Interpolating spatial data in contiguous sea areas only

A very neat approach for optimal interpolation, which consider not only breaklines along the coast but also anisotropies caused by currents and horizontal diffusion, was given by Lynch & McGillicuddy (2001). Their approach is quite elegant and takes advantage of the finite element methodology to avoid the transfer of information across boundaries.


What kind of climate could you expect in a mountainous area in a subtropical region?

Do any of the resources here help you with historical rainfall trends for your area? Those are probably going to be a better guide than any approximation based on your latitude, altitude, and terrain as to what you can grow. I say this because at 5800ft the mountains are going to control your weather way more than a lot of other factors that are important at sea level.


Which type of convergent boundary creates the tallest mountains?

The type of convergent boundaries is not the only factor. From the current configuration of the world one could be tempted to say that Continental-Continental collisions would form the tallest mountains. And they are indeed the most dramatic tectonic collisions and they formed the Himalayas, that are almost 2,000 m taller than any other mountain on Earth. However, the india-Asia collision wasn't any collision it was the most dramatic collision in a long time with convergence rates of 16 cm/year, way more than any current convergence rate.

From USGS

Therefore, the convergence rate is also a very important factor. The tallest mountain outside the Himalayas is mount Aconcagua in an oceanic-continental boundary. With a convergence rate of about 6 cm/year, and that have been below 16 cm/year at least for the last 22 million years.
So it is difficult to say how tall would be Mount Aconcagua if you speed up the convergence rate between Nazca and South America plates by 260%.

I don't think there is a definite answer to your question, unless you constrain other factors, like convergence rate, plates thicknesses, etc.


From my understanding, you are thinking along the right lines but also need to take mountains into account.
Ireland's mountains are lower than Japans. I think that Japan's mountains are a similar height to Oregon's but the high mountains are closer to the coast in Japan. (I don't know either area well, so this statement could be wrong.)
Another thing to consider is that in winter, convective showers are common over the sea. A longer sea track will have more showers and therefore more mixing of the atmosphere, raising the temperature of the air mass.
Winter convection cuts off over land, but showers can penetrate inland a little with the momentum they already have. The closeness of the mountains to the coast in Japan, as well as their height, will give more orographic enhancement to the amount of precipitation as well as possibly reinvigorating the unstable convection by forcing it to rise. Ireland's lower lying status won't have this effect as much.
Oregon has two ranges of mountains, the lower Coastal Range (<1000m) and the higher but 150km inland Cascades (~3000m). The Coastal Range has a similar height to the Irish mountains but are longer in their extent. The orographic enhancement of the Coastal Range will be much less than in Japan. The Cascades will then be in a rain shadow as the air will be less humid downwind of the Coastal Range. While the Cascades still cause orographic enhancement, this is nowhere near as much as if the Cascades were by the coast, which in Japan they effectively are. You can see this effect on the annual average precipitation map of Oregon:

As an aside, I had wondered if the Sea of Japan might be warmer than around Oregon and Ireland; this would provide more heat, moisture and instability to the air reaching Japan. I had a quick look at February sea surface temperatures, and they seem broadly comparable to the other areas, at least for the past three years, so this enhancement mechanism seems unlikely. February appears to be the month that Japan gets the most snow, although I'm not sure if that's talking about peak snowfall or peak accumulation.
I found a few articles about Japan's snow online:

National Geographic: The world's snowiest place is starting to melt
Ski.com: Why is there so much snow in Japan?


Is the seafloor of the Gulf of Mexico and Caribbean Sea mostly sedimentary rock?

Yes and no. Caribbean Sea and Gulf of Mexico have sedimentary materials and rocks at the top, but seabed sensu stricto is composed by sediments and not by rocks.

Oceanic Crust is composed by basalts and gabbros, both igneous rocks as you notice, and sedimentary materials above. We know that because of drillings and fossilized ophiolites:

  Source: earth.s.kanazawa

The Gulf of Mexico is not an exception and has sediments at the top, as said in this paper:

  "Most sediment originates from the adjacent land, primarily via fluvial transport. Direct precipitation of calcium carbonate and evaporate minerals takes place primarily on the Florida and Yucatán platforms and some coastal lagoons. The deep environments tend to be dominated by mud in a combination of terrigenous and biogenic sediments." (Davids Jr, R.A.,2017) 1

Caribbean Sea is neither an exception, as remarks Encyclopedia Britannica:

  "The ancient sediments overlying the seafloor of the Caribbean, as well as of the Gulf of Mexico, are about a half mile (about one kilometre) in thickness, with the upper strata representing sediments from the Mesozoic and Cenozoic eras (from about 252 million years ago to the present) and the lower strata presumably representing sediments of the Paleozoic and Mesozoic eras (from about 541 to 66 million years ago)" (Menzies,R.J. et al, 2019) 2

This article says there is one kilometre of sedimentary materials, enough to diagenesis to take place and so, there are sedimentary rocks under the unconsolided sediments.

At open oceans diagenesis may have still do not have place and there is only the ophiolitic sequence with thin sediments, but, as you can read in this related answer, Caribean Sea have old igneous rocks with a big stack of sediments above that have litified to sedimentary rocks (coming from continental rivers and carbonaceous platforms), becoming the biggest oil source zone on Earth after Arabian Gulf.

1) Davis R.A. (2017) "Sediments of the Gulf of Mexico." In: Ward C. (eds) Habitats and Biota of the Gulf of Mexico: Before the Deepwater Horizon Oil Spill. Springer, New York, NY

2) Menzies, R.J., Ogden, J.C. (2019) "Caribbean Sea." In: Encyclopedia Britannica.


How can I downscale daily values of relative humidity?

Your approach to calculate an hourly temperature and relative humidity independently could be problematic, as these variables are dependent on one another.  I'd be interested to see a plot of one such day of $t$ and $rh$ and then to calculate the water vapor mixing ratio or dewpoint from your values and see how it varies in response and whether it is realistic looking.

If all you have in mean $rh$ and and a min/max temperature, one approach might be to derive a mean temperature and then from that a mean water vapor mixing ratio.  This mixing ratio can vary through evaporation, condensation, boundary layer mixing, etc, but for a rough approximation you could assume it is constant.  If you assume a constant mixing ratio and a temperature profile (e.g. your sinusoidal assumption) you could calculate the $rh$ profile for the day.  Note that you'll have to assure that your temperature curve does not cool below the dewpoint. You have the mean $rh$ as a crosscheck for this method and can use that to iteratively adjust your method for obtaining the water vapor mixing ratio.

Your diurnal temperature profile will vary based on latitude, time of year, proximity to large bodies of water, and weather.  If you discount the weather you can get by with your sinusoidal approximation with your minimum temperature at local sunrise and your maximum temperature in the mid to late afternoon.  The amplitude of the sine wave will be dependent on the your location (e.g. coastal locations will have small amplitude changes and inland desert locations will have large changes).  With a constant water vapor mixing ratio this will yield the highest RH at the temperature min at sunrise and the lowest RH in the mid afternoon.

If you can provide a $t_{max}$, $t_{min}$ and $\overline{rh}$ and a rough idea of where on earth your are looking at, I can run some numbers and provide more detail on this method.


How do they get "deep lunar mantle" samples?

There are three ways samples of the mantle could arrive on the surface of the Moon.

Drilling deep holes into the mantle, take a sample and send to the
surface.
As ejecta from a large deep impact crater, particularly where the
crust is thin.
During volcanic eruptions, the upward moving magma tears of chunks
of mantle from the walls of the volcanic "vent" and ejects pieces of
mantle embedded in the resulting lava as xenoliths.

We know the Apollo astronauts only drilled down about 20 cm into the regolith, so there are no drilled samples of the Moon's mantle. This means that the only way we might have a sample of the mantle is by serendipitously picking up a sample from the surface after it was ejected by the other two methods.
The Chinese rover Yutu, on the far side of the Moon, in the South Pole Aitken Basin

... which was formed by a celestial collision over four billion years ago. With a diameter of 2,500 km and a depth of about 13 km, the basin is the moon’s oldest and largest impact crater. Very large impact craters can potentially penetrate through the crust and enable probes to sample the lunar mantle.
... the lunar soil at the landing area contained a large amount of olivine, low-calcium pyroxene and a small trace of high-calcium pyroxene, which are very likely from the lunar mantle.

Notice the term "very likely" near the end of that quote.
If no one has ever seen it, how do we know what the lunar mantle looks like?

The properties and composition of planetary interiors are inferred by indirect evidence.  Seismometers left on the surface by Apollo crews measured the velocity of seismic waves inside the Moon, an indirect measure of the density of the deep interior.  The density of the mantle is high enough so that common surface rocks cannot make up a significant portion of it; the rocks must contain large amounts of the minerals olivine and pyroxene.  In addition, the mantle rocks were partially melted to make the mare basalts that cover the surface in places.  The chemical composition of these lavas show they were made by melting a rock rich in magnesium and iron.  Finally, xenoliths of the Earth’s mantle are sometimes found entrained in lavas – these pieces are made up of the olivine-pyroxene rock peridotite (after the mineral olivine (the gem form is peridot) that makes up most of it.)  So the idea that the rocks of the mantle are olivine-rich is a well-grounded concept for which we have abundant independent evidence.

