There is one timezone that is completely uninhabited: the UTC-12:00. It covers only two islands: Baker Island and Howland Island that are both uninhabited (owned by US). Because of the weird way timezones are divided in the pacific there are timezones that practically use the same time (e.g. UTC+12 and UTC-12), but are actually in two different days. However if you strictly interpret the question no-one is lonely here as there is no-one here, so this might not comply.

The second least population is at UTC+08:45 that covers village of Eucla and other villages in Australia with a population of around 200. The area is surrounded by signs to remind you to turn your clocks, but it is unofficial so it might not comply either.

The third least population is at UTC+10:30 that covers an island called the Lord Howe Island that belongs to Australia and inhabits 382 people. If you don't accept timezones that aren't in integer changes from UTC then this UTC+10:30 might not satisfy your curiosity.

The first full integer timezone shift from UTC (that has any population) is UTC-02:00 that consists of Atlantic islands of Brazil like Fernando de Noronha, Trindade, Martim Vaz etc. Also South Georgia and South Sandwich Islands of UK belong in this timezone. The total population then is somewhere around 2700 people. Unfortunately these are the places that use this timezone all year round and other areas like densely populated Brazilian cities use this timezone as daylight saving during their summer increasing the population drastically so even this timezone might not satisfy your criteria.

Finally UTC-11:00 being full integer change from UTC, with only all year round usage (isn't a daylight saving timezone for anyplace) consists of American Samoa, Midway Atoll, Jarvis Island and Palmyra Atoll of US and Niue of New Zealand and has under 60000 inhabitants.

Ps. The estimated population numbers are from the wikipedia pages of the locations mentioned.


Your idea has merit. Shale is classified by geologists as being a mudstone. It is composed of silt and clay sized minerals.

According to this geology website, shales can be crushed to produce a clay and then mixed with water. These days, items that were once made from natural clay, such as terracotta pots and tiles for roofs, are now made from crushed shale.

Extra Information

One thing to be mindful of is that clays expand when wet and contract when dry. Anything you make from it, such as bricks, that isn't baked or protected from water by a sealed coating will expand and contract according to it moisture content.

Another application which you may want to consider is to supply crushed shale as a garden mulch or other such landscaping product.


Any idea what are these circular rock marks?

It looks like onion skin weathering. It appears in places with large temperature differences between night and day and associated thermal expansion and contraction of rocks on daily basis. That creates weaker spherical zones, where cracks may form later. I have seen that several times in basalts but not limestones, though.


What would be the phase shift and polarity of a seismic wave upon reflection

In general, the answer is not simple as it depends on the angle of incidence of the wave and the properties of the medium.
The Zoeppritz equations are used to understand the behavior of seismic waves incident on reflectors (or the free surface). The solutions give the reflection and transmission coefficients for P and S waves, which depend on the densities and wave speeds of the lower and upper media as well as the angle upon which the wave is incident. In general, the coefficients are complex valued; the phase shift is encoded in the phase of the complex number.
I have used the Zeoppritz explorer program for this calculation.


Why does it rain more at night than during the day?

First off, your observation that Tamil Nadu gets more rainfall in the evening is partially backed by records. Sahany, Venugopal, and Nanjundiah, 2010 provide data on diurnal scale rainfall distribution during the Southwest monsoon season shows that Tamil Nadu is dry from 0530-1430 each day, and likely to be wet from 1730-0230:

The Northeast monsoon is different. From Rajeevan et al, 2012 the NEMR (North East Monsoon Rainfall) peaks in the evening for most of Tamil Nadu but the coast facing the Bay of Bengal (including Chennai) peaks in early morning (0330-0630):

Regarding the reasons for this, here are some excerpts from Basu, 2007:

  In the Tropics most of the rainfall is from the tall clouds (Cu or Cb)
  formed by convection within a deep layer of the atmosphere. The usual
  forcing for such clouds to form is the heating from below by the solar
  radiation absorbed by the ground during the day. This forcing is
  maximum near the time of maximum surface temperature and the first of
  the thunderstorms caused by insolation start near 1430 local time

and

  Over the sea areas along the east coast (south of 15°N) too, the
  maximum in precipitation occurs in the early morning hours as the
  synoptic-scale westerly is weak over this region and the diurnal
  variation is dominated by the land–sea breeze.

Also worth noting, from Roy and Balling, 2007:

  The strength  of  the  diurnal  cycle  is  greatest  in  the
  peninsular region with close to 96% variance explained for stations
  located in Tamil Nadu.

My interpretation of this is that inland Tamil Nadu sees high surface temperatures from sunlight through clear skies striking the ground. The resulting heat is released in the late afternoon and evening, which causes cumulus or cumulonimbus cloud formation and rainfall. During this, the ground cools off at a rate faster than the nearby Bay of Bengal. This causes oncoming sea breezes laden with moisture and coastal rainfall peaks in the early morning hours. In Tamil Nadu especially, this pattern is very stable.


largest earthquake not in a subduction zone

08/15/1950 Assam, tibet, 8.9 magnitude. according to the USGS, https://earthquake.usgs.gov/earthquakes/browse/largest-world.php

Note you are talking about a very small window of time there are only 5 earthquakes of 9.0 or greater within that time frame.


Interpolating world data to a local grid in Python

As @gansub implicitly suggested, you may have a better outcome by defining the output grid as well.
Check this very similar question:
How to interpolate scattered data to a regular grid in Python?

After comments, I realize I missed the irregular target grid. Maybe this answer helps:
https://stackoverflow.com/questions/3242382/interpolation-over-an-irregular-grid


Help understanding radar data in subglacial lake complex beneath Devon Ice Cap

In the figure:
The top panel is the radar gram measured in depth below ice surface (m). It is flat because when you do the measurement it starts from the surface which is 0m. The distance from the aircraft to the surface would have been relatively constant but the plot starts from the air-ice boundary at 0m.

The middle panel is a cross section measured in m above sea level showing the ice surface and bedrock (black), the hydraulic head (blue) relative to sea level. The hydraulic head is calculated by working out the pressure of the ice sitting on top of the bedrock. It is basically the water table of the ice sheet. Whats important is the differences in hydraulic head (gradient) which can tell you if the water is moving or not.

The bottom panel is the reflectivity (black) and specularity (blue) of the basal surface. Specularity is a ratio of reflected to scattered energy. Simply put, high reflectivity means the boundary is wet and high specularity means the boundary is flat (Ice-Water), and low specularity means its rough (Ice Rock).


Would you see a correlation between detrital zircon age and grain shape?

My thought is that you would not see any correlation because grain roundness has to do with how long it has been in the sedimentary system rather than its crystallisation age. That is, if one sampled a modern sediment in which a 650 Ma zircon grain from a 650 Ma granite has only recently been eroded from its granite source then one would expect this zircon to be euhedral (and this is not taking into account magmatic effects like resorption which would affect its shape!). But a 650 Ma zircon in the same sediment may have been eroded from a different Neoproterozoic granite during the Cambrian, in which case one would expect that it has been rounded by multiple cycles of sedimentation. Therefore no correlation could be made between the shape of the zircon grains and their crystallization age.


How can we calculate the temperature of the atmosphere, including the greenhouse effect?

One can account for greenhouse gas effect for Earth's temperature in simple energy balance model in following manner.
Assume that fraction $f$ of longwave radiation emitted by Earth's surface is captured by green house gases in the atmosphere. Suppose Earth's surface temperature is $T_e$ and temperature of the atmosphere is $T_a$. The energy received from Sun should balance as follows
$$\pi {r_e}^2 F_0 (1 - A) = 4 \pi r_e^2 (1-f) \sigma {T_e}^4 + 4 \pi r_e^2  \sigma {T_a}^4 $$
where $F_0$ is solar constant (Energy received from sun per unit area per unit time), A is Earth's albedo, $\sigma$ is StephenBotlzmann constant and $r_e$ is Earth's radius.
Since the black body radiation are isotropic, 50% of radiation emitted by atmosphere travels toward Earth's surface and remaining 50% of radiation travels toward the space. Also, assuming that atmosphere receives all of its energy from Earth's surface through longwave radiation, it gives following energy balance equation
$$f \sigma {T_e}^4 = 2  \sigma {T_a}^4. $$
which leads to
$$ T_a = \sqrt{\sqrt\frac{f}{2}} T_e $$
Nearly 80% of the radiation emitted from Earth's surface is absorbed by greenhouse gases (including water vapour) and clouds. Substituting value of $f$ 0.8 and solving it for $T_e$ will get you the answer you are looking for.
Reference
Chapter 7 The Greeenhouse Effect in Introduction to Atmospheric Chemistry by Daniel Jacob
http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap7.html


Taken straight-out from Prof. L. Braile's collection of earthquake hazard information, that explains it quite nicely:

  The magnitude scale is really comparing amplitudes of waves on a seismogram, not the STRENGTH (energy) of the earthquakes.

While one unit of magnitude is 10 times the amplitude on a seismogram, one unit of magnitude represents $10^{1.5}$ times (approximately 32 times) the energy, based on the long-standing empirical formula

$$\log{E} \propto 1.5M$$

thus

$$E \propto 10^{1.5M}$$

where $E$ is energy and $M$ is magnitude.

The example set in the webpage is to compare how much bigger would a 9.7 magnitude earthquake be in comparison to a 6.8 magnitude earthquake:

The magnitude scale is logarithmic, so a magnitude 9.7 earthquake is $\frac{10^{9.7}}{10^{6.8}} = 794.328$ times bigger on the seismogram than a magnitude 6.8 earthquake.
Measuring the change in energy, however, shows that the 9.7 earthquake is $\frac{{10^{1.5}}^{9.7}}{{10^{1.5}}^{6.8}} = 10^{1.5 \times (9.7-6.8)} = 22~387$ times the energy of a 6.8 earthquake.

Comparison of earthquake "size" on seismograms: this image from Nevada Seismological Lab's Living with Earthquakes in Nevada

A graphical comparison of earthquake energy release, a video by the US NWS Pacific Tsunami Warning Center (PTWC).

The USGS has a calculator for magnitude difference.

