Where did the carbon, neon and nitrogen go?

The reason Carbon and Nitrogen are rare on Earth compared to their abundance in space is because elements containing carbon and nitrogen didn't survive the heat of the sun at Earth's distance during the protoplanetary disk stage.   Carbon can form carbonate rock, but only under certain circumstances.  Carbonate rock is rare in space and most of the carbon is in the form of Carbon dioxide.

Oxygen, unlike Carbon or Nitrogen, bonds readily with Silicon, Magnesium, Iron and other heavy elemets, which is why Oxygen is very abundant in rocky planet formation.  It's one of the elements abundant in space-dust, unlike CO2, H20, CH4, NH3, which can form, in colder regions, ice or snow like formations as they begin to clump together, but only in cold regions of space.

The sun didn't precisely have an "event", though young stars after formation can be much more violent.  The initial heat of formation can be very bright and very hot, and young stars are usually rotating very fast and prone to much bigger solar storms and very large mass ejections.   Pretty much all stars go through a violent youth.  It's not a unique event to our solar-system.

Common elements in space, such as CO2, H20, CH4 and NH3 are gaseous at Earth's distance from the sun and as a result, are unlikely to stick to anything in the Earth's formation region.   This is true for all 4 inner planets and likely all rocky worlds.   Rocky planets likely can only form close to their star, just as gas giants, ice giants or other icy abundant bodies like comets and low-density moons, can only form further out.

Gases like the 4 above can begin to be retained around a planet after it reaches a sufficiently large mass with low enough surface temperature to retain those gases by gravity.

The boundaries where CO2, H20, CH4, NH3 and other gases can be found in the protoplanetary disk is called the frost line.  Different gases have different frost lines depending on their freezing point.

It's thought that much of Earth's water, CO2, CH4 and NH3 came to the Earth by comet after the planet formed.  There's still some uncertainty on the percentages, as some of those elements could have been trapped during formation.

Just to add, hydrogen and helium are obviously abundant, but will only begin to accrue around a planet of a certain mass.  In our solar-system, only Jupiter and Saturn are massive enough to accrue hydrogen and helium.   That's why Uranus and Neptune are relatively low on hydrogen and helium compared to the universal abundance.

Argon is in Earth's atmosphere because it forms from gradual radioactive decay of Potassium-40.   Earth's Helium is also present as a result of radioactive decay.


In geology, what is apparent dip and how is it related to true dip?

From https://en.wikipedia.org/wiki/Strike_and_dip

  Apparent dip is the name of any dip measured in a vertical plane that is not perpendicular to the strike line. True dip can be calculated from apparent dip using trigonometry if you know the strike. Geologic cross sections use apparent dip when they are drawn at some angle not perpendicular to strike.

see http://www.webpages.uidaho.edu/~simkat/geol345_files/2012lab2.html


How is known that the Earth core is solid?

This is a good observation. The reason we can measure S-wave (transverse) propagation in the inner core is because P-waves can set up S-waves and vice versa. When an S-wave hits the mantle-outer core boundary at an angle it has a vibration component which is normal to the boundary and this sets up a P-wave in the liquid inner core. The opposite happens at the outer core-inner core boundary, where the P-wave at the boundary sets up an S-wave in the solid inner core. In this way, we can measure S-wave transmission through the inner core.


Subrelluric forces in a volcanic eruption

This term does not exist in volcanology. I can’t even think of a similar sounding term that can be misheard in the song, or misheard by the authors and then put in the song.

It’s possible it exists in a different language but I am not familiar with any options.

Sounds like your best bet would be to ask the band.


Equation for solar radiation at a given latitude?

Ignoring meteorological factors and any dust or satellites, this is still an incomplete problem. You would also need to know the rotation axis. For example, Uranus rotates completely on its side (i.e. it rotates at 97.77 degrees, while earth rotates at 23 degrees, 26 minutes and 21.4119 seconds). Such things become important for factors like the Arctic Circle. You are also missing the distance between the planet and the star. That becomes important when you consider that Pluto is colder than Mercury. This is needed for the formulation of the sterdian.

In your question, you said to ignore atmospheric effects. However, the atmosphere also acts as a secondary source of radiation (the infamous greenhouse effect). Even if you neglect eddies, advection, etc. you also need to consider that the atmosphere can absorb radiation and emit it back to the surface, otherwise you would find the average temperature of the surface to be the same as the average temperature of the earth.

Edit: I found a decent approximation (approximation being the key word).

Let $Q_S$ is the incoming solar radiation flux
$$Q_s= S(1-\alpha)(\frac{\bar{d}}{d})^2cos(\zeta)\tau_s $$
Where $S$ is the solar constant, $\alpha$ is the albedo, $d$ is the distance of the earth from the sun, $\bar{d}$ is the mean distance of the earth from the sun and $\tau_s$ is the transmissivity of the atmosphere (including any clouds above).

The last factor, $cos(\zeta)$ can be computed by$$cos(\zeta)=sin(\psi)sin(\delta)+cos(\psi)cos(\delta)cos(h)$$ where $$\delta=23.45\times\frac{\pi}{180}cos(\frac{2\pi\times(d-d_{solst})}{d_{year}})$$
Where $d$ is the Julian day, $d_{solst}$ is the julian day of the solstice (173) and $d_{year}$ is the number of days in the year (365.25)

Additionally, $h$ is the local hour, as defined by $$h=\frac{(t_{UTC}-12)\times\pi}{12}+\frac{\lambda\pi}{180}$$ where $\lambda$ is the longitude and $t_{UTC}$ is the time in UTC (in hours).


What is the purpose of analyzing the bed-load of a river?

Typically rivers can be divided into three areas when it comes to erosion:

far upstream there is the area where most erosion happens
in the middle mostly transport of material happens
downstream rivers mostly deposit material

Which also can be determined by the shape and size of rocks in a streambed, which correlate directly to erosional force at that point of the river.

larger, rough rocks are rather freshly broken off the bedrock, it takes a lot of force to move these rocks, ergo there is a lot of erosion happening, due to a combination of inclines, amount of water and shape of the riverbed
smooth, smaller pebbles have been in the river for a longer time. They usually have been transported some distance from where they came into the riverbed, which wore them down to their current form. It also takes considerably less force to push/roll a smallish pebble compared to rough chunks of rock. Ergo the erosion at this point of the river is smaller
sand and silt (which still are some form of rock) are typical riverbeds close to the rivers mouth. It takes ages to grind rocks to sand, and it is much easier to transport sand over long distances, so when the sand drops to the riverbed, the erosional force is close to nothing.

For some more information, look here e.g.: http://www.alevelgeography.com/the-long-profile-changing-processes-types-of-erosion-transportation-and-deposition/


The heat equilibrium depth will vary for different locations due to:

Differences in geothermal gradient at different locations (heat emitted by rock). It is generally accepted that the global geothermal gradient is between
${25 ^o C/km}$ & ${30 ^o C/km}$. At some locations the gradient can vary between ${15.4 ^o C/km}$ & ${102.6 ^o C/km}$.
The temperature of the air will increase with depth due to
auto-compression of the air (also known as lapse rate). [Environmental Engineering of South African Mines, 1989, pp 403-404]. The increase in dry bulb temperature of air due to auto-compression is ${9.66 ^o C/km}$, if there is no change to the humidity of the air.
Moisture content of the air. The greater the humidity, the greater
the heat in the air.
Ventilation of the hole being dug and how much heat the moving air is
removing from the bottom of the hole.
Temperature of the air entering the hole from the Earth's surface
The presence or absence of other sources of heat such as machinery, electrical equipment, warm water springs entering the hole and warm bodies.
The age of the hole and its exposure to ventilating air. New holes expose fresh warm rock to air in the atmosphere and the air eventually carries away the heat via ventilation. New holes, or new extensions to holes, are warmer/hotter than old holes.

The shape of the hole will be determined more by its function and geotechnical conditions, such as ground stability, than temperature.


How do I find the temperature of the air mass, and how do I use a t-skew chart?

I don't want to answer your question explicitly because it will ruin your education. Instead, I will guide you by asking three questions:

Where on the Skew-T are you?
Where on the Skew-T do you want to go?
What type of process do you want to undergo to get there? If it is dry and adiabatic, follow the dry adiabat ($\theta=T\left(\frac{P_0}{P}\right)^{\frac{R_d}{c_p}}$)

I recommend drawing the process out. Does the result make sense?


Snow fall can occur under several conditions. In this I am assuming conditions typical for mid to high latitudes. Association with cold-warm fronts are probably most common. Snow fall in mountainous areas can be associated with orogenic clouds and precipitation, when air is raised due to topography creating conditions for precipitation. In addition it is possible to have convective precipitation although such conditions are much more common during summer conditions yielding rain (and when severe e.g. hail).

So when snow fall occurs in association with warm fronts, one could expect a warming since warm air replaces the cold when the front s passing. My guess is that it is this that you have experienced. However, since it is also possible to obtain snow fall during the passing of a cold front the opposite may occur. The orographic conditions concern a more steady situation where the air is affected by  a mountain which is stationary so I would not expect large changes in air temperature unless the air moving across the mountains itself changed temperature for one or another reason. Convective snow fall would not likely yield marked changes in temperature as I see it since the snow would be created by vertical movement of warmer air, cooling to form the snow. I would rather expect a slight cooling, similar to what happens under a heavy rain shower in summer.

So in short, the warming you mention is not generally  associated with snow fall per se but likely associated with the passing of a warm front.


In nature, iron can be either metallic ($\ce{Fe^0}$), ferrous ($\ce{Fe^2+}$) or ferric ($\ce{Fe^3+}$).

In hematite, all of the iron is ferric: $\ce{Fe^3+_2O3}$. In magnetite, it is a combination of both ferric and ferrous: $\ce{Fe^2+Fe^3+_2O4}$. Thus, whether it is magnetite or hematite that are stable is mostly determined by the oxidation state of iron.

Let's look at an Eh-pH diagram:

This $x$ axis is the pH - the acidity of the system. Low pH means acidic, high pH means basic. The $y$ axis is a measured by volts which may not be intuitive, but let's assume that higher values mean that there's more oxygen around and lower values mean that there's less oxygen around.