Concerning the Apollo samples,

Despite an exhaustive search of the Apollo samples, no samples of the mantle have been found, either as a fragment of basin ejecta or as a xenolith in the mare basalts.
... Data from the orbiting Japanese Kaguya mission shows that olivine is present in the surface deposits of some lunar craters.
... they mapped out the occurrences of these olivine deposits and found that many of them occur within the rims of large impact basins.  Based on models produced from gravity mapping, the crust of the Moon is thought to be thin here and the mantle is close to the surface.  Thus, these large impact basins could have excavated chunks of the mantle, throwing them out onto the surface of the Moon.
... Why is the mineral olivine important?  Olivine is a silicate mineral rich in magnesium and iron; it forms one of the basic, silicate building blocks of the rocky planets.  In magma (liquid rock), olivine crystallizes first and its composition is a key indicator of the composition of the magma.
... Being dense, crystallizing olivine would sink in the liquid magma, slowly accumulating deep in the Moon.  As the entire Moon solidified, these “cumulate” layers of olivine and other iron-rich minerals would make up the mantle.
... Olivine is a very common mineral and abundant in the lunar crust.  A curious fact is that olivine grains in lunar highland rocks tend to have high amounts of calcium, a minor element but a key diagnostic of the crystallization environment.  In Earth rocks, olivine formed at depth has very low concentrations of calcium.
the olivine crystals in dunite (a rock made up almost completely of olivine) from the Apollo 17 site – a sample proposed as a piece of the lunar mantle – likely came from the accumulation of crystals at a depth of only a few kilometers, far shallower than the tens of kilometers depth to the mantle.
... Because the Kaguya spectral mapper is detecting only the presence of olivine, we cannot distinguish between pure olivine and olivine crystallized with plagioclase, what lunar scientists call troctolite.  Troctolite is common in the Apollo highland samples, but is a relatively rare rock on Earth.  It consists of (more or less) equal parts olivine and plagioclase, a calcium- and sodium-rich silicate mineral.  Troctolites make up some of the most deeply derived rocks found in the Apollo collections, but all studied to date seem to be of crustal, not mantle, provenance.  There is no objective evidence that the olivine seen by Kaguya is not derived from troctolites and/or dunites of crustal (not mantle) origin.

In short, the sample tested most likely wasn't from the mantle but because of mineralogical similarities it is being used as an analogue for a mantle sample.


Measuring the circumference of the earth - revisited

You can use the fact that the Earth's rotation period is known.  Then divide that period (use the solar day of 24 hrs 00 minutes instead of the sidereal day of 23 hrs 56 minutes) by the actual amount of time between your two solar noons and multiply the resulting factor by your 1260 km distance.
The result is the circumference ... of your latitude circle.  To get the circumference of a great circle and thus the Earth, you need to divide the calculated number above by the cosine of your latitude.  To get the latitude perform your experiment on an equinox and measure the shadow angle at solar noon.
Have fun, good luck!


Data of terrestrial evapotranspiration over large areas?

Millimeters per year measurements have an area component built into them, they're actually in cubic millimeters per square millimeter. So one millimeter of rainfall is enough to cover the given area that rainfall is for to an average depth of one millimeter. For example if the area is a 100 square kilometer catchment then 1mm of rainfall is 100,000,000 cubic millimeters (also millilitres), or 100,000 litres of water. Evapotranspiration is measured using exactly the same unit conventions. Hope that helps.


Earth's interior heat ratio between pressure and atomic decay

There is no heat caused by pressure. Heat increases with depth, like pressure, so the two show a correlation, but this does not imply causality.

The two main sources of Earth's internal heat are radiogenic heat (as you said) and primordial heat, that is the kinetic energy turned into thermal energy during the accretion of the planet. There are also minor sources, like tidal heat caused by the Moon, and latent heat caused by crystallization of the liquid core.

The total heat budget of the Earth is pretty well constrained: we can just measure the heat flow coming out at the surface (in W/m$^2$) and multiply this by the Earth's area. The current estimate is ~47 TW (Davies & Davies, 2010). Getting ratios between sources, however, is more difficult, and rely mostly on modelling. See for instance the work of Dye (2012), who proposed a radiogenic heating of 15–41 TW, while other authors (referenced by Dye) proposed 12–30 TW of primordial ("fossil") heat. As you can see, the uncertainty is still quite high...


Farthest point from the center of the Earth

It's Chimborazo, Ecuador, but only just, beating Huascarán, Peru, by less than 50 metres. Both are over 2 km 'higher' than Everest.

I made a plot of some mountains — height above centre of the earth vs absolute latitude. You can download the IPython Notebook source code here. Warning: v. hacky.

I can't find anything on the position of the centre of the earth. The formula I used for the latitude-dependent radius requires major (equatorial) and minor (polar) radii, but I don't have citations for them either. Argus in his article Defining the translational velocity of the reference frame of Earth gave some numbers for its temporal variance, but I have no idea how this might affect these mountain heights.

Last thing: Apparently, the floor of the Arctic Ocean is the closest point on the surface to the Earth's center (about 6353 km, 30 km 'below' Chimborazo), if you call the bottom of the sea the 'surface'.


What is the explanation of using pressure units (hPa) to express height when dealing with wind speeds?

There are several reasons. From the theoretical point of view it is beneficial to use isobaric coordinates, due to the vanishing density in the equations of motion. While in cartesian coordinates the wind is determined by the pressure gradient in isobaric coordinates the wind is determined by the geopotential gradient. The geopotential is defined by $\Phi = gz$. In the hydrostatic relation $p = \rho g z$ we can relpace $gz = \Phi$ and therefore any term containing $p/\rho = \Phi$. The geostrophic wind relation for example differ as follows:
Pressure coordinates: $\vec{V_g} = \frac{1}{f} \vec{k} \times \nabla \Phi$
Cartesian coordinates: $\vec{V_g} = \frac{1}{\rho f} \vec{k} \times \nabla p$
Notice the density as an additional variable in the latter formula.
Another reason arises historically. The vertical structure of the atmosphere could only be measured using balloons or radiosondes until around the seventies when satellites became an additional source of information. Until today radiosondes provide the most detailed profile of a vertical slice in the atmosphere. Radiosondes can not measure height in meter or feet but they can measure pressure. Also GPS is not be the best alternative. While it is quite accurate regarding the horizontal position it lacks accuracy in the vertical compared to pressure measurements.
Edit:
I forgot one of the most important aspects: Looking at pressure surfaces also allows us to compare heights in a more meaningful way. What we experience as weather happens to 99% within the troposphere. However, height of the tropopause varies a lot from poles (~9km) to equator (~16km). Looking at a pressure level allows us to make sure the mass of air above that level is approximately the same everywhere and thus makes variables comparable. Note that comparing what happens at 12 km altitude in the tropics to 12 km altitude at the poles does not make sense at all, because at the poles we are already dealing with the stratosphere, while in the tropics we are still way below the tropopause. Staying on a pressure level ensures that we take these differences into account.


I can't prove it, but I strongly suspect that most, if not all, of the earthquakes in that north-south lineation along the eastern Bass Strait are caused by slumping of sediments in a series of listric faults. That whole continental edge is a very thick heap of deltaic and continental sediments of about Kimmeridgian (late Jurassic)to late Eocene age. There is a brief summary in: Submarine canyons of the continental margin, East Bass Strait (Australia).

As to 'the hook', it is surely no coincidence that this exactly coincides with 'Flinders Canyon', which you can see on Google Earth. What you can't make out on G.E. is the enormous size of the Canyon and its sedimentary catchment area. The sediments here are up to about 3 kilometers thick, and a massive submarine amphitheater funnels sediment into the canyon in periodic surges. I would bet a month's beer money that the 'hook earthquakes' were caused by occasional turbidite collapses of sediment down this steep canyon. The magnitudes, location, slope and approximate frequency are all spot on.
If you include the smaller canyons along the same continental edge then it is estimated that some 80,000 to 90,000 cubic kilometers of sediment have collapsed from this continental edge since the Late Eocene, i.e. over the last 40 million years.


If the earth were completely smooth and covered in water, what would occur with ocean waves?

Consider ocean waves in the middle of a large ocean. They are being powered by the wind, but also lose energy due to viscosity, breaking and similar factors. Since the timescale for a wave changing is much smaller than the timescale of it crossing an ocean, for all practical purposes they already experience an infinite ocean.

A featureless ocean world would presumably have many somewhat constant wind systems that could add a lot of energy to wave motion, but with an absence of shores to break on these energetic waves will just keep on going with an amplitude where the average energy gained and lost are equal. Since even a powerful tsunami is nearly invisible in deep water, the ocean world would look relatively calm with merely a lot of ocean swell.


The free oxygen (O$_2$) in the atmosphere is largely a result of what process?

You are correct in thinking that oxygen comes from photosynthesis. In fact it is so much associated with photosynthesis, as opposed to any inorganic process, that the presence of oxygen in the atmospheric spectrum of other planets (solar or exoplanets) is reckoned to be one of the best indicators of life beyond Earth - not that such oxygen has been discovered yet.
Ozone is made from pre-existing oxygen but with an atmospheric half life of only about 12 minutes, it spontaneously turns back into oxygen again very rapidly, and is highly sensitive to ozone-disrupting agents such as CFCs.
Meteorites have little, if any free oxygen. Indeed, many meteorites contain Ni-Fe which would rapidly mop up any free oxygen if it were originally present. Volcanic activity reflects the fugitive gasses of a magma chamber, which contains F, Cl, CO2, CO, H2O, H2S, N2, inert gasses, and hydrogen. Oxygen can occur in in a few volcanic emanations but this is rare and of small scale. On balance, volcanoes are oxygen absorbers rather than emitters. Photo-dissociation occurs to some extent high in our atmosphere in response to both solar and cosmic radiation. The result is H2O = H+ +OH- so there is no free oxygen involved. In any case, the two ions recombine fairly rapidly. Photo-dissociation is important in dense interstellar gas clouds far out in space where they may be subject to intense UV-radiation. Even here, the tendency is to mop up rather than release free oxygen.
The photosynthetic activity and mechanism on Earth has changed dramatically. It is the only known mechanism which can and does release large quantities of free oxygen. This started more than 3 billion years ago, but didn't raise the atmospheric oxygen level significantly prior to about 2.5 billion years ago. Evolution of the Earth's oxygen has been a long and complex affair, with high levels of oxygen only starting to emerge in the Eocambrian. The Earth's first oxygen would have been a noxious, toxic, and horribly reactive gas from the perspective of the Earth's earliest unicellular organisms.

New information just in: Nature magazine, 28th October 2015, has reported an astonishingly high oxygen concentration, of 3.8%, from the gaseous emissions from comet 67P, as measured by the Rosetta space probe. This has taken everyone by surprise (including myself) and may require a re-think about comet formation.


The answers so far are broadly correct. Iceland has formed from a coincidence of a constructive plate margin and a mantle plume, or "hot spot". But to really understand why Iceland is there we need to look at a normal constructive plate boundary.

A normal mid-ocean ridge is formed where two plates spread apart so that the mantle, which is at a certain temperature, rises upwards and experiences a decrease in pressure. The lower pressure together with the temperature of the mantle allows some (not all) of the mantle to melt - a process called partial melting. Only a small proportion of the mantle actually melts. This melt rises up through the overlying crust in a series of magma bodies, dykes, and lavas, to form the crust. Crucially, the thickness of the crust that is formed depends on the amount of melt that is created, referred to as the melt thickness.