And there's a calculator for seismic energy and several equivalences. Unfortunately, most of the equivalences are related to the USA.

See Brian Hill's answer that explains that with the original Richter scale, one unit of magnitude is apprimately $31^{1}$ times the energy, and two units of magnitude are $31^{2}$ times the energy, and so on.

In short: you are half-right (one unit of magnitude it is 10 times bigger on the seismogram, not in energy), and the book is right (two units of magnitude are 1000 times stronger).


There are a couple of very cool animations on YouTube of the future supercontinent: Pangea Proxima. One is by Christopher Scotese (video) and the other is by Algol (YouTube or also a longer animation with a longer history). The PALEOMAP Project page contains a fair amount of information as to how they estimate the evolution. With regard to the future climate, that is a really tough question that I don't feel qualified to answer.

Also, even though it does not include the future supercontinent, I really like the EarthViewer interactive tool. It has lots of information and it is very intuitive to use.


Coal fires affecting seismic activity, and also volcanoes

I'm assuming you mean underground fires within coal seams whether they are caused naturally or through human neglect or error.

Regarding the possibility of them "triggering volcanic eruptions by affecting the flow of magma or by some other means", the answer is no.

Underground coal seam fires are mostly smoldering type fires rather than raging fires, due to the lack of oxygen underground. Most are located far away from sources of magma: either laterally or in terms of depth.

Concerning whether coal seam fires can "cause, ... prevent or postpone earthquakes", they cannot prevent or postpone earthquakes. Can they cause a seismic earthquake? Unlikely.

Coal seam fires create a void underground. If the fire is extensive and the extensive burnt out zone abuts an active geological fault the resultant void may cause a ground stress redistribution which might cause a minor earthquake. The other possibility is that the geological strata overlying the burnt out void is weak and eventually subsides, either slowing or quickly. A quick subsidence can create a minor earth tremor and could cause a hole to puncture the surface of the earth, depending on the depth of the coal seam and the void.


What's the background concentration of trace gas/pollutants?

Background pollution is what would be measured if no anthropogenic emissions existed.  In other words, if you shut off human activity (or avoid the emissions from it), you can measure the background.  Sometimes this is called the natural background.  There are also regional backgrounds, like "the US background", which additionally includes anthropogenic sources from outside the region.  In order to measure background concentrations, you need to be in a remote area that is not influenced by human activity (e.g. see "Influence of background particulate matter on urban air quality in the Pacific Northwest" by Timonen et al., 2013).

Background concentrations of particulate matter can approach zero in pristine areas, but will be seasonally influenced by natural events like wildfires and dust storms.  Background NOx also approaches zero in pristine areas but can be perturbed by lightning generation and soil processes.  In contrast, background concentrations of ozone can rise naturally without an emissions source, especially in mountainous areas that are exposed to air from stratospheric intrusions.  Ozone is one of few the air pollutants whose background concentrations are significantly influenced by sources not at the surface.

Using an air quality model, a researcher can "zero-out" anthropogenic emissions in order to estimate the background.  There are also source-apportionment techniques that can be used to estimate the background (see "Comparison of background ozone estimates over the western United States based on two separate model methodologies" by Dolwick et al., 2015).

You might enjoy this white paper that the EPA recently released about the complexities involved with estimating background ozone.


Why do tropical cyclones get more attention than extratropical cyclones?

Extratropical cyclones are relatively well understood. They often follow the Norwegian Cyclone model, which was developed in the 1910's and 1920's. Because of their spatial extent, extratropical cyclones are often less intense than their tropical counterparts. Since they are so much larger and live longer over land, it is easy to get data about an extratropical cyclone.

Tropical cyclones, on the other hand, have faster winds and affect people in a more dramatic fashion. If an extratropical cyclone is announced in winter, a grocery store may run out of bread. If a tropical cyclone is announced, there may not be a clerk available to restock the shelves. Tropical cyclones often don't live very long over land and are smaller, so it is hard to get data about them. Because they are smaller and the wind speed change over distance is so much greater in extratropical cyclones than tropical cyclones, errors in the forecast tend to have more of a dramatic effect on tropical cyclones.

To summarize:

Extratropical cyclones are often less intense.
We have an abundance of data on extratropical cyclones.
The theory behind the development of extratropical cyclones is longstanding and generally well established.
Tropical cyclones are much more dramatic and concentrated.
Forecast errors impact tropical cyclones more severely than extratropical cyclones (i.e. less predictable).


Database of color wavelengths of minerals

This type of information is made available through the USGS Spectroscopy Lab.

There is a researchable database of their current spectral library with the appropriate information for each mineral signature (formula, sample_id, type and more). Here is an example of the signature for Hematite:

Further, there is an up to date publication accompanying the database titled USGS Spectral Library Version 7, available here.


Why does Colorado have so many days of partly cloudy skies?

I'd personally theorize the main answer is mountains.

Thinking the key is localized "mesoscale" features that disrupt large-scale patterns.

In Florida, it's the surrounding oceans that generate daytime seabreeze storms in the summer and provide moisture return (and thus clouds) more quickly after frontal passages in the winter.

In Colorado, would think it's the mountainous terrain causing circulations like the Denver Cyclone creating daytime clouds in the summer, and vertical motion that may well disrupt some of the foggy, stable winter days.

Some mesoscale influences create almost continual cloudiness, such as the cold oceans along the US Pacific Coast.  Others remove more cloudiness, like the terrain and resulting deserts in much of the US Southwest.  For more in-depth details on cloudcoverage, including annual and monthly totals maps, see this us-climate.blogspot.com article.

But one key aspect of both the Florida seabreeze and mountainous circulations is that they are diurnal.  So, often, whatever they bring in one part of the day, they generate the opposite at the other end of the day.  For more about how mountain winds vary through the day, look into mountain and valley breezes.

I'd also suggest the greatest proportion of cloudiest (foggiest) days in the US are winter periods where cold air is in place under a high pressure and moisture builds up within the stable conditions.  Being elevated in Colorado may additionally aid prevention of some such days by having lower moisture depth and also by being more exposed to winds [while Florida instead is less often deeply entrenched in cold airmasses].

Just thoughts, but hopefully that offers some direction for why it may be!


Earthquake severity during supereruption at Yellowstone caldera?

Volcanic earthquakes aren't actually all that strong. That's quite easily understandable by just looking at length scales: In the largest earthquakes that happen on earth, tens of kilometers of subduction zones rupture at once, releasing the stress that has built up from two plates moving past each other (but being locked) for decades.

Even large calderas cannot produce faults of this length that are sufficiently long and linear and can rupture in the same quake. Consequently, earthquakes in volcanic zones are usually much smaller than the largest ones we experience on earth.

The global effects of supereruptions are not due to earthquakes or tsunamis, but due to the gases, ash and sulphur that ends up in the atmosphere and that leads to global cooling for several years.


How do I calculate Oxygen requirement in an aerobic waste water pond?

you can actually calculate the theoretical oxygen requirement using the following formula:
O2 req (kgO2/d) = [Q * (S0-S) / (BOD5/BODL)]/ 1000
Where:
Q= flowrate m3/day
S0= infulent BOD/COD concentration (mg/L)
S= efulent BOD/COD concentration (mg/L)

FYI Successful decreasing of BOD and COD can be obtain by using high volume Oxygen Generator such as Submersible Aeration


Is it possible to have an AR(0) for streamflow?

Autoregressive models are mathematical models, and like all models, are based on a conceptual model of the system. The conceptual model is that prior flow is a parameter in prediction of current flow. So it doesn't really make sense to have a model where it does not do so.

Furthermore it is difficult to conceive of a natural system where prior flow is not a predictor. This is where I disagree with Gordon's answer. Even in small catchments, prior flow is a good surrogate for the physical conditions that contribute to flow. The conditions include precipitation history, soil moisture, filling of depressions so flow can accumulate, capacity for trees to intercept precipitation (are the leaves already wet), water-table stream connectivity, etc.

If you don't see a relationship to prior flow in small catchments, that may just mean your daily timestep is too large. I care about the flow variation in very small catchments and monitor the flow on 30-minute intervals.


Why don't pyroxenites and peridotites appear in Streckeisen's QAPF diagram?

Why don't pyroxenites and peridotites appear on this diagram?

Because they do not have any quartz, feldspars, or felspathoids.

The same Wikipedia page also says this:

  QAPF diagrams are also not used if mafic minerals make up more than 90% of the rock composition (for example: peridotites and pyroxenites).

Instead, we use a different diagram, that has olivine, orthopyroxene, and clinopyroxene at the vertices. Like this one right here.

  Aren't they igneous rocks?

Not necessarily, actually. But that's a completely different question.


Is it meaningful to assume static pressure to be constant along a streamline?

If you assume both hydrostatic and pure geostrophic balance, that is a valid assumption.

In Einstein notation, $$u_i=-\frac{1}{f \rho}\frac{\partial P}{\partial x_j}\epsilon_{ij3}$$

If we look at the equation for the streamline:$$u_i=-\frac{\partial \psi}{\partial x_j}\epsilon_{ij3}$$, then we can see that

$$-\frac{\partial \psi}{\partial x_j}\epsilon_{ij3}=-\frac{1}{f \rho}\frac{\partial P}{\partial x_j}\epsilon_{ij3}$$

which simplifies down to $$\frac{\partial \psi}{\partial x_j}=\frac{1}{f \rho}\frac{\partial P}{\partial x_j}$$. Thus, for isochoric (incompressible) geostrophic flow on an f-plane, the streamfunction only depends solely on pressure.