As you can see, the lower left area of the diagram is dominated by soluble ferrous iron (all the 2+ you see in there) whereas the top right is dominated by ferric iron. You may notice that there is no hematite here and magnetite only exists at the bottom right, but that's because this diagram is for water saturated ambient conditions. The important thing is where you get the ferric and ferrous iron.

Igneous, metamorphic and some sedimentary rocks have an oxygen fugacity (another measure of how much oxygen is around) that results in most of the iron being ferrous, and some being ferric. This is why in these rocks you end up having ferrous iron bearing minerals (olivine, amphiboles, pyroxenes, biotite) and some ferrous+ferric iron bearing minerals (such magnetite). Once you expose those minerals to the surface, where there's loads of oxygen around from the atmosphere, you oxidise the ferrous to ferric iron, and you get hematite instead. Basically, the rocks begin to rust.

Now, there are some processes where buried rocks can get highly oxidised, thus precipitating hematite, but that's not too common. It does happen though, and when it does it usually has something to do with groundwater (which are rather oxidised). Notice that according to the diagram, sometimes you don't need the system to be that much oxidised if it's basic enough (in terms of pH).

There's also this open access paper that talks about conversion of magnetite to hematite:

Jing Zhao, Joël Brugger, Allan Pring, Mechanism and kinetics of hydrothermal replacement of magnetite by hematite, Geoscience Frontiers, Volume 10, Issue 1, 2019, Pages 29-41,
https://doi.org/10.1016/j.gsf.2018.05.015.


Remote Sensing System (RSS) historical atmospheric data continually updated

Being remote sensing, algorithms for inverting the raw data to get physical quantities may be improving with time. Perhaps a slight adjustment in algorithm or calibration happened between July and Sept of this year. However you would expect this to introduce a systematic adjustment, not a scatter.

One might reasonably wonder why the data is steady before 1999. That may be because there were fewer (or different) remote sensor parameters measured then, or the data wasn't as precise.

Another possibility is that the calculation was simply done more precisely, and you are looking at the elimination of round off errors, or different round offs.


What is the earliest sedimentation we know of?

The oldest known metasedimentary rocks are about 3.8 billion years old, formed in the Eoarchaean era.

'Metasedimentary' just means they have been metamorphosed, so they started out as sediments. They are found in the Isua Greenstone Belt of southwestern Greenland. You can read about their discovery in Moorbath (2009). Quoting from there:

  Published zircon dates strongly suggest that the depositional age of at least part of the [Isua supracrustal belt] could be closer to 3.8 Gyr than to 3.7 Gyr.

According to the International Commission on Stratigraphy (Cohen et al. 2013), this puts them firmly in the Eoarchaean era.

References

Cohen, K, et al. (2013). The ICS International Chronostratigraphic Chart. Episodes Journal of International Geoscience 36 (3). Link to PDF.

Moorbath, S (2009). The discovery of the Earth's oldest rocks. Notes and Records 63 (4). DOI: 10.1098/rsnr.2009.0004


The atmosphere has various layers.  Going upwards they are - troposphere, stratosphere, mesosphere, thermosphere, exosphere. (There are "pause" layers between, like tropopause, stratopause etc.) The density gets less and less and the exact height to the top of the exosphere is difficult to determine because the gas is so thin. However, we normally talk about the height of the troposphere which varies from about 7 to 10 km at the poles to about 18 km above the Equator. The reason it is higher at the Equator has to do partly with centrifugal force being greater there. For example, if a jelly-like sphere is rotated it starts to bulge outwards in the central, faster moving region.  Even the solid Earth itself bulges at the Equator due to centrifugal force.  See this blog post for details.


To what extent has the Earth's surface been geologically mapped?

As far as I know there are no official data on this. All I can do is give a rough estimate, based upon work and personal interest in about 30 countries, over 40 years.

We can say with certainty that everywhere has been mapped at the 1: million scale although, at this 'reconnaissance scale', at least half of the land surface is only sketchily known, with sparse ground-truth in areas covered by ice, dense forest or drifting sand. In such areas the best detail is probably from geophysics rather than from actual surface mapping.
For example, gravity anomaly by satellite, or aeromagnetics.

At 1:100,000 scale most areas (I'm guessing 80 to 90%) are mapped wherever there is reasonable bedrock exposure. Certainly in Europe, the America's and most of the world's mountain chains you would be hard-pressed to find areas that haven't been mapped at this scale, although the maps are not all available ('commercial, in-confidence', etc.).
The only exception I can think of is parts of the less accessible Himalayas, where the scales of around 1/2 million seem to be the best on offer. That's not to say that there isn't much scope for further mapping at 1:100,000 scale. Rock exposure changes over time, and many of the existing maps could use a more detailed upgrade, especially in respect of microfossil zonation, facies zonation and structural analysis.

1:10,000 scale or even finer detail is only for the 'very interesting' bits, such as ore deposits, mining tenements, reservoirs and engineering site investigations. There are thousands, if not millions of such maps, most of which are not publicly available. Your guess is as good as mine about what percentage of land is covered by such maps, but I would guess <<1%.

PS I forgot to add that most geology students and academics undertake geological mapping for thesis or teaching purposes. Again, they are often not published, and one has to search quite hard for a copy. These scales are usually somewhere between 1:10,000 and 1:100,000


How do glaciers move? Could Antarctica be separated?

Glaciology is a large field of research, and I cannot include all aspects in a short answer. I'll try to give some concepts that can help you in your understanding of the cryosphere.

Glaciers are, per definition, moving due to gravity towards lower altitudes. There are some exceptions, e.g. rock glaciers are the stagnant remain of a moving glacier.

Large bodies of ice are called either ice caps (if smaller than 50,000 km$^2$) or ice sheets (if larger). Today, we only have the Antarctic ice sheet and Greenland, but during times of larger glaciation, large parts of the Northern Hemisphere were covered. Within the ice sheets, fast flowing areas are referred to as glaciers. Where those areas are formed depends on many parameters such as the mass balance, the basal melting, the topography, etc.

If the glacier or ice sheet reaches the ocean, it becomes buoyant. For larger glaciers, the section near the coast remains bulky enough to remain in contact with the ground.  The point of extent where the ocean reaches under the ice is called the grounding line - a subglacial beach, if you like.
As it's floating, tidal variations moving the ice sheets help it to break up, but in some cases, depending on thickness and topography, it can float in a rather uniform shape which we call an ice-shelf.

The same way as rivers and lakes are formed as rainwater floats towards the oceans, ice sheets and ice caps are formed as snow falls in cold areas, where it doesn't get warm enough to melt during the summer. As the snow accumulates it forms firn and later ice. The ice starts moving as the gravity and shear forces make it unstable.

Eventually the ice will melt, either on the surface due to warm air, e.g. during summer months, or in the oceans as it calves off into icebergs and is warmed by the ocean. Glaciers can also melt on the base due to heat flux from the Earth beneath or due to pressure. In this way, subglacial lakes are formed under the ice.

Large parts of Antarctica are situated below sea level. Partly this is due to the intensive erosion of fast moving ice, but the main reason is that the weight of the ice pushes down the crust into the mantle. If the ice sheet melts, the mass decreases and the land under it will rebound. This happens almost on a human timeline. Some areas, such as Hudson Bay, Scandinavia, and the Antarctic Peninsula, have a fast uplift making sea into land.

Maps from Quantarctica. 1: Ice flow velocity. 2: The topography under the ice. 3: Geoid height (not so relevant for your question). 4: Snow accumulation and blue (=old, hard) ice.

As I've suggested before, I recommend you to download the Quantarctica package. It's rather big but free and easy to use. You can investigate how the ice flows are forming the ice sheet and how the bed map looks under.

The large chunk of Larsen C Ice Shelf that just broke off, doesn't directly reshape the Antarctic continent or cause any change in global sea level, as it was already floating. However, if the ice shelf becomes more unstable, it can affect the ice sheet left trailing it and the flow pattern of the glaciers, and that would have a large impact on most human activities - and beyond.


Publicly available data set with ensemble forecasts and observations?

You can try if this looks simple enough. Still requires registration, but it is free for reasonable use: Global Ensemble Forecast System (GEFS).


Does the amount of rainfall relate to temperatures of a place?

Yes, with exceptions

Rainfall is related to temperature. However temperature is not the only thing that dictates rainfull.

In general, the more hot a place is, the more water evaporates and the more rainfall is able to be produced.

For example, the equator has a belt of rain-forests precisely because it receives the highest amount of heat from the sun and thus high amounts of rain-fall.

However, not all hot places make a lot of rain. Deserts occur when there is a lack of rain fall. Yet deserts can occur in cold temperatures (the north pole) and hot temperatures (Sahara desert).

To sum, temperature is certainly related to the amount of rainfall. However, you can't just presume the level of rainfall by temperature as many other factors are invovled.


Fictional Land - How can I keep dense fog in an area for half a day?

The heat of the Sun can "burn off" fog. So a lack of direct sunshine, cool temperatures & humidity (evaporation of water from a nearby body of water or saturated or wet ground) are key to maintaining fog. The air must be moist!


Giant Cavern the Size of Manhattan Under Thwaites Glacier in West Antarctica

The cave is created by warm water, so the ice has been replaced by the water.

It is common to find areas under the front of glaciers that have been melted away by warm water.

Warm water here means just warmer than the ice.

The thing that's making this news is the scale of the area that has melted away.

This is the situation scientists have been predicting to happen as our planet warms, water advancing inland below the ice and possibly making the glacier move faster.

Ice that is connected to bedrock will create friction making the ice move at a slower pace. When ice is no longer connected to the bedrock under it will loose this friction and possibly speed up the flow.

This might be one of the tipping points making the ice melt at a faster pace.

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

As fred say in his comment ice moving over bedrock will create friction this friction will create a layer of liquid water lubricating the ice and make the ice flow faster,And when ice melts at the surface of the ice the melt water will run down cracks in the ice and reach the bedrock lowering the friction even more.


How to count lightning in a thunderstorm?

There are many types of devices used for measuring lightning. The first natural radio wave receiver was also the first lightning detector invented by Alexander Stepanovich Popov. In 1896 Popov presented a paper on a wireless lightning detector he had built that detected radio noise from lightning strikes.

