What does the unit cell of petitjeanite look like?

Should one assume that the mineral petitjeanite and the chemical discussed in the recent Chemical & Engineering News article Photocatalyst shreds drinking water contaminant PFOA are probably the same crystal configuration and unit cell, or can there be some variety?

No you cannot assume the structure from the formula, many materials have polymorphs (think graphite vs. diamond). To know if the structures are the same you must look at the diffraction pattern from the paper. In the paper the synthesized bismuth oxyhydroxyphosphate matches that of petitjeanite so in this case that is the prototype structure.

Using the information about diffraction, from the ICDD Databse (pdf 01-082-8058)we find that petitjeanite is a triclinic system of the $\mathrm P\bar 1$ space group (#2). with lattice parameters of:

$\require{mediawiki-texvc}$
$$a = 9.798\AA; ~ b =  7.250\AA; ~ c= 6.866 \AA; \qquad \alpha = 88.280^\circ \beta = 115.270^\circ ~ \gamma = 110.700^\circ$$

and atomic positions of:
$$\begin{array}{c|lll}
\text{Atom}&x&y&z\\
\hline
\ce{Bi}&~~~0.52327&~~~0.41421&~~~0.7523\\
\ce{Bi}&~~~0.29838&~~~0.74044&~~~0.55549\\
\ce{Bi}&~~~0.07735&~~~0.1609&~~~0.28045\\
\ce{P}&~~~0.6952&~~~0.0172&~~~0.9215\\
\ce{P}&~~~0.0961&~~~0.372&~~~0.7862\\
\ce{O}&~~~0.3777&~~~0.5382&~~~0.4759\\
\ce{O}&~~~0.3066&~~~0.1549&~~~0.5579\\
\ce{O}&~~~0.859&~~~0.0275&~~~0.8943\\
\ce{O}&~~~0.5569&-0.2084&~~~0.8602\\
\ce{O}&~~~0.621&~~~0.1596&~~~0.7526\\
\ce{O}&~~~0.7684&~~~0.1052&~~~1.1811\\
\ce{O}&~~~0.2584&~~~0.5101&~~~0.7497\\
\ce{O}&-0.0468&~~~0.4637&~~~0.6902\\
\ce{O}&~~~0.0209&~~~0.1498&~~~0.6362\\
\ce{O}&~~~0.1695&~~~0.3727&~~~1.0506\\
\end{array}
$$

and last but not least this renders to an image of:

Purple: Bi
Orange: P
Red: O


How much is Solar Radiation effected by Axial Tilt or Obliquity?

Check out this matlab program that is presented in a paper by Kostadinov and Gilb, 2014. The paper is worth reading, and they have their full matlab code in the "supplement" link (top right corner under downloads).

The code launches a GUI. From it you can control the values of obliquity, eccentricity, precession, total solar irradiance, day of year, calendar start year and end year,  and latitude. Section 2.1 in the paper explains the coordinate system.

I don't think anyone could answer off the top of their heads the question "what is the difference between 1920, 1939, etc... of solar radiation at a particular geo-location". But with this program, you can mess around with the data and find out. So let us know what you discover! (ps, if you don't have Matlab, you can probably use this in octave which is free).

Here's a screenshot of the gui

And here's what some of the output looks like

Here's some alternatives to matlab:
1) nasa has online calculator that spits out raw text tables of insolation.
2) If you are savvy with fortran then you may like this fortran code.
3) The fortran code above also has an online interface
4) If you like python, then you may like this python code, climlab, where there are detailed instructions here on how to use the code and visualize the information.
5) If you like R, then try palinsol which has a little documentation here.


How are deposits of metals like tantalum located?

Metal oxide minerals like tantalite (tantalum) and columbite (niobium) often form placer deposits within basins and drainages. The placer deposits are a secondary ore deposits created by the weathering of tantalite/columbite bearing granite and the transport of heavy sands by water and gravity.

Based on this information, a good approach to prospecting for tantalum / niobium would be collect dark/black sand samples from stream beds within a granite mountain range and to collect samples from riverbeds flowing out of mountain ranges with exposed granite. Larger rivers with steep terrain can carry heavy sediment further away from its source area.