Are weather changes periodic? (Do the same weather patterns repeat over years?) (Cycles) (Journal paper suggestion)

I'll address this part of the question first:
"Or a similar question can be: the weather measurements of how far ago can affect today's weather measurements? Does the weather forget about the weather events of long time ago? If so, how long is that window?"
The answer is "approximately two weeks". Even with nearly perfect knowledge of the atmospheric state (the distribution of pressure, moisture, aerosols, etc), the chaotic nature of fluids means that beyond two weeks, one would be better of predicting the weather from a climatological estimate (i.e, the average of the weather on that date for the last ~30 years). Research into this very question was foundational for the field of Chaos theory (Lorenz, 1963 is a famous example). This isn't just an artifact of the predictive models, but the natural system itself. The weather has effectively 'forgotten' what it was doing a few weeks before.
While the atmosphere has a short 'memory', other parts of the Earth have longer 'memories'. Notable examples are the Oceans and the Landsurface. A warm anomaly in the Ocean will stick around for a while, since ocean currents are much slower than air for mixing things around (and diffusing out the anomaly). The atmosphere is very influenced by what happens on the surface, so the warm/cool anomaly can affects the weather in various ways. This is what happens in the case of ENSO that you have mentioned. The land can also have an impact. The amount of saturation in the soil can have quite a big impact on weather, especially for things like thunderstorms and monsoon systems. Continental snow cover extent may also impact atmospheric predictability. Stratosphere/troposphere coupling mechanisms might also be a source of longer term predictability.
And this part:
"I am wondering if there is long term (10 year, 7 year, 20 year) periodic patterns Similar to short term seasonal and periodic patterns in weather such as sea/land wind, monsoon, ENSO, ocean sea-saw, etc."
The most well known ~10 year climate oscillation is the Pacific Decadal Oscillation.


How to determine constant $C$ in $p(x) = Cx^{-D}$?

There are two solutions using the least square method for calculating $C$ and $D$. Both methods yield different results for your constants. There is no correct method.

Method of least Squares

We define the least square error as follows:
$$\text{lse} = \sum_{i}{\left(y_i - f(x_i)\right)^2}$$
The $y_i$ and $x_i$ are our data through that we want to fit a function $f(x)$. The aim is to reduce our error $\text{lse}$.

The solution (minimal $\text{lse}$) for a linear function $f(x) = a \cdot x + b$ is described here. The basic idea for calculating the minimum of $\text{lse}$ is to set $\partial \text{lse}/\partial a$ and $\partial \text{lse}/\partial b$ equal to $0$ and solve the resulting equation system to $a$ and $b$.

Having said that we come to two solutions for calculating $C$ and $D$ in $f(x) = C\cdot x^{-D}$

Solution 1: Logarithmize the Function

We rewrite
$$y_i = C \cdot x_i^{-D}$$
to
$$\ln{y_i} = \ln{\left(C \cdot x_i^{-D}\right)} = \ln{C} - D\cdot \ln{x_i} $$

Now we have a function of the form $\tilde{y_i} = a\cdot \tilde{x_i} + b$ with $\tilde{y_i} = \ln{y_i}$, $\tilde{x_i} = \ln{x_i}$, $a=-D$ and $b=\ln{C}$. Thus, we logarithmize our measured $x_i$ and $y_i$ values and put them into the formulas of the linear least square error method. From the resulting $a$ and $b$ we than calculate $D$ and $C$.

Solution 2: Insert the Function as it is

We set $f(x) = C\cdot x^{-D}$, insert it into our $\text{lse}$ formula:
$$ \text{lse} = \sum_i{\left(y_i - C\cdot x^{-D}\right)^2}$$
and minimize the resulting formula with respect to $C$ and $D$ for the given set of $x_i$ and $y_i$. This is a tricky and not as straight-forward as it is in the linear case. You could make $\partial \text{lse}/\partial C$ and $\partial \text{lse}/\partial D$ and look how far you come.

I personally, prefer the answer of Gordon Stanger :-) .


A pH of 6.2 is pretty acidic for soil . A more obvious method to lower acid would be limestone as gravel. And for a fast start ,add lime powder, available at any agriculture supply. Rototilling would be good ,but just sprinkling on the surface would be some help.  You can measure soil pH yourself easily. Put a soil sample in distilled water and shake in a sealed container ( to avoid CO 2 from the atmosphere ) .Then get pH indicator solution from a pet shop ( bromthymol blue ?) and test the water after the soil settles. Aquarium water is routinely tested with this indicator.


What is the "pressure gradient" within the richards equation

The pressure as measured at a point z+dz (dz infinitesimally small) and z.

At the surface, pressure is the atmospheric pressure. Just below the surface, let's say at 1 cm depth, pressure is atmospheric pressure + whatever weight of the water column (taking into account saturation and so on).

If the pressure gradient is in equilibrium with the gravity, you will have no flow (water in a glass do not mix, although at the top of the glass the pressure is lower than at the bottom, the water at the bottom feels a little push upwards equal and contrary to the push downward it receives from the weight of the water just above)

Think about this: you are at the bottom of a water reservoir (bottom not sealed). Pressure is the atmospheric pressure + depth of the reservoir. This is enough to induce a flow of water outwards from the reservoir, seeping below/through the dam.

Figure is not my own work, it is from a publication of Olsen and Stephens (2016) that can be found at this URL https://www.researchgate.net/publication/319206472_RELEARNING_HOW_TO_LOOK_AT_PIEZOMETRIC_DATA_FOR_SEEPAGE_EVALUATION


Why is Olympus Mons the largest volcano in the whole solar system?

This is mostly due to the fact that Mars does not have plate tectonics. Therefore the plate stays above the hotspot without moving, allowing magma to rise and pile up at the same place for millions and millions of years. Above the Hawaii hotspot, the oceanic plate is moving, so volcanism tends to drift away with time (actually the volcanism happens at the exact same place from a mantle point a view, but its surface expression moves with the plate). It's why rocks of the Hawaiian-Emperor seamount chain are older in the West and younger in the East. This is true even at the scale of Hawaii island itself, where Kohala and Mauna Kea are extinct, while volcanism$-$or rather the plate$-$has shifted to Mauna Loa, Kīlauea and Lōʻihi.
Imagine if all the magma comprising these islands had piled up at the same place, it could have built a gigantic volcano like Olympus Mons! Well... not really. There is another parameter to account for: a theoretical limit to how high a mountain can possibly get, because of compressive strength of rock (or glacial erosion in some theories). See for instance answers in these questions:

How high can a mountain possibly get?
Why is Mauna Kea taller than the maximum height possible on Earth?

On Earth the limit is ~10 km. So even if magma kept piling up at the same place, the resulting mountain would start to laterally spread or collapse. But on Mars gravitational acceleration is lower, making the limit much higher.


Ice Coverage on the Laurentian Great Lakes

April and later ice cover is primarily on Lake Superior, since this lake is in the coldest region and also because it is the largest lake.

Raymond Assel analyzed the Great Lakes ice coverage for the winters of 1897-1982 in AN ICE-COVER CLIMATOLOGY FOR LAKE ERIE AND LAKE SUPERIOR FOR THE WINTER SEASONS 1897-1898 to 1982-1983 INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 10,731-748 (1990).

According to table IV of Assel, in the winter of 1911-12 Lake Superior had an ice cover of 80% or greater for 74 days.  No other winter had more than 52 such days.

According to this NOAA file in the winter of 2013-14 Lake Superior has an ice cover of 80% or greater on 68 days.

Assel also studied Lake Erie, and finds that 1911-12 had 72 days with 80% or greater ice cover.  This compares to 70 such days in 2013-14.

Based on the above, it is very likely that 1911-12 was the most recent winter with similar April ice cover to 2013-14.


Why is northern Australia unsuitable for agriculture?

Erratic Climate

Lets take Broome, Australia as our example. Broome gets 615mm of rain a year (24 inches), including 58/182/180/102mm in Dec through March. Coupled with average highs in the low 90s, this would be fine for the sort of agriculture you see in South Texas. However, Broome's rainfall is very erratic. For example, in 2016, the rainy season started January 15th, with 23 mm of rain over three days. In 2017 (really 2016, again) the rainy season started December 4th. December 2016 also featured 222mm of rain (remember the average is only 58mm) including 113mm on Dec 23rd and 24th. 2016-2017 featured 222/230/249/114mm of rain, with significant rainfall later into April. 2015-2016 featured 0/119/26/28mm of rain. One year saw too little rainfall to grow even millet, while the next year had enough rain to support paddy rice.

Laterite

Old tropical soils in rainy or monsoonal rainy regions tend to have their soils leached of useful nutrients. The resulting soil is called laterite, and it is heavily enriched in aluminum and iron ore. On the one hand, this explains the mineral wealth of tropical Australia. On the other, laterite (alternately called ferralsols, especially by the UN Food and Agriculture Organization (FAO) ) is hard to farm, with few minerals for the plants, poor moisture retention, and the tendency to form an iron-hardened crust in the dry season.

Not enough people

This is sort of a meta-reason, but Northern Australia is a long way from anywhere. Without very many people, it is hard to build a stable agricultural economy. If a bunch of people where sent there and forced to survive, they'd probably eke something out (for example, like the people who first populated Sydney, or South Africa). But since that never happened...population of the reason never happened. Sort of circular reasoning, but without ever having a reason for a lot of people to show up in Northern Australia (prison colony, religious persecution, etc) no one has ever made the infrastructure that successful farming operations could be based off of.


Can runaway methane gas emissions be an extinction level event?

IF, and it's a very big IF, all the methane hydrate were to be released rapidly, then the planetary climate would be stuffed. But it won't happen.

How much methane hydrate will be released due to global warming? Run 30 different atmospheric-ocean-coupled global climatic models, and you will get 30 different answers - all of them based upon arguable assumptions. The scaremongering doomsayers love to fanfare the worst case. In which case, some of your dire forebodings may come about. But first, take a balanced view of the physical reality. The vast majority of all the world's methane hydrate is sufficiently deep, on or in the sea floor, that it will be millennia, if ever, before they melt, thereby contributing to global warming. The deep ocean floor is everywhere only a few degrees above freezing, whereas almost all of the oceanic warming is in the uppermost few hundred metres. Check out the diagram in http://worldoceanreview.com/en/wor-1/ocean-chemistry/climate-change-and-methane-hydrates/ and you will see that the pressure-temperature control is such that most of the methane hydrate will always be stable.

The current consensus is that some methane is already being emitted from the thawing tundra, mainly in Siberia, Canada and Alaska, and some more will be released from shallow seas as and when they warm up. But this won't dominate the global warming process. In fact methane release is just one of at least two dozen feedback processes, some negative but mostly positive, which will influence the rate of global warming for the next few centuries.

