What does "rapid" mean in terms of igneous rock formation?

Obsidian is volcanic glass of felsic composition (i.e. SiO2-rich) whereas basalt is a volcanic rock which may or may not be (partially) glassy of mafic composition (i.e. SiO2-poor). So when you're saying

  obsidian as opposed to basalt

...you're comparing apples and oranges. So instead of discussing obsidian versus basalt, let's discuss phaneritic versus aphanitic versus glassy rocks, in the context of being melted by dragons (because that's what you're asking in your question).

Phaneritic rocks are those with coarse crystals, easily observable to the naked eye. The best example is granite, like the stuff you see in pavements and kitchen tops. These rocks form by slow underground cooling so this is not something that dragons can make.
Aphanitic rocks are those with very fine crystals that are only visible with a microscope. Basalt is the most obvious example. To the naked eye they may look like glassy, but they do not have the characteristic conchoidal fractures you see in obsidian.
Glassy rocks (that I'm pretty sure have a fancy name that starts with hyalo, I just can't remember what it is) have no crystals in them so they're basically glass. Obsidian is the best example.

Note that there could be combinations of those, just to confuse you even more: for example you can have aphanitic rocks with large crystals of minerals (known as porphyritic textures) or a rock that's mostly glass but has some crystals floating around in it.

When you have dragons melting rocks, the cooling of the rock is done very rapidly in air. This can be minutes to hours, depending on the size of the block being melted. This is definitely rapid enough to form rocks. But, the final form of the rock also depends on the chemical composition. Felsic rocks have very high viscosities and low diffusion rates, and even relatively slow cooling (days?) can form obsidian. That's actually the reason that obsidian is most common in felsic rocks. Mafic rocks, on the other hand, require very rapid cooling to form glass (for example, erupting into water), and even then they make have some "quench" crystals of olivine or pyroxene.

Felsic rocks also have lower melting points than mafic rocks. This all leads to the conclusion:

Yes, dragons can make obsidian, and it's quite easy

Take a granite (or even sand-bearing mud), melt it with some dragon fire, and let it just cool. The high SiO2 content will make the melting point rather low (let's say below 1000 °C). The high viscosity will ensure that it stays where it is rather than flow somewhere else (think of basalt flows of Hawaii versus Mt St Helens felsic lava domes). Obsidian will surely form.


How does multiple layer seismic reflection work? How do we distinguish arrivals from different layers and their velocities?

It is impossible to to convert one recorded time-series into structural information. As you correctly note, the equation
$$ v_i = \frac{z_i}{t_i}, \tag{1a}$$
or
$$ t_i(z,v) = \frac{z_i}{v_i}, \tag{1b}$$
is difficult to solve when you only a know one time $t_i$. That is, choosing $z_i$ to twice its value would provide twice $v_i$! If you only record time $t$, but try to turn it into two values $(z_i,v_i)$, you have an underdetermined problem.

However, if you have multiple traces, you know from the theory that a flat reflector produces a hyperbolic move-out (I believe it's the following equation, but I'm not 100% certain. Don't quote me on it!):
$$ t_i(x,z,v) = t_0 + \frac{x^2}{v_\text{stacking}}. \tag{3}$$
As you know the location $x$, knowledge of two (rather than one) traces would perfectly constrain $t_0$ and $v_\text{stacking}$! Just like the slides you provide in the link, the velocity $v_\text{stacking}$ is usually simply found by trying many values for the move-out correction velocity, and seeing which velocity value flattens the reflector best! From that knowledge, suddenly you can constrain also the depth, etc.

Reflection seismics deals with the situation that is described in the 5 slides preceding the slide you post. We have a lot of traces, and based on the assumption of hyperbolic moveouts we can perfectly obtain the stacking velocities. The slide you post approaches the problem from the other way around: what are the stacking velocities $v_\text{rms}$ you would find if you know the depth and velocity structure already? This is not necessarily the method used to get structural information from your data! I think that is the cause of the confusion..!


If you see more than one mineral you frequently can call it rock, but not always. You could have a gem incrusted into another mineral or rock.
You need to know each rock uses to have one or more mineral -by definition-, but there are monomineral rocks as limestones, wich can be only composed by calcite.
If you give me a limestone I could say I have a rock, and I see also calcite, normaly with a magnifying glass.
When we are searching for minerals or thinking on minerals, we use to search for well formed species. If you see a big cristal, you can affirm it is a mineral. Sometimes they are twinned. If you see an aggregate of little minerals, most times you have a rock independently if it has one or more mineral types but not all times again.
What characterizes a rock at surface uses to be diagenesis -compaction of minerals- if the rock is sedimentary. Igneous and metamorphic rocks are also well formed mineral aggregates, consistent bodies.
Sedimentary rocks have a lot of minerals/mineraloids cemented by a kind of microcrystaline matrix -that are also minerals crystallographically talking!-.
Igneous and metamorphic rocks are compact bodies were there is a texture, minerals have textural relation (some kind of order).
If you are at an ore, you could be confused again if you don't know basis concepts. You then could think the aggregates of minerals are rocks, wich is not the case. Then you have an aggregate of well formed minerals, wich is not the same as a rock.
There are several definitions of rock and mineral. I took this ones:

Rock:"mineral matter of variable composition, consolidated or
unconsolidated, assembled in masses or considerable quantities in
nature, as by the action of heat or water."
Mineral:"any of a class of substances occurring in nature, usually
comprising inorganic substances, as quartz or feldspar, of definite
chemical composition and usually of definite crystal structure, but
sometimes also including rocks formed by these substances as well as
certain natural products of organic origin, as asphalt or coal."
source: http://www.dictionary.com


How much heat was released from the 2019-2020 Australian bush fires?

Right. We can make some estimates of the scale of the problem, but they will come with a healthy margin of error.

If we assume that wood has a calorific value of 18.5 GJ/t (from the phyllis2 database)
The area burned is 18.6 Mha (from Wikipedia here)
The standing volume of material is circa 1500 m3/ha (an educated guess based on Eucalyptus values in Forest Yield)
The density of timber is circa 0.5t per dry m3 (from Forest mensuration handbook)
and only 90% of that material actually burns (a guess)

Then:

There's around 675 tonnes of material burned per ha releasing 12,150 GJ of energy which is equal to 225,990,000 TJ for the total area or 3,587,143 Hiroshima bombs (at 63 TJ each)...

This is a (very) rough calculation, but it gives a scale of the amount of heat released. This is about 10 day's worth of solar constant radiation over the same area, so it might appear in local temperature readings, but bear in mind that 1) there was already unusually high temperatures in the area, and 2) fires like this produce a lot of smoke which will have had an effect on the local radiation budget.

In terms of all that CO2, you can expect it to be reabsorbed by the surrounding biosphere which is described in the impulse response function described in the IPCC AR5 WG1 CH8 technical supplement (8.SM.11.1 Equations for the Global Warming Potential). You can also expect the burned areas to regrow - which will absorb CO2 as well. Depending on rates of growth, I would expect this to take several decades. - but there is a lot of very complex processes, so this is open to a lot of discussion!

Hope this helps.


Identification of Iguanodon and Maiasaura

The easiest way to distinguish iguanodon from maiasaura is to look for iguanodon's hands, which are very peculiar indeed. The hand has five digits. The thumb has a large, prominent spike on it for defensive purposes. The three middle fingers are fused and end in hoof-like nails for walking on all fours. The fifth digit corresponding to our little finger sticks out at an angle from the others and is flexible. It is believed that this enabled it to gather food. It is apparent from these strange forefeet or hands that iguanodon, a herbivore, often stood upright like a biped.


What is the significance of amphidromic points related to tides?

This will be a bare-bones answer, because I don't have time to do more. If somebody wants to do a more complete answer, with a figure or two, feel free; otherwise I'll try to come back and expand this in a day or two

Good question! If one is familiar with the simple explanations of tides (bulges of water following the moon around the earth), this doesn't make sense.
However, that way of thinking only gives us equilibrium tides, which are what we would have if Earth was an ocean planet. In reality, we have continents, and they get in the way.

Most tidal movement actually consists of water "sloshing" around ocean basins - e.g. across the Atlantic between North America and Europe. But because the planet is spinning, Coriolis force applies and tends to impart rotation to straight-line movements. This results in the tide tending to form two-dimensional waves that go around ocean basins in a roughly circular pattern. You can get a similar wave going in a hot-tub, with a bit of effort! At the outside of the basin, where the wave meets the land, the amplitude tends to be the greatest - but in the middle, it's close to zero.


The forecast hour of the product is the hour after the model cycle runtime that the forecast is valid at. For example, if the the cycle runtime is 12Z and the forecast hour is 9, then the the forecast is valid for 21Z. If the cycle runtime is 6Z and the forecast hour is 48, then the forecast is valid at 6Z two days later.


"Atmospheric modeling, data_assimilation and predictability" by Euginia Kalnay, is an introductory book, which is good to get an overall overview of the subject.

If you are more interested in the numerics I would recommend "Numerical Methods for Fluid Dynamics" by Dale R. Durran.


You would have to cut somewhere along this circle:

The only landmass here is New Zealand, eastern Australia, eastern PNG, western North America and some Pacific islands. I'm pretty sure you can tweak it a bit, but that's the basic idea.
Notice that this actually shows less than a half because of the relatively low altitude. If you "zoom out" infinitely you'll get some more Australia and more America in this, but it's still going to be mostly ocean.


What evidence is there for geological mechanisms that formed the Siberian traps flood basalt?

This answer will focus on recent research evidence found within the Siberian Traps deposits.  For the purposes of this answer, the theory that a possible Wilkes Land impact resulted in the Siberian traps as an antipode volcanic response will not be included (please see the question and answer to Can impact events cause widespread volcanic activity on the other side of the planet? for details of current modelling doubts of this mechanism).

Many researchers cite that the initial cause of the Siberian Traps was a mantle plume, some refer to it as a 'superplume' that inpinged into the upper mantle, as shown in the diagram below:

Image source: The Permian Period, Palaeos.

However, according to Sobolev et al. (2011), observations and measurements of the region affected by the Siberian Traps exhibit no evidence of pre-magmatic uplift nor lithospheric stretching that can be associated with mantle plume activity (e.g. the Afar Region in Ethiopia), their models suggest that there was extensive plume erosion of the cratonic crust over a considerable length of time.