A normal mid-ocean ridge creates a very thin crust - usually about 7 km. That's just 7 km between the ocean and the mantle. But Iceland is not normal. It sits above a mantle plume, which is a region of anomalously warm mantle. So what happens when we depressurise an area of mantle at a higher temperature than normal? We create a much greater melt thickness. This means the crust that is produced above the plume is greater - as much as 30 km. Since the icelandic crust is so much thicker than normal oceanic crust, the upper part of it is able to rise above the level of the sea. And thus Iceland exists.

To answer your followup questions:

  Why do not mid ocean ridges often rise above the sea surface to form islands?

Because it's very rare for a hot spot to coincide with a mid-ocean ridge.

  Why are islands more common along convergent plate boundaries where they often form archipelagos?

Because these islands form through very different processes. Convergent plate margins introduce water and other volatiles into the mantle, and these have the effect of reducing the melting temperature of the mantle. This produces melt, which rises up and forms volcanoes and islands. This process occurs at virtually every single destructive plate boundary because the subducting oceanic crust contains water which is liberated during subduction.


By what objectively correct process could we determine the truth about the actual severity of anthropogenic climate change?

We have reasonably good observations of the present.  We have moderately decent observations of the past (with larger uncertainties the further back we go).  Unfortunately, we have no observations at all of the future.

There are fundamentally only two ways to know about future impacts:

We can wait.  20 years, 50 years, 300 years.  We will know for sure, but it will be far too late to act on the knowledge to prevent the worst consequences.
We can model the impacts.  All models are wrong, but some are useful.  There is no "objectively correct process to determine the truth about the actual severity", because "actual severity" is not an objectively defined quantity.  However, we can model the impacts on biodiversity loss, sea level rise, desertification, food security, economic losses, and other measurable quantities that we care about.  From a strictly mathematical point of view, we can never be 100% sure.  However, if we are 99% sure of net impacts that most people would consider to be very bad indeed unless we act, the precautionary principle suggests acting is the wisest thing to do.

Source: USA Today, but has been published in many newspapers.


Is there an upper bound to the amount of rain that can fall in an hour?

From http://www.srh.noaa.gov/eax/?n=holtmorecrain1947

A very moist airmass was in place across Missouri during the afternoon and evening of 22 June 1947, as evident by dewpoint temperatures in the middle 70s across Missouri during the afternoon hours
Advances in meteorological science led Locatelli to speculate that the thunderstorm that produced the historic rainfall of 22 June 1947, did not develop along a classic surface cold front, but to the east of a surface dryline (drytrough) and underneath a cold front aloft that had origins in the Mexican plateau.  Regardless of the causative surface and upper air features, a complex of storms at a scale not measured well in the data-spare period of the 1940s developed near Kansas City and moved across Holt, Missouri, depositing 12 inches of rain in less than one hour.  Rain continued to fall on Holt after the 12 inch deluge for the next couple hours, but only amounted to an additional one-half inch.

A rare meteorological event occurred that day.  I offer a semi-empirical frame of reference that takes  into account that the most extreme rainfall rates occur for a short duration (e.g. a few minutes).
In "A methodology to classify extreme rainfall events in the western mediterranean area" by Casas et al., (2004):
http://link.springer.com/article/10.1007%2Fs00704-003-0003-x
they show rain rates of up to 0.5 cm/min sustained for several minutes (based on a large network of rain monitors in Barcelona).   IF that could somehow be sustained for an hour, that would give a rate of 30 cm/hr (which is what Holt saw).
For comparison, the most extreme rainfall rate measured in one minute in the USA is 3.1 cm (1.2 in; see http://wmo.asu.edu/world-greatest-one-minute-rainfall ). Actual rain doesn't continue at such an extreme rate for much longer, but would equate to 186 cm per hour (6 times what Holt, Missouri saw in 1946).  The link that kwinkunks provides http://www.bom.gov.au/water/designRainfalls/rainfallEvents/worldRecRainfall.shtml shows a world rate record of 3.8 cm/min which, if sustained, would equate to 228 cm per hour.


Is the Principle of Fossil Succession accurate?

Your analogy with burying a box is not as accurate as you think. It needs specific sedimentary conditions for the remains of an organism to fossilize: being buried in soil is far from enough.

Fossilization is such that, eventually, the fossil will be embedded in its stratum, meaning that tectonic events (as you suggest) that would displace the fossil will also displace the stratum around it.

However you are right to question the principle of succession in the sense that, things can happen before the fossil is embedded in its stratum. Namely you have three common phenomena: reworking, downworking, and time averaging.

Reworking, the more common phenomenon. It can occur when the sediment that originally contain the fossil is being eroded. What the sediment contained is therefore once again put in the system and need to be either dissolved or re-sedimented in a new stratum.

Downworking is (I think) more frequent in marine settings: before the sediment is consolidated, the fossil sinks into it, into an as-well unconsolidated but older sediment.

Time averaging. It can take a lot of time for a sediment to consolidate into a stratum, time during which organism remains continue to rain on the sediment. The stratum will therefore not represent a point in time but a time-span corresponding to the time it took to the sediment to consolidate.

Of the three phenomena, only reworking is really problematic (the two other being only moderate time displacement, rarely more than a couple of $10^5$ years). However it is usually manageable to recognize the fact that a fossil was reworked (different alteration compared to other fossils in the same stratum for instance, and if the sediment was already consolidated when the fossil was displaced you will find bits of the old sediment still attached to it).

There is also another problem (regarding your example of a Jurassic species deposited in South America and the same species deposited in Europe), which is biogeography: a species does not appear and disappear at the same time everywhere on Earth (see illustration below). In most cases the time discrepancy is small but in some case it isn't: this is what we call, in biostratigraphy, diachronism.

Taken from Peter Sadler's short course on biochronology. The grey area represent the taxon extent in time and space.


I had a rather difficult time telling how the rest of the cloud structure looks; however, I would tend to believe your weather-enthusiast friend might be correct.

A wall cloud - rotating or not - can also be known as a pedestal cloud and is made up of cumulonimbus clouds; generally forming in the strongest part of the storm.
From what I can tell in the picture and judging by the weather that came from it; it sounds like it was a non-rotating wall cloud. Here is an additional reference page that may help you identify it.


Why would volcano eruption cause cardiac arrest?

Michael's comment is correct, in Japan, according to the article Japan volcanic eruption: Mt Ontake rescuers find more than 30 people in 'cardiac arrest' (Radio Australia), state

  Police said the 31 people were found in "cardiopulmonary" arrest on Sunday but declined to confirm their deaths pending a formal examination, as per Japanese custom.

and more directly, from More than 30 feared dead on Japan's Mount Ontake after volcano erupts (Washington Post)

  using the terms for heart and lung failure that Japanese authorities employ to describe bodies. People cannot be declared dead in Japan until doctors have examined them.

It is very likely, given how close they were to the eruptive crater and the sudden inhalation of hot volcanic ash, gases and other materials, the victims went into cardiopulmonary arrest due to their lungs being overwhelmed by the sudden quantity.  Additionally, burns, fear, debris could have likely caused shock causing cardiac arrest.

Several case studies from other volcanoes are presented in the article The respiratory health hazards of volcanic ash:
a review for volcanic risk mitigation (Horwell and Baxter, 2005).


Do tornadoes usually avoid areas with many tall buildings?

It is especially rare to see a tornado destroying a series of skyscrapers.

Yes, it's rare, but not for the reasons you think. The reason that tornados striking downtown areas is rare is that cities are but a tiny fraction of the land area in places where tornados most often occur, and downtown areas are but a tiny fraction of the land area in those cities.

That said, downtown St. Louis, Missouri (the center of tornado alley) has been hit by tornados six times, and downtown Shrevesport, Louisiana (the center of Dixie alley), five times. The list of tornados that have hit the downtown areas of large cities goes on and on and on.


Your map of lighting tells you where thunderstorms occur.  Your second map of watches tells you where a subset of thunderstorms exhibiting severe threats (high winds, large hail or tornadoes).  The type of thunderstorms that frequent Florida are air-mass thunderstorms and generally will not warrant a severe thunderstorm watch.  The storms in the midwest that do get watches are typically of the supercell variety or associated with squall lines or bow echoes.

Your thesis that "The midwest clearly has the highest concentration of thunderstorms" is incorrect.  What your data says is that the midwest has the highest concentration of thunderstorms producing severe weather threats.  This is not the same as concentration of thunderstorms.  All thunderstorms produce lightning (by definition), not all of them are severe.

Convection in Florida is driven by the sea breeze and afternoon storms happen there like clockwork.  These storms produce lightning but no threats that would warrant a severe thunderstorm watch.  These storms last about 45-60 minutes and produce lightning.  This also makes Florida the lightning capital of the US, as the data in your question shows.


Australia does get widely referred to as an island as well as as a continent - an island-continent sometimes. My understanding is that "continent" in terms of geology refers to the largest land mass of a continental plate and is more a matter of convention - a general agreement - than precise definition. Such definitions have been subject to revision.

This definition would have come after continental plates and plate tectonics were confirmed and widely accepted; proposed first by Alfred Wegener in 1912, acceptance did not come until the 1950's and 60's. Naming Australia an island predated this definition and still persists in popular usage but using the current definition it is a continent.

Greenland, being a part of the North American Plate but not it's largest landmass, gets defined as an island and is now considered the world's largest island.


For this question, Wikipedia is probably your best recourse.

To summarize, the heat in the earth's core comes from two places: it is left over from the formation of the earth and it is still being generated by radioactive decay of isotopes that were trapped in the earth as it formed.

The radiogenic heat is still being added to the earth through decay of long lasting isotopes. When the earth formed, there were probably many significant heat generating isotopes, but now after 4.5 billion years, it is pretty much just Thorium-232, Uranium-238, Potassium-40, and Uranium-235.

So there are multiple answers to this question in the sense that there are the two sources listed above, but otherwise, no, this is the answer.

This question has some more information related to heat transport to the surface that you may find relevant.


