Direct measurements of three-dimensional ocean currents are carried out with acoustic Doppler current profilers (ADCPs). The ADCPs are usually moored and bottom mounted instead of being ship-based or attached to a floating mooring to minimize the vertical displacement associated with the vertical motions of the ocean surface caused by waves.

The ADCP does not measure horizontal or vertical velocities at a point but determines Doppler shifts along three to five acoustic beams that are typically slanted (most commonly 60°) from the horizontal plane and spaced around the horizontal compass. The most typical configuration (Janus) includes four orthogonal beans. The Doppler shifts measure slant velocities of suspended acoustic backscattering particles moving with the water relative to the instrument. Pairs of slant velocities are combined to produce vertical and horizontal velocities. The underlying assumption is that velocities are horizontally uniform over the beam separation. Other instruments (e.g., Teledyne Sentinel V ADCP) have an integrated fifth beam to provide a third vertical velocity measurement.

Indirect estimates of vertical velocities can be obtain in several ways. The most common approach is to take advantage of the principle of conservation of mass (continuity equation, as described in the answer by Neo).
$$
\dfrac{\partial w}{\partial z} = -\dfrac{\partial u}{\partial x}-\dfrac{\partial v}{\partial y}
$$
where $w$ is the vertical velocity. Assuming $w=0$ at the bottom, then measuring the horizontal velocities throughout the water column will give you an estimate of the vertical velocity. This method, while useful, tend to produce really noisy results as the vertical velocities in the ocean tend to be quite small and are masked by the noise in the horizontal measurements.

A completely different approach was recently introduced by Klein et al. (2009). It uses the surface Quasi-Geostrophic approximation to estimate low-frequency vertical velocities in scales between 20 km and 400 km from the surface down to 500 m. The needed data is some high-resolution Sea Surface Height (SSH, usually from satellites) and an approximation of the large-scale vertical stratification. Vertical velocities are estimated from the buoyancy equations at the surface and at depth in a modified version of the Omega equation (Hoskins et al., 1985).


How likely is it for coastal cities to survive next 40 years?

I also live on the coast and have been concerned about what to expect with regard to sea level rise in the near future. The following graph illustrates the observed rise in sea level over the last 30 years:

As you can see from the image, satellite data indicates a linear increase in sea level rise of 3.3 mm per year for the last 30 years. If this trend continues for the next 40 years, we will see an increase in sea level of 133 mm. The real question is whether or not the linear trend will continue or will it accelerate as a result of climate change?
One possible way to look at this is to compare what temperature has done over roughly the same time period to see if there is any indication that temperature change is accelerating. The following image shows three sets of data with regard to temperature:

The data in this image represents observed temperature changes from balloons and satellites and temperature predictions from computer models. The interesting aspect of this image is the balloon and satellite observations track very close to each other while the model predictions of temperature change are roughly 3 times greater than the observations. Another interesting point is that while the temperature is trending upward for the overall duration, there are multiple periods where the temperature is getting cooler.
There is no obvious sign of acceleration in the observed data, but the current climate orthodoxy would indicate otherwise as indicated by the climate models and as a result of increased CO2 in the atmosphere. So the next logical step is to see what the CO2 levels have done over roughly the same period of time.

For the last 30 years the CO2 has increased linearly at about 2 parts per million (PPM) per year.
Just looking at the data, it would appear the 133 mm increase in the next 40 years would be a good conclusion, but again the current climate orthodoxy disagrees because it is believed small temperature increases resulting from increased CO2 is amplified by the positive feedback caused by the additional water vapor in the atmosphere. Water vapor is the most powerful of all greenhouse gases according to the IPCC.
The counter argument to the positive feedback hypothesis is the negative feedback provided by increased cirrus cloud cover when temperatures rise. There is also the issue of the diminishing global temperature effect of CO2 as described by the five studies in the following image:

Although the numbers are different in each of the 5 studies, they all conclude the heat retention of CO2 decreases logarithmically as the concentration increases. Using the question's time period of 40 years, the CO2 will have increased by 80 PPM to approximately 490 PPM which falls within the first level of the above chart. Using the numbers from the last three columns, the increase in temperature from CO2 alone would range from  0.2 to 0.466 degrees centigrade.
One interesting conclusion from this chart is these 5 studies do not agree in the magnitude of the change which would indicate the science is not settled. Another point to be made is while CO2 concentrations increased constantly, temperatures fluctuated up and down over the same time period which indicates there are other factors in play besides CO2. These differences along with the lack of understanding of the effect the negative feedback of clouds are possible explanations of why the computer models fail to accurately mimic the actual temperature observations.
Since the computer models represent the gold standard upon which future temperature predictions are being made and coupled with the fact their predictions to date have been so wrong, it is reasonable to conclude the 133 mm rise is sea level is likely to be an accurate outcome over the next 40 years. If that is the case, then the action to be taken by various coastal cities would depend upon their specific circumstances. As for me, I do not intend to sell my coastal property based on the existing evidence.
Update:
The lowest parts of St. Petersburg, Russia are about 4 m above sea level. If my estimate of 133 mm sea level rise over the next 40 years is correct, then St. Petersburg will not be much worse off than they already are. I would assume the portions of the city that are that low are already having flooding issues during storms or even during high tides.


Can I use radar data to estimate snowfall, or is there a better way?

Full disclosure: Being in Florida, I don't spend as much time watching winter weather, and don't have great experience correlating radar precipitation totals to actual snowfall.  Is it spring yet?

But I do at least some background and information, and so hopefully can add some insight.

Using radar is certain to have imperfections...

Smaller Radar Caveats:

Radar beams increase in height with distance from the radar.  They really don't tell you what is actually happening at the ground, but instead up at some height aloft... this may mean that, especially further from the dish, light precipitation shown on radar can actually be evaporating before hitting the ground... or you may not get any precipitation showing up at all because sometimes convection can be so shallow that it is only below the radar beam and thus undetected (example [2.5 km ≈ 8200 ft]))
Radar beams are also blocked by elevated terrain, such that some areas in mountainous regions may not return any data.  See for example this map of the regions that are visible to US weather radars, and note the jagged/non-circular shapes common in the west indicative of mountains.

The exact radar setup is very important in determining the utility of the data.  In addition to the range and terrain issues, the beam angle and width alter what returns mean, some frequencies attenuate or reflect certain drop/flake sizes better than others, etc... so exact radar details are very crucial.

I was able to dig up this site that shows the range outlines of nine Japanese radars and then the full JMA radar specs page.  Looks like probably the radar spacing is pretty quality generally, but the frequencies are quite different than the radars I'm used to.  In the end, understanding the nuances and return characteristics of a radar's setup can be a very intensive life-long process for even the best of meteorologist!

Greater Complications of Estimating Snow

Also note that winter precipitation adds an extra complication because the particles are lighter in weight and can thus be blown about more by vertical and horizontal winds.  Raindrops (and hail) are quite likely to fall unless extreme updrafts exist because they are heavy.  But drizzle, snow, and sleet may be blown around quite a bit.  Without a time-intensive dual-Doppler analysis, you cannot know the wind motion in the storm thoroughly, and therefore will have varying results at times.
And finally, the big wrench is unfortunate inherent to how radars work.  They measure the percentage of their sent energy that is reflected back to them.  That's great because that's directly connected to the diameter of the item falling (to the 6th power).  But unfortunately the grand problem is that in a storm, there is a huge variety of drop/flake sizes mixed together at once... such that we can't extract which combination of particle sizes created it (and thus can't calculate volume to actually know the rain/snow amount that falls).  It could be like 6 medium size flakes causing the 10 dBZ echo... or 2 large flakes and 10 small flakes... and each combination is a different volume/snow total.  (to see the nitty-gritty math details on this, read more here.)  So we can never know for sure the exact rain/snow falling using just radar.  The good news is we've at least done lots of experiments and come up with some fairly useful best-practice formulas for using the Z-R ratio in different scenarios.  Good, but not perfect.
But when it comes to winter precip, it gets even uglier.  For one, the reflectivity of ice is way more than water (making it look like a ton is falling!)... but we typically can determine where the changeover line to ice is and work from that.  But the bigger issue is that ice crystals form an amazing range of shapes.  And you can imagine that each of those is going to reflect a radar beam in different percentages... and then take up different amounts of room on the ground.  In the US, the switch to polarimetric radar has helped with the shape issue a fair bit.  But if you don't have that in Japan, you could have quite a bit of error in some formation regimes.  Regardless, we have certainly come up with a few fair rules of thumb for winter precip, such as discussed in this article, but they're far from perfect.

Now that doesn't mean working from radar isn't helpful.  The "precipitation nowcasts" are probably better for you, taking out the complexity of all that Z-R relationship stuff just mentioned to just give you a mm/hr (though the site may well not be taking enough into account to give worthwhile values in all situations).  But you can have some comfort from the fact that in the US we do regularly use basically the same idea to what you're doing to identify floods and even roughly track snowfall areas.  But unfortunately it's a real pity it doesn't seem most countries like Japan offer as many detailed radar products for free as we get.  In the US, the NWS gives us storm-total precipitation plots directly, which provides us the total return accumulation (since last reset) so we don't have to track the aggregation ourselves.  Plus we have direct access to the full radar data files, which would remove the overcome the value stratification issues from the imagery and simplify the process.  But unfortunately I couldn't find anything about any rawer data files in my searching other than for the US site in Okinawa.

Your method does sounds fairly decent, particularly for Nagano since it appears to have it's own radar (based upon that earlier list).  I do imagine it'll still have some errors at times, being off by a fairly decent percentage sometimes.  Even here in the US, we're only just starting to cautiously venture more into more high resolution official snow analyses.  So it won't be nearly perfect, but it'll probably have some reasonable utility, and perhaps is your best method on this avenue.