Popov's discovered that lightning produces radio waves. Popov discovery originates from the fact that lightning produces light and sound. If the sound of the thunder is produced by the rippling of air because of the expansion of air produced by the heat of the lightning, then Popov thought that lightning could produce other forms of energy too. This other form of energy turned out to be radio waves.

Popov's designed a very sensitive coherer (a primitive radio signal detector) connecting it to an antenna that received the radio waves from the lightning. The coher was also connected to a circuit with a battery and a relay that rang a bell and sent a pluse to a chart recorder that could mark the occurrence of the lightning.

Popov built a radio receiver that could only receive natural radio waves from lightning (then the only good source of radio waves) leading him after to build an artificial radio transmitter.

The radio waves of lightning travel much farther than the light and sound it produces so a lightning detector can measure the distance to the lightning strike. Some of today's lightning detectors use this basic concept. With four of them you can combine the time at which each device measures the radio signal from the lightning and determine the strike location. Meteorologist today call this detector a ground-based lightning sensor.

There are other devices used to measure lightning using other kinds of antennas and signal processing techniques like radar and temperature data. Lightning detection can also be from advanced devices on artificial satellites. Using direct observations such as with the Geostationary Lightning Mapper a near-infrared optical transient detector can detect changes in an optical scene, indicating the presence of lightning, frequency and location of lightning events.

Alexander Stepanovich Popov radio receiver and lightning detector.

Further information:

Alexander Stepanovich Popov: https://en.wikipedia.org/wiki/Alexander_Stepanovich_Popov

The Popov Lightning Detector: http://weatherbreak2.creighton.edu/?p=1809

A Brief History of Lightning Detection: http://scijinks.jpl.nasa.gov/lightning-detection/

Geostationary Lightning Mapper (GLM): http://www.goes-r.gov/spacesegment/glm.html


It depends what your practical purposes are. Maybe you can treat it as 0. But in general, no, because it is not closed, due to geothermal heat flux, and anthropogenic imbalances. Also, even if assuming 0, that would be over long time scales and integrated over the earth surface. There are spatial heterogeneities.


Is it theoretically possible to artificially create amber?

Yes, and this has been done since at least the mid 19th century (Răducanu, 2006) initially it was done to keep up with the demand, but now is a source of scrutiny for valuation of samples (Pederson and Williams, 2011; Răducanu, 2006).

Imitations have been produced by heating the following (Răducanu, 2006):

Polymers, such as polyester and polystyrene
Casein
Glass
Celluloid
Other resins, such as phenolic resin
Copal - this is referred to as 'pre-amber tree resin', a natural intermediary substance between tree resin and amber.

Both Răducanu, 2006 and Pederson and Williams list several techniques as to how to tell them apart from authentic amber.  Pederson and Williams, 2011, also detail that some artificial samples are so close to amber that spectroscopy techniques are required to tell them apart.

References

Pederson and Williams, 2011, Copal vs. amber, Organics

Răducanu, 2006, Actual Exigencies Concerning the Quality of Amber
Pieces Commercialized in Romania, Universităţii Petrol – Gaze din Ploieşti


Can winds also arise due to a statistical probability that more air molecules suddenly gets an equal direction?

This is perhaps more of a physics question than an earth science one. Thus, answering with the caveat that I am not a practicing physicist:

Yes, it's possible. But it's VERY unlikely. Without doing the maths, I'm guessing "probably won't happen in the lifetime of the universe" unlikely. The reason for this is that there are a LOT of molecules in any macro-scale parcel of air, and a huge majority of them would all have to randomly move the same way at the same time. (plus, I'm guessing there are some Newton third-law, ie action & reaction, reasons why a spontaneous mass movement wouldn't really work)


How is surface pressure generally measured, and at what actual height?

When you look on meteorological maps the "surface pressure" is actually the reduced MSLP (mean sea-level pressure) value.  See this NWS page for more info.  So whatever height the sensor is at above the ground, they regardless compare that height back versus the sea-level to report the pressure.

I always figured barometers were sited along with the main instrument set.  Those indeed will all generally be raised up off the ground certain heights (aside from any soil temperature thermometers) to prevent issues with any standing water or snow cover.  See for example the instrument list and extensive pictures for Oklahoma Mesonet site locations (slightly different setup, but the 2 meter temperature and 10 meter wind are widespread standards).

But I was surprised to read in the ASOS User's Guide that:

  At virtually all locations, the pressure sensors are located indoors
  within the ACU.

And:

  The ACU, which is the central processing unit for the ASOS, is usually
  located inside a climate controlled structure, such as an observing
  office or control tower building. It ingests data from the DCP(s) and
  pressure sensors, and is capable of accepting information from the FAA
  New Generation Runway Visual Range (NGRVR) system.

So it sounds like the barometer is often not on site, and there are indeed no specifications for height.  But since it's reduced to sea level regardless, the elevation is all that really matters to reduce it to MSLP, and so some variation in height of the sensor shouldn't matter.


Which part of solar radiation (VIS, NIR) keeps Earth warm?

Electromagnetic radiation converts based on frequency and exposure. Visible light and Infrared waves are the predominant energy sources that can penetrate the atmosphere. Higher energy wavelengths (UV and above) do interact but are often bounced by significant portions. Those radiations interact with atmospheric gases; emit infrared waves in the process.


Seeking details for the "historical rate" of arable land loss

No context is given, but at face value this is a meaningless quotation. Globally there is a net increase in arable land from close to zero about 8000 years ago, to the current maximum of just over 40% of the gross biological productivity of the planet. 'Arable land loss' can refer to the land lost to urbanization, salinization or desertification. One might also make a distinction about agricultural land lost to hydrologic intervention, as in the decreasing flows of the Amu Darya, and Sur Darya in Central Asia. In addition, over the coming decades we will begin to see agricultural land lost to climate change impacts. No single assessment of the 'historical rate' of arable land loss is meaningful. One has to evaluate the various processes separately, and then aggregate them at regional level.


How many buildings in tornado prone-areas have storm shelters?

Have you perhaps contact the National Weather Service or FEMA about that ? If not, then maybe find out from real estate that they might have data for each houses in your state. They may have the data or not, but it is hard to know. All I know is that each state has different types of soils that can or can't built storm shelter. I heard in Texas almost 1/2 of the buildings there do not have a storm shelter, because the soil in Texas are not strong enough to withstand against the flooding. That kind of thing ...

I do not know if you have seen this, https://stateimpact.npr.org/oklahoma/2013/09/27/mapped-which-oklahoma-schools-have-storm-shelters/

http://www.esri.com/news/arcuser/0104/storm.html

Another one is the reason why an individual passed away from flooding in a storm shelter
http://mashable.com/2015/05/07/oklahoma-city-storm-fatality/#KGEHNAxU5sqq


The reliability is dependent on the quality, (for instance is the mineral reworked or porous and thus prone to contamination),  and size of the sample, (small samples result in poorer measurement). There is also of course the date range issue, use a sample that is too old or too new and the amount of each element is so tiny it can't accurately be measured. Thats why multiple measurements are always taken, if they vary wildly you know something is wrong. A good general rule for modern studies is expect a date to vary by ±5%.

Potassium-argon can be compared with relative dating methods like fossils and bedding as well as absolute dating methods like Uranium-Thorium, Uranium Lead, Rubidium Strontium, and even it's own dates to check for consistency. This is always being improved upon and multiple dates from different methods are sought whenever possible so there are tens of thousands of comparisons.

There is a good article about it here. They also provide a good example study (under the title a good example) which compares several methods for dating the K-T boundary and yields an error of about ~1 million years between them . Beware of older studies (1970's or older) which can have much larger error bars.

For other studies comparing lots of dates your best bet is large scale timescale reconstructions like this one which will compare dozens if not hundreds of individual dates.


List some common metrics to analyze the atmospheric vertical motion?

First of all, I am unsure if your question relates to Numerical Weather Prediction (NWP) or field-experiments. I would say divergence is one of the best variables to look at since vertical motion is both difficult to measure and to model. Also, some nowcasting models which includes a nudging method to increase precipitation intensity in the model, based on the observed intensity does this by nudging the divergence field directly, to generate more or less vertical motion.


What would be the sea level rise if all fossil fuel resources are burned?

At the upper end of that range, all ice on Earth would melt.

That would ultimately give roughly 70 metre sea level rise from melting ice alone, but it may take thousands of years before it reaches equilibrium.

Add a bit to that to account for the thermal expansion of sea water.


Why do some planets have lots of $\mathrm{N_2}$ and others none?

For Earth, Titan and Venus, I think there are continuing processes that are providing $\ce{N2}$ to the atmosphere of these planets.

Concerning the Earth, there is the well documented Nitrogen cycle based on flora.  There are also other significant sources for nitrogen from inorganic processes.

Deep crust/mantle core sources for nitrogen: Nitrogen solubility in mantle minerals
Volcanic eruptions : Volcanic gas
Metamorphic processes : Anomalous nitrogen isotopes in ultra high-pressure metamorphic rocks from the Sulu orogenic belt: Effect of abiotic nitrogen reduction during fluid–rock interaction

Assuming the rock processes on Earth are also occurring on Titan and Venus, similar inorganic processes may be occurring on other worlds. I think it is a good educated guess even though we really have very very little hard evidence of rock processes other planets.

As for Mars, its thin atmosphere may indicate that is cannot hold onto $\ce{N2}$ and there may be very little $\ce{N2}$ currently being created on Mars.


What Makes Round Holes In Superior Agates?

Agate sometimes contains fossils. Your specimen seems to contain a fossil crinoid disc, and probably there are more than one. Crinoids are plant-like animals anchored to the sea bed, and are sometimes called sea lilies. Many species  became extinct millions of years ago, but a few survive today. The stems of ancient crinoids were made up of stacked discs, rather like the one in your agate. When the crinoids died, their stems often disintegrated, and the discs became scattered. The hole you mention is the hole found at the centre of all crinoid discs. For some reason it did not become full of agate, perhaps because there was a gas bubble or some other obstruction in there. I can't predict what you would find if you cut it in half, that decision is entirely up to you. I think it would probably be best to leave it as it is.


