into it is used to simulate the outlet hydrograph
of the synthetic catchment in response to a series of rainfall events, and
considering groundwater pumping and evapotranspiration. The calculated HMC
baseflow is used as the control experiment with which baseflow separations of the
simulated hydrograph are compared.
3.2.3. Baseflow separation using automated methods
The automated methods for baseflow separation used in this study are
implemented using the programs HYSEP (Sloto and Crouse, 1996), PART
(Rutledge, 1998) and BFLOW (Arnold and Allen, 1999). The Eckhardt filter
(Eckhardt, 2005) is also used. All of these approaches are well established
methods, are readily available, and were previously compared in the study of
Eckhardt (2008). However, they were judged subjectively based on hydrological
plausibility. Detailed descriptions of all approaches can be found in the above
53 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
cited literature, hence only a very brief overview of these methods is provided
below.
The HYSEP program allows the use of three curve fitting methods of hydrograph
separation; sliding interval (HYSEP1), fixed interval (HYSEP2) and local
minimum (HYSEP 3), as detailed in Pettyjohn and Henning (1979). For these
three methods, an empirical relationship is used, which relates the catchment area
to the number of days until baseflow makes up all streamflow, after a streamflow
peak.
PART uses a form of streamflow partitioning based on antecedent streamflow
recession (similar to the local minimum method of HYSEP), details of which are
given in Rutledge (1998). The determination of the antecedent recession
requirement in PART is done in three ways (see Rutledge, 1998) and thereby
provides three baseflow estimates: PART1, PART2 and PART3.
The BFLOW program uses the Lyne and Hollick (1979) filter, which is a low-pass
filter. This separation method uses signal processing theory, and is based on the
hydrological reasoning that baseflow is the low frequency component of
streamflow. The filter equation for baseflow is expressed as (Eckhardt, 2005):
1(cid:4)(cid:2)
b (cid:3)(cid:2)b (cid:5) (Q (cid:5)Q ) subject to b (cid:21)Q (3.1)
t t(cid:4)1 2 t t(cid:4)1 t t
Where b [L3/T] is the baseflow at time step t [T], (cid:2) [dimensionless] is the filter
t
parameter and Q [L3/T] is the streamflow at time step t. It is worth noting the
t
constraint b (cid:21)Q , which is required in applying (1) to avoid predictions of
t t
baseflow greater than streamflow (Chapman, 1991; Eckhardt, 2005). This
constraint is discussed further in Section 3.4.3. The BFLOW program carries out
three passes of the filter: forwards (BFLOW1), backwards (BFLOW2) and
forwards again (BFLOW3) and uses a filter parameter (cid:2) = 0.925 as suggested by
Nathan and McMahon (1990). Each pass of the filter acts to attenuate the
baseflow signal. Despite having no physical basis, the baseflow separation of
BFLOW has been found to agree well with manual separation techniques (Arnold
and Allen, 1999).
54 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
The Eckhardt filter is a two-parameter filter based on the assumption that aquifer
outflow is linearly proportional to storage. This filter limits the maximum ratio of
baseflow to streamflow. Eckhardt (2005) describes this as potentially beneficial
following the demonstration of Spongberg (2000) that runoff has a non-negligible
low-frequency component. The equation for this filter is given by (Eckhardt,
2005):
(1(cid:4)BFI )ab (cid:5)(1(cid:4)a)BFI Q
b (cid:3) max t(cid:4)1 max t subjecttob (cid:21)Q (3.2)
t 1(cid:4)aBFI t t
max
Where a [dimensionless] is the baseflow recession constant and BFI
max
[dimensionless] is the maximum value of the baseflow index.
As the BFI cannot be identified prior to separation, Eckhardt (2005) suggests
max
using a value of 0.80 for perennial streams with porous aquifers, 0.50 for
ephemeral streams with porous aquifers, and 0.25 for perennial streams with hard
rock aquifers. The use of BFI = 0.50 yields an equivalent filter to that proposed
max
by Chapman (1991). In the formulation of Chapman (1991), a filter is developed
to overcome baseflow being constant in the absence of direct runoff (similar to the
Lyne and Hollick (1979) filter; Nathan and McMahon (1990)). This gives the
filter parameter physical meaning in the form of the baseflow recession constant
a. The recession constant for the Eckhardt (2005) filter is determined using the
method outlined in Eckhardt (2008). This method involves plotting the flow Q
t
against Q for periods where streamflow is decreasing for five consecutive days.
t-1
A linear regression that passes through the origin is then calculated for these data
points. The slope of this regression gives the recession constant a.
All streamflow data generated from the numerical model are translated to daily
time-steps before being processed by HYSEP, PART, BFLOW and the Eckhardt
filter. This translation is done in order to be compatible with the automated
methods. The translation is carried out by calculating the average flow for each
day. The influence of this constraint is discussed in Section 3.5.
55 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
3.3. Model Simulations
To provide varied catchment responses and streamflow regimes, the synthetic
catchment is subjected to varied rainfall and antecedent moisture conditions.
These different conditions are used to examine the extent to which the HYSEP,
BFLOW, PART and the Eckhardt separation methods reproduce and capture the
HMC calculated baseflow signal. Two of the simulations are also subject to near-
stream groundwater pumping. The simulations with groundwater pumping allow
investigation into the common scenario of a modified catchment. Although some
separation methods are specified for use in undisturbed catchments, they are still
applied in this study to simulations with pumping. However, for this reason, the
simulations with pumping are considered separately from the simulations without
pumping. The baseflow separation methods are evaluated quantitatively and
qualitatively against the simulated baseflow using measures that account for total
baseflow volume, as well as baseflow dynamics.
Initially, eight model scenarios are simulated (Table 3.2). The first three scenarios
(1, 2 and 3) consider the influence of pumping for the sandy catchment. Scenarios
4 and 5 consider different initial conditions as the starting points for scenarios 4
and 5, respectively. Scenarios 6, 7 and 8 consider a change in soil properties of the
sand to loamy sand. As well as providing the controlled baseflow signal for
evaluation of baseflow separation methods, the variation of aquifer properties
provides insight into their influence on streamflow generation mechanisms.
Table 3.2: Scenarios for simulating catchment response. Scenarios with an
asterisk denote scenarios where groundwater pumping is applied in the
catchment.
Scenario Soil Initial Water table Pumping
1 Sand WT3 -
2* Sand WT3 pump 1
3* Sand WT3 pump 1and 2
4 Sand WT2 -
5 Sand WT1 -
6 Loamy sand WT3 -
7 Loamy sand WT2 -
8 Loamy sand WT1 -
56 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
The initial hydraulic heads and water table elevations are obtained by draining the
fully saturated catchment for a period of 7, 8 and 9 months without applying any
rainfall forcing or subsurface boundary recharge. The initial conditions used are:
water table 1 (WT1) = 7 months drainage, water table 2 (WT2) = 8 months
drainage and water table 3 (WT3) = 9 months drainage. For each of these initial
conditions the stream is still flowing at the end of the drainage period, whilst
providing significantly different initial conditions.
The catchment’s response is controlled by modifying the forcing functions (e.g.
rainfall, pumping and ET) to scenarios with a series of different initial conditions.
The rainfall varies in intensity and duration over three rain events throughout each
of the simulations. The same rainfall boundary is applied in each of the eight
scenarios as follows:
1) 10 days without rainfall, then rainfall at a rate of 2 mm/h for 24 h followed by
10 days without rainfall; and
2) rainfall at a rate of 4 mm/h for 48 h followed by 5 days without rainfall; and
3) rainfall at a rate of 40 mm/h for 3 h followed by 30 days without rainfall (58
days and 3 h total)
The idealised rainfall events are uniform and constant with sufficiently large
recovery periods such that the streamflow generation processes resulting from
individual events can be clearly identified. The rainfall rates and durations are
chosen to represent a range of streamflow generation mechanisms.
Pumping is applied in scenarios 2 and 3 at two locations (shown in Figure 3.1):
Pump 1 located at (x, y, z) = (1550 m, 500 m, 0 m), and pump 2 located at (x, y, z)
= (1550 m, 1500 m, 0 m). The pumping rate is increased linearly from 0.00 to
0.01 m3/s for pump 1 over the first day of simulation in scenario 2, with pump 2
inactive. In scenario 3, the pumping rate is increased linearly from 0.00 to 0.015
m3/s for both pumps 1 and 2 over the first day of simulation. For scenarios 2 and
3, pumping is applied over the entire simulation. This pumping rate induces losing
conditions locally along the stream near the pumping location. Pumping therefore
57 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
allows the effect of varied flow regimes (i.e. gaining and losing sections) on
streamflow generation to be explored with respect to baseflow.
Based on the initial simulations, evapotranspiration (ET) is applied to 5 additional
scenarios (denoted as 9, 10, 11, 12 and 13; not listed in Table 3.2). The setup and
forcing functions of scenarios 9, 10, 11, 12 are the same as for scenario 1, except
that constant specified evaporation rates of 2, 5, 10 and 26 mm/day are applied,
respectively. Some high evaporation rates (10 and 26 mm/day) are chosen to
explore the influence that high ET in the catchment has on the baseflow
separation methods. ET is also applied to scenario 13 with the same setup and
forcing functions as for scenario 6, but with a constant specified evaporation rate
of 5 mm/day. The simulations with ET are performed in order to examine the
influence of ET on baseflow dynamics, baseflow recession and performance of
separation methods against the simulated baseflow.
3.4. Results
3.4.1. Fully integrated model simulations
The simulated streamflow hydrograph at the outlet and the corresponding
streamflow generation components (calculated from the HMC method) are shown
for scenarios 1 (Figure 3.2) and 2 (Figure 3.3). The streamflow generation
mechanisms varied in response to different rainfall events. In all scenarios that
were based on sandy material properties, streamflow was dominated by baseflow
because the high infiltration capacity of the sand allowed for quick recharge.
Consequently, there was only a small overland flow component due to saturation
excess runoff. The almost horizontal slope of the catchment limited the vertical
extent of the unsaturated zone to less than 1 m, resulting in a short delay between
infiltration and recharge. As the timing between infiltration and recharge was
short, there was a rapid response in the baseflow component of streamflow. As
illustrated in Figure 3.2, after a short and rapid initial increase, baseflow did not
change significantly during the first two rainfall events and reached an apparent
steady-state. As opposed to baseflow, streamflow changed during this apparent
steady-state. Therefore, the ratio of streamflow to baseflow changes as a function
of time, but not consistently across events.
58 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
The apparent steady-state baseflow was only observed during the first two events.
However, in the third event no apparent steady-state was reached. In this event, an
initial rapid increase in head in the subsurface quickly increased the hydraulic
gradient from the aquifer to the stream. During this rainfall event, the time delay
from rainfall starting to the onset of overland flow is much slower than the time
delay to the increase in groundwater discharge caused by the rapid aquifer
response. After 1 hour, the overland flow and accumulating direct rainfall to the
stream increased the stream stage, thus reducing the hydraulic gradient between
the aquifer and stream. This is a clear demonstration of the forcing functions
controlling the baseflow dynamics.
The baseflow response from all three rainfall events did not follow the typical
pattern of baseflow response as presented in standard textbooks, e.g. McCuen
(2005) and Linsley et al. (1958). This is an important observation because these
patterns are the basis for graphical approaches of baseflow separation. The pattern
of baseflow during rainfall events obtained from the HGS model demonstrated a
fast and transient response in stream-aquifer interaction. This was apparent at the
beginning and cessation of the rainfall events, where an abrupt change in baseflow
occurs, rather than a smooth and delayed response. The high transience of the
stream aquifer interaction was also apparent in scenarios 2 and 3. The drawdown
around the pump induced a loss in the adjacent stream, creating a variable flow
regime with dynamic losing and gaining sections. The drawdown also increased
the time between infiltration and recharge, further affecting the system dynamics.
The effect of ET (at a rate of 5 mm/day) is shown in Figure 3.4 for the example of
scenario 10. In comparison to scenario 1, the inclusion of ET in scenarios 9, 10,
11 and 12 slightly reduced event peaks and the baseflow component. These
changes are due to the reduction in storage through losses from ET. However, it
can be seen by comparison of Figure 3.2 and Figure 3.4, that the baseflow
dynamics were very similar; the reduced overland flow component lead to a
slightly higher proportion of baseflow with respect to streamflow.
59 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
Figure 3.4: Streamflow hydrograph at the outlet and HMC flow components
for modified scenario 1 (with 5mm/day ET), with highlighted events. An
apparent steady-state baseflow rate was still observed in the first event (10.5-
11 days) and second event (21.4-23 days).
3.4.2. Recession analysis
Following the approach of Eckhardt (2008), the recession periods were identified
as periods in which streamflow was decreasing for 5 consecutive days. These
periods were used to calculate the recession constant a (as defined in section
3.2.3). The slope for each linear regression of Q vs. Q passing through the
t+1 t
origin was used as the recession constant a, which was then applied using the
Eckhardt separation method. Figure 3.5 shows the resulting recession constant a,
and R2 value obtained from the linear regression for each scenario. It can be seen
in Figure 3.5 that the R2 for each regression was very close to 1. For all scenarios,
this high R2 value supports the assumption of a linear reservoir during recession
periods, which is inherent in the Eckhardt method.
61 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
Figure 3.5: Values of recession constant a and R2 value for the linear
regression of Q vs Q , for sand and initial conditions WT1, WT2, WT3 and
t t+1
without/with pumps 1 and 2 active. The high value of R2 suggests a linear
storage-discharge relationship at the outlet during recession periods.
Adding ET in scenarios 9 to 13 reduced slightly the recession constant a, by less
than 2% and it also slightly reduced the linearity of the storage-discharge
relationship (R2 > 0.96) of the catchment during recession periods. The linearity
assumption for the storage-discharge relationship for this synthetic catchment was
therefore still deemed reasonable.
3.4.3. Comparison of baseflow separation methods
All of the automated separation methods used are subject to the condition that
baseflow cannot exceed streamflow. This is imposed because without this
constraint, all of these methods can yield baseflow estimates above streamflow.
By contrast, Furey and Gupta (2001) suggested that such a condition should not
be imposed on physically-based methods. This way it is possible to identify time
periods where estimated baseflow exceeds streamflow and diagnose these
estimation errors. Steps can then be taken to modify the method while honouring
physical processes so that these errors are reduced or fully removed. This
constraint has repercussions for our analysis. In recession periods, the baseflow
calculated from the automated separation methods is perfectly matched to the
HMC calculated baseflow, because streamflow is entirely composed of baseflow.
Therefore, an assessment of the differences between the simulated and
approximated baseflow hydrographs is only meaningful during rainfall events.
Consequently, this comparison is carried out during the rainfall events (i.e. 10-13
62 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
The baseflow index (BFI), Nash-Sutcliffe efficiency (NSE) and percent bias
(PBIAS) are given for each of the three rainfall events in Table 3.3,Table 3.4, and
Table 3.5, respectively, for scenarios 1-8. The values for NSE < 0.5 and │PBIAS│
> 25% are highlighted. The BFIs calculated across the entire simulation for each
scenario are ranked for each separation method in Figure 3.6. Ranking is in order
of best to worst BFI relative to the BFI observed from the HGS model (based on
the HMC calculated baseflow). The results for the testing of the inclusion of ET
for scenario 1 are shown in Table 3.6.
For event 1, the NSEs were satisfactory over all scenarios for HYSEP2, PART1,
PART2, PART3, BFLOW1, BFLOW2 and the Eckhardt separation methods.
However, in scenario 3, HYSEP1, HYSEP3 and BFLOW3 had a NSE less than
0.5, with BFLOW3 showing a very unsatisfactory performance indicated by a
negative NSE. The BFLOW1 separation had a single instance of NSE less than 0.5
and the Eckhardt separation had two instances of NSE less than 0.5. However,
these were only slightly below this value, indicating that the performance of these
methods was almost satisfactory. The PBIAS was at a maximum of 33.8% for
event 1 of scenario 3 for the BFLOW3 separation method, showing a large
underestimation of the HMC calculated baseflow. All separation methods for
event 1 tended to underestimate baseflow. Only BFLOW1 overestimated
baseflow, which occurred for the sandy loam in scenarios 6-8.