The borders are fluent between continentality and maritimity. However, there are several indices, aiming to clarify this question. For instance, the probably earliest one is from Gorczynski (1920):
$$K_{Gorczynski} = 1.6 \cdot \frac{A}{\sin \varphi} - 14$$
where $A$ is the annual temperature amplitude of the location and $\varphi$ the latitude of the location. Another one, which is more often used, is from Iwanow (1956):
$$K_{Iwanow} = 260 \cdot \frac{\Delta T}{\varphi}$$
where $\varphi$ is the latitude again and
$$\Delta T=T_\mathrm{max} - T_\mathrm{min}$$
where $T_\mathrm{max}$ is the temperature maximum and $T_\mathrm{min}$ the temperature minimum. The results are characterized as following:

K < 100: maritime
100 < K < 200: continental
K > 200: strongly continental

To answer the second part of the question: as the indices show, the latitude needs to be considered. Currently I do not have the original publication by Gorczynski or Iwanow here, however there are some papers comparing different indices (there are several more), for example this one. Furthermore, the indices can be looked up in the most climatology basic literature and encyclopedia. At least, it is needed to mention that Gordon Stanger hits the point in his answer in the last sentence: The continentality is just one variable - there are several more. Look for climate classifications, like those from Köppen & Geiger or Schultz.

Edit: Original reference

Gorczynski, L. (1920): Sur le calcul du degre de continentalisme et son application dans la climatologie. In: Geografiska Annaler 2, p. 324-331.


What are the striations or ridges in the eastern Pacific Ocean?

They are fracture zones.

I've annotated your image with the names of these very long, tectonically important features. They even have names, such as the Mendocino Fracture Zone:

I also labelled some survey tracks (rather subtle, very straight, very regular in width), which are data artifacts — these are the things you noticed radiating from the vicinity of Los Angeles.

There are yet other types of linear feature on the sea floor:

Transform faults are strike-slip faults connecting segments of spreading centres in the oceanic crust.
The spreading centres themselves.
Roughly linear archipelagos like Hawaii.
The long, curved trenches at convergent plate margins.

Images from Google Maps. Note: I edited this answer substantially after the OP clarified the question... and I learned about the difference between transform faults and fracture zones.


Landsat products obtained via various sources (ex the EROS Center) can have their own requirements when using their products. For instance the EROS Data Citation page indicate that they are quite open regarding how their documents are cited and require the following acknowledgement only. For example

Acknowledgement:
Data available from the U.S. Geological Survey.
See USGS Visual Identity System Guidance (link is external) for further details.
Questions concerning the use or redistribution of USGS data should be directed to: ask@usgs.gov (link sends e-mail) or 1-888-ASK-USGS (1-888-275-8747).

Metadata files attached to images are often filled with useful information. Usual relevant information for a technical or scientific paper are the moment of acquisition, the scale, the bands, the name of the sensor, maybe the series of the product, maybe there is a serial number too, possibly a URL.
I have cited in a recent paper the following for Landsat 7, and did not went into much details because it was a reworked product (a special issued mosaic), which was convenient for our scope:
NRCan, Canada Centre for Remote Sensing. A complete orthorectified Landsat-7 mosaic
of the Canadian Arctic archipelago, August 2010. URL http://geogratis.gc.ca/api/en/nrcan-rncan/ess-sst/-/(urn:iso:series)a-complete-orthorectified-landsat-7-mosaic-of-the-canadian-arctic-archipelago


What would be the extent of the feedback on climate of unattended deaths event?

Mass of Earth's atmosphere: $5 \times 10^{18} kg$

Concentration of methane in Earth's atmosphere: $1866 ppb$

Mass of methane in Earth's atmosphere, present day: $9.3 \times 10^{12} kg$ = 9,300,000,000 tons

If all those dead mammals were composed entirely of methane, they would increase the atmospheric concentration of methane by about 2%. They aren't, and (as @trond hansen commented) most of their carbon would be converted to $\ce{CO_2}$ with a 30-fold smaller global warming footprint.

So, I think it's safe to say the impact of decomposing mammals would be relatively small.

Worry more about effects on plants, which constitute 80% of the Earth's biomass; bacteria, which constitute 15%; and fungi, which constitute about 2%. The entire animal kingdom amounts to much less than half a percent of global biomass, and half of that is arthropods (which have their own concerns for the future).

(Source: figures from The biomass distribution on Earth, Yinon M. Bar-On, Rob Phillips, and Ron Milo, PNAS June 19, 2018 115 (25) 6506-6511; first published May 21, 2018 https://doi.org/10.1073/pnas.1711842115)


How can you explain this storm phenomenon?

This case is an excellent example of urban-induced convection.

Urban areas have very different surface and soil properties, leading to a different heat balance relative to more natural environments. At times when solar shortwave radiation forcing is high - summer time, early afternoons - urban areas act as heat islands. Sensible heat flux and outgoing longwave radiation are then increased relative to the environment. While latent heat fluxes are decreased because of lack of soil moisture and vegetation in the cities, there is enough moisture coming from the environment to trigger convective cloud formation and rainfall downwind from the urban area.

As to the question why did this occur in four urban areas at the seemingly similar time, it just happened so.

See this review article on urban-induced convection and associated physical processes for more details.


How to convert mol/m^2 to total mass ( e.g gram, kg etc )?

$\rm \frac{mol}{m^2}$ shows the amount of $\rm{NO_2}$ in the atmosphere over a square meter of surface area - in mols.

The molar mass of the $\rm{NO_2}$ is $14+2\cdot 16=46$. It means, the mass of 1 mol of $\rm{NO_2}$ is $\rm{46g}$.

The surface area of the Earth is 510million $\rm{km^2}$. Thus, 1 $\rm \frac{mol}{m^2} \rm{NO_2}$ translates to $\rm{46 \frac{g}{m^2} \cdot 5.1 \cdot 10^8 km^2}$, what means a total mass of $23.46\cdot 10^9 \rm t$ in the whole atmosphere.

Here we assumed a constant distribution of the $\rm {NO_2}$ in the atmosphere, which is typically not the case in earth science-related problems. Also your research question is about the visualization of a highly non-level distribution. Here you need to integrate (or, considering your digital evironment, sum).


Guinea Current existence in the Atlantic

The Guinea Current is in geostrophic balance with isopycnals sloping upwards towards the north. The current is not directly related to wind direction and magnitude and that makes rather especial. As many other eastern boundary currents, it is characterized by the presence of coastal upwelling (Bakun, 1978), which delivers nutrients to the surface waters and results in increased primary production.

 Source: RSMAS

The Guinea Current is connected with the North Equatorial Counter Current (NECC) and in fact it can be considered the eastern continuation of the NECC. The seasonal variations in the position of the Intertropical Convergence Zone affect the connection between NECC and Guinea Currents. The Guinea Current is also connected to the Canary Current flowing southward along the African coast. In this sense, the Guinea Current is at least partially related to the Indian and Pacific Equatorial Counter Currents. The difference is that there is no long stretch of coast parallel to the Equator in those oceans.

RSMAS ocean currents project provides a complete description of the main characteristics of the Guinea Current with references.

Also, the Guinea Current does not disappear during the northern summer. In fact, there is a tendency for the current to intensify (check Figure 3 in Bakun, 1978 for instance).

Bakun, A., 1978. Guinea current upwelling. Nature, 271(5641), pp.147-150.


Difficulty interpolating near poles using lat/lons

$\color{blue}{\text{The answer here presumes that Earth is a sphere.}}$
$\color{blue}{\text{This is not fully true, but the question seems to build in that assumption.}}$
$\color{blue}{\text{That should be clarified to determine if this answer is relevant.}}$
Do not use a 2D-plane which does not generally exist for four points.  Use a tetrahedron.  You can interpolate inside the tetrahedron and then project the interpolated point (which will be inside the globe) radially onto the globe's surface.
Say you pick the South Pole, S, and three points A, B, C at 60° south latitude and longitude 0°, 90° east, 90° west.  Converting these coordinates to Cartesian form with the South Pole at $(0,0,-1)$ prime meridian passing through $(1,0,0)$, we get the coordinates
South Pole = $(0,0,-1)$
A = $(1/2,0,-\sqrt3/2)$
B = $(0,1/2,-\sqrt3/2)$
C = $(0,-1/2,-\sqrt3/2)$
Now suppose you want to interpolate with a weight of 1/2 for S and 1/6 for each of the other three points.  Take the linear combinations of the above coordinates with those coefficients to get a point P inside the tetrahedron:
$P=(1/2)(0,0,-1)+(1/6)(1/2,0,-\sqrt3/2)+(1/6)(0,1/2,-\sqrt3/2)+(1/6)(0,-1/2,-\sqrt3/2)=(1/12,0,-(2+\sqrt3)/4)$
Point P has the following physical significance:  if you draw the smaller tetrahedron PABC, opposite S, then this tetrahedron has 1/2 the volume of the big tetrahedron ABCS, where 1/2 is the coefficient you put in for S.  For this choice of P the corresponding tetrahedra opposite A,B,C will each have 1/6 the volume of the big one.
Now we need to project this point onto the surface ofthe globe.  Work out its distance $d$ to the origin:
$d^2=(1/12)^2+0^2+((2+\sqrt3)/4)^2=(16+9\sqrt3)/36\approx 0.8775, d\approx 0.9367$
Note that $d<1$. Divide this $d$ into the coordinates of P getting the approximate result
$P'\approx (0.0890, 0, -0.9960)$
Converting back to spherical coordinates then gives a latitude of $\approx 84.90°=84°54'$ south and longitude zero, the latter due to equally weighting the eastern and western hemispheres in this example.  The interpolated point is more than halfway from the 60° south latitude circle to the South Pole because we interpolated from a distribution of points along this circle rather than a single point; the centroid of of this distribution ( $\triangle ABC$) is at more than 60° south latitide.


Do rising CO2 levels change the appearance of the sky in infrared?

Due to man made climate change, from space, the Earth currently looks a little darker in Infra-red (IR) and a little colder (longer wavelength), but the change is small and would be hard to notice without sensitive photon-counting equipment.   The earth doesn't exactly glow in steady color in IR either, it swirls and looks like a circulating, 100% cloud covered planet, which makes sense when you consider that our atmosphere, mostly the H2O and CO2 in the atmosphere is opaque to much of the infrared spectrum, so it looks a little like Venus in the IR, but not quite as dense with clouds.   What's more, you'd see seasonal variations and day/night variations, so it would be hard to notice a pretty small climate variation over that.