However, I want to give you a couple more options that may well end up being better for you, depending upon your interest:

Initial model plots:
Global models, like the American GFS, use large amounts of data to create their initial conditions.  And so among their products, they offer current snow cover plots.  Pivotal Weather offers a useful tool to mouseover and get values at any point in a plot like this one:

Don't know if it's perfect for you, as the GFS resolution is around 30 km, so even at maximum resolution it's going to lump some mountains and lower areas together.  A pity Pivotal Weather also is a little zoomed out in your area.  If you were really wanting to go all in, you could definitely dig up the data files to download the data directly out of the model for peak resolution and information.  Otherwise if content, you can just check each day (or every 6 hours) and compare to the previous image (which you can pull up in the dropdown on Pivotal's site).

Satellite data:
I was able to come across one satellite that does offer a snow analysis product, the NASA TERRA/MODIS pair.  On that same page they have a further link to download the data at 0.05 degree resolution, which would be less than 1 km!!!  I have no idea how good these plots are, but the potential sounds great.

So just maybe model and satellite can offer to bypass some of the flaws of radar data (though just may add their own challenges).  All of it is likely better than relying on the town's reporting station... it's unfortunate there's a lack of reliable reporting stations on mountains (but it's a problem we have here too, and a matter of simple economics/utility).  But hopefully those help you better get the data you wish for!  Happy skiing :-p


Ocean currents can be described as flow oscillations that are forced at different frequencies. In the absence of any external forces (wind, friction), the resulting flow is the inertial motion, which is the response to the balance between Coriolis and inertia. The Coriolis parameter, $f$, can be described as a frequency: the effective planetary rotation frequency of a parcel of water. So, $f$ is called Coriolis frequency or inertial frequency.

There are many examples of currents that do not oscillate at the inertial frequency. The simplest examples are the tides. For instance, at 43.5N, the Coriolis frequency is $10^{-4}$ $s^{-1}$, which is equivalent to an inertial period of $17.4 h$. The main semi-diurnal tidal constituent, $M_2$, has a period of $12.42 h$, which results in a frequency larger than the inertial frequency (at mid-latitudes). The oscillations that happen at frequencies larger than Coriolis are called super-inertial flows. On the other hand, the diurnal tides (e.g., $K_1$, $O_1$) have periods of around $24h$ and thus have frequencies smaller than the inertial frequency (at mid-latitudes). The oscillations that happen at frequencies smaller than Coriolis are called sub-inertial flows.

Flow spectrum showing energy peaks at certain frequencies: diurnal tides ($O_1, K_1$), semidiurnal tide ($M_2$), and Coriolis (inertial) frequency ($f$).

In the real ocean, the balance between planetary vorticity (Coriolis) and inertia is only part of the story. There are usually other forces acting on the flow. For instance, when the balance is between Coriolis and the pressure gradient, we end up with the geostrophic balance. The resulting geostrophic currents can be described as a zero-frequency motion as there is no acceleration (steady-state).

Another important force is the effect of the wind. When we consider the balance between Coriolis (planetary rotation) and the frictional force (stress) caused by the wind, the balance results in Ekman flow. In the Ekman case, the mixing in the layer near the surface (boundary layer) needs to be considered. The same type of balance is present in the ocean in the vicinity of the bottom, as another boundary layer is established there for the flow to go to zero at the bottom. The resulting effect of these frictional forces is that the flow does no longer oscillate at inertial frequencies.

In the paper you mention, they describe how the frictional effects near the boundary (Ekman balance) influence the interior flow. The interior of the ocean tends to be in geostrophic balance (frequencies smaller than inertial). The boundary flow effects tend to propagate into the interior modifying the geostrophic balance. A good example of this effect is Ekman pumping: cyclonic winds cause Ekman transport, that in turn causes a surface divergence, and in order to balance the flow, result in vertical flow (upwelling). This effect is called Ekman pumping and modifies the interior flow to compensate boundary flows.


Pressure of condensation of an air parcel

The lifting condensation level (LCL) is the level at which a rising particle reaches 100 % relative humidity by adiabatic cooling.

Please have a look at Wikipedia: LCL and LFC (level of free convection!).


Why would Google's map of areas affected by Hurricane Harvey have advisories for the west coast and other far away areas?

It seems like there is more than just a hurricane going on. According to the National Weather Service there are excessive heat advisories, gale warnings, etc.


Calculating exoatmosphereic flux and figuring out amount of SW Earth will absorb at an albedo of 0.3?

Agree with Ash, I think it's a mistake.  Dimensionally:

$$\frac{S}{4}(1−A)$$ is going to have the units of $S$ has because $A$, albedo, is a unitless ratio.

Insolation comes in over an area, so is measured in $W/m^2$ as you've got.  The only way I can see you'd get units of $W/m$ is by multiplying by a distance somewhere, perhaps by integrating its values over a latitudinal distance or something... but that's not really insolation (or exoatmosphereic flux as you call it!) anymore.

No, all values of S should be $W/m^2$.


How do I find the volume of ocean between any two layers of ocean depth?

You can find gridded topography and bathymetry data, freely accessible, on the website of the NOAA. For instance you have the ETOPO1 dataset here.

Once you downloaded it you can work it out with your favourite GIS software or GIS-supporting programming language.

The equations to calculate the volume based on the gridded cells is given on this page from the NGDC website.

  Volume Calculation

  Volumes were calculated for each ocean grid cell in ETOPO1 using
  Equation 1 to determine cell area, and Equation 2 to determine cell
  volume. Cell areas and volumes were then summed over each ocean or
  marginal sea.

  Equation 1: $dA = \frac{a^2\cdot cos(ø)\cdot (1-e^2)\cdot dø\cdot dl}{(1-e^2 \cdot sin^2ø)^2}$
  Equation 2: $dV = dA \cdot depth$

  where:
  Latitude (ø)  = latitude of cell's center (in radians)
  Unit of Latitude (dø) = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)
  Unit of Longitude (dl)    = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)

  The WGS84 spheroid was used for values of Earth's radius and
  eccentricity:
  Equatorial radius (a) = 6378.137 km
  Eccentricity (e)  = 0.08181919


Where does the symmetry of cloudy bands come from?

The symmetry is caused by the the spherical nature of the Earth, the typical weather features that form at certain latitudes, the formation of circulation cells at specific latitude zones, and the effect of the Coriolis force on the weather systems and cloud bands within them.

The latitude (and hence temperature from insolation) controls to a certain extent the broad scale atmospheric circulations. In the zone just North and South of the Equator, you find the trade winds converging towards the Equator from an easterly direction. Their direction is broadly determined by the Coriolis effect. (I think you can just make them out in the photo).

In the mid-latitudes (30-60 degrees) you frequently find extratropical cyclones in both hemispheres. Their formation is beyond the scope of this brief answer (see Cyclogenesis), but they are effectively a result of consistent suitable conditions to at those specific latitudes for cyclones to form. They are noticeable in the image as being quite spiral shaped.

The symmetry of cyclonic features is perhaps most enhanced by the Coriolis effect, caused by the rotation of the Earth deflecting moving objects (the weather systems including the clouds) in the atmosphere. This (in combination with the pressure gradient force) causes the spiral-shaped features at the mid-latitudes that you can see in the image. The effect works in opposite directions in respective hemispheres, so in the North, the cloudy bands appear to be turned anticlockwise, and in the South they appear clockwise, enhancing the overall symmetries present.

This is one of my favourite widgets for seeing this:

http://earth.nullschool.net/#current/wind/surface/level/orthographic=199.59,9.44,293


My personal experience of rainforest is confined to Malaysia, where it is too damp to burn unless it is first cut down and allowed to dry out in the sun. The fires on these ladangs, as they are called, never spread to nearby rainforest, and abandoned ladangs eventually become rainforest again.  I have some knowledge of other rainforests and have come to the conclusion that true rainforest is similar to Malaysia's. Throughout the wetter parts of the tropics, where there is not rainforest  there is a kind of forest called monsoon forest which is only wet for a few months of the year. After that it dries out and eventually loses it's leaves as though it were winter.

Often it is fairly close to real rainforest, so there is a gradual transition from monsoon forest to rain forest. Both kinds are found in Amazonia and Central America, Dropping 5,000 gallons of gasoline into a rainforest to see if it would burn would be regarded as very odd nowadays, but it frequently happened in WW2. Allied and Japanese aircraft were frequently shot down and crashed into the jungle, seldom with 5,000 gallons of fuel aboard but certainly enough to cause a fire. In Malaya and Borneo the jungle never caught fire, and although this happened all over S.E.Asia, surprisingly enough I have never heard of an incident where the jungle caught fire. There is some monsoon forest in India, but the fighting there was confined to Assam, where it is rainforest.

In modern times a large jet occasionally crashes into jungle, but again I have never heard of one setting he jungle alight. Jet fuel, of course, is not as inflammable as gasoline. Some of the fires in Brazil currently shown on TV look as though it is the sort of scrub which springs up on land which was once cultivated.


Is there a name for this type of ice crystal?

This is needle ice which forms when moist soil freezes, for example during a cold night. Freezing starts at the ground surface and as ice is formed moisture gradients develop which draws water to the freezing front and growth continues. Ideal conditions may be a sub-freezing night after a rainy day or a sub-freezing night after a day of snow melt.

According to the National Snow and Ice Data Center (NSIDC) site needle ice be up to 40 cm in length. Since the favourable conditions are not unique to soils, although most often encountered in soils, needle ice can develop from freezing of, for example, vegetation


Why is there no High-Resolution Infrared Radiation Sounder (HIRS) on Metop-C?