Making the world 'toxic', or 'like Venus' or the 'atmosphere turning brown', or 'poisoned birds dropping out of the sky' are all absurd, but that's no reason for complacency. The rise in global atmospheric methane amounts to about 6 parts per billion per year since 2006, or slightly more than 6 ppb in polar regions; significant, but not at all catastrophic. I am far more worried about the accumulating global CO2, which still shows no sign of slowing down despite a dirge of conference resolutions, ineffective carbon taxes, and empty political rhetoric.

As for an 'extinction event', the extreme rapidity of global warming, habitat loss, sea level rise, and ocean acidification, all adds up to the fact that we are already in an extinction event - not for humans, most of whom will be able to engineer their way through a 3 to 4 degree C global temperature rise, but for the rest of the biosphere - with, or without, extra methane.

Notwithstanding the scientific facts, maybe we can all relax, because Donald Trump assures us that climate change is just a fictitious Chinese conspiracy.


What are the phenomenon (artificial and natural) in play in this photograph "350m beneath Berezniki in Russia"?

As stated in the caption for the picture this is an inside view of a potash mine.

Mining professionals regard potash, like most coal, to be a soft rock; unlike hard rock such as most metal sulfides.

With hard rock mining, the rock is mined by drilling holes and using explosives to break up the rock. The rock is then loaded and transported out of the mine.

Most soft rock mines, and particularly potash mines, do not use drilling and blasting as the main means of removing rock. Instead they use specialized cutting machines to cut the rock. The shapes left in the rock, in the picture are marks created by the cutting heads of such machines. Usage of such a machine can be seen at the 3:30 mark in this You Tube video.

I answered the question What would you call this mining vehicle? (Ural-20R, used in mining) on SE Engineering two years ago, when someone asked about the purpose of an unusual mining machine.

Such machines are typically called continuous miners.


It's all in how one chooses to define it M.Connor.

Often in physical science courses, we define the Earth system as the lithosphere (rocks), atmosphere (air), biosphere (life), and hydrosphere (water) [also sometimes separately defining a 5th aspect, the cryosphere, which is ice]

In the end, we often just think of the Earth as everything confined by its gravity (not including in orbit) as that's everything still controlled by the Earth.

But in a very true sense, you're still leaving the Earth when you take off on a plane.
Just you're still in a state/region of the Earth's system where what goes up must come down.  So you won't be gone long!


How important is understanding linear algebra in groundwater modeling?

Relatively important, depending on the basic principles of the modeling you are interested in, and to what extent you want to get yourself involved in it.

In many areas of computational geophysics, e.g. atmospheric, oceanic, hydrological modeling etc., there are modelers, modelers, and modelers. First group of modelers get model output from somebody else, do some analysis, make some plots, and write about what they found. Then, there are modelers who design their own experiments, play with tunable parameters, maybe even change a few lines in the code and run the model. Finally, there are modelers - these spend most of their time on building and improving models, both in terms of numerical methods and software design. They could go for few years without publishing a single paper, but boy did they work hard.

If you are interested in computational science aspects of modeling, i.e. the inner workings of the model and how to improve it, understanding linear algebra as well as numerical methods will prove to be very valuable. While it is likely that you will never end up having to implement that matrix inversion or sparse matrix multiply yourself, and instead use one of many well documented production libraries, it is important to understand how they do it and why they do it in a particular way. From my own experience, I can say that most of the time it won't matter, but sooner or later there comes a situation where having knowledge about how low-level operations work will save you from pulling your hair out for weeks.

And this does not go only for linear algebra - I would extend this advice and urge you to strive at also understanding differential equations, discretization, computer architecture, floating-point arithmetic.


Why do meteorological seasons start earlier than astronomical seasons?

Meteorological seasons are based on temperature, whereas astronomical seasons are based on the position of the earth in relation to the sun.  So meteorological winter is the three coldest months of the year (December, January, and February) and meteorological summer is the three warmest months of the year (June, July, and August).  More information can be found on this NOAA web site.


Does the heating of the oceans due to greenhouse effect negate the acidification due to increased CO2 levels?

This is a very complex issue, and therefore I'm not entirely convinced I am qualified to answer that, considering how little I understand chemistry, but I'll give it a try.

The Flux of CO2 can be expressed as follows (see e. g. Wanninkhof et al. 2009):

$$F = kK_0(p_{\mathrm{CO}_2sea} - p_{\mathrm{CO}_2air})$$

By convention a negative $F$ means a flux from the atmosphere to the ocean.
$k$ is the transfert velocity and $K_0$ is the solubility which indeed decreases with temperature, as you noted.
$p_{\mathrm{CO}_2sea}$ and $p_{\mathrm{CO}_2air}$ are respectively the partial pressure of CO2 in the sea and in the atmosphere.
Now, with $T$ increasing, $K_0$ (and also $k$ I believe)  decreases, but, as long as the partial pressure of CO2 is larger in the atmosphere than in the ocean there still is a flux toward the ocean.

So worst case scenario, increasing temperature slows down the absorption of CO2 by the ocean but does not negate it. However of course, if the temperature increase to begin with, it is because $p_{\mathrm{CO}_2air}$ is increasing, so this is a bit of a moot point anyway.

As far as the ocean buffer goes, we're talking here of an uptake of ca. 2 Pg (i.e. $2\times10^{15}$g) of carbon dioxide per year (the preindustrial uptake being ca. 0.5 Pg according to Takahashi et al. 2009), which is too much to be buffered. For comparison, phytoplankton net primary productivity is ca. 50 Pg of fixed carbon per year (Falkowski et al. 1998).

Falkowski, P. G., Barber, R. T., Smetacek, V., 1998. Biogeochemical Controls and Feedbacks on Ocean Primary Production. Science, 281: 200-207.
Takahashi, T., et al. 2009. Climatological mean and decadal change in surface ocean pCO2, and net sea–air CO2 ﬂux over the global oceans. Deep Sea Research II, 56: 554-577.
Wanninkhof, R., et al. 2009. Advances in Quantifying
Air-Sea Gas Exchange and Environmental Forcing. Annual Review of Marine Science, 1: 213-244.


Resources for learning the technical parts of atmospheric modeling

For fundamentals on numerical methods applied in atmosphere and ocean modeling, see the GARP publication by Mesinger and Arakawa: Numerical Methods Used in Atmospheric Models. This old, but certainly not outdated text provides the basics on time and space discretization and stability, with particular focus on solving advection equations, and gravity-inertia wave (read: shallow water) equations, and is relatively easy to digest. A must read for any meteorologist or oceanographer using or developing numerical models.

Then, an excellent textbook by Dale Durran, Numerical Methods for Fluid Dynamics: with Applications in Geophysics maintains similar application focus as Mesinger and Arakawa, but expanded with more numerical algorithms and in-depth analysis. It covers the basics as well, so it can be used as a stand-alone text.

There are many other more general CFD textbooks that contain material applicable to ocean and atmosphere modeling. The majority are more geared towards mechanical engineering applications, so you may need to apply a filter (hur hur).

On the other hand, if you are more interested in physics parameterization schemes used in atmosphere models, such as cumulus convection, microphysics, or boundary layer parameterization schemes, a book by David Stensrud, Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models, is an excellent summary of current state-of-the-art. It covers a wide area of unresolved physical processes in the atmosphere, so it does not go into too many details - if you are interested in fully understanding a particular scheme, you will need to follow the reference chain and read the particular papers on the topic. I highly recommend this one if you are interested in gaining an overall understanding of parameterizing atmospheric physics processes.


What is the temperature of the flowing water in icy river?

This is a complex question.

I will assume the following to be able to frame an answer properly:

Let's take a general cold area as a baseline, such as the High Arctic or 70°+ N latitude;
The reference for this example can be Pond Inlet, on Baffin Island, an example where long-term records are available (72° N). The following data assumptions will be based on the normals provided by this station. But what is discussed is likely to be valid for a large area of the High Arctic - like 70°+ N latitude;
In this area, the normal (1981-2010) mean annual air temperature is -14.6° C is fairly representative
Also, in this area, the normal yearly degree days to reach thawing (TDD - the sum of daily average temperatures above 0° C) is 473 degrees.
The bulk of the TDD sum (473 degrees) occurs during June, July and August; only 2 degrees in May, 31 in September and 1 in October, so thawing is most likely minimal outside these three months. As a consequence there are two fairly distinct seasons: the thaw season (summer, duration 3 months) and the freezing season (winter, duration 9 months).
Pro-glacial rivers are not considered (river taking their source from glaciers, different story)
Lakes are not considered (different story)

This all means that the cold region's rivers are not thermally static through time. Even in the High Arctic, an icy river can be frozen along both its vertical and horizontal profile during a good part of the long winter, and thaw completely during the short summer. But other considerations exists.

Let's examine what can happen when the snow thaw is sometime in June. The discharge signature for a river in the High Arctic is nival, with a discharge peak occurring during early summer due to the massive input of snowmelt water, and additional weaker responses from the small rain amounts. This looks like this:

Source:  Woo (2012) Permafrost Hydrology, fig 10.14; from river McMaster, 74° N.

So what basically is happening here?

Peak is during June.
Afterward, once the snow had melted completely, the discharge lowered drastically.
By late August, there is almost no more water in the river, and it may be completely recessed.
Then winter arrives.

During the next several months, snow will accumulate in the landscape. In a landscape there are snow sources and snow sinks (Pomeroy et al. 1997);  sources may be higher lands, outcrops, plateaus, or exposed areas, and sinks lower areas, such as depression or channels. Our typical nival river will be a sink in this context.

Because of this, it is not only patches of ice that will be found in the river channel, but tightly packed snow that builds up at the base when it is a thick layer (or is looser when the snowpack is thin). In any case snow will be most likely metamorphized in structure as a result of surface thaw and the water snowmelt infiltration -> snow percolation -> re-ice events during the winter.

What is happening in June, in more detail?
Let's analyse this further with a more detailed (though raw and unprocessed) graph from a small stream in a gully near Pond Inlet, with resolution available up to the nearest day:

Source: Stream temperature and water pressure in a stream located in a gully on Bylot Island, 85 km from Pond Inlet; raw, partial data from my PhD work. Temperature in blue, scale on the right, and pressure in black, scale on the left. Dates on the x-axis.

