expression of Q in equation (1) gives the differential equation dS/dT = A·S, of which the solution is: S = exp(− A·t) . Replacing herein S by Q/A according to equation (1), it is obtained that: Q = A exp(− A·t) . This is called the instantaneous unit hydrograph (IUH) because the Q herein equals Q2 of the foregoing runoff equation using R = 0, and taking S as unity which makes Q1 equal to A according to equation (1). The availability of the foregoing runoff equation eliminates the necessity of calculating the total hydrograph by the summation of partial hydrographs using the IUH as is done with the more complicated convolution method. Determining the response factor A When the response factor A can be determined from the characteristics of the watershed (catchment area), the reservoir can be used as a deterministic model or analytical model, see hydrological modelling. Otherwise, the factor A can be determined from a data record of rainfall and runoff using the method explained below under non-linear reservoir. With this method the reservoir can be used as a black box model. Conversions 1 mm/day corresponds to 10 m3/day per ha of the watershed 1 L/s per ha corresponds to 8.64 mm/day or 86.4 m3/day per ha Non-linear reservoir Contrary to the linear reservoir, the non linear reservoir has a reaction factor A that is not a constant, but it is a function of S or Q (figure 2, 3). Normally A increases with Q and S because the higher the water level is the higher the discharge capacity becomes. The factor is therefore called Aq instead of A. The non-linear reservoir has no usable unit hydrograph. During periods without rainfall or recharge, i.e. when R = 0, the runoff equation reduces to Q2 = Q1 exp { − Aq (T2 − T1) }, or: or, using a unit time step (T2 − T1 = 1) and solving for Aq: Aq = − ln (Q2/Q1) Hence, the reaction or response factor Aq can be determined from runoff or discharge measurements using unit time steps during dry spells, employing a numerical method. Figure 3 shows the relation between Aq (Alpha) and Q for a small valley (Rogbom) in Sierra Leone. Figure 4 shows observed and simulated or reconstructed discharge hydrograph of the watercourse at the downstream end of the same valley. Recharge The recharge, also called effective rainfall