Example: Sawtooth Mountains in Central Idaho are a large granite batholith complex..  Salmon river and its tributaries would excellent areas to look for placer deposits (except of course most of this area is designated as National Forest land.)


Historical atmospheric partial pressure & Henry's law constant

The source you mentioned tries to explain why CO2 lags by about 1000 years in historical records.
Henry's law tells you something about the equilibrium between the CO2 level in the surface layer and the atmosphere. However, this is not the reason for the 1000 year time-lag mentioned. There's not enough CO2 in the surface layer to cause these increases in atmospheric concentration. What is important is the exchange of CO2 between the deep sea and the surface layer. This seems to have a typical timespan of 1000 a.
Citing from your source:

  As the Southern Ocean warms, the solubility of CO2 in water falls (Martin 2005). This causes the oceans to give up more CO2, emitting it into the atmosphere. The exact mechanism of how the deep ocean gives up its CO2 is not fully understood but believed to be related to vertical ocean mixing (Toggweiler 1999). The process takes around 800 to 1000 years, so CO2 levels are observed to rise around 1000 years after the initial warming (Monnin 2001, Mudelsee 2001).

So the initial increase in CO2 levels due to Henry's law trigger via feedback mechanisms changes in the vertical circulation pattern thereby transporting more CO2 from the deep sea to the surface. It's this time constant that is seen in the records.


This is going to be brief as on a phone : I welcome somebody posting a more complete answer. But the basic principle of large waves appearing from wind is:
 from a smooth water surface, the wind can produce only small ripples. But those ripples mean that the surface is no longer smooth. The higher the ripples get, the more surface there is for the wind to act upon, thus enlarging them more. Thus are local wind waves formed. For these wind waves to build into the large swell that is found in the oceans, this process needs to continue for a number of days, and some hundreds or thousands of miles. Large swell waves hitting the coast may have been formed in a storm the other side of an ocean.


How much could Earth's temperature increase by the time we run out of oil reserves?

That estimation is based on current extraction rates and based in 2013, so we would have oil reserves until 2066.
Assuming that's correct, it would resemble the "business as usual" future emissions scenario, a.k.a. RCP8.5 (more about RPCs).

According to the last IPCC report, the range of mean global temperature predictions for RCP8.5 looks like this:

We are now 0.5°C above the figure's baseline, and in the next 80 years, which is about year 2100 the temperature would be about 3.5°C above current temperature. But the range spanned by different predictions goes from 3°C to 5.5°C.

Note that the warming effect of putting additional $\text{CO}_2$ in the atmosphere last many centuries, so even if emissions stop suddenly bu year 2066, the planet will keep getting hotter and hotter for a long time.

Also note that the warming is not homogeneous, some areas will warm much more than others, in RCP8.5 scenario many areas would warm by more than 6°C, this animation by NOAA gives you a nice idea of the rate and pattern of warming.

And regarding your question:  Is that a problem to really be worried about? the answer is definitely YES! The RCP8.5 scenario is the most pessimistic one, if that one realizes we will be in a lot of trouble, dealing with climate change, weather extremes, sea level rise and massive migrations.


Potential explanations of Red Sea crossing

To my knowledge, the best study looking at potential explanations for the Red Sea crossing is the one by Nof and Paldor (1992). They present a couple of plausible scenarios for the crossing. The main one is the effect of strong winds blowing along the Gulf of Suez and they find that the sea level drop could be sufficient:

  It is found that, even for moderate storms with wind speed of about 20 s−1 receding distance of more than 1 km and a sea level drop of more than 2.5 m are obtained. These relatively high values are a result of the unique geometry of the gulf (i.e., its rather small width-to-length and depth-to-length ratios) and the nonlinearity of the governing equation. Upon an abrupt relaxation of the wind, the water returns to its prewind position as a fast (nonlinear) gravity wave that floods the entire receding zone within minutes.

The second mechanism involves a tsunami propagating along the Gulf of Suez from the Red Sea, but it seems like way more of a stretch.