Why does the salt in the oceans not sink to the bottom?

When dissolved in water, salt breaks up into sodium and chlorine ions, which combine with water molecules so they cannot easily sink. However, there is a tendency for streams of fresh water to float on salt water and rise to the top. This caused problems for British submarines in the Dardanelles Straits during WW1. Moving from almost fresh water to the denser salt water, they suddenly became more buoyant and rose involuntarily to the surface, making them visible to Turkish gunners on the shore. There are also parts of the ocean where there are pools of very salty water lying on the bottom in such a way as to clearly show the pool to any diver who happens to see it, as though it were a pool on land, so in some circumstances very salty water can sink.


Acoustic impedance in geophysical context

This concept actually comes from the electrical. They define the impedance as $Z=\frac{V}{I}$.
Where V is potential difference/ voltage and I is current.

In acoustics, a similar expression can be obtained using the plane wave equation.
Since,
                $$\partial_t V = -\rho^{-1}\partial_xP$$
where $P$ is pressure and $V$ is velocity.
Now take fourier transform of both sides and defined impedance as $$Z(\omega)= \frac{P(\omega)}{V(\omega)} = \rho c$$
Where, obviously, $P$ is analougous to potential difference and $V$ is analougous to current.

You may refer to any wave theory book for details.


Do daily operations (max, min etc) on climate model data reference different periods because of UTC?

Yes, your understanding is correct.

(this is a really short answer because I can't think what else to say!)

I'm no expert on this type of simulation, but I suspect that any application where you care whether something happens in day 158 or day 159 is probably not an application that you want to be using a global climate model for...


What factor(s) could cause this sort of temperature increase, mid-night/early morning?

Temperature swings opposite from those expected by the diurnal radiation pattern (warming during the day, cooling at night) are typically due to air coming in from other locations.  Synoptic (large-scale) fronts can bring such rapid shifts, but often tend to be more sharp (rather than gradual) and in one direction (as the front passes).  However occasionally there can be interesting oscillations near more stationary fronts, such as this event from Oklahoma in February 2018:

More often, smaller nighttime fluctuations have to do with more mesoscale (local) features.  Different regions cool differently, and the pressure differences caused by the resulting differences in density move the air around... two common causes of such shifts can be circulations around oceans or other large water bodies (probably not pertinent to you!) and terrain-induced circulations (probably much more pertinent!).  The ones that are probably most impactful at night are downslope winds, which are caused by more rapid cooling on the mountain than the air around it, and downvalley winds, caused when enough air builds up from downsloping.  This lecture from Stephan De Wekker gives some more details on some of these features and other terrain flows.
Often slight shifts in larger-scale wind direction and the varying temperatures over different degrees of mountains and valleys can lead to quite a complicated set of rises and falls in temperature through the night.
It's also not impossible that are some issues with your station, I was initially concerned with a few things:

The winds in particular seemed odd -- due north the entire time is always suspicious, and less than 1 mph for an entire night and early morning, while certainly not impossible, makes it a bit more questionable as to whether significant temperature advection could occur.
Plus it's also rare to see temperature and dewpoint changing almost 100% exactly in step over long periods of changes -- moisture tends to be slower to alter except around sharper fronts (and on nights when the temperature nudges lower while the air is saturated [$T=T_d$]).

But a look at observations across the region for the time period:

does show perhaps your data isn't impossible.  The meteograms from Libby [KS59] and Missoula [KMSO] below do show very weak/calm winds and fairly similar temperature/dewpoints movement.

Still, there's no north winds (except when calm, which is a placeholder when there is no wind), and a slight bit more fluctuation between temperature and dewpoint, so it wouldn't hurt to check whether the station is properly observing.
I believe typically flows down a local mountain tend to be cooling at night, as the densest air (coldest) collects along the river.  Other features driven by forced air movement can bring warm air to valleys, like foehns and large-scale downsloping, but those tend to bring drier air in.
So assuming it's a valid feature, it appears to be something complex.  It can take years of observations to really understand the flows around complex topographic areas.  But I would posit a guess that maybe a slight wind shift gradually pushed the pooled dense valley air away from you far enough to get you into slightly warmer air away from the river valley bottom.  Or maybe winds become enough to mix down warmer air above.  Differences in snowcover/melting effects or clouds/precipitation might also play a part in what you experienced.  But in that part of the world, I'd expect you'll see many more peculiar local temperature fluctuations over your time observing!


Why are frontal zones connected to low-pressure systems but not to high-pressure systems?

Not only are fronts associated with (extratropical) lows, but by in large, fronts are extensions of those lows, as shown by the following hand analysis (from the US Storm Prediction Center):

There's a lot going on in the image, but try to focus on the many black lines, which show pressure: they're kinked around each front (and even the dryline).  This indicates that the pressure is higher on either side of the front.  (for another good example: this set of images from the 1993 Storm of the Century from the National Weather Service).  Now the kinks in these drawings aren't caused by the actual layout of observation in the image, but added by the understanding of the meteorologist performing the analysis.  Generally observation sites are too widely spread out to see the small pressure kinks.  However, they do sometimes show up in high-resolution numerical weather models forecasts, even despite not being in the initial observation data they run from:

(From Hartung as indicated... note that the kinks are up instead of down, but that's actually the same result, still pointing away from the low, showing lower pressure at the center of the kinks.)

Though pressure troughs can be spatially hard to see without extremely dense observation networks, they can be made out instead in temporal plots at single locations.  After all, falling pressure has been noticed as a sign of bad weather as far back as the the dawn of America (I often hear Benjamin Franklin cited, but it appears it goes back further to Otto von Guericke in the 1600s).  For example, this trace of temperature and pressure from a 1911 cold front in Louisville, Kentucky:

(source: Louisville NWS)

So, WHY are fronts low pressure areas?

It goes to its nature in connection to winds.  Consider the images below:

(ETA images courtesy of Iowa State's MTArchive)

The plots are two days apart.  So how do you get the conditions to change from the left image to the right over such a period?  While clouds, storms, and sunlight differences can help drive small contrasts, the only way to get such a large, widespread boundary... is to have winds develop that draw the contrasting temperatures tighter together...

Indeed, this is exactly what forms and sustains a front.  You can look at surface weather maps and almost always see this convergence, or gathering together of winds, at fronts, even if only slight, as indicated in this idealized diagram set:

(Image modified from OKFirst, the education arm of the Oklahoma Mesonet program.  See comments for modifications I made.)

The thing is, there's only a few basic forces that drive wind formation... and in the lower atmosphere, it turns out that the pressure gradient force outweighs the others enough such that, on the large-scale, air always flows from higher pressure towards lower pressure.

So if you put those two ideas together:

To create/strengthen/sustain a front, you need wind converging together
Air at low-levels flows from high pressure to low pressure...

The resulting conclusion is that the location where winds are flowing together... which is the front itself... must be a low pressure area.

(What causes low formation in the first place?
Winds aloft typically coupled with terrain enhancements or other small-scale perturbations.  The strengthening temperature gradients actually feedback to intensify and favorably realign the winds aloft... such that, despite the influx of air into the low pressure (which one might think would "fill in" the low pressure with more air, dimi), the air is actually ventilated from the system, allowing it to deepen to yet lower pressures values and strengthen further... continuing on until finally the upper-level storm system surges ahead of the surface low and/or the frontal boundary occludes, cutting warm air from continuing to flow into the surface low center.)

Can you get divergent winds near a developed front?
Yes... in fact, there's a name for that process, it's called frontolysis. Divergent wind does indeed work to destroy a frontal gradient.  And so rising pressure is found connected to dissipating fronts.  However, rising pressure has a long ways to go before it's actually a high pressure itself!  Long before it would create a bona fide high, the early pressure rises only REDUCE the strength of that local pressure minimum... and during that time the temperature gradient will very quickly begin to blur out and fall below the strength of which we really notice.  At the same time, even in this period of decrease, note that this dissipating "front" would no longer have any of the other typical conditions we expect with fronts (no more rising air motions [UIllinois], which is what in turn creates the unsettled weather, clouds, strong winds, storms, etc).

Why is a front so quick to dissipate?  Well, in large part because it's not a level situation; indeed, some storm energy is continually lost away to friction.  Because of this, a front actually needs continual reinforcement to even maintain its gradient.  Some times the pattern will permit fronts to continue through repeated periods of weakening and intensification as upper troughs pass by.  As a trough comes by and then shifts by on east (in tandem with the primary surface low), the front will start to weaken some... perhaps gradually becoming stationary... only to reignite when the next upper system comes in from the west [stationary fronts aren't, as may often be suggested, a cold front and warm front "at war", but instead rather more like a lull in the "battle", where the cold front has run out of steam, but readied next for the warm air to start surging back north should another trough/low move in to re-fire the convergence].  Often you can see quite a long chain of fronts (troughs) connecting together lows pressure systems across continents... (which work into the shape and positioning to the polar jet stream).  Other times, when the upper systems come less consistently or the upper flow starts to break down/shift into other regions, the front will quickly fade from existence.  So much so that I don't believe you're ever not going to see anything like a true front anywhere near a formative synoptic high pressure... unless maybe a giant meteor or as-of-yet-unseen-in-size nuclear bomb were precisely set loose upon a front.  And then... well I suggest trying to witness the brief time that the high pressure is connected to the frontal boundaries... should probably be the least of your concerns!

Of course an important note is that not all lows have fronts, not nearly.  Only "extratropical" (baroclinic, cold-core) lows have fronts.  Tropical (barotropic, warm-core) lows are symmetrical, and don't generate their energy from horizontal temperature imbalances, but instead when overall warming temperature, typically in the mid-levels, decreases the amount of air in the entire tropospheric column...

Found on the AOML, but originally adapted from Merrill, R. T., (1993): "Tropical Cyclone Structure" - Chapter 2, Global Guide to Tropical Cyclone Forecasting, WMO/TC-No. 560, Report No. TCP-31, World Meteorological Organization; Geneva, Switzerland

And for those of you better versed in the more rigorous science... while looking for material for this answer, I came across an absolutely great resource that may prove helpful to those looking to dig much more at the mathematical formulations of frontogensis/frontolysis, the consequential flow types involved in them, and how they impact forecasting: this awesome guide from NOAA's Warning Decision Training Branch.