For event 2, the NSEs were below 0.5 for each separation method in at least one of
the eight scenarios. The BFLOW3 separation showed very poor performance with
negative NSEs in scenarios 2-5. In each of these scenarios, BFLOW3 had a PBIAS
showing underestimation of baseflow by more than 25%. The HYSEP1, HYSEP2,
BFLOW1 and Eckhardt methods showed poor performance for sandy loam
(scenarios 6-8) with negative NSEs in each scenario. The PBIAS for HYSEP1 and
BFLOW1 separation showed overestimation of baseflow ranging from 40%-73%
in the sandy loam scenarios. It is interesting to note that the scenarios in which
HYSEP1, HYSEP2 and BFLOW1 performed well, HYSEP3, PART1, PART2,
PART3, BFLOW2 and BFLOW3 performed poorly and vice versa.
64 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
More interestingly, where the HYSEP1, HYSEP2 and BFLOW1 methods
performed poorly, these methods largely overestimated baseflow whereas where
the HYSEP3, PART1, PART2, PART3, BFLOW2 and BFLOW3 methods
performed poorly, these particular methods largely underestimated baseflow.
For event 3, the NSE was greater than 0.5 for every method in each scenario, with
values close to 1. The largest PBIAS was for BFLOW3 in scenario 3, showing
underestimation of baseflow by just over 25%.
The inclusion of ET in scenarios 9-13 showed that as the ET rate was increased,
the BFI increased. ET also lead to a reduction in performance (both NSE and
PBIAS) for every separation method, except HYSEP1.
The rankings of separation methods (shown in Figure 3.6) based on BFI over the
entire simulation provide a summary of the performance of each of the separation
methods. The best replication of BFI resulted from the HYSEP1 method in
scenarios 1-5, from PART1 in scenario 6, and from HYSEP2 in scenarios 7-8.
The BFLOW3 method was worst in scenarios 1-3 and 8. The Eckhardt method
performed worst in scenarios 4 and 5.
10 HYSEP1
9 HYSEP2
8 HYSEP3
7 PART1
6
PART2
5
PART3
4
BFLOW1
3
BFLOW2
2
BFLOW3
1
ECKHARDT
1 2 3 4 5 6 7 8
Scenario
Figure 3.6: Performance based ranking using BFI over the whole simulation
for HYSEP, PART, BFLOW and the Eckhardt separation methods. 1
indicates best performance, 10 indicates worst performance.
The baseflow separations from the streamflow hydrograph in scenario 1 obtained
using HYSEP, PART, BFLOW and the Eckhardt separation methods are shown in
Figure 3.7. Visual inspection of baseflow curves in Figure 3.7 shows that the
ability of these separation methods to match the simulated baseflow was poor in
69
gniknaR
ecnamrofreP |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
almost all cases, despite the fact that they had satisfactory NSE and PBIAS values.
It is clear that despite reasonable estimates of the BFI for each scenario, the
dynamics of baseflow during rainfall were missed.
Figure 3.7: Comparison of simulated daily baseflow and baseflow estimated
using HYSEP, PART, BFLOW and the Eckhardt separation methods for
scenario 1.
3.5. Discussion
The baseflow hydrographs obtained using HGS (with the HMC method) were
used as a control experiment to test the performance of a series of automated
baseflow separation methods. The initial conditions (antecedent moisture), forcing
functions (rainfall patterns, pumping and ET) as well as the physical properties
(soil properties) of the catchment were varied across simulation scenarios. The
varied conditions across the different model scenarios allowed the generation of
unique baseflow behaviour, controlled by a range of hydrological processes. The
application of the HMC method allowed quantification of the relative importance
of hydrological processes to the streamflow hydrograph. While the structure and
geology of the synthetic model used in this study were simple, the hydrological
processes considered were simulated in a physically based way. Despite the
simplified nature of the catchment, the baseflow separation methods consistently
70 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
failed to perform satisfactorily. This is easily attributed the variability of the
baseflow dynamics as observed across all simulation scenarios. Increasing the
complexity of the catchment (e.g. heterogeneous geology, more realistic
topography and rainfall patterns), is likely to lead to an even more complex
baseflow response. With increased complexity, it is expected that the variability
seen in baseflow dynamics will remain and hence that the simple automated
baseflow separation methods examined will not perform any better in estimating
baseflow.
An initial analysis of the hydrographs revealed that the behaviour of baseflow was
fundamentally different between rainfall events. For the first two events, baseflow
remained constant and reached an apparent steady-state despite the changing
forcing functions. In contrast, baseflow dynamics during the third event were
highly transient. This illustrates that the controlling processes of baseflow are not
always static, but instead change in response to different forcing functions. It also
challenges the common assumption (based on hydrological reasoning) of the
simple automated baseflow separation methods, that a simple fixed relation
between baseflow and streamflow exists, for all rainfall events and antecedent
moisture conditions. It is observed that this is not necessarily the case.
In the synthetic catchment used in this study, an apparent steady-state of baseflow
discharge was reached for certain rain events. Once this apparent steady-state was
reached, streamflow only increased with increasing overland flow. This led to a
baseflow response that is dependent upon the rate and duration of rainfall. For all
three events, the relationship between baseflow and streamflow was not
consistent, as assumed by the BFLOW1, BFLOW2, BFLOW3 and Eckhardt
separation methods. The variation of the ratio of baseflow to streamflow was
observed in response to different rainfall events, as well as for the different initial
antecedent moisture conditions. The variation observed in these simulations
highlights an inability to accurately capture the average baseflow with the various
baseflow separation methods examined. Moreover, it demonstrates the often
acknowledged, but seldom addressed ambiguity of the separation methods used.
The results from this numerical experiment suggest that quantifying baseflow in
catchments with non-stationary processes, such as varied climatic conditions that
71 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
are outside of seasonality, will alter the streamflow generation mechanisms and
hence the BFI.
The NSEs for rainfall events 1 and 3 for each of the scenarios indicated
satisfactory results for the baseflow separations. The agreement between the
simulated baseflow method and separation methods for event 3 was significantly
better than for the other two events. For rainfall event 2, the NSEs showed a poor
match between the automated separation methods and HMC calculated baseflow
for different methods in each scenario, with both large overestimation and
underestimation of the HMC calculated baseflow in some cases. This variability
in each of the methods’ ability to match the HMC calculated baseflow across
scenarios and corresponding rainfall events highlights that no single separation
method performed consistently well in the control experiment. The BFI based
rankings of the separation methods show that, on average, PART1 and HYSEP2
performed best overall in capturing the baseflow volume across the eight
scenarios.
One of the limitations found in the use of the automated separation methods was
the constraint of using daily streamflow data. It can be seen from the results in
Figure 3.2 and Figure 3.3 that the behaviour of the baseflow varied on at least an
hourly time scale, much smaller than could be captured in a daily time step.
However, this is only a limitation when it is essential to accurately capture
baseflow behaviour at finer timescales (e.g. flood modelling). In the context of
low flow hydrology, where estimates of annual baseflow contributions are
required, the nuances seen in the baseflow behaviour during rainfall events is not
important as long as the average baseflow is captured. However, it is possible that
the nuances seen in the hourly time step of this catchment present themselves in a
larger catchment at the daily time step, in which case use of these filters would be
problematic and would fail to capture even the average behaviour.
The automated separation methods result in the largest difference during rainfall
events in which recharge is also occurring. This means that any perennial streams
that are subject to significant and extended rainfall periods will be the most
difficult to accurately determine the BFI for. This is because the proportion of
72 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
time that streamflow is not driven purely by baseflow affects the relative
magnitude of the potential baseflow error.
3.6. Conclusions
Whilst commonly used automated baseflow separation methods are known to be
somewhat ambiguous and arbitrary, the potential errors have not been quantified
previously using a 3D fully integrated physically based flow model. The
numerical experiments in this study strongly suggested that baseflow dynamics
are complex, even in a simple catchment. The complexity of baseflow dynamics
was seen to affect the performance of the simple automated separation methods.
The frequently used automated baseflow separation methods could not perform
satisfactorily across all events and scenarios considered. This suggests that
caution should be used when applying these methods, depending on the flow
dynamics of the catchment being studied. Unfortunately, there are no clear
indicators as to which separation methods are most and least appropriate under
particular conditions, which is not surprising given the absence of a true physical
basis in the simple methods examined. This is cause for concern because baseflow
separation is an important tool influencing decisions and outcomes of the various
applications it is used for, such as the analysis of event runoff; recharge
estimation; low flow forecasting; hydrogeologic parameter estimation; hydrologic
model calibration; and the identification of source areas; and dominant processes
producing runoff (Schwartz (2007)). Large errors will undermine the many
applications baseflow separation is used for.
Further work is required to understand the appropriate use of baseflow separation
methods. More complex baseflow separation methods than those considered in
this study should be tested in future studies. Physically based filters (e.g. Furey
and Gupta, 2001, 2003; Huyck et al., 2005) could prove to be more robust. This is
because they provide a physically based relation of rainfall and ET (and other
physical parameters) to baseflow. However, such methods clearly require more
data (e.g. rainfall time series) which may not be readily available. It is perhaps the
case that the uncertainty associated with simple automated methods precludes
their use for providing anything more than very rough estimates of baseflow.
73 |
ADE | 3. Evaluation of outputs from automated baseflow separation methods against
simulated baseflow from a physically based, surface water-groundwater flow
model. (Paper 2)
An improved understanding of baseflow dynamics is required for a broader range
of catchments. With respect to baseflow dynamics, future studies should aim to
elucidate: (a) scale dependence of baseflow generation to test if the baseflow
response seen in the hourly time step of this small synthetic catchment occurs at
the daily time step for larger catchments (e.g. > 20 km2); (b) testing how the BFI
varies as a result of non-stationary processes; (c) testing of the impact of
variations in geology, topography and vegetation, by incrementally adding layers
of complexity to similar models in order to try and understand baseflow
dynamics. Further investigation within numerical models should play a role in
establishing physically based recommendations as to the appropriateness of
commonly used automated baseflow separation methods in different catchment
types and settings. Given the reality of the physical interpretations and subsequent
calculations that such simple automated separation methods are used to support,
there is a need to establish either stricter guidelines for such methods, develop
improved methods (e.g. physically based methods) or at least provide error
bounds on such estimates.
Acknowledgements
The authors gratefully acknowledge the reviewers’ comments, which greatly
improved the final manuscript. This work is supported by the Australian Research
Council through its Linkage grant scheme and the South Australian Department
for Water as industry partners under grant number LP0668808. Part of this
research was funded by the Swiss National Foundation, Ambizione grant
PZ00P2_126415.
74 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Abstract
The understanding of streamflow generation processes is vitally important in the
management of water resources. In the absence of the data required to achieve
this, Integrated Surface-Subsurface Hydrological Models (ISSHM) can be used to
assist with the development of this understanding. However, the standard outputs
from these models only enable elicitation of information about hydrological
drivers and hydrological responses that occur at the same time. This generally
limits the applicability of ISSHMs for the purposes of obtaining an improved
understanding of streamflow generation processes to catchment areas that do not
exhibit significant storage, travel times or flow depletion mechanisms. In order to
overcome this limitation, a previously published Hydraulic Mixing-Cell (HMC)
method is improved so that it can be used to follow surface water derived from
direct rainfall and groundwater discharge to the stream and adjacent overland flow
areas. The developed approach was applied to virtual experiments (based on the
Lehstenbach catchment in south-eastern Germany), which are composed of two
ISSHMs of contrasting scales: (1) a riparian wetland of area 210 m2, and (2) a
catchment of area 4.2 km2. For the two models, analysis of modelling results for a
large storm event showed complex spatiotemporal variability in streamflow
generation and surface water-groundwater interaction. Further analysis with the
HMC method elucidated in-stream and overland flow generation mechanisms.
This study showed within a modelling framework, that identification and
quantification of in-stream and overland flow generation better informed
understanding of catchment functioning through decomposition of streamflow
hydrographs, and analysis of spatiotemporal variability of flow generation
mechanisms.
4.1. Introduction
Understanding streamflow generation and surface water-groundwater interaction
is of great importance for the management of water resources, as highlighted in
reviews by Winter (1999), Sophocleous (2002), and more recently Fleckenstein et
al. (2010). In the absence of relevant data, distributed physics-based Integrated
Surface-Subsurface Hydrological Models (ISSHM) (see Gaukroger and Werner,
2011; Sebben et al., 2012) represent a useful alternative for providing insight into
79 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
hydrological processes at detailed spatiotemporal resolutions (e.g. Mirus et al.,
2011b). This is because ISSHMs are capable of simulating feedbacks between the
surface and subsurface, including all forms of overland flow generation and re-
infiltration (Kampf and Burges, 2007). In addition, ISSHMs can assist with
analysing and interpreting hydrological processes and in developing conceptual
understanding of catchment processes (Ebel and Loague, 2006). ISSHM examples
include HydroGeoSphere (Therrien et al., 2009), InHM (Vanderkwaak, 1999),
ParFLOW (Kollet and Maxwell, 2006), CATHY (Camporese et al., 2010) and
MODHMS (HydroGeoLogic Inc., 2006). In recent years, studies related to
understanding streamflow generation and surface water-groundwater interaction
using numerical models have become increasingly widespread (e.g., Brunner et
al., 2009; Frei et al., 2010; Maxwell and Kollet, 2008; Park et al., 2011).
The aforementioned studies focused on processes in small-scale synthetic
systems, enabling insight to be gained into the controls on flow generation (Frei et
al., 2010; Maxwell and Kollet, 2008; Park et al., 2011) and depletion (Brunner et
al., 2009). However, difficulties arise when attempting to gain the same level of
insight for larger, catchment-scale systems. This is because in small-scale
systems, hydrological outputs at a particular place and time are generally only
affected by hydrological drivers that occur at the same location and at the same
time (i.e. by ‘active’ processes (Ambroise, 2004)). However, this is not the case
for larger-scale systems, where local hydrologic response is not only affected by
local processes but largely by processes taking place in other locations and at
other times. This is a result of the influence of surface and groundwater flow
travel times, flow impediments (e.g. riparian wetlands or weirs), and losses (e.g.
infiltration or evaporation). Consequently, hydrological drivers that occur at a
particular point in time (active processes) do not necessarily end up contributing
to the hydrological output at that or a later time. As a result, when considering
streamflow generation processes at the catchment scale, there is a need to
distinguish between ‘active’ and ‘contributing’ processes (Ambroise, 2004), where
contributing processes are those that contribute to flow at a particular location at a
particular time, and necessarily include active processes upstream of the point of
interest. It follows therefore, that all contributing processes are derived from
active processes, occurring both upstream and at the point of interest; however,
80 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
not all active processes will become contributing processes downstream of where
they occur, due to flow depletion processes such as evapotranspiration, and
infiltration to the subsurface. This distinction is particularly important in
catchments with relatively long travel times for water and/or where flow depletion
processes are significant.
While information on active processes is provided as standard output from
ISSHMs, the same is not the case for information on contributing processes. For
example, the lag-times between individual recharge events and resulting stream
flow increases are not reported. As a result, previous studies that have used
ISSHMs at the catchment scale (e.g. Goderniaux et al., 2009; Goderniaux et al.,
2011; Loague and Vanderkwaak, 2002; Ebel et al., 2008; Li et al., 2008; Shen and
Phanikumar, 2010; Mirus et al., 2011a; Camporese et al., 2010) have been unable
to identify and quantify the individual contributions of various catchment
processes to streamflow generation processes. Although Vivoni et al. (2007)
quantified the contributing processes of streamflow generation at the catchment
scale, their model was based on a number of simplifying assumptions that did not
necessitate the distinction between active and contributing processes. In
particular, they assumed that surface water flows to the catchment outlet without
loss or impediment once it enters the surface domain (see Ivanov et al., 2004).