See YouTube video and article of the Earth in IR: Planet Earth in Infrared (Synchronized)

and the article: Our Planet Has the Vapors.

The video isn't quite right, because it's only one wavelength designed to track water-vapor not the entire IR spectrum, but I thought it was close enough to use as a starting point.

The short answer is, at least for now, the Troposphere is warming but the stratosphere is cooling and contracting, so from space, in IR, Earth is both a little smaller and a little colder/darker, at least, for now.

The longer answer is that when the Earth is in energy equilibrium, that is, not undergoing climate warming or cooling, the Earth gives back to space  the same amount energy it receives from the Sun, at least, more or less.  There's some variation, but it's largely the same.

The only way Greenhouse driven warming can happen, is for the Earth to hoard heat, and gives back less heat to space than it takes in from the sun.   When the Earth grows colder, it's the opposite, the Earth needs to return more energy to space than it takes in from the sun.  This variation doesn't have to be all that big, for example, a fraction of 1% variation over enough time can be enough to start or end an ice age, but that's the only way warming or cooling can happen.  It has to be an imbalance in Earth's energy equilibrium (technically, also, it could be a change in Earth's orbit or a solar minimum), but Earth's orbital changes take tens of thousands of years and Earth's climate changes mostly take 1,000 or so, and solar minimums are relatively weak and thought to only last a couple hundred years or so.  So the primary driver for climate change, warmer or colder, man made or natural, is the Earth hoarding or losing energy.

This doesn't have to happen entirely in infrared.  Changes in albedo/reflection can play a role too, for example, as snow cover and permanent glaciers grow, the visible light reflected off earth gradually but steadily increases resulting in the Earth giving back more energy than it takes in, leading to a cooling, sometimes an ice age, and the energy imbalance continues until the Earth is sufficiently cooled to reach a new equilibrium.

Currently, the Earth is hoarding heat and it's albedo is relatively unchanged, meaning that it's giving back less IR into space than it used to, so, in IR, the Earth looks a little bit darker than it used to before man made climate change.   Ballpark, about 1% darker in the IR.   As to changes in color, there's some variation in wavelength on both warmer and colder, but on average, slightly colder/longer wavelengths.

Estimates vary, but, ballpark, Earth is trapping roughly 2 extra watts of energy per square meter due to climate change and most of that trapped energy/heat goes into the oceans, very gradually warming them.  The lower atmosphere is more effectively absorbing and reflecting thermal radiation from the surface so less IR is reaching the upper atmosphere and less is going into space, so while the surface of the Earth does grow brighter in IR what is mostly seen from space is the cooling upper atmosphere.

Over time, as the Earth's surface and lower atmosphere grows warmer, it will emit more IR and the upper atmosphere will, in time, give back into space just as much IR as it used to before climate change, and probably more, but that will take 100 years or so, perhaps longer.   Also, as Earth's ice cover drops and it's oceans rise, Earth's albedo will mean less visible light is being reflected into space, so the thermal radiation will need to increase to make up for that.  So, in a century or two, the warmer Earth should glow brighter in IR and on average, a bit warmer/shorter wavelength, too.   How much will depend mostly on how much ice cover melts, but we're probably not looking at more than maybe a 1% increase, 2% tops.

For some numbers and pretty charts, see here.

Earth is hit by about 340–341 watts per square meter of energy from the sun, that's on average, summer/winter, equator/poll and night/day.  Direct sunlight on a perpendicular surface to the Sun's rays is about 4 times that.

Of that 340–341 watts, currently about 29% or 100 watts is directly reflected back into space as mostly visible light.  The remaining 240 or so watts (per m2) leaves the Earth in the form of infra-red or thermal radiation.

About 170 watts of that 240 comes from the high atmosphere.  About 30 from cloud tops and about 40 watts from surface radiation.   While the Earth's surface does grow warmer during climate change and brighter in IR, 90% of that gets re-absorbed by or reflected back by the atmosphere and only 10% reaches space, so the added brightness you might expect to see off the warmer surface makes up only a small part of the total.

If we say the Earth's surface has warmed about 0.8 °C, say from 288K to 288.8K, using the 4th power rule, that should emits about 1% more thermal energy than it did before climate change, but 1% of 40 watts comes to about 0.4 watts per square meter increase, and perhaps decreased overall due to the more opaque atmosphere with higher CO2.   The biggest factor for the earth's IR image is the temperature of the upper atmosphere.

As an FYI, there are other imbalances to the heat in/heat out equilibrium equation, for example, a really big volcano might release enough heat into the surface to unbalance the ratio temporarily and following a big volcano there's an increase in the amount of light reflected off earth which leads to a relatively rapid but temporary cooling.   A large enough meteor impact could also create a variation, and the Earth is hit by solar wind and cosmic rays and it loses some heat in very fast moving particles that exceed escape velocity (mostly hydrogen from water molecules).  The Earth also has internal heat coming from it's warm interior, which means the Earth does emit a bit more heat than it receives overall, at least on average, which does throw off the expected equilibrium a little bit.

And, final and curious sidebar, you might ask, how the Earth's surface can emit 400 watts per square meter, which is more energy than Earth receives from the sun.  That has nothing to do with your question though, but it's a curious statistic I think.   It's because our atmosphere acts like a blanket, warming the Earth overall.

Hope that wasn't tl;dr.


Slope of Saturation vapor pressure versus temperature-A parameter in Penman's equation

You can convert mm Hg to kPa with the conversion factor $0.133322368\ \mathrm{kPa\ mmHg^{-1}}$.

Saturation vapor pressure as a function of temperature is

$$ e_s(T) = e_{s0}\exp\left[\left(\dfrac{L_v(T)}{R_v}\right)\left(\dfrac{1}{T_0} -\dfrac{1}{T} \right)\right], $$

where $L_v(T)$ is the specific enthalpy of vaporization, $R_v$ is the specific gas constant for water vapor, $T_0$ is reference temperature (273.15 K) and $e_{s0}$ is the saturation vapor pressure at $T_0$ (611 Pa).

You can find the slope of this curve by taking the derivative $\dfrac{d e_s}{dT}$.

Note that the units of $e_s$ and $T$ are Pa and K respectively in the equation above.


What are good metrics to compare climates?

The Köppen climate classification is a classic metric to classify climates:

Source: Wikimedia Commons
It classifies climates based on the number of months with temperature below and/or above certain thresholds, and on whether rainfall is evenly distributed or concentrated in a particular season.  You will find details on the definitions on Wikipedia.
An alternative is the Trewartha classification:

Source: Wikimedia Commons.
Note that the climate you seek may not exist:

I was initially seeking to discover areas with a high mean temperature, low variance in temperatures annually and daily, and low rainfall.

A low temperature variance tends to happen in humid climates.  Dry climates tend to have large temperature variances.  A subtropical highland climate may come closest to what you seek, although it's not particularly dry.  In the Köppen classification, this would be Cwb.  From the Wikipedia article:

Cwb = Subtropical highland climate or Monsoon-influenced temperate oceanic climate; coldest month averaging above 0 °C (32 °F) (or −3 °C (27 °F)), all months with average temperatures below 22 °C (71.6 °F), and at least four months averaging above 10 °C (50 °F). At least ten times as much rain in the wettest month of summer as in the driest month of winter (an alternative definition is 70% or more of average annual precipitation received in the warmest six months).

I don't think any place with Cwb climate exists in the United States.  Quito is famous for being the city of eternal spring, and some areas of Mexico are classified as Cwb, as in Johannesburg.  I suspect the closest you'll get in the USA will be somewhere not too high, not too low in the Sierra Nevada.


Why the $\delta \, ^{18}\text{O}$ in foraminifera shells decrease with temperature even if the oceanic $\delta \, ^{18}\text{O}$ stay constant?

That is because the chemical reactivity of $^{18}\text{O}$ is slightly higher than that of $^{16}\text{O}$. For that reason, the biochemical reactions that produce calcium carbonate in foraminifera prefer $^{18}\text{O}$ over $^{16}\text{O}$.

However, the temperature dependence arise from the fact that the difference in reactivity is smaller when temperature increase. Therefore, in warmer temperatures the $\delta ^{18}\text{O}$ will be more similar to seawater (no preference for any isotope), but at colder temperatures the chemical preference for $^{18}\text{O}$ will be stronger and, therefore, the $\delta ^{18}\text{O}$ will increase.

This correlation with temperature is also known as the "paleotemperature equation", but as it is an empiric equation there are many slightly different versions, however all of them are pretty consistent. Several ones are summarized in figure 5 of the paper Oxygen isotopes in foraminifera: Overview and historical review (Pearson 2012) copied below, showing how the excess of $\delta ^{18}\text{O}$ in shells ($\delta ^{18}\text{O}_{\text{cc}}$) relative to the $\delta ^{18}\text{O}$ in seawater ($\delta ^{18}\text{O}_{\text{sw}}$) correlates with water temperature.

The deeper reason that explain the chemical preference for $^{18}\text{O}$ come from a process named "equilibrium isotope fractionation", associated  to the vibrational characteristics of the light and heavy isotopes related to covalent atomic bonding.
As explained by Gussone et. al (2003):

  "Equilibrium fractionation occurs as a consequence of covalent atomic
  bonding. During molecule formation the incorporation of heavier
  isotopes is preferred because covalent atomic bonds formed with
  heavier isotopes show larger bonding energies and, hence, are more
  stable than covalent bonds formed with lighter isotopes."

There is a competing effect called "kinetic isotope fractionation", that that leads to a correlation with temperature in the opposite direction (because heavier isotopes have slower diffusion times and are slower crossing membranes), but in the case of Oxygen isotopes, its effects is overcome by equilibrium fractionation.


Why did Hurricane Harvey have so much lightning associated with it?

The storm and basics:
Here is an animation I got from this NOAA Tweet of the lightning in Harvey hours before landfall:

https://mashable.com/2017/08/31/harvey-weather-satellite-maps-lightning/, where I found the imagery, offers some basic thoughts, including the key concept that:

As with most hurricanes, you'll notice that the most active area of lightning production is well away from the center of the storm.