Petrological evidence by Sobolev et al. (2011) suggest that some recycled oceanic crust existed at the head of the plume. This contamination was noted in $\delta^{34}\ce{S}$ analysis of melt inclusions by Bryan and Ferrari, (2013) and Black et al. (2014), who determined that the mantle melt source was close to that found in mid-ocean ridge basalts.

Black et al. (2014) also note that a significant contributor to $\delta^{34}\ce{S}$ (up to 25%) was derived from evaporitic sources. This related to the observations made by Jerram et al. (2013) of the contact metamosphism around the doleritic dykes and sills, indicating that the basaltic magma was injected into an organic and salt rich sedimentary basin.  This interaction between the organics an salt and molten rock would have released halocarbons, $\ce{CO2}$ etc that are attributed to the mass extinction at the time (Jerram et al. 2013; Self et al. 2014).

This, and the prevalence of tuff leads to Jerram et al. (2013) questioning whether the Siberian Traps were the result of widespread explosive volcanic activity, related.  The dyke and sill intrusions are believed to have caused episodic explosive eruptive sequences, according to Self et al. (2014).  Some of these eruptions were phreatomagmatic depositing mafic volcaniclasts according to Bryan and Ferrari, (2013).

As, the crust eroded due to the plume (Sobolev et al. 2011), the eruptive sequences transitioned to basaltic lava flows, these are believed to have also been episodic, according to Self et al. (2014) with pulses of magma production and lava eruptions.

The map below shows the distribution of sill intrusions, pyroclasts and lava of the Siberian Traps.

Image source: IAVCEI - the red are sill intrusions, the light purple are pyroclasts and the dark purple is lava.

References

Black et al. 2014, Sulfur isotopic evidence for sources of volatiles in Siberian Traps magmas, Earth and Planetary Science Letters

Bryan and Ferrari, 2013, Large igneous provinces and silicic large
igneous provinces: Progress in our understanding
over the last 25 years, Geological Society of America Bulletin

Jerram et al. 2013, What happened at the start of the Siberian Traps? Understanding the onset of flood volcanism, American Geophysical Union, Fall Meeting 2013

Self et al. 2014, Emplacement characteristics, time scales, and volcanic gas
release rates of continental fl ood basalt eruptions on Earth, The Geological Society of America
Special Paper 505

Sobolev et al. 2011, Linking mantle plumes, large igneous provinces and environmental catastrophes, Nature


Are the "polar vortex" and "cut-off lows" over/near the Great Lakes new phenomena?

The polar vortex
The AMS glossary defines the polar vortex as:

A planetary-scale mid- to high-latitude circumpolar cyclonic circulation, extending from the middle troposphere to the stratosphere. The Northern Hemisphere vortex often features two centers—one near Baffin Island and the other over northeast Siberia—with analogous circumpolar asymmetry atypical in the Southern Hemisphere. The westerly airflow is largely a manifestation of the thermal wind above the polar frontal zone of middle and subpolar latitudes. The vortex is strongest during the winter in the upper troposphere and stratosphere when the pole-to-equator temperature gradient is strongest. The stratosphere component of the circulation may be referred to separately as the “polar stratospheric vortex.” In summer, the strongest westerly circulation is largely confined to the troposphere, and the polar stratospheric vortex reverses in the upper stratosphere because of solar heating during the polar day.

This first descriptions of the polar vortex date back to the 1940s.  You'll also note that the description above describes an upper tropospheric and stratospheric circulation e.g. this is is something happening well above the surface of the earth.
The recent popular use of polar vortex to describe any particularly cold air mass can probably be traced back to someone (either a meteorologist of psuedo-meteorologist) on twitter making reference to it and then "going viral".  However the media got a hold of the word, they are quite consistent in misusing it.
The definition above mentions

The westerly airflow is largely a manifestation of the thermal wind above the polar frontal zone of middle and subpolar latitudes

What this means is that the position and strength of polar vortex (the circulation up around the stratosphere) is strongly influenced by the position of strong surface cold fronts coming out of the poles.  The strong cold snaps are not the polar vortex, and the southern push of the high altitude polar vortex is a response of the cold snap, not the other way around.
Cut off lows
Cut off lows are not new either.  A mid-latitude trough can be cut off from the westerly flow and you end up with a cutoff or closed low.  These tend to be persistent, stationary mid and upper level lows that can last for days.  You can see an example of a cut off low in the flow over the US in this video.  Focus over the southern tip of Lake Michigan and you'll see it.  These type of cutoff lows can occur anywhere in the mid-latitudes.


Could dust blown up by a comet impact render the air unbreathable?

That doesnt seem realistic since eventually all the dust from all the volcanic activity, as well as that caused by our doing, eventually makes its way back down to earth. Most dust particles end up being soaked up by earths cloud layer coming down in rain. I have to agree with Gimelist but volcanism can and has produced conditions you mentioned by expelling caustic and poisonous gases and for what I understand nuclear detonations and the radioactive dust they send into the air is far worse in the long run.


where are the thickest limestone layers on earth ? (CaCO3)

Reading your comments I see that you're asking:

  so could we find for example 1km high limestone layers on earth ?

The answer is definitely yes. Here's an example of a stratrigraphic geological section from Israel:

source: Chronostratigraphic table and subsidence curves of southern Israel, Gvirtzman 2004, Israel Journal of Earth Sciences, 53
You can see that in the north of the country there is an almost entirely continuous section of "platformal carbonates" which is just a fancy name for limestones. That's 5 kilometres of limestone. And I'm pretty sure that's not the deepest - that's only the one I personally know.

That's a sedimentary basin where you can drill and still find fossil-bearing limestones deep down. This gets even better if you start adding tectonics to this. Plate movements can do funny stuff to rocks, including burying them really deep. If you take limestones and do that to them, you actually transform them into marble. Basically marble (proper) is limestone buried deep and cooked. And by deep I mean really deep. Some marbles from the Alps are known to come from more than 100 kilometres deep! Note that I'm not saying it's limestone all the way down, but there are chucks of marble (formerly limestone) down there.

If you want to be really extreme, there is an article where the authors say:

  ...carbonate sediments were subducted into the upper mantle...

Upper mantle is 200-300 kilometres deep. And you know what? That's only the ones we know of. Who knows, there might be some limestones that were subducted all the way down to the core-mantle boundary, almost 3000 kilometres deep.


What is this island or reef 600 km east of Marianas Islands?

To better pin down the location, I georeferenced the map getting good match of all land and sea features with a reference map. The figure below shows it overlaid over a reference map with seafloor releif:

And the location of your mystery Island is were the red dot is, plus a 25 km search radius.

And the coordinates are (Lat/Lon): 17.0619° N, 152.177° E.

It nicely coincides with a seamount, so it might be more than an error on the map (but that seamount acoording to the data in Google Earth is more than a kilometer under the surface). What definitely seem to be an error, is including such island as part of the Northern Mariana Islands, because in all the references and maps I saw, that denomination only covers the 15 islands on the chain to the west.

I did a search for something in that location first looking as MODIS images (250 m resolution) on WorldView I had to browse trough months of images to get cloud free images, but I couldn't identify any island

Therefore, if there, it must be tiny.
After looking at the catalogs for higher resolution images, there are no Landsat images there at all (something that suggest there is no land there) but there are two Sentinel-2 scenes (10 m per pixel), and happily the cloud cover is not too bad.
I did a search in those two images within the 25 km radius displayed above.

This is the first image

And this is the second

And again I didn't found anything.
Therefore I'm inclined to think that there is nothing. But I can't rule out that something very small can be hidden by the clouds. However, I doubt it.
If you want to perform the search yourself over a larger search radius, just let me know and I can give you the images.

I also searched the seamount catalog for those coordinates and the only one that show up is Vlinder Guyot about 224 km to the East. So there is no information on the one below your mystery island.

However, in this publication. It is refereed as "I'l Ichev" and is part of the "Magellan Seamounts".

I also looked over the seamount you suggested ("Pegas" in the above map and located at 16.136° N, 151.968° E approximately), that is about 100 km away from the location pointed on the map you posted, but I didn't found any island there either (on a search box 22x26 km):

After browsing many other maps, I've also failed to find other map showing that Island. However, in a relatively similar location some old maps show "Los Jardines" Island. It is a know "phantom" island, some more info on its wikipedia page. Here a 1932 German map showing it:

Despite it is not in the same location, it might be the source of the confusion.

Here a list of good quality maps that DO NOT show that island:

https://www.interkart.de/media/catalog/product/r/e/re01020331_1_1.jpg
https://www.maps.com/media/catalog/product/cache/1/thumbnail/17f82f742ffe127f42dca9de82fb58b1/p/a/pacific_ring_of_fire_wall_map_42x31.jpg
https://www.nationalgeographic-maps.com/media/catalog/product/cache/7/image/8ecabcfb697832bc77ac7e2547ded39f/x/n/xng196910a.jpg
http://www.melbmap.com.au/site/resources/overseas_map_samples/hema_asia_west_pacific_thumbnail_image.jpg
http://universoguia.com/wp-content/uploads/2012/12/mapa_politico_oceania.jpg
http://www.gifex.com/images/0X0/2009-11-11-10993/Mapa-Fsico-de-Oceana.jpg
http://www.xxlmaps.com/maps/1/map3.jpg