This assumption is problematic in more complex systems where significant
fractions of overland and in-stream flows are depleted (e.g. due to reinfiltration of
overland flow on the hillslope, or losing sections along a stream) or retained in
particular parts of the catchment (e.g. due to wetlands, weirs or other flow
impediments and water storages).
In order to enable ISSHMs to be used for the identification of both active and
contributing streamflow generating processes, it is necessary to first classify water
as it enters the surface by the active flow generation mechanism, and then track
that water on its journey through the catchment, to the point at which the
hydrograph is being measured. Partington et al. (2011, 2012) and Li et al. (2013)
achieved this by developing and applying a Hydraulic Mixing-Cell (HMC)
method in order to identify the groundwater discharge components of hydrographs
for a relatively flat synthetic catchment that exhibited dynamic gaining and losing
reaches along the stream, and furthermore displayed clear time lags for flow from
81 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
upstream areas. However, this approach has not yet been applied to larger-scale
catchments, or for the identification of overland flow generation mechanisms.
In this paper, the HMC method introduced by Partington et al. (2011) is modified
to enable information about active and contributing processes to be obtained as
outputs from ISSHMs. This enables the identification and quantification of
contributing in-stream and overland flow generation mechanisms at larger (e.g.
catchment) scales which informs the understanding of catchment functioning.
This is particularly important as there are still difficulties in the capability to
conduct or scale up the measurements of active processes that are required in
order to gain an understanding of surface water-groundwater interactions and
streamflow generation at the catchment scale (Fleckenstein et al., 2010). The
Lehstenbach catchment is used as the basis for virtual experiments with the
modified HMC method. Two models of contrasting scales are used to investigate
both in-stream and overland flow generation mechanisms within the catchment.
In-stream flow generation mechanisms are defined as those occurring on the
boundaries of the stream, i.e. direct precipitation to the stream, direct groundwater
discharge to the stream and overland flow into the stream. Overland flow
generation is distinguished by rainfall runoff from the hillslope (without
distinguishing infiltration-excess and saturation-excess) and groundwater
discharge on the hillslope adjacent to the stream. Using the HMC method, this
paper aims to demonstrate the value of quantifying in-stream and overland flow
generation mechanisms to better understand processes at the catchment scale
within the virtual experiments by:
1. Separating flow hydrographs into the constituent in-stream and overland
flow generation mechanisms at the outlet and other select points;
2. Quantifying the spatial and temporal variability for in-stream and overland
flow generation mechanisms at contrasting spatial (wetland 210 m2 and
catchment 4.2 km2) and temporal (days vs. year) scales; and
3. Quantifying the differences between active and contributing processes
within the catchment.
82 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.2. Case study: Lehstenbach catchment
The Lehstenbach catchment, (4.2 km2) located in South-eastern Germany
(50°8'35'' N, 11°52'8'' E, see Figure 4.1), has been the subject of a number of
previous studies (Lischeid et al., 2002; Lischeid et al., 2007; Frei et al., 2010).
Elevations within the catchment vary between 877 m above sea level in upslope
areas and 690 m above sea level at the catchment’s outlet. Average annual
precipitation amounts to about 1150 mm/yr, the average annual evapotranspiration
is approximately 600 mm/yr, and average annual runoff from the catchment is
approximately 550 mm/yr (Gerstberger, 2001). The annual mean air temperature
is approximately 5°C (Gerstberger, 2001).
The main regional aquifer in the Lehstenbach catchment is made of regolith
material (around 40 m thick) originating from the weathering of the granitic
bedrock (Lischeid et al., 2002). Nearly one-third of the catchment’s total area can
be classified as riparian wetlands, adjacent to the major streams. These wetlands
are preferentially located in the centre of the bowl-shaped catchment, where
subsurface flows converge. Within the wetland areas, groundwater levels typically
fluctuate within the uppermost 0.5 m of the organic peat soil. In the upslope areas,
which are mainly forested (Picea abies), groundwater levels are generally
between 5 m and 10 m below the surface. Locally, the hydraulic connectivity
between the groundwater in the riparian wetlands and the deeper regolith aquifer
is restricted by an up to 2 m thick basal clay layer.
Figure 4.1: Location of the Lehstenbach catchment, after Frei et al. (2010).
83 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Previous studies of the Lehstenbach catchment indicated that the dominant runoff
generation processes (e.g. saturated overland flow and shallow subsurface flow)
during rainfall events take place within the wetland areas (Lischeid et al., 2007;
Frei et al., 2010). Large areas of these wetlands, predominantly located near the
catchment’s outlet, are characterised by a pronounced micro-topography,
consisting of sequences of hollows and hummocks formed by the wetland’s
vegetation (Knorr et al. 2008). A conceptual hillslope plot depicting the in-stream
and overland flow generation mechanisms in the Lehstenbach catchment is shown
in Figure 4.2.
Figure 4.2: Conceptual diagram of in-stream and overland flow generation
mechanisms typical of the Lehstenbach catchment during intense storm
events. The in-stream and overland flow generation mechanisms shown are
groundwater discharge to the channel (GW-CH) and wetland surfaces (GW-
WL), direct rainfall to the channel (RF-CH) and wetland surfaces (RF-WL),
and runoff from the forest.
Previous modelling by Frei et al. (2010, 2012) has been carried out for a synthetic
riparian wetland typical of those within the Lehstenbach catchment. Frei et al.
(2010) demonstrated a hysteretic relationship between wetland water storage and
channel discharge. They concluded that enhanced mixing between surface and
subsurface water had potential implications for the water quality within the
catchment. However, Frei et al. (2010) did not explore mixing of rainfall and
discharged groundwater at the wetland’s surface, which necessitates quantifying
the different overland surface flow and ponding generation mechanisms. These
complex processes in the wetland suggest an analysis of only the active
84 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
mechanisms is insufficient to quantify the contributing overland flow generation
mechanisms. In the present study, application of the HMC method to the wetland
model expands on the work of Frei et al. (2010), and is used to quantify the
fractions of overland flow that are generated from either rainfall running off the
wetland or groundwater discharging to the wetland. However, their wetland model
does not include the surrounding influences of adjacent wetlands, upslope forested
areas and groundwater flows from upslope and deeper aquifers within the
catchment. To investigate the catchment-scale processes, a model of the entire
Lehstenbach catchment is developed, allowing analysis of in-stream and overland
flow generation across the entire stream network and catchment, as well as
accounting for contributions to the wetlands from deeper groundwater that
originated from upslope areas.
4.3. Methodology
The modelling investigation within the study area is carried out at two different
scales, as mentioned previously. Firstly, the model of a synthetic wetland typical
of those in the Lehstenbach catchment is revisited, following Frei et al. (2010)
(Section 4.3.2.1). Secondly, a model of the entire Lehstenbach catchment is
developed (Section 4.3.2.2). In-stream and overland flow generation is analysed
using an improved HMC method detailed in Section 4.3.3.
4.3.1. The fully integrated modelling platform
Numerical modelling in this study uses the ISSHM HydroGeoSphere (HGS).
HGS is a fully integrated surface-subsurface flow model that incorporates 3D
variably saturated subsurface flow using a modified form of the Richard’s
equation and 2D surface flow using the diffusion wave approximation to the St
Venant equations. Further details of the numerical formulation of HGS can be
found in Therrien et al. (2009) and Brunner and Simmons (2012). The surface and
subsurface are coupled using a first-order exchange coefficient (Liggett et al.,
2012). An important characteristic of fully integrated models such as HGS is that
there is no requirement for a priori assumptions of specific streamflow generation
mechanisms (Mirus et al., 2011a). Consequently, it is necessary to interrogate the
model outputs to characterise the streamflow generation processes that are
predicted by the model.
85 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.3.2. Development of case study models
4.3.2.1. Wetland model setup
The wetland model setup is described by Frei et al. (2010), and so only a brief
description is presented here. The wetland model (Figure 4.3) is at the plot scale
(21 m x 10 m), representing a relatively flat hillslope (average slope of 0.03 m/m)
made up of a sequence of hummocks and hollows. The spatial structure of the
micro-topography is represented using geostatistical indicator simulations based
on a Markov Chain model of transitional probabilities (Carle and Fogg, 1996).
The model domain is made up of 10 layers, with a total of 410,832 elements and
210,000 nodes, providing a fine discretisation of 0.1 m in the X, Y and Z
directions. The organic peat is represented as homogeneous and isotropic with a
saturated hydraulic conductivity of 0.2 m/d, a value that is based on a previous
Figure 4.3: Geometry of the wetland segment: a) planar reference model
showing the main drainage direction and channel location; b) smoothed
realisation of the wetlands’ hummocky micro-topography, with simulation
results of developed overland flow in the wetland (after Frei et al. (2010)); c)
cross section (Y = 5 m) of the micro-topography model (after Frei et al.
(2010)). The division of overland flow into two distinct flow networks
(denoted as FN1 and FN2) is shown by the surface flow lines. The model
observation points for flow in this study are denoted by the red arrows,
which correspond to surface water discharge from the wetlands to the
channel from FN1 and FN2, and channel discharge at the outlet of the model.
86 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
modelling study from the field site (Hauck, 1999) and which is in line with values
reported for similar wetlands (Kruse et al., 2008; Schlotzauer and Price, 1999).
Constitutive relationships for unsaturated flow are assumed to follow the van
Genuchten model of the soil-water retention and relative permeability functions
(van Genuchten, 1980). The parameterisation of the van Genuchten model is
based on field measurements from similar wetlands located in Alberta, Canada
(Price et al., 2010). Frei et al. (2010) showed that the pronounced micro-
topography resulted in distinct flow networks in the wetland model as shown in
Figure 3b. The division of two flow networks (denoted as FN1 and FN2) and their
discharge points to the channel are shown in Figure 4.3b.
The simulation period in this study focuses on a large storm event (13th - 21st July,
2001) from the 2000-2001 hydrological year (1/11/2000 – 31/10/2001). The
simulation starts with a recession period (i.e. no rain) lasting 14 days. After day
14, an extended rainfall event occurs. The rainfall event persists for 8 days leading
to the depressions on the slope filling until they spill to the adjacent down-slope
depressions. Details of this ‘fill and spill’ mechanism (after Tromp van-Meerveld
and McDonnell, 2006) and its influence on overland flow are described in Frei et
al. (2010).
4.3.2.2. Catchment model setup
A digital elevation model (DEM) with a spatial resolution of 5 m x 5 m is used to
represent the bowl-shaped topography of the catchment. Vertically, the model is
discretised into two main geological units of variable thickness to represent the
major soil types and subsurface geology of the Lehstenbach catchment. Within the
wetland areas, the upper surface unit (1 m thick) represents the organic peat soils.
This upper unit is represented in the grid by 10 sub-layers of uniform vertical
thickness equal to 0.1 m (see Table 4.1).
For the ten sub-layers, the saturated hydraulic conductivity (K ) decays
sat
exponentially with depth to account for effects related to the transmissivity
feedback mechanism, which has been described for peat forming wetlands
[Bishop et al., 2004; Jacks and Norrström, 2004). Values for K for the different
sat
sub-layers ranged between 20 m/d for the uppermost layer (representing fresh and
less compacted organic material) and 8.6x10-3 m/d for the basal clay layer, which
87 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
separates the wetlands from the deeper aquifer (Table 4.1). The values for K for
sat
the wetland areas are within the range reported by Jacks and Norrstöm (2001)
who performed slug tests for similar wetlands located in the Luntoma catchment
in South-western Sweden. The lower model unit (20-40 m thick) is represented in
the grid by 10 sub-layers and is used to represent the main regolith aquifer.
Similar to the wetland model, parameters for the soil-water retention functions are
applied uniformly to the upper wetland layers based on field measurements from
similar wetlands in Alberta, Canada (Price et al., 2010). Uniform parameters for
the van Genuchten model as well as for K (0.24 m/d) of the main regolith
sat
aquifer are obtained from a previous calibration of the model to field observations
of aquifer heads and stream discharge at the catchment outlet for the 2000-2001
hydrological year (1/11/2000 – 31/10/2001) (see Werb, 2009).
Horizontally, the model uses a triangular mesh with variable node spacing (Figure
4.4). Nodal spacing in the mesh varies between 10 m in the direct vicinity of the
streams, 30 m within riparian wetlands and 100 m for upslope areas. Within HGS,
the locations of streams develop from flow between the surface and subsurface
and tend to occur at topographical lows. However, the DEM used is too coarse to
resolve differences in elevation between stream channels and the surrounding
areas. Therefore, the elevations of surface nodes which coincide with stream
locations are manually lowered by 1 m to correct for the smoothing of topography
in the coarse DEM. For the subsurface flow domain, the bottom and lateral model
boundaries are set to no flow to represent the contact with the low-permeability
granitic bedrock and because it can be assumed that there is no exchange of
groundwater with areas located outside of the Lehstenbach catchment. For the
surface flow domain, a combination of variable rainfall, interception and
evapotranspiration is applied over the catchment. Interception and
evapotranspiration (Panday and Huyakon, 2004), within HGS, are simulated as
mechanistic processes governed by plant and climatic conditions, as described by
Kristensen and Jensen (1975) and Wigmosta et al. (1994). At the edges of the
surface flow domain, a critical depth boundary is used to simulate surface water
outflow from the model. Manning’s roughness coefficient for the forested upslope
areas are assigned uniformly to 1.9x10-6 d/m1/3, representing areas of minor
88 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
ground vegetation (Shen and Julien, 1993). Friction slope for the wetlands are set
to 8.1 x 10-5 d/m1/3, typical for high grass (Shen and Julien, 1993).
Topography and land use for the Lehstenbach catchment are shown in Figure 4.4.
The elemental type distribution shown in Figure 4.4 is used to delineate the
stream, wetlands and forest areas. The detailed micro-topography of the wetland
model cannot be included explicitly at the catchment scale due to computational
constraints. Instead, the rill storage concept is used (see Therrien et al., 2009),
whereby a ponding depth is specified at surface nodes which must be reached
before surface flow is induced. Spatially distributed rill storage height zones are
used to represent the micro-topographically induced threshold-type behaviour of
runoff generation from the wetlands. These storage zones mimic the depression-
storage characteristics and the typical fill and spill mechanisms of the wetlands’
micro-topography. However, the behaviour of the wetlands in the catchment-scale
model (as opposed to the wetland model) is influenced additionally by variable
groundwater heads at the upslope boundaries, which are driven largely by
recharge originating from infiltration in the upslope forested areas. The simulation
period is the hydrological year 2000 (11/1/2000 - 10/31/2001), although a focus is
placed on the large July storm (13th - 21st July, 2001) simulated in the wetland
Figure 4.4: Model spatial discretisation of the Lehstenbach catchment and
distribution of the stream, wetland and forest areas (the z-axis is exaggerated
by a factor of 5). Model observation points are at locations 1 to 6 and the
outlet.
89 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
model. Note that because the whole year is simulated in the catchment model, day
0 in the wetland model is the same as day 200 in the catchment model. Evaluation
of simulated stream discharge to the observed discharge for the 2001-2005
hydrologic years yields a Nash-Sutcliffe efficiency of 0.51, which is deemed
reasonable for this study.
