Relation between fault rupture aspect ratio and slip rate?

Ok, so this is a somewhat complicated question, and while this isn't a full answer I think I may be able to help you find the right direction.

It sounds like you are doing a completely theoretical study, so in this case I would advise you to look at Fault Maximum Displacement vs Fault Length Ratios (commonly referred to as D/L in te tectonics community). Here is an older but good study on D/L ratios: ftp://ftp.gps.caltech.edu/pub/avouac/OwensValley/Dawers-Geology-1993.pdf

You will have to make some assumptions based on the type of faulting that occurs in your model.

I found a observational study on D/L ratios and slip rate: http://www.sciencedirect.com/science/article/pii/S0191814101000360

Which seems to be a well cited article on the subject. It seems there is some correlation, but perhaps it is different depending on the area. I know that Mars, Earth, and Icy Moons around Jupiter/Saturn all have different average D/L ratio which is directly correlated to the strain rates and material properties. Slip rate should have a similar, if not identical correlation (though slip is usually calculated on the surface where strain is often subsurface from my understanding).

What software are you using to model this fault surface? Is it a homebrew or is it a community code? I realize you might need to be a little secretive about what you are researching when posting on the internet, but a little more information might or might not go a long way in helping people provide a better answer.

Hopefully this helped.


Confirmation of historical El Niño events

The best article about the 1789-1793 El Niño is probably Grove (1998) Nature study. There is also a lot more information in Grove's 2007 paper. In the second paper, he explores the global consequences of the El Niño event (some evidence is mostly circumstantial), which he describes as being quite severe: famine ("By November 1792 over 600,000 deaths were being attributed directly to the prolonged droughts"), revolution (French Revolution), economic hardship...
He provides rainfall and temperature records and many historical reports as evidence of the conditions.

  While further archival research is needed to more fully characterise the 1789–93 event, the evidence of a strong global impact already indicates that it was one of the most severe El Niños recorded.

In El Nino History and Crisis Grove talks of the idea of a Mega Niño in relation to the continuous series of El Niño events that occurred during the period 1788-93.

  In terms of severity,the Indian droughts of 1788-1793 surpassed anything
  that  had  occurred  since  the  events  of  1685-88,  and  stand  out  as  having  both an unusually long duration and extraordinarily wide effects,   within and beyond  India. Indian  droughts  that  co-occurred  with  El  Ninos  in  the  interim, in   1701-2,   1707-9,   1737   and   1783,   while   serious,   did   not   approach the ferocity  of  the  years 1685-1687  in  southeast  India and  it  was  not  until  1788—
  1793  that  a  comparable  series  of  extreme  events  took  place.


What started the US Dust Bowl of the 1930s, and could it happen again?

The Dustbowl occurred during the 1930s because of a combination of man-induced drought and the (mis)use of relatively new farming practices.

In the 1920s, the spread of automotive (and tractor) technologies made it possible to "plow up" the Great Plains. This resulted in the loss of a lot of natural moisture and the creation of drought conditions in lands that had been marginal to begin with regarding the adequacy of the water supply.

Even by the 1930s we still had not learned our lesson. There were conservation techniques using the new technologies, but we weren't using them. For example, the tractors would still plow up and down slopes (the "easy" way) making it easy for topsoil to run down hills and into the rivers. More to the point, the newly dry and loosened topsoil would then go into the air and create a "Dust Bowl" when the winds kicked up. There was a real fear that the agricultural Midwest (basically the Plains states) would turn into a desert.

It was only after an additional half a decade of bitter trial and error (and a new generation of better educated farmers) that things changed. By the mid 1930s, it was a relatively new technique called contour farming, which consisted of using motor vehicles to plow horizontally around hills instead of vertically, that saved the day. Also, farmers started planting trees as "windbreaks" in strategic locations.

IMHO, it could happen again, probably in a developing country like China, which is trying to "catch up" to the United States, and has been prone to adopting our bad habits of an earlier era.

Bottom line, the Dust Bowl was (largely) a man-made, not a natural phenomenon. And the operative principle was attributed to Confucius:

  "Men are the same everywhere. Only their habits are different."


How does the pole-to-equator temperature gradient scale with height contours?

It depends on the season. The figures below shows zonal mean temperature for June-July-August from ECMWF ERA-40 reanalysis.  As you can see, at 100 hPa, the equator is actually colder than the sunlit hemisphere.

June-July-August

December-January-February

For getting the "facts" on this kind of questions, the ECMWF ERA-40 atlas is a good source.  Now as to why this is the case; that is a much more involved question on atmospheric dynamics and circulation.  The Earth heats the surface, in particular where it's sunlit.  It also heats the spring and summer stratosphere, where ozone absorbs solar radiation.  Heating causes air to rise from the surface to the tropopause, where it's forced poleward creating a Hadley cell.  Meanwhile, the Earth rotates and everything becomes a highly chaotic and dynamical system.  So the fact that winds are strongest near the tropopause (see, for example, DJF winds) is not a direct consequence of where the heating occurs, but rather the effect of a lot of dynamics.

For further reading on why atmospheric circulation is as it is, one needs to study textbooks.  Some famous textbooks on dynamic meteorology and atmospheric science are:

James Holton, An Introduction to Dynamic Meteorology
Wallace & Hobbs, Atmospheric Science: An Introductory Survey


What's the distance between the center of mass and geometrical center of Earth (CM-CF offset)?

There is no inconsistency between the 2012 paper and the older reference(s).

Fig. 2 arbitrarily sets all the components (x,y,z) of all the displacement vectors of all the centers to zero at the beginning of the time period (about 123,000 years ago).

Furthermore the 2012 article states:

  The horizontal movement of
  topography associated with plate motion will then change the CF.
  Over time, these slow phenomena can create large offsets, up to
  hundreds of meters, between CM and CF. When the evolution of
  the internal load is reasonably inferred from other sources, then
  these processes may be able to explain a significant bulk of the current
  static offset between CM and CF.

Planetary Sciences, table 1.2, says the distance between CF and CM is 0.80 km, citing to Yoder 1995.

See also Evidence for convection in planetary interiors from first-order topography The Moon March 1973, Volume 7, pages 172-180

  It has been known for some time
  that a center of mass-center of figure offset exists for the Earth (e.g. Jeffreys, 1962).
  From a spherical harmonic analysis of the Earth's topography with the oceans replaced
  by an equivalent mass of rock, Balmino et al. (1972) find the center of mass
  displaced by 1.1 km from the center of figure in the direction 145°W long and 42 ° S lat.

And from the NASA memorandum Reports of planetary geology program - 1981:

  For Earth, with its combination of sialic ([denisty]~2.7) and simatic ([density] 3.0-3.3) crusts, the CF is displaced toward 41.6°N, 34.7°E, in the direction of the Eurasian shield, and close to the center of the continental province at 46°N and 27°E (Bills and Ferrari, 1978).

See also Geocenter - Degree 1 :

  The spherical harmonic coefficients of degree 1 represent the distance between the center of mass of the Earth and its 'center of figure', which in practice is the center of a set of tracking stations on the surface of the Earth. Because of their physical meaning, time changes in degree 1 coefficients can be expressed in several equivalent forms (1) as distances in mm along the Z (along the axis of rotation), X and Y axes; (2) as (fully normalized) coefficients of the geopotential; (3) as the changes in mass (per unit area) that would give rise to the geopotential coefficients, expressed either in kg/m^2 or cm of equivalent water thickness.  The relation between these forms can be found in Swenson et al (2008), equations 5 and 4...

And Planetary Surface Processes (2011):

  In fact, the Earth itself has a substantial center of mass – center of figure offset if the water filling the ocean basins is neglected. The floor of the Pacific Ocean is about 5 km below sea level, whereas the opposite hemisphere is dominated by the continental ... The waterless Earth's center of figure is thus offset from its center of mass by about 2.5 km at the present time.


What is the effect of sea-level changes on the extent of the Earth's atmosphere?

90% of earths atmosphere is from 0-10000m this means an increase of 0,001%.

But this is wrong the melting ice will be replaced by air so there will not be any change in volume.

Ice have a larger volume than water have so the result will be a very slight drop in air volume.

I have not taken hight for air under pressure in the ice here but you get the point,You are only redistributing material on our planet so nothing is added or removed from the system.


Is there a standard definition of the term "mountain"?

There does not appear to be an agreed international definition of a mountain.

In the UK there is a colloquial definition that a mountain must be "a thousand feet high". This definition is sufficiently firmly established in a "folklore" sense that the 1995 film "The Englishman Who Went Up a Hill But Came Down a Mountain" centred around it for its plot, and this plot is allegedly based on an older story in the region.

According to the UK's Ordnance Survey,

  There is no precise international definition of a mountain... However,
  it is generally agreed that the minimum height is 610 metres (2 000
  feet). (Source)

This definition does not make clear whether a 2000' rise from the surroundings is required, or whether a peak must simply be 2000' above sea level.


How could this pyramidal Mountain have been formed?

Such forms tend to be created by glacial activity, which, ahem, the ice-covered continent is known for. Much discussion of this in the related question in Skeptics: Are there three pyramids in Antarctica?

Here's the generic answer in Wikipedia:

  A pyramidal peak, sometimes in its most extreme form called a glacial
  horn, is an angular, sharply pointed mountain peak which results from
  the cirque erosion due to multiple glaciers diverging from a central
  point. It may be an example of a nunatak.

Here's a diagram of the formation process posted on Ace Geography:

Not knowing the specifics of the featured peak, as I understand it there are two general mechanisms of glacial erosion that apply:

Assume we begin with some sort of mounded terrain, or a relatively small protrusion on a larger continental surface like Antarctica. In a very cold environment, precipitation will fall as snow, mound up, and turn into ice. Generally, more ice will form on whatever side of the mound that is sheltered from sunlight (north slopes in the northern hemisphere, south slopes in the southern. Eventually the ice will move under its own weight, abrading the surface as it goes in a manner that will tend to exaggerate the original geometry of the mound. If the mound starts with or develops a slight dip in the slope, ice flowing off the back and side walls will dig a cirque or bowl. Depending on the starting conditions, your mound may develop several cirques; as ice grinds away at the lower elevations, you may wind up with a central, relatively slender peak with several ridges and valleys.
A second mechanism is having a glacier coming down a broader slope and cutting through an existing ridge. (Your ridgeline may begin with a triangular cross-section, or may have developed one from the glacial processes mentioned above.) At some point, ice from a higher elevation will flow across or through your ridgeline (just as a river would), eroding a gorge through the ridge.