HIRS is an old NASA heritage design that flew on both European and US weather satellites as part of the EUMETSAT/NOAA Initial Joint Polar System.  The Inrared Atmospheric Sounding Interferometer (IASI) will take over the duties of HIRS, since IASI is a more powerful instrument with European design for a European satellite.  You can see this discussed here:

http://www.esa.int/Our_Activities/Observing_the_Earth/The_Living_Planet_Programme/Meteorological_missions/MetOp/About_HIRS_4/(print)

My perspective on this is that historically the US was the international leader in environmental satellites.  The Europeans now have better designs and more committed plans to environmental satellites over the next couple decades.  So, essentially, they don't need our out-dated hardware anymore.


Can a cosmic impact break Earth's crust in large area exposing the magma ocean?

Let me first correct a small misconception. Where you are talking about 'the magma ocean', you are implying that one exists. This is in fact false. There is no 'magma ocean' in the Earth at the moment (and it has been like that for several billions years). The lavas you see erupting in volcanoes are not coming from a magma ocean. They are coming from either the crust or the mantle, both of which are solid. Magma generation is a localised anomaly in what would otherwise be a solid mass.

That said, the upper mantle has a section called 'the asthenosphere' which is slightly more ductile than the rest. Think about chocolate in a hot day. Still solid - but it can flow given enough pressure. The modern lithospheric plates (of plate tectonics fame) sort of float on the asthenosphere already now, and that's why you have plate movement and earthquakes and everything.

The asthenosphere is quite deep - some 100 to 200 km deep below the surface. If a cosmic impact is going to create a crater 100 km deep in the Earth, no one will be left around to care about whether they will survive on the 'iceberg'-like lithospheric plates. Again - this is irrelevant. The asthenosphere is ductile in timescales of hunderds of years (at least). If you were to pick up a piece of it now, it will just be like any other rock (albeit quite warm).

A magma ocean event probably occurred very early in the Earth's history (which is not going to happen again since Earth is already here), and the moon forming event also likely liquified quite a lot of the Earth. But this is not going to happen since there is no other big enough body that seems like it's going to collide with us at the moment.


What is the area with the largest velocity vertical shear in the ocean?

Areas associated with velocity shear at a stratified interface are notably strong in the region of the Equatorial Undercurrent, straits (ex: strait of Gibraltar, the Bosphorus) and regions of the thermocline where internal waves are strong (South China Sea).
These areas are typically associated with strong turbulence as a direct result of the strong velocity shear and shear instabilities that trigger Kelvin–Helmholtz billows (if the Richardson number is less than 1/4 for a sufficient amount of time) and subsequent hydrostatically unstable configurations and mixing.
Examples of magnitude of shear:

Maximum in Equatorial Undercurrent: $du/dz \approx 0.02$ s$^{-1}$
At the base of the mixed layer but above the core of the Equatorial Undercurrent the shear is the largest. See plot from Peters et al (1988) https://i.imgur.com/YbmAtV2.png

East of the Carmarinal Sill in the strait of Gibraltar: $du/dz \approx 0.024$ s$^{-1}$
In the Mediterranian, water flows westward into the Gulf of Cadiz as an undercurrent through the strait of Gibraltar, as these waters make a sharp turn northward, they may give rise to sub-surface eddies or "Meddies" when encountering canyons and underwater bathymetric features off the west coast of Portugal.

Very large amplitude internal waves in the South China Sea: $du/dz \approx 0.05$ s$^{-1}$
In the South China Sea very large amplitude internal solitary waves are ubiquitous features propagating on the thermocline with inherently large shear across the interface. See plot from Lien et al (2014)  https://i.imgur.com/qhQBI9g.png

References:
Ren-Chieh Lien, Frank Henyey, Barry Ma, and Yiing Jang Yang, 2014: Large-Amplitude Internal Solitary Waves Observed in the Northern South China Sea: Properties and Energetics. J. Phys. Oceanogr., 44, 1095–1115.
Fernando, Harindra JS. "Turbulent mixing in stratified fluids." Annual Review of Fluid Mechanics 23.1 (1991): 455-493.
Thorpe, Steve A. The turbulent ocean. Cambridge University Press, 2005.
Peters, H., M. C. Gregg, and J. M. Toole. "On the parameterization of equatorial turbulence." Journal of Geophysical Research: Oceans (1978–2012) 93.C2 (1988): 1199-1218.


weather.us

If somebody is looking for free global ECMWF forecasts the above site provides a fairly complete set of links that provide information 10 days into the future. You can track the control member(which I believe is a deterministic forecast) and also the ensemble output.  In addition you can look at worldwide lightning detection sites as well as radar images of US and other selected countries. For followers of tropical meteorology  hurricane tracks of ECMWF are also available - ECMWF  cyclone tracks.
The availability of free ECMWF forecasts comes via the courtesy of Jörg Kachelmann who owns the site.


What is the distance between the tropics?

Let's start by the quick rule of thumb, I'll follow the way I do it mentally as I think the mnemonics I use could help you too.

First, the tropics are at 23.5° of latitude. And remembering that the original definition of meter is "A ten-millionth of an Earth's quadrant", it means the perimeter of Earth is 40,000 km, that consist on 360° of latitude, then:

$1^\circ = \frac{40,000 \, km}{360^\circ}= 111.11 \, km/^\circ$

Now, the distance between the tropics in a first approximation would be

$\text{Distance} = 2 \times 23.5^\circ \times 111.1 \, km/^\circ = 5221.7 \, km$

Now there are a few sources of error in this calculation. First, the actual latitude of the tropics is 23.43692° (or 23°26′12.9″). Second, the perimeter of Earth is not exactly 40,000 km (it is 40,075.017 km along the equator and 40,007.86 km along a meridian). And third, Earth is not a sphere, therefore not all the degrees of latitude cover the same distance. Taking all those factors into account the actual distance is 5,185.9 km (Calculated using a GIS software).

If you want more accuracy than a few hundred meters, you have to specify the date, because the actual latitude of the tropics oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. And it is currently changing at a rate of about 0.5 arc seconds of latitude per year, that translates in a displacement of about 14 meters every year.

NOTE: To make the answer more readable to everyone I decided to keep it in metric units (it also makes sense for the mnemonics I use to derive the length of a degree of latitude), so I leave the transformation to imperial units to you.


How much carbon is sequestered out of the atmosphere through marine snow?

This probably doesn't answer your question but might help the thought process:

The part of the carbon cycle you are inquiring about is referred to as the biological carbon pump.
Phytoplankton total net primary productivity is estimated to be ca. 45 to 50x1015g of (fixed) Carbon per year (Falkowski et al. 1998). In comparison land plants are producing an estimated 50 to 60x1015g of (fixed) Carbon per year (Field et al. 1998), hence a roughly 50-50% situation.

Of course not all of it is being buried: some is being recycled by heterotrophs and some decomposed (and thus released).

As far as the zooplankton and zoonekton (fishes, marine mammals, swimming molluscs and arthropods,...) are concerned, although I do not have numbers to back this claim, I would assume their impact on the carbon cycle to be (necessarily) smaller than that of the phytoplankton (since the carbon they are exporting comes, ultimately, from recycling the phytoplankton).

Source:
Falkowski, P. G., Barber, R. T., Smetacek, V., 1998. Biogeochemical Controls and Feedbacks on Ocean Primary Production. Science, 281: 200-207.
Field, C. B., Behrenfield, M. J., Randerson, J. T., Falkowski, P., 1998. Primary Production of the Biosphere: Integrating Terrestrial and Oceanic Components. Science, 281: 237-240.


Helium (He) is formed by radioactive decay of uranium (U) and thorium (Th) to lead (Pb).

There's another name for the nucleus of a 4He atom: It's an alpha particle. Alpha decay is one of the pathways by which radioactive elements eventually decay into non-radioactive elements. For example, 238U decays to 234Th via alpha decay. There are three key isotopes that lead to the generation of helium: 238U, 235U, and 232Th. Each of these is a "primordial" radioactive isotope. they were present when the Earth formed, and their half-lives are sufficiently long so that a good fraction of that original content has not yet decayed.

So how much helium does the decay of these isotopes produce?

238U eventually decays to 206Pb via the uranium decay series (aka radium series). This decay process ultimately produces eight alpha particles.
235U eventually decays to 207Pb via the actinium decay series. This decay process. This decay process ultimately produces seven alpha particles.
232Th eventually decays to 208Pb via the thorium decay series. This process ultimately produces six alpha particles.

After the alpha decay, the parent nuclide suddenly has an excess of two electrons orbiting it. The alpha particle has a deficit of two electrons. The alpha particle quickly grabs those two excess electrons and becomes a helium atom.

Most of the helium deposits in the Earth are thought to be the result of alpha decay. For example, see Helium Facts: Where Helium is Found.


There is a parameter ice water mixing ratio in the gfs.t<hour>z.pgrb2.0p25.f<step> file given at isobaric levels.


Are we now and/or have we been in the RCP8.5 scenario?

In short, I would say that it is too soon to say. But, if I were forced to guess: I would indeed incline to say that we live in a RCP 8.5-ish scenario.

I'm not an expert at all on climate models or RCP scenarios, but I found the question interesting, so this is my attempt to answer it based on the most reliable data sources I found. I hope to motivate expert to jump in to comment, improve, challenge or support this answer.

RCP scenarios

The scenarios involve future pathways in the emissions of a large range of different chemicals (Greenhouse gases and aerosols), so if we look at how actual emissions of $CO_2$ have matched the scenario we might think we are in one scenario, but is we instead look at the emissions of $NH_3$ we might find ourselves in another scenario. The best way to summarise all those different parameters is to consider the total radiative forcing, that is the combined effect of all those compounds in Earth's energy balance. In fact the numbers that label the different RCP's are the expected total radiative forcing by year 2100 in $W/m^2$.

The following figure shows the radiative forcing (this time as $CO_2$ equivalent) of each scenario. And as you can see, by 2018, the differences are so small that I think it is too soon to say with any reasonable certainty that we are flowing one or another scenario.