Do forests affect local rainfall and climate significantly?

For rain to fall, water vapour must exist in sufficient quantities in the atmosphere. The main source of atmospheric water vapour is evaporation from oceans. However, evaporation from large bodies of water such as lakes and dams also contributes. Another significant contributor, on a local level, is transpiration from forests.

  the Amazon alone creates 50-80 percent of its own rainfall through transpiration

Removing forests has

  the biggest impact on cross-continental transport of water vapour

Removal of trees from an area of forest immediately stops transpiration in the that area. This causes less rain to fall in that area. It changes the way light is reflected from the Earth's surface, which changes the heating characteristics of the ground, which changes air movements. It will also have an influence on ground water levels and depending on local geology can bring salt to the surface causing salt scars and eventually desertification.


Why aren't seismic stations installed very deep underground so as to pre-warn from earthquakes?

The simple answer is that you can't drill to 50 km depth.

The deepest holes ever drilled were to a little more than 12 km, one is named the Kola Superdeep Borehole in Russia, which was a scientific drilling project. The very few others were oil exploration boreholes.

Drilling that deep is extremely expensive and hard. If you go and ask anyone who ever worked on a drill rig, drilling the second 100 metres is always harder than the first 100 metres. And we're talking about kilometres here! There are several problems with drilling that deep. It's extremely hot down there, and the drilling equipment just breaks and stops working. You also need to pump cooling water in and pump out the stuff you're drilling and it gets harder with depth.

This is simply not feasible. Now let's say that you did somehow manage to drill a hole to that depth. How would you put monitoring equipment inside? That equipment has to sustain heat and pressure and still keep working, while being able to transmit whatever it's reading back to the surface. This is not going to happen, not at 50 or 10 km depth.

Another problem is that not all earthquakes are that deep. Some earthquakes originate near the surface, or just several km deep. Having a monitoring station down there isn't going to help. The 2011 Tohoku earthquake (the one that triggered the tsunami at Fukushima) was only 30 km deep. Same thing for the 2004 Indian Ocean earthquake.


Are there other divisions of Earth following beyond hemispheres?

Not, IMO an ES question, but depending on what level of division, and if you are talking about the surface only or a partition of the sphere extending to the core, terms such as spherical sector, spherical cap, and quadrant would be fairly common descriptive terms for parts of a sphere.

Cap would be the portion of the sphere cut by a plain passing though the sphere.  The Hemispheres are caps cut by the plane passing through either the equator or the poles.  Normally a cap would describe an area formed by cutting the plane parallel to the equator, as in the lines of latitude.

A sector would be a cone centered and the center of the sphere and extended to the surface.  Think of a cone capped by a cap as described above.

A quadrant would typically be a wedge, think of an orange wedge, or a part of one.

I do not think any of there really are especially common to use in relationship to Earth though they are valid descriptors.  Lines of longitude and latitude are the common differentiation that describe these divisions, and phrases such as above/below the 45th parallel to describe the halves of the Northern Hemisphere.


Why did the Australian bushfires cause pitch darkness during the daytime?

It's a combination of both the density and amount of smoke in the air and ash produced by the fire.

The thing about cold fronts and bush fires is they make the conditions for fire worse by pushing hot air in front of them. They have been blamed for the severity of the bush fires in Victoria in 2009, 1983 and 1939.


How to interpret the use of late and early Tertiary from older literature?

I think this is very hard to answer this question as it is exactly this ambiguity that caused the International Commission on Stratigraphy to discard the names Tertiary and Quaternary for there are no clear limits to these era's. For example, the name Quaternary was only introduced some 70 years after the name Tertiary (source), and Neogene covered both the last part of the Tertiary as well as the Quaternary era (source), until in 2009 the Quaternary was reinstated as a period while at the same time redefining the boundary of the Pleistocene (source), so interpretation should take into account when the article was written as well.

The meaning of Late and Early Tertiary is therefore dependent on the context, and is probably only safe to be interpreted as relative ages (unless exact ages are given, but in that case there is no question of interpretation), not well defined periods in time. It might help to look for articles by the same author or from the same year to see what the common interpretation was at that time.


Why would geostrophic theory be invoked in the tropics with regards to the MJO?

Recent literature points to an attempt to understand the theoretical dynamics behind the MJO as seen in these two publications - Dynamics moisture mode vs. moisture mode in MJO dynamics and A general theoretical framework for understanding essential dynamics of Madden–Julian oscillation

As concluded in the original paper by Madden and Julien oscillation the key is to observe that original MJ observations were either in a in phase relationship of the surface pressure and the zonal wind(850 hPa) or out of phase relationship. No such relationship was observed with the meridional wind.

So the "geostrophic balance" in the MJO(in it's non dimensional form) is simply this equation

$$  \beta * y*u = -(\frac{\partial \Phi}{\partial y}) $$

So $\Phi$ here represents the first baroclinic mode (the meaning of baroclinicity in the tropics is quite different to it's meaning in the mid latitudes). In the tropics what it means is that vertical structures of winds and currents that reverse directions (cf. MJO review). So the MJO has a baroclinic mode of vibration because the winds reverse direction from 850 hPa to 200 hPa.

So in the assumption (proven by observations) that the  MJO can be characterized as a low frequency wave with an anisotropic horizontal length scale where the zonal length scale is much larger than the meridional scale by a magnitude of 10.So the meridional acceleration in the v-momentum equations can be neglected. With this approximation the zonal wind is in approximate geostrophic balance with the meridional pressure gradient  and all high frequency inertio gravity waves, mixed Rossby-gravity waves as well as short Rossby waves are all filtered out. So that only leaves the moist Kelvin and long Rossby waves as well as the MJO.

Alternatively if one were to consider the Rossby radius of deformation in the case of the MJO the horizontal wavelength of the disturbance if equal to the Rossby radius of deformation then both the velocity and mass fields undergo mutual adjustment as illustrated in these slides - Waves in Atmosphere  on page 52.

Similar conclusions were arrived at to derive balanced dynamics in the tropics by assuming linear theory and a shallow water model - Balanced dynamics in the tropics

UPDATE
Looking at other peer reviewed references that attempt to provide an explanation of the MJO it appears that an assumption of linear theory wrt to the MJO is not universally accepted and that non linear advection does have a role to play in the slowly propagating planetary scale disturbance(cf.Simple model of the 40-50 oscillation. A later paper by Madden(cf.Seasonal variations of the 40-50 oscillations in the tropics reports that  there can be substantial meridional wind perturbations bringing into question whether the assumption of geoostrophic balance is universally valid or not in the case of the MJO.

The original paper by MJ in the light of the observations obtained then perhaps made a conclusion that the structure and dynamics of the signal could resemble a Kelvin wave in which case the geostrophic balance of the Equatorial Kelvin wave (no large scale meridional wind perturbations and the equator acts as a wave guide ) could be used to explain the geostrophic balance in the case of the MJO. Later observations have proved this assumption incomplete.


Relationship between illuminance and cloud cover

I don't believe such a formula or table exists (but admittedly, I have not attempted a lit review in this subject).  Sky coverage (cloudy, mostly cloudy, etc) is a the fraction of the sky covered by clouds, not how much light penetrates to the surface.  Even with a mostly cloudy day, all it takes is one break in the clouds between the sun and your instrument to give the same illuminance as a clear sky day.  You might take a time series of illuminance obs and consider the fraction of time with clear sky readings, but this will be faulty unless you can take into account cloud motion.
From the AMS Glossary:

cloud cover
(Also called cloudiness, cloudage.) That portion of the sky cover that is attributed to clouds, usually measured in tenths or eighths of sky covered.

The term "partly cloudy", for example, varies in interpretation but is generally around 0.3 or 0.4 to 0.6 or 0.7 cloud cover (where 0.0 is clear sky and 1.0 is overcast).
The type of cloud will also vary the light transmitted.  A high cirrus or altocirrus cloud layer will transmit light to the surface, whereas a low stratocumulus overcast will only transmit a small fraction of light (note how grey and dreary a northern winter day can be under those clouds).  The fraction of light transmitted will depend on the depth of the cloud layer. The light transmitted will also be a function of time of day and day of the year, both of which determine the position of the sun.
For a look into how these issues play out in a real experiment, take a look at Pfister et. al. (2003) who look at how cloud fraction and irradiance are related over New Zealand.  I think you'll find most of the literature deals with solar irradiance, so it may help you in searches to look for that term rather than illuminance.
Note that the linked Ametsoc article is free to read, as area all Ametsoc articles at least 2 years old.
References
G. Pfister, R. L. McKenzie, J. B. Liley, A. Thomas, B. W. Forgan, and C. N. Long, 2003: Cloud coverage based on all-sky imaging and its impact on surface solar irradiance. J. Appl. Meteor., 42, 1421-1434. doi: http://dx.doi.org/10.1175/1520-0450(2003)042<1421:CCBOAI>2.0.CO;2


What controls how quickly groundwater gets recharged from rainfall?

What controls how quickly they refill with rainwater?

Really it depends on where the aquifer is. Letting rain top off a Hawaiian aquifer may take a few weeks. However, refilling the aquifer beneath the Atacama desert may take tens of millions of years. That assumes that the recharge source is actually overlying the aquifer; in many cases, it's not, thus adding lateral distance that recharge must travel.

Regardless, drawing down an aquifer does lasting damage and they will never refill to the same reservoir capacity. Once groundwater is pumped out, the solid materials are then free to further compact and reduce the pore spaces that would be re-filled. In the case of California's San Joaquin Valley this sediment compaction, or, surface subsidence, has caused a permanent loss of nearly %10 of the aquifer's recharge volume.

  Could these reservoirs be refilled faster if an outside pump refilled
  them using rainwater?

In one sense, sure, there are groundwater recharge systems that work as closed-loop systems: groundwater is pulled out of the ground for use by a community, treated by the waste-water system after being used, then pumped back underground some distance upgradient. Aurora, Colorado, for one, has such a system in place. Note that the system isn't used to filter the used groundwater, but to keep it from being wasted when draining it to a local river. Furthermore, groundwater levels must be kept stable lest compaction ruin reservoir capacity.