Inevitably, given enough material to work from, and even with a relatively smooth starting surface, the erosive power of ice will give you steep slopes and some pyramidal structures.


Centrifugal Force in the Navier Stokes Equations

Based on the state of the discussion in the comments I was not sure whether this has an answer now, but I stumbled over it, and I think I can give a short answer from which one can learn a lot.

I'll base my discussion on polar $(\rho,\phi)$ coordinates, for the sake of clarity. In classical mechanics we use for the position vector $$\vec r= r \vec{e}_r = r \; (\cos\phi, \sin\phi),$$ because $\dot{\vec{e}}_r = \dot{\phi} \; (-\sin\phi, \cos\phi) = \dot{\phi} \; \vec{e}_{\phi}$. In 3D spherical coordinates, we need a few more of those identities, but the algebra remains the same. From this follows $$\dot{\vec r}=\dot{r}\vec{e}_r + r\dot{\phi}\vec{e}_{\phi} $$ and finally
$$\ddot{\vec r}=(\ddot{r}-r \dot{\phi}^2)\vec{e}_r + (r\ddot{\phi} + 2\dot{r} \dot{\phi})\vec{e}_{\phi} $$
where we have already taken into account the change of coordinates, as well as unit vectors.
The next step would decompose $\dot\phi$ as $\dot\phi = \Omega + u/r$, whereas $$r\dot\phi^2 = r\Omega^2 + 2\Omega u + u^2/r$$
where we identify (in order of the terms) 1.) the centrifugal term, 2.) the coriolis term and 3.) the "curvature/metric" term. This procedure works wonderfully also in spherical coordinates and one recovers perfectly the terms that i.e. Holton or Vallis get in their books via lengthy and opaque 'proof-by-picture' methods.

I'm saying the latter because now I draw conclusions for the complete equations, from my derivations which was done from the incomplete ones:
Conclusions:

Centrifugal terms are not what meteorologists call 'curvature/metric' terms. They can seem the same, if one is sloppy and writes $\Omega=vr$. Or what is often done is in order to calculate the orbit of a satellite to set centrifugal force and gravity equal, whereas one uses $u^2/r$, which is in fact the 'curvature' not the centrifugal term. Also the physically metric term is already $r\dot{\phi}^2$, as this one arises from having a curved coordinate system.
As pointed out in the comments, the centrifugal term $r\Omega^2$ is customarily hidden in meteorology with the gravity. We would suspect this happens also in your set, because the Coriolis term appears, which hints that the above computation has been carried out to first order and thus the centrifugal term must float around somewhere.
The curvature terms are nowhere to be found in your set of equations. This is probably due to the terms simply being neglected. Also when viewn in their full form in spherical coordinates, they seem quite messy and I didn't find any convenient way of expressing them through a nice vector-or matrix operation. Therefore I strongly suspect, that people when giving the vectorial form of the NS equations usually neglect them, and only add them when presenting the NS equations in component form.
The above minimalistic derivation makes it clear that the curvature, centrifugal and Coriolis terms originate from having a curved coordinate system. Any curved coordinate system is necessarily non-inertial. Thus in Cartesian coordinates, which are inertial, those terms must necessarily vanish.


Where does the 2015 Nepal earthquake rank amongst earthquakes since 1900?

About 80th.

I counted the earthquakes of each magnitude on the List of deadly earthquakes... article. If the Nepal earthquake is about M7.8, then it's in the range 69th to 86th on that list:

Note that there are more earthquakes than this in recent history, the list has already selected for deadliness. Also note the point in the comments about different magnitude measures in the list, and the fact that the list is a few years out of date. I don't think these things change the answer.


Name of majorite endmember $\ce{Mg3(FeSi)Si3O12}$

Yes, it's called (unsuprisingly) majorite.
This is an IMA-approved name, first described from a meteorite.

More information: https://www.mindat.org/min-2546.html


Are the oceans rising or the continents going down? How can we know?

To the best of our knowledge, sea-level is rising because the volume of water is increasing.

There is substantial local variation in sea-level change; it's falling in some parts of Canada. But of the dozens of controls on local and global sea-level, the net effect is currently an average global rise of about 3 mm/y. It's not really 'a riddle'. The phenomenon is well documented and there isn't too much mystery about the various causes. One could certainly debate their relative contributions.

Satellites already contribute much of the data that reveals the sea-level rise (and the relative stasis of the continents), and that substantiates some of the causes. For example, the TOPEX and Jason-2 satellites, constrained by gauges on earth, are important sources of data.

Two prominent causes of sea-level rise are thermal expansion and ice loss (for example in Greenland), but there are lots of others. Tectonic plates do definitely move up and down — it's an important phenomenon in geology and geomorphology, and it does affect sea-level in all sorts of ways (see that link).


Who would know how to manage rainwater erosion on a sloped property?

Erosion:

Establishing a deep rooted vegetation may help.  What would work best
is dependent on where you live.  Your local conservation office would
be able to help with what would work best in your area.  This
site has some good information for choosing plants on slopes.
Rip-rap (rock) is also commonly used to help slow erosion.  The size
you would need would depend on the slope and flow of a the drainage,
if it would be within a drainage area.

Source: http://www.erosioncontrolnetwork.com/rip-rap/rip-rap.aspx
Another option would be gabion baskets, however they would be one of
the most expensive options.  Gabion baskets often look like chain
link fencing wrapped around rock.  In this way the rocks stay in
place and the can be placed in a more vertical position.

Source: http://www.svca.on.ca/page.php?page=erosionandfloodcontrol

Flash Flooding:

The first thing I would do is establish who is responsible for maintenance of the ditch.  The capacity may need to be re-established or increased if run-off from additional developments have been added to it.  If increasing the capacity of the ditch is not an option, I would see if I could construct either berms (a slight rise in topography) or swales (a minor trough in topography) to direct the water away from any structures on my property.  However, you would need to make sure that you are not increasing flow onto any other neighboring properties or impeding flow from any other properties.

Ponding:

Dry wells are often used to address ponding in yards.  They are
basically an underground chamber that water is directly to through
pipes.  Holes in the container let water slowly soak back into the
surrounding soils.  These need to be sized properly to accommodate
the volume of water one is trying to remove from the surface of their
yard.  Also, these may not work well in clay soils that the water
would percolate slowly into.  More information can be found at the
source link below.

Source: http://www.svca.on.ca/page.php?page=erosionandfloodcontrol
Rain gardens are a more decorative option that includes water storage
in a depression, water infiltration,and native vegetation. The basic
idea of a rain garden is captured in the image below.  Additional
helpful information can be found here.  Some municipalities may
also have funds available for installing rain gardens on private
property.

Source:
http://vienna-wv.com/portal/2013/07/18/what-is-a-a-rain-garden/

Again, I would definitely contact the local jurisdictional authority before I do anything.  There are many government agencies that have codes that need to be met.  Additionally, they would know what works best in your area and may have subsidies that would help defray costs.


Why is there a seasonal cycle to the amount of CO2 in the atmosphere?

Overall, the measured amount of $\mathrm{CO}_2$ increases, but in a cyclic pattern, as can be seen in observations shown below:

Image source: NOAA: Trends in Atmospheric Carbon Dioxide (numerous observation data sets and graphs are available from that website)

The fluctuations are seasonal, which is explained in the web page Seasonal carbon dioxide range expanding as more is added to Earth's atmosphere (NSF, 2013) summarises the seasonality as being

  Levels of carbon dioxide in the atmosphere rise and fall each year as
  plants, through photosynthesis and respiration, take up the gas in
  spring and summer, and release it in fall and winter. Now the range of
  that cycle is expanding as more carbon dioxide is emitted from burning
  fossil fuels and other human activities.

Specifically, the effect is more pronounced in the northern hemisphere, with

  more carbon is accumulating in forests and other vegetation and soils in the Northern Hemisphere during the summer, and more carbon is being released in the fall and winter

Daily as well as seasonal variations were observed in northern Japan, reported in the article Diurnal and seasonal variations in atmospheric $\mathrm{CO}_2$ in Sapporo, Japan:
Anthropogenic sources and biogenic sinks (Miyaoka et al. 2007).


Why are the seas difficult to navigate at the "southern edge" of land?

Fetch.  The longer the wind has to act on the water the larger and more developed the waves become, see this site from the NOAA.  If you look at the southern portion of our planet you will note that there are few land masses to affect the wind or the wave development.  In the Wikipedia entry about prevailing winds you can see that the Southern Westerly winds are only affected by the Cape of Good Hope, Cape Horn, and to a lesser extent Australia.  Contrast this to the Northern hemisphere where North America, Europe and Asia divide the seas into smaller isolated sections.

There are additional factors involved particularly around the capes.  If you look at the prevailing ocean currents, see global map on this site you will see there are strong currents, driven by the wind, around the southern pole region.  At the capes, these currents become more chaotic and lead to eddies.  Sometimes the eddies make the current flow against the wind.  This results in even larger and less predictable sea states.


Extraterrestrial Planetary Sky Color: does it have to be blue?

Not necessarily blue, although pure nitrogen, ozone, methane and hydrogen- cyanide  all appear as various shades of blue (assuming the incoming starlight is white). Nitrogen dioxide would be a deep brownish red. Some organics and chlorine dioxide are yellow, whilst chlorine is yellowish green. There are many other coloured gasses, but they are not likely to form planetary atmospheres. However, the question implies vegetation, and hence Earth-like photosynthesis, in which case it also implies an Earth-like atmosphere, in which case a normally pale-blue sky is inevitable.


How do climatologists define the "start" of a rainy season in a unimodal monsoonal climate?

I find the following method very straightforward and elegant. So maybe I can convince you to consider it.