How is the concentration of particulate matter calculated per cubic meter

The data that you are having are called emission fluxes. If these data are available as global averages then one can calculate global mean concentration by multiplying the residence time of the species with emission flux.
However, at the city or grid level, it is not straightforward to calculate concentration from emission fluxes. In order to calculate, concentration, one requires information of rate of dispersion in three dimensions as well as species amount brought-in by the wind. The dispersion is generally estimated using atmospheric transport models. See for example Gadhavi et al. (2015) have estimated concentration from emission fluxes for black carbon particles.
Technically speaking, one can calculate concentration by first dividing the region where the concentration is needed in three dimensional grid-boxes and by calculating mass fluxes at each interface of the grid-boxes as well as chemical transformation within box. The chemical transformation for species like PM10 or PM2.5 may not be significant but it can be significant for species like SO2. The mass flux calculations will require knowledge on wind velocities across interfaces, diffusion mixing and turbulent mixing within the box as well as removal processes such as dry deposition and wet deposition.
Here, a confusing issue is the size of grid-boxes. A different size may lead to a different concentration number. Though, there is no hard and fast rule about size of grid-boxes, the decision often depends on resolution of available flux and meteorological data as well as end purpose. Suppose, one is looking for comparing satellite based columnar concentration, he/she may take grid-box height that covers entire atmosphere but if one is planning to compare a surface mass concentration measurement typically obtained by air pollution monitoring stations, vertical height of grid-box should be as small as possible preferably less than boundary layer height.
Most emission flux data or emission inventories are available for the emission near Earth's surface. They should be considered as emission flux across the bottom face of the lowest grid-box. The grid box that one but the lowest grid-box will have emission fluxes from top of the lowest grid-box dictated by meteorology and dispersion physics. And the gain of this grid-box will be losses (or negative flux) of the lowest grid box. Besides, losing mass to above, the lowest grid-boxes will also loose mass through process called dry deposition. If the grid-boxes covers the region with rain, then all the grid-boxes from cloud level to surface will also have wet deposition or wet removal. Same applies to mass fluxes in horizontal direction. The lowest grid-box gains mass from bottom face because of emissions but looses to neighboring boxes by horizontal wind. A balance between mass fluxes across all the faces will be concentration of given grid-box.
A crude estimation of surface concentration can be obtained by making a certain assumptions, like by taking grid-box height equal to mixing layer height and assuming horizontally uniform emission fluxes across large region. Under this assumptions one can calculate concentration by multiplying emission fluxes with characteristic time period say 24 hour and dividing it by volume of grid-box. The scientific rational behind this assumption is that mixing height is the height of the atmosphere were turbulence is very high and the loss process becomes dominant only after this volume is filled. Also, when the emission region is sufficiently large, horizontal movement of mass will cancel out across opposing face of the grid-box.
Reference
Gadhavi, H. S., Renuka, K., Ravi Kiran, V., Jayaraman, A., Stohl, A., Klimont, Z., and Beig, G.: Evaluation of black carbon emission inventories using a Lagrangian dispersion model – a case study over southern India, Atmos. Chem. Phys., 15, 1447–1461, https://doi.org/10.5194/acp-15-1447-2015, 2015.
Chapter 2 Atmospheric Trace Constituents in Atmospheric Chemistry and Physics by Seinfeld and Pandis, 2006.


What is it about ancient craton geology that results in associated kimberlite pipes containing economic diamond deposits?

The Science Daily article How diamond-bearing kimberlites reach the surface of Earth: Acidification provides the thrust (Ludwig-Maximilians-Universitaet Muenchen (LMU)) reports of research completed by an international research team led by Professor Donald Dingwell, Director of the Department of Geo- and Environmental Sciences at LMU.

They state that ancient cratonic crust provides silicate minerals that result in the originally basic magma to become more buoyant and as they are forced through the pipes, it causes the buoyant magma to move fast.  With the authors describing that as the magma ascent increases in velocity, the more silicates it gathers (entrains), increasing the dissolved silicate concentration - until the amount of released $\mathrm{CO}_2$ and $\mathrm{H_2O}$ greatly increasing the velocity of ascent, as the authors state 'like a rocket'.

A more thorough geochemical description is provided in the article Kimberlite ascent by assimilation-fuelled buoyancy (Russell et al. 2012), the proposed model mechanism as the original kimberlite melt to be carbonatite-like - poor in silica content, this magma assimilates materials during its accent through the upper mantle and crust, becoming more silicic, causing the $\mathrm{CO}_2$ solubility to decrease, reducing density and increasing buoyancy, causing the magma to accelerate.

In terms of why cratonic crust is the locale of many diamond rich kimberlite pipes is described from Professor Dingwell as being due to the silica rich cratonic crust is thick enough to provide the magma to make contact with the silicate rich minerals therein.


Why does the Inter tropical Convergence Zone shift?

On a broader scale the ITCZ and monsoons are related. This is because the global circulation shifts as a result of the tilt of the earth's axis relative to the orbit around the sun. In northern hemisphere summer, the northern hemisphere is tilted towards the sun and receives more radiation (energy) than the southern, and vice versa for northern winter, The southern hemisphere is affected in the same way. Without the tilt we would not experience any seasons.

In the tropics the largest amount of energy reaches the region where the sun is at the zenith. In northern summer this region is north of the equation, where as in winter it is at the south. At the spring and fall equinox it coincides with the equator. Hence the region of maximum energy input wanders seasonally to the north and south of the equator.

Climatologically the region with maximum energy input sets up a circulation in the form of so-called Hadley cells where warm air rises where it is heated the most and then transported at elevation to the north and south. At the location of upward air flow formation of convective clouds yielding precipitation becomes the norm. This zone to which ground winds flow towards the region of maximum energy influx is the ITCZ and because the zone of maximum solar energy influx wanders, the ITCZ flows. The zone is fairly wide so the regions around the equator sees the effects of tropical precipitation more or less without seasonality, actually two rain periods and two drier periods as the ITCZ moves once to the north and once to the south over the region each year. Away from the equator the resulting period of precipitation becomes more and more marked as one moves to the north and south resulting in strongly seasonal rains.

This movement of the large scale circulation on the earth produces several associated effects and the different monsoons are such phenomena. There are several monsoons on the earth created by weather phenomena typical for the specific region. The Asian monsoon is perhaps the most known. The specific conditions leading up to this monsoon is found in the high elevation Tibetan plateau. During the northern winter the plateau sees a larger high pressure forming which generates winds flowing south over India and causing a dry climate. During the northern summer large parts are heated generating a low pressure over land which draws in moist air from the sea yielding strong precipitation. Hence the monsoon follows the same seasonality as is seen in the wander of the ITCZ but the cause for the regional change in seasonal wind and precipitation pattern has a different cause.

So to understand the large scale weather systems and their seasonal patterns, you must start by understanding how solar energy drives the atmospheric circulation. This causes a specific and typical pattern which is locally disrupted by the distribution of land and oceans on the earth. Land masses can be heated more and more quickly than oceans on a seasonal basis, land masses also includes topography that can impede the atmospheric circulation, so it it perhaps obvious that land masses contribute on regional and local scales.


Is the urban heat island effect stronger during a particular season or part of the year?

As with so many concepts in geography, I don't think there is a definitive answer -- it would very likely vary from city to city and from year to year. Urban heat island (UHI) effect is affected by so many different variables, such as albedo (reflectivity of surfaces), specific heat of the materials receiving and releasing radiation from the sun, thermal conduction into the ground, cloud cover, wind, and as you mentioned, anthropogenic heat production.

Throughout the year in a city with four distinct seasons, most of these variables change independently of each other (except for probably the specific heat of the materials). For instance, in a hypothetical city that receives a great deal of snow, albedo might be much higher in winter due to the high reflectivity of snow covering low-reflectivity surfaces (such as asphalt, roofs, etc.), which might reduce its contribution to UHI by causing fewer surfaces to absorb radiation from the sun. However, as mentioned in the question, anthropogenic contributions to UHI Effect might be higher in winter in the hypothetical city from latent heat from buildings, water/sewer pipes, vehicles, and so on. Further, wind patterns might shift in winter, bringing in more cool air in winter rather than summer, which would counter the increase from the anthropogenic sources.

Also, impacts from urban heat island are actually generally most pronounced during dusk, which is when much of that short-wave radiation from the sun (which was being stored all day in the sun) is released as long-wave radiation. With that in mind, another factor that could contribute is day-length. Many cities with four distinct seasons are in the mid-latitudes, which have variable day lengths between the seasons. Longer daylight in summer, then, would suggest that the UHI Effect would be worse in summer, as there would be more time for the surfaces to absorb short-wave radiation from the sun.

Great question - sorry for not definitively answering it. It appears there are some gaps and conflicts in the limited research on this topic.

A grad student at UMN suggests that UHI effect is worse in winter (without really explaining why), while TR Oke suggests it is worse in summer, while James Voogt  suggests that UHI effect is generally stronger in summer and winter compared to spring and autumn (in the mid-latitudes).


What data does a skilled meteorologist look at to predict thunderstorms?

For same day forecasting of afternoon thunderstorms, I'd start with the morning observations and the 12Z† model runs (I choose 12Z because that is the morning here in the Americas.  For Europe you might be more interested in the 00Z or 06Z runs to start your day).  In particular I'd start with the output of the 12Z GFS and NAM, and then give that some time to propagate into the RAP and finally the HRRR models which are initialized from each other starting with GFS.

For observational data, I'm interested in the 12Z balloon launch, surface fields (temperature, dew point, winds, pressure), upper air data (850 mb temperature, 500 mb wind and vorticity, 300 mb wind) and satellite imagery (for cloud cover).

At 12Z the morning soundings are going often going to have the remnants of a nocturnal inversion and the previous days boundary layer.  Give cloud cover and surface temperature and moisture advection you can get a rough idea of how that boundary layer will evolve.  An hour or two after 12Z the GFS and NAM will start coming in and you can look at forecast soundings and how the model thinks things will evolve.  Around 15-17Z I'm looking at the HRRR for some additional guidance.

CAPE and wind shear only tell part of the story.

Image credits: Pierre_cb via Wikipedia. Licensed under GFDL 1.2+/CC-ASA 3.0U.

CAPE (convective available potential energy) is a measure of buoyancy and its opposite, CIN (convective inhibition) is a measure of the negative buoyancy a parcel must overcome to reach its level of free convection.  You can have a lot of CAPE, but more than a little CIN can keep any thunderstorms from firing.  If you have no CIN on the other hand but lots of CAPE you'll generally get a mess of storms everywhere but nothing organized.  The bulk 0-6 km wind shear is a good predictor of the type of storms you can anticipate.  Little shear tends toward air-mass thunderstorms while lots of shear tends toward supercell thunderstorms.  In between these two are multi-cell thunderstorms.  The shear will also influence whether multiple storms along a boundary stay discrete or build upscale into a linear feature (e.g. squall lines or QLCS).

What the above things tell you is whether the environment favors convection and what type of convection.  It does not tell you if there will be a storm or not.  You can have a perfect environment for storms, but unless something acts to initiate convection, you won't have a storm.  Storms like to initiate along boundaries (cold fronts, dry lines, gust fronts, etc).  You can also initiate with daytime thermal boundary layer convection eroding CIN until parcels can freely convect.  Upper level divergence can also promote initiation by providing large scale ascent.