This may well explain the reason you experienced more lightning if you are in a location nearer Houston, as it was quite far from the hurricane.  Landfall was about 180 miles SW of Houston, and by the time the storm made it near the Houston metro, it was much weaker; maximum sustained winds around the metro were generally only 25-40 mph (see table starting on page 30).

Deeper Look At Causes of Lightning in Tropical Cyclones:
I don't think I've come across horizontal wind shear used as an explanation for the reduced lightning in hurricanes, though that doesn't mean it isn't.  But upon more consideration, I really don't think horizontal wind shear in hurricanes is actually particularly extreme.  Certainly there are higher overall wind speeds than many weather features, but the horizontal gradient generally occurs over the scale of 10s of miles (10s of km) or much more in most of the storm.  Whereas in typical summer thunderstorms, there can quite often be like a 50 mph (75 kph) gradient over just a mile (or even km).  I guess the horizontal shear can be quite big right near the outer and especially inner eyewall edge... but these are such small geographic areas to explain the lack of lightning in the large part of a hurricane.  (Looking at figures 3 and 5 from this paper looking at Hurricanes Ivan and Dennis, it looks like the broad horizontal shear only peaks at like 10 m/s over a distance of 5 km, or about 7 mph per mile in Ivan, and less in Dennis.  I don't think that's a big amount really?)
And you may know that hurricanes tend to have low vertical wind shear.
So what is the cause of reduced lightning in hurricanes?
The paper Reflectivity, Ice Scattering, and Lightning Characteristics of Hurricane Eyewalls and Rainbands. Part I: Quantitative Description by Cecil et al. from 2002 summarized it as:

Despite extreme horizontal wind speeds, the vertical motions
encountered in tropical cyclones are typically rather modest
(Jorgensen et al. 1985; Black et al. 1996), with magnitudes similar to
those found in ordinary tropical oceanic convection. Convective
systems over the tropical oceans produce weaker vertical motions than
their continental counterparts (LeMone and Zipser 1980; Jorgensen and
LeMone 1989; Lucas et al. 1994; Igau et al. 1999). These vertical
motions are normally too weak to suspend large ice particles or
supercooled raindrops above the melting level.

This summary of how lightning forms on a course website by Dr. David Newman at University of Alaska and this NOAA page help explain the main theory on lightning formation.  And Observations of the Distribution of Ice in Hurricanes by Black and Hallett from 1985 helps indicate what is missing in hurricanes.
Basically it looks like with a weaker updraft, when moisture reaches the height of freezing, it "gathers" into the larger ice (graupel and hail) that falls relatively shortly up more, since it rises so slowly.
And so you there isn't much supercooled water (and the smaller hail\graupel grows more slowly when it collides and so falls more slowly as well)
Whereas with a stronger updraft, the more rapid rising motion means the moisture gets higher up before attaining hail/graupel... and so leaving a larger layer with just supercooled water\ice crystals below.  And that supercooled water is the vital thing, causing the heat release when freezing to falling ice.  And so you have different particles with different charges.
So only areas of stronger rising motion can form those better depths of "unglaciated" areas with supercooled water.  How do you get more rising motion?

Pockets of more unstable air (hotter moist air near the ground or cooler air aloft).  These will typically only be found at far extents from the storm, as nearer the center you tend to have moistened and well mixed the entire region.  Sometimes well placed dry air intrusions into a storm may offer a bit of help.
Additional forced rising by converging air below... this can be big features like eyewall replacement cycles, shear tilting, or frictional convergence as a storm makes landfall or more localized embedded supercells.

The answer for Harvey is probably all of the above.  Places like Houston were first in the further extents of the storm the early days and so were able to see the more typical fluctuations of strong rising updrafts and stronger sinking downdrafts more typical of normal thunderstorm convection and the outer rainbands in tropical cyclones.  And then had a storm seeing important structural changes by the time it moved nearer Houston (as marked by the significant tornado outbreak)
And areas nearer the center of Harvey saw rapid intensification (indicating there was more instability nearer the storm center still), eyewall replacement, plus the usual frictional convergence at landfall all favoring a bit of an uptick in lightning.  Harvey may well have not been too different from most landfalling hurricanes, but had the benefit of rapid intensification to help lightning production some... and it was dark so it could be seen more!


Why clouds are not moving in NASA's video of the Moon passing in front of the Earth?

The clouds can be seen moving but of course it's subtle at first glance.

Frame 16:

Frame 20:


One can only speculate based upon a photograph - however they look very much like mineralized fractures. At some time in the past this rock mass may have fractured in response to thermal or tectonic stresses. Fluid may have then penetrated relatively long distances along the fractures into the area and infiltrated shorter distances into the wall rock along small scale porosity such as cracks and grain boundaries (and also possibly diffusions.)  The fluid and rock were most likely not in chemical equilibrium when they came into contact and there were chemical reactions that produced additional minerals along the trace of the original fracture. This is probably what you see - the result of a process of fracture, mass transport, and fluid-rock chemical reaction. But a geologist would need much more information about this system (than available from one photograph) to describe the details.

Seeing something like this in the field is always very exciting because it raises so many questions. Where did the fluid come from? What was the temperature? When did the rock fracture?


What's it like inside a natural gas cavern on Earth?

A cavern filled with natural gas would look like an ordinary cavern. However, natural gas is rarely abundant in caverns.

Most natural gas reservoirs occur in the pore spaces of sandstones. These pore spaces are generally up to about 1 mm in diameter. Here's a photomicrograph of a sandstone — the green-blue colour is the pore space; Q, F, L, and M are quartz, feldspar, lithic fragments and mica respectively:

The pores of reservoir rocks also contain 'formation' water in various proportions. The relationship between the water and the hydrocarbons can be quite complex, depending on the fluid composition, the reservoir temperature and pressure, and the mineralogy of the rock.

So what about caverns? Trace amounts of methane probably occur in many, if not most, caverns — we're talking here about abundant methane. This is much less common, but it happens. In certain limestones pore spaces can be quite large — up to several metres in diameter. This is called vuggy porosity. If the limestone is charged with natural gas, the vugs will fill with gas, just like the other pores. The space would look like any other limestone cavity. Very large ones are rare, based on a typical power law size distribution. There are (copyright and unlicensed) images of such super-pores here and here. Recently Mattey et al. (2013; EPSL 374) wrote about methane in a karst in Gibraltar. I'd estimate that less than 1% of the world's gas is held in vuggy reservoirs.

There's another kind of cavern in which you can find natural gas: man-made ones. Natural gas is often stored underground, usually in porous rocks, but sometimes in caverns dissolved out of salt. Around a quarter of natural gas stock is stored this way in the US. Here's a video from such a salt cavern.

Last thing: methane seas can only occur at low temperature. As far as I know, liquefied natural gas or LNG is only stored above ground or on ships in tanks. Lots of natural gas reservoirs have very light hydrocarbon liquids in them — but again the liquid would be in tiny pore spaces, not caverns.


How has and how does the lithosphere affect climate change?

This is a huge and interesting topic.
Certainly there are many ways the climate is affected by the lithosphere (and also what is going on in the asthenosphere). The lithosphere is naturally also affected by the climate. I find it difficult to distinguish the 'components' as matter and energy can flow from biosphere to lithosphere and from hydrosphere to atmosphere etc. Somehow it might be appealing to think about lithosphere as a slow 'component' but keep in mind that the atmospheric circulation have been much more stable than the locations of the continents. Deserts have been in the same latitudes, even as continents have been moving.

A few areas of influence to consider:

Location of landmasses affects ocean currents and climate e.g. closing of Isthmus of Panama.
Supercontinents certainly had a very different climate than what we experience today.
Uplifts and orogenies can have local, regional and global effects.
Carbonates in the lithosphere plays an important role the carbon cycle. See e.g. this.
Rate of vulcanism also follows tectonic conditions.


What would happen if the inner core bulged and moved a tiny bit?

The following paragraphs are reproduced from https://www.nationalgeographic.org/encyclopedia/core/
"Growth in the Inner Core
As the entire Earth slowly cools, the inner core grows by about a millimeter every year. The inner core grows as bits of the liquid outer core solidify or crystallize. Another word for this is “freezing,” although it’s important to remember that iron’s freezing point more than 1,000° Celsius (1,832° Fahrenheit).
The growth of the inner core is not uniform. It occurs in lumps and bunches, and is influenced by activity in the mantle.
Growth is more concentrated around subduction zones—regions where tectonic plates are slipping from the lithosphere into the mantle, thousands of kilometers above the core. Subducted plates draw heat from the core and cool the surrounding area, causing increased instances of solidification.
Growth is less concentrated around “superplumes” or LLSVPs. These ballooning masses of superheated mantle rock likely influence “hot spot” volcanism in the lithosphere, and contribute to a more liquid outer core.
The core will never “freeze over.” The crystallization process is very slow, and the constant radioactive decay of Earth’s interior slows it even further. Scientists estimate it would take about 91 billion years for the core to completely solidify—but the sun will burn out in a fraction of that time (about 5 billion years)."


Does the regional localisation of global temperature trends suggest contamination by urban development?

The blog article suggests that the increase in "waste heat" from growing urbanisation is biasing the temperature observations.  The problem with this argument is that the heat generated directly from burning fossil fuels is far too small to make a difference, compared to the change in the Earths energy balance due to increasing greenhouse gasses.  See:

  Integrating anthropogenic heat flux with global climate models Authors

  Mark G. Flanner

  Atmospheric Science, Volume 36, Issue 2, January 2009.
  DOI:10.1029/2008GL036465

  Abstract 1 Nearly all energy used for human purposes is dissipated
  as heat within Earth's land–atmosphere system. Thermal energy released
  from non-renewable sources is therefore a climate forcing term.
  Averaged globally, this forcing is only +0.028 W m−2, but over the
  continental United States and western Europe, it is +0.39 and +0.68 W
  m−2, respectively. Here, present and future global inventories of
  anthropogenic heat flux (AHF) are developed, and parameterizations
  derived for seasonal and diurnal flux cycles. Equilibrium climate
  experiments show statistically-significant continental-scale surface
  warming (0.4–0.9°C) produced by one 2100 AHF scenario, but not by
  current or 2040 estimates. However, significant increases in
  annual-mean temperature and planetary boundary layer (PBL) height
  occur over gridcells where present-day AHF exceeds 3.0 W m−2. PBL
  expansion leads to a slight, but significant increase in atmospheric
  residence time of aerosols emitted from large-AHF regions. Hence, AHF
  may influence regional climate projections and contemporary
  chemistry-climate studies.