For the South American (SA) monsoon, Silva et al. (2007) and Carvalho et al. (2012) proposed the Long-scale South American Monsoon Index (LISAM), based on the annual cycle of some fields.

For the 2012 paper, where several precipitation datasets are used to calculate what you want, the methodology is as follows:

Compute the empirical orthogonal function (EOF) of a precipitation gridded data on land over SA. (There are some details as weigth by latitude, you may want to do combined EOF etc etc... but the essence of the idea is the same). Note that EOF is computed on raw precipitation, not anomalies.
The first EOF represents the annual (seasonal) cycle of the monsoon. The First PC (PC1) shows it clearly (Figure 2 in Silva et al. 2007)

At last, having the time series of PC1, you can determine:

Start (onset): the day in which PC1 turns positive.
End (demise): the day in which PC1 turns negative.

Further detailes are given in the cited papers. Hope it helps.


Where to find an accurate Mercator Projection world image?

So here is the way I do that personnally with NaturalEarth data and R (but you can do something similar i m assuming with any programming language that can deal with GIS or any GIS software):

Fist download and unzip the file:

download.file("http://www.naturalearthdata.com/http//www.naturalearthdata.com/download/10m/physical/ne_10m_coastline.zip", "10m_coast.zip")
unzip("10m_coast.zip")

Then reads in the shapefile:

library(rgdal)
library(maptools)
a <- readShapeSpatial("ne_10m_coastline.shp",CRS("+proj=latlon +ellps=GRS80"))

Then project it:

a_merc <- spTransform(a,CRS("+proj=merc +ellps=GRS80"))

And plot it:

pdf(w=20,h=20,file="merc.pdf")
par(mar=c(0,0,0,0))
plot(a_merc,asp=1,xaxs="i",yaxs="i")
dev.off()

This is a very minimalist example of course, it only draws the coastlines (as a line by opposition to drawing the continents as polygons, that would allow a more advanced colouring scheme but the projection to mercator of polygons is more complex, as Antarctica creates problems).


Looking for fun and illuminating weather visualizations

Try Windy.com  It looks very similar to the EarthWindMap, but appears to offer more controls.  It is simple to change the heights and what variables are of interest.


Does the snow come from local moisture or transported moisture?

It comes from nearby bodies of water, such as the ocean.

Precipitation of any kind (in this case snow) comes from water that is evaporated from bodies of water like lakes or oceans nearby due to heat (usually not far from where it's going to precipitate). The evaporation forms clouds, which move a certain distance (depending on the cloud, cloud type, and atmosphere temperature and/or conditions) across the globe. Eventually, the vapor in the clouds condenses into rain after cooling enough to do so; thus, creating precipitation.

Even though only half of the water cycle is explained in my first paragraph, the other half is not needed to answer the question. If you wish to learn more about the water cycle, please visit this link.

So to answer your question, a little bit of precipitation is from the atmosphere, but most of it is from water that has been evaporated from bodies of water nearby. And in the scenario you've mentioned, the moisture most likely came from the Atlantic Ocean.

  So the real answer is kinda both :/

The moisture comes from nearby water bodies, and then it's transported to where it's going to precipitate. It is local and transported moisture.

Sources:

Worldbuilding SE (convenient)
Rookie Parenting Science (same link as shown in second paragraph)
Google search for Atlantic Ocean (and I guess all the links on that google search too)


What is the definition of "ground-up shell"?

I'm not sure this is the best place to ask.

Ground-up shell means just that - shells that have been ground (reduced to small particles or powder by crushing it).

Shell tempering is one of the hallmarks of Mississippian cultural practices. It is often characterized by the adoption and use of riverine, usually mussel shells, (or more rarely marine) shell-tempering agents in the clay paste.

Read more here: https://www.revolvy.com/main/index.php?s=Shell%20tempered%20pottery&item_type=topic


How/where is randomness/stochasticity used in weather prediction

Probability is used in weather forecasting. I will only highlight some examples due to my lack of knowledge in some areas.
Before initializing a forecast model the data needs to be assimilated. That means we need to somehow put measurements from ground based stations, satellites etc. into the model and fit this data to the grid. We then have an "atmospheric state estimate". This usually involves the minimization of cost functions. Typically the uncertainty of this "atmospheric state estimate" is used in the process of ensemble forecasting. An introduction to data assimilation can be found here at ECMWF. Every operational weather forecasting model has to do this data assimilation process. Since you specifically asked for names, here are a few: Global Forecasting System (GFS, probably the model you weather app uses), ECMWF model (European Center for Medium Range Weather Forecasts), Icosaheadral Nonhydrostatic Model (ICON, operational model of german weather service),High Resolution Local Area Modelling for numerical weather prediction (HIRLAM, operational model of some Scandinavian countries).
In an ensemble forecast the equations are solved as you stated in the question. However, there are certain aspects of the model that are varied to account for uncertainties. These aspects can include the initial conditions (including time, sometimes time-lag is used), variations of parameterizations (and there are a lot of them, basically for every process that can not be resolved by the model grid) and sometimes even multi-model ensembles. The model is then initiated many times to obtain multiple and different forecasts. Again, there is a nice introduction at ECMWF. Some ideas on how to visualize ensemble forecasts can be found here.
All of the above focussed on probability in the course of initializing a model. However, even if no ensemble is used and if we'd know the state of the atmosphere without error - we'd still have to rely on probability due to sub grid scale processes. A prominent example is cloud cover. Suppose we have a mean humidity $q$ in a grid cell (which is what the model gives us). Clouds will only form if $q > q_s$, where $q_s$ is the saturation humidity. Depending on other parameters like temperature a probability density function $Q(T,...)$ is assumed. A possible parameterization for cloud cover could be that the fraction of $Q(T,...)$ larger than $q_s$ defines cloud cover. I will not give examples for typical distributions used, since this is an active area of research. Once more I'd like to refer to ECMWF if you wish to see some details and examples of pdf's used.
Finally, I'd like to add that a main source of uncertainty in models (there is not necessarily probability used) is the parameterization of of convection (shallow and deep). Precipitation is highly related to humidity and convection and therefore large errors are often the result of parameterization.
I hope this helps somewhat.
Edit: Regarding the precipitation problem. What you see at google or the typical weather app is based on model simulations but most certainly not a model output. If google tells you "30% rain probability at your place" then this will most likely refer to a 30% chance that precipitation in an (by google unspecified) area exceeds a certain threshold. The certainty is
is generated by looking at the ensemble. The threshold is exceeded in 30% of the simulations. This is also the reason why a high resolution model is less accurate. It is easier to predict that it's raining 0.1 l somewhere in New York tomorrow than to predict that it rains 0.1 l in the central park tomorrow.


Fundamentally your reasoning is flawed because the major composition of the atmosphere is nitrogen and oxygen.  "Pumping a few parts-per-million" of some other gas into the atmosphere won't do anything to the relative contribution of GHGs to global warming.  GHG's contributions will still be felt the same, regardless of the presence of any other gas.  The "anti-greenhouse gas" that you refer does not exist.  All gases scatter and absorb different wavelengths of light in unique ways, and this all varies by temperature. However, no gas destroys light energy.  A realistic answer is to increase clouds and aerosols, which will reflect more energy back to space before it can be absorbed by the Earth's surface.

Humans now account for the majority of greenhouse gases in our atmosphere.  Regardless if we shut off all our GHG emissions, our climate will still be warm for at least the next century.  Realistic solutions to reduce climate warming include:

grow massive tree farms; increase algae production and forest cover.
stop emission sources
cover disturbed and urban surfaces (and rooftops) in reflective color/material
cloud-seeding (which can also increase snow-cover)
Injecting aerosols/particles into the stratosphere to mimic a major volcanic event


Why does haze and poor visibility present in stable air?

Traditionally, haze has been regarded as,

  an atmospheric phenomenon in which dust, smoke, and other dry particulates obscure the clarity of the sky...

  Sources for haze particles include farming (ploughing in dry weather), traffic, industry, and wildfires...

  Whereas haze often is thought of as a phenomenon of dry air, mist formation is a phenomenon of humid air. However, haze particles may act as condensation nuclei for the subsequent formation of mist droplets; such forms of haze are known as "wet haze" ...

  In meteorological literature, the word haze is generally used to denote visibility-reducing aerosols of the wet type. Such aerosols commonly arise from complex chemical reactions that occur as sulfur dioxide gases emitted during combustion are converted into small droplets of sulfuric acid. The reactions are enhanced in the presence of sunlight, high relative humidity, and stagnant air flow. A small component of wet-haze aerosols appear to be derived from compounds released by trees, such as terpenes. For all these reasons, wet haze tends to be primarily a warm-season phenomenon.

A haze can also be considered an atmospheric colloid, where,

  one substance of microscopically dispersed insoluble or soluble particles is suspended throughout another substance.

Examples of atmospheric colloids include: fog, mist, clouds, condensation, smoke and atmospheric particulate matter.

The forces behind the suspension of haze particles includes: electrostatic interactions, Brownian motion, van der Waal forces, and entropic forces. The effect of these forces on the light (low mass) particles within a haze counter gravity to keep the particles suspended in air.


Distinctive in this case means, does not match well with the first but is explained by the later. This is not the greatest sentence format, but distinct means stands out from. Generally when you refer to something as distinct with respect to X, then it means X is the odd part about it or it stands out from X. In this cased because they are talking about a predictive model and the thing being predicted, then it means it is odd because it does not fit the predictions of the prevailing climate model. But it is also distinct because it is better explained by local factors, for a given value of "local", which is not normally the case for an event so large. It also might be a reference to more recent research showing the anomaly is likely not global. Combining these two slightly different usages is not great sentence composition but is grammatically correct.
In this particular case the regional forcing mechanism is believed to be a large volcano erupting.


What does a "closed basin" mean in groundwater terms?

An endorheic basin refers to the surface-water flow. The Great Artesian Basin refers to the groundwater aquifer (the artesian part of the name), not the the Lake Eyre surface water basin, which is endorheic. Part of the land area above the GAB is closed with respect to surface water flow. Endorheic basins may or may not be closed with respect to groundwater. In fact they may be closed with respect to water in local groundwater flow systems but open with respect to deeper flow systems.