Nof D. and N. Paldor, 1992: Are There Oceanographic Explanations for the Israelites'Crossing of the Red Sea?. Bull. Amer. Meteor. Soc., 73, 305–314.
doi: http://dx.doi.org/10.1175/1520-0477(1992)073%3C0305:ATOEFT%3E2.0.CO;2


Yes, there have been recent research in this field.

In the article Oceanic minerals: Their origin, nature of their environment,
and significance (Kastner, 1999), who asserts that

  The zeolites phillipsite and analcime mostly reflect on
  diagenesis of volcanic matter; clinoptilote and heulandite occur in Si-rich
  diagenetic environments.

and confirm that

  In addition to diagenetic opal-CT and quartz that
  form from the dissolution of biogenic opal-A, other common
  authigenic alumino-silicate minerals are smectites and zeolites.

This is further confirmed by a 2007 paper Clinoptilolite as a new proxy of enhanced biogenic silica productivity in lower Miocene carbonate sediments of the Bahamas platform: Isotopic and thermodynamic evidence (Karpoff et al) which determined that

  Seawater–rock modeling specifies that clinoptilolite precipitates from the dissolution of biogenic silica, which reacts with clay minerals. The amount of silica (opal-A) involved in the reaction has to be significant enough, at least 10 wt.%, to account for the observed content of clinoptilolite occurring at the most zeolite-rich level. Modeling also shows that the observed amount of clinoptilolite (∼ 19%) reflects an in situ and short-term reaction due to the high reactivity of primary biogenic silica (opal-A) until its complete depletion.


Language to modernize a scientific Fortran codebase

The modern language you are looking for is called modern Fortran 2018. Fortran 2008 and 2018 have everything a numerical computing project would need and so many features that many other languages mentioned here lack (including extremely pleasant array-syntax which has inspired all other languages such as MATLAB, Python, R, Julia, ..., even C++ numerical libraries). It is the only language that has native built-in parallelism and is the only language, along with C, for which the official MPI parallelism standard is released. It has also excellent vendor support for GPU parallel computing and as I heard in SC18, some vendors like NVIDIA/PGI have already started implementing the native parallelism features of Fortran via GPUs.
Modern Fortran is a high-level language comparable to MATLAB and Python, yet 100-500 times faster than both (https://modelingguru.nasa.gov/docs/DOC-2783). Using Coarray Fortran you can seamlessly parallelize your code with minimal effort to run it from your laptop to the largest supercomputers in the world. No other language has such capability at the moment. Fortran is also the only language that has all levels of parallelism, from instruction level to vectorized, concurrent, and coarray-distributed parallel computing. If such features are not considered "modern", perhaps "post-modern" would be a better description.
Fortran has been a reliable lasting language for almost 3 quarters of a century and has excellent highly-optimized compiler support (Intel, GNU, NAG, IBM, PGI/NVIDIA, ...). If you want to write code that lasts decades, then port your FORTRAN77 code to modern Fortran with minimal effort and save yourself time, energy, money, and computational power.
A good start with modern parallel object-oriented Fortran is "Modern Fortran Explained: Incorporating Fortran 2018" by Metcalf et al.
If you decide to port your code effortlessly to modern Fortran, you can also get help from the official Fortran language website https://fortran-lang.org/ and the community of programmers on Fortran discourse: https://fortran-lang.discourse.group/
Update Nov 17, 2020
Just yesterday NVIDIA released a news post on its GPU implementation of the concurrent features of Fortran 2008 / 2018. Users can now write code in pure modern Fortran and let the compiler automatically offload it to GPUs for thousands-way parallelism.
What is the relevance and importance of this achievement? The same Fortran code that a user writes can now be parallelized via GPUs, distributed CPUs, OpenMP threads, or auto-parallelization features of the Fortran compiler depending on the user's platform and compiler choice. All of that complexity is hidden from the user. No need for preprocessing and conditional compilations anymore. This further enhances the excellent existing portability of Fortran programs across platforms and architectures.


ERA5 mean evaporation rates data - Why is that negative?