(Figure from Wikipedia commons originally here)

Scenarios versus measurements

Nevertheless, we can attempt to plot the actual measurements against what was predicted  by the scenarios. The best variable to contrast would arguably be the total radiative forcing. However, that is a quantity difficult to calculate and I haven't found published values like those in the IPCC Assesment report 5 (AR5) Annex II table AII.1.2, beyond 2011. Up to that year, the forcings were beautifully summarized in figure 8.18 of AR5 chapter 8:

Given the lack of total radiative forcing data, we can instead make the comparison with some other variable. Such analysis will be liable to depend on the chosen variable as pointed out before. Therefore, to minimize that problem let's pick a variable with a large influence in the difference between the four scenarios. I think that would be $CO_2$ emissions from fossil fuels and industry.

The the emissions predicted by each scenario can be obtained at the RCP Database (version 2.0). That data looks like this:

Now, for the actual estimated emissions, perhaps a reliable source is the Global Carbon Project, that provide the emissions data up to 2016. Putting all that together we get the following figure:

So, it looks RCP8.5-ish, but the differences between the scenarios are still quite small, so it is difficult to say.

Another good variable to compare would be $CO_2$ concentration, that can be directly measured instead of just estimated. In that case using NOAA's Global Greenhouse Gas Reference Network data for global $CO_2$ concentration, against the ones prescribed for each scenario (taken as well from RCP Database (version 2.0)) the figure looks like this

That looks more like RCP4.5-ish. But again, probably too soon to say.
Also, it might be that even given more time, the path followed by the climate system would be like one RCP in some aspects and like other RCP in other aspect. For example, $CO_2$ emissions might follow roughly RCP8.4 but methane emission might follow RCP4.5. Or somewhere in between.

Another approach would be to use use an actual climate model forced by RCP8.5 (not just the RCP), so you can compare mean surface temperature, but that would be tricky for many reasons and also model dependent.

If anybody knows of published estimated total radiative forcing from 2012 onward, that would be nice to add and compare. It might make the answer a bit more clear but I think that in any case, it is too soon to give a definite answer.


GOES image: parallel trains of clouds. What to make of them?

The species is Stratocumuls undulatus Sc un.

They can form for example when cold, dry air moves over a warmer ground layer. A sharp wind shear at the boundary layer blows these waves. (Wikipedia on Sc).

They are not to be confused with Sc radiatus or yet another form, the so-called "cloud streets", which form along the wind direction.


What's the difference between topography and orography?

Topography, in the eyes of Earth Scientists, is the study of the surface features of the Earth (or other planet), and includes all features of that surface, natural or artificial.

From the Oxford Dictionary:

1.The arrangement of the natural and artificial physical features of an area

Topography comes from the Greek topos, meaning 'place'. It is a study of all the features of any specific area, not necessarily just elevation, as depicted in topographical maps.

Orography is a specific study of the features and 'topography' of mountains:

The branch of physical geography dealing with the formation and features of mountains

Comes from the Greek óros meaning 'hill'. Orography can also be known as orology, oreography or oreology... It is concerned with the formation and development of mountains, hills and ranges, for example the formation of a mountain range or ranges is know as an 'Orogeny'. Earth Scientists can refer to groups of mountains or ranges as 'Orogens'.

Orography falls more broadly under the study of Geomorphology, which is not necessarily just constrained to surface features, as in the case of topography.


Can ionospheric plasma disturbances effect the weather?

Apparently it is possible for the ionosphere to influence the conditions in the lower atmosphere.

The following are relatively recent results from a paper in 2009, and a summary and up-to-date state-of-the-art can be found in this paywalled, upcoming chapter in a book.

As it turns out, at least in the arctic regions, the ionosphere can have quite an impact on the temperatures.

Geomagnetic storms provide large numbers of energetic electrons, which follow the magnetic field lines. As the magnetic field lines only intersect with the atmosphere in the polar regions, those electrons will preferentially precipicate there.
What follows is Ozone destruction and generation of $NO_x$-species in the Mesosphere and Stratosphere. $NO_x$ molecules are classical long-lived Ozone killers.

The Ozone depletion leads to direct heating of the Polar surface of up to $\Delta T \approx 4.5 K$ by increased UV irradiation. Furthermore, the $NO_x$ can be transported towards lower latitudes, and geostorm induced chemistry seems to have influenced mid-latitude Ozone concentrations measurable in the past for short times. A nice summary also in the Science case for the EISCAT3D-radar (not paywalled, and one can skip directly to page 7 where those effects are described and further referenced).

Those indirect effects are intriguing in that, while some might argue that the ionosphere cannot have any influence on the troposphere, it is forgotten that the radiative energy balance links the whole atmosphere. And it is this balance that can be altered by geostorm induced ozone destruction in the middle atmosphere. It's not exactly what OP was going for (no rise in lightning strikes in the troposphere), but the ionosphere knows their own version of lightning , called Sprites (also a more recent finding in research), which are sure to appear with those events.

Keep in mind that this is still ongoing research.
While a correlation of geomagnetic storms with changing polar temperatures has been already noted in the past, and seems undisputed, the exact mechanism responsible for the correlation is still under scrutiny. Personally I feel there must be more to it, as $4K$ temperature difference just from increased UV irradiation seems a bit much.


How to interpolate scattered data to a regular grid in Python?

It is straightforward to do so with numpy, scipy.interpolate.griddata, and matplotlib. Here is an example:

import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import griddata

# data coordinates and values
x = np.random.random(100)
y = np.random.random(100)
z = np.random.random(100)

# target grid to interpolate to
xi = yi = np.arange(0,1.01,0.01)
xi,yi = np.meshgrid(xi,yi)

# set mask
mask = (xi > 0.5) & (xi < 0.6) & (yi > 0.5) & (yi < 0.6)

# interpolate
zi = griddata((x,y),z,(xi,yi),method='linear')

# mask out the field
zi[mask] = np.nan

# plot
fig = plt.figure()
ax = fig.add_subplot(111)
plt.contourf(xi,yi,zi,np.arange(0,1.01,0.01))
plt.plot(x,y,'k.')
plt.xlabel('xi',fontsize=16)
plt.ylabel('yi',fontsize=16)
plt.savefig('interpolated.png',dpi=100)
plt.close(fig)

Result:

How to use this:

x and y are locations of points - these correspond to lon and lat values of your stations;
z are the values of points - this corresponds to your temperature observations from stations;
xi and yi are target grid axes - these will be your target longitude and latitude coordinates, which must match your landmask field;
zi is the result;
This example includes a simple way to mask the field. You should replace this mask with the landmask on your grid.

Notice also the method argument to griddata. Besides linear, this can also be cubic or nearest. I suggest you play with each to see what yields the best result for your dataset.


When searching for a place to publish Earth Science stuff, have a look at the two big continental scientific societies: the American Geophysical Union (AGU) and the European Geosciences Union (EGU). Both have a wide array of publications in the various fields of geosciences. AGU has JGR Oceans, while EGU has Ocean Science (open access). If you want to reach a broader, less specialized audience, you could also aim for Frontiers in Earth Science (open access): they have a Hydrosphere section.


Skew-T Log-P diagrams can be plotted in most mathmatics software.  I have seen examples in Matlab (and by proxy Octave), GrADS, NCL, IDL and I have my own code in Python that generates Skew-T plots.  There are also some programs such as NSHARP and BUFKIT that are more full featured.  You can also find websites that plot forecast soundings such as twisterdata and real data soundings.

The major variances arise from the specific use case of whoever wrote the code you are using.  The most basic code will generally be able to tell you the lifting condensation level (LCL), level of free convection (LFC), equilibrium level (EL) and perhaps the 500 mb lifted index, all for a surface parcel.

The more advanced code will generally be able to calculate the above quantities not just for surface parcels, but also for the mixed layer and be able to find the most unstable parcel.  Convection oriented code will give you CAPE, storm tops and other severe weather parameters and will also tend to be able to analyze the hodograph.  BUFKIT can do analysis to identify snow growth levels and some other winter weather related quantities.

One of the subtle differences in skew-T plotting software is how they handle the moist adiabats.  This can be modeled as a fully reversible process or a pseudo reversible process and this produces subtle temperature differences aloft on the adiabat.  There can also be differences in whether the moist adiabat only considers liquid water and vapor, or if ice process are included in the latent heat release.

Here is an example of what my Python code produces:

Var          SFC            ML              MU
CAPE  J/kg   1877           1877            2415
CIN   J/kg   46.9           46.9            0.4
LI_max       -9.5           -9.5            -11.3
LI_500       -7.3           -7.3            -8.4
LI_30        -4.8           -4.8            -6.4
TOPS  m      14800          14800           15400
LCL   mb (m) 892 (1000)     892 (1000)      862 (1292)
LFC   mb (m) 831 (1604)     831 (1604)      857 (1343)
PRS   mb     1000           1000            871


What's the partition coefficient (D) of Nb for apatite?

Yes, in the paper Trace element partitioning between apatite and silicate melts (Prowatke and Klemme, 2006), where they present experimental apatite/melt trace element partition coefficients for a large number of trace elements, including $\ce{Nb}$.  The experiments were performed at pressures of 1 GPa and at a temperature of 1250 C.

What the experiments revealed were:

An average of $D$ = 0.0018 for $\ce{Nb}$ (this value is an average of Table 5: Trace element partition coefficients between apatite and different silicate melt of the linked document).
$D_{Nb} \approx D_{Ta}$
The partition coefficient was not significantly affected by changing melt compositions.


Checking the bedrock with radiowaves - how does it work?

Do you mean Ground Penetrating Radar? This is typically limited to very shallow depths though - eg. archaeological investigations, police forensics (finding graves), and civil engineering site investigations. The latter can go to tens of meters and would be used for planning foundations, excavations, etc (I know of an example where it was used for site characterization for a planned rowing lake). The depth limit is typically due to attenuation in brackish groundwaters. Ice applications can typically go further due to the lack of conducting liquid water.