It is common for endorheic basins to be open to groundwater flow. This can occur in a number of ways. The groundwater flow may only be affected by recharge within the basin and not discharge to surface water bodies within the basin. In the case of confined aquifers, it may be essentially separate and unaffected by the surface water or shallower groundwater in the basin but may flow under the basin and exit the other side. Groundwater can discharge to flow-through lakes. These lakes receive groundwater discharge on one side but recharge the groundwater downgradient.


Which greenhouse gas has the most influence over global warming?

The annual amount of CO2 we emit from using carbon that was in relatively long-term sequestration (coal, natural gas, petroleum) is on the order of 40 GT. To put this in perspective: the amount of food humans consume over the same period of time is on the order of 4 GT. Our CO2 production is an order of magnitude larger than worldwide food consumption. And the problem with it is that it takes weathering to remove it from the atmosphere - meaning it can stay around for millennia, and we're very definitely the ones extracting it from the ground.

H2O only stays in the atmosphere as long as the temperature allows. This means that it won't be the driving factor. There is a slight positive feedback with more H2O leading to a warming so it can hold more H2O, but there's also a negative feedback of about the same size with cloud formation reflecting the sunlight back to space.

Ozone in the upper atmosphere is responsible for the warming at the Stratopause. It's the reason why we have our atmosphere divided into layers with the Troposphere getting cooler with height, the Stratosphere getting warmer with increased height, and the Mesosphere getting cooler again with height. The Ozone absorbs the very energetic solar radiation that would otherwise destroy the DNA in your skin and cause cancers, but as it's a triatomic molecule, it's also very good at absorbing longwave radiation. In this case, a hole in the ozone above the Antarctic may be allowing slightly more longwave radiation to escape - and repairing the hole so we humans can survive might also be trapping additional heat. https://climate.nasa.gov/faq/15/is-the-ozone-hole-causing-climate-change/

CH4 stays in the atmosphere on the order of a decade before chemically reacting with oxygen molecules to become CO2 and H2O - but while it's present, the effect is about two orders of magnitude greater than that of CO2. But since the methane hydrates have been stable, they're not culpable in the warming. Although there are large quantities in tundra and ocean shelves, there's little point in making it the talking factor for anything except scare tactics.

This page https://www.epa.gov/ghgemissions/overview-greenhouse-gases discusses the relative sizes emitted, but temper this with the measurements of these gases. CH4 us currently less than 2 ppmv and CO2 is over 400 ppmv, making it easily the biggest factor in our warming, and in fact, the warming from CO2 is what's causing the tundra to melt and the East Siberian Arctic Shelf (the largest on the planet) to warm and release its methane.

This is why we concentrate on CO2 (it being the largest factor and also the only one we seem to have much control over).

Hopefully this puts it into perspective, and you can do your yandex.com searches for more details.


Meanders amplify themselves--the stream tends to erode on the outside of the meander (forming a cut bank) and deposit sediment on the inside (forming a point bar).  Eventually, the meander will propagate so far from the stream's mean path that the stream cuts across it.  Eventually, the old meander will turn into an oxbow lake and fill in.

As to why it erodes on the outside and deposits on the inside, the simple answer is that the water has to travel farther on the outside, so it flows faster and erodes more, while the water on the inside moves slower and deposits its sediment.  A more complete answer involves vortices crossing the river bed carrying sediment from the outside to the inside.


Physiography explains the physical characteristics of the area more generally describing the physical processes or forces that formed the landscape, while topography describes particular features, typically associated with elevations. For example in geomorphology (as your post is tagged) the physiography of Canadian prairies may describe deep fertile soils, ancient lake bed remnants, multiple sloughs or ditches that fill with water, etc. The topography would describe the extreme flatness with many depressions in the landscape. In practice, physiography is quite broad and topography refers to elevation data (I.e. a topographic map would have elevation points or contours).

Take a look here at WikiDiff as well.


Might not be the answer you're looking for but the most obvious effect would be a sinking of land and a spreading out of the oceans.   Granite, basalt, glaciers and oceans are in a sense, balanced like weights on a scale by their enormous mass and the gravity of Earth.   By replacing a mile or so of basalt rock with water at the bottom of the oceans the weight would be unbalanced and the continents would sink, similar to how some land is currently rebounding from the last ice age.  The net effect over time would be a few hundred meters of sea level rise if the oceans were to become that much deeper.

But I suspect that's not what you were looking for in your question.   You probably wanted to know about weather or oceanic temperature effects.   That's a little harder.   I can give a sort of answer.

Larger oceans would mean more dissolved atmospheric gas.  I had no luck finding good estimates as to how much atmosphere is dissolved in the deep oceans overall, I was able to do a very crude calculation using this website and estimates that there's about 50 times as much CO2 in the Oceans as there is in the atmosphere.   Now, my estimate is hugely crude, but there may be an entire Earth's atmosphere, both Oxygen and Nitrogen trapped in the oceans.   The deep oceans hold a fair bit of Oxygen and Nitrogen so by making the oceans bigger, the effect might be a thinner atmosphere.   10% thinner?   20%?   5%  I couldn't guess the amount, but something somewhere in that range seems probable.

Regarding deep ocean currents, it's difficult (perhaps impossible) to say how currents might change.  In general, ocean currents, while not simple, seem to follow fairly simple patterns.   My guess is that the amount of depth you've added isn't enough to change that, though if you were to make oceans significantly deeper, you might get a few layers of circulation, not the three, sometimes four layers we currently have.  (see pictures).

Source of pictures

Larger, deeper oceans would also provide a greater heat sink that would take longer to warm up or cool down with the rise and fall of glacial periods.   It's possible that there would be no glacial periods with these changes, but predictions get kind of speculative there.

That's all I can think of.  I invite corrections and additions.


How can I tell the difference between granite and syenite?

It is confusing - both rocks are commonly pink overall. But, granite has abundant quartz, syenite has no quartz to very little. Quartz will be the grey translucent mineral that looks just like a blob with no distinct shape.

You can use this website: https://www.virtualmicroscope.org to see examples of syenite and granite (use the search box).


Minimum temperature on 15km height on equator in JJA?

That's because the tropopause, the boundary between the troposphere and stratosphere, is highest in equatorial regions. The high amount energy from the Sun in equatorial regions makes for a lot of convection, which in turn pushes the tropopause to about 16 km above the surface (and sometimes to 18 km) in those equatorial regions. Near the poles, sinking air and reduced solar intensity makes the tropopause much closer to the surface, where it is only 8 km or so high.

The lapse rate in the upper troposphere is roughly the same as the dry adiabatic lapse rate, 9.8 °C/km. The 8 km difference between the tropopause height between equatorial and polar regions results in about 80 degrees more cooling in equatorial regions than polar ones.


Here is a map of seismic hazards for the United States from the United States Geological Survey. Link.

Link to interactive fault map for the US (source: USGS)
Here is a link to a nice article on top 5 earthquake prone areas outside California.

It is presence of fault zones, geological structures (like volcanos, subduction zones, tectonic plate junctions, basins, and mountains), geological evidence of past events, and record of earthquake events that go into the calculation of a seismic hazard for a specific region.


Why is there a logarithmic grid on this plot?

It's a mistake.

You probably know this, but for anyone who's interested, these wireline logs are:

DRHO — density ('RHO') correction (delta, or 'D') in g/cc.
DPHI — porosity ('PHI') from density ('D'), as a fractional proportion.
NPHI — porosity from the neutron log ('N'), as a fractional proportion.

All of these logs are usually displayed on a linear scale. Indeed it wouldn't make sense to display them on a log scale, which is mainly for displaying resistivity logs, e.g. the induction log. Even if they were, it wouldn't make sense to show the usual 4 octaves (0.2 to 2000 for resistivity), given the range of the data and the scale of porosity values geologists are interested in.

It's not clear if the data have actually been displayed on a log scale, or if it's just that the grid has been erroneously added. I would treat the data with suspicion.


Which Earth minerals would Moon colonists miss the most?

The composition of Moon rocks is pretty much the same as that of Earth. However, none of the processes that concentrate specific minerals in one location (i.e. into a mineral deposit useful for mining) exist on the Moon.  This is due to the lack of tectonic activity. Therefore in the Moon you would expect the rocks to be much more homogeneous than on Earth. Only maybe meteorites, their impact craters, and ancient volcanic activity (as pointed by @userLTK) might have provided a way to concentrate some minerals in various places. So, due to this homogeneity, to get one gram of let's say copper, you would have to process hundreds of times more rock than would be needed in an Earth-based copper mine.
Also as Fred mentioned, there would be many challenges for mining in the Moon, but in the context of your plot those might have been solved. Having enough energy, you can probably get pretty much any mineral from the Moon (for example a mass spectrometer would be an effective but highly inefficient way to mine all the elements from within a piece of rock).

If your plot doesn't require that it be a mineral, I think what they might need the most is some sort of organic compound. Even with current technology there are many chemical compounds that can't be synthesized, and we rely on plants or animals to obtain them. A famous example is Maitotoxin, a small molecule that chemists have tried to synthesize for 22 years without success.

So perhaps there could be a particular organic compound that has been recycled and reused over time in the bodies of the plants and animals on the lunar colony, but over time that compound degrades (by cosmic rays, UV light, or whatever), so animals and/or plants start developing problems due to the lack of this compound that none of the organisms placeable in the colony are capable of synthesizing. Therefore, they need to go back to Earth to get it from some ocean-dwelling creature.

Perhaps it would be something like a vitamin required by plants.  Or maybe a compound that could be needed to cure a disease.


Connection between microbes and serpentinite?

The most common explanation for microbial activity in serpentinites is the exploitation of abiogentic hydrogen and methane formed during the serpentinisation process.

Quoting the abstract of a recent authoritative review:

  The process of serpentinization creates strongly reducing conditions and produces fluids that are highly enriched in molecular hydrogen and methane. Some microorganisms are able to exploit these compounds to gain metabolic energy and to generate biomass, leading to the development of biological communities based on chemical energy rather than photosynthesis. The abundance of chemical energy and favorable conditions for organic synthesis make serpentinites a strong candidate for the site of the origin of life on Earth, as well as a prime target in the search for life elsewhere in our Solar System.