Putting this together, I'm looking at observations and model output to identify favorable storm environments.  I'm also looking at them for features that promote initiation.  As we near showtime, I'll also be looking at radar.  On the radar I'm looking for evidence of convergence zones (radar fine lines, fronts, etc) to narrow down where I'd expect storms to fire.

† The Z suffix is shorthand for the historical Zulu time zone, which in modern times we call GMT or Greenwich Mean Time.  All meteorological products are referenced to this time zone and this is done for simplicity.  For example, no matter where you are on Earth, you know balloons are going to go up at 12Z and 00Z, and that the GFS will come out at 00,06,12 and 18Z.  The conversion to local time exactly that as from GMT or UTC.  For example 12Z on the east coast of the USA (in eastern daylight time, EDT, at the time of this writing) is GMT-0400, so 12Z - 4 = 08, or 8 AM EDT (and 7 AM EST the other half of the year).


Why did it take so long to discover the volcanic nature of mid-oceanic ridges?

If it weren't for WW2 and the search for German submarines, the discovery of mid-ocean ridges might have waited until satellite based gravimetric mapping in the 1980s. It was the use of fine magnetometers (if I remember correctly) used to detect submarines that discovered the banding of magnetic stripes on the Atlantic ocean floor, followed by it's mirror image after a certain mid-point in the ocean basin. When superposed with bathymetric maps, it was further discovered that these magnetic stripes had their counterpoint in the same topographic region on the other side of a high point.

The analysis of thousands of these ship transect records (released by the Navy following WW2)  led to the creation of partial ocean floor maps revealed very long parallel strips of rocks containing magnetic reversals reflected in mirror symmetry on the opposite of a mid-ocean rise. Ocean drilling then confirmed that only a spreading volcanic ridge, spewing magma over tens of millions of years could create such features. Following that, precise seismological mapping also confirmed this developing "theory" of plate tectonics, that laid to rest Alfred Wegener's model.

These were heady times for the geologic community in the 60s and early 70s! All thanks to the Navy and WW2!


Where does molecular hydrogen in the atmosphere come from?

Besides man-made sources, hydrogen can be produced naturally through a process called serpentization.  Mafic and ultramafic rocks, which are rich in magnesium and iron silicates, react with water to produce a variety of breakdown products summarized in the Wikipedia article on serpentine

Serpentinization is a geological low-temperature metamorphic process involving heat and water in which low-silica mafic and ultramafic rocks are oxidized (anaerobic oxidation of Fe2+ by the protons of water leading to the formation of H2) and hydrolyzed with water into serpentinite. Peridotite, including dunite, at and near the seafloor and in mountain belts is converted to serpentine, brucite, magnetite, and other minerals — some rare, such as awaruite (Ni3Fe), and even native iron. In the process large amounts of water are absorbed into the rock increasing the volume, reducing the density and destroying the structure.[1]

The density changes from 3.3 to 2.7 g/cm3 with a concurrent volume increase on the order of 30-40%. The reaction is highly exothermic and rock temperatures can be raised by about 260 °C (500 °F),[1] providing an energy source for formation of non-volcanic hydrothermal vents. The magnetite-forming chemical reactions produce hydrogen gas under anaerobic conditions prevailing deep in the mantle, far from the Earth's atmosphere. Carbonates and sulfates are subsequently reduced by hydrogen and form methane and hydrogen sulfide. The hydrogen, methane, and hydrogen sulfide provide energy sources for deep sea chemotroph microorganisms.[1]

Roughly speaking, the magnesium-bearing component of the mafic/ultramafic rock is basic and undergoes acid-base reactions with water, generating no hydrogen (but possibly producing magnesium hydroxide, which indicates said basic conditions).  The iron-bearing components, by contrast, are reducing, especially under the basic conditions associated with the magnesium compounds, and they do generate hydrogen:

Serpentine is the product of the reaction between water and fayalite's ferrous (Fe2+) ions. The process is of interest because it generates hydrogen gas:[2][3]

$3 \text{Fe}_2\text{SiO}_4 + 2 \text{H}_2\text{O} → 2 \text{Fe}_3\text{O}_4 + 3 \text{SiO}_2 + 2 \text{H}_2$

The reaction can be viewed simplistically as follows:[4][5]

$6 \text{Fe(OH)}_2 → 2 \text{Fe}_3\text{O}_4 + 4 \text{H}_2\text{O} + 2 \text{H}_2$.

In addition, in the presence of carbonates and sulfates the reduction process can also produce methane and hydrogen sulfide.  The references cited in this passage explore these processes as sources of raw material and chemically stored energy for undersea life both in Earth and in subterranean ocean worlds elsewhere in the Solar System.
Cited references:
1.
"Serpentinization: The Heat Engine at Lost City and Sponge of the Oceanic Crust".  Link
2.
"Methane and hydrogen formation from rocks – Energy sources for life". Retrieved 6 November 2011.  Link
3.
Sleep, N.H.; A. Meibom, Th. Fridriksson, R.G. Coleman, D.K. Bird (2004). "H2-rich fluids from serpentinization: Geochemical and biotic implications". Proceedings of the National Academy of Sciences of the United States of America. 101 (35): 12818–12823. Bibcode:2004PNAS..10112818S. doi:10.1073/pnas.0405289101. PMC 516479. PMID 15326313.
4.
Russell, M. J.; Hall, A. J.; Martin, W. (2010). "Serpentinization as a source of energy at the origin of life". Geobiology. 8 (5): 355–371. doi:10.1111/j.1472-4669.2010.00249.x. PMID 20572872.
5.
Schrenk, M. O.; Brazelton, W. J.; Lang, S. Q. (2013). "Serpentinization, Carbon, and Deep Life". Reviews in Mineralogy and Geochemistry. 75 (1): 575–606. Bibcode:2013RvMG...75..575S. doi:10.2138/rmg.2013.75.18.


Why is the bedrock buried so deeply in much of northern Minnesota?

As njuffa mentioned I don't believe you are looking at soil 100s of meters deep you are looking at unconsolidated sediments 100s of meters deep.

Depending on the geological process it is possible to deposit 100s of meters of sediments in a very short time.  The conditions for deposition of large amounts of sediments are frequently found during the period of time that the glaciers are melting.  During this time the sides of the glacier end up forming the glacial fluvial terraces and the toe of the glacier often breaks into pieces of ice that the sediment can build around.

This site from the Minnesota State University describes the majority of the lakes in Minnesota as Kettle Lakes, which suggests that the tail end of the ice age was a time of significant sediment deposition.  The North Eastern area would have likely be covered by ice while the South Western portions would have been experiencing the deposition of materials from the rapidly melting glaciers.  There is a whole wikipedia site devoted to the glaciation of Minnesota that describes the events relatively well.


Does the existence of limestone nodules in a clay soil horizon indicate a limestone bedrock?

There are three possible sources for the reported limestone nodules from the clay horizon from colluvium and alluvium. First, as noted before, they could be either detrital gravel of limestone either eroded from limestone bedrock. Given that the bedrock source from which this gravel was eroded and transported from could be either local or regional, such gravels tells a person nothing about the composition of the bedrock at your site. Second, the "limestone nodules" might also be limestone gravel that was either brought in either as construction material or eroded and redeposited from larger limestone blocks at some ancient ruin. Again, such gravel could come from any source within either the local area or region. This means that the presence of such material tells a person nothing about of what the local bedrock consists.

Finally, it is interesting that the "limestone nodules" occur in a clay layer. Normally, gravel-size pieces of limestone are not deposited together with clay. This and the clay layer being part of a soil suggest that the limestone nodules" are caliche nodules / concretions that precipitated and formed in place within the soil as part of a Petrocalcic “K” horizon of a soil developed in clayey colluvium and alluvium. Since caliche (calcrete) forms in Quaternary colluvium and alluvium independently of the type of local bedrock, the presence of caliche tells a person nothing about the local bedrock might be. The Soil Map of Tunisia at https://library.wur.nl/isric/kaart/origineel/afr_tnped.jpg might tell a person whether such soils are present within the area. The presence of "limestone nodules" does not indicate what the local bedrock might be composed of as there are multiple possible origins for them that are independent of the underlying bedrock.

A possibly useful map is:

Ben Haj Ali, M., Jedoui, Y., Dali, T., Ben Salem, H. & Memmi, L. (1985): Carte géologique de la Tunisie, echelle 1:500,000.– Office Topographie Cartographie; Tunis

Petrocalcic Horizon - https://en.wikipedia.org/wiki/Petrocalcic_Horizon

caliche / calcrete - https://en.wikipedia.org/wiki/Caliche


tl;dr

  Has our understanding of the East African Rift significantly changed recently?

No.

We already know that it is splitting

The headlines suggest that the fact there is splitting (i.e. a rift) is a "maybe": "East Africa could be splitting in two", "Africa could eventually split into two continents".

We already know that it is splitting. There is plenty of evidence for that happening from a variety of fields in geoscience. GPS measurements, geodesy and kinematics tell us how fast it is splitting. The type of magma erupted in volcanoes located in the rift is consistent with what you would expect in a rift (alkaline volcanism and carbonatites). We know that there's a mantle plume below the rift, which is one of the causes of the rifting. We can even see it with deep earth geophysics.

The Kenya crack is not because of said splitting

  apparently because some large fissures opened up.

The crack in Kenya is not the result of this rifting. The link provided by JeopardyTempest in the comments is an excellent summary of what it is: erosion caused by heavy rains.

I will note though that some people suggested the crack to follow a pre-existing fault line, so splitting and earthquakes in the past may have formed a "weak spot" for the erosion to occur, but the erosion itself did was not triggered by any seismic or tectonic activity.


What are the differences between an LES-SGS model and a RANS based turbulence model?

The biggest difference between LES and RANS is that, contrary to LES, RANS assumes that $\overline{u'_i} = 0$ (see the Reynolds-averaged Navier–Stokes equations). In LES the filter is spatially based and acts to reduce the amplitude of the scales of motion, whereas in RANS the time filter removes ALL scales of motion with timescales less than the filter width.

I would recommend reading Fröhlich, Jochen, and Dominic von Terzi. "Hybrid LES/RANS methods for the simulation of turbulent flows." Progress in Aerospace Sciences 44.5 (2008): 349-377.