  What are the energy economics on doing this for a place like Nebraska
  or Bangladesh?

They may be entirely manageable, but the politics would be NUTS! After all, rainwater is a "surface" resource that is promised to users downstream from where it falls. Diverting it underground for the exclusive use of a community would be like trucking parts of Himalayan glaciers to Delhi with no regard to downstream users who depend, for example, on the Ganges.

You could fill a couple of academic libraries with proper answers to your questions, by the way!


You could try building one using a global Digital Elevation Model. There are several freely available like TanDEM-X, SRTM, or ASTER GDEM. You'd have to look for all the pixels containing a negative value. Adjacent negative pixels would give you connected regions below sea level, and you could easily estimate their area just by multiplying the number of pixels of a region by the area of one pixel.
I'm not saying it would be easy. The main challenge would probably be that some regions would be split across several tiles.

An update on this. I spent a couple hours trying this as an exercise. I downloaded three tiles from the ASTER global DEM centered around Badwater Basin (Death Valley, USA), one of the regions in the Wikipedia list. I wrote a small (~20 lines) Matlab script that does the following:

Binarization of the images, so that every pixel above sea level is set to 0 (black) and every pixel below sea level is set to 1 (white).
Concatenation of the three arrays in order to have only one image for the next step (I manually added a fourth, all black array for the sake of dimension consistency).
With a binary image, Matlab has a useful function called regionprops that finds all connected regions and returns their properties, such as their area (as a number of pixel).

Here is the result:

I'm pretty happy with it, as it looks very similar to the yellow area labelled "below sea level" on this USGS map.

Now, how does it translate in terms of area? According to Matlab, the white region has an area of 1 236 989 pixels. Each pixel being approximately 30x30 meters, it yields a below sea level area of 1 113 km$^2$. The only figure I could find online is 1 425 km$^2$ from Encyclopedia Britannica, with no source. But for me that's close enough to have confidence in my estimate!
Some shortcomings:

I knew exactly which tiles contained this particular below sea level region. If you were to go through all tiles (almost 23 000!), you'd have to figure a way to detect when a region is split across multiple tiles in order to reconstruct the region by concatenation. Doesn't seem that hard, but not trivial.
I did not take into account the fact that there is a one pixel overlap between adjacent tiles (it should not change change the result much).
I did not take into account the fact that pixel size actually vary (the resolution is one arc second, which is ~30 meters at the equator but changes with latitude).


If storms form above low pressure regions, why doesn't the eye of a hurricane, a low pressure region, have any storms?

While hurricanes are low pressure systems, their structure, determined by the Coriolis Effect as you mentioned, is determined by winds getting deflected slightly from rushing directly into the center of the storm.  This deflection causes the characteristic rotation of large scale low pressure systems, including hurricanes.  When a hurricane forms and surface low pressure deepens, a balancing anticyclonic high pressure system actualy forms in the upper troposphere, above the budding storm.

Air at this altitude actually spirals out and away from the center of the cyclone, pulling more air below in toward the eye (causing a positive feedback loop).  However, some of this high pressure, high altitude air "leaks" inward towards the center of the storm instead of outward, and pressure eventually increases enough that it counteracts the strength of any updrafts in the center/eyewall of the storm. This air begins to descend (subsidence) in the center of the eye, stifling any convection and causing clearing at the mid and lower levels - creating the famous stadium effect.

The convection/rising motion in the storm is caused by air converging as it approaches the center of the hurricane.  Essentially, when there is a bunch of air rushing toward the center of low pressure, it has nowhere to go when it arrives but up, thus forming updrafts!


Is a hotter climate making trees grow faster and have lighter wood?

Nothing to do with climate change . Faster growth produces somewhat lower density and strength. There are strength tables for wood written more than 50 years ago that have separate listings for "new " growth and "old" growth. "New " growth being trees growing faster in clear cut areas with less competition for water, light and nutrients. Old is trees in areas that not previously been harvested and grew slower in crowded conditions.  Power line failure is related to the increase in numbers of power lines in expanding populated areas, and to how much money utilities spend trimming trees near the power lines.  When I drove in western Europe  in the 80's , I was impressed by how many of the forests had been "managed". Large old trees had been planted in regularly spaced straight lines ,maximizing growth speed = lower density . As silviculture is a minor hobby of mine I expect I noticed things others would not.


A frost-gley is a waterlogged permafrost soil. IOW, a gleysol that has undergone cryoturbation.


What is a typical value of the Péclet number for internal waves?

I don't have personal experience with this situation, but reading around suggests it depends what kind of mixing you are talking about, for example whether it is vertical or horizontal.

Looking around for recent examples, I see Chao et al. (2007) had a value of 4.0 m2/s for horizontal diffusivity. This larger value would give you a smaller Péclet number of 150. Your use of wavelength for the characteristic length suggests you might be more interested in that dimension?

Chao et al. used ~10–5 m2/s for vertical diffusivity, and I find Bogucki et al. and Lien et al. using ~10–2 m2/s and ~10–2 m2/s respectively. Those are not too distant from your number, and it looks like Moum et al. are talking about vertical mixing. However in this case I am not sure you want to use horizontal length and velocity; you might consider asking about this in Physics.SE, using the fluid-dynamics tag.

In any case, as we hone our intuition about such things, I like this quote from Durran (1999):

  The Péclet number is completely analogous to the more familiar
  Reynolds number, which is the ratio of momentum advection to momentum
  diffusion. The difference between the Péclet and Reynolds numbers is
  due to the difference in the diffusivities of heat [or mass] and
  momentum. [My addition]

I like this because it suggests that some of the same intuition we have about Re may apply to Pe too, especially the fact that it can vary by several orders of magnitude (from here):

Whale swimming at 10 m/s, Re = 3 × 108
Duck flying at 20 m/s, Re = 3 × 105
Copepod swimming at 0.2 m/s, Re = 3 × 102
Larva swimming at 0.001 m/s, Re = 3 × 10–1
Bacterium swimming at 0.00001 m/s, Re = 1 × 10–5

Reference
Shenn-Yu Chao et al., 2007, Assessing the West Ridge of Luzon Strait as an Internal
Wave Mediator, Journal of Oceanography, Vol. 63, pp. 897 to 911, 2007. Available online.
Durran, D, 1999, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer. Google Books.


Why limestone formation was not a concern in atmosphere oxidation event?

First, let me clarify this again:
Al2O3 is not clay.
Now, back to topic. You are mixing apples and oranges here. The geological section you are referring it was deposited 2 billion years after the GOE. This was long after all surface iron was oxidised, and abundant oxygen was present in Earth's atmosphere.

Nowhere you will see the (oxidized) Ferrum in noticeable amounts

Iron is not present in this geological section, but it is present elsewhere. You are looking at one specific section in one specific locality on Earth's surface. It is flawed logic to infer what you are based on this.

How could Fe be the major consumer of the oxygen despite calcite is present in much larger amounts?

Because at this stage, neither calcium nor iron were "consumers" of oxygen. Oxygen has been consumed before, and then this consumption stopped once all of the iron was oxidised. This is why oxygen today exists in the Earth's atmosphere.
From the comments:

@Pont The layer is younger, it is basically made of oxides. A terrible amount of oxides appeared after the GOE but their formation did not delay the atmosphere oxidisation the way free Fe did.
I have checked the chemistry. Calcium + water gives me hydroxide. It will exchange CO2 for H2O to from the limestone. This suggests that we still consume Oxygen from the atmosphere. Which pre-oxidization are you talking about?

Metallic calcium probably never existed in the Earth at all. The GOE was a process in which only iron was oxidised (out of the major components of the Earth's crust). The oxidation of calcium, aluminium, silicon, etc, occurred much before that. It occurred when the Earth was forming, and possibly even in the solar nebula that existed before Earth even formed. This was 2 billion years before the GOE.
Let's put this on a time line:

~4.5 billion years ago, Earth formed. Calcium, aluminium, silicon were all oxidised. Only some of the iron was oxidised.
~2.5 billion years ago. Photosynthesis causes oxygen to rise, but the rise is limited because of the presence of iron in the crust. Any oxygen that is produced, is consumed by the oxidation of iron. Eventually all iron is oxidised and oxygen contents can freely rise.
~0.5 billion years ago. The section you refer to is deposited.


How to map (survey) the structure of crust

What you have probably seen in the movies, as used by the oil and gas industry is reflection seismology. This is where you shoot off a sound source (explosives, airguns, etc) and track the reflections of the sound waves from the various rock layers below the surface.

At a smaller scale, there is Ground Penetrating Radar, good for a few 10s of meters at best, which is higher resolution and good for detecting voids.


What is this weird looking structure in Ethiopian desert?

Zoom in for the clues. The lines are not radiating out from the village, but from the cattle kraals. These kraals are irregular enclosures built of acacia thorn, agave and other thorny bushes. The cattle are kept in these kraals at night to protect them from hyenas and packs of wild dogs. The cattle themselves are likely African longhorn or various local cross-breeds with Sebu. They are creatures of habit, walking out from the kraal in the early morning, and back in the evening. They follow the same track for several hundred metres before the cattle diverge in slightly different directions. In the more concentrated paths decades of hoof-prints erode the dusty soil, often in trenches to depths of 60 or 70 cm. When it rains, runoff drains into the paths where it collects as red mud, the latter being derived from the deep weathering of basalt. The cattle are led by villagers who each have allocated pasture land, hence the constancy of direction.

This is the most striking example I have seen. Often it is not as obvious because, at least in wetter areas, there is more local grass, and the cattle are tempted to disperse 'closer to home'. On the ground one can see these in many parts of East Africa, from the Simian highlands of Ethiopia to the Simiyu pastures of northern Tanzania.


Terminology

The term "average" isn't a specific term.  Are you talking daily average or annual average?  The question "What is the average?" begs the question of "Across what timeframe?"

To explain that point, let's look at a chart:

This is the groundwater level of a well in Georgia (US).  The "Average" for this well in December 2003 would be 176.9 feet below ground level.  However, for the year 2003 altogether, it would be around 177 feet below ground level.  For the previous decade, the average would be around 175 below ground level.

Timeframe

To answer the question, the best timeframe is the largest timeframe you can afford to gather.