Just leaving this for future readers. I finally found in some ECMWF documentation (referring to a different variable) that: "The ECMWF Integrated Forecasting System convention is that downward fluxes are positive. Therefore, negative values indicate evaporation and positive values indicate condensation". This applies also to other variables.
Thanks to Daniel and Spencer for their help.


How can a non-geologist identify a rock?

OK, so you've found yourself an interesting rock and you want to know how to identify it. I am going to go ahead and assume that you haven't studied Geology before (apologies if that's an assumption too far).

The first thing you can do is to head to your local public library and find a basic "rocks, minerals and fossils" identification book, and try to match up what you have with something in the book. Most of these books will include some kind of description of the various tests you can do (Mohs Hardness Tests, Acid Tests, Flame tests etc).

A quick google search for the geology of the area in which you found the rock might also give you a good starting point. You are more than likely not going to find an exact match by doing this, but it will help later if you have some idea of what you might have. It also means that you will have to look at the rock critically and you'll gain far more for having tried to identify it yourself. (I work with helping ID fossils on a regular basis, and it's far more rewarding if the person who has found the fossil has some idea as to what they have, or at least a reason for their identification).

If that doesn't get you anywhere, you can turn to the internet, there are places such as the NHM's Nature Plus where you'll find other people including experts and amateur rock hounds who might be able to give you more help. You will want to have good photographs with a scale (coins, Lens Cap, Rulers all apply).

If all else fails, Head to your local museum with a geological collection and look at the collection. You can also ask to speak to a geological curator and they should be able to help you identify your specimen (as your profile lists London as your location, the Natural History Museum's Angela Marmot Centre, The Horniman Museum, or British Geological Survey are all good bets).


There is still some uncertainty, but some recent research is detailed below:

In research reported in the article Barite in the ocean – occurrence, geochemistry and
palaeoceanographic applications (Griffith and Paytan, 2012), recent observations and research found that

  Using the non-carbonate Sr content in
  suspended particles to track the presence of
  acantharia, van Beek et al. (2007) suggest that
  acantharian dissolution does contribute signifi-
  cantly to barite formation in the upper 500 m of
  the water column

However, a lack of a definitive correlation between the barite concentrations and acantharian distributions suggest that

  these organisms are
  not required for the formation of barite in the
  water column (Bertram & Cowen, 1997)

and that further observations

  provided direct evidence to support
  the water column micro-environment mechanism
  of marine barite formation and to verify that
  barite can form in the absence of acantharia.

The concentration of strontium in barite is a record of the Sr isotopic composition of the formation fluids, which according to the article has its source from sea water, sediments (both marine and terrigenous) and hydrothermal fluids.

It is this last point, particularly about the Sr concentrations in sea-water, which according to the article Sedimentation of acantharian cysts in the Iceland Basin: Strontium as a ballast for deep
ocean particle flux, and implications for acantharian reproductive strategies (Martin et al. 2010) state can fluctuate by several percent

  By precipitating celestite, Acantharia can reduce surface
  seawater strontium (Sr) concentrations by up to 5%

Experimentally the authors found that

  Sr fluxes we report are
  too high to be attributed to nonacantharian sources.


How can we predict if it's raining, drizzling or there is snow fall by using precipitation intensity (inches/hour)?

TL;DR: When reporting precipitation types, we still have to manually look out the window.

TL;SR: You do not mention how the information is gathered, so I will go over the different ways.

The first and most obvious one is the air temperature.  If the air temperature is above freezing then you have rain, below you have snow.  Until recently reporting stations were all manned, and so someone would go out and look and determine what kind of precip is falling.  Reports such as if it was raining or snowing, cloudy or sunny, are based on the observation at that moment, not over the course of time.  With technology, a simple camera and light source can determine precip type.  Snow reflects light back to the camera whereas rain lets the light pass through the drop.

Radar is a little more complicated.  We now use what is known as Duel Polarization (Duel-Pol) radars.  Using signals polarized in different directions, we can measure the shape of the precipitation.