From that paper, specifically the section 'Structural similarity of LES and RANS equations', you can see that the equations being solved are essentially the same for LES and RANS, however, the physics are different. The main difference being that in RANS the unclosed term is a function of the turbulent kinetic energy and the turbulent dissipation rate whereas in LES the closure term is dependent on the length scale of the numerical grid. So in RANS the results are independent of the grid resolution!

  A model qualifies as an LES model if it explicitly involves in one or
  the other way the step size of the computational grid. RANS models, in
  contrast, only depend on physical quantities, including geometric
  features like the wall distance.

As far as typical processes, this figure summarizes it pretty well. DNS resolves all scales of motion, all the way down to the Kolmogorov scale. LES is next up and resolves most of the scales, with the smallest eddies being modeled. RANS is on the other end of the spectrum from DNS, where only the large-scale eddies are resolved and the remaining scales are modeled.

The figure above is from André Bakker's lectures: http://www.bakker.org/dartmouth06/engs150/10-rans.pdf

DNS: Very small scale flow (ex:turbulent boundary layers). Currently computationally intractable for most problems.

LES: Aims to solve the computational cost that DNS poses and reveals the eddies hidden behind the mean in RANS. Good for coastal scale scale 2D simulations and possibly lab-scale 3D simulations with a highly optimized parallel code.

RANS: It is the least computationally expensive method that is used for turbulent modeling, but it is really not very good when certain phenomena cannot be averaged, such as instabilities. Acoustic waves are also incorrectly modeled because they are inherently unsteady processes which can't be averaged, so typically modelers will crank up the turbulent and numerical viscosity to remove acoustic waves from the system.

This shows the main difference between LES and RANS.


Less pollution: moving hurricane debris to other regions for use, or burning?

As the question was changed, my answer attempts to evaluate only the difference between burning and transporting. Please correct my values if my quickly found sources are inaccurate or you find more representing. I know there is quite a few unwritten assumptions that simplify this problem.

On average transporting via trucks emit 161.8 $\frac{CO_{2}}{short-ton-mile}$ (according to this Environmental defense fund handbook). Short ton equals to 2 000 lbs.
The amount of $CO_{2}$ equivalent from burning wood is $1900 + 200 + 70 = 2170 \frac{CO_{2} eqiuv.}{kg}$ from carbon dioxide, nitrous oxide and methane respectively (according to this article, the link to the source of these numbers fails so please comment if these numbers aren't correct).

Now we can write an equation out of this and solve for the kilometer distance that produces equal amount of carbon dioxide equivalent.$$\frac{2170\frac{CO_{2}eq.}{kg}}{161.8\frac{CO_2}{short-ton-mile} \cdot 0.0011\frac{short-ton}{kg} \cdot 0.6213\frac{mile}{km}} \approx 20000 km$$
This is quite a large number in my opinion. I would've expected less. So quite a long distance is needed until transporting produces more $CO_2$ pollution than burning.


Has Earth's climate ever changed? Sure.

[1]

There are many feedbacks within the climate system, some negative as you mention but some also positive. A well-known positive feedback is the greenhouse gas effect, which in the present age is caused by anthropogenic fossil fuel emissions. Increasing greenhouse gases (GHG) causes the atmosphere to trap more longwave radiation and increase the temperature. Negative feedbacks can occur in the climate, such as the "Planck" feedback which describes the T$^4$ dependence of radiation emission--so as the planet warms it emits an even larger amount of radiation.

Climate models already take into account many of these feedbacks, but one of the largest unknowns is the effects of clouds and aerosols on the climate. The distribution of phase of clouds may change as the climate changes, which could possibly counteract the warming (as made popular in the hotly-contested Iris hypothesis [2]) or further enhance the warming.

A forcing related to clouds that further complicates their feedback is the aerosols that they form on. Let's say the climate warms a lot and the planet goes into a major drought. That will cause more deserts which will increase the amount of dust in the air. That dust (for a given amount of water) could potentially suppress precipitation in the clouds, thereby extending their lifetime and increasing the amount of sunlight reflected. Without fully knowing the distribution and effects of aerosols (and their respective impacts on clouds), an accurate estimate of cloud feedbacks is difficult.

A runaway effect on Earth could technically be possible. You talk about feedbacks as a mechanism to prevent that, but some mechanisms are not easily reversible. Thinking about the ice coverage in Earth's polar regions, if all of that ice melts for a given increase in T, decreasing T does not necessarily allow that ice to grow back to the same coverage...and especially not at the same rate.

So a changing climate is a complex system with many different interrelated components that cannot simply be predicted by a $dT/dt = dGHG/dt$ relationship. There are numerous feedbacks that are all dependent not only on each other but also sometimes-irreversible processes.


Monsoonal interactions with mid latitude disturbances

Here are two parts of an answer, but this is by no means complete.

Most monsoonal research is focused on explaining the monsoonal passage through the plains of the Indian subcontinent. Very few papers can be found on how the same troughs cause rainfall at 3000 meters. I would like an authoritative reference on Monsoonal Mountain Meteorlogy. All that is known is that the MJO (BSISO) troughs and ridges at the 850 hPa seem to be damped at the Himalayan foothills.
Regarding the 500 hPa propagating downwards I cannot get further more information than introducing the concept of a downward propagating Rossby wave.
And as  far as the physics that explains what happens when these two disparate systems meet it is at best an open research topic.
I have read recent discussions(no reference available yet) that the two systems may need to "line up" in other words the geometric center of the upper level system needs to pass through the center of the lower level trough.Very recently Tropical Cyclone Hudhud moved up northwards towards the Himalayas and caused a blizzard in Nepal. There was a corresponding mid latitude disturabance at around the same time over the western Himalayas but extraordinary damage was prevented because the two systems did not line up.

What is of more serious concern is the fact that there have been four such incidents in recent times - 1) Pakistan Floods 2010 2) North Indian Floods 2013. 3) Indian Pakistan floods of 2014. 4) The near miss with Cyclone Hudhud.
What climatic changes are causing  these collisions between disparate systems is a new field of study. Both weather and climate models will be stretched to predict these sort of collisions.


To my eyes, the belt of Venus looks purple, which didn't makes sense to me, as the very short wavelength of purple light should have been scattered long before arriving back there. Then all made sense when I realized that if you mix blue and red light you get purple.

You got that part right. Purple is not violet. Violet is a spectral color at the high frequency end of the visible portion of the spectrum, while purple is a non-spectral color on the line of purples that spans from nearly ultraviolet to nearly infrared. We see color as a wheel rather than as a line. One possible explanation is that the long wavelength ("red") cones have a secondary response in the violet end of the spectrum. Spectral violet light excites both the short wavelength and long wavelength cones, but so does a non-spectral mix of red and blue light.

And that's what you're seeing in the Belt of Venus -- a muted mix of red and blue, or a purple (or perhaps magenta, or a rosy pink).

  So the color comes from the blue mixed with the red light backscattered by the high atmosphere that is still illuminated by the Sun. However, I can't still figure out why the Earth's shadow looks blue.

The backscattered red light doesn't come from the high atmosphere. It comes from the troposphere. The high atmosphere (the stratosphere and above) contains very few particulates. The upper atmosphere is the only part of the atmosphere that remains sunlit above the eastern horizon after sunset. The sunlight hitting the upper atmosphere is Rayleigh scattered, so you see that very faint blue scattered light. You don't see the backscattered reddish light from the particulate-containing lower atmosphere at the eastern horizon because that part of the atmosphere is fully in the Earth's shadow above the eastern horizon.


'Fertile ash' is not a scientific term, but neither is it a misnomer. Unless the ash is deposited really hot - hot enough for the particles to weld together as 'ignimbrite', then the ash deposit has high porosity and permeability. As soon as water infiltrates, the anhydrous minerals start weathering to clay - generally smectite, or mixed layer clays. This released aqueous magnesium, silica, and low concentrations of other elements crucuial to plants. Thus, both the texture and chemistry of volcanic ash is conducive to plant growth.

When the volcanic island of Surtsey emerged from the Atlantic, just south of Iceland, in the 1970s, plants started to establish themselves in the volcanic ash within a matter of months.


USA and UK government report on plane emissions: 200% difference... which is right?

I've looked into this briefly and noticed a few things that are worth pointing out.  First, your EPA table looks like it was based on Table 8 of this EPA pdf:

https://www.epa.gov/sites/production/files/2018-03/documents/emission-factors_mar_2018_0.pdf

There’s a note in the table that,

  Air Travel factors from 2017 Guidelines to Defra / DECC's GHG
  Conversion Factors for Company Reporting. Version 1.0 August 2017.

So, with a lovely bit of irony, those EPA air travel numbers are taken from the UK/DECC/Defra, which are available here:

https://www.gov.uk/government/publications/greenhouse-gas-reporting-conversion-factors-2017

Note that they’ve translated the names of the air travel distance categories so they make sense in the US market:

US short-haul (< 300 mi) = UK domestic (UK to UK)
US medium-haul (300 - 2300 mi) = UK short-haul (< 3700 km)
US long-haul (> 2300 mi) = UK long-haul (> 3700 km)

Taking some numbers from US short-haul/UK domestic as an example, the CO2 emissions are,

0.14002 kgCO2e/pass km = 140.02 gCO2e/pass km = 225.3 gCO2e/pass mi

which is just basic units conversion and agrees with your EPA table and the EPA pdf.  The same is true for the CO2 emissions in the other distance categories.  Note that the EPA are using the numbers for the CO2e emissions without radiative forcing feedbacks from water vapor, contrails, NOx, etc., which is the dark blue portion of the bars in your plot from the BBC.  You should be comparing that portion of the emissions, not the full bar including the light blue.

There's a further problem with the CH4 and N2O values in your EPA table.  Taking the same example as above but for CH4 emissions,

0.00006 kgCO2e/pass km = 0.06 gCO2e/pass km = 0.097 gCO2e/pass mi = 0.0039 gCH4/pass mi

This is correct in the EPA pdf, but has been mis-transcribed in your EPA table as 3.9 gCH4/pass mi.  Oops! someone got confused between grams and kilograms, and they've made the same mistake in the CH4 and N2O entries for all modes of transport.  They’ve then used this to calculate the overall GWP column, so their values are oversensitive to CH4 and N2O:

GWP = 225*1 + 3.9*25 + 7.2*298 = 2468.1

The correct calculation is,

GWP = 225*1 + 3.9e-3*25 + 7.2e-3*298 = 227

The bottom line is that I think the GWP column in your EPA table is nonsense and the aircraft emissions factors have the same source (albeit the BBC are probably using more recent UK emission factors).  The respective CO2 emissions for cars in the sources I've linked to aren't wildly different (297 gCO2/mi in UK, 343 gCO2/mi in US) and for motorcycles are almost identical (183 gCO2/mi in UK, 189 gCO2/mi in US).