Or are you thinking of Reflection ('Active') Seismic Surveys, which work on a similar principle but using sound waves. Sound waves can travel to the far side of the Earth (cf. large earthquake 'P' waves), but reflection surveys are typically looking at the upper crust (few km) and rarely go beyond the base of the crust (aka the 'Moho') which is a strong seismic reflector. Reflection seismic surveys are widely used in the oil business.


Why does the rising of high clouds due to climate change impart positive radiative feedback on radiative forcing?

The primary mechanism at work here is the type of clouds that exist at different altitudes.

Low clouds of the cumulus or strato-cumulus variety are optically thick and reflective.  These types of clouds will scatter more light than they transmit or absorb, and the energy scattered upward and back into space will not contribute to warming.

High clouds outside of convection tend to be cirrus clouds, which are icy and not optically thick.  These clouds let light pass through freely (you can see the sun through these clouds).  This lets solar energy through but they will absorb longwave (terrestrial) radiation, and this is what will contribute to warming.

This is where a lot of the uncertainty in cloud feedbacks in a warming climate comes from.  If we get more clouds -- low, bright clouds, then this could contribute to cooling, wheras high, transparent (to shortwave) clouds would contribute to warming.  Again, it is not so much the high vs low that matters here, it is the properties of typical clouds at these heights.


How does agriculture release so much greenhouse gas?

There are several contributing factors,

livestock, Livestock is easy animals produce co2 but their methane is a bigger problem, methane is a better greenhouse gas than the co2 that the feed plants took in.   Livestock waste is also a problem , people do not realize how much waste modern factory farms produce, specially when stored as a liquid is it produces all the problems of rice production with addition release of methane from the waste itself.
transportation, transportation of ag products to market are almost all petroleum based. Depending on the source this may or may not be included in agricultural emissions.
Landuse, changing land, especially things like draining wetlands and burning forest for farmland are big contributors, Wetlands in particular produce huge amounts of co2 and keep doing so for decades if not centuries, all the organics built up in wetland start oxidizing when drained, this is basically the same as burning petroleum without actually getting any usable energy out of it.
Fertilizer produces a plethora of problems, and could justify an question all its own.
Rice, rice production has been called out as particularly problematic.  You would think this would produce the opposite effect to draining wetland but it is actually worse. Bacteria in flooded soil produces methane instead of co2 and as I said methane is better greenhouse gas, too top it off rice fields are supplied with enough nutrients to keep the bacteria producing way above normal wetland levels and keep it from being trapped the way carbon in mostly anaerobic wetlands will be.

Source


How does the lifetime of methane vary in the atmosphere?

This wikipedia article, says that the hydroxical radical is the most important sink of atmospheric methane:

In addition to being the largest known sink for atmospheric methane, this reaction is one of the most important sources of water vapor in the upper atmosphere.
$$\ce{CH4 + ·OH -> ·CH3 + H2O}$$
This reaction in the troposphere gives a methane lifetime of 9.6 years. Two more minor sinks are soil sinks (160 year lifetime) and stratospheric loss by reaction with ·OH, ·Cl and ·O1D in the stratosphere (120 year lifetime), giving a net lifetime of 8.4 years.

However, it goes on to say:

increasing emissions of methane over time reduce the concentration of the hydroxyl radical in the atmosphere. With less OH˚ to react with, the lifespan of methane could also increase, resulting in greater concentrations of atmospheric methane.


Yes it is used and it works. I've heard varying viewpoints on it's accuracy and dependability though. I remember my earth science lecturers were in three camps with it:

one felt that the dates weren't consistently reliable, the data he'd gotten from astro-dating in the past had very poor independent confidence margins when there was no radiometric calibration. He implied that the results felt as though they had been pulled out of thin air.
two would gather testable material for future study but didn't use astro-dating themselves. It was an interesting but immature technique that might be useful in future but not to them.
only one felt that it was really, immediately useful.

Do note that this is in New Zealand, we're a geologically young and active country, so much so that we rarely need longer range radiometric testing like Uranium-Lead or even Potassium-Argon, we can Carbon date most of the sites we're interested in. Fine calibration of longer range datings is much less of an issue here than in older, more settled, locations.


Mars maar craters explosive style formation gravitational effect

I recently saw a video lecture given that went through a calculation of how the size of volcanoes is related to the mass of a planet.  I don't remember the details or the math but the conclusion was that the smaller the planet the bigger the volcano.  This explains why Olympus Mons on Mars is so much bigger than anything on earth.  I can find a link to the lecture if that will help.  The equations are given in the lecture.


How to calculate the snow cover area from satellite data in better and efficient way?

Identification of snow in satellite images is done using multiwavelength measurements and including ancillary information. Snow obviously has far more reflectivity compared to barren soil, water or vegetation and any edge identification algorithm on visible channel images will identify their extent. The biggest trouble comes from clouds which can appear as bright as snow in visible channel images. Satellite measurements in the infrared region of spectrum help in the discriminate snow vs cloud. Infrared emissions of an object depend on temperature and clouds being at a higher altitude has far less temperature compared to snow. The algorithm may use other information also, for example, day to day variability. Clouds have a very short lifetime and display large variability whereas snow/ice disappears far slowly compared to cloud.


There is a decent explanation in Glacier Man Science 30 Oct 2009:
Vol. 326, Issue 5953, pp. 659-661. (alternative link)

  Norphel’s idea was to divert the lost winter
  water from its course down the mountain,
  along regularly placed stone embankments
  that would slow it down and allow it to spread
  and trickle across a large, shaded surface
  depression a few hundred meters from the village.
  Here, the slowed water would freeze and
  pack into a glacier that would begin melting
  when the sun rose high enough in spring to
  expose the thick ice

...

  Norphel has built nine glaciers since that
  first one, which he began in the late 1980s
  and worked on until 1994. They average
  250 meters long by 100 meters wide; the
  Phuktse glacier remains the largest. Norphel
  estimates that each one provides some 6 million gallons (23,000 cubic meters) of water,
  although there has been no accurate analysis to
  date, and the undulating ground makes it difficult to guess the volume of ice in each glacier.
  Each artificial glacier is built using local
  labor and materials for about 3 to 10 lakh
  Indian rupees (6000 to 20,000 US dollars),
  depending on the size and site, compared
  with about US$34,000 for a cement water
  reservoir, Norphel says.

Personally, I wouldn't call these glaciers.  It is more that water is being dammed so it freezes rather than runs off, and stays frozen into the spring then eventually melts before the end of the season.


Is the net amount of CO2 sequestered by trees from the atmosphere simply related to the mass of new growth?

Simple answer: No. The process "carbon sequestration" considers the whole Earth system holistically (otherwise it would not serve its purpose), and in your case, you only look at the plant-atmosphere system so nothing can be said of the amount of carbon sequestered.

What you are describing is more close to Net Primary Production, which is defined as carbon fixation from photosynthesis minus carbon released from autotrophic respiration (which is somewhat different from transpiration that you mentioned).

Carbon sequestration refers to the transfer of atmospheric carbon into a relatively stable pool of carbon (on a climate-relevant time scale, usually at least in decadal-scale). "New growth" implies all the biomass gains of the tree over time, not necessarily "stable" biomass only. One obvious case arises for deciduous trees where large portion of "gained" leaves fall and decompose relatively rapidly.


How can poor tropical soils be enriched by biological means?

There are two main problems that "wear out" soil, and people working on this deal with both of them.

A soil might be low in organic matter and nitrogen, perhaps because all the crops were sold away and the topsoil eroded off. This would also happen on a new sandbank, or where a landslide had revealed a lot of subsoil. Naturally what happens is that the site is colonized by "primary succession" plants that are good at surviving there. These plants photosynthesize carbon compounds, and have bacteriological associates that fix nitrogen out of the atmosphere. The plants and bacteria live and die and leave detritus that slowly turns into richer soil, and somewhat more complex "secondary succession" plants move in. Reclamation agriculture or reforestry helps this along, and agroforestry tries to forestall soil loss by growing trees instead of arable crops.

But C and N are not all that plants and bacteria are made of -- just about everything else, eg P and K and Mg and Ca, comes from the geological parent material of the soil. When as anions and cations these elements are being traded and fought over by plants and microbes, they are soluble, and over time they will weather out of the soil. Over geological time they weather out of the underlying rock, which is the problem in the oldest parts of the Earth, and then it's difficult for even primary succession plants to grow.

Hawaii is a beautiful natural laboratory for this, as the islands are made of the same lava but are of very different ages. The classic work on this is by Vitousek; here's an open access paper following up on it: Primary Succession on a Hawaiian Dryland Chronosequence.

There's a ecology-economy group trying to fix this problem in Haiti. Haiti has exported so much, for historical reasons, that their soil is terrible and they have to import a lot of food although they were recently a very NPP-productive place. SOIL works on designing and introducing composting toilets so that the elements imported as food are incorporated into agricultural soil instead of running off (causing public health and fisheries problems as they go!). It's a very nice virtuous-circle, though it takes a lot of work to keep it going.


Terrain correction for gravity data using Nagy, 1973

Instead of the Nagy prism formula, I suggest you to use the formula quoted in the following paper:

  B. Banerjee, S.P. Das Gupta (1977):
  "Gravitational attraction of a rectangular parallelepiped"
  Geophysics, vol. 42, n. 5, pp. 1053-1055
  doi: 10.1190/1.1440766

I wrote, in Fortran, a TC program based on that formula. If you read the paper you better understand why the algorithm proposed by Banerjee-das Gupta is easier to program, but in any case, I would like to point out some features that are described at the pp. 1055:

1)"...our expression contains only a tan inverse term facilitating computer work in all respects".