Wind resistance flattens out rain drops, making them wider than tall.  Hail tends to be round.  Snow may present itself on it's face appearing as hail, or side, appearing as rain.  The ratio of height to width gives the Spectral Differential Phase.  Snow has a lower value and rain has a higher value with some overlap.
Another important calculation is the Correlation Coefficient, which measures how similarly the two polarizations interact with the precip.  In the image below is a map of different precip types and their CC.  Note that snow has a much wider range of values than snow.  Snow type is determined by temperature, wet snow closer to freezing, drier snow as you get colder.

These and other calculations give on the fly estimations for precipitation type.

However, what you see on the radar on TV still uses the old way of mapping station reported temperatures onto the radar screen.  On this rain/snow radar loop You can make out the rain in green and yellow, the mix precip in pink, and snow in blue.  Note however the mix line (where the air is at 32°F/0°C, moves five times over the 10 frames, and it is not smooth.  This line is calculated by the measured temperatures from weather stations scattered over the area, drawing a line that marks the freezing point, much like drawing terrain contours.  While the radar updates every 10 minutes, weather stations are only sampled hourly or quarterly.

So without knowing the exact way your data was gathered, I would say someone stuck their head out the window and marked on the computer that it was rain.

Extra reading:
http://www.nssl.noaa.gov/tools/radar/dualpol/
https://www.weather.gov/media/lmk/soo/Dual_Pol_Overview.pdf
http://training.weather.gov/wdtd/courses/dualpol/documents/DualPolRadarPrinciples.pdf


Why are the mountains predominately grey or dark brown?

As Gary Kindel in his answer correctly said, mountains may consist of either magmatic, metamorphic or sedimentary rocks or all three together.

The greyish to brownish color is thus due to a mixture of all sorts of rocks and minerals that is covered by layers of eroded material of different grain sizes. This way, mountains appear to be of a single color when observed from a distance. This is similar to mixing a couple of watercolors together - the result will either be a greyish or a brown color. However, if we would magnify the watercolor mixture under a microscope, so that we see the individual pigments, we could tell that it isn't actually grey/brown. Same applies to the mountains. From a far, they appear to be grey/brown but when you get closer you can depict all sorts of colors.

The only exceptions to this are mountains, where the material is very well stratified, so that different colors can be seen from a distance.

To answer your second question: Please note that Olivine, Pyrite and Tourmaline are not rocks but minerals.

Olivine is mostly abundant in earth's mantle (check out Moho). The chance that a mountain is build solely by a material from the mantle is highly unlikely. What happened to the material that was on top? Secondly, Olivine is not stable at earth's surface according to the Goldich dissolution series. It alters into clay minerals and iron oxides that are easily eroded by e.g. rainwater. Thus, if there was a mountain made of olivine it would have surely been eroded by now.

Tourmaline is a mineral that forms in pegmatites and is thus far too rare to form an entire mountain. Especially since there is no process that individually picks Tourmalines from nature to build a mountain out of it.

Pyrite; there is still a great debate in the literature about the formation processes of Pyrite. But it is most likely a mineral that forms in a secondary process due to the intrusion of hydrothermal mineral-rich water. Thus, Pyrite is not concentrated in one area and is, like Tourmaline, far too rare to form a mountain.


How Japan Filled That Ginormous Sinkhole In Just One Week:
The Fukuoka sinkhole measuring 8,700 square feet (808 square meter), 65 foot (20 m) deep: they poured a mixture of soil, water, and cement into the hole—they use more than 7,100 cubic meters of the stuff in all. YouTube timelapse.

How To Fix a Giant Sinkhole about the two in Guatemala: The first from 2007 one they filled with a soil cement made from cement, limestone, and water known locally as lodocreto ("mudcrete").

  It's not clear whether cement is the best option, however. A 6,500-cubic-foot wad of concrete may serve to concentrate water runoff in other areas, leading to more sinkholes. Many engineers prefer the graded-filter technique, in which the hole is filled with a layer of boulders, then a layer of smaller rocks, and, finally, a layer of gravel. This fills the hole, more or less, while permitting water to drain through the area.

Whether this was actually done with the 2010 one I could not find (yet). Even the Wikipedia entry on the 2010 sinkhole (which you are also refering to) says This section needs to be updated.

It seems to be closed now, look at this video fragment compared with the bottom picture here.