From Serpentinites, Hydrogen, and Life (may be paywalled).

You might also find this review interesting: Serpentinization, Carbon, and Deep Life (should be free to access).

These two papers present the current thinking in this subject.


What could possibly be a rational basis for rejecting climate science?

If the issue is assessed on other grounds than science ones there can be rational reasons to reject climate science. e.g. if it is being assessed with respect to how addressing versus not addressing AGW impacts costs, competitiveness and profitability of specific business enterprises then rejecting climate science and encouraging other business operators as well as governments, courts and regulators to reject it, to avoid compliance costs of addressing it appears rational. The advice given by lawyers to people and companies facing lawsuits to admit no responsibility and seek to undermine the plaintiff's arguments, including questioning the veracity of expert witnesses is not irrational. Unethical perhaps, but it is not irrational.


What formations are to be expected to develop between the transform boundaries of oceanic and continental plates?

The San Andreas Fault system is an excellent example of what can happen in an oceanic–continental transform fault.

It's also important to remember that plate boundaries are usually never 100% transform-like and are at an angle. This would cause either compression or extension, depending on the local geometry. A pull apart basin is an example of something like this. For instance, the dead sea is a basin on a transform fault between Israel and Jordan, and a few hundreds kilometres to the north, on the same transform, you have mountains between Lebanon and Syria.


Effect of reducing conditions on melting point

As you probably know, the melting temperature in the mantle is a function of H2O contents. The more H2O you have, the lower the melting point of the rocks (i.e. dry vs wet solidus in the sketch). A less known phenomenon is the decrease of melting point with the addition of CO2.

The CO2 melting curve has a weird shape. At low pressures nothing much happens, but there's a certain pressure where all of the sudden CO2 is soluble in the melt and it greatly depresses the melting point. This kink is known as the "carbonate ledge". The exact depth of the ledge depends on the composition of the rocks and the experimentalist that performed the experiments, but it's somewhere around two to three GPa, corresponding to about 65 to 100 km deep. Low degree melts above the solidus (the yellow area) are proper carbonatites, and higher degree melts are all kinds of carbonated alkaline melts, with more CO2 dissolved in them at higher pressures. True hybrid carbonate and silicate melts are only possible at pressures of let's say 4-5 GPa and higher. Below that an immiscibiliy gap exists (also dependent on the alkali contents of the melts - more alkalis = more miscibility).

redox melting

Now, for this to happen you obviously need to have CO2 in the mantle. But CO2 is the oxidised form of carbon. In general, the deeper you go in the mantle the more reduced the conditions are. The roots of cratonic lithospheric mantle are very reduced and any carbon in there occurs in the form of reduced carbon: diamonds. Diamonds are no good in facilitating carbonated melting of mantle rocks. However, if a process of metasomatism of fluid flow causes oxidation of the diamonds, they transform to CO2 thus enabling the formation of carbonated mantle melts.


Is increase in atmospheric $\mathrm{CO}_2$ concentration affecting Earth's atmospheric pressure?

The air in the atmosphere is a fluid. The pressure exerted by a fluid on a horizontal surface can be calculated using the formula.

$$ P = \rho\,\mathrm{g}\, h $$

Where:

$P$ is pressure
$\rho$ is the density of the fluid
$\mathrm{g}$ is the acceleration due to gravity
$h$ is the height of the fluid

The acceleration due to gravity is a constant and the height of atmosphere can be considered constant. That leaves only the density of the air in the  atmosphere as the only variable that will affect pressure on the surface of the Earth, in this situation.

The amount of carbon dioxide in the atmosphere is around 400 parts per million — a very small proportion.

Air density varies according to temperature and pressure but is within the range of $1.146$ to $1.422\ \mathrm{kg/m}^3$. By comparison, water has a density of $1000\ \mathrm{kg/m}^3$.

If the quantity of carbon dioxide were to increase, even tenfold, it would have a negligible affect on the density of the air and thus a negligible affect on the atmospheric pressure on the surface of the Earth. Its effect on temperature is another matter.

Edit

Answer to the additional question: Can you expound on what effect the increase in temperature will have on pressure?

The relationship between pressure, temperature and volume for gases is given by the universal gas law which states,

$$ PV = m\, \mathrm{R}\, T $$

Where:

$P$ is pressure
$V$ is volume
$m$ is mass
$\mathrm{R}$ is the universal gas constant
$T$ is temperature

Rearranging the equation,

$$ P = \frac{m\mathrm{R}T}{V} $$

When considering the affect of temperature on atmospheric pressure, $\mathrm{R}$ is already a constant and the mass and volume of the atmosphere can be considered to be constant because any changes due to increased $\ce{CO_2}$ will be exceedingly small and can be regarded as being negligible.

Consequently $m\mathrm{R}/V$ is a constant $\mathrm{k}$ and the equation becomes,

$$ P = \mathrm{k}T $$

The Kelvin temperature scale, used in the equation, is an extrapolation of the Celsius temperature scale, thus a rise in temperature of $1^\circ\mathrm{C}$ ($1\ \mathrm{K}$) will increase atmospheric pressure by $1\ \mathrm{pascal}$.

The average atmospheric pressure is $101\,325\ \mathrm{Pa}$. Assuming a very bad case scenario of a rise of $10^\circ\mathrm{C}$, the pressure would increase $10\ \mathrm{Pa}$, or $0.0099\%$, which is insignificant.

Weather reports report atmospheric pressure in units of hectopascals ($\mathrm{hPa}$). A pressure of $101\,325\ \mathrm{Pa}$ is $1013.25\ \mathrm{hPa}$. A rise of $10\ \mathrm{Pa}$ is the same as $0.1\ \mathrm{hPa}$. Atmospheric pressures vary between $890\ \mathrm{hPa}$ and $1090\ \mathrm{hPa}$.


Does a climate change big data provider exist?

I happened to catch a 60 minutes interview piece on Bloomberg... while the interview was honestly more adulation than journalism, they showed a little bit about the Bloomberg Terminal at times which really caught my eye.  (The transcript has a few details, but the video would hopefully be more thorough... looks like you can watch the full interview here if you happen to have the pay CBS All Access service).  It really seemed like it was a remarkable tool at gathering diverse data together into sort of like a master dashboard or real-time encyclopedia, and making it very flexible and easily consumable.  It seems to be something that could be of amazing use, and I suggest folks look into to get an idea of what can be done with technology applied well, it may spark some creativity and reshape views.  Knowing what that software is about, the questions seems a very valid one, as I'd always be eagerly on the look out for such a comprehensive and thorough collection of unified data on the topic of climate change.

But that said, I'm quite sure the answer is a firm no; such a comprehensive source of climate data likely doesn't exist.

Bloomberg has really done what they've done because the information they're collecting is worth huge value in the markets, and they can then sell that utility for great prices.

But there's likely not such money in most other topics, including much of scientific data.  If there were such tools developed in science, one would think they may well focus more on aggregating and simplifying subjects that are clearly more lucrative, such as genetic data, or detailed medical records, or, if venturing nearer our fields here, oil/mineral data, or perhaps maybe meteorological data, rather than climate data and one particular prong of it (how it is changing/why).

Yes, there's a lot of attention in climate change these days, and so research may well be funded a bit more than it used to be.  But the focus in the study is still really on developing conclusions to convince the public and policy makers, rather than on generating some tangible asset/information that owners could practically apply to thereby excel in some lucrative market field.  While there are indeed some industries with significant connection to the topic, such as energy generation and pollution credits, their focus is generally on gathering the very specific information they need (e.g., wind/solar data/modeling for renewable energy siting, forecasting politics for predicting policy shifts in generation balance and pollution controls, etc).  I've not known anyone to forsee any giant particular financial use of drawing all the climate change data together.  [Then again I wouldn't have imagined that a group like Bloomberg's would have recognized the potential and then had such technological vision and success in culling such wide-ranging access to make something like there tool... until I saw the story)  But it just doesn't seem there are the obvious grand benefits to doing similar for climate change.

The closest I can think of would be IBM's initiative towards meteorological big data.  Others sites like NOAA's Climate Data Online have a few items, and this open data collection appears it may also offer a good starting point.  But overall, it may well more often still come down to tracking down separate specific datasets yourself when getting into more of the specifics.  Of course you're in a good place here to try asking if you decide there's something specific you're after!
But in terms of company by company data, I expect being related to corporate affairs, there's more hope in finding that using Bloomberg itself than in finding another such source built around this specific subject.  There likely are websites that monitor news stories and such.  And there may be at least some separate piecemeal datasets findable on specific impacts to people/countries/industries/etc.

I've indeed found it frustrating for years that even as piles of articles and webpages have been made focusing on climate change, there really still aren't fantastic options that allow typical folks and experts in other subjects to quickly and easily explore the past and current data very flexibly and graphically, more in line with it appears Bloomberg's software is.  Yes, it's still possible for even novices to dig in with enough work, as even this question here at ESSE did a great job of.  But we have miles to go of improvement in such true accessibility.

I do hope if you unfortunately have to go through the painstaking effort to source and gather such data, that you'll take the time to give back as you're able, to help others who come after you!  We really only do advance anywhere by the progress of those who came before us.

Best of luck, and hope the input was at least of some help to you or others somewhere along the way at least.


Are "monoliths" giant, isolated rocks sitting in dirt, or are they continuous with bedrock

the trick is not all isolated rocks are produced the same ways. Of the two in your pictures  the first is an old volcanic events; intrusions, dikes, ect. depending on which rock in the region you are talking about. The whole deccan plateau region is full of them, some have been exposed on the surface via erosion. Basically everything else eroded faster than they did leaving them sticking out.

The second was produced by the same effect (eroding slower than the rock around it) but this time it was just a hard massive sandstone formation surrounded by more easily eroded rock. It is part of the bedrock.