2)"The argument of the tan inverse term of our expression is simpler than the argument of sin inverse term in Nagy’s formula"...

3)"...in the Nagy's formula when the signs of x1 and x2, for example, are opposite (i.e., the y-axis is crossed), the prism is divided in two, and the integral is separately evaluated from 0 to x1, and 0 to x2, and finally they are added. In this process, some logical control is required in programming his formula. But from our expression (3), it easily follows that separation of the r.h.s. term into two is not required; similarly, when the x-axis is crossed or both x- and y-axes are crossed. This is because the signs of x’s and y’s are automatically taken cam of in our subroutine".

The formula to be programmed is quoted at pp. 1055 n° 3), but in any case I could provide you the code (in Fortran) that I wrote 30 years ago writing to palmieri.gravimetry@libero.it

Kind regards and best wishes to all, Francesco


What is the importance of mixing caused by outgassing in the ocean?

Outgassing is a process by which $O_{2}$, $CO_{2}$ and other chemicals are released as a result of heat or increase in temperature. It is different from advection and diffusion which are mixing processes as a result of temperature and concentration gradient. Outgassing is an abrupt release of gases from where they are stored trapped dissolved, in this case  $O_{2}$ and  $CO_{2}$ in the ocean. Like the ocean some materials are prone to outgassing when heated. For example chemicals released from plastics (e.g. the odor of a new car).

  What is the relative importance on mixing of the vertical flow of
  gases in the ocean water column?
  How does the mixing compare with physical mixing (e.g., wind, internal wave breaking) and molecular diffusion?

The rate of outgassing in ocean is comparable to molecular diffusion of the gases. However, the mechanisms of outgassing and diffusion are different,i.e, outgassing occurs due to some sort of pumping mechanism but diffusion occurs due concentration gradient. Both mechanisms are important to stratify saturation,i.e. homogeneous distribution of chemicals.
Having said this, comparison of diffusion and outgassing needs further investigation. However, I don't think outgassing like diffusion can be triggered by saturation. Some kind of pumping mechanism attributed to difference in surface layers (e.g. the creation of temporary vacuum layer) may trigger outgassing.
In connection with climate change, ocean oxygen and carbon dioxide outgassing into the atmosphere are decreasing ocean oxygen and increasing atmospheric carbon dioxde. Both events have negative consequences. Decrease in ocean oxygen has impacted ocean plants and animals. So, outgassing if occurs within the ocean can be taken as a mixing process but if it throws out the molecules out of the ocean has negative consequences both for the ocean and atmosphere.


You need to use the following line in your model setup:

COORDINATES SPHERICAL

Otherwise SWAN will try to calculate wave properties on a curvilinear grid with coordinates provided in meters. In your present case, the computational area is 0.47 m x 0.24 m instead of degrees longitude and latitude.


How are barometric pressure measurements traceable over centuries to 100 parts per million accuracy?

Mark's answer about mercury barometers is correct - but it is not the complete story.

Barometers were initially constructed using water, not mercury, on the manometer principle.  Water is lighter than mercury, so a water barometer requires a 10.3m tube.  1mbar is therefore roughly 1cm, and 0.1mbar measurement is clearly trivial using a ruler with 1mm gradations.  Of course the exact units of measurement would depend on the country in which the measurements were taken, but it should be clear that measurement to this precision was perfectly possible, albeit with an inconveniently-large barometer!

Mercury barometers, with around 75cm height of mercury at 1bar, were significantly more convenient.  As Mark says, this does require a much more accurate ruler to measure it though.

But the accuracy of a simple ruler is not the complete story either.  The Vernier scale was invented (or at least popularised) around the same time.  With a floating Vernier marker, mercury barometers could be read accurately to around 1/10th of the ruler scale.  For a ruler marked in 1mm intervals, a 75cm column of mercury could therefore be read to 133ppm accuracy, which is close enough in accuracy to the original water-based barometers.


Sources or strategies for stone identification

Are your stones raw or are they cut & polished as they would appear if mounted in jewellery pieces? There are tests such as streak & hardness which can be done to raw stones but not to polished stones because these test would damage the polished surface.

There are a number of websites that can be used, such as:

Rock Identification Made Easy
Rocks: Igneous, Metamorphic and Sedimentary

Tests that should be done include:

Color
Luster
Hardness - usually involves testing with the blade of a pocket knife
or similar
Grain size - the size of mineral grains in the stones. If no mineral
grains are obvious the stone may be "glassy"
Streak - the color left on a piece of white ceramic when the stone is
rubbed on the ceramic.


The relation between the magnitude and duration of earthquake

It is helpful to start with the USGS definition of magnitude, which can be seen as:

  based on measurement of the maximum motion recorded by a seismograph.

According to the Seismology Research Centre page Earthquake Size and the USGS FAQ page What was the duration of the earthquake? Why don't you report the duration of each earthquake? How does the duration affect the magnitude?, the duration and magnitude are generally related, specifically given that an earthquake is the movement (motion) of an area of a fault, rather than a single point -

  So the larger the area of the fault that ruptures, the longer the duration of the earthquake. And larger magnitude earthquakes have larger fault areas.

In the case of the recent Nepalese earthquake, if the fault movement area was larger, then this potentially could have resulted in a larger magnitude, longer duration earthquake.

However, a major reason for the uncertainty (why the USGS page refers to the relationship as a 'general' relationship) is due to the geology of the affected area, from the USGS:

  The duration of shaking at a point on the ground depends on how long the earthquake took to occur and how the waves move through the ground to that point. If there are a lot of reflections and resonances near the point (for instance in a sedimentary valley) the shaking will last longer. In an area without resonances (for instance on a hard block of rock) it will last a shorter time.


In an unconfined aquifer the 'storage' is that fraction of the saturated void space that can be drained. In a confined aquifer, what you are effectively measuring is the compressibility of the aquifer - that is, the water released by depressurizing the aquifer per unit head. They are really two different things.
In an unconfined aquifer, the water that is drained comes from a narrow cone of depression. In a confined aquifer, although the numerical storativity is very much less, the cone of depression extends very much further because it is a general pressure release which propagates far into the aquifer, in all directions, so the yield can still be very high.


How many days has it been since the Cambrian explosion?

As a very rough approximation, one could start with equation (9) from Arbab (2009), https://arxiv.org/abs/physics/0304093 to get the effective number of days per year:

$$T_{\text{eff.}} = T_0 \left(\frac{t_0-t}{t_0} \right)^{-2.6}$$

with

$t$ the time difference between now and then
$T_0 = 365.25$ the current number of days per year
$t_0=(13.799 \pm 0.021) \cdot 10^9$ the present age of the universe (from Planck Collaboration et al. (2015), https://arxiv.org/abs/1502.01589 )

Assuming the Cambrian explosion happened about $t_c =(541 \pm 0.13) \cdot 10^6$ years ago (from Bowring et al. (2007), https://core.ac.uk/download/pdf/62875.pdf), then the number of days since can be approximated as

$$n = \int\limits_0^{t_c} T_0 \left(1 - \frac{t}{t_0} \right)^{-2.6} \mathrm{d}t  = \left[0.625 \cdot T_0 t_0 \left(1-\frac{t}{t_0}\right)^{-\frac{8}{5}} \right]_0^{t_c} \approx 2.1 \cdot 10^{11}$$

(of course one has to keep in mind that the error on this value is rather large, but to have some ballpark figure it should be good enough)

For comparison $t_c \cdot 365.25 = 1.98 \cdot 10^{11}$


Why does winter get colder after the solstice?

Primarily because of inertia.  This phenomenon is called seasonal lag.

It is true that the December solstice is the moment that the northern hemisphere gets the lowest total amount of insolation.  Conversely, the June solstice corresponds to the moment of maximum insolation.  The oceans, and to a lesser degree the land, absorb a lot of heat.  Due to the large heat capacity of water and the large amounts of water, the seasonal lag can be considerable.  In general, mid-latitude areas near large bodies of water have the largest seasonal lag, to the extent that the warmest month of the year in most of western Europe is August.

It is illustrated very well by this Warmest day of the Year map that NOAA NCDC (now NCEI) produced for the contiguous United States:

As expected, areas with a humid climate, such as southern Texas and nearby areas, tend to have the warmest day of the year in August.  The west coast is even more extreme, with some places having the warmest day in September.  Conversely, desert areas in the southwest (southern Arizona, New Mexico, western Texas) have the warmest day of the year in June.  For the Big Bend area in Texas, it's even in the first half of June, which must have entirely different reasons (probably related to dynamics) because a negative seasonal lag doesn't make much sense.
 There is a corresponding map for coldest day of the year:

(Source: NCEI)

The detailed structure is somewhat different, which has to due with local climate and circulation, but the overall trend related to humidity and proximity to ocean shows up in both.  We can also see the mountains, which I would guess to be a snow albedo feedback effect (ever notice how nights get colder when the ground is snow-covered?).  At NCEI you will also find similar maps for the rest of the USA.


Easy homework questions about seasons and daytime

The figure depicts the Northern hemisphere summer solstice, given that, there is no information missing:

At which width circle does the sun shines perpendicularly?

The one labeled "13 1/2 uur" that corresponds to the Tropic of Cancer

How long is a day south of the southpole circle?

If we understand "day" as the length of daytime, the answer is zero: The sun never rises that day south of the southern polar circle.

Which season starts at the southern hemisphere?

Winter


Why does climate change generate desertification?

Most arid and semi-arid regions are normally far inland. Often those also have terrain features that don't allow for the moist air to reach, such as mountain ranges, etc.

So now if global temperatures increase, the evaporation in semi-arid regions increase as well, reducing the amount of water available for plants. At the same time moisture coming from the ocean still precipitates as rain before reaching those regions.


Why are weather service atmospheric pressures systematically different from those I measure in Johannesburg?

They apply a correction to the actual barometer readings and report what the estimated pressure would be at sea level.