4.3.3. HMC method
The HMC method developed by Partington et al. (2011) allows separation of the
streamflow hydrograph by the in-stream flow generation mechanisms (i.e.
groundwater discharge to the stream, direct rainfall to the stream, and overland
flow to the stream). The HMC method works by utilising the spatiotemporal
information of active in-stream flow generation mechanisms to obtain the
contributing flow generation mechanisms. The HMC method treats each stream
node in the surface domain of the model as a mixing cell. The method utilises the
nodal fluid mass balance from the ISSHM at each model time-step, to calculate
the fraction of water in each cell that derives from different in-stream flow
generation mechanisms. For example, if a cell has a water volume of 0 units at the
start of the time step and 2 units at the end of the time step, and during that time-
step 1 unit of groundwater discharged into the cell and 1 unit of rainfall fell on the
cell, then the fraction of groundwater discharge and direct rainfall in the cell
would be 0.5. This becomes more complex if there is also outflow from the cell,
because a mixing rule must be chosen for the mixing-cells, which dictates how the
fractions are calculated at the end of each time step. The HMC method uses the
“modified mixing rule”, which simulates a mixing regime between perfect mixing
and piston-flow (see Campana and Simpson, 1984).
Each in-stream flow generation mechanism is assigned a unique fraction f. Over
each time-step of the model simulation, inflowing water into a cell from either the
subsurface (e.g. groundwater discharge) or surface boundary conditions (e.g.
rainfall) is classified by the corresponding unique fraction. The sum of all
fractions in each cell, for an error-free fluid mass balance, is equal to 1. Inflow
from adjacent cells is assigned the fractions from the upstream cell. Partington et
al. (2011) derived an equation for the fraction f for each in-stream flow generation
mechanism k at time N in cell i as:
91 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
(cid:12)(cid:14) (cid:7)m V N (cid:9)(cid:11) (cid:7)n V N f N(cid:4)1
(cid:12)VN(cid:4)1 ij N(cid:4)1(cid:9) ji N(cid:4)1 j(k)
f N (cid:3) (cid:12) i (cid:4) j(cid:3)1 (cid:9)f N(cid:4)1(cid:5) j(cid:3)1 (4.1)
i(k) VN VN i(k) VN
(cid:12)(cid:12) i i (cid:9)(cid:9) i
(cid:13) (cid:10)
Where there are n sources and m sinks for cell i; f N-1 denotes fraction k at time
j(k)
N-1 in the neighbouring cell j, V denotes the volume with the superscript denoting
time state and subscript i denoting the cell, ij denoting volume into cell j from cell
i over the time-step from N-1 to N, and ji denoting volume from neighbour j into i.
To achieve the aims of the current study, some limitations from previous
implementations of the HMC method must be addressed. Firstly, Partington et al.
(2011, 2012) does consider the contributing mechanisms for overland flow, as
groundwater discharge adjacent to the stream was negligible. Secondly,
Partington et al. (2011) notes that the HMC method was only numerically stable
if the ratio of outflow to storage was less than 1, and the fluid mass balance
convergence criterion was very small (<10-10 m3/s). These stability conditions
require very low convergence criterion (<10-10 m3/s) for the solution of the fluid
mass balance equation, and very small time-steps (<100 s), thus increasing
simulation time significantly. Use of the HMC method in this study expands on
previous implementations by: (1) accounting for overland flow generation
mechanisms in the HMC method, (2) modifying the HMC scheme to allow
operation at sub-time-steps of the ISSHM flow solution time-step, and (3)
developing stability handling criteria for HMCs to prevent instabilities from
occurring. Addressing these limitations enables the quantification of contributing
in-stream and overland flow generation mechanisms for the more complex virtual
experiment considered in this current study.
4.3.3.1. Capturing in-stream and overland flow generation
mechanisms
Overland flow generation mechanisms are considered by using additional HMC
fractions to those used in Partington et al. (2011, 2012). All in-stream and
overland flow generation mechanisms are delineated by surface node definition:
e.g. ‘stream’ or ‘overland’. Surface nodes may also be defined as ‘other’ nodes,
which could be lakes, reservoirs, upstream inflow boundaries or areas for which
internal flow generation may not be of interest or are not known. In this study,
forested areas are treated as ‘other’ nodes. With respect to groundwater discharge
92 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
and rainfall, flow generation at ‘other’ nodes is not captured explicitly. Instead,
any water flowing from ‘other’ nodes to a stream or overland node is assigned an
‘other’ fraction of 1 (i.e. f = 1), i.e. without delineation of this water into
other
components of groundwater discharge and rainfall. Unless water in the surface
domain at the start of a simulation is assigned stream, overland or ‘other’ fractions
from a previous simulation, then it is not possible to know which flow generation
processes were responsible for initial surface water. Therefore, an “initial”
fraction is also included; initial conditions for existing surface water in each cell
default to the “initial” fraction (i.e. f = 1, and all other fractions are set to zero)
initial
unless predefined otherwise.
4.3.3.2. Sub-timed HMC algorithm to ensure stability
The stability of Eq. 4.1 in the HMC method is dependent on the ratio of outflow to
storage (Partington et al., 2011). ]. Stability requires that the volume of water
leaving a cell over a given time step is less than the volume in storage. The
volume leaving a cell is calculated using the fluid mass balance, accounting for
small errors in the water balance (i.e. ∑ f N ≠ 1) within each cell (for outflow and
i(k)
storage). Absolute error (ϵ) within cells is calculated as ϵ = |1-∑ f N|. The HMC
i(k)
ratio for each cell i is defined as:
(cid:7)m
V N f N(cid:4)1
ij N(cid:4)1 i(k)
HMC ratio(i)(cid:3) Vj(cid:3) i1 N(cid:4)1(cid:7) f i(N k(cid:4) )1 (4.2)
(cid:18)k
Instability in the HMC method results when the cell ratio is greater than 1 in any
HMC. For small HMCs, the storage volume may be quite small relative to the
outflow. Maintaining the HMC ratio below 1 can necessitate very small time-steps
when the cell’s storage is small relative to the flow. This is problematic for long
term transient simulations requiring large time-steps in the flow solution. As part
of the improved HMC method, a sub-timed HMC method is implemented to
prevent relatively small time-steps. This implementation removes the stability
restriction (i.e. Eq. 4.2) imposed by the HMC method on the maximum time-step
for the HGS flow solution. The sub-timed HMC method is applied when the
maximum HMC ratio at any of the cells is greater than 1. It works by subdividing
the fluxes and storage changes within a time-step. This subdivision between time-
93 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.3.3.3. Stability constraints for efficient execution of the HMC
method
The sub-timed HMC scheme allows time-steps in the flow solution to be as large
as convergence criteria allow. However, a very large HMC ratio (> 10000), results
in a large number of sub-time steps. In terms of computational efficiency, a very
large HMC ratio is not desirable, particularly for cells that only have very small
volumes of water storage. In near dry cells, large HMC ratios will often arise at
the onset of rainfall, groundwater discharge or overland flow, as the outflow can
be significantly larger than storage. The large HMC ratio problem tends to occur
in simulating ephemeral reaches of streams whereby particular stream cells
become dry. Similarly, this problem occurs in simulating overland flow whereby
the overland cells are often dry (due to overland flow only normally occurring in
rainfall events). In these cases of a large HMC ratio, particular cells can become
numerically unstable due to propagation of errors from the fluid mass balance.
Fortunately, this occurs at cells that are of little interest in a physical sense (i.e.
where active processes take place but with relatively insignificant volumes of
water).
To address these problems and ensure stability and computational efficiency,
criteria are added to the method and used to determine if each cell should be
evaluated. If any of the above criteria are met, then the cell being evaluated is
reset, which means that all fractions f in the reset cell are set equal to zero, and
that the cell is assigned the reset fraction (f = 1). The criteria (a-e) for a reset
Reset
cell are checked at each time-step allowing it to become active if the reset criteria
are no longer met. The reset fraction allows the tracking of the fraction of water
for which the flow generation is unknown (due to the cell being reset), which
quantifies the effect of the reset fraction. Tracking of the reset fraction highlights
through inspection of calculated HMC fractions if this unknown flow generation
is significant. If the reset fraction of flow in the streamflow hydrograph is high
(>1%) then each criterion can be modified to bring this to a satisfactory level
(<1%).The reset criteria are as follows:
a) Minimum volume. Cells with relatively small water storages are reset
unless surface flow is greater than zero (10-10 in this study).
95 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
b) Ponding only. Cells with no surface flow are reset if the inflow or outflow
is greater than the volume of ponded water.
c) Maximum HMC ratio. Cells with a large HMC ratio (Eq. 4.2) are reset
(104 in this study).
d) Relative volume error too high. Cells in which the ratio of the ‘absolute
volume error’ to storage is large are reset, where the absolute volume error
denotes the absolute value of the error in the volumetric cell balance (2.5
in this study).
e) Error in HMC excessive. Cells with a large absolute error (ϵ) are reset after
updating the fractions in the cell at each time-step or sub-time-step (0.5 in
this study).
4.4. Flow generation analyses conducted using the HMC method
The in-stream and overland flow generation mechanisms analysed for the case
study (see Figure 4.2) are: (1) groundwater discharge to the stream channel (GW-
CH), (2) direct rainfall to the stream channel (RF-CH) and overland flow to the
stream channel. The overland flow generation mechanisms analysed are: (3)
groundwater discharge to wetland surface areas (GW-WL), (4) direct rainfall on
wetlands surface (RF-WL) and (5) overland flow from forested areas (Forest).
The unique fractions f used in this HMC analysis are: (1) GW-CH, (2) RF-CH, (3)
GW-WL, (4) RF-WL, (5) Forest, and also (6) initial water (Initial) and (7) reset
water (Reset). In-stream and overland flow generation mechanisms are
determined based on surface cell type: i.e. stream, wetland or forest cells. Each
analysis outlined below corresponds directly to aims 1 to 3. To aid the reader
through the following sections, Table 4.2 below summarises the flow generation
mechanisms analysed, and the corresponding unique HMC fractions and fraction
types.
96 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Table 4.2: Considered flow generation mechanisms, HMC unique fractions,
and HMC fraction types.
Flow generation mechanism Unique Fraction
fraction type
Groundwater discharge to the stream channel GW-CH In-stream
Direct rainfall to the stream channel RF-CH In-stream
Groundwater discharge to the wetlands GW-WL Overland
Direct rainfall to the wetlands RF-WL Overland
Surface flow from the forest area Forest Other
Unknown Initial Initial
- Reset Stability
4.4.1. Separating flow hydrographs by in-stream and overland flow
generation mechanisms
The main output from the HMC method is the values of the unique fractions f at
each cell, which are used to separate the flow hydrographs by multiplying the total
flow at each time step by each of the unique fractions at the corresponding time
step. Each flow hydrograph at the outlet and selected model observation points
(see Figure 4.3 and Figure 4.4) is made up of a collection of cells. At each cell,
the surface outflow is separated by the unique fractions into the corresponding
flow generation mechanisms, and then these are summed for each collection of
cells.
4.4.2. Analysing spatiotemporal variability of in-stream and overland
flow generation
Spatial variability of in-stream and overland flow in both models is demonstrated
in three ways. Firstly, visualisation of the HMC fractions across the model surface
domain is shown in each model at different points in time. Secondly, flow
hydrographs are shown at select observation points within each of the models.
Lastly, the different flow generation mechanisms driving total flow at each of the
locations are summarised. The summarising of the flow components is achieved
by integrating over the flow curves for each of the flow generation mechanisms, at
each selected observation point.
97 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.4.3. Analysing active and contributing processes
The analysis of active and contributing processes is carried out over the entire
year long simulation for the catchment scale model. In particular, the components
analysed are GW-CH, RF-CH and wetlands surface discharge to the stream
channel (WL-CH = GW-WL + RF-WL). Runoff from the forested areas to the
stream channel is also considered (Forest-CH). The active flow generation
processes are determined by summing the inflowing fluxes to the surface domain
(GW-CH, RF-CH, WL-CH, Forest-CH) at each time-step, and the contributing
processes (taken at the outlet) are determined from the HMC analysis. A long-
term ratio of contributing to active flow generation mechanisms is calculated to
quantify the cumulative difference between these two.
4.5. Results and discussion
4.5.1. Wetland model
4.5.1.1. In-stream and overland flow generation mechanisms
driving flow
The applied rainfall and the resultant outflow and corresponding flow generation
components are shown in Figure 4.5a-b. From the time rainfall starts, streamflow
increases slightly until day 17, at which point the rainfall rate increases
significantly. The rain falling directly on the channel contributes to runoff
immediately. The infiltration across the overland area increases the subsurface
head, which in turn increases the groundwater discharge to the channel. The rapid
response of rainfall directly on the channel (RF-CH) is clearly seen to follow the
pattern of the rainfall input. During the highest rainfall period, over day 17, the
groundwater discharge to the channel rises to an apparent quasi-steady-state. In
the four days that follow, the GW-CH component only changes slightly in relation
to the total streamflow. All major changes in streamflow between days 17 to 22
are attributed to changes in overland flow to the stream. It can be seen in Figure
4.5c that at approximately 17.6 days, overland flow from FN1 reaches the channel
and causes a rapid increase in streamflow.
98 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Figure 4.5: Hyetograph, simulated outlet hydrograph, simulated FN1
hydrograph, simulated FN2 hydrograph and simulated surface water storage
graph for the wetland model during a large storm event. GW-CH and RF-
CH are direct groundwater discharge and rainfall to the channel. GW-WL
and RF-WL represent groundwater discharge and rainfall to the surface of
the wetland area respectively. Initial represents the initial water in the
surface domain at the beginning of the simulation. The reset fraction of flow
was negligible and hence is not shown.
Figure 4.5d shows that almost half a day after FN1 starts discharging to the
channel, at approximately day 18, FN2 starts contributing to streamflow. Whilst a
greater proportion of rainfall to the wetland surface area (RF-WL) is evident, there
is also a large component of groundwater that discharged to the wetland surface
(GW-WL). This large component of GW-WL in the outflow hydrograph appears
not only to be an increase in this overland flow generation mechanism at this
particular time, but also a result of the mobilisation of the ponded water generated
99 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
from GW-WL. The total surface water storage across the model and also the flow
generation mechanisms that created the storage are shown in Figure 4.5e. The
ponding of water in the hollows makes up almost 100% of the surface storage
(with the GW-CH and RF-CH water being relatively insignificant). There is only
a relatively small variation in the total storage after day 18. A small component of
initial water is contributing to streamflow at the outlet at day 18. The initial water
was mobilised after the hollows fill and then spill toward the stream. This shows a
slow rate of turnover (>18 d) of ponded surface water due to the time taken for the
hollows to ‘fill and spill’, i.e. prior to the activation of the flow networks.
4.5.1.2. Spatiotemporal variability of in-stream and overland flow
generation
Two snapshots of in-stream and overland flow generation are shown for the
wetland model, just before the rainfall event at the start of day14 (Figure 4.6), and
6 days into the storm event at day 20 (Figure 4.7). The distributions of (1) GW-
WL water in the hollows, and (2) GW-CH water, are shown in Figure 4.6 and
Figure 4.7. After 14 days, the rainfall event begins and therefore there is no RF-
CH or RF-WL fraction of surface water (not shown in Figure 4.6). The reason that
the fraction of GW-WL water is not equal to 1 across the hummocks and hollows
is because of the persistence of initial water, of which a small volume resides on
the surface.
The development of overland flow in the wetlands is well established at day 20.
An increase in the GW-WL component of streamflow is explained by the
increased subsurface heads leading to a more developed seepage face along the
bank. Close examination of the two flow networks (FN1 and FN2) highlights
variations in the overland flow generation across the wetland. The overland flow
network on the left (FN1) has a slightly higher component of groundwater
discharge, whereas the flow network on the right (FN2) has a slightly higher
component of rainfall, with clear spatial variation in each. The flow network FN2
has a higher rainfall driven component because of the larger surface area of the
stored water, which receives more rainfall. The reset of cells at the top of the
hummocks and the upper part of the stream bank is due to the fact that these cells
have no surface flow to other cells and also the inflow from rainfall at these cells
is much greater than the ponded water volume.
100 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Figure 4.6: Wetland HMC fractions at day 14 (pre-storm event). The in-
stream and overland flow generating mechanisms shown are: a) groundwater
discharge to the channel (GW-CH), b) groundwater discharge to the wetland
surface (GW-WL). The initial and reset fractions are also shown in c) and d)
respectively. A GW-WL fraction of 0.5 denotes that 50% of the water at that
cell was generated from groundwater discharging to the wetland surface.