The blog article says:

  My guess is that 80% of this energy ends up as heat (2nd law
  thermodynamics). Assuming that  energy consumption is concentrated
  mostly in urban areas then the net “anthropogenic”  heating in those
  areas works out at around 5 watts/m2. This  then leads to  an average
  1.4 degreeC. rise in temperature for urban areas.  Anyone who has lived in the city knows from experience that the surrounding
  countryside is indeed  some 1-2 degrees colder.

Indeed the climatologists know that as well, they are not stupid, and hence "homogenise" the observations to remove these sorts of biases.  Note that if the bias were due to increasing urbanisation, this would be easily detectable by comparison with the observations from rural stations in the same region.  This is not rocket science (see my answer here for links on homogenization)!

Note also that increasing urbanisation would not necessarily cause an increase in local forcing, because as you increase the fossil fuel use, you also increase the area over which it is dissapated, which the author of the blog post also appears to have missed.


How does heat get transported between the surface layer, twilight zone, and the deep ocean?

I think the simplest answer is through water mass formation, the resulting thermohaline circulation, mixing caused by wind predominantly in shallow regions, and through downwelling processes. The heat exchanged with the atmosphere in the surface layers determine the temperature of the near-surface water. From there, mixing (caused by wind, for instance) will transfer some of the heat to lower layers in the ocean. In the case of areas of water mass formation, the sinking of surface waters is usually enhanced. When the water masses are away from the ocean boundaries (surface and bottom), then the thermohaline circulation controls the transport and exchange between water parcels and thus the heat transfer.


Flight time differences between flying east and flying west

The Jet Stream is the cause for slower flight times to the West. It flows from West to East at high altitudes and therefore helps planes flying East but causes extra resistance for planes flying West.


Is evapotransporation accounted for in climate models?

Now most models include changes in evapotranspiration, it is usually grouped together with a few other factors (like draining wetlands) under the heading "Land Usage"

Now the question does "Could additional crops being planted within the last 100 to 50 years account for additional moisture in the air now" the answer is no, not by itself.

To get more moisture into the air long term you need the air to be warmer, otherwise it just rains it out. Another issue is different crops affect evapotranspiration in different ways. For instance irrigation induced evapotranspiration, likely the largest evapotranspiration effect, may actually have a cooling effect, by increasing cloud cover and precipitation. Lastly land usage is only a small impact not counting the increased greenhouse gas emission it can cause.


Significance of crystal classes in crystallography

The references you and @farrenthrope cited (or a good introductory mineralogy text) should have answers.

In brief:

The crystallographic class is significant to mineralogy because it is direct result of the mineral's crystalline lattice (its most fundamental property.) Each mineral can belong to only one crystallographic class.

How can I determine the [crystallographic] class an [unidentified] mineral [specimen] falls under?

You'll need to inspect your specimen and try to recognize the symmetry operations (like rotations and reflections) present in some physical properties of your specimen, commonly the symmetry of euhedral crystal habit, the symmetry of optical properties, or the symmetry of an x-ray diffraction pattern etc. Each crystallographic class is defined by a unique set of symmetry operations.

How were the 32 classes determined?

A combination of observation and mathematics. The law of rational indices was deduced by Haüy (1784, 1801) from the observation of the stacking laws required to build the natural faces of crystals by piling up elementary blocks, for instance cubes to construct the faces of the rhomb-dodecahedron observed in garnets or the pentagon-dodecahedron observed in pyrite, or rhombohedrons to construct a scalenohedron of calcite. Hessel (1830) proved that, as a consequence of the law of rational intercepts, morphological forms can combine to give exactly 32 kinds of crystal symmetry in Euclidean space, since only two-, three-, four-, and six-fold rotation axes can occur.


This isn't a rock at all, but a seed of Entada Gigas, sometimes called the sea heart or sea bean.

(CC-BY-SA-3.0)

Entada Gigas is called the "sea bean" for good reason: it's a member of the bean family Fabaceae. In fact, this species has the family's largest seed,  a flattened heart shape 6 cm in diameter and 2 cm thick.  These hollow seeds are washed into the ocean and drift on currents for up to 2 years, on the chance that one will wash up somewhere to germinate.  It seems that sea beans have evolved to propagate in this way, similar to coconuts.


Why can isotopes reflect the age of the Earth rather than the age of the supernova that created them?

Suppose you purify a sample of uranium 238, removing all of the lead. Half of those U-238 atoms will have decayed into lead 4.468 billion years from now. If the lead is removed from that half-uranium/half-lead sample 4.468 billion years from now, half of the U-238 atoms in that purified sample will have decayed into lead in yet another 4.468 billion years. The clock is reset when the decay products are removed. It doesn't matter whether those U-238 atoms were created in one of the very first supernova over ten billion years ago, a supernova shortly before the Earth formed 4.6 billion years ago, or even a supernova that occurred after the Earth formed. Those U-238 atoms do not have a memory.

Some natural processes do this purification and reset the clock when a rock first forms as a solid object. I'll address two; there are others. Zircons readily bond with uranium and thorium but strongly reject lead. Any lead present in zircons now is a result of the radioactive decay of uranium and/or thorium encapsulated within the zircon when it first formed. Potassium-40 sometimes decays into argon-40. The argon simply bubbles out If that decay happens in molten rock. They argon remains trapped if the decay happens inside a solidified crystal. Any argon present in a rock crystal now is a result of the radioactive decay. In both cases, (zircons containing uranium-238 and rock crystals containing potassium-40), the clock was reset when the rock first formed.


To what degree does historical measurement inaccuracies contribute to climate change models?

I would estimate 0%, as long as we are considering the same types of models. See, climate models and in the regard that you may think of observations. Climate models aren't really initialized on observations of the system, but rather on inputs/forcings and mean state.
Observations of today's climate may validate the accuracy/tuneness of a climate model, but the types of observations used to run climate models may be different from what you expect. For example, the thermometer was invented either near 10 AD or in the 17th century, so it was obviously not a widespread invention then. Usually, those temperature measurements are taken as proxies, such as the amount of oxygen isotope or atmospheric composition in ice cores. So the answer to the climate skeptic is that it isn't just the temperature itself, but the modern day observations of temperature proxies that show past warming.


Can the atmosphere affect the composition of igneous rocks?

I figure you're looking for more exotic examples, and some geologists may well have some offhand, but I want to say "yes" because of the example of carbonatite rocks described in this geology page from San Diego State University:

  Carbonatites are perhaps the most unusual of all lavas. They are
  defined, when crystalline, by having more than 50% carbonate
  (CO3-bearing) minerals, and typically they are composed of less than
  10% SiO2.

Which would rely on the carbon cycle and the deposition of atmospheric CO2 onto the seafloor by biological processes.

However:

  Some scientists believe that the Ca-carbonatites are generated by
  fractional melting of crustal carbonate rocks. However, others believe
  that the Ca-carbonatites are not primary magmas at all, but rather
  derived from the alteration of Na-rich natrocarbonatite lavas.

There is an interesting paper in GeoScienceWorld titled Atmospheric K-feldspar as a potential climate modulating agent through geologic time that addresses your topic as the author tries to estimate K-feldspar (Kfs) flux through geologic time -- which addresses your question from the other direction: assessing atmospheric content (in some cases simple dust deposition) over billions of years by evaluating its traces in the geological record.


How can scientists be confident of isotope ratios in past eras and varied locations, used for radiometric dating?

"Doctor! It hurts when I do this! «bonk»" "So don't do that then!"

One way around the issue of an unknown initial distribution of isotopes is to not do that. One of the most reliable mechanisms for dating the Earth is uranium-lead dating of zircons. Uranium can take the place of zirconium in the zircon crystal because of the chemical similarity of uranium is and zirconium. Lead on the other hand is very dissimilar chemically from zirconium and uranium. The crystal formation process strongly rejects lead. At the time a zirconium crystal forms it will contain no lead. All the lead in zircons comes from the decay of uranium. Two decay chains lead to lead, with 235U eventually decaying to 207Pb and 238U eventually decaying to 206Pb. Those two decay chains provide two independent mechanisms to date the same crystal.

Another approach is to find that initial distribution of isotopes. This is the approach Claire Patterson used in his estimate for the age of the Earth. See Claire Patterson, "Age of meteorites and the earth", Geochim Cosmochim Ac 10 (1956). He used a non-radioactive iron meteorites to establish the primordial distribution of isotopes of lead. With this as a baseline, he then used the disequilibrium ratios in meteorites to find the age of the Earth.

With regard to varying 234U/238U ratios, that's a red herring used by some who don't like the results of radioactive dating in a failed attempt to throw suspicion at those dates. The 256 thousand year half life of 234U means that there is no primordial 234U on the Earth. All of the 234U we see now came from the decay of 238U, via 238U→234Th→234Pa→234U. Those decays weaken rock at the site of the decays. When the rock weathers and is exposed to water, that weakened rock around a 234U atom means that 234U is preferentially leached from the rock.


Where on Earth does the atmosphere have the most $O_2$ concentration?

You may find bigger O2 levels at the upper layer of rich oceans -biologically talking-. There is Henry's Law, an equilibrium between gas pressures/concentrations of the ocean and the atmosphere, so you might find it at the contact between an ocean bacterial rich system and the atmosphere, but maybe on arboreal forests at light.

I have no data about O2 levels at both suggestions, atmosphere/ocean contact at a rich ocean system & a very rich arboreal forest on hot season. Just a caution for a possibly answer from a botanic. There may be maps about O2 levels at ocean surface but that at NASA and so and I am a student with no access to Science papers Muze and don't know how to get them. For arboreal system they can give you absolute maximum O2 levels registered, and then comparison.

The maximum level will happen at a certain time, and even I think satellites can measure gas levels the layer to search is about 1mm or so. maybe doing a comparison between highest O2 levels measured at the interface of a rich estuary or so and a tropical forest coming from local studies we find a non exactly answer but giving the environment where to find it and an approximate concentration.