Note that 7000-8000 m3 sounds like a lot, but that is only 400-500 truck loads.

BTW (I know, that is not answering the question, but it was too nice to not add):Instead of filling them up you can also make a garden in them:

Photo credit: KnitSpirit/Flickr


Database of mineral with images for a neural network application

First of all rruff.info is an excelent site done by chemists to take data quickly, and you can totally trust the source.

Second, for images, most of the listed +5000 species are not shown in nature, and you cannot have pictures of all of them. You will only find on the net pictures from common minerals on nature.

Third it depends if your work is gonna be published or not, as you would need permission or CC licensed images if so.

Copyrigthed database of pictures and data:

Webmineral
Mindat.org

Mindat can share with you their data, and they are going soon to open them on CC format with an API, but the pictures they have belong to each author and many of them are copyrigthed (and gonna stay copyrigthed if they open data, you would need to ask permission individually for each picture).

CC license pictures:

I wondered how to obtain pictures from common minerals on CC license because I am writing a mineral app and my choise was Dr Lavinsky collection uploaded to wikipedia from his mineral shop iRocks.com.

At his website they have plentifull of high quality well described pictures of common minerals you can maybe download with a script making GET petitions, and you can ask them for permission, even for the pictures that are not uploaded to the wiki. I did it myself for my mineral guide and they just ask me to quote iRocks.com; they are very fair people. Aparently they are happy to share if you quote his shop.

At Wikipedia you can find on CC license >2000 pictures uploaded from mindat.org, and >5000 uploaded from iRocks.com

You have the complete list of minerals with picture on Wikimedia Commons where to start to collect the data. I don't know if you could somehow extract all the images url using GET petitions with code. Myself I only took the iRocks pictures because my guide covered only 180 minerals, the descriptions Dr Lavinsky provides are valuable (example), and then I only needed to quote one author (I ended by taking them directly from iRocks and link on my work to each piece on his shop, they got very happy about that, they answered my mail with "many thanks").


Percentage of Oxgen left after burning all the available biomass

Estimates of earth's total biomass vary widely, from 0.5 to 4 trillion tons C, so instead of citing a source, I'll just go with an assumption of $1\times10^{15} \text{kg C}$. Measuring biomass in carbon is a convenient segue to the next assumption: assume that all biomass burns only in $\text{CX + O}_2\,\rightarrow\,\text{CO}_2 + \text{X}$.

Given these assumptions, $1\times10^{15} \text{kg C}\cdot \frac{1 \text{mol C}}{0.012 \text{kg C}} = 8.3 \times10^{16} \text{mol C}$. To react with so many mol's $\text{C}$ we will need the same number of mols of $\text{O}_2$, at molar mass $0.032 \text{kg O}_2$, which gives us a total of $2.7\times10^{15} \text{kg O}_2$ needed.

Oxygen is 20% of the atmosphere, which means there is $5.1\times10^{18} \text{kg atm} \cdot 0.2 \frac{\text{O}_2}{\text{atm}} = 1.0 \times 10^{18} \text{kg O}_2$ available.

Since we have calculated that there are three orders of magnitude as much oxygen available as is needed to burn all biomass, I feel confident saying that global loss of oxygen due to burning biomass was not a cause of the P-Tr extinction.

Also relevant: there is nowhere near a consensus that an asteroid impact caused the P-Tr extinction. To the best of my knowledge, an asteroid strike is not the most popular theory for that specific extinction event.


Has the Olema earthquake fence continued to spread apart?

If your question is only about the location of said fence I can not answer it. If, however, you are interested in the greater area around that location or the San Andreas fault in General, the short answer is, yes, there has been additional displacement and the movement is ongoing.

This displacement is related to what one can call the earthquake cycle of surface deformation. Usually people differentiate between co-seismic (directly caused by an earthquake, the Olema fence is a beautiful example for this), post-seismic (caused by secondary earthquake effects, keywords are poroelastic and viscoelastic effects) and inter-seismic (which is the tectonically driven creep of a fault in between earthquakes).