Figure 4.8 shows a summary of the percentage of total volume of water derived
from different in-stream and overland flow generation mechanisms. This
summary is provided at the outlet and for each of the flow networks (FN1 and
FN2). All volumes were determined by integrating over the flow hydrographs in
Figure 4.5 (b-d). The contributions towards total flow from the two overland flow
networks were calculated to be 34% and 10% for FN1 and FN2, respectively,
making a total overland flow contribution of 44% over the simulation period. The
components of initial water and reset water, are insignificant (<1%). The volume
attributed to cumulative error was extremely small at the outlet (4 x 10-16%).
101 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
100%
90%
ERROR
80%
RESET
70%
60% INITIAL
50%
RF-WL
40%
30% GW-WL
20%
RF-CH
10%
GW-CH
0%
Outlet FN1 FN2
Figure 4.8: Comparison of different streamflow generation mechanism
contributions at the outlet, FN1 and FN2. The initial and reset fractions and
the cumulative error in the cells were insignificant, as can be seen at the top
of the stacked columns.
To summarise, HMC analysis of the wetland model demonstrates clear spatial
variability in overland flow generation, as depicted in Figure 4.6 and Figure 4.7.
This variability is clear in the discharge hydrographs of the two flow networks
(Figure 4.5), highlighting a complex relationship between rainfall input and runoff
from the wetlands into the stream. However, despite this spatial variability, the
flow networks have similar compositions of overland flow generation components
at the point of discharge into the stream, with both FN1 and FN2 being dominated
by RF-WL flow generation (Figure 4.8). The HMC analysis showed that the RF-
WL component of flow is larger by about 5% over the GW-WL component in
driving the overland flow contribution at the outlet (Figure 4.8). As evidenced in
the Figure 4.5 discharge hydrographs, the storage across the overland area shows
that the relationship between overland storage and overland flow contributions to
streamflow at the outlet is non-linear. As noted in Frei et al. (2010) this non-linear
relationship is caused by the complex nature of the ‘fill and spill’ mechanism. As
expected, the direct RF-CH component of in-stream flow generation followed the
rainfall input. This is because there are no significant time lags or losses along the
stream to the subsurface. Similarly, the response to rainfall of groundwater
discharge in the channel (GW-CH) is also as expected, although it has a slower
response than the RF-CH component.
103
noitcarf
demmuS |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.5.2. Catchment model
Three snapshots from the model simulation for the large storm in July 2001 are
examined for surface water distribution and surface-subsurface exchanges. These
snapshots are taken just prior to the storm (day 216), at the peak of the storm (day
218), and 2 days after the peak (day 220). Figure 4.9 shows standard HGS outputs
of surface saturation, exchange flux and depth distribution across the catchment at
each of these times. Figure 4.9a shows that saturation at the surface boundary
increases across the catchment as the storm event progresses.
Figure 4.9: Simulated surface saturation (a), exchange flux (b) and surface
water depth (c), prior to the storm, at the storm peak and 2 days after the
storm peak. A losing section on the right arm of the stream is highlighted in
the third frame of row b). Positive values of exchange flux indicate
groundwater discharge to the surface and negative values indicate
infiltration of surface water to the subsurface.
The exchange flux (Figure 4.9b) across the catchment shows where water is
exfiltrating from the subsurface to the surface (positive values) and where water is
104 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
infiltrating into the subsurface from the surface (negative numbers). Prior to the
storm event, there is no exchange across the forested areas, water is being lost
from the wetlands to the subsurface, and groundwater is discharging to the stream.
At the peak of the storm, the infiltration rate peaks in the forested areas, but the
infiltration from the wetlands decreases. The area of groundwater discharging to
the stream is slightly increased, but not significantly. At the cessation of the storm
event, the infiltration rate is varied across the forested area. In Figure 4.9b at day
220, about two thirds of the reach on the right arm of the stream is losing
(highlighted by a red ellipse).
The surface water depth distribution (Figure 4.9c) across the catchment highlights
the wetland areas, where most surface ponding occurs. Excluding the stream,
these wetland areas lie at the lowest elevation in the catchment. It is these ponded
wetlands that provide the overland runoff during the storm event. There is
discharge of groundwater at the upper part of the right arm of the stream,
however, this water is returned to the subsurface across the losing stretch of this
reach of the stream (highlighted in Figure 4.9b).
4.5.2.1. In-stream and overland flow generation mechanisms
driving flow
The separated streamflow hydrograph at the outlet is shown in Figure 4.10. In
Figure 4.10b, the GW-CH component of streamflow is seen to respond
immediately to rainfall events with no clear lag, possibly due to propagation of a
pressure wave. As rainfall ponds on the hydraulically connected wetlands, this in
turn increases the head in the underlying aquifers. The GW-CH component of
streamflow is seen to make up ~97% of the flow in dry periods – the GW-WL
component of streamflow contributes a very small amount to streamflow during
dry periods (~3%). The RF-WL and GW-WL components of the outlet
hydrograph (Figure 4.10b) show that the wetlands only provide a significant
component to streamflow during the larger storm events (e.g. at the storm peak,
day 218). After the large storm event from day 221, the streamflow is supported
mainly by GW-CH discharge to the stream. Overland flow from the forested areas
had a negligible contribution to overland flow in the wetlands and hence also to
streamflow, and for this reason is not shown in the hydrographs.
105 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Figure 4.10: Hyetograph (a), separated discharge hydrographs at the outlet
(b), as well as the HMC fractions in surface-storage across the catchment (c).
Note that overland flow from the forest was negligible (< 0.2%) in
contributing to streamflow and so is not shown in (b).
The total surface water storage across the Lehstenbach catchment and the storage
of water from different flow generation mechanisms, i.e. the mechanism by which
the water came into storage are depicted in Figure 4.10c. This figure shows that
much of the storage in the surface is ponded water in the forested areas. The
second largest component of storage is rainfall stored in the wetlands. Notably,
the GW-CH and RF-CH generated surface storages are relatively insignificant
with respect to total storage, yet provide the largest contribution to streamflow.
The surface water volumes of initial, reset and cumulative error are relatively
insignificant (i.e. appear as horizontal lines along y = 0 in the graphs) to the flow
generation mechanisms and are therefore not shown.
4.5.2.2. Spatiotemporal variability of in-stream and overland flow
generation
The in-stream and overland flow generation calculated by the HMC method (at
the same snapshot times as in Figure 4.9) for the large July storm are shown in
Figure 4.11. Prior to the storm, at day 216, the GW-CH component of streamflow
over the entire stream is high and dominating. At this time, there are small patches
of RF-CH generated stream water in places where little to no groundwater is
discharging and where there is no upstream flow passing through. A portion of the
wetland areas prior to the storm show GW-WL generated surface storage, a small
106 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
portion of which is feeding into the stream, which is more clearly apparent in the
hydrograph of Figure 4.10. The speckled RF-WL water existing prior to the storm
highlights areas where some ponding from rainfall has occurred that is yet to
either runoff, infiltrate or evaporate. The source of this rain is attributed to smaller
recent rainfall events (not shown). The bottom row of Figure 4.11 shows the
amount of reset (or unknown) fraction across the catchment during the storm.
Areas where the reset fraction is high correspond to areas where either no surface
flow is occurring or ponding is insignificant (as defined in Section 4.3.3.3). This
highlights areas where ponding processes take place, but in such small quantities
of water that they are not of interest, particularly in relation to the streamflow
hydrograph. As noted in Section 4.3.3.3, any reset cell is still tracked, which
means that any surface flow out of a reset cell is also tracked so that the influence
of these cells is accounted for.
At the peak of the large storm, at day 218, the fraction of GW-CH generation
becomes diminished across the stream as rainfall generation mechanisms become
dominant. The reduction of the fraction of GW-CH generation is matched by an
increase in fractions of RF-CH, GW-WL and RF-WL generation. At day 218, an
increase in the active part of the stream on the right arm (including upstream of
the losing section) is shown in the RF-CH generation. The GW-WL generation on
the wetlands at the peak of the storm is reduced. However, it is worth noting that
the GW-WL water appears in the same area as where water has ponded, shown in
the depth distribution in Figure 4.9.
As described in the stability criteria section 4.3.3.3, surface nodes containing less
than 10-10 m3 of water are excluded from analysis and are reset, which causes the
‘speckled’ effect that is seen adjacent to the upper reaches of the stream. This
effect is attributed partly to the spatial variations in rill storage height across the
wetlands. The small water storage at some wetland nodes relates to those wetland
nodes not being saturated and water infiltrating quickly due to the high hydraulic
conductivity near the surface.
107 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
After the peak of the storm event, at day 220, the GW-CH generation component
starts to increase. This increase is most apparent in the lower reaches of the stream
where the RF-CH generated streamflow has been mostly flushed from the stream.
The RF-CH component is still strong in small isolated areas in upstream parts of
the stream that are not flowing, and instead, are ponding. The wetlands receive
more groundwater discharge after the storm, which is reflected in the extent of
GW-WL generation across the catchment.
Analysis of the entire 2001 hydrological year allowed comparison of the longer
term flow generation across the catchment to the July large storm event. Figure
4.12 shows box plots of the percent contribution of each of the flow generation
mechanisms across the 7 model observation points depicted in Figure 4.4. The left
plot shows the spread for the entire hydrological year and the right shows the
spread for the large July storm (between days 17 and 20). The volume of water
that passed through the outlet and locations 1-6 is determined by integrating over
the streamflow hydrographs for each component of flow and dividing by the total
volume of streamflow that passed through. Not shown are the fractions of ‘forest’
(maximum 0.3%), initial (maximum 0.05%) and reset (maximum 0.41%) and the
cumulative error resulting from imperfect nodal fluid mass balances over the
simulation (maximum -0.9%). These components are relatively insignificant in
comparison to the four main flow generation mechanisms. This volumetric
analysis indicates that the mechanisms for flow generation did not differ
significantly across the Lehstenbach catchment, although greater variation can be
seen across the focused period of the large July storm compared to the entire year.
However, it is worth noting that the ‘outliers’ in the ‘event’ plot correspond to
observation point 1, which contributes less than 1% of the flow over this event.
Comparison of the distribution of individual flow generation processes across the
entire hydrological year showed surprising uniformity across the catchment. The
similarities in flow generation processes over the year long time scale at the seven
model observation locations are possibly due to the uniformly applied rainfall
events and the simplified representation of the micro-topography across the
wetlands.
109 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Figure 4.12: Box plots showing the spread of the average in-stream and
overland flow generation mechanism contributions for the entire year and
during the large storm event, across the 7 different model observation points.
The thick black line represents the median; the box covers the inter quartile
range (IQR) bounded by the lower and upper quartiles; the whiskers extend
to the lowest and highest data point within the fences (where the fences are
1.5 x IQR above and below the upper and lower quartiles respectively); the
circles represent data above and below the upper and lower fences
respectively.
The distributions for the event scale show a larger spread across the seven model
observation locations, which was also evident in the individual hydrographs. This
difference in the drivers of streamflow across these observation points is possibly
due to timing of the activation of WL-CH flow across different areas of wetlands,
and the differences in head gradient at the stream interface driving GW-CH flow.
The catchment model shows a combination of simple processes varying in space
and time, which leads to a complex culmination of in-stream and overland flow
generation processes at the outlet. Rain falling in the forested areas mainly
infiltrated and then recharged the underlying unconfined aquifer, which in turn fed
the adjacent down-slope riparian wetlands and stream. Because of the ‘rill
storage’ within the wetland areas, there is an aggregated ‘fill and spill’ mechanism
that is averaged over the wetland areas. The rill storage provided a threshold to
rainfall inducing runoff from the wetland areas. The GW-CH response to rainfall
mimicked a dampened rainfall input. This GW-CH component appeared more
110 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
sensitive than the GW-WL component, which contributed very little to
streamflow. The sensitivity of the GW-CH component is caused by the heads in
the riparian wetlands controlling groundwater flow. As the wetlands and
underlying unconfined aquifer are connected, increases in water levels in the
wetlands from rainfall increases subsurface heads and hence increases the
discharge of groundwater to the stream channel (i.e. GW-CH generation
mechanism). Conversely, the slower, almost filtered response from the GW-WL
generation mechanism is caused by: 1) the time delay in percolation recharging
the unconfined aquifer from the forested areas; then 2) the slow flow of
groundwater through the unconfined aquifers into the wetlands; then 3) the
mobilisation of ponded water in the wetlands into the stream once the wetlands
overtop into the stream.
4.5.2.3. Active versus contributing flow generation mechanisms
A comparison of the active and contributing flow generation processes for GW-
CH, RF-CH and WL-CH is shown in Figure 4.13. In Figure 4.13a, the active
component of GW-CH flow is clearly seen to be higher than the contributing
processes which predominantly results from losing areas along the stream. It
should be noted that the time lags in the stream also lead to a difference between
the active and contributing components, although these are small in this catchment
and hence do not play an obvious role. Similarly in Figure 4.13b and Figure 4.13c
a much larger flux is evident of active RF-CH and WL-CH flow as opposed to the
contributing portion at the outlet. This figure highlights the transient difference
between the active and contributing processes in this catchment.
The long term ratio of contributing to active flow generation processes for WL-
CH (0.78), RF-CH (0.34) and GW-CH (0.25) highlights the significant differences
between active flow generation processes across the catchment and contributing
flow generation processes driving outflow. Furthermore, the cumulative lines
show how this dichotomy develops through time. This supports the need to
differentiate between these active and contributing processes in interpreting
streamflow hydrographs, and therefore, the need to separate the streamflow
hydrograph properly.
111 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
Figure 4.13: Comparison of active and contributing processes with respect to
a) GW-CH, b) RF-CH, and c) WL-CH (where WL-CH = RF-WL + GW-
WL). Note that the contributing component is superimposed on top of the
active component in each of these graphs, i.e. they are not stacked. The long-
term ratio of contributing to active processes is also noted in each of the
plots, which highlights the average difference between the two. The dashed
and dotted lines on each plot represent respectively the cumulative active and
contributing components.
4.5.3. Comparison of wetland and catchment models
At the outlet of both models, GW-CH streamflow generation was fairly consistent
across storms with only minor changes relative to the total streamflow
hydrograph. The GW-CH component was seen to respond immediately to rainfall
with no obvious lags in both models. Large changes in streamflow at the outlets
for both models can be attributed to the overtopping of rills within the riparian
wetlands driven by both RF-WL and GW-WL mechanisms. However, in the
catchment model, the RF-CH component contributes significantly to total
streamflow during the large storm event, which is attributable to the coarse model
discretisation of the stream network. This discretisation does not capture the
narrow nature of the actual channels, so that the channels in the model are wider
than they are in reality. The surface area of the stream in the model captures
additional rainfall that would not usually be attributed to the RF-CH flow
112 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
generation mechanism within the catchment. Overland flow from the wetlands in
both models is dominated by RF-WL flow generation. The GW-WL component is
almost as large as the RF-WL component in the wetland model; however, the
GW-WL component is almost negligible at the outlet of the catchment model. The
difference in the GW-WL component between the two models can be attributed to
the discretisation of the wetlands. In the catchment model, the threshold behaviour
to overland flow is captured, which is evident in the wetland model, but the
catchment scale model does not capture the enhanced surface-subsurface mixing
of the wetlands model, which results in a lot of the RF-WL water infiltrating and
then discharging as GW-WL.
4.5.4. Limitations of wetland and catchment models
A number of assumptions were made within this modelling that limited the
representation of reality, as well as any generalisations that can come from it. The
main limitation of the wetland model is that it does not replicate a particular
Lehstenbach wetland, hence there are no observed data to compare with, meaning
the model can only be used for virtual experimentation.