Convert air vapor pressure to relative humidity

$$1\:\mathrm{N/m^2} = 1 \:\mathrm{Pa}$$
$$100 \:\mathrm{Pa} = 1 \:\mathrm{hPa} = 1 \:\mathrm{mb}$$

So yes, you do have valid units of pressure.  And can easily convert it.

The calculation $ RH = 100* \frac{e_{a}}{e_{s}}$ will work as long as the pressures are in equal units, whether Pa, mb, Gbar, etc, since it's just a ratio.  They just need to be the same.  So, you can convert your given $e_a$ into mb by multiplying by 100, convert your $e_s$ into Pa by dividing by 100, or just apply the change in the $e_s$ equation to get $e_s$ in $\:\mathrm{N/m^2}$.

We often use your $e_s=6.11∗exp(17.27T_a/(237.3+T_a))$ in meteorology since we work with pressures in mb (or equivalently hPa).  But indeed the same equation simply works with the constant adjusted to the proper units as:

$$e_{s} = 0.0611*\exp\left(\frac{17.27T_{a}}{237.3+T_{a}}\right)$$

giving answers in Pascals ( = $\:\mathrm{N/m^2}$).

So long story short: yes, all of your equations and reasoning are good, your units are all pressures, they just don't match form.  But you can indeed adjust at any step to account for that.  Simplest is multiplying your $e_a$ (in $\mathrm{N/m^2}$) by 100 or dividing your $e_s$ (in $\mathrm{ mbar}$) by 100 to make them match.

Also of note, the first equation you gave is exactly valid.  The second equation, as you indicate, is an estimation.  The longer version described in this paper would give exact values if you wish, but it looks like you're unlikely to be off by more than 0.1%, so what you're doing is likely fine unless you're need very exacting precision.


What proportion of the energy input to the ocean tide system comes from the sun?

From [1, 2], the oceans are dissipating about 3.5 TW of energy. The moon and sun input about 3.2 TW and 0.5 TW, respectively. (0.2 TW of the 3.7 TW are dissipated by the solid Earth and the atmosphere.) Another estimate of tidal energy dissipation [3], looking at the 8 major tidal constituents, estimates 0.411 TW of solar tides dissipated by the ocean. (With an additional 0.03 TW dissipated by a moon-sun interaction constituent.)

[1]: Munk and Wunsch, 1998, https://doi.org/10.1016/S0967-0637(98)00070-3

[2]: Jayne and Laurent, 2001, https://doi.org/10.1029/2000GL012044

[3]: Egbert and Ray, 2003, https://doi.org/10.1029/2003GL017676


Typically we are not answering Rock Id questions, though this is a somewhat unique question because the rock is unique.  Your rock is likely a tufa (never heard it called tuffy).  It is a rock that is formed when water with high carbonate content is released to the surface.  Depending on the conditions at the surface the dissolved carbonate comes out of solution, this can be through cooling, depressurization and reduction of the partial pressure of CO2, or through biological precipitation by organisms such as blue-green algae.  There may also be other means that the deposition occurs but overall the water solution is initially oversaturated with the carbonate minerals.  These deposit out in the patterns shown on your sample.  If you were to perform an acid test your rock should show a strong reaction.  The area around the California Nevada boundary has a large number of locations with this type of deposit both active, Mono Lake, and inactive like the Trona Pinnacles.  Nevada itself has some of these deposits in the Black Rock Desert, Pyramid Lake and Fly Ranch areas.  Deposits are likely found world wide but these are the ones I am familiar with.  The pattern of deposition on your rock suggests to me an association with algae when it was deposited.  See the following sites:

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

https://www.blackrockdesert.org/wiki/index.php?title=Geology


Which are the mechanisms of the correlation between atmospheric carbon dioxid and global warming/cooling?

Except from the obvious that carbon dioxide is more soluble in cold water and perhaps that some carbon dioxide is trapped in glacial ices, which are the known mechanisms?

Those obvious mechanisms, particularly the first, are the primary mechanisms. Atmosphere carbon dioxide content gradually drops to very low levels during a glaciation precisely because cold water can dissolve much more carbon dioxide than can warm water.

When the Milankovitch cycles reaches a stage where the Earth starts warming up at the end of a glaciation, the Earth's waters start warming up, too. The warmer waters cannot hold as much CO2 as they held during the glaciation. The CO2 comes out of solution, adding to the Milankovitch-driven warming. This is one of the key reasons why the exit from a glaciation is much more abrupt than is the entry into one.

Based on comments by the OP, the OP appears to doubt that carbon dioxide and other polyatomic gases are greenhouse gases. The three principal components of the dry atmosphere, nitrogen (N2), oxygen (O2), and argon, are not greenhouse gases. Electronically neutral monatomic gases and diatomic gases comprising two atoms the same substance have zero dipole moment. These gases have essential zero cross section to low energy (e.g., thermal infrared) photons.

On the other hand, polyatomic molecules have many more degrees of freedom than do the homogeneous diatomic molecules and monoatomic gases that comprise the bulk of our atmosphere. Some such as water vapor have a marked permanent dipole moment. Others such as carbon dioxide nominally have a zero dipole moment, but transients due to thermal vibrations can temporarily given them a non-zero dipole moment. The combination of increased degrees of freedom and a non-zero dipole moment make these polyatomic gases very good at absorbing some parts of the thermal infrared spectrum.

All other things being equal, adding greenhouse gases to the Earth's atmosphere increases the Earth's equilibrium temperature. It's important to note that this greenhouse effect is essential for life. Without it, the Earth would be a frozen icefall, from pole to pole. In fact, during the Cryogenian (850-635 million years ago) the Earth apparently was covered or nearly covered with ice from pole to pole.

The end of a glaciation adds significant portions of the two most important greenhouse gases to the Earth's atmosphere. Water vapor increases because a warmer atmosphere can hold more water vapor than can a cold one. Carbon dioxide increases because a warmer ocean can hold less carbon dioxide than can a cold one.

While the OP asked about the end of a glaciation, the real question being asked was about what is happening now. What happened at the end of glaciations and what is happening now are one and the same thing. Adding greenhouse gases to the Earth's atmosphere increases the Earth's equilibrium temperature. The end of a glaciation added greenhouse gases to the Earth's atmosphere, making the subsequent warming very rapid. Humanity is adding greenhouse gases to the atmosphere, carbon dioxide in particular, resulting in an even more rapid warming than that that occurred at the end of a glaciation.


Do higher global temperatures increase volcanic activity and earthquakes?

Define 'significant' effect. Yes, in principle, both volcanoes and major fault lines can, in some cases, be affected by higher global temperatures. It works like this: higher temperatures cause glacial melt and thermal expansion of seawater, which causes sea level to rise. In ocean sediments and coastal aquifers this raises the hydrostatic pressure, increasing groundwater circulation, and hence providing more 'lubrication' to fault planes, and increasing the seepage above magma chambers. However, the effect is small.


Pyroclastic flows have often been considered to be by and large, unsurvivable, especially since the devastation in 1902 of St. Pierre on Martinique, many fatalities are due to hypoxia and severe thermal injuries (Hansell et al. 2006; Baxter et al. 1998).

According to the USGS webpage about pyroclastic flows, these events can occur very suddenly, without much warning at all (e.g. Mt. Ontake) and travel fast, and can be several hundreds of degrees Celsius. Pyroclastic flows also contain considerable amounts of toxic gases and rock fragments.  The presence of water bodies in the path can result in lahars and mudflows.

As pyroclastic flows are variable in nature and can be sudden, there is no one-way of volcanologists protecting against its effects, except to get out of the way (if possible).  The use of fire suits will limit mobility and still may not protect from the flow itself.

In the AGU blog So you want to be a volcanologist?, Jessica Bell, a volcanologist from the USGS makes the point that being prepared is crucial for greater chances of survival, emphasising the point of 'doing your homework' about the eruptive history of the volcano before going to the volcano.  Gas masks, gloves, long sleeves and long pants are also crucial.  Critically, a volcanologist must be:

  very careful to avoid areas that could be dangerous – within the path of pyroclastic flows or mudflows or lava bombs, near gas vents or lava flows, or unstable ground are just a few.

It should be noted that several media reports mention that not all volcanoes have these kinds of shelters.

But where the shelters are present, they could provide an obstacle that could affect pyroclastic flow propogation but only when the shelter is distal to the eruption and if the flow does not last too long, related to modelling performed by Todesco et al. (2006) and earlier by Baxter et al. (1998) who assert that this situation is survivable.

Baxter et al. (1998) also state that through their models, the most effective shelters can shield against the dynamic pressure and heat transfer associated with a pyroclastic flow, especially if the flow is of short duration.  This effectiveness obviously diminishes when the flow lasts a considerable amount of time, is large-scale or the shelter is too close to the eruptive source.

What these shelters won't protect from is fine ash dust, and not everyone sheltering will necessarily have a gas mask (as per the volcanologist above).  Another problem with this, as noted after the Mt. Unzen eruption of 1991 is that even if shelters are spaced evenly apart - time is a major factor - the time to reach the shelter against the time it takes for the pyroclastic flow to reach that location.

A lot of shelters around some volcanoes that have had a past history of pyroclastic flows have 'exclusion zones' with the shelters in the distal regions of previous eruptions, this method of exclusion zones is claimed by Hansell et al. (2006) as being one of the only effective protective measures from proximal effects of an expected pyroclastic flow - which also describes, alongside the modelling by Baxter et al. (1998), the way that these shelters can have any effectiveness by being in the distal regions.

References

Baxter et al. 1998, Physical Modelling and Human Survival in Pyroclastic Flows, Natural Hazards

Hansell et al. 2006, The health hazards of volcanoes and geothermal areas, Occupational Environmental Medicine

Takahashi, 2007, Unzen-Fugendake Eruption Executive Summary 1990－1995, Unzen Restoration Project Office,
Kyushu Regional Construction Bureau,
Ministry of Land, Infrastructure and Transport

Todesco et al. 2006, Pyroclastic flow dynamics and hazard in a caldera setting: Application to Phlegrean Fields (Italy Geochemistry, Geophysics, Geosystems


According to the pages Plagioclase composition (from the textbook: Introduction to Mineralogy Nesse, 2000), the percentage definitions are due to the mole percent of $\ce{Ca^{2+}}$ (from anorthite) and the presumed subsequent $\ce{Na+}$ (from albite) ions present in the sample.