Basically they use an imaginary column of air between the barometer and sea level and add its weight to the pressure measured at the barometer.

This lets them make pressure maps instead of just almost altitude maps.

https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/pilot_handbook/media/PHAK%20-%20Chapter%2011.pdf

https://www.ec.gc.ca/manobs/default.asp?lang=En&n=4349ABDA-1


Why do loose, soft soils amplify earthquake vibrations rather than dampening them?

I think there are a few more options than bedrock/loose.  But I owned a house 3 miles from the San Andreas fault, and a geophysical engineer explained it to me like this after telling me earthquake insurance would be a waste of money.

The worst situation is landfill, like the Marina district in San Francisco that took much of the brunt of the 89 quake.  That is just loose sand and gravel, and when shaken it acts like a liquid - in fact, they call it liquefication.  The foundation shifts and sinks in it, like if you had a jar of sand and gravel and put a heavy rock on top and shook it.

However, if you are on bedrock - or something tightly bound above it (like Franciscan shale), you get all the shaking transmitted, but the earth stays in place under and around the foundation.

Earthquake damage can happen a few ways: from shaking up and down as well as sideways.  The Mendocino quake in the 90s (I think) had more side-to-side movement than ever seen before, and house held together but slid off their foundations.  After that they upped the degree to which house are bolted to the foundation to avoid lateral shifts.

I am not sure soft soil 'amplifies' the shaking.  There are a bunch of failure modes in buildings: they can come off the foundation; the foundation can shift and sink; the shaking can cause framing to collapse (which is why they put in shear walls); etc.

Incidentally, wood structures often do better because they can flex.  You'll never see a real brick house being built in a seismic zone anymore.

In the end, it is about making the building live through the accelerations, and the hardest thing to deal with is loose soil that itself moves and flows under the structure.


Is it possible that we can reduce climate change given our current actions?

Our current actions are most definitely not enough to reduce the rate of climate change.  Yes, it is possible that someday we could do enough to start reversing the damage, but we aren't anywhere close to that reality given our social customs that constantly rely on combustion.  Definitely not anything "soon".

The reality is that emissions still go up nearly every year.  This is largely because most of the world (especially China) is actively converting to "western" lifestyle, which uses a lot of resources per capita.  Also, it takes hundreds of years for CO2 to decrease in the atmosphere naturally.  So, while there are many efforts to reduce CO2 emissions, the amount of carbon in the atmosphere still goes up every year.  If we could somehow advance carbon sequestration methods to  the point where we can reduce both oceanic and atmospheric carbon, then we could theoretically get back to "normal".  To truly make a change in the right direction, though, the industrialized world needs to stop relying on combustion as the dominant energy source.  See the http://www.globalcarbonproject.org/carbonbudget/index.htm slides (excerpt below) for more information.

Emissions from fossil fuel use and industry:

And here is the atmospheric concentration as measured at Mauna Loa:


A planet has been theorized that forms in a primordial disk of high carbon content. See https://en.wikipedia.org/wiki/Carbon_planet. This planet's crust would have a high hydrocarbon content and thus not be very "solid". However, such a planet might theoretically have volcanoes that erupt diamonds, so an alien could build there home out of diamond!

Another hypothetical planet is a waterworld or ocean planet. If there is indigenous life then the only "above water surface" would be composed of life (ie: mats of algae type material floating on the sea).

As far as mountains go, this is not a question of solid or not solid. A large superearth would likely not have much in the way of mountains because of the high gravity at the surface. It might be noted that with out plate tectonics, we wouldn't have mountains and the Earth could arguably be covered in a global ocean.


Why is a mild earthquake often mistaken as dizziness or vertigo?

Having experienced many minor earthquakes (Mag 3 to 5 in the East African Rift Valley, Samoa, Solomon Islands, Philippines and Indonesia), and one major life-threatening earthquake (Magnitude 8, Nepal), I can make a few personal observations about physiological reactions.
First, You are quite correct about the body picking up any swaying feeling, and interpreting this as dizziness. I was in an 11th floor hotel room in Bangkok when an aftershock of the Aceh earthquake occurred. My first thought was "Did I drink too much beer this evening"? I wasn't alone. When I opened the door into the corridor, the occupants of nearly every room were looking out and wondering much the same thing.

Second, after experiencing a big one the body becomes hypersensitive - conditioned to pick up vibrations that could be the onset of a major quake. Now, at the onset of any vibration, my brain goes straight to "how big is it - should I run to the nearest exit"? This response is now much faster than the sensation of dizziness. Also I now pick up many vibrations that nobody else around me seems to notice.

Thirdly, I am not sure I agree with you about vertical motion being the trigger. It seems to me that lateral motion - moving one's feet sideways relative to the head, creates a slight imbalance, which the ears interpret as 'dizziness'.


Does dirt compact itself over time? If so, how does this happen?

Soil is a collection of various sized minerals grains, of various types of minerals produced by the weathering of rock. Typical soil minerals are clays, silts and sands.

The properties and behavior of different soil types depends of the composition of the soil: the proportion of clays, silts and sand in a soil. Sandy soils are well draining and clayey soils are sticky.

Between the grains of minerals that comprise a soil are spaces, called pores or pore spaces. The pores can be filled with either water or air, depending the location of water tables and wetting events like rain, snow melts or other forms of water inundation.

The density of a soil is dependent on the degree of compaction of the soil. For to a soil to be compacted, a stress has to be applied to the soil to realign the grains of soil which reduces the total volume of the pores and reduces the amount of air within the pores.

Consolidation of a soil occurs when pore space is reduced and water in a soil is displaced due to an applied stress.

Regarding having something buried and soil compacting around it over time, yes that will occur but it is a question of how much stress the soil experiences, the duration of time and the nature of the soil - sandy or clayey. Something buried for a day without any stresses not much will happen. But, something buried for thousands of years with people and animals walking over it, rain falling on the soil, vibrations from nearby human activity and an occasional earthquake all add to the stresses the soil will experience and increases the degree of compaction or consolidation over time.


Beside some unnecessary simplifications (like assuming the whole Earth is cover with water) The numbers looks right. IPCC predictions are between 0.3 and 0.8 meters by year 2100 for the most likely scenarios, and I find that perfectly consistent with your numbers.

Your calculation yields about 0.98 mm per year from glaciers, which using the actual surface of the sea (361,132,000 km$^2$), gives a more accurate value of 1.39 mm per year.

Look at the IPCC observations and models summarized on table 13.1 of the Chapter "Sea level Rise" of the Assesment Report 5:

For the latest period, if you add up all land ice contributions you get that they are between 0.87 and 2.05 mm/yr, totally consistent with your estimation (of ~1 mm).

The largest single contribution is thermal expansion with 0.8 to 1.4 mm/yr.

Also note that the observed contribution don't quite add up to the observed sea level rise, so we are either sub-estimating some contributions or ignoring significant ones.

If you multiply the current 3.2 mm/yr by 80 years you get ~26 cm by year 2100, but the point is that the rate of sea level rise is increasing (see this answer). That is why all predictions are above that value.

For future predictions, thermal expansion is still the leading cause of sea level rise, as you can see on figure 3.10 of the same IPCC report:

I find these predictions consistent with your numbers if you consider the current acceleration on the sea level rise rate. Unless you are talking of other predictions, not the IPCC ones. Or maybe you think that half a meter of sea level rise over 80 years is not much. If that's the case, I suggest you to research what would be the impacts in land loss, infrastructure loss and human populations displacements of such sea level rise.


The short answer is: BECAUSE THE ICE IS BLUE.
Now we have to explain why it seems perfectly transparent on ice cubes and industrial ice blocks.

It has to do with the fact that most transparent materials are not perfectly transparent, and instead absorb (and/or scatter) part of the light that hits them. And when the transparency is better for one specific color (wavelength), the material will look that color, much like how stained glass gives a tint to the white light going through it.

Now the important fact is that this "tint" effect is stronger the thicker the material is. Let's take a standard glass as a example: When looking through the glass it seems perfectly transparent, because the thickness is too small to make its color noticeable. However, if you look at the edge of the glass, it looks green, which shows that glass is indeed green, but that only became noticeable when looking through a section thick enough.

(Picture taken from peakglass.ca)

In the same way, glacier ice is blue, but that can only be appreciated if the piece of ice you are looking at is thick enough. We can see this effect in the following picture of an iceberg, where sections of different thicknesses displays a color gradient ranging from transparent to blue.

The remaining questions is: Why are glaciers not always blue? As we know, many icebergs (and snow) are white.

The key here is "bubbles". The reason is that for each ice/air interface, part of the light gets reflected and only a fraction goes through. Therefore the greater the number of bubbles a piece of ice has, the less light will be able to proceed deeper into the ice.  As such, when you view light from more bubbly ice, most of it will have traveled through less ice, and thus have had less distance to obtain the blue tint. I've made this figure to help understanding the idea:

On the left, a piece of ice with very few bubbles allows a longer travel path through the ice, inducing a marked blue tint in the outgoing light. On the right, in contrast, if there are many bubbles the light will go bounce back right away with only a very subtle tint, or no tint at all.

Snow is the extreme of this, because it is mostly air (bubbles), and only some small pieces of ice, that's why it looks so white.

An interesting ramification of this: those deep blue pieces of ice started as snow. But as the snow piles up, the weight of the snow on top compacts it, squeezing air out changing it from snow to firn until you finally reach the density of being a block of ice (with bubbles). In a big glacier, hundreds or thousands of meters of ice can exert such a pressure that the bubble spaces get compacted smaller and smaller until they disappear and the air is dissolved into the ice itself.
Therefore this means that the more blue (and bubble-less) a piece of ice is, the more it has come from deeper within the glacier... meaning it also has traveled from further up in the glacier basin and it is, therefore, older. So, now you can identify deep, old ice just by its color.