There are those ozone/O3 layers with a very high concentration at industry zones,but i guess you ask for O2 gas. There are also hyperbolic conditions,eg at a Erlenmeyer flask of a lab, but I guess you are asking for levels on Earth's Atmosphere sensu stricto at a relative big atmosphere's surface/volume. I think others will appreciate more the question if you write eg "higher O2 concentration measured on an Earth's Atmosphere area despite labs or natural micro-layers" or something like that if that's you want to mean. Also sensu stricto more oxygen no matches with saturation (saturation is function of Temperature and Pressure).


Is climate change homogenous globally?

Not at all. The Arctic (both the Arctic Ocean and far northern land masses) has and will continue to experience greater temperature changes than other parts of the Earth. Other than the Arctic, land masses have and will continue to experience greater temperature changes than the oceans.

The warming seen to date is a portrayed below. This image portrays annual temperature anomalies averaged over the last ten years, with anomalies relative to a 1951 to 1980 baseline.

Source: https://data.giss.nasa.gov/gistemp/maps

  Can anyone point me to clear sources on climate change trends per region or continent?

The IPCC reports is always a good start. The most recent is the fifth assessment report. The site I used to make the above map, Global Maps from GHCN v3 Data is also a good source.


I understand that the integral of the spectrum over all frequencies is the variance which means that the integral should have $m^2$ units? Please correct me if I am wrong.

You are correct. If elevation $\eta(t)$ is the measured quantity (units of $m$), the Fourier transform of wave variance $\eta^2$ yields spectrum $S(f)$ with the units of $m^2/Hz$, or if you are working with angular frequency $\omega = 2\pi f$, it yields $S(\omega)$ with the units of $m^2/rad/Hz$.

More details can be found in the answer to this question.


What are the sunniest places on Earth? (including oceans)

It is an interesting question, and despite that latitude is the main control of the amount of solar radiation that reaches the top of the atmosphere at a given location, the answer will be determined by how exactly weather patterns distribute across the different latitudes. Therefore, a solid answer will require to be supported in data.

A good dataset for this propose is the one at the Surface meteorology and Solar Energy. I recently used it to answer a somewhat similar question. In this case I'll use the Insolation Incident On A Horizontal Surface dataset, that provides a 22-year average (July 1983 - June 2005) of solar insolation in kWh/m^2/day (kWh per square meter per day) derived  from satellite measurements, allowing worldwide coverage at 1° resolution (~110 km).

The dataset looks like this:

Where the numbers in the color scale on the left have to be interpreted as average kWh/m^2/day. We can see a clear latitudinal gradient were the equatorial latitudes receive much more energy than polar ones, however there are significant longitudinal variations due to the different climates that can be found at the same latitude.

In a first look, land areas doesn't seem to receive more energy. Land over the equator seem receive relatively less energy (due to cloud cover), and the deserts "hot spots" like Atacama and Sahara are quite far from the equator (~2000 km). In the other hand, there seem to be extensive equatorial waters that receive a lot of energy.

The figure shows the maximum of the data set (6.98 kWh/m^2/day), giving to the Atacama desert in Chile the title of the area that receive more solar insolation on Earth. However, it is a fairly small area.

The following picture show the same dataset overlaid on top of a world map to make land areas highlight a bit more, and contours on the areas receiving more than 6 kWh/m^2/day

It is clear here that despite that the Sahara and Atacama deserts are within the areas with more insolation, the vast majority of such areas lay over the oceans.

So, in regard to your first question, I would say that despite the first place of the highest solar irradiation contest go to the Atacama desert, the rest of the podium belongs to the oceans. In fact if we look at the "pixels" of the dataset with values above 6.9 kWh/m^2/day, there is two in the Atacama desert and 16 in the Pacific ocean. So in general I would say that it is false to say that no place in the surface of oceans gets as much solar energy as a sunny place on land.

To answer the second question we can have a look at the dataset of the Monthly Averaged Clear Sky Days (i.e.  cloud cover less than 10% over the same 22-year period), and it looks like this:

 This time the color bar numbers have to be interpreted as average clear sky days per month. Here we can see that the high insolation in the Atacama desert is explained by a very large amount of clear sky days (17 per month) while in that sunny Pacific ocean spot there is at most 10 clear sky days in average. But wen it comes to the record of the most clear skies days, the winner is Antarctica, with large expanses with 20-22 clear sky days ion average. However, if there is several month without sunshine I don't know if it could be translated as the "sunniest" place.

So, in regard to your seconds questions, I would say YES, oceans have in average a much more persistent cloud cover than land. In fact, pretty much all the areas with more than 10 clear sky days per month in average are on land, and the vast majority in Antarctica.

Now, to answer your third question we have to separate the data of the first dataset (first figure) into land and sea. To do that, I've used the ETOPO1 Global Relief Model, saying that any place at an elevation of 0 meters or more would be land, and anything below zero is ocean. I've also transformed the data to an equal-area projection, to make the calculation easier, as in the original data a "pixel" near the poles was much smaller than one at the equator.
The land area insolation looks like this:

And the sea insolation like this:

And the mean total insolation received by land is 6.45e14 kWh/day or 645 PWh/day (peta watts per day), in contrast with 1,656 PWh/day by oceans. Therefore 72% of the energy end up in the oceans.
The total is 2,301 PWh/day, which as a sanity check, we can see that it have the same order of magnitude than the total amount of energy hitting the top of the atmosphere, a value that we can easily calculate using the solar constant and Earth's radius (24*1.362*pi*6378100^2 = 4.177e15 Wh/day= 4,177 PWh/day). These two totals don't match as expected because a significant fraction of the energy gets reflected (Earth's albedo is 0.3) or absorbed by the atmosphere.

To wrap up all this information in the context of your question. There is indeed a great potential for offshore solar power, that maybe we will tap into in the future. However, the transport of the energy could be now the main constraint. Making offshore project viable only in areas of high real state prices, making too expensive to build them on land, and therefore making the offshore alternative a sensible one. In those cases the location is mostly dictated by the location of the demand more than the location with higher solar irradiation. If I let the imagination loose, maybe those large high-irradiation zones in the Pacific could one day host floating industrial complexes, producing and using the power on the spot for manufacturing or other industrial processes.


Is my understanding of saturation and cloud formation correct?

The height at which clouds form is called the cloud condensation level (CCL), where air lifted by convection powered by temperature differences cools and condensates. When it comes to basic physics, yes, evaporation would need to be less (i.e. zero) for condensation to occur.
However, this is not necessarily the correct way to look at it, as relative humidity is the determining factor for cloud formation. Relative humidity depends on temperature and pressure.
As a volume of unsaturated air cools, its relative humidity increases. If sufficiently cooled, the relative humidity becomes 100%, the temperature equals the dew point, and clouds form. So it's less to do with evaporation and condensation than the amount of humidity, and the temperature (and temp gradient) and pressure of an air mass.


Is it possible to get trapped in a circle of water in a rip current?

Ok, i try an answer based on your clarification.

Diving in a straight line in such a regime is near impossible, because sight is obstructed. A specially trained free diver may have more of a chance but will have to go to the surface several times.

Now let's assume that an unlucky swimmer finds him-/herself in exactly the depicted situation and quickly analyzes and realizes what's going on (unlikely). If they are cold blooded enbough they can try and swim to one side, then with the stream either once around or back again towards the beach. But ... things aren't usually like in a picture book. There are coast parallel streams, waves and rocks can make it difficult to get out of the water unhurt, and maybe the stream turns too far outside or not at all. There may be undertow or a breaking wave throws the swimmer on the rocks. And when outside, even in 20° warm water the survival chances are low, until a helicopter or the rescue boat arrive. And even then, finding a head of a swimmer between the waves is pure luck for the rescue forces. People have actually drowned in the middle of regattas and dense trafic searching for them. That is why it is strictly forbidden to go overboard ;-)

There is a reason why people do die in such or similar situations. In any case, the answer to your question is "Yes", a swimmer can easily find himself in a situation where reaching the land is impossible. A snorkler with fins may have better chances.

Edit: just so that you know what i am talking about, 3 random videos. Medium conditions, waves 1-2m. Dynamic conditions, waves 6-8m. Calm conditions, .5m waves.


What is the geologic origin of the Bauxite deposit in Bauxite, Arkansas, and could there be more?

The short answer is, bauxite requires a particular alumina-rich source rock and a specific set of conditions and processes to concentrate the aluminum in a specific order.

From the  Encyclopedia of Arkansas:

  The Arkansas bauxite region covers about 275 square miles in the northern part of the West Gulf Coastal Plain and is divided into two mining districts. One area is in Pulaski County, south and east of Little Rock, and the other is in nearby Saline County, northeast and east of Benton.

(Source, Arkansas Geological Survey; a very detailed map can be downloaded here)

The source rock (nepheline syenite) for the bauxite appears as two isolated blue spots in the middle of the map above, surrounded by (orange) Tertiary sedimentary deposits. The town of Bauxite is just to the northwest of the southern spot.

Rather than cut and paste EOA's description of the process, I decided on the following summary:

Magma was intruded during a Cretaceous volcanic event as the Mississipi Rift opened, and this formed nepheline syenite, which has aluminum-rich nepheline where granite would have quartz.
The syenite decomposed, eroded, and was deposited as a soil on the edge of a shallow sea that filled the rift.
In the Paleocene, tropical conditions caused the aluminum minerals toleach down into the soil, becoming concentrated into a hard layer called a laterite
In the Eocene, some of the laterite was eroded and deposited as alluvial bauxite ore as the sea slowly filled in.

Both the original laterite and the alluvial deposits have been mined for aluminum.

Your assertion that there are no other bauxite deposits in the US is not true; other deposits formed in similar conditions in the southeastern US, and there is also bauxite in Montana.


Where can I find a list of snow fall recording stations in my zip code?

Were to find hourly data will depend on your location, as you will probably need to access the national weather network of the country of your interest. Global climatic databases usually record data on daily basis. Like the Global Historical Climate Network, you can search for all the station in that network and query snowfall data in the KNMI Climate Explorer. This is a example query of all the stations between 50 and 51° North and 120 and 122° West (to convert ZIP codes to coordinates you can use geocoder or other similar services):

It returns 39 stations, each one with a record like this:

And you can also download the raw data.