By looking at the pressure line (in black), it can be interpreted that there was no water until June 16th when the pressure increased drastically. Temperature (in blue) stayed at -2 °C until the 17th. Water was infiltrating into the snow at this time, contributing to the slowly rising pressure, but the water did not reach the sensor until the 17th when the temperature starts rising. During the 18th, temperature rises to -0.5 °C, then hovers in these negative temperature for almost 24 hours. This supercooled water temperature is due to a mix of factors, such as increased pressure from the water on snow, the release of latent heat due to the metamorphized snow thawing, and the near zero temperature of the water, in balance with the snow.

When a critical mass of water accumulates near the logger emplacement in the stream channel, the bulk of the snow melt and water then shifts to positive temperatures, still near zero, with diurnal/nocturnal shifts (blue line becoming wave-like).

Note: This small stream is minimally impacted by the geothermal flux (heat flowing up from the ground below).

Summary, in relation to the questions:

Temperature will be mostly above zero; but may be under and near zero for short periods when the water is mixing with snow and ice in a channel;
Yes - as shown in the second figure, water was at -0.5 °C for about 24 hours;
I think it is common, as thawing temperatures do reach very high latitudes such as Ward Hunt Island (83° N), and thus this process likely concerns a large area, including probably the entire Canadian Archipelago (lowlands at least).  But this transition process does not last long at any location. Additionally, it is worth noting that High Arctic rivers are difficult to access, monitor, and study, so it is difficult to generalize this with confidence; other factors or contexts could exist where conclusions may differ.


Isn't a warmer climate better for energy generation?

The real problem, of course, is that it's not going to be limited to a small rise in temperature.

However, WRT energy generation in particular, most forms of generation become less efficient as temperature increases.  For thermoelectric generation - fossil fuel, nuclear, & geothermal - that's obvious thermodynamics.

Photovoltaic cell efficiency also decreases with increasing temperature (e.g. https://www.sciencedirect.com/science/article/pii/S1876610213000829 ).  The drop in energy production during winter is a product of factors like the shorter day and lower sun angle, not the temperature.

Unless I've missed something, that leaves just hydroelectric & wind generation.  AFAIK, they aren't directly affected by temperature.  Changes in weather patterns might produce more or less precipitation and stronger or weaker winds in any particular location, but I don't think the effects are predictable, or necessarily a net increase.

Finally, increased temperature affects the efficiency of power transmission.  Electrical resistance increases with temperature, so an increase in temperature leads to increased transmission losses, and a decrease in the effective capacity of the lines: https://iopscience.iop.org/article/10.1088/1748-9326/11/11/114008


Which parts of the ocean have been explored?

The simplest way to find out the basic information about your nearby ocean is to check Google Earth, which has an Ocean layer that often includes details about noteworthy features and discoveries.

This story from Scripps Institution of Oceanography explains some of the updates that were made in late 2015:

  The new global gravity map, recently published by [geophysicist David] Sandwell and
  colleagues in the journal Science, was used in combination with
  available depth soundings to provide a more detailed picture of the
  mountains and valleys along Earth’s most unexplored expanse – the
  ocean floor.

This essay in Scientific American helps explain some of the extent of our knowledge:

  So the “95% unexplored” meme doesn’t really tell the full story of our
  exploration of the oceans. When it comes to having a large-scale map,
  the ocean floor is perhaps not as unexplored as we might think, with
  100% coverage to a resolution of 5km and 10%-15% coverage at around
  100m resolution. That 10%-15% is similar in resolution to the current
  global maps of Mars and Venus.

  But our exploration of the oceans depends on what we want to know
  about them. If our questions are: “What does it look like down there?”
  or: “What’s going on down there?”, then the area that has been
  “explored” is arguably even less than the 0.05% mapped so far at the
  very highest resolution by sonar.

The areas mapped in most detail will be near coasts and common ship routes. Oceanographic vessels run their sonar systems almost continuously, so the maps will have lines of very high resolution detail running through them (artifacts that are often interpreted to look like lost cities or roadways).

But surprising discoveries are still made. It was only in 2012 that a Scripps expedition found a methane seep that was later determined to support an elaborate chemosynthetic ecosystem just 20 miles off the coast of Del Mar in Southern California.


Carbonate reef not horizontal in seismic section?

This phenomenom is called velocity pull-up. The seismic waves that reflected off the top of Layer 2 beneath the carbonate layer have also travelled through the carbonate. Because carbonate (at least in this case) has a faster P-velocity than the surrounding shale, waves that have travelled through the carbonate will return to the surface receivers in a shorter amount of time, relative to waves that only travelled through the shale. Thus the carbonate/Layer 2 interface appears at an earlier two-way-time relative to the Layer 3/Layer 2 shale interface.


What periods of the fossil record are most lacking in specimens?

The biggest temporal gap would be (IMO) the Precambrian, specifically pre-Ediacarian. Accordingly the biggest gap in the evolutionary history is the origin of eukaryots, both because of the paucity of pre-Ediacarian formations but also because few of the early protists were likely to be fossilizable.

From the probable apparition of life ca. 3.8-3.5 Ga (e. g. 1 for a review of Archean fossils) to the Ediacarian (ca. 600 Ma) in which metazoans (i. e. "animals") are already diverse (e. g. 2), this is more than 3 Ga of life history for which we have very little fossils (though our knowledge of this fossil record increases currently thanks, in part, to our better understanding of the "chemical" fossil record).

1: J. W. Schopf, 2006. Fossil evidence of Archaean life. Philosophical transactions of the Royal Society, B., 361: 869-885.
2: S.Conway Morris, 1993. The fossil record and the early evolution of the Metazoa. Nature, 361: 219-225.


In -20 °C weather, creeks below waterfalls here form ice columns. What are these called? Ice-canoes?

These are classed as ice spikes. You are correct in noting the occurrence downstream of waterfalls, as this extra turbulence is part of the formation process. The USGS page here has information on the formations, photographs and a list of criteria involved in their formation:

  The winter conditions at each of the ice formation’s locations were
  similar:

  Freezing or sub-zero temperatures and low flow in channel during    winter months
  Ice covered the surface of the stream and accumulated at depths long    the banks restricting flow
  In each instance, water flowed over a structure such as a weir or    beaver dam causing turbulence in the flow
  Due to the turbulence and restriction in flow, water emerged from    small surface openings downstream of the structure and began to
  freeze – probably rapidly in some cases due to the sub-zero
  temperatures at times
  Whether the freezing water resulted in a “columnar” or a “frothy,    bubble” ice structure depended on the unique conditions at each
  location and the weather conditions over time


Can El Niño/La Niña occur again after normal state?

If you look at the ENSO index record, you can see many instances of El Niño or La Niña occurring multiple times in a row. For instance, the period 1977-1983 and even after that is a succession of El Niño events with normal conditions in between and no La Niña period.

Multivariate ENSO Index (MEI) from NOAA


Are we experiencing lower level of gravity now compared to past?

Earth's radius is about 6400 kilometres. That's 6400000 metres. Let's say that you have a mound 20 metres high, burying an older settlement. Your new "radius" is now 6400020 metres.

Let's say that $g = 9.8\ \rm m/s^2$ at 6400, your new gravity will be $g = 9.799939\ \rm m/s^2$.

Clearly, this is hardly "lower level of gravity".

To make this even less significant, the 20 metres of extra dirt underneath you have their own contribution to the gravity. Even though the overall mass of the Earth is the same, local mass variations cause gravity anomalies. Not much, but $g$ changes by a bit. So adding more dirt directly underneath you will increase $g$, counteracting the fact that you're 20 metres farther away from the centre.


I'm going to answer assuming you are referring to the time between the moment when the organism absorbs the carbon and the moment when it is trapped in sediments. I'm also going to answer by talking about what I know best, i. e. diatoms, which happens to be the major component of the biological pump.

The variation you are referring to is consistent with the fact that coastal diatoms only have a few hundred meters to sink before reaching the seafloor, whereas open-ocean diatoms are sinking for ca. 1000 to 5000 meters.
According to a compilation by Lisitzin (1972), so arguably a little dated, the settling velocity of marine diatoms in the water column is only of a few meters per day (he advances the number of 0.2 to 1.2m/day for 20 to 50µm-sized marine diatoms). But it can vary according to many factors and some of the coarsest, heaviest forms (such as resting spores) or diatoms that travel down in fecal pellets of copepods can be faster and reach the seafloor in an open ocean setting in only a few hundred days.

We don't usually consider this as being part of the biological pump sensu stricto but of course most of the organic matters created by diatoms from atmospheric CO2 is recycled by the zooplankton that grazes on them, which is in turn recycled by what feeds on that zooplankton, etc. Eventually some of them will end up trapped in sediments as well. This lengthens the process of course.

Lisitzin, A. P., 1972. Sedimentation in the world ocean. Society of Economic Paleontologists and Mineralogists, Special Publication 17: 218pp.


A formation is a unit of stratigraphy. It refers to a set of sedimentary layers which are somehow distinct from those above and below them in the stratigraphic sequence. This may be because they have a different lithology, different sedimentary structures, or different fossil assemblages, or something else entirely.

A sedimentary facies is a set of rocks which where deposited in the same sedimentary environment. Typically deposition in this environment will leave behind distinctive signatures in the rock which can help to identify the environment of deposition.

Within a formation the facies can change both vertically and laterally. Equally, the facies may not change at all over several formations.


Has Antarctica's coastline been completely mapped? (map discrepancies)

The key sentence here is

(not sure where the dataset is from)

Every cartographer has to decide what level of detail to use. Mathematicians discovered the Coastline paradox for themselves in the 1960's, but it has always been a fundamental part of cartography.
Different sources of data will come out of different methods of data collection, digitization, and storage.
Regardless of the method used, somewhere there has to be a cutoff. You can't represent a detail smaller than the pen you (or computers) draw it with. The cutoff may be a concsious decision of the cartographer based on the purpose of the map, or an effect of the software used. Or just carelessness.
But this means that different datasets and choices of representation will result in a radically different appearance of the map.