Take a look at this article by Lisowski and others to see surface displacements along the SAF. Fig. 7 shows the area of interest and , though a bit hard to see, there is significant relative motion in between areas east and west of the fault. The number that they give for average relative plate motion is 35 mm/yr (which would be roughly 4m/13ft in 110 yrs).

To return to the fence, I can only assume that it has spread further apart in the last 110 years, but not having been there I can not be certain. It is possible, that the surface manifestation of the fault has turned to another spot. I do think it is unlikely that not at least part of the deformation can be seen at the fence's location. According to this book the co-seismic offset of the fence was 4.7 m, might be interesting to know what it is today.


Why does Google maps (in terrain mode) space thier topo lines 80 feet apart?

Based on USGS (Department of the Interior – United States Geological Survey) toopgraphic maps, where on a 7.5 min Quadrangle map, the contour interval is commonly 40 feet.  Larger maps 15 min to 1'-2' maps the interval is commonly 80-100 feet.

All maps of the United States are commonly sourced from USGS based maps.  I am certain Google or Google's map provider is using USGS base maps.

Reference:
http://geology.isu.edu/geostac/Field_Exercise/topomaps/vert_scale.htm


Why do snowflakes form into hexagonal structures?

Ice grows in many forms.  As mentioned in the other answer, all of the ice we are going to observe is Ice Ih, but there are many other forms.  See this phase diagram of water:

Image courtesy of Cmglee on wikipedia

The different ice regimes grow different crystalline shapes.  Ice Ih grows hexagonal crystals and in certain regimes you can find triangular and cubic ice crystals.  The hexagonal shape is a consequence of the bond angles within the water molecule as it forms into a solid crystal lattice.

This phase diagram says we'll experience Ice Ih between 0 C and -100 C and throughout tropospheric pressures.  This ice crystal is hexagonal, but within this crystal form there are many ice habits of crystal growth.

Image used from Weatherwise magazine, AMS

The axes of this plot are supersaturation with respect to ice ($e/e_{si} > 1$) and temperature.  All of of these crystals are hexagonal but some are long skinny hexagonal prisms and some are very thin and wide hexagonal plates.  The snowflake is a dendrite and these crystals grow between -10 and -22 C in and supersaturation with respect to liquid water.

What happens is that the hexagonal crystal has 6 vertices connecting its 6 edges.  These vertices produce an increased gradient in vapor (indeed, the sharper the angle, the stronger the vapor gradient becomes).  At high supersaturations vapor is quickly deposited in the areas of the enhanced vapor gradient and the arms of the dentrite form.  The particular shape of the dendrite will depend strongly on the vapor gradient it is experiencing, which in turn is influenced strongly by its current shape and the environment it is growing in.

References:

Lamb, D. and Verlinde, H., 2011: Vapor-growth of individual ice crystals. Physics and Chemistry of Clouds. Cambridge University Press, Ch 8.3, 342-369.


Why there are no sharp corners in nature?

The premise of your question is entirely wrong. There are many examples of sharp corners in nature, the most obvious being well formed crystals.

Pyrite is a classic example that was mentioned by @wienein in the comments. In a ideal situation it forms cubic crystals with sharp edges.

A classic non-crystalline example would be volcanic glasses such as obsidian, which fracture to produce extremely sharp edges and were historically used by some cultures for making blades and other sharp tools.


This gif, prepared by the United States Department of Agriculture - Natural Resources Conservation Services (USDA-NRCS) soil scientists at the National Soil Survey Center, has soil colors based on the Munsell Color System for the United States at different depths:

The soil colors nearest the surface are darker due to more organic matter and are lighter at depth with varying colors by region.

Source: http://munsell.com/color-blog/soil-colors-national-parks-anniversary/

This link also has soil colors of select United States National Parks.  For example:


Why do winter temperatures account for most of the increase in global temperature?

Energy balance in the winter is highly dependent on the total amount of area covered by snow or ice.   Snow increases the albedo of the Earth which directs the short-wave radiation from the Sun back to space, stopping it from being absorbed by the Earth.  Winters with minimal snow/ice cover effectively allow more solar radiation to be absorbed by the Earth.   Depending on the winter, the amount of snow cover can be quite different from year to year, which can cause great variability in temperature.   In contrast, summer months generally have more stable temperatures because snow cover is less dynamic during those months, and there is roughly the same total solar radiation absorbed from year to year.