For the catchment scale model, only outflow time series were available for
calibration. As this was the only data used in evaluation of the model, there are
likely to be multiple parameter sets that could yield the same Nash Sutcliffe
efficiency, i.e. equifinality. Alternative parameter sets with equivalent model fits
could potentially lead to significant differences in the spatiotemporal distribution
of flow generation processes and hence influence the dynamics of contributing
processes at the catchment outlet. The resulting non-uniqueness of processes
elicited with the HMC method might not be representative of the actual processes
occurring in the Lehstenbach catchment. This limitation could be addressed (at
least in part) by using additional hydrometric data in model calibrations to further
constrain the problem.
HMC analysis shows that the response of the wetlands in the catchment scale
model seems to be consistent with the understanding of wetland runoff processes
and the catchment behaviour in general; however, the effect of the mesh
discretisation of the stream and wetlands in the catchment model mesh on the
GW-CH response and WL-CH response still requires quantification. Refining the
113 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
coarse mesh would allow for better representation of the enhanced surface-
subsurface mixing, as exhibited in the wetlands scale model, which is important in
consideration of biogeochemical processes (Frei et al., 2012).
The subsurface response is affected by the subsurface boundary conditions, and
no-flow boundaries in the subsurface prevent groundwater from flowing out
through the subsurface, which leads to increased groundwater exfiltration near the
outlet. Although this is generally consistent with the understanding of subsurface
flows in the catchment based on previous studies (Hauck, 1999; Lischeid et al.,
2002), a more thorough assessment of the effects of the subsurface boundary
conditions on catchment outflow would be helpful to further refine our
understanding of the system.
Model simulations would likely have been influenced by: (1) simplification of
heterogeneity within soil types, (2) exclusion of preferential subsurface flow, and
(3) spatiotemporal resolution of rainfall and evapotranspiration inputs (spatially
uniform rather than distributed, daily rather than hourly rainfall and ET). It is
expected that additional heterogeneity (e.g. within each soil layer) would lead to
more complex stream-aquifer exchange patterns, although it is not expected that
this would significantly alter the catchment response. Inclusion of shallow
macropores in the forested areas of the catchment would allow rapid infiltration to
the upper layer of the soil; however, this infiltrated water would be limited in
recharging the aquifer due to the soils’ saturated hydraulic conductivity below the
extent of the macropores. The spatiotemporal resolution of the rainfall and ET
could potentially have a large impact on the catchment response, particularly
where short intense rainfall events lead to flashy streamflow responses, which
would not be captured using the average daily rainfall. With respect to these
assumptions, it is still expected that increased complexity of inputs would lead to
at least the same or greater spatiotemporal variation in the different flow
generation mechanisms. It is not expected that increased complexity would yield
more homogeneous responses in in-stream and overland flow generation
processes, although this is clearly yet to be tested. Furthermore, the influence of
surface flow travel times, flow impediments and flow depletion processes are still
important with respect to spatiotemporal variability of contributing flow
generation processes.
114 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
4.5.5. Evaluation of HMC method implementation
The sub-timed scheme of the HMC method is an important improvement which
allowed application to more complex problems than those studied in Partington et
al. (2011, 2012) and Li et al. (2013). The sub-timed scheme was necessary in both
of the models, significantly reducing the number of flow solution time-steps that
would have been required with the previously developed HMC method (by 106 in
the catchment year long simulation). The sub-timed scheme allowed the adaptive
time-stepping scheme of the flow solution to perform as normal without tight
restrictions on the maximum time-step. Complementary to this improvement, the
stability constraints used in the improved HMC method were able to ensure
stability of the cells in the simulations. The reset fractions resulting from cells that
were reset when they met the criteria outlined in Section 4.3.3.3, highlighted areas
that were of little interest with respect to overland flow generation processes. The
reduction of active cells allowed faster computation and highlighted areas of little
activity with respect to flow generation processes, which is reflected in the spatial
distribution of the reset fraction (Figure 4.6, Figure 4.7 and Figure 4.11) and in the
actual contributing fraction of flow from reset cells.
4.6. Conclusions
In this paper, an improved Hydraulic Mixing-Cell (HMC) method was developed
that enables both active and contributing processes to be obtained from the
outputs of Integrated Surface-Subsurface Hydrological Models (ISSHM), thereby
enabling streamflow generation processes to be identified for catchments that
include significant storage, travel times and losses. Specifically, the following
improvements to the HMC method were made: (1) accounting for overland flow
generation mechanisms, (2) implementing a sub-timed scheme, and (3)
implementing HMC stability constraints.
This improved HMC approach was applied to two virtual experiments based on
the Lestenbach catchment and a wetland typical of the catchment, which enabled
(i) separation of simulated streamflow hydrographs into their constituent in-
stream and overland flow generation mechanisms, (ii) quantification of the spatial
and temporal variability for in-stream and overland flow generation mechanisms
at contrasting spatial and temporal scales, and (iii) quantification of the degree to
115 |
ADE | 4. Interpreting streamflow generation mechanisms from integrated surface-
subsurface flow models of a riparian wetland and catchment. (Paper 3)
which the active and contributing processes differ within the catchment model,
leading to an improved understanding of simulated streamflow generation
processes. The application of the HMC method in this study is a promising first
step in the refinement of the method; however, as discussed in the model
limitations, the catchment model would benefit from some improvements. Further
development of the catchment model by further calibration using additional
hydrometric data will serve to improve the veracity of the model for quantifying
spatiotemporal variability within the Lehstenbach catchment. Furthermore,
investigation into the influence of the no flow subsurface boundary conditions
used and the areal mesh discretisation would also help to make the catchment
model more representative of the Lehstenbach catchment.
Further development of the HMC method is recommended by greater subdivision
of the rainfall driven overland flow generation mechanisms into saturation-excess
and infiltration-excess. It would be extremely useful to also develop an automatic
definition of the stream based on flow depth, velocity and direction. In addition,
the HMC method should be further expanded to track flow in the subsurface,
which would allow tracking of other flow domains, for example, from macropores
and fractures. Extension to the subsurface would also allow identification of the
source areas of groundwater discharging to the surface. The inclusion of time
stamps to the HMC fractions would also improve the HMC method, and allow
analysis into event and pre-event water contributions.
The composition of streamflow with respect to the different surface runoff
generating processes entails important information on runoff processes and
mechanisms during large rainfall events and during dry periods. The methodology
presented here provides a tool to decipher and deconvolute the integrated
streamflow signal using numerical models. This improves assessment of
catchment functioning within the ‘hypothetical reality’ of the model. This is an
important aspect of the HMC method when applied to physically distributed
models that have no a priori assumption of flow generation processes. Use of the
HMC method provides a necessary assessment of whether or not a catchment
model behaves in the way desired, or more importantly, the way the catchment
processes are conceptualised. In that sense, it is useful for a ‘soft calibration’
based on understanding of catchment functioning from field observations. This
116 |
ADE | 5. Thesis Conclusions
Chapter 5
5 Thesis Conclusions
The streamflow hydrograph entails important information on flow generation
processes during large rainfall events and during dry periods. The streamflow
hydrograph is one of the most important hydrological descriptors available,
containing the pertinent information of flow maxima and the total volume of
water flowing out of a catchment over time. This information is critical for
management of flooding and water resources. The understanding of where stream
water originates from in the hydrosphere and the processes by which it reaches the
stream underpins catchment hydrology. Research to understand these processes is
being increasingly carried out utilising physics-based fully Integrated Surface-
Subsurface Hydrological Models (ISSHM). In the absence of required field data,
such models are necessary for improving our understanding of catchment
hydrological response. To understand the response, it is critical to understand the
nature in which the processes of flow generation across a catchment and at
different periods in time express themselves in the streamflow hydrograph, whilst
accounting for the processes of flow depletion. However, even though detailed
spatiotemporal outputs from ISSHMs have provided some insight into catchment
functioning, the interpretation of all of this information into an understanding of
how all of the flow generation processes across a catchment express themselves in
the streamflow hydrograph has yet to be realised. In a modelling framework, this
research has achieved this through the development and application of a new
method which identifies and quantifies streamflow generation contributions
allowing full deconvolution of the streamflow hydrograph into its constituent
components of streamflow generation.
119 |
ADE | 5. Thesis Conclusions
5.1. Research contributions
The overall contribution of this thesis was in improving the interpretation of in-
stream and overland flow generation mechanisms from ISSHMs (Objective 1),
and the applications this allowed (Objectives 2 to 4). The improvements in this
thesis were achieved through development of a new method that enables
identification and quantification of the active and contributing processes from the
outputs of ISSHMs, thereby enabling streamflow generation processes to be
analysed for catchments that include significant storage, travel times and losses.
Use of the HMC method provides a necessary assessment of whether or not a
catchment model behaves in the way desired, or more importantly, the way the
catchment processes are conceptualised. The method can be used for a ‘soft
calibration’ based on understanding of catchment functioning from real
observations. This can only serve to strengthen the relatively small arsenal of
tools currently available for analysing catchment models.
Specifically, in meeting the objectives of this research laid out in the introduction,
the following research contributions were made:
1. A Hydraulic Mixing-Cell method was developed to quantify the
contribution of flow generation mechanisms to streamflow, allowing
separation of the streamflow hydrograph into its constituent flow
generation components (i.e. groundwater discharge and direct rainfall to
the stream, and groundwater discharge and direct rainfall to overland
areas). Because the HMC method tracks the streamflow generation
mechanisms along the stream, temporal and spatial components that affect
these mechanisms can be accounted for. The HMC method correctly
handles dynamic complex flow regimes (rapid changes of gaining stream
to losing stream and vice versa), accounts for storage effects, flow
impediments and the travel times that occur within a catchment. The
method easily handles the dynamic nature of varying flow regimes in large
and complex systems (e.g. the Lehstenbach catchment). The only data
requirements for the HMC method are the fluxes at each cell and surface
water depths, which are part of the flow solution. By using this method,
contributing processes can be identified and quantified. Improved
knowledge of catchment processes as simulated by HydroGeoSphere was
120 |
ADE | 5. Thesis Conclusions
obtained through Hydraulic Mixing-Cell analysis, with meaningful
separation of the streamflow hydrograph indicating how overland and in-
stream flow generation processes drive streamflow.
2. A benchmark against which baseflow separation methods can be tested
was developed by simulating flow in a hypothetical V-catchment in HGS
and using the HMC method to provide the baseflow contribution to total
streamflow at the outlet of the catchment. This benchmark was used to
determine the potential error in commonly used automated methods for
estimation of in-stream groundwater contributions to streamflow. The
numerical experiments in this showed that even in the “simple”
hypothetical V-catchment, baseflow dynamics are complex. This
complexity in baseflow dynamics affected the performance of the
commonly used automated separation methods, which resulted in
unsatisfactory performance of each method examined in at least one of the
events and scenarios considered. The potential error was found to be
significant in automated methods for estimating groundwater contributions
to streamflow, and this warrants caution in overvaluing their outputs. It is
perhaps the case that the uncertainty associated with simple automated
methods precludes their use for providing anything more than very rough
estimates of baseflow.
3. The first investigation – using an ISSHM – was conducted into the
spatiotemporal variability in both overland and in-stream flow generation
mechanisms. This was done using two models of a wetland and catchment,
from a case study of a real catchment. The spatiotemporal variability was
analysed through snapshots in time during a large storm event, and
through hydrographs at a number of points within each of the models.
Both models exhibited significant spatial variability in flow generation
processes. In the catchment model, temporal variability of streamflow
generation at a number of locations was seen to be significant over a large
storm, but similarities increased using a longer term annual average of
flow in-stream and overland flow generation processes.
4. The first investigation – using an ISSHM – was conducted into the
dichotomy that exists between ‘active’ and ‘contributing’ streamflow
generation mechanisms within a modelling framework. Differences
121 |
ADE | 5. Thesis Conclusions
between the active and contributing processes were quantified by the long
term ratio between active and contributing processes. It was found that
accounting for in-stream and overland losses and in-stream and overland
flow travel time is necessary in accurately quantifying the constituent in-
stream and overland flow generation components of streamflow. It is
therefore recommended to employ the HMC method in ISSHM studies of
various flow generation processes.
5. The HMC method developed in this research was implemented in the HGS
code. This implementation means that all of the analyses conducted in this
research can be carried out in models built in HGS using simple
instructions in the HGS pre-processor.
5.2. Research limitations
Limitations of this research were due to current modelling limitations, scope of
research and time-constraints. The limitations that arose are detailed as follows:
1. Modelling limitations: A main limitation of this research lay within the
ability to run a large number of (tens and hundreds of simulations) or long
term models scenarios (years). This is due to the lengthy model run-times
(of the order of weeks for each simulation in each of the research papers)
that result from solving the highly non-linear partial differential equations
describing flow. A parallel version of HGS has now been developed which
should reduce the model run-times and allow a greater number of
scenarios to be explored in future research. Another limitation associated
with the run-times relates to the accuracy required in the HGS flow
solution in order to ensure stability in the HMC method and also ensure an
acceptable level of error. Despite this being highlighted as a limitation, it
should be noted that it is good modelling practice to ensure tight
convergence criteria, resulting in minimal nodal fluid mass balance errors
as opposed to global mass balance errors.
2. Limitations in investigation of automated baseflow separation methods:
The investigation of commonly used automated baseflow separation
methods was limited by the number of scenarios run and scenario time-
length in the hypothetical catchment used. The shape of the catchment
considered was rectangular, however, effects of convergent and divergent
122 |
ADE | 5. Thesis Conclusions
catchment shapes were not considered. The characterisation of physical
parameters within the catchment was relatively simple, without
consideration of multilayered soils or heterogeneous soil properties. The
hydrological forcing was applied in a spatially uniform manner and at a
coarse temporal scale (daily) in these simulations, although these effects
may be important in the catchment response of baseflow generation. This
research focused on commonly used automated methods that rely only on
the streamflow hydrograph for the baseflow separation, however there has
been an emergence of physically based filters (e.g. Furey and Gupta,
2001, 2003; Huyck et al., 2005) which were not considered.
3. Limitations of streamflow generation analysis: The HMC method
developed in this research was used to delineate the direct groundwater
discharge and rainfall to streams and overland areas. A common
consideration of overland flow generation mechanisms not considered in
this research was the rainfall runoff mechanisms of infiltration excess
(Hortonian) and saturation excess (Dunne). These processes were not
considered in the case study of this research, although in most other
catchments, these mechanisms will be of interest. The use of ISSHMs in
building intuition of catchment functioning is highly valuable, although it
is also dependent on the assumptions in the model (even if these are
deemed reasonable). In consideration of streamflow generation
mechanisms, real observation will always be the most important driver for
advancing the science. However, as highlighted throughout this thesis, the
conceptual understanding of streamflow generation processes can be built
from ISSHMs.
5.3. Recommendations for future work
This research has opened up a new way of analysing and interpreting flow
processes using ISSHMs. There are still further applications of the HMC method
that would benefit research utilising ISSHMs and address the limitations
identified above. It is recommended that the HMC method be expanded to
improve analysis and interpretation of subsurface flow processes including flow
through: saturated and unsaturated dual continuum media, fractures, and macro-
pores. Further development of the HMC method is recommended by greater
subdivision of the rainfall driven overland flow generation mechanisms into
123 |
ADE | 5. Thesis Conclusions
saturation-excess and infiltration-excess. Extension to the subsurface would also
allow identification of the source areas of groundwater discharging to the surface.
Furthermore, the inclusion of time stamps to the HMC fractions would serve to
improve the HMC method, and allow analysis into event and pre-event water
contributions. Application of the HMC method encompassing all of the above
recommendations would provide a highly comprehensive analysis of catchment
functioning and provide complete analysis of the different aspects of streamflow
generation as shown in Figure 5.1 (adapted from Sklash and Farvolden, 1979).
This research considered the flow generation delivery mechanisms without
distinction of the overland flow generation mechanisms, i.e. infiltration excess
and saturation excess overland flow.