This is done under the assumption that the anorthite% + albite% = 100% in a plagioclase sample.

The mole percent are usually represented by percentage proportions of the plagioclase end member anorthite, often in the form of Anx, where 'x' is the mole percent of $\ce{Ca^{2+}}$ present in the plagioclase sample.

Consider the following diagram below - the relevent part for your question is across the base of the triangle:

Image source.

For example, oligoclase is An10%-30% means that it would possess a $\ce{Ca^{2+}}$ mole percent of between 10% to 30%, and a corresponding $\ce{Na+}$ mole percent of between 70% to 90%.


Does the Earth receive a net charge from the aurorae?

No. If that were the case, the Sun would eventually develop a net charge. Let's imagine that's the case and the Sun develops a net  positive charge. That charge would eventually stop negative particles from flying away and facilitate the ejection of positive ones. This regime would then restore the neutral charge of the Sun.
This negative feedback makes sure the Sun remains neutral and that Solar winds carry no net charge.

See this Q&A for more details:Does the solar wind correspond to a net electrical current?


What is a reasonable forecast of sea level in 2100?

An important aspect of this is location.  Sea-level rise will not be exactly uniform across the globe and tides/storms will cause a lot of regional variability in terms of coastal change.   Local governments should not necessarily be planning for an average global sea-level rise but instead develop a regional understanding of the coastal effects they will likely experience.  For instance, see California's recent CALIFORNIA COASTAL COMMISSION
SEA LEVEL RISE POLICY GUIDANCE here:  http://documents.coastal.ca.gov/assets/slr/guidance/July2015_Full_RecFinal.pdf
which says

Sea level at the San Francisco tide gauge has risen 8 in (20 cm) over the past
century, and the National Research Council (NRC) projects that by Year 2100, sea level in
California may rise by 4 to 56 in (10 to 143 cm) for areas north of Cape Mendocino and 17 to 66
in (42 to 167 cm) for areas south of Cape Mendocino (NRC 2012). While the California coast
regularly experiences erosion, flooding, and significant storm events, sea level rise will
exacerbate these natural forces, leading to significant social, environmental, and economic
impacts.

The estimate of 0.6 meters has increased as recent research shows Greenland's melt rate is a bit faster than previously estimated and ocean warming, which causes expansion, is also happening more rapidly.
Below  is some useful information from the 2014 US National Climate Assessment ( http://nca2014.globalchange.gov/report/our-changing-climate/sea-level-rise ).

Global sea level has risen by about 8 inches since reliable record keeping began in 1880. It is projected to rise another 1 to 4 feet by 2100.
Projecting future rates of sea level rise is challenging. Even the most sophisticated climate models, which explicitly represent Earth’s physical processes, cannot simulate rapid changes in ice sheet dynamics, and thus are likely to underestimate future sea level rise. In recent years, “semi-empirical” methods have been developed to project future rates of sea level rise based on a simple statistical relationship between past rates of globally averaged temperature change and sea level rise. These models suggest a range of additional sea level rise from about 2 feet to as much as 6 feet by 2100, depending on emissions scenario.
Recent projections show that for even the lowest emissions scenarios, thermal expansion of ocean waters and the melting of small mountain glaciers will result in 11 inches of sea level rise by 2100, even without any contribution from the ice sheets in Greenland and Antarctica. This suggests that about 1 foot of global sea level rise by 2100 is probably a realistic low end. On the high end, recent work suggests that 4 feet is plausible.,,,, In the context of risk-based analysis, some decision makers may wish to use a wider range of scenarios, from 8 inches to 6.6 feet by 2100., In particular, the high end of these scenarios may be useful for decision makers with a low tolerance for risk
In the next several decades, storm surges and high tides could combine with sea level rise and land subsidence to further increase flooding in many of these regions. Sea level rise will not stop in 2100 because the oceans take a very long time to respond to warmer conditions at the Earth’s surface. Ocean waters will therefore continue to warm and sea level will continue to rise for many centuries at rates equal to or higher than that of the current century

The discussion paper, which is still undergoing peer-review at the time of this post, brings into question the semi-empirical methods used to calculate the rate of sea-level rise on the decade-scale.  As an alternative, they use paleo-climate data and doubling times to make their own approximation, which predicts faster sea level rise.  Let us be clear, though, the amount of possible net sea level rise over the next few hundred years or so is not really in question. The timing of how fast the sea will rise over the coming century is what is less certain.  So, a coastal community doing long term planning could consider sea-level rise even further in the future.  Most of Greenland could melt over the next few hundred years, which would contribute nearly 6 meters of sea level rise. If we are strictly talking about the year 2100, though, that is a difficult forecast to make. For planning purposes, it would be wise to assume at least 1 meter of sea level rise by 2100, with definite continued increases.


What are the factors that dictate a given topology for seismometer placement around a volcano?

A general statement about the placement of seismometers around a volcano is provided on the USGS page Monitoring Volcano Seismicity, that a significant factor in their placement is to detect 'microquakes':

  Seismic networks are made up of several instruments. Having enough of the right instruments located in strategic places is especially important for detecting earthquakes smaller than magnitude 1 or 2; sometimes, these tiny earthquakes represent the only indication that a volcano is becoming restless.

They state that detection of these microquakes requires seismometers to be placed near the crater.

Placing them in rings around the volcano (in accessible and safe areas) allows scientists to accurately model the seismic changes, hence changes in the nature of the underlying magma chamber and the movement of magma and fluids.

An example is presented in the presentation Deploying a Sensor Network
on an Active Volcano using Tungurahua and Reventador volcanoes in Ecuador, seismometers are typically separated by at least 100m, across and up-and-down the volcano - this allows the identification of where the movement is occurring (whether the event is from the cone or deep within the volcano).

Practically speaking, according to the article A wireless sensor network for monitoring
volcanic tremors (Pereira et al. 2013), the spacing ought to be

  The sensors must cover a region where the entire
  phenomena can be evaluated. Therefore, the coverage area must comprise, at least,
  one wavelength of distance between the two sensors farther away from each other.
  Since both the direction and speed of the tremor wave need to be estimated, at least,
  two sensors in each one of the cardinal points are required.

The authors emphasise the need for the networks to be flexible in terms of their location.

The authors also state that cost is a major factor - not only of the instruments, but of personnel to monitor and analyse the data.


Why are the clouds white and Australia black in weather satellite infrared images?

I had a very similar question in a job interview!  The only difference is that it was an image from SEVIRI on Meteosat.

The imager on HIMAWARI is called the Advanced Himawari Imager (AHI).  The AHI IR1 channel is actually channel 13 with a central wavelength of 10.4 µm, which is in the window region (apparently it's called IR1 in reference to an older satellite).  The clear-sky atmosphere is mostly transparent in this region of the electromagnetic spectrum, so we can see the surface or clouds mostly unobstructed by water vapour, ozone, or other gases.

In an infrared image such as this one, high clouds are cold.  Forecasters who look at such images for a living like to see clouds as white.  I'm a physicist and I prefer to map values of high intensity to white, which would make clouds black, but forecasters are the most important users so they get their way.  :)

To display cold areas as white, hot areas must logically be displayed as black.  So what we are seeing in this image:

Central Australia is hot.  This is expected, because it is a hot desert with high emissivity.  The image is apparently taken at 12:00Z, which should be between 20:00 and 22:00 legal standard time in mainland Australia, so it's not long after sunset, when the land is still hot.  Australia should appear less "black" at an image taken 8 hours later.  The image is apparently taken at 12:00 "local" (140°E) time (03:00 UTC).  It's February and summer in Australia, and the northern hemisphere looks a lot less hot (it's also earlier in the morning there, compared to sunrise).
Cloud tops are cold.  This is expected, because they are in the upper troposphere.  Those white clouds are ice clouds.
There are grey-ish clouds too with little contrast to the ocean.  Those are lower, liquid clouds, they are warmer.  The lowest clouds may be difficult to identify in infrared images, which is why (for example) night time fog detection from satellites is difficult.

(I got the job!)


How can half a degree of average temperature result in such devastating impact on coral reefs?

Coral die because of coral bleaching, a process in which the symbiotic algae living in the coral (which give the coral its colour), leave the coral host.

Bleaching can occur for a variety of reasons, but the ones that relate to a warming climate are:

Ocean acidification caused by dissolution of carbon dioxide in the water.
Thermal stress. According to this website, "Corals do best when ocean water is between 73 degrees F and 84 degrees F." (22–29 °C). Long durations of heated sea surface water exceeding that would cause bleaching and coral death. For example, a recent bleaching event in the Great Barrier Reef had temperatures of 4 °C above average, where the average is around 27 to 28. This puts it above the comfort zone of the coral.


Methods and Software for Interpolating/Modelling of Stratigraphic Well Data in 2D/3D

OpendTect may do this, however getting to that stage would be a painful experience.

Petrel can do this very easily, however, that is not anywhere near free...

If you're a student, your department may have access to a few decent programs to achieve this. If you could find out what you have available, we might be of more help!


As often in geology of any scale, the surface is only a manifestation of a 3-dimensional body.

It's typical for igneous rocks (e.g. granite see here) that the polished surface have the Voronoi-like-pattern. The minerals grow from a nucleus until they reach the next crystal and the melt is finished. Every point in the rock can be related back to its closest crystal nucleus, depending on the solidus conditions for the chemical composition.

Check this short animation.

You can see the same pattern in the microstructure of metals, e.g. ferrite and pearlite in steel e.g. here.


How do you infer what a cross section might look like below sea level?

I would say it's reasonable to infer that the strata stay at roughly the same dip angle and thickness in areas not directly visible on the chart you're using.


How to estimate the settling time of atmospheric particulates as a function of aerodynamic size?