Why is Thermohaline Circulation (THC) pivotal to life on Earth?

My answer is a bit off topic to your actual question, but addresses something you said:

  oceanographers have stated that less than 5% of the worlds' oceans has been explored

I would venture that less than 5% of the ocean floor or deeper ocean depths is perhaps where less than 5% has been explored.

We've really been over the vast majority of the ocean surface at some point (and have tools like satellites that give us significant data on the rest).  Here's the current location of floating buoys:

(Argo Website)

It looks pretty comprehensive near the surface!  Still, there's often hundreds of miles between sites, so while it means we have\do cover a fair bit of the area (more than 5%!), we aren't everywhere at once.

And it's important to note that a a significant part of thermohaline circulations are near the surface, generally the red areas on this map:

[
(Wikipedia)

But the big thing to take home is that even where we don't have as much data, we can see the large thermohaline circulations well because of its scale and relative continuity.  It's quite comparable to the upper atmosphere, where we also don't get data on large parts of the upper atmosphere, but can rather well diagnose jet stream fluctuations.  Here's the upper air sounding network:

(Weatherstem.com upper air observations lesson)

Both networks are aided some by satellite and ship/plane observations, but overall, despite fairly limited observations, the circulations are quite evident because of their size and impacts.  So we have a pretty good handle on what's going on.

Hopefully someone else is able to better address your central question about why it is vital to life on Earth!


Is there a table available for the maximum potential intensity of hurricanes?

This perhaps only indirectly addresses the question, but maybe it might be helpful. According to Kerry Emmanuel's book "Divine Wind", a hurricane can, in a sense, achieve super-Carnot efficiency without violating the Second Law of Thermodynamics. A hurricane's heat reservoir is the ocean surface at temperature Th and its cold reservoir is the tropopause at temperature Tc. Heat flow Q, mainly via water evaporating from the warm ocean and condensing in the cold upper troposphere is, according to the Carnot efficiency (Th - Tc)/Th, converted into work W as per W = Q(Th - Tc)/Th. But a hurricane's work output is the kinetic energy generation for its winds. With a hurricane in steady sate (constant wind speeds) kinetic energy generation is matched by frictional dissipation. Frictional dissipation of W into the hot reservoir reduces the net heat input required from the hot reservoir from Qh to Qh - W = Qc and raises the hurricane's efficiency to (Th - Tc)/Th X Qh/(Qh - W) = (Th - Tc)/Th X Qh/Qc = (Th - Tc)/Th X Th/Tc = (Th - Tc)/Tc. The Second Law of Thermodynamics is not violated because it allows work to be dissipated via friction as heat at any temperature --- at Th as well as at Tc. Of course the above assumes perfect or reversible operation. Like all real heat engines, hurricanes are imperfect. But perhaps it at least illustrates the point.


What "blobs" of molten material in Earth's interior are responsible for the rapidly moving north pole? Where are these blobs exactly?

The "blobs" referred to in the IFLS article are, more correctly, areas of strong magnetic flux at the Earth's surface. The term "blob" is not scientifically significant, it just refers to a region where the magnetic field coming from Earth's core is stronger than elsewhere. Often we'd depict the magnetic field with a contour map of field strength, giving peaks and troughs of strong and weak field the appearance of "blobs" or patches, like this summary image from the publication in question:

(source: P. Livermore, via ESA: http://www.esa.int/Applications/Observing_the_Earth/Swarm/Magnetic_north_and_the_elongating_blob)

The maps show the radial magnetic field strength at Earth's surface in 1999, and then the field in 2019, this time with a trail showing the movement of the North magnetic dip pole (the star) since 1999. The two "blobs" of stronger field can be seen to change, the one over Siberia gets bigger and pulls the pole towards it, away from the now smaller Canadian one.

These "blobs" of strong field on the maps aren't "molten material in Earth's interior", but we can infer from maps like this what the field would look like at the surface of the outer core, and