STORM RUNOFF
EVENT
TIME ASPECTS FLOW GENERATION SOURCE
MECHANISM ASPECTS ASPECTS
Infiltration excess overland flow Groundwater
Water added by
specific event
(event water) Saturation excess overland flow Vadose Water
Channel interception Direct Rainfall
Water in basin prior
to specified event
Groundwater discharge to stream Direct Runoff
(pre-event water)
Groundwater discharge to hillslope Combination
Combination
Figure 5.1: Comprehensive conceptualisation of catchment response to
rainfall (adapted from Sklash and Farvolden, 1979). The dashed red line
indicates the aspects considered in this research, although without distinction
of overland rainfall driven mechanisms (i.e. infiltration excess (Hortonian) or
saturation excess (Dunne)).
The HMC method presented in this thesis can be applied within any ISSHM, and
as part of this research has been coded into the HGS code to allow other HGS
users the ability to easily utilise it. For example, this HGS implementation has
already been used outside of this research in Sebben (2011) and Li et al. (2012)
and is currently being used in a number of other research projects. It is
recommended that the HMC method be employed in future versions of other
124 |
ADE | 5. Thesis Conclusions
ISSHM codes. This is relatively simple as the coding of the HMC method requires
only that all components of the nodal fluid mass balance (inflows, outflows, and
changes in storage) and nodal neighbour relations be output or passable within the
code. The HMC method could be very beneficial in future model inter-
comparison studies to compare the constituent components of the streamflow
hydrograph and spatiotemporal flow generation.
With respect to the application of the HMC method in investigating potential
errors in commonly used automated baseflow separation methods, further work is
required to understand the appropriate use of baseflow separation methods. More
complex baseflow separation methods than those considered in this study should
be tested in future studies. Physically based filters (e.g. Furey and Gupta, 2001,
2003; Huyck et al., 2005) could prove to be more robust. This is because they
provide a physically based relation of rainfall and ET (and other physical
parameters) to baseflow.
In all of the simulations carried out in this research, the characterisation of
hydrological forcing and distribution of catchment characteristics could be
improved. Future studies should aim to elucidate the spatial and temporal scale
dependence of flow generation mechanisms. In the studies using hypothetical
catchments for numerical experimentation, the impact of variations in geology,
topography and vegetation, should be investigated by incrementally adding layers
of complexity to similar models in order to try and understand flow generation
dynamics.
125 |
ADE | Abstract
Water is a vital resource to society and complex interactions between nature and
human infrastructure are constantly required. Water transmission and distribution
pipelines are critical for modern cities; however, their sheer size and the fact that most
of them are buried underground, makes the health monitoring of pipelines challenging.
In addition, some water transmission pipelines cover long distances through remote
areas that are not easily inspected regularly. Fluid transients have been used over the
last 25 years as part of techniques to assess and monitor the condition of pipelines by
interpreting the pressure response to the presence of anomalies (e.g. leaks, blockages)
and the occurrence of abnormal events (e.g. bursts). Nonetheless, existing techniques
require detailed information with regard to the properties of the pipe system (model-
based techniques), and require manual interpretation of the measured pressure signal
or involve optimization methods that result in large amount of computer processing
time to obtain results. Consequently, the research in this thesis presents new
noninvasive techniques for the active and passive inspection of the condition of a
pipeline combining custom-designed machine learning algorithms based on Artificial
Neural Networks (ANNs) and fluid transients.
An active inspection technique has been developed that is based on the interpretation
of high-frequency pressure measurements using ANNs after the generation of a small
and controlled transient event in a pipeline. The initial transient pressure wave
produced by the rapid closure of a side discharge valve propagates through the pipeline
and interacts with any anomalies that are present in the pipeline. The measured
transient pressure trace is then processed using an ANN trained with transient pressure
traces obtained from a physical model of the pipeline to locate and characterize the
anomalies. The other method that has been developed is a passive inspection technique
that is also based on high-frequency pressure measurements; however, in this case,
there is no artificial generation of a transient event. This methodology provides for the
iii |
ADE | Abstract
continuous transient pressure monitoring of the pipeline by analyzing changes in
pressure due to the occurrence of abnormal events such as bursts. This method uses
ANNs at different stages of the process to determine if the pressure condition of the
pipeline is normal or whether a potential abnormal event, such as a pipe burst, might
have occurred.
The major research contributions of this thesis are presented in three journal
publications. These publications describe i) a novel framework for the use of ANNs
for the active inspection of pipelines based on measured transient pressure traces
applied to the detection of junctions and leaks in a numerically modeled pipeline, ii) a
complete methodology for the active inspection of pipelines for the detection of leaks
in a laboratory pipeline using an array of ANNs trained with datasets using different
noise intensities to obtain robust, accurate and fast predictions when background
pressure fluctuations are present in the pipeline, and iii) a complete methodology
passive inspection of pipelines for the detection, location and characterization of bursts
in numerical and laboratory pipelines.
The overall contribution of this research is the development of new non-invasive
techniques for the active and passive condition assessment of pressurized pipelines
using machine learning algorithms. These techniques have the advantage of being
data-driven, meaning once the ANNs have been trained using a physical model of the
pipeline, no model of the analyzed pipeline is required when new measured pressure
traces are interpreted by the ANNs. In addition, results can be obtained fast (near real
time) and are accurate in locating and characterizing leaks and bursts in pipelines.
iv |
ADE | Statement of Originality
I, Jessica Maria Bohorquez Arevalo, certify that this work contains no material which
has been accepted for the award of any other degree or diploma in my name, in any
university or other tertiary institution and, to the best of my knowledge and belief,
contains no material previously published or written by another person, except where
due reference has been made in the text. In addition, I certify that no part of this work
will, in the future, be used in a submission in my name, for any other degree or diploma
in any university or other tertiary institution without the prior approval of the
University of Adelaide and where applicable, any partner institution responsible for
the joint-award of this degree.
I acknowledge that copyright of published works contained within this thesis resides
with the copyright holder(s) of those works.
I also give permission for the digital version of my thesis to be made available on the
web, via the University’s digital research repository, the Library Search and also
through web search engines, unless permission has been granted by the University to
restrict access for a period of time.
22/01/2021
Signed: ……… ……. Date: ……………………….
v |
ADE | Chapter 1
1 Introduction
Water is a vital resource for the survival and productivity of a society. The complete
urban cycle of water requires complex infrastructure including dams, water treatment
plants, pumps, storage facilities and pipelines. In this water cycle, water transmission
and distribution pipelines are critical because these elements are responsible for
transporting treated water to users. The fact that these complex systems are often
underground or located in remote areas makes their monitoring and maintenance very
challenging.
The ageing of pipelines and its lack of maintenance have recently contributed to water
supply crises in important cities in the world due to high percentages of water losses
(Mukherjee et al. 2018; Ahmadi et al. 2020). For instance, a median of 19.9 breaks/100
km per year occurs in major water utilities in Australia (Bureau of Meteorology 2020).
Modern, versatile, cost-effective and accurate inspection techniques for water
pipelines are urgently needed. Existing noninvasive techniques, although successful,
have a short inspection range, are time consuming or only provide information at the
time of the test.
This thesis proposes a new set of techniques for the active and passive noninvasive
inspection of pressurized1 water pipelines using custom-designed Artificial Neural
Networks (ANNs) for the interpretation of transient pressure traces. The active
inspection technique identifies the existence, location and characteristics of anomalies
in pipelines (such as leaks) after the generation of an artificial transient event. The
1 This thesis has been written in American English to preserve the language used in the main chapters.
The journal papers presented were published or submitted to the Journal of Water Resources Planning
and Management of the American Society of Civil Engineers (ASCE).
1 |
ADE | Chapter 1 - Introduction
passive inspection technique detects and identifies the occurrence of abnormal events
(such as bursts) in pipelines by interpreting the transient pressure wave that these
events cause along the pipeline. Unlike previous studies, the proposed techniques are
data-driven because no detailed information is needed with regard to the analyzed
pipeline when the techniques are applied. These techniques can provide accurate, fast
and reliable predictions. This thesis has opened up the possibility of using deep
learning merged with high-frequency pressure measurements for a fast and reliable
condition assessment of pipelines.
1.1 Research Background
The inspection of water pipelines is challenging. Most of these elements are
underground and condition problems can often be ignored until a highly disruptive
burst occurs. Water utilities spend significant resources on reactive maintenance each
year, but in general, the condition of urban water assets is unknown (Infrastructure
Australia 2019). For instance, it has been predicted that about half of these assets will
need to be replaced in the coming three decades in Australia and the situation is no
different in other countries as pipelines are reaching the end of their life cycle (Water
Corporation 2014). To respond to this challenge, water utilities have allocated
important resources to switch to preventive maintenance of the pipelines. However,
pinpointing the location of deteriorated pipelines to replace is also challenging
considering the sheer size of these systems.
Different techniques have been developed to estimate and monitor the condition of
pipelines as part of water losses management strategies (Mutikanga et al. 2013).
Methods including visual or CCTV inspection have been used to inspect the internal
surface of the pipeline mostly in sewerage pipelines (Guo et al. 2009) with no wide
applications in pressurized pipelines. In addition, these methods are time consuming
both in the collection of data and its interpretation.
Ground-penetrating radar methods detect underground voids created by leaking water
around the pipe or detect the saturation of the soil due to a leak. These methods
produce a cross-section profile of the subsurface, identifying different features
underground (Hunaidi and Giamou 1998; Amran et al. 2017). Although these methods
have shown potential, other anomalies present in the subsurface could alter the
predictions of the pipe-related anomalies (Puust et al. 2010). Other electromagnetic
2 |
ADE | Chapter 1 - Introduction
methods include magnetic flux leakage, remote field eddy current, broadband
electromagnetic techniques and ultra-wideband pulse radar systems. However, some
of these methods require complex calibration, accessibility to the external surface of
the pipeline or are limited to a certain type of pipelines (Zheng and Yehuda 2013).
Acoustic methods have also been widely used and are under constant development.
These methods capture and analyze sounds emitted by material deformation, structural
motion, or external impact that are usually inaudible to humans using vibration sensors
(Juliano et al. 2013). The nature of the signals produced by a leak depends on its
magnitude, orientation and the surrounding soil. In addition, background noise can
complicate the interpretation of acoustic signals. Although important progress has
been made regarding these methods (Stephens et al. 2020), their inspection range is
limited and the detection process requires a deep understanding of the acoustic signals
obtained (Puust et al. 2010).
Other pipeline condition assessment methods include ultrasound, radiographic and
thermographic methods (Zheng and Yehuda 2013). Ultrasound methods use guided
waves propagated through the pipeline wall to detect defects on its surface. These
methods have been applied to buried pipes, but the range of inspection is short due to
the rapid attenuation of the signals (Luo and Rose 2003). Radiographic methods use
gamma or X-rays to analyze the pipeline material by emitting these signals from inside
or outside the pipeline but its functioning depending on the ability to isolate and
emptying the pipeline of interest. Similarly, thermographic methods use an external
heat source to analyze the heat emission of different parts of the pipeline. The
efficiency in the transferring of infrared energy is used to assess the condition of the
pipeline wall. Although this method can provide detailed assessment of the condition
of the pipeline, it requires access to the external wall.
Considering the importance of assessing the conditions of pipelines without having
physical access to it and without disrupting water supply, a group of techniques known
as transient based methods have been developed. These methods consider the use of
fluid transients waves for anomaly detection which usually involves the generation of
a transient event that travels through the pipeline allowing its inspection similarly to
the functioning of radar and sonar techniques (Puust et al. 2010). The idea of using
fluid transient pressure waves to detect anomalies in pipelines was first proposed by
3 |
ADE | Chapter 1 - Introduction
Liggett and Chen (1994). These authors proposed the calibration of pipeline
parameters including potential locations for leaks to adjust the results of an unsteady
flow numerical model to transient pressure measurements.
Since then, transient based methods have received special attention given that fluid
transient pressure waves allow the inspection of large sections of a pipe with relatively
simple tests (Gong et al. 2013c). These techniques have proven successful in the
detection, location and characterization of anomalies in pipelines (i.e. leaks, pipe wall
deteriorations, blockages) given the significant quantity of information that can be
retrieved from transient pressure data. Similarly, these methods have been used for the
detection of abnormal events such as bursts. Transient based methods can be organized
into four groups: a) time reflectometry techniques, b) inverse transient methods, c)
transient damping methods, and d) pipeline frequency response techniques.
Time reflectometry techniques identify the arrival time of the anomaly-induced
reflections in the generated transient wave. Using this time and a known or estimated
value for the wave speed, the anomaly location can be determined (Vítkovský et al.
2003a; Ferrante et al. 2007; Gong et al. 2013c; Gong et al. 2016b). Inverse transient
methods apply an optimization approach to find the characteristics of a leak that
minimize the difference between the measured transient pressure and a transient
pressure signal obtained from a numerical model (Liggett and Chen 1994; Covas et al.
2001; Capponi et al. 2017; Zhang et al. 2018; Zhang et al. 2019).
Transient damping methods analyze the effect that an anomaly induces in the
dissipation mechanisms of a transient wave (Wang et al. 2005; Nixon et al. 2006;
Brunone et al. 2018; Asada et al. 2020). In the case of leak detection, for instance, the
analysis of this damping rate allows the determination of the leak size and the ratio of
damping rates for different harmonic components enable the prediction of the leak
location (Wang et al. 2002). Finally, pipeline frequency response techniques identify
the effect that the presence of an anomaly has in the resonant amplitude peaks of the
frequency response function of a system after an oscillatory excitation of the system
at specific frequencies (Mpesha et al. 2001; Lee et al. 2003; Lee et al. 2005; Sattar and
Chaudhry 2008; Gong et al. 2013a; Gong et al. 2013b; Gong et al. 2014b; Duan and
Lee 2015; Duan 2017; Rubio Scola et al. 2017).
4 |
ADE | Chapter 1 - Introduction
While each of these methods has had successful applications, they also have associated
disadvantages. Transient based techniques are highly sensitive to multiple system
characteristics and understanding what the pressure signal response should look like
when a specific fault is present in realistic cases is often challenging (Xu and Karney
2017). In addition, existing techniques are in most of the cases model-driven since
they require extensive and accurate numerical modeling, an estimation of certain pipe
parameters based on an intact condition or the processing time to get an estimation of
the anomaly characteristics can be long. There is a need for data-driven techniques
that can quickly interpret transient pressure data obtained from a test and locate
anomalies accurately.
Artificial Neural Networks (ANNs) have been widely used in a variety of fields and
they have become a powerful tool in machine learning. Their use has proven effective
and robust, provided that enough information for their training is available (Caputo
and Pelagagge 2003). Multiple applications have focused on the use of large datasets
to find system patterns and behaviors revealing important characteristics of the
analyzed system; however, ANNs can also be used in combination with well-
established techniques to provide for informed and robust decisions. In fact, ANN
architectural design choices should ideally be performed with a semantic insight about
the data domain at hand (Aggarwal 2018).
In water-related research, ANNs have been successfully applied to a variety of
problems including water availability under climate change scenarios (Swain et al.
2017), asset failure prediction (Harvey et al. 2014), water demand prediction (Guo et
al. 2018), cyber-physical attacks location (Taormina and Galelli 2018), among many
others. Belsito et al. (1998) used ANNs to predict the location of leaks in liquefied gas
pipelines. Steady-state pressure signals were used in their research as input
information for the ANN but transient waves were not considered. In general, the use
of ANNs for the inspection of pressurized water pipelines using fluid transient waves
has not been previously explored.
1.2 Research Questions
Considering the existing background on active and passive pipeline inspection
techniques, this thesis aims to answer the following research questions:
5 |
ADE | Chapter 1 - Introduction
How can Artificial Neural Networks (ANNs) be used to interpret pressure
head traces without specific information of the topology of a water
system?