I took a class once, and we had an approximate equation for an particle (equation sheet is still up):
$$\frac{d\vec{v}}{dt}=\frac{\rho_{particle}-\rho_{air}}{\rho_{particle}}\vec{g}-\frac{3\rho_{air}C_D}{4\rho_{particle}CD_{particle}}\vec{v}|\vec{v}|$$ where $\rho$ is density, $\vec{g}$ is the gravity vector (usually $=g\hat{k}$ but can be changed if the particle has a charge), $C_D$ is the surface drag coefficient, $C$ is the Cunningham correction factor, $\vec{v}$ is the particle velocity, and $D_{particle}$ is the aerodynamic diameter of the particle.
Solving for $\frac{d\vec{v}}{dt}=0$ to get the terminal velocity is one option. I can't remember if the above equation considers environmental motion. You can work through the other equations in the equation sheet and see that even getting a terminal velocity is complicated and requires an iterative method since $C_D=C_D(\vec{v})$. This might work for engineering purposes, but may not practical for atmospheric modeling.
There is another take on this issue of deposition. One parameterization for dry deposition is the (see pgs. 6-9): $$v_{deposition}=\frac{1}{r_a+r_b+r_a r_b v_s}+v_s$$
$$r_a=\frac{1}{ku_*}\left[\ln\left(\frac{z-d}{z_0}\right)-\Psi_h\left(\frac{z}{L}\right)\right]$$
$$v_s=\frac{D_p\rho_{particle}g}{18C\mu}$$, where $v_s$ is the settling velocity, $\mu$ is the dynamic viscosity, $L$ is the Monin-Obukhov length, $\Psi_h$ is the integrated similarity/Businger-Dyer function for heat, $k$ is the von-Karman constant, $z_0$ is the roughness length, $d$ is the displacement height, $u_*$  is the friction velocity, and $r_b$ is the viscous  sub-layer resistance.


Do different lavas have different volcanic volatiles associated with them?

I do not have access to the full-text, but the abstract of Giggenbach (1996)[1] suggests that

  The variability in the composition of volcanic gases accessible to sampling, therefore, is largely due to shallow processes, such as reequilibration in response to cooling and dilution by meteoric water, and interaction with fluids of associated hydrothermal systems.

The section Gas Compositions and Tectonic Setting in [2], from Oregon State University has quite a nice table showing that the different volcanoes do seem to have different gas compositions, depending on where they are found and consequently what type of tectonic setting they occur in. I am not sure if these variations are actually significant though, not being a vulcanologist.

This is certainly not a complete answer, but it does look like it might not be that easy to use the volatiles as a diagnostic feature. Hope that this helps somewhat....

http://link.springer.com/chapter/10.1007/978-3-642-80087-0_7
http://volcano.oregonstate.edu/gas-compositions-and-tectonic-setting


When sediments are deposited, do they sink into the earth?

The rivers transport most of the sediments to the coastal or marine basins where they accumulate. An exception are lacustrine basins, but most of world rivers sediments are deposited on shallow or deep marine basins.

When the stack of sediments is large, listric faults develop, and the bottom layer get pushed down into the earth. This process is called subsidence.

Source: apg-pro.com

As new sediments accumulate, faults are activated and the basin becomes larger. Elevation of a given section of the basin remains approximately the same, as this is a slow process.

In the case the bottom layer reaches great depth, burial metamorphism can develop:

  "Burial Metamorphism: occurs when sedimentary rocks that had undergone diagenesis are buried
  even deeper. Diagenesis grades into burial metamorphism, a relatively
  mild type of metamorphism resulting from the heat and pressure exerted
  by overlying sediments and sedimentary rocks. Although partial
  alteration of the mineralogy and texture may occur, bedding and other
  sedimentary structures are usually preserved".

  Source: uh.edu


Review of calculation of CO$_2$ contribution to warming

This reminds me of using Bjørn Lomborg's book in statistics, as examples how not to do statistics, his calculations never make any sense or just make unfounded leaps to conclusions.
Erik seems to have the same problem he just throws numbers together with no rhyme or reason.
Let's just break down his calculation.
1 °C × 0.30 × 0.04 × 1/4 = 0.003 °C.
Why are we multiplying by 0.25, he says CO$_2$ is only 25% as good as water, but water is nowhere in this calculation, there is no reason for this to even be here much less to be multiplied. Also why can't he solve 1/4?
1 °C × 0.30 × 0.04 = ??
This is just plain wrong, CO$_2$ comprises 0.04% of total gas and ~93% of trace gasses, even more of greenhouse gasses, unless he is arguing some undiscovered change in nitrogen or argon is acting as a greenhouse gas, this has no place in the calculation. Also again why is he multiplying by the increase in CO$_2$? Does he think ALL gasses in the atmosphere increased by 30% that the atmosphere got 30% heavier in 150 years?
1 °C × 0.30 = ??
What is this calculation meant to do? One times anything is always whatever you multiply it by, so all you are calculating is units, but units are ignored in the calculation, and what purpose does multiplying degrees of change times percentage of increase do?
There is no point arguing with Larsen, either he does not understand math (in which case you are wasting your time) or he is purposefully being misleading (and it just gives him attention). Either way there is no benefit to arguing with him. Your best case is he does not understand math otherwise he is just using a completely unjustified string of numbers to have something that looks scientific because it has a equation in it counting on the fact most people who read it don't know enough about math to see the problem.


For dolomitization to occur, either by primary precipitation or by diagenesis, requires a highly magnesian environment and alkaline conditions. The most favourable environment for this to occur is by deeply circulating seawater into the upper mantle which underplates oceanic crust. I don't mean the hydrothermal circulation around spreading centres (which is acidic), but the relatively mild temperatures of submarine groundwater. In the occasional cases where this upper mantle is obducted onto land as ophiolites you will find magnesite predominating, with minor huntite, and dolomite of various early and late-stage paragenesis. The process of serpentinization releases aqueous magnesium, and reaches pHs as high as 12. Moreover, the associated dolomitization starts in the marine environment, and continues after the ophiolite becomes land. For example, you can go to the Semail ophiolite in Oman and find primary and secondary dolomite precipitating - along with occasional metastable huntite and hydroxycarbonates.


How are the thickness of ice sheets from previous glaciation periods determined?

There is no direct way to determine past ice thickness. The only solid information that exists are past areal extent. But, even this information is not necessarily clear since later advances may have overridden the past terminal positions and dating may not be exact. A main issue is the synchronicity of all such positions.

With a past extent it is possible to calibrate numerical ice sheet models, based on our understanding of ice physics and dynamics and generate likely ice sheet configurations. Such models generate a three-dimensional ice sheet which includes ice thickness. In essence this is the best possible scenario for estimating such past ice thicknesses. Advanced models also include some form of isostacy depending on the overlying ice load. For the last Glacial Maximum, the rebound values are also used to constrain the ice sheet geometry.

The problem is, however, that the response of the Earth's crust to loading depends on the loading history and it would be possible to accomplish similar results with different scenarios since the depression of the crust is in part the loading but also the time scale of the loading. For a long time we though the latest glaciation was one long period of glaciation but we now know that, at least the Fennoscandian ice sheet, experienced two major advances, the mid-Weichselian and the Last Glacial maximum and both were relatively short in duration. This allows us to modify the loading history of the latest glacation. With the earlier glaciations, we do not yet have such detailed loading histories and are thus not able to make detailed models of ice thickness.

It should be added the the understanding of the variations of the last ice sheet come from a series of indirect sources such as sea-level changes, paleo-climate records e.g., (ice cores) and interstadial paleoclimate reconstructions. This means that as our understanding of these indirect records are improved, we can also improve our ice sheet forcing. Add to that uncertainties about basal conditions beneath past ice sheets that affect their dynamics and it is easy to see that past ice thickness values are uncertain. We can, however, obtain reasonable estimates from the models which could be accurate to within, perhaps 500 m (my guestimate).


Building massive seawall around endangered Islands like Mauritius to save from climate change

This is more of an engineering question. For some situations it may be possible to build such a wall around some islands. Such a sea wall would be a cofferdam, which have been used for small scale temporary projects.

Complicating factors would be:

The height of the sea wall and how much water would need to be held back.
The depth of to the sea floor. If the island is the tip of a seamount with steep sides and a large depth to the sea floor then a sea wall would be impossible.
The depth into the sea bed that the wall would need to be anchored into, or the wall would need to sink into, for the wall to be stable.
The wall would have to be able to withstand typhoons/cyclones/hurricanes,  small tsunamis and seismic events.

A metal wall would not be a long term solution due to corrosion of the metal. The most suitable material would be rock or concrete. Such a wall would need to be very wide. However, over time, even such a wall would need to be replaced/repaired due to sea erosion and battering.

Securing the wall against leaks would be critical and such a system may require solar power pumps to continuously move excess water out of the enclosure.


Do fluctuations in radioactive isotope decay rates affect carbon dating techniques?

First off, the purported variations were reported to be cyclical. So the net effect on archeological dating would be null even if these variations existed.

Secondly, these purported variations are very dubious. Scientists are not immune from "crackpot syndrome". If anything, scientists are more susceptible to this than the average public. There's a bit of a crackpot lurking in every good scientist. Their job, their very being, is tied up in pushing the boundary of human knowledge. Very good scientists listen to their inner crackpot but keep it inside until they are very sure that their inner crackpot has revealed something new. Not so good scientists regularly expose their inner crackpot for the whole world to see.

What this means is that when you read some extraordinary claim you should be extraordinarily suspicious, at least at first. They might have found something, then again, they might just be exposing themselves.

In this case, I suspect the latter. What I suggest in the case of extraordinary claims: Go to a site such as scholar.google.com and search for the journal article in question. Scholar gives a citation count (oftentimes inflated, but that's a different story). Click on it and you'll get a new page that lists the articles that cited the article in question. In this case, you'll see that there have been a paltry 25 citations in the 8 years since the article was published. That alone is very noteworthy. This article that you think is significant is anything but.

If you dig deeper, you'll see that almost all of those 25 citations are self-citations, subsequent articles by one or more of the original authors who have cited their own work. That makes this article even more suspicious. If you filter out the self-citations, you'll see that the original list of 25 citations dwindles down to two or three, and most of those say "There's nothing to see here. Move along, move along."