If we look at the Raw data for the above chart, what we see is that for the year 2003, the groundwater levels went up!  If you only gather one year of data, this well would show a dramatic rise in water levels, which would clearly not be accurate.

If you extended the search back five years, you would see a large downward trend.  March 1998 shows 173 feet depth and March 2003 shows 178 feet depth.  This trend indicates a dramatic loss of water volume.  However, without a larger timeframe, it's impossible to tell if this is just a negative trend or a cyclical one.

Even in the chart above, the mid-1960s may just have been a high point in the water table.  (Indeed, Georgia saw 15% more percipitation in 1967 than is historically average and 1999-2001 were historically low.)

Summary

The best timeframe to gather data is the longest timeframe that you can get.


Would a hurricane increase intensity due to increasing translation speed?

It is not the quite the numerical relationship you have described  in your question but YES the effect of translation(or forward speed) upon the intensity of tropical cyclones in the tropical oceans has been studied in this peer reviewed reference - Tropical cyclone translation speed and intensity correlation

The conclusions that the authors have reached  is that there is a positive correlation with translation speed and tropical cyclone intensity. The explanation for this correlation is that a tropical cyclone with a faster translation speed reduces the exposure time of the cooling to the TC. The sea surface cooling is induced by the effect of the surface winds on the ocean and and strong winds can bring cooler subsurface water to the ocean surface . A slower moving TC is exposed to the sea surface cooling for a longer period of time and hence contributes to a negative SST feedback and has lesser chance for  reaching higher intensity.

You  can read a popular science version of the peer reviewed reference in this website - Hurricane speed intensity


What is the second thermometer in the image from the Esperanza Antarctic temperature record?

Doing a quick calculation that looks to be around the wet-bulb temperature at the time of observation so that thermometer on the right side should be a hygrometer. Hygrometers measure the level of moisture in the air as opposed to a thermometer that measures the temperature level.

Edit: The calculation was based on a recorded observation scoured from here as finding the history of observations at the station was proving difficult. The observation marked a temperature around 64 degrees F with a relative humidity value of 34%. Using this online based calculator which gives a rough estimate of the Wet Bulb Temperature, the calculated value came out to be 49.47 (F) or 9.7 (C) which was close enough for me to determine that the thermometer on the right was a hygrometer. Aiding that assumption was the fact that thermometers and hygrometers are sometimes paired together for observations.


Are cloudy nights warmer than nights without clouds?

Is there a correlation between temperature and cloud, during the night?

Very much so. It's called radiative cooling. Three factors come into play: cloudiness, relative humidity, and windiness. Nighttime radiative cooling is greatest under clear skies, low relative humidity, and light or no winds. The temperature drop (in degrees per hour) can be a factor of more than four greater under conditions of clear skies, low humidity, and light winds compared to that under conditions of thick low clouds and high relative humidity. That increased cooling can make for a significant temperature drop on a long winter night.


I normally use Google Scholar, but Elsevier also has the non-public Scopus (which means I have to use a campus proxy). Also CiteSeerX but the semantic side is not as rich.


What exactly is a published climatologist?

Not answering the question asked, but the underlying motivation:

The level of consensus hasn't been verified by a poll. The way the 97% figure has been arrived at, AIUI, is by going through every single peer-reviewed and published paper on the topic of anthropogenic climate change and looking at whether says that it does or does not exist, and then assigning these views to the authors of the papers. Why bother with a sampled poll when you already have studies using the entire literature?

If you want more detail on the methods used, the various studies that came up with the 97% and similar figures are themselves peer-reviewed and published. This is a review paper looking at them.


In what sense did the Oklo reactor "trap" its own nuclear waste?

According to Record of Cycling Operation of the Natural Nuclear Reactor in the Oklo/Okelobondo Area in Gabon, the Xe is trapped in crystalline cage-like structures formed of the aluminum phosphate that are similar to zeolites.

The reference also explains that the aluminum phosphate structures grow quickly under hydrothermal conditions of 270-300 degrees C.


Why is carbon dioxide the gold standard in greenhouse emissions - and not nitrous oxide?

There isn't enough nitrous oxide in the atmosphere to make a major contribution to global warming, which in some ways is a pity, because we'd all bee in a much jollier mood if there was (N2O is sometimes known as laughing gas). It also depletes the ozone layer if it gets up that high, though depleting ozone at ground level, where it is harmful, is a good thing. Compared to N2O, there are vast quantities of CO2 in the atmosphere, enough to create millions of tons of wood and other plant materials every year. The whereabouts of N2O in the atmosphere, whether it is high up or low down, probably has some bearing on the matter.


How can we calculate the total water mass that falls during a flood?

I don't have the answer for you, but I can point you to the tools that can be used to get such an answer.  The Advanced Hydrologic Prediction Service compiles rainfall grids using radar, surface observations, and a variety of other sources.  Options offered include daily, month-to-date, and archived data.

You can probably quite reasonably put the Shapefile download option into a GIS application, such as Grass GIS or ArcGIS, then limit it to the state (or area of interest) and compute an average or total.

Alternative, you can download it as NetCDF, which I know you'd be able to open in GrADS/OpenGrADS, mask it to a certain area using some sort of shape file or geometry, and then run an areal average on it.

I really do wish more straightforward, user-adaptable data were easily available (and no guarantee it's not, I just don't know a source).  But at least this will give you the tools to figure out.

And while you're focused on rainfall, perhaps read up on central California's Great Flood of 1852!

One other way to get an estimate of the total volume of water would be to use stream flow values combined with reservoir level changes, and attempt to estimate what percentage of rainfall escapes the reservoir system.  But at that point you're getting a very rough estimate, because the monitoring system doesn't measure every small stream emptying into the sea... and a significant (and varying) percentage of the water infiltrates the soil or evaporates.  Those complications could be incorporated into the calculation, but in the end, that seems a complicated way to solve a problem we already have more complete information on.

You asked for how much water that is.  Well, we can just as easily get a fair estimate from the map:

(month to date as of February 22nd)

If that's an average of 8" over the state of California, that's:
$ \pu{8 in} \times \pu{163,696 mi}^2 =$ 23 trillion gallons

Even if we're off by a factor of as much as 2 on the estimates, such that it's only 4" average, or alternatively 16" average, that just changes it to 11.5 trillion gallons and 46 trillion gallons.

Which begs the point... we don't often think in terms of trillions of gallons.  Trillions of gallons seems a ton, but even just a meager 0.35" over the state would equate to a trillion gallons.  Perhaps normalizing it to the area... such that it'd be $ \pu{140000 gal/mi^2}$... is a little better.  But still, a typical person would struggle to recognize whether any given value in this form would result in a flood or a droughts.

That's why we often just work in terms of percentiles, or graphs, or return periods, or just give the average in terms of inches itself.  It may not click great with everyone, but for many, such units are just a little more interpretable.

(And in case you wondered, a gallon of water weighs about 8.36 pounds, so that's about 100 trillion pounds of water, again sounding like a lot, but to most people, so does 1 trillion pounds of water from a little 0.10" inch rain system)


Yes. In fact there are already volcanos associated with the San Andreas fault system.

Neenach is an extinct Miocene volcano split in half by the San Andreas fault. Garry Hayes wrote a nice blog post about this volcano system: A Volcano Sundered: A Field Trip Along the San Andreas Fault.

If you'll allow some latitude in what counts as 'a San Andreas volcano', then there is active volcanism too. The Salton Buttes are a group of rhyolitic volcanos in the Brawley Seismic Zone, a set of oblique transform faults — actually in the axis of the active Gulf of California rift — on the south-east shore of the Salton Sea. You can see them in this Google Maps image (on the right; the big fields are 800 m across):

The Space Shuttle photo (left) of the Imperial Valley annotated by the USGS shows the relationship between the San Andreas fault, about 5 km from the volcanos, the Brawley Seismic Zone (BSZ), and the Imperial Fault to the south. At this scale, it's essentially one big fault system.


Why antarctic research stations are built above ground instead of on the ground or underground?

Antarctica is a whole continent and it is as diverse as any other continent.

There are two reasons buildings are often built off the ground on pillars.

1.- Avoid snow accumulation: Although in average Antarctica is a dry continent, in some coastal areas there can be massive amounts of snow accumulation. Building on pillars spare the buildings to get buried and most importantly allows the wind to blow the snow away. If you build on the surface, the snow will accumulate on the lee of the building. This happens even if there is very small snow fall, because wind transport the snow for long distance and the lee of a building is favourable for accumulation. Therefore, even it snows 1 mm, the millimiter that fell in all the ground 100 km upwind can end up piled behind your hut, and block your door.

2.- To rise buildings: Many of the bases are built on ice, and all those are buit on the accumulation area of glaciers or ice sheets. Therefore, with time the surface will rise relative to the building and will eventually swallow it. Therefore, in many cases (like the Amudsen-Scott base at the South Pole). The pillars are designed to be extended, therefore allowing to rise the building as the ice below thickens, keeping it at an optimal distance for the ground.

Regarding the inquiry about soil temperature, again that is too broad. Imaging asking about the soil temperature in North America, the answer would be quite different for Mexico than for Alaska. The same contrast can be found between bare ground areas of the Antarctic Peninsula at latitude 60°S and at almost 5,000 m of elevation on Mount Vinson plateau at latitude ~80°S


Is this article self-contradictory, or am I missing something?

There's no contradiction. Firn is an intermediate form between snow and ice, with a density between that of snow and ice.

The frozen fluffy stuff that falls from the sky -- that's not ice, it's not firn. It's snow. It's also not very dense, typically less than 0.5 grams/cm3. As the snow sits and gets compressed by snow atop it, some of the gas gets squeezed out. The snow changes from ice to firn. The authors are using density between 0.55 and 0.82 grams/cm3 as the definition of firn. As the firn sits even longer, it changes from firn to ice. Note that solid frozen water (no air pockets whatsoever) has a density of about 0.934 grams/cm3. Compressed former snow with a density of 0.82 or higher acts a lot like ice. It is ice, not firn.


What causes the semi-annual mesospheric meteoric potassium variability?