Yes sand is, on average, quite insulative with the temperature at the surface being rather higher than that at depth when the surface is being actively heated, as by sunlight. The actual degree of insulation depends on at least three factors;

Moisture content, wetter sand is less insulative than dry sand because the water in it's pore spaces conducts heat better than air filled pores would.
Average grain size, courser sand has more pore spaces and thus more of it's total volume is made of air so it's more insulative at a given water content.
Grain size distribution and sorting, sand composed of grains that are all of a similar size will have more pore spaces than sand composed of many sizes of grain. Grains of the same size act like stacked ball-bearings leaving a lot of empty spaces but with larger and smaller grains the pores between the large grains are filled by the small ones leaving little space for insulative air pockets.

Due to the complexity of the processes involved it is very difficult to have any single formula that gives you a measure of sand in general. You may be able to find, or create, data sets that allow you to predict the insulative value and thus temperature at depth of a particular sand under a particular set of circumstances. Generally speaking it's easier to take field measurements, unless there's a really long-term project involved.


Why do cold-core lows slope towards the cold air with heigth? How to show mathematically that wind intensifies with height in this case?

I've managed to show why wind speed increases with height in a cold core low, as follows. Considering low is in the Southern Hemisphere, the wind blows clockwise around the low. In natural coordinates, the normal vector points outwards. Since the center is colder than the surroundings, we have
$$ \frac{\partial T}{\partial n}> 0 $$
from the thermal wind relationship,
$$\frac{\partial  V_g}{\partial ln p}\boldsymbol{\widehat{t}}= \frac{-R}{f}\boldsymbol{\widehat{k}} \times\nabla_p{T}=\frac{-R}{f}\boldsymbol{\widehat{k}} \times\frac{\partial T}{\partial n}\boldsymbol{\widehat{n}}=\frac{R}{f}\frac{\partial T}{\partial n}\boldsymbol{\widehat{t}} $$
Where $\boldsymbol{\widehat{t}}$,$\boldsymbol{\widehat{n}}$ and $ \boldsymbol{\widehat{k}}$ are the tangent, normal (in the horizontal plane) and vertical unit vectors.
Since $ f < 0$ and $ \frac{\partial T}{\partial n} > 0 $, we have $\frac{\partial  V_g}{\partial ln p} < 0$, which implies $\frac{\partial  V_g}{\partial z} > 0$, i.e., wind intensifies with height in a cold low.
I still have not understood why the low is displaced towards cold air with height. Since the wind intensifies with height, I would expect the low to be further ahead at higher levels than at the surface.


Why does climate science divide total insolation by 4?

For two reasons, each of which halves the effects of insolation:

At any point in time, only half of the Earth is illuminated by the Sun. Another name for this factor is "daytime" versus "nighttime".
At any point in time, the surface area of the Earth's hemisphere that is illuminated by the Sun is about $2\pi r^2$, where $r$ is the radius of the Earth. But the cross section of that hemisphere to solar radiation is the area of a circle of radius $r$, which is $\pi r^2$, half of the area of that hemisphere.

? Why do you need to average out the sun's energy over the whole planet at the same time when that's not what actually happens?

The Earth rotates fairly quickly, so that is what happens. If the Earth was tidally locked with the Sun, there would be one side of the Earth that would be very hot and one side of the Earth that would be very cold. That is not what happens.
If the Earth rotated once per month (which is what our Moon does do), the sunlit side would eventually come close to being in thermal equilibrium with the incoming sunlight while the dark side would cool to much colder temperatures than are experienced anywhere on the face of the Earth. That also is not what happens. Even the sunlit Sahara does not get as hot as do equatorial regions of the Moon, and even South Pole does not get as cold as do portions of the Moon.
The periods of daytime heating by sunlight and periods of nighttime cooling by the lack of sunlight are both far too brief to bring those portions of the Earth into thermal equilibrium with the sunlight at daytime or with the 2.7K cosmic microwave background radiation at nighttime.


Predicting rainfall with governing equations

The Barotropic vorticity equation is insufficient to model rain. Part of this is due to the word 'Barotropic,' which indicates a lack of thermal gradient. The other reason is that while vorticity is a useful quantity, it lacks explicit information on the atmospheric state.

The primitive equations are a system of partial differential equations that are used by most numerical weather prediction models to model various quantities. Rainfall rate is a parameterized variable, a diagnosed formula (or formulas) based on atmospheric state, based on research. Sometimes the results of the research can give wildly different answers given the same data, which is a weakness of parameterizations. The idea is to model the Reynolds-averaged primitive equations and intermittently invoke the parameterizations (including turbulence, radiation, cloud cover, and so on).

Here is a good book that discusses parameterization schemes in general.


Why does New Zealand and cold countries have volcanoes?

Surface temperatures on Earth are a consequence of solar heating and radiative cooling - in other words, the heat energy which drives climate comes from sunlight falling on the Earth "now".

On the other hand, the heat energy driving volcanism is left over from the formation of the Earth (4.5 billion years ago), stored deep inside the planet, with some additional heat generated from the radioactive decay of elements contained in the rocks.

Deep within the Earth, the temperature is on the order of 5000-7000 K. It's obviously much cooler at the surface. The high temperatures cause the rock and metal of which the Earth is composed to melt. The temperature gradient results in a slight density gradient, which drives convection (flow of hot material up to the surface). When that hot material breaks through the surface, you have a volcano.

Consider that the hottest places on Earth (in terms of climate) don't have surface temperatures anywhere close to what it takes to melt rock (maybe 50 °C compared to 1000s of °C). Heat can only move from where the temperature is higher to where it is lower. Less heat falls on the planet from the Sun than the Earth radiates away into space; that difference is heat finding its way up to the surface from within. So, the heat driving volcanoes cannot possibly be coming from sunlight striking the Earth; it can only come from heat stored inside the planet from long ago. Consider also that the difference in temperature between the hottest places on the Earth and the coldest (in terms of climate) differ by little more than 100 °C. That's a tiny fraction of the temperature difference between molten magma and even the hottest desert. Bottom line: climate has no effect on volcanic activity.

Since the Earth is losing more heat to space than is falling on it from the Sun, and that heat is coming up from below, the core is gradually cooling. But there is so much heat inside the Earth and the rate is so slow that our Sun will die before Earth's core cools enough to solidify.


Are there any weather services that provide hourly forecasts beyond 7 days?

The trouble is, any skill above climatology beyond about 5-7 days is very very low.

So sites could offer such forecasts, but they wouldn't be worth much of anything.

The main thing they could offer that has any use that is an indication of what typically happened in previous years (i.e. climatology)... but unfortunately I don't know any site that offers such on an hourly basis.  We could use more of that!  Still, if you're familiar with the area you're looking up for, you're probably fairly used to the typical weather for a given time of year.

There has been some small skill at making blurrier longer range forecasts... basically estimating either within a large range (such as hurricane forecasts) or (more often) giving probabilities of whether the weather will be above or below that climatological expectations.
(Basic summary for those wondering about how successful some such probabilities are: on these graphs, 0 is no skill, 100 is perfect skill... so 8-14 days temperature and precip have a bit of skill, but lower for temperature and almost no skill for precipitation for a monthly forecast given 2 weeks ahead of time)

But such long-range forecasts don't have nearly the precision to offer hourly forecasts to be of any legitimate use.

So basically if you're eagerly planning for a trip in 10 days or a wedding in a month or two, you're much better off staying far away from such novelty longrange forecasts until the event gets much closer.  Until then, all you can really figure on is what's typical for the given time of year.


What properties must a rocky body possess in order to exhibit plate tectonics?

Plate tectonics appears to require multiple factors all arraigned in feedback loops.

The planet must be large enough that it's surface to volume ratios is low enough to trap enough heat from radioactive decay to power tectonic motion. Convection requires a minimal threshold of energy trapped in the material before that trapped energy causes mechanical motion. Planets smaller than earth radiate internal heat away to quickly because of their larger surface to volume ratios. Thus little convection and little tectonic motion.
The planet must have sufficient mass such that it's escape velocity exceeds that of a hydrogen ion ejected from a water molecule via UV hydrolysis. If the planet does have sufficient mass, then the hydrogen release by UV hydrolysis will be recaptured. If not, the hydrogen will escape the planet and its orbit and the planet will eventually desiccate. Earth has enough mass to retain hydrogen, Mars and Venus do not. In the past, Mars had water but it leaked hydrogen over the eons until it became a desert. Venus likely suffered the same fate.
Oxygen producing life: Even with sufficient mass to trap hydrogen, a planet will still leak free hydrogen from having the hydrogen rise to the top of the atmosphere and there being knocked off by the solar wind. Free oxygen prevents this by a) forming ozone thus blocking the UV that breaks down water molecules and b) recombining with the free hydrogen that does form to produce water again.
The presence of large amounts of water produce hydrated minerals which, on the size and time scales of tectonic motion, behave more like a deformable putty than solid rock. These deformable minerals allow tectonic motion. Without them, tectonic forces would cause shattering instead of drift. (See: Plate Tectonics and Water, and, Role of water in the tectonics of Earth and Venus.)
Tectonic subduction recycles carbon trapped in carbonates by chemical weathering and organisms in the ocean. Subduction draws the carbonates down to the lower crust where they are "cooked" and the carbon converted to $\mathrm{CO}_2$ and $\mathrm{CH}_3$ which are returned to the biosphere via vulcanism. Without this recycling, all the carbon in the biosphere would end up as limestone on the ocean floor. Starved of carbon, all life would perish.
It appears that the Earth has a much thinner and much more heterogeneous crust than either Mars or Venus. Likely, this is a result of the collision that produced the moon. The thinner crust is easier for geothermal convection to move. Also, it's possible that the collision "stirred" the distribution of heat producing radioisotopes leaving more near to the top of the mantel.  On Venus and Mars, it is likely that the very heavy radio isotopes sank to the core. This would make the upper mantel on Earth hotter than the other planet and hotter than it would have been without the collision. That would drive convection faster.