To give a more familiar example of how adding bubbles can turn something transparent with a tint into something white, take the case of egg whites, which are transparent with a yellowish tint. But as you whip it, adding in bubbles, it begins to turn into meringue which is perfectly white.

However, there is a trick that can even make the blue color of seemingly-white snow noticeable. If you let a ray of light bounce on it many times, each time it will travel through a little bit of ice, getting a bit of blue tint each time, and after enough bounces it will look unquestionably blue. That's what you see when looking at the entrance of a snow cave or a crevasse in a glacier. The light that comes from deeper in the cave has bounced many more times around the walls and becomes bluer:

(Picture taken from outdoorlifenorway.com)


How vertically deep do lava conduits go?

As mentioned in the comments, lave caves and tubes are surface features. You get a lava tube when there's a lava flow and the external part in contact with air (or water) cools down and solidifies while the interior is still flowing. National Geographic made an excellent feature on it, all with diagrams and photos and stuff.

Why do these tubes not go far deeper?

Because lavas are liquid, and they flow downwards. If there's a hole that goes deep, the lava will fill it. It's possible to explosively eject lava out of a hole (as commonly happens), but these are violent events that will cause the collapse of the conduits, forming breccia pipes, with collapsed calderas.

I think of magma - liquefied hot rock erupting out of volcanoes - as coming from even deeper than that depth
...terminating at the threshold of the asthenosphere?

Let me clear a common misconception here: there is no magma ocean in the interior of the Earth. There is no large reservoir of magma in the deep earth, and volcanoes are not just holes through which this (non existent) magma is coming out. Both the crust and the mantle are essentially solid rock. The asthenosphere is solid rock.
Melting is an uncommon occurrence in the Earth's crust and mantle. It needs exceptional circumstances to happen, which mostly happen above subduction zones (i.e. the Pacific Ring of Fire) or above hotspots (East Africa, Hawaii, Yellowstone). The erupting magma can come from anywhere that's as shallow as less than a kilometre below the surface (which can be above sealevel if you're on a high volcano) to several tens of kilometres. Very rarely these magmas come directly from asthenospheric depths. These magma chambers can have complex plumbing systems beneath them and all sorts of morphologies of feeders.


Obtaining hourly weather data, including direct and diffuse insolation

If reanalysis data (ERA, ECMWF, CSFRR) is too aggregate for you, try looking for the datasets used to calibrate photovoltaics models (PVGIS, PVWATTS and the like) - they include both direct and diffuse insolation.

Also, follow the citation trail for papers that describe the calibration of the PV models, and the reanalysis models - some of the datasets you are seeking will be somewhere in that trail.

Barry Carter has pointed you at the NOAA ISD-Lite dataset, and I'd like to extend that pointer to the whole Integrated Surface Data from NOAA, which is enormous: 20,000 global stations. Because it's an amalgamation of many different sources, they don't all share the same metadata, but this pdf lists the breadth of the metadata: the insolation variables are on pages 64-77.


Yearly changes of solar irradiation and atmospheric feedback

I think your ~2 figure for CO2 greenhouse amplification is in error.
* In the last 200 years it's gone from the high 280s to low 400s.  This is an increase of about 50%  Good thing it's not linear as the previous greenhouse effect is overall about 18K.  If there was no effect, the earth would average about 0 C.
* As CO2 increases it takes more bounces for an infrared photon to escape.  But you get some degree of diminishing returns.  Doubling the CO2 doesn't double the greenhouse effect.

But to your question.

Right now we have about 1 degree of additional greenhouse effect.  Compared to the 18 degrees of existing greenhouse effect this is about 5%.

I would expect that this is the factor to use.  So the eccentricity amplification should be about 5%  So 5.25K instead of 5.  or observationally 1.05 * 3.8K


What would be the predicted/calculated ages using several samples of soil with the help of carbon 14 test?

Radiocarbon dating cannot be used to date rocks or lava, only organisms that absorbed carbon from the atmosphere in the last 50'000 years or so.

The older the samples, the more difficult it is to get an accurate age because the amount of 14C remaining becomes close to zero and thus the more likely it is that a few atoms of 14C from sample handling or atmospheric exposure may significantly change the number. That is why, for instance, coal contains trace amounts of 14C.

More generally, sample age does not always correlate with sample depth and it is strongly dependent on the geological setting. In a sedimentary basin, deeper rocks are older than shallower rocks but tectonic activity such as thrust faults and folds can upset this relationship.

In granitic and metamorphic terranes, there is no general correlation of age with depth, because granites intrude into older rocks


Is there any animation to demonstrate if the sea level rise up?

There is this NASA animation showing 12-13 years between 2002 and 2015. It is interesting for showing the counter-intuitive lowering of sea levels nearest to land based ice mass losses, especially around Greenland and Pacific Alaska. This is due to local gravitational effects, ie less ice mass reduces the pull on ocean water near where the ice melts, so water levels actually fall in such places, whilst places furthest from them experience the greatest sea level rise.

(Any tips for embedding this video?)

https://youtu.be/VY_SeZiBcM4


Are there known ore deposits under cities?

One example of an ore deposit that runs under a city is the banded iron formation ore in Kiruna. In this case the ore has been mined outside of the city since the turn of the previous century. The ore has been found to run under the city and there are now plans to move the city more detailed information. This has led to a process where the city has to be re-established in a different location including moving a large number of historically significant buildings.

A similar situation is also present in Malmberget (about 120 km S of Kiruna), part of the twin town of Gällivare-Malmberget. In this case the plan is to have Malmberget inhabitants to move to Gällivare. The mining activities at Malmberget have resulted in several collapse features see images on this link. There is also some information in English on the Gällivare web-site.

In both cases there are significant restructuring of the societies. It is also worth noting that the definition of ore is economical which means that what is worth mining depends on market prices. In the case of Iron the market has been strong but has fluctuated significantly. The result is that the planning and decisions for a move such as these  are difficult since they are costly and depend on the market to be financially viable (it is the mining company that largely pays for the move).


As @kwinkunks and @Gordon Stanger say, it's not possible to comment usefully on your particular observation without at least a picture and further information about the site. However, if you're asking “Is this even possible?” as a general question, the answer's yes, but under special circumstances. As an example, picture a scene in ancient East Africa: some individuals made their way across a layer of volcanic ash on the ground, leaving footprints in the process. Whether the ash was already wet or later rainfall fell on a dry ash layer (light enough not to destroy the evidence), the wet ash hardened and the footprints were buried under more ash fall - the “Laetoli” footprint tracks, discovered in Tanzania in the 1970s by Mary Leakey and her team, are remarkable evidence of bipedalism in our ancestors of ~3.7 million years ago.

References:

https://en.wikipedia.org/wiki/Laetoli

http://www.sciencedaily.com/releases/2011/07/110719194356.htm


Estimated volume, daily or annually, of sea level rise due to melting ice?

I don't know if this helps, but since you have no response yet perhaps I can offer some thoughts.Your question is problematic due to the fact that volume itself is variable according to the temperature of the water. If you look at the Nasa site concerning sea level change:

  Sea level rise is caused primarily by two factors related to global
  warming: the added water from melting ice sheets and glaciers and the
  expansion of sea water as it warms.

(some nice graphics here showing change amounts)

This expansion due to warming literally changes the volume of the water, adding to the sea level rise. So glacial melt may be measured or estimated, but the change in sea level caused by this volume of water is variable; over time it will change temperature and expand. But this isn't straightforward either. Nasa again:

  Thermal expansion of seawater can be the product of regional
  phenomena, such as El Niño, the periodic warming of the eastern
  tropical Pacific. But some of these regional cycles so far show no
  direct link to long-term global climate change—despite, at times,
  independently exerting a powerful short-term influence on global
  climate.

So bottom line is that it is easier to measure the amount of change, then to calculate direct figures concerning how much actual water was involved in causing that change. Hope this helped.

Update: There is some specific data on another page of the Nasa site concerning the volume of water being generated by the melt of the Greenland Ice Sheet:

  The estimated total loss is in the range of more than 200 to more than
  300 gigatons per year (1 gigaton is approximately 264 billion gallons
  of water. Melting 365 gigatons of ice would add 1 millimeter to global
  sea level; there are 25.4 millimeters in an inch).

This does give you some approximations in gallons per year of one of the main contributors to the sea level rise.


All numerical atmospheric models are built around calculations derived from primitive equations that describe atmospheric flow. Vilhelm Bjerknes discovered the relationships and thereby became the father of numerical weather prediction. Conceptually, the equations can be thought of as describing how a parcel of air would move in relationship to its surroundings. For instance, we learn at a young age that hot air rises. The hydrostatic vertical momentum equation explains why and quantifies under what condictions hot air would stop rising. (As the air rises it expands and cools until it reaches hydrostatic equilibrium.) The other equations consider other types of motion and heat transfer.

Unfortunately, the equations are nonlinear, which means that you can't simply plug in a few numbers and get useful results. Instead, weather models are simulations which divide the atmosphere into three-dimensional grids and calculate how matter and energy will flow from one cube of space into another during discrete time increments. Actual atmospheric flow is continuous, not discrete, so by necessity the models are approximations. Different models make different approximations appropriate to their specific purpose.

Numerical models have been improving over time for several reasons:

More and better input data,
Tighter grids, and
Better approximations.

Increasing computational power has allowed models to use smaller grid boxes. However, the number of computations increases exponentially with the number of boxes and the process suffers diminishing returns. On the input end of things, more and better sensors improve the accuracy of the initial conditions of the model. Synoptic scale and mesoscale models take input from General Circulation Models, which helps set reasonable intial conditions. On the output end, Model Output Statistics do a remarkable job of estimating local weather by comparing the current model state with historical data of times when the model showed similar results.  Finally, ensemble models take the output of several models as input and produce a range of possibly outcomes.