What will be the temperature on Earth when Sun finishes its main sequence?

Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.

So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.

In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").

The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question

$\Large \frac{T}{T_0}=\left(\frac{L}{L_0}\right)^{\frac{1}{4}}$

Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot of Luminosity and temperature versus time looks like this

And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.

Age         Radius      Lumin.  Temperature
[Billion    [solar      [Solar  [°C]
 years]     radius]     Lumin.]
0.00        0.89        0.7     -41.4
0.25        0.90        0.7     -40.2
0.50        0.91        0.7     -39.0
0.75        0.91        0.7     -37.8
1.00        0.92        0.8     -36.6
1.25        0.93        0.8     -35.4
1.50        0.94        0.8     -34.2
1.75        0.95        0.8     -32.9
2.00        0.95        0.8     -31.7
2.25        0.96        0.8     -30.4
2.50        0.97        0.8     -29.2
2.75        0.98        0.9     -27.9
3.00        0.99        0.9     -26.7
3.25        1.00        0.9     -25.4
3.50        1.00        0.9     -24.1
3.75        1.01        0.9     -22.8
4.00        1.02        1.0     -21.5
4.25        1.03        1.0     -20.2
4.50        1.04        1.0     -18.9
4.75        1.05        1.0     -17.6
5.00        1.06        1.0     -16.3
5.25        1.07        1.1     -15.0
5.50        1.08        1.1     -13.7
5.75        1.08        1.1     -12.3
6.00        1.09        1.1     -11.0
6.25        1.10        1.2     -9.6
6.50        1.11        1.2     -8.3
6.75        1.12        1.2     -6.9
7.00        1.13        1.2     -5.5
7.25        1.14        1.3     -4.1
7.50        1.15        1.3     -2.8
7.75        1.16        1.3     -1.4
8.00        1.17        1.3     0.0
8.25        1.18        1.4     1.4
8.50        1.19        1.4     2.9
8.75        1.20        1.4     4.3
9.00        1.21        1.4     5.7
9.25        1.22        1.5     7.2
9.50        1.26        1.5     9.2
9.75        1.32        1.6     11.9
10.00       1.38        1.6     14.7
10.25       1.44        1.7     17.5
10.50       1.51        1.8     20.3
10.75       1.58        1.8     23.1
11.00       1.66        1.9     25.9
11.25       1.74        2.0     28.8
11.50       1.82        2.1     31.7
11.75       1.90        2.2     34.7
12.00       2.40        3.1     65.0
12.25       4.08        7.8     151.9
12.50       6.94        19.6    261.2
12.75       11.68       57.8    427.2

Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.

According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.


Why is the Lithosphere-Asthenosphere Boundary an Isotherm?

Reading this question, I'm not sure if you realize what an isotherm is - in this case, imagine peeling rock from the surface of the earth until you reached a temperature of 1300 degrees Celsius. Now, in some areas, such as mid ocean ridges, you wouldn't have to peel back much rock at all, perhaps only a few dozen kilometers. Whereas in regions of old, continental crust, you would have to peel off hundreds of kilometers of rock to get down to rock at 1300 degrees centigrade.

The result would be a lumpy sphere at a constant 1300 degrees, which is your isothermal surface or isotherm. The thickness of the lithosphere is very variable.

Interestingly, the Asthenosphere - Mesosphere boundary is created by a mineral phase transition, which is very pressure-dependent; this makes it far more of a smooth sphere.


If two adjacent tectonic plates are moving in the same direction, is there significant interaction at the boundary?

It’s relative motion that matters. So in your case, I assume one side is moving faster than another, so you would have a right lateral or left lateral transform fault depending on which side is moving faster. It’s “significance” would depend on the amount of relative difference in motion and, as usually defined, its potential impact on man.

Note that if they are moving at the same rate there would be no fault (and therefore no boundary.)

There has to be relative movement of the two plates towards one another for it to be “convergent.” Convergent plate boundaries are where one plate is being subducted (e.g. Japan) or pushed against (e.g. Himalayas) another. Having a combination of movements is not really uncommon, but typically of secondary importance. Good example this situation exist along the San Andreas Fault where it locally bends a bit, adding localized convergent components to what is an overall transform fault system.


Does within-canopy wind direction correlate with wind above the planetary bounday layer?

Turbulence is a property of the flow, not a physical characteristic of the fluid. Turbulent flows in nature are evolving due to external influences and at present time there are very few evolving turbulent flows which are well understood. The boundary conditions, such as distribution of canopy, geomorphology, all play a crucial role in determining the turbulent dynamics. All turbulent flows are different but they have similar intrinsic dynamics and through statistical means one can relate the properties of the mean flow to the turbulent dynamics.

"Big whorls have little whorls
That feed on their velocity;
And little whorls have lesser whorls;
And so on to viscosity."

Lewis Fry Richardson

Turbulence is a multiscale phenomenon where small eddies in turbulence have very short timescales. This alone tends to make them statistically independent from the mean flow. Therefore, smallscale motion depends only on the rate at which it is supplied energy from the larger scales, and the rate at which kinetic energy is dissipated into heat. The two rates of change are assumed the same so that the net rate of change is small comparing to the rate of dissipation.

This is the basis for Kolmogorov's universal equilibrium theory. It basically says that the rate of energy supply to smallscale eddies is equal to the the dissipation rate:

$$U^3/L \sim \epsilon \, .$$

In other words, the dissipative effects of viscosity can be estimated from the large scale dynamics, which are effectively inviscid. Inertial effects cause a transfer of energy from small to large wavenumber space by vortex stretching.The mean flow kinetic energy transforms into turbulent energy in the form of large eddies which cascade down to smaller eddies and so on, the remaining fluctuations are ultimately dissipated by viscous damping.

Turbulent velocity fluctuations generate large momentum fluxes between different regions of the flow which is a process analogous to stress (Reynolds stresses). The Reynolds stress is what quantifies the contribution of the turbulent motion to the mean flow. Because the momentum transfer mechanism resembles molecular diffusion, turbulent moment exchange is modeled with an eddy viscosity.

All this discussion is still inside the boundary layer itself. Outside the boundary layer is the mean wind which supplies the necessary shear for turbulence inside the boundary layer. Although this wind is not affected by the turbulent fluctuations within the boundary layer, it is the reason why they exist.


The transmissometer setup should be quite easy to build in principle, but it could be hard to get accurate values. I did a very similar instrument but to measure water transsmisivity (a.k.a. turbidity).

If you are new to Arduino you can start with the Arduino UNO board, and this is a good guide on how to get started. I got started myself with the video tutorial Arduino Course for Absolute Beginners.

Practice with a couple simple programs. In particular "Blink" to get used to switch pins on and off and "Analog Read Serial" to learn how to output data to the computer.

You need a laser diode like this one. It should be powered (or at least turned on/off) by the Arduino. Because you will need to do measurements with the laser on and off to know how much light is ambient light and how much light is coming from your laser.

To sense the light intensity of the laser after it travelled trough the air, you can use a photoresistor to make it simple and cheap, or a luminosity sensor like this one. You can find here a tutorial and example code to wire and read data from that sensor into your Arduino.

Then you need to calibrate the sensor, and it will be challenging for this project. You will need to put the system in the outdoors, measure the visibility by finding out the distance to the further object you can see, and record the reading of your Arduino. The reading would be the difference between the luminosity with the laser on and off.

After you have many calibration points over a wide range of visibilities, you can plot visibility vs reading and hopefully the points will follow a nice pattern that you can then fit with a suitable function (a line, a polynomial or logarithmic function), and then code that function into the Arduino so it can output the actual visibility.

If the pattern isn't nice, you will need to find ways to make the reading more accurate and sensible to changes in visibility. Some options for that (that you should consider also in your initial design) are:

Increase the travel length of the laser through the air.
Use a blue laser, as blue light is absorbed quickly in low visibility conditions.
Use a hood with black interior (like the photographic lens hoods) around the sensor to minimize the contribution to ambient light.
Use a luminosity sensor with larger resolutions (12 or 16 bits)
Make sure the laser voltage is stable.
Make sure the laser (and mirror if you use one) have a good and stable alignment.
Make sure readings are not affected by temperature or compensate otherwise.
Get multiple readings and take the median.

There is an Arduino Stack Exchange where you can find help if you need help to make the sensors to work or problems with the coding. However, there are tons of online resources and tutorials, so I'm sure you will find answers to all your questions.


research question for modelling extreme rainfall event with coupled 2D surface and 1D sewersystem model

It sounds as though you have ideas on the tools you'd like to use, but not on an actual question that you want to use them to answer.

You probably need to either come up with such a question, or focus instead on methodology - in studying the tools and the effectiveness of using them in a given scenario.

For nearly any modelling project, its viability will be affected by whether data are available to validate the model. If no appropriate data are available for the area you're looking at, you probably don't have a project (because what use is a model if you have no idea whether it's right?).

Bear in mind that these comments are all generalisations based on very limited information. The best advice is still "talk to your advisor".


How is the Rossby Radius used to determine that synoptic weather systems are 1000-2000km across?

The Rossby radius of deformation ($\lambda_{R}$) is a length scale over which  adjustment will occur while a system approaches geostrophic equilibrium.  In my class noted I have this defined as the distance at which buoyancy becomes as important as rotation.
Some examples are given here but do not show their derivation.