How can Artificial Neural Networks (ANNs) be used to accurately
localize and characterize anomalies in pressurized pipelines?
How can Artificial Neural Networks (ANNs) be used to accurately detect,
localize and characterize abnormal events occurring in pressurized
pipelines?
1.3 Research Aims
The overall aim of this research is to develop and apply data-driven methodologies for
the inspection of water pipelines using fluid transients and Artificial Neural Networks
(ANNs). Considering the broad spectrum of applications that machine learning
algorithms have had in the recent past, it is hoped that ANNs can be used as a tool to
inspect water pipelines to obtain accurate and fast results by interpreting fluid transient
waves. To achieve the overall aim of this thesis, four main aims with a number of
specific sub-aims have been proposed and are shown in Figure 1-1.
Figure 1-1. Framework of research aims.
6 |
ADE | Chapter 1 - Introduction
Aim 1: To develop a framework to merge the use of fluid transient waves and
Artificial Neural Networks for the condition assessment of water pipelines by training
ANNs with numerical transient pressure traces to detect anomalies, topological
elements or the occurrence of abnormal events.
Aim 2: To develop a data-driven technology to use fluid transient waves and Artificial
Neural Networks for the active inspection of water pipelines.
Aim 2.1: To develop a methodology to use fluid transient waves and Artificial
Neural Networks for the active detection of anomalies and the identification of
topological elements.
Aim 2.2: To design a framework to adapt the active inspection of water
pipelines to more realistic conditions for the detection and location of leaks as
an example of an anomaly.
Aim 3: To develop a data-driven technology to use fluid transient waves and Artificial
Neural Networks for the passive inspection of water pipelines.
Aim 3.1: To design a methodology for the real-time interpretation of pressure
transient signals with Artificial Neural Networks for the passive detection of
abnormal events in water pipelines.
Aim 3.2: To develop a methodology to use fluid transient waves and
Artificial Neural Networks for the passive identification, location and
characterization of the occurrence of bursts in water pipelines.
Aim 4: To validate the developed methodologies for the active and passive inspection
of water pipelines with numerical and laboratory experiments.
Figure 1-1 presents the relation between the four objectives of this research. First, the
combined use of fluid transient waves and Artificial Neural Networks (ANNs) for the
condition assessment of pressurized pipelines is explored with the creation of a
framework for the training of ANNs using numerical transient traces (Aim 1). This
framework constitutes the fundamental basis for the techniques developed in this
research.
Two core approaches for the inspection of water pipelines are considered in this
research. The development of an active inspection technique for water pipelines
7 |
ADE | Chapter 1 - Introduction
addresses the analysis of a fluid transient pressure wave after the generation of an
artificial, small and controlled transient event in the pipeline using previously trained
ANNs (Aim 2). The existence of specific anomalies or topological elements induces
extra reflections in the transient wave which are to be identified and interpreted by the
ANNs to predict a location and size for the specific feature. A complete methodology
for the application of this active inspection technique for the detection of a leak, as an
example of an anomaly and the identification of junctions as an example of topological
elements in single pipelines is developed (Aim 2.1). In addition, to ensure that the
active inspection methodology has the potential to be applied under more realistic
conditions such as the location of subtle anomalies in pipelines with presence of
background pressure fluctuations, the robustness of this methodology is to be
enhanced with the proposal of a novel application framework (Aim 2.2).
A second approach considers the development of a technique for the passive
inspection of water pipelines without the generation of an artificial transient event to
detect the occurrence of abnormal events (Aim 3). To detect the occurrence of
abnormal sudden changes in the pipeline pressure, a monitoring methodology for a
continuously measured pressure signal is developed (Aim 3.1). This methodology is
then coupled with a methodology for the location and characterization of bursts (Aim
3.2). Finally, the last aim in this research (Aim 4) considers the validation of both the
active and passive techniques with numerical and experimental experiments.
1.4 Thesis Outline
This thesis is organized into eight chapters with the main body corresponding to a
collection of three journal papers (in Chapter 5, 6 and 7) that summarizes the
undertaken research. Chapter 2 provides a critical review of literature on anomaly
detection and topological identification using fluid transient waves summarizing past
contributions and highlighting limitations of existing techniques. Chapter 3 presents
an overview of Artificial Neural Networks (ANNs) to provide context to this research
including a succinct review of the literature regarding the use of ANN for pattern
recognition, the training of ANNs with numerical data and the use of ANNs in water
research. Chapter 4 provides a synopsis of the publications that form the main body of
this thesis and illustrates the contribution of each publication to this research by
describing how each publication is connected to the aims described in Section 1.3.
8 |
ADE | Chapter 1 - Introduction
The main body of this thesis is included in Chapters 5 to 7. Each of these chapters is
developed from one of three journal publications produced in this research. A
foreword section is included in each of these chapters providing relevant additional
information that has not been included in the publication. The manuscripts of these
publications have been reformatted and sections have been renumbered for inclusion
in this thesis; however, its content is included as in the published or submitted journal
paper.
Chapter 5 and 6 are associated with the active inspection of water pipelines. Chapter
5 provides a new framework for the interpretation of transient pressure traces using
ANNs and a methodology for the active inspection of water pipelines for the location
and characterization of leaks and junctions. This chapter includes the definition of an
appropriate ANN architecture for the interpretation of the transient pressure traces and
a methodology for the generation of the numerical samples required for the ANN
training and testing. The methodology proposed in this chapter has proven successful
for the location of leaks and junctions in numerically modeled pipelines. Chapter 6
studies the importance of stochastic resonance for the extension of the methodology
for the active inspection of water pipelines under more realistic conditions where
background pressure fluctuations are present in the pipeline. The introduction of
artificial noise with different intensities during the training of the ANNs has shown to
be effective in enhancing the performance of the ANNs for the detection of a leak in
a pipeline in a laboratory setting.
Chapter 7 focuses on the passive inspection of water pipelines and presents a new
methodology for the detection, location and characterization of bursts in a pipeline
using continuous transient pressure measurements and ANNs. The methodology
presented in this chapter has been applied in a numerically modeled pipeline and
validated in a laboratory setting demonstrating its accuracy and potential to be applied
in more complex systems.
The final chapter, Chapter 8, summarizes the main contributions of this thesis and
presents recommendations for future work in the use of fluid transient waves and
Artificial Neural Networks for the active and passive inspection of water pipelines.
9 |
ADE | Chapter 2
2 Anomaly detection and topological
identification in water pipelines using
fluid transient waves
The inspection of pressurized pipelines to find anomalies is a challenging task because
most of these pipelines are underground or in remote areas. In addition, considering
the age of these systems, which can exceed 100 years in some cases, its exact topology
might be unknown due to different repairs that may not have been recorded properly.
Amongst the existing techniques to inspect pipelines (Hunaidi and Giamou 1998;
Juliano et al. 2013; Li et al. 2014), the use of fluid transient pressure waves has been
explored for almost three decades with successful results because it is a non-invasive
technique that allows the inspection of long segments of pipelines in one test.
Transient based methods extract information about potential pipeline faults by
analyzing the measured transient pressure trace considering that its internal and
external characteristics alter the flow and pressure in the system (Xu and Karney
2017). These methods have been applied for the detection of different types of
anomalies and topological elements in pipelines and can be grouped in four main
categories: a) time reflectometry methods (Lee et al. 2007a), b) inverse transient
analysis (Liggett and Chen 1994), c) transient damping methods (Wang et al. 2002),
and d) pipeline frequency response methods (Mpesha et al. 2001). Table 2-1 presents
a summary of the advantages, disadvantages and applications of these techniques to
pipeline conditions assessment.
11 |
ADE | Chapter 2 – Anomaly detection and topological identification
Table 2-1. Summary of techniques for anomaly detection and topological identification.
Applications
Technique Advantages Disadvantages Leak Topological Burst
Detection Identification Detection
- Requires manual interpretation
Visual - No processing of the signal - Sensitive to other elements in
X X X
Inspection required the pipeline (e.g. junctions,
valves, other anomalies)
- Determines pressure signal
Time - Require manual interpretation
Wavelet discontinuities
Reflectometry - Effectiveness depends on X X X
Analysis - Not sensitive to noise in the
mother wavelet selected
pipeline
Impulse
- Independent of the shape of - Requires a numerical model of
Response X - -
the transient the intact pipeline
Function
- No processing of the signal - Numerical model is required to
required extract damping parameters
Fluid Transient Damping X - -
- Does not require modeling of - Sensitive to other elements in
the boundary conditions the pipeline
- Rapid convergence on simple
systems - Requires exact numerical
Inverse Transient Analysis - Flexible application with modelling X X X
different optimization - Computationally expensive
algorithms
- Only one measurement point
Pipeline Frequency - Success depends on input signal
required X X X
Response - Time consuming test procedure
- Not computationally expensive
12 |
ADE | Chapter 2 – Anomaly detection and topological identification
This chapter presents an overview of the development of these techniques focused on
three applications: leak detection, topological identification and burst detection.
2.1 Leak Detection
The detection of leaks using fluid transient based methods has been widely explored.
After the generation of a transient event, the presence of a leak in a pipeline disrupts
the propagation of this input transient wave. If a positive transient wave is injected
into a reservoir-pipeline-valve system through a rapid valve closure, the measured
transient pressure trace will show two effects: 1) a drop in the pressure from the
reflection of the wave at the location of the leak in the first 2𝐿/𝑎 seconds (where 𝐿 is
the pipe length and 𝑎 is the wave speed of the transient wave) after the valve closure,
and 2) an increase in the damping of the transient wave. These two effects are
presented in Figure 2-1. The magnitude of the reflected transient wave presented in
Figure 2-1(a) depends on the leak flow and the relationship between the incident
transient wave and the steady-state pressure in the pipeline (Jönsson and Larson 1992).
Therefore, this reflection might be subtle depending on the leak size and it could be
confused with other elements of the system making the identification of the leak more
difficult (Colombo et al. 2009).
(a) (b)
Figure 2-1. Effect of the presence of a leak in a single pipeline on a transient
pressure head trace. a) pressure drop after initial transient wave, b) damping of
transient pressure head trace.
Time reflectometry methods have been proposed based on the premise of identifying
the arrival time of the leak-induced reflections to determine the leak location given
that the wave speed is known or can be determined. These methods have been used to
locate leaks by directly analyzing the transient pressure signal obtained after a test
13 |
ADE | Chapter 2 – Anomaly detection and topological identification
(Lee et al. 2007a), by processing this signal to obtain a wavelet transform (Ferrante
and Brunone 2003) or by obtaining the impulse response function of the system
(Vítkovský et al. 2003a).
The direct interpretation of transient pressure signals has been used to detect leaks in
single pipelines by using equations to compute the leak location based on the arrival
time of the leak reflected wave to the pressure measurement point. The estimation of
the arrival time of the reflected wave can be determined by visual inspection of the
signal (Brunone et al. 2008; Lazhar et al. 2013) or by using change detection
algorithms that compare the measured transient signal with a numerical signal from
an intact pipeline (Lee et al. 2007a). Once the arrival time is known, various equations
have been proposed to calculate the leak location based on the system configuration
in terms of the transient generation point and the pressure measurement location (Lee
et al. 2007a).
Time reflectometry methods using the measured transient signal directly have been
applied in numerical applications (Lazhar et al. 2013), under laboratory conditions
(Lee et al. 2007a; Guo et al. 2012) and in real pipelines (Brunone 1999; Brunone et al.
2008) with successful results. Similarly, transformations to the transient pressure
signal have been proposed such as the use of wavelet transforms or impulse response
functions. Wavelet transforms have been used to enhance the interpretation of the
transient pressure signals by exposing discontinuities that improve the determination
of the arrival time of the reflected wave from the leak (Ferrante et al. 2007; Meniconi
et al. 2011a). On the other hand, the analysis of the impulse response function (IRF)
of a system has been proposed considering that the presence of a leak created
additional spikes in the IRF that can be used to determine its location disregarding the
transient generation method (Liou 1998; Vítkovský et al. 2003a; Nguyen et al. 2018;
Zeng et al. 2020).
Although past applications of time reflectometry methods have been accurate and
successful in the detection and location of leaks, these methods require numerical
modeling of the analyzed systems or visual inspection of the measured transient
signals or the obtained transforms to determine the reflected wave arrival time. These
limitations make the application of transient based methods in real systems more
difficult as it requires additional analysis delaying the location of the leak and
14 |
ADE | Chapter 2 – Anomaly detection and topological identification
reflections from the leaks can be overshadowed by other elements in the systems such
as joints or entrapped air.
Another group of transient based methods for the detection of leaks is known as
Inverse Transient Analysis (ITA). First proposed by Liggett and Chen (1994), this
method proposes an optimization problem to find the characteristics of a leak (i.e.
location and size) that minimize the difference between the measured transient signal
and a numerical transient signal generated for those leak characteristics. Depending
on the knowledge of certain parameters of the system, an ITA can be extended to a
simultaneous process of calibration and leak detection (Kapelan et al. 2003; Covas and
Ramos 2010; Soares et al. 2011). This method has been widely explored in different
system configurations (Soares et al. 2011; Kim 2014), pipeline materials (Vítkovský
et al. 2007; Covas and Ramos 2010) and system background conditions (Keramat et
al. 2019).
ITA methods have proved successful to detect leaks in systems that are well known
and to calibrate systems with simple configurations. However, depending on the
unknown parameters of the system and its topology, the number of decision variables
and therefore the size of the solution space can become too large and the application
of this method becomes impractical. In addition, for an ITA method, each time a
transient test is conducted, a different optimization problem needs to be solved to
determine the location and characteristics of a pipeline thus making this method
computationally expensive and not practical for a real-time application.
Other leak detection transient methods include damping methods and frequency
response methods. The analysis of the additional damping effect induced by a leak (as
it is shown in Figure 2-1(b) is the core of transient damping methods (Nixon et al.
2006; Brunone et al. 2018). The analysis of the damping rate allows the determination
of the leak size and the ratio of damping rates for different harmonic components
enable the prediction of the leak location (Wang et al. 2002). However, previous
applications of these methods require the development of numerical models to extract
damping parameters for an intact pipeline to compare with extracted damping rates
from the analyzed system.
On the other hand, frequency response methods have been proposed to detect leaks by
identifying additional resonant pressure amplitude peaks in the frequency response
15 |
ADE | Chapter 2 – Anomaly detection and topological identification
function of a system obtained after an oscillatory excitation of the system at specific
frequencies (Mpesha et al. 2001; Gong et al. 2013a; Gong et al. 2016a). Although
these methods are successful in detecting leaks, its success depends on the
characteristics of the input signal generated in the system (Lee et al. 2006) and they
often need the frequency response function of the intact system (obtained numerically
or by previous experiments) to locate existing leaks (Duan 2017).
2.2 Topological Identification
Any internal or external characteristic of a pipeline affects the transient response by
altering the flow and pressure in the system (Xu and Karney 2017; Bohorquez et al.
2020b). Thus, existing elements of the topology of a pipeline system can potentially
be identified by interpreting a transient pressure signal obtained after the generation
of a transient wave in the pipeline. The use of fluid transient pressure waves for the
identification of topological elements such as junctions (expansions or contractions)
and branches has been addressed in past; however, it is a less common application in
comparison to active fault detection. A potential reason for this is that the presence of
a topological element usually causes larger perturbations to the initial transient wave
in comparison to the effect of the presence of a leak, a wall deterioration or a blockage
(Bohorquez et al. 2018). To illustrate this, Figure 2-2 presents the resulting transient
signal if a step wave is induced in a reservoir-pipeline-valve system with a pipeline
expansion and a pipeline contraction located at 30% of the total length of the pipeline
downstream of the reservoir. Figure 2-3 presents the resulting transient signal if a
transient wave is induced in a pipeline with a branch.
(a) (b)
Figure 2-2. Effect of the presence of a) pipeline expansion and b) pipeline
contraction on a transient pressure head trace.
16 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.