Recent observations and modelling by Plane et al. (2015) and Plane et al. (2014) have described the most likely mechanisms for why potassium has its unique semi-annual variability, with a small summertime maximum and minima occurring at the equinoxes (Plane et al. 2015).  The semi-annual variability is consistent across the globe (Plane et al. 2014).

In both papers, the cause of the unique semi-annual variability are narrowed down to 2 main atmospheric chemical dynamics, based in no small part on unique K chemical properties:

(Note: MLT = Mesosphere-Lower Thermosphere)

In summertime, the maxima observed is due to the cooler MLT temperatures being low enough to neutralise K+ ions to K.
During the equinoxes, O is at a minima, while CO2 and H2 exhibit a maxima - so, according to Plane et al. (2015)'s model, decreasing O, while increasing CO2 and H2 causes a reaction with K to form KHCO3, thus resulting in K being at a minima.

According to their models, KHCO3 returns to K by largely temperature independent photolysis.

Plane et al. (2014) describe there is a slight decrease in K in high latitudes in the presence of polar mesospheric clouds.

References

Plane et al. 2015, Resolving the strange behavior of extraterrestrial potassium in the upper atmosphere, Geophysical Research Letters

Plane et al. 2014, The Mesosphere and Metals: Chemistry and Changes, Chemical Reviews


How big a risk is Mount Vesuvius for the local population?

There are lot of studies on the past activity of Mount Vesuvius. Eruptive deposits have been studied and dated in order to reconstruct the type and timing of past eruptions. This can give some indication of what to expect even if, and I cannot stress this enough, past activity patterns of a given volcano does not predict its future activity. It can give a tendency, but volcanoes remains unpredictable, as shown by recent examples in well-monitored countries like Japan (Mount Ontake 2014 eruption) or Italy (paroxysmal eruptions at Stromboli last summer).

That being said, a study by Cioni et al. (2008) came up with some interesting results. They found that there is a positive correlation between the magnitude of an eruption and the repose time before this eruption. Meaning: the longer we wait before an eruption of Vesuvius, the larger the eruption will be. It's their figure 6:

You can see that Strombolian (= small) eruptions happen after a few years of repose while sub-Plinian and Plinian (= large, like the one that destroyed Pompei) eruptions are preceded by long repose periods. However there is some scattering, especially in the zone shown by a red box:

  In particular, a large variability in the magnitude and eruption style of the past eruptions is apparent for a window of repose time from dozens to hundreds of years.

And now we are exactly in this box: the last eruption of Vesuvius was in 1944, 76 years ago... So according to this study, and assuming the volcano will keep following this pattern (which is not sure), if Vesuvius does erupt tomorrow, it could be up to a violent Strombolian eruption. This type of eruption would not be a major threat to the local population; the main threat is pyroclastic density currents (PDC), which happen mostly with sub-Plinian and Plinian eruptions (their Table 2). The last eruption (1944) falls in the "violent Strombolian" category; lava flows destroyed several villages, but no one was killed.


If a person uses public transport, how much carbon is added to the footprint?

I'm no expert on such subjects, but did Google and immediately this Guardian article offering a dataset apparently attributed to Camden Council/travelfootprint.org/Clear Zone Partnership.  There are a lot of different values, but (if I understand the columns labels correctly), a rough breakdown of the footprints would be ranges of:

Bus: 20-90 g CO$_2$/km
Train, Diesel/Diesel-Electric: 30-150 g CO$_2$/km
Train, Electric [Long-Distance or Subway]: 10-70 g CO$_2$/km
Flight: 190-460 g CO$_2$/km

Walking: 5-25 g CO$_2$/km
Biking: 7-18 g CO$_2$/km

Basic car, Diesel: 40-180 g CO$_2$/km
Basic car, Gasoline: 40-200 g CO$_2$/km
Basic car, Liquefied Petroleum: 30-180 g CO$_2$/km
Basic car, Natural Gas: 30-150 g CO$_2$/km
Basic car, Gasoline Hybrid: 30-150 g CO$_2$/km
Basic car, Electric: 7-110 g CO$_2$/km
Motorcycle: 20-190 g CO$_2$/km
Scooter, Electric: 4-30 g CO$_2$/km

[See the report for other automobiles, including family cars, SUV, and minis]

(The best end of the range is the more efficient models run at peak capacity in best conditions [rural roads/medium distance short-haul flights]
The worst end of the range is less-efficient models at quite low capacity in less-efficient conditions [urban roads/very short or long-haul flights]
[Rail appears fairly similar in all usage circumstances, thus only depending on model/network setup, at least in this UK data])

This data attempts to take into account secondary sources (such as power plants for electric vehicles or needs of the agriculture which is used for the energy to walk/bike).  As you can see there's a wide range depending on how most transport is used.  You're best suited diving further into the table to find the most applicable use case for you.

My list only shows CO$_2$... the database also includes NO$_2$ and some others pollutants (if you can break down the abbreviations!) which can be very important too.

And this is UK-specific.  So the equipment models used, network efficiency, and even climatological conditions will vary for other locations.

The date on the article also suggests its almost a decade old.  So we have likely seen some additional improvements in some formats (though it seems unlikely that they are giant leaps in most cases).

Hopefully someone will come along with more recent and wide-ranging data, but this seems like a good start at some rough estimates.


Is it possible to obtain the richter grade of an earthquake with the data of an accelerometer?

The Richter Number is a measure of total energy released in an earthquake.  To calculate it, even roughly, you need to know the epicenter of the earthquake (that needs at least three measurements from three locations) and the length and intensity of the shaking to determine the energy contained in the waveform.  All you seem to have with your accelerometer is the peak intensity of the shaking at a single point.  So the answer is no.


Time relativity relating to Carbon dating?

Earth travels along its orbit at about 30km/s. If you plug that number into a time dilation calculator, you'll find that one second on Earth passes every 1.0000000050069 seconds in a Sun-centric reference frame.

Carbon-14 dating is good only to about 40,000 years into the past; Earth's time dilation would reduce that 40,000 years by a little under two hours, or far below the precision of the technique.

Edit: I'd like to address three more issues. First, the rotation of the Earth's surface only results in about 0.5km/s at the equator, and so is insignificant compared to the orbital velocity. Second, nothing has changed the Earth's orbit for many millions of years, probably for billions of years, so that would also have no effect on the dating.

Third, and more important, we're all traveling along on the Earth at (approximately) the same speed. So you, I, and a group of C-14 atoms in a fossil will all experience the same time dilation.


Can the Air Mass Factor (AMF) be negative?

No, AMF is always positive. Depending on the retrieval algorithm, negative SCDs can occur as artifacts. You should look at your retrieval algorithm but in general I'd treat negative values in such a situation as "below detection threshold" values. Depending on what you are doing replacing them by 0 might be a valid course of action.


How to know to which PC (Principal Component) a sample belongs in EOF/PCA

I recommend you read Monahan et al. (1990) for a thorough explanation of Empirical Orthogonal Functions. I suggest you pay attention to the way the principal components are extracted. Ultimately, there is no guarantee that a sample belongs to a specific component. What you are working with is eigenvalues/eigenvectors and thus a specific data point can have influences from multiple components. The EOF provides a time series of eigenvalues for each component. The larger the eigenvalue for that component at a specific time, the more that component explains the data point.

If what you need is to assign a data point to a component, I would recommend a cluster analysis instead. For instance Smith & Aretxabaleta (2007) present an improved methodology to separate regimes that outperforms the EOF analysis in an ENSO-influenced dataset.


This is related to a similar question on April 29th in that the apparent colour of the sky is mainly caused by the absorption of different wavelengths of light by a wide range of atmospheric pollutants. I strongly suspect that if you compare the antecedent rainfall with the colour of the sky (in a given direction at a given time of day) you will find a marked correlation. The rain scrubs the atmosphere clean, so, facing away from the sun, you are likely to see a brighter blue after any period of significant rain.
So what is the typical amount of rain in spring, summer, autumn and winter, in your part of France?


What are these features in the Tombouctou Region?

Those blue colors are basically artefacts due to image processing.

The last one in Bing Maps doesn't look blue at all. It's just somehow slightly darker with some trees or large animals. The local change of color might be caused by humidity (maybe a seasonal pond) or animals, or both - if animals come to drink. Interestingly, there are similar shapes in the area and Bing Maps traces paths converging on them. I don't know how Bing gets those paths (I can't see them in the aerial imaging) but they are consistent with animal paths leading to ponds.

And the second one is just the bed of a dry lake, with salt pans.

The first one lacks coordinates, but we can assume it's just a another color enhanced rather normal piece of desert.

Edit

To actually answer the question "I am wondering if this is some kind of satellite imagery to detect heat or moisture? Or is this the actual colour of rock/mineral?", as requested by comments:

The answer is "No, it is neither the colour of rock/mineral or a heat or moisture detector. Blue color is just an artifact due to image processing, as can be seen from comparing those Google Maps images with linked Bing Map images of the same places, which aren't blue at all".


In radiometric isochron dating why is at t=0 D*/Dref=const but P/Dref not?

1) D* (radiogenic isotope) and Dref (stable reference isotope) are two isotopes of the same element. P is the radioactive parent of D*, and is a different element. Chemical fractionation between P and Dref occurs as the rock solidifies because different elements are preferentially incorporated in different minerals depending on how well their ionic radii and valences are compatible with the mineral's crystalline lattice.

Although there can be some mass-fractionation of isotopes of a same element, it is usually very small (IE negligible) relative to the chemical fractionation.
Often, for making such isochrons, geologists choose different mineral species with very different P concentrations (and thus varying P/Dref) to provide spread along the isochron line; this allows for more precise regression and determination of the slope / age.

2) The second diagram you show is a concordia plot, not an isochron. There is no common isotope on the ratio denominator. Rather, this plot shows two different isotope systems each with their own decay chain (238U->206Pb and 235U->207Pb), these two Uranium decay chains have different half lives. The curved line is the "concordia" curve, which is the expected result if the sample exhibits closed-system behaviour (IE Pb has not diffused out of the crystal).

In this case a mineral (probably a zircon) was formed at 2.6 Ga and had open system behaviour at around 0.4 Ga. (IE the radiometric clock was partially reset). The straight line is called a "discordia line" and is a mixing line between the two time points on the concordia curve.