Likely, the critical difference for Earth was the collision that formed the moon. That both "stirred the pot" and added more mass. Earth retains both heat and hydrogen. Retaining hydrogen means retaining water which means life and hydrated minerals. Life produces oxygen that protects the water. Hydrated minerals provide the elasticity needed for tectonic motion. Tectonic motion recycles carbon needed for life.

Take away anyone of these factors and a planets tectonic motion will eventually wind down in less than a billion years.


Sea breeze - magnitude of horizontal pressure gradient?

In his book, Simpson (Simpson, J. E. (1994). Sea breeze and local winds. Cambridge University Press) shows a figure that includes the pressure difference between Jersey in the Channel Islands and Paris. It gives an idea of the magnitude of the pressure difference. As was mentioned in the comments, sea breeze tends to be perceived as a density current on constant pressure surfaces.


Is there any simple way of using the Coriolis effect to determine what hemisphere you are in?

You can use the Foucault pendulum to determine the hemisphere: Its plane of movement rotates:

anti-clockwise in the southern hemisphere;
clockwise in the northern hemisphere.

The rotation of the plane can be explained by the Coriolis force.


Solar irradiation is a measure of the energy delivered by the sun per unit area, watts or joules per square metre for example.. It is often recorded over a specific time period, so it is very much to do with solar radiation, but not exactly the same thing.


Are there minerals which are not been found on earth but which are still possible to exist?

To answer the first part, there are many minerals on earth which do not involve silicate bonded structures. For instance, non-silicates (minerals of carbonates, sulfides, sulfates, phosphates, and oxides are common non-silicate varieties). For a detailed list of mineral species, you should check out the Dana Classification here: Minerals Arranged by the New Dana Classification.

There are indeed Fe minerals which have no occurrence on Earth, outside originating from meteorite impacts. These minerals are various lattice polymorphs of Fe wit Ni. Kamacite and Taenite are examples of minerals which are found exclusively in meteorites, often distinguished by a Widmanstätten pattern.

The question as to how many possible mineral-producing elemental combinations are possible outside the bounds of our own planet, is outside my personal knowledge in a numerical sense, but the current known naturally occurring mineral species recognized by the IMA numbers around 5,141 valid species: The official IMA-CNMNC List of Mineral Names.

I may be outside the bounds of certain knowledge here, but restrictions on extraterrestrial mineral formation are likely akin to those on Earth: temperature, pressure, time, fluid composition (be it magma, or some aqueous solution), gravity, and atmospheric composition, just to name a few. Some minerals may be unable to exist on our planet because the formational/stability conditions of Earth do not offer much permanence. These prohibiting conditions could well be absent on certain other planets/stellar bodies.


Could a "sunbrella" parked at L1 block enough solar energy to counter global warming?

There are several journal articles on this topic, for example Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.

Being truly at the L1 point is unsuitable because the radiation pressure of the photons acting on the shade (like solar sail) would disrupt the equilibrium, so the equilibrium point is shifted toward the sun from the L1 point and depends on the degree to which the shade reflects versus absorbs.

The shade should be made of black material to minimize the effect of radiation pressure on the equilibrium point, thereby permitting it to be as close as possible to the L1 point, and closer to the Earth, where it can more effectively shade.

The size required is roughly a 1,500 kilometer diameter structure.

All parts of the Earth would be shaded to some degree. From Earth, the sun would appear as it does during a transit of Venus or Mercury, but the position on the sun's disc would vary more with ones location on Earth since the shade would be much closer to Earth than Venus is.


The way hillsides are farmed generally depends on the steepness of the hillside. Gentle slopes can be farmed the same way flat land is farmed.

Steeper slops require the hillside to be divided into terraces. The steeper the slope, the narrower the terraces.

Terracing of hillsides in farming reduces erosion because terraces reduce the flow rate of water down the hill. Furrows running down slope can easily transform into erosion gullies.

Terrace farming has been all over the world and for thousands of years. It is speculated that the Hanging Gardens of Babylon,

  may have been built on an artificial mountain with stepped terraces, such as those on a ziggurat.

Slopes in the Andes of South America were terrace mining before AD 1000.


What would a rock thin section look like without any polarizers?

It would look almost identical to the image obtained using plane-polarised light.

Some minerals would look darker, especially those with strong pleochroism such as biotites and amphiboles, because all light is now transmitted or blocked regardless of orientation.
Minerals with large relief differences such as carbonates (e.g. calcite) would cease to have the differences and would just have high relief.

From a static image it could actually be hard to tell that there is no polariser. A careful and experienced observer might deduce it from small hints, given some prior knowledge on what the rock contains.


What denotes a parameterization in a model? (semantics )

As defined in the AMS glossary, a parameterization is a simplification of one or several processes in a model. I add that a parameterization commonly adds an error and increases the uncertainty in the model results. In most cases, a parameterization is not derived from physical laws but a fit to data.

These simplifications are employed for different reasons. You probably know the following examples and this answer could have been shorter ;-) but I added them for other readers who might not be aware of them.

Parameterization due to spatial constraints

When we model meteorological and atmospheric chemistry processes in a certain domain, we split this domain into individual grid cells of a given size - such as grid cells of 10 km x 10 km size. Some atmospheric processes have a lower spatial extend than the grid cells - such as small scale turbulence and clouds smaller than 10 km. These things cannot be explicitly calculated by the model (except if we reduce the model resolution). Therefore, we approximate these things taking place on a spatial scale below 10 km. These approximations are denoted as parameterizations.

Parameterizations due to computing effort

When we consider processes such as particle formation, growth, and coagulation we could consider every particle or even every molecule in a model. However, in real world atmospheric applications we have too much particles than we could consider them individually. Therefore, we need to calculate the growth of particles on the base of some parameters and apply it on (log-normal) particle number/volume/... distributions.

Parameterizations due to missing and condensed information

Biogenic emissions are a nice example. We do not know exactly where which trees and plants are located (and which atmospheric conditions like humidity and temperature prevail). For some regions we know it: e.g. for the city of Hamburg there is a detailed (non-public) tree inventory existing. When we do not have this information and work in a gridded domain (i.e. 10 km x 10 km) we need to make a simplified assumption - such as 10% of the grid cell ground is covered by urban area, 30% by grassland, 10% by desert and 50% by forest (of which 70% are pine trees and 30% other trees). From this information and the average ground level temperature and humidity we need to estimate the amount of various emitted volatile organic compounds. Doing this, is a parameterizations because we over-simplify the actual real world.

But

From my feeling I would describe a process representation in a model as explicit/non-parameterized when it is included according to the best current/state-of-the-art knowledge. In contrast, when it is considerably simplified, I would denote it as a parameterization.

However, when we presented gas phase chemical processes by differential equations - like as it is done in the gas phase chemistry mechanisms of chemistry transport models -, I would not consider it as parameterizations because due to a large number of identical molecules (and the law of large numbers - probably) we do not actually introduce a large error.


Does the heat of reentry affect the reliability of radiometric dating of meteorites?

Current consensus says heat does not affect the rate of radioactive decay and if it does it is due to time dilation, the effect of whihc is very small. Thus the heating of meteorites as they enter Earth's atmosphere will not affect their radiometric dating.


These are most certainly boundary layer rolls and not gravity waves. While there exists a visual similarity between the two phenomena, and both may exist in similar atmospheric conditions, they can be distinguished by two key characteristics:

Unlike gravity waves, which develop in the downwave direction (perpendicular to the crest), boundary layer rolls develop downwind (parallel to the apparent "crest");
Unlike gravity waves, whose crest propagates with intrinsic phase speed (related to interfacial density difference and gravitational acceleration) and whose energy propagates with intrinsic group velocity, the large-scale structure of boundary layer rolls is quasi-stationary.

Despite the visual resemblence between gravity waves and boundary layer rolls and possible interactions reported in the literature, it is my opinion that stating that boundary layer rolls are a form of gravity waves is incorrect and misleading.

It is clear based on the satellite picture that the wind is northwesterly because of the distance from land that the convection occurs over the ocean, which is approximately 50 km from the coast uniformly in the SW-NE direction. As the cold and dry air moves over (relatively) warm water, air rises and saturates with water vapor, forming clouds downwind from the coast. For these to be gravity waves, wind would have to be perpendicular to the wave crest, i.e.  in the SW-NE direction, which is not the case.

Now that we agree that the wind is northwesterly, we see that the convective lines, the so-called "cloud streets", are aligned with the wind. They are long rolls of counter-rotating air that stretch the depth of the atmospheric boundary layer in height (~1 km) and are of width between 1 and 10 km. Water vapor condensation and cloud formation happens on the upward side of the roll, and evaporation happens on the downward side of the roll. Notice that in this particular example, they start off very thin, and become wider downwind. While these rolls are still not very well understood, the main mechanism for formation is likely to be a combination of rotation and friction (Ekman spirals) in presence of thermally unstable bottom boundary layer, and stable boundary layer cap, thus constraining the circulation into organized cells.

A review paper on boundary layer rolls by Etling and Brown (1993) can be found here.


Isothermal, as you are likely aware means constant temperature. Your problem has the givens:

The 0 - 1 km layer has a constant temperature of 0 C
A surface parcel initially has a temperature of 0.5 C

We can likely assume the parcel is not saturated and you are aware that that a parcel with a positive relative temperature perturbation is buoyant and will rise.

To question you need to look at next is: what happens to a parcel of air as it rises?  Your 0 - 1 km layer has a constant temperature but not a constant pressure so the parcel will expand as it rises.  If the parcel expands then its temperature will decrease.

At what rate does the temperature of an unsaturated parcel of air decrease as it rises?  This number will allow you to calculate the height that the parcels temperature decreases by 0.5 C and neutral buoyancy is attained.


This hypothesis has been studied here as a possible explanation of selenogenesis (formation of the Moon). (Forming the Moon from terrestrial silicate-rich material. R.J. de Meijer, V.F. Anisichkin, W. van Westrenen. 2013.)
The only place cited as suitable for spontaneous criticality is the Core-Mantle Boundary (CMB).