The distance that cold pools of air can spread under the influence of the Coriolis force.
A cold pool will initially spread out toward and under warmer air because of higher pressure under the cold, denser air. However, as the spreading velocity increases, the Coriolis force will increasingly turn the velocity vector until it is parallel, rather than perpendicular, to the pressure gradient. At this point, no further spreading will occur and the winds will be in geostrophic equilibrium. The final equilibrium distance traveled by the edge of the cold air equals the external Rossby radius of deformation, $\lambda_{R}$:
$$\lambda_{R} = {\sqrt{(gH\Delta\theta/\theta_0)}\over f_c}$$

I'm not familiar with the particular derivation used to come up with the 1000-2000 km $\lambda_R$ for synoptic weather patterns but it likely starts with Rossby waves and a wave solution for their propagation.
One example derivation for $\lambda_{R}$ I can think of is in a shallow water model in a rotating frame from Holton (2004) p 211.  In his setup he starts with the height ($h'$) of his shallow fluid with a discontinuity along $x$ defined as $h' = h_0 \mathrm{sign}(x)$ where sign($x$) is the sign of x.  As the fluid equilibrates, the heights will change at the discontinuity and at some distance from the discontinuity.  How far away?  That is what the Rossby radius of deformation tells us.  For Holton's shallow water model, he finds $\lambda_{R} \equiv f_0^-1\sqrt{gH}$ where $f_0$ is the Coriolis parameter, $g$ is gravity and $H$ is the mean depth of the fluid.  At distances less than $\lambda_{R}$, we will observe the height changes but further than $\lambda_{R}$ we will not notice any changes in fluid height.  In this case we can interpret the Rossby radius of deformation as the length scale over which the height field changes during geostrophic adjustment.


Relationship Between Ratio of Atmospheric Gases and Ocean Gases

The law that governs the pressure of gas at equilibrium over a dissolved liquid is called Henry's Law. Note, the equilibrium assumption, as there is some time dependence. That is, if you start with no dissolved gas in pure water, then in a relatively short amount of time, the amount of dissolved gas will be less than equilibrium.
Let's talk in abstractions. Henry's law's temperature dependence resembles the Clausius-Clapeyeron equation, so we can draw some parallels. From the Wikipedia link, for a given gas, the Henry's law constant is $$H(T)=H(T_0)\exp\left[-\frac{\Delta K}{R}\left(T^{-1}-T_0^{-1}\right)\right]$$ .$-\frac{\Delta K}{R}$ is Wikipedia's version of $-\frac{\Delta_{sol} H}{R}$, but I used $K$ to not cause confusion. For pure water, this link shows the solubility of different gases at different temperatures, but most relevant is the temperature at 0$^\circ$C (that is, it gives $H(T_0)$).
But all of this doesn't answer the two questions that your question boils down to.

Raising the temperature decreases the solubility of a gas.
If the pressure increases, then the amount of gas that can be dissolved increases per Dalton's Law. If the system is not in equilibrium, then the amount of solute will increase in proportion to Henry's Law.


Using an accelerometer as a geophone to conduct a seismic survey

Accelerometers have already been used for acquiring seismic data in a lot of studies: see this review, and references therein.

As for the code part, there is a Python framework for seismology: ObsPy.


What do you call boulders of non sedimentary rock that were lithified into sandstone?

The technical term for a sedimentary rock that has a lithified fine-grained sediment with larger pieces of rocks suspended in it upon lithification is a conglomerate. The fine-grained interstitial part is called the matrix, and the large pieces suspended in it are called clasts. Clasts can range from gravel- to boulder-size. These are technical terms used by sedimentologists.

It is tempting to refer to these fragments as xenoliths but as that word has a very specific meaning in igneous petrology, it is best to avoid it to remove any confusion.


It sounds like there are two primary ones:

No, these are not the two "primary ones". The method used depends on what you are dating, and what age you expect it to be.

Radiocarbon dating is relevant to things younger than a few tens of thousands of years, and it's only relevant for things that were living (or growing), and incorporated atmospheric carbon.

Other methods such as U–Pb (the "gold standard" when dating igneous rocks), Rb–Sr, Re–Os, Sm–Nd, K(Ar)–Ar, Lu–Hf, and many more, are used for older things in the millions to billions of years. The one used depends on what you're analysing (Re–Os for sulfide minerals, U–Pb for zircons, Rb–Sr for micas, Sm–-Nd or Lu–Hf for garnets), and what is present in the rock, and what has textural evidence for being preserved.

You might call U–Pb on zircon the "primary" one, because most of the dating is done on zircon. It's robust, easy, gives good ages, quick and relatively cheap.

  First, I am wondering if there are any data formats used for storing the data (which will help with search).

Most U–Pb data is reduced using IsoPlot, so the data will look like something that came out of that software. But in general, no. There is no standardised  data format for geochronology, unfortunately.

  And third, if there's not any "centralized repositories" of this sort of data

There are several of those. You can search EarthChem, that has some geochronological data. Australian government agencies also have some geochronology data in them, for example GA or NTGS.

  If it matters, I am interested in particular in fossil radiometric data.

Fossils are among the hardest thing to date. If the fossils are relatively young (few thousands of years), there's radiocarbon. Anything older than that, and it becomes much harder. There's U–Th disequilibrium series which may work for some slightly older fossils (~1 million years). Anything older than that in deep geological time has to be dated with indirect methods. Finding a database of that is probably wishful thinking, and to understand their dates you need to have some geological background to understand the geological relations and considerations that allow the indirect dating.


Why does wind direction change in a front?

An answer I got on Reddit which seems to make sense is that fronts are usually accompanied by a pressure change which locally reinforces the "normal" geostrophic wind which changes the wind direction.
If anyone has a more in depth answer I'd love to hear it.


What are the major differences between weather models and climate models?

The major differences between weather and climate models are many.  At their core lie the same set of primitive equations, but from here there are many differences.

A weather model only (skillfully) predicts about 10 days into the future, while a climate model integrates forward in time for hundreds of years.  The main difference here is that in a weather model, we care about the when and where of a storm or front.  In a climate model, you get weather, but you don't really care too much where or exactly when the weather is as you are looking for a long term means (e.g. a weather model cares where a hurricane is, and when/where it will impact land, whereas a climate model may only care the average number of hurricanes per year and not about where the details of those storms).

Other differences:

Spatial / temporal resolution

Because climate models run for much longer into the future than a weather model, it will have more integration timesteps for the same temporal scale.  This is relaxed by increasing the model timestep, but for numerical stability reasons the higher your timestep the more coarse your spatial resolution must be.  As a result, in general, climate models run at larger temporal and spatial scales than weather models.  The coarser resolution may force more parameterizations in the climate models.  For example a 3 km weather model may explicitly resolve convection, whereas a 30 km climate model will certainly not and need to parameterize convection.
Data Assimilation (DA)

Weather and climate models vary in their use of DA.  The biggest difference is how DA is used to "spin up" the model to the initialization time.  For weather models, if DA is used at all, you may only have a few DA steps spaced a few hours apart before the model starts integrating into the future.  For a climate model the DA period may be 100 years long before the present time is reached and forecasting begun.   However:

  This incorporation [of DA into climate models] occurs at a number of stages of the model development, including parametrization of sub-grid scale effects and model tuning. The process is not, however, done systematically and current practice is not thought of as "data assimilation."  There seems to be a growing realization that DA will have a significant role to play in future climate model development. This is, in part, driven by the need to quantify uncertainty in the model predictions. Nevertheless, there is not a consensus as to how DA should be used in these large-scale climate models. (source: http://www.samsi.info/working-groups/data-assimilation-ipcc-level-models-climate-uq )

Coupled models

Weather models may represent the ocean as a parameterized surface flux (of momentum, moisture, etc) or perhaps handle it through data assimilation.  Climate models typically couple the atmosphere model to an ocean model and simulate the ocean as well.  The climate models in actuality are typically suites of models that all communicate with each other.  You may have a model for atmosphere, one for soil, one for ocean, one for vegetation, one for chemistry, etc.  A weather model may have these features, but typically as parameterizations.
Spatial coverage

Weather models vary from global models to very localized regional models, which can in some cases be very idealized.  Climate models tend to be global.  This doesn't change the physics involved, but can influence the specific forms of the equations.  A global model will solve in spherical coordinates and many use spectral methods.  Regional weather models will use Cartesian coordinates and may make other assumptions that simplify the physics for the specific purpose the model (e.g. a storm scale idealized weather model may neglect Coriolis).


Someday in future, the length of a day will be longer than 86400 atomic seconds. Then what should future human do?

Having a time standard that works well with the ever improving capabilities of physics and having a time standard that stays in sync with the Earth's rotation are at odds with one another. One solution is to continue to do what we do now.
The length of a day is already longer than 86400 atomic seconds. Every once in a while a leap second is added to keep time as measured by the rotation of the Earth in sync with time as measured by an atomic clock. To date, 37 leap seconds have been added since 1972. This concept will continue to work, at least for the next few to several hundred years. Eventually the Earth's rotation rate will have slowed to such an extent that the leap second trick will no longer work.

Will the definition of the second be changed?

Almost certainly.
Scientists will eventually find something that is even better than is the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom as a timekeeping device. That science advances is what science does. It has already been proposed to use pulsars rather than atomic clocks as a more precise timekeeping drive. One thing is certain: The second will not be redefined to be 1/86400 of a day.


How would plate tectonics differ if Earth had no water?

One way of looking at this question is to determine if Earth would possess an active-lid (multiple plate), stagnant-lid (single plate) or an intermediary state (e.g. episodic or sluggish) tectonic regime.  This is one of the reasons comparisons are often made with Venus, especially in regards to the main difference been that Venus has a stagnant-lid with possible episodic active tectonic regime (see question and answer to Can Venus be considered to be tectonically active?, compared to Earth's active-lid tectonic regime.

However, there are other differences between Venus and Earth that also may account for the differences in tectonic regimes, asides from the relative absence of water on Venus. Some modelling by Bouffard, (2013) indicated that different plastic yield strengths of lithospheric rheology could account for the different tectonic regimes.

How water interacts oceanic lithosphere is a vital consideration for this kind of question, considering that most spreading ridges and all subduction zones are based on the oceanic lithosphere.

This answer is based on how the absence of water may have prevented a key theorised tectonic mechanism from even starting.

A crucial role for water is modelled by Regenauer et al. (2001) for the initiation of subduction and as they assert the beginning of plate tectonics, based on the theory that long term build up of sediment at a passive continental-oceanic boundary (e.g North American east coast) may have caused the strain to build up to a point where the oceanic crust 'breaks' and starts subducting, as shown in the diagram below:

Image source

In the absence of water, this process of subduction initiation (should it be true) could not have started; as the authors believe could be the case for Venus where volcanism is evident, but the mechanism appears to be hotspot activity through the current stagnant-lid tectonic regime observed there - if this theory were true, then the absence of water would mean that Earth would potentially have had a stagnant-lid, punctured by hotspot activity.

References

Bouffard, 2013, Role of water in the tectonics of Earth and Venus, University of Lyon

Regenaeur et al. 2001, The Initiation of Subduction: Criticality by Addition of Water? Science


regeride netcdf file to template netcdf file resoulution

Disclaimer: I have not looked at your particular files.
You can regrid the data in Python using the NetCDF-4 module. If you want to interpolate vertically, you can use the WRF module. And for horizontal interpolation, you can use the Scipy Interpolation module.
Here is how you would go about this regridding.
Let $(\psi_1,\phi_1)$ be the  latitude and longitude of the original data and $(\psi_2,\phi_2)$ of the regridded data. Let $y_1$ be your original data, and $y_2$ be the regridded data.

Open the original dataset.
Create an interpolation function trained on your original data $f(\psi_1,\phi_1)$ for the data you will regrid.
Using the NetCDF module, declare the dimensions, variables, and necessary metadata for your regridded dataset.
Use your interpolation function, so you get $y_2=f(\psi_2,\phi_2)$.
If necessary, interpolate to your required vertical level.
Repeat starting on step 2 for every time for every variable that you want, at every vertical level (if required).


Prevailing winds between 30 to 60 degrees latitude

Although not 100% sure, after some additional searches, I think the answer is the law of inertia. If one throws a ball from at the equator to the north pole, the ball also moves to the right even if one did not intend to do so. The same effect we see when one throws a ball from a moving car (example).

The speed is faster near the equator. Therefore, even through Coriolis effect is working, the law of inertia overrules the effect. That is, the movement (to right) of the ball is faster than the rotation of the earth.

Regardless of from north to south, or south to north, Coriolis effect and the law of inertia work in opposite directions. Stronger one determines the direction.


How often does the moon "set" for us compared to the sun?

As noted in comments, the earth rotates on its axis in about 23hrs 56 minutes. This is known as the sidereal day, that is, the day with respect to background stars. (that's not quite true, but it's good enough unless you're dealing with periods of thousands of years with high accuracy - see the linked wiki article if you care about the detail).

At the same time, the Earth is also orbiting around the Sun in the same direction, and the combination of the Earth's spin and its orbit around the Sun gives us the 24-hour solar day that we are familiar with, and that you have already modelled in your game.

Now consider how the Moon rises and sets, when seen from a position on Earth. The primary cause of this is, again, the Earth's rotation with it's just-less-than-24-hours period. In addition, this time, one must consider the motion of the Moon around the Earth, which is again in the same direction as the Earth's spin. This results in a period of about 24 hr 50 mins for the apparent motion of the Moon across the sky (Source). For your game that may be sufficient info, although if you want to be accurate it is complicated.

Remember to also take account of the phases of the moon - because the whole earth-moon system is also in orbit around the sun, and because the moon is only visible via reflected light, the mere fact that the moon is above the horizon when seen from a given point on earth does not mean that it is visible.


How much excess water prevents planting of a crop

In practice you really don't want to plant a field that is even close to capacity.  Doing so will result in ruts, soil compaction, breakdown of soil structure and a large increase in fuel consumption.

One of the advantages of zero tillage systems is the ability to get out on the field in wetter (earlier in spring) conditions.  All those roots help reduce the sheering between soil particles.


If plants convert a greenhouse gas into a non-greenhouse gas, do they cool?

Plants are natural machines that convert $CO_{2}$ into $O_{2}$ when there is sunlight. This process is known as photosynthesis because photons provide the energy that triggers the reaction,
$$6CO_{2} + 6H_{2}O -> C_{6}H_{12}O_{6} + 6O_{2}$$

The question then is where do the plant products,such as leaves, fruits, flowers,roots that are composed of $C_{6}H_{12}O_{6}$  stored? If these plant remains are stored in the ground more than they are decomposed and then release $CO_{2}$ into the atmosphere, then we can positively say they are the natural cleaning robots, sorry super-robots or cleaning freaks!


How much has the total transport of the Antarctic Circumpolar Current changed over time?

From reading the literature on the subject, my impression is that we don't know that much on the subject, primarily due to a scarcity of measurements. My understanding is that the first and only year-long time-series was made at the Drake Passage in 1979 (e. g. Whitworth & Peterson, 1985) by the ISOS programme (International Southern Ocean Studies). In addition to that NOAA's WOCE (World Ocean Circulation Experiment) added yearly data from 1990 to 2002.

According to Rintoul & Sokolov 2001 and Rintoul et al. 2001, most of the variability south of Tasmania is due to changes in currents north of the ACC itself.
Cunningham et al. 2003 show that the moderate interannual variation in baroclinic transport they observed seem to be coeval with variations in the location of the Polar Front (it moves north or south on a 90km range). But overall the variability seems to be relatively low, and the ACC relatively steady.

White & Peterson, 1996 showed an interesting phenomenon that they called the Antarctic Circumpolar Wave: it is a "wave" in the ACC circling the globe in ca. 8 yrs with a period of 4yrs at any location and it is defined by anomalies in sea-suface temperature, sea-level pressure and sea-ice extent. However no evidence for corresponding anomalies in volume transport was showed, to my knowledge.

So, to summarize, as far as I can see:

not enough data for seasonal trends (only one yearlong time-series);
some interannual variability (possibly as a consequence of variabilities in other water masses);
not enough data to study decadal variation.


How are data from tiltmeters used to monitor volcanic activity?

Tiltmeters placed on the flanks of an active volcano can measure changes in the slope angle of the flank. These changes are often inferred to be related to changes in the shape and activity of the magma chamber.

This article provides a quick and dirty example of how these instruments can be used, as well as their limitations.

In this case, the tiltmeters were able to capture the deflation of an erupting magma chamber, but not the precursory inflation. This leads to some inferences about the nature of the magma's ascent through the subsurface.

The article also references studies that were able to detect magma chamber inflation as well.

These kinds of observations definitely add to the body of evidence volcanologists use to assess risk of an eruption, but it's far from a slam dunk.

Here are some examples from that paper, both the long-term trend, and a higher time resolution display during a small eruption:

Fig. 2. Tiltmeter data from V-net (KRMV, KRHV) and Hi-net (MKNH, SUKH) stations during the period from January 23 to February 2, 2011. From here.

Fig. 10. Enlarged view of tiltmeter data during the period from 0:00 to 21:00 on January 26, 2011. Vertical line shows the occurrence time of the small eruption at 7:31 and the beginning of the sub-Plinian eruption, when the amplitude of the seismic tremor increased at 14:49.  From here.


Is there any video evidence of animals raining from the sky?

Brian Dunning already went into this extensively in episode 4170 of Skeptoid: It's Raining Frogs and Fish

  In 1901, a rainstorm in Minneapolis, MN produced frogs to a depth of several inches, so that travel was said to be impossible. Fish famously fell from the sky in Singapore in 1861, and again over a century later in Ipswich, Australia in 1989. Residents in southern Greece awoke one morning in 1981 to find that a shower of frogs had blanketed their village. Golfers in Bournemouth, England found herring all over their course after a light shower in 1948. In 1901, a huge rainstorm doused Tiller's Ferry, SC, and covered it with catfish as well as water, to the point that fish were found swimming between the rows of a cotton field. In 1953, Leicester, MA was hit with a downpour of frogs and toads of all sorts, even choking the rain gutters on the roofs of houses. The stories go on and on: More frogs in Missouri in 1873 and Sheffield, England in 1995, and more fish in Alabama in 1956.

From everything he read, waterspouts seem unlikely:

  Not once in a single case of several dozen that I read was there ever a report of a tornado or waterspout in the vicinity, or even at all, no matter how far away. I conclude that waterspouts have no connection, either hypothetical or evidentiary, to the phenomenon of frogs, fish, or any other animals, falling out of the sky.

For frogs it seem to be coincidences of bad weather and frog migration.Well, not really coincidence: they probably migrate more (often) when it's wet.
And for fish:

  You don't find mass migrations of fish crossing overland, do you? Well, maybe not mass migrations, but believe it or not, there are fish species that occasionally take to the ground in search of better waters. There are many species of "walking fish" in the world.

The main reason that they did not fall from the sky is simple:

  Drop a fish off a building, and that's a dead fish

That's why you won't find actual videos.

Brian concludes:

  Go back and read any story you've ever seen about frogs and fish falling from the sky, this time allowing for the possibility that the animals were already naturally on the ground when the witnesses first discovered them. Allow for the possibility that some elements of the report, like the falling part, could be based originally on witness conjecture or assumption.

Which is more or less what Stephan also writes in his answer.


How much Uranium is there in the Earth's Crust?

According to wikipedia, there are around 5.5 million tonnes of uranium in ore deposits that are commercially viable at current prices, and perhaps 35 million tonnes that are potentially viable if prices increase.

Also according to wikipedia, the Earth's crust (to 25 km depth) contains an estimated 10^14 tonnes (100 trillion tonnes), while the oceans may contain 10^10 tonnes (10 billion tonnes). This presumably includes the ore figures stated above.

The previous link states that "The decay of uranium, thorium, and potassium-40 in the Earth's mantle is thought to be the main source of heat", however no estimate is given for quantities. Allègre, Lewin and Dupré (1988) state that "The concentration of U in the primordial mantle (bulk Earth) has been determined to be ~21±1 ppb". Back of the envelope calculations would then give us that the mantle is 84% of the Earth by volume (probably slightly less than that by mass?), and the mass of the earth is 6*10^21 tonnes, which would give us, very approximately, 0.84 * (6*10^21) * (2.1*10^-8) ~= 10^14 tonnes, or roughly the same as is in the Earth's crust.

Allègre, C.J., Lewin, E. & Dupré, B., 1988. A coherent crust-mantle model for the uranium-thorium-lead isotopic system.
Chemical Geology, 70(3), pp.211–234.


What kind of mine pit in northeastern Minnesota could make residue that turns water turn bright red?

From the red stain in the water & the rocks in the lower left of the picture it looks like iron ore.

Also, the red stain in the water appears to be a colloidal suspension, consistent with minor erosion of a bank rather than an aqueous stain caused by water reacting with sulfide minerals in the bank.

The Iron Range occurs in north eastern Minnesota.