The calculations above show that without additional concentration factors, $\mathrm{U}$, $\mathrm{Th}$ and $\mathrm{Pu}$ concentrations in the CMB are insufficient to reach criticality. Additional concentrations can be achieved by a combination of two processes: growth of the relative concentration of the fissile materials by a transient pressure wave, induced by an impact at the Earth’s surface (Anisichkin, 1997; Voronin and Anisichkin, 2001), and/or the development of compositional heterogeneities (de Meijer and Van Westrenen, 2008).
As shown by Voronin (2011) for fissile material at the CMB, an impact of a 100km- diameter asteroid can create a transient pressure increase of several TPa at the CMB, sufficient to concentrate fissile material from a subcritical to a supercritical condition followed by a nuclear explosion. Regarding the development of compositional heterogeneities, it should be noted that small-scale heterogeneities exist in the core-mantle boundary region even today (e.g., van der Hilst et al., 2007): volumes exhibiting both higher-than-average and lower-than-average wave propagation speeds, with diameters as small as 30 km, are now resolvable. Some studies suggest that the bottom of the mantle is partially molten today, forming a so-called ‘basal magma ocean’ (e.g. Williams and Garnero, 1996; Labrosse et al., 2007; Lee et al., 2010).

For another take on natural nuclear explosions, see this paper (Evidence for a large, natural, paleo-nuclear reactor on Mars. J. E. Brandenburg, Orbital Technologies Corporation. LPI 2011 Proceedings.), citing an anomaly in Mare Acidalium on Mars.
It should be noted that nuclear explosions need both critical mass and very low times of reactivity insertion. A gun-type bomb would be the best analogy for low-yield natural explosions on the surface/in the crust, and it is very unlikely to have a naturally occurring acceleration hurl a uranium-rich boulder against a uranium-rich wall.
To detect natural explosions on the surface, one would need to look for fused silica and anomalous $\mathrm{Xe}$ and $\mathrm{Kr}$ isotope ratios at the margins of our instruments' sensitivities.


"The world will start COOLING DOWN in 2017"?

I gave a longer answer linked to a similar question in the comments above, I'll give a quick one here:

  There's a story going around the low-grade news factories that one Dr.
  David Evans . . .

Everyone knows there's a fair bit of "I know you are but what am I" in the climate change debate (if you can even call it a debate), but whichever side you agree with, David Evans is without question, actively arguing the skeptic side.  His position has been consistently in disagreement with man made climate change for nearly a decade, so anything of his you read, keep that in mind.

He's made two climate "denier lists" here and here and he has been called out by skeptical science, here.    In another article related to yours, here, it says his work is "undergoing peer review", so for now, his calculations aren't publicly available or verified.

  . . . has predicted that the world will start cooling down in 2017

One problem here.  We're currently in an El Nino and 2014 was the warmest year on record (38% probability to some, but lets not go there) with 2015 likely to break that record and 2016 - too soon to say but the El Nino is expected to extend into 2016, so 2017 is an ideal year to predict cooling.  The global temperature often drops within a year after an El Nino ends, but this is a normal cycle and temporary and it has nothing to do with man made climate change.

  What would be the best way to show that he is wrong?

Well, a personal favorite, I'd go with something like:

"He's just using a mathematical model to predict the future.  I thought you people hated mathematical models to predict the future. -

You could also bring up this list of examples where David Evans has been wrong in the recent past.

But the more scientific answer to your question is that until his research is available and peer reviewed, then there's no way to disprove it, but there's also, no good reason to agree with it.   Without peer review and transparency, it's not science.   It's just a blog.


Why doesn't the Earth's outer core dissolve into the mantle?

From the comments:

And indeed, after browsing trough a few sections they seem to assume that "Liquid metal separates rapidly from liquid silicate", like oil and water, and they don't mix later. Very interesting. I wonder what's @Gimelist opinion about this.

You are very correct.
The answer is simple: the core and mantle are immiscible. The core doesn't dissolve into the mantle because it's not soluble in the mantle.
This is precisely why we have the core and mantle to begin with.
My answer here is very relevant: https://worldbuilding.stackexchange.com/a/123951/39999

Let's take a hypothetical very simple core and mantle composition:
The core is made of pure iron ($\ce{Fe}$), and the mantle is fayalite ($\ce{Fe2SiO4}$).
What happens when you chemically react the two by $\ce{Fe + Fe2SiO4}$? Absolutely nothing. There is no intermediate $\ce{Fe3SiO4}$. Does not exist. So they just stay as separate iron and fayalite. And because iron is much denser than fayalite, it stays down at the core, whereas the fayalite is the mantle above it.

Edit:
Here's a recent paper describing the overall redox conditions of Earth compared to its neighbours:
https://doi.org/10.1038/s41467-020-15757-0
May be of relevance.


What's the difference between snow cover and fractional snow cover?

Fractional Snow Cover (FSC) is a property of snow cover.  The fractional snow cover property is used in a variety of contexts, most common of which is meteorological models.  Snow cover algorithms applied to visible imagery remote sensing data are used to derive fractional snow cover for each pixel.  This information is typically re-gridded and time-averaged for use by external users.

This GOES site explains:

  Most satellite-based snow cover products provide a "binary" map, whereby each pixel is classified as either "snow" or "not snow". In contrast, the FSC algorithm is an optimized spectral mixture analysis that uses the broad spectrum from ABI to determine the fractional cover of snow, vegetation, and soils.

More information about snow cover products from GOES and MODIS can be seen here:

http://www.goes-r.gov/products/baseline-snow-cover.html

https://modis.gsfc.nasa.gov/data/dataprod/mod10.php


Can anyone explain the reason why CO$_2$ increases global temperatures (not the simplistic greenhouse analogy provided for public consumption)?

Borrowing an explanation from one of my other answers, the basic mechanism of the greenhouse effect is roughly as follows (note this is also a simplified model)

  The Earth is in (to all intents and purposes) a vacuum, so it can only
  gain or lose heat via radiation. The sun emits most of its radiation
  at visible and UV wavelengths. The Earth's atmosphere is fairly
  transparent at these wavelengths and so the Sun's radiation mostly
  passes through it and hits the surface. Some of this radiation
  (determined by the Earth's albedo) is reflected from the surface back
  out into space, but the rest is absorbed by the surface, which causes
  the surface to be warm. The surface loses heat by radiating in
  infra-red wavelengths. Greenhouse gases absorb some of the IR
  radiation, which causes the atmosphere to warm up (the GHG molecules
  transfer some of this heat to non-greenhouse gasses by collisions, but
  heat is also transferred upwards by convection). The warm atmosphere
  re-radiates some of this energy both upwards into space and downwards
  back to the surface. The part that is radiated downwards is also known
  as "back-radiation" (and is directly observable). Now the important
  factor is not the amount of outbound IR radiated from the surface that
  is absorbed, but the altitude at which there are not enough greenhouse
  gases above to absorb the IR radiated upwards from that layer, so that
  it can escape out into space. The lapse rate means that the
  temperature of the atmosphere decreases with increasing height. This
  means that the more CO2 we put into the atmosphere, the higher this
  emitting layer becomes, and the colder it is. As the amount of IR
  radiated depends on the temperature of this layer, if this height
  increases then the amount of IR radiated from the planet falls,
  leading to an energy imbalance, with the planet absorbing more of the
  sun's radiation than it emits as IR, and so the planet warms up. This
  continues until the radiating layer warms up enough for the outbound
  IR to be in balance with the incoming radiation from the sun. So the
  more CO2, the warmer the mean surface temperature, all things being
  otherwise equal.

Thus it is irrelevant that most IR emitted by the surface is absorbed by the atmosphere, it is the height from which IR is not absorbed that matters.  If it is colder than the surface, it will emit less IR than the surface is emitting and hence less energy is radiated into space.

For a more detailed explanation of why absorption at the surface is of little relevance, see this RealClimate article by Spencer Weart.

Just to add a historical note, this explanation goes back at least as far as Ekholm's paper of 1901 "On The Variations Of The Climate Of The Geological And Historical Past And Their Causes":

  The atmosphere plays a very important part of a double character as to the
  temperature at the earth’s surface, of which the one was
  first pointed out by Fourier, the other by Tyndall. Firstly, the
  atmosphere may act like the glass of a green-house, letting through
  the light rays of the sun relatively easily, and absorbing a great
  part of the dark rays emitted from the ground, and it thereby may
  raise the mean temperature of the earth’s surface. Secondly, the
  atmosphere acts as a heat store placed between the relatively warm
  ground and the cold space, and thereby lessens in a high degree the
  annual, diurnal, and local variations of the temperature.

  There are two qualities of the atmosphere that produce these effects. The
  one is that the temperature of the atmosphere generally
  decreases with the height above the ground or the sea-level, owing
  partly to the dynamical heating of descending air currents and the
  dynamical cooling of ascending ones, as is explained in the mechanical
  theory of heat. The other is that the atmosphere, absorbing but little
  of the insolation and the most of the radiation from the ground,
  receives a considerable part of its heat store from the ground by
  means of radiation, contact, convection, and conduction, whereas the
  earth’s surface is heated principally by direct radiation from the sun
  through the transparent air.

  It follows from this that the radiation from the earth into space does
  not go on directly from the ground, but on the average from a
  layer of the atmosphere having a considerable height above sea-level.
  The height of that layer depends on the thermal quality of the
  atmosphere, and will vary with that quality. The greater is the
  absorbing power of the air for heat rays emitted from the ground, the
  higher will that layer be, But the higher the layer, the lower is its
  temperature relatively to that of the ground ; and as the radiation
  from the layer into space is the less the lower its temperature is, it
  follows that the ground will be hotter the higher the radiating layer
  is.”

 [Ekholm, 1901, p19-20]

(h/t Steve Easterbrook's blog article)


How to get single value of NDVI value from four different directions?

After given some information about the data source I have a simple answer. Since the underscores SW etc. represent the four pixels around the city center and all the pixels cover the same physical area, taking a mean of the values will represent the average NDVI of the total area.

It is all about what you will do with the NDVI data. E.g. if something interesting occurs when somewhere near the center vegetation amounts are low (high), then the minimum (maximum) of these might provide you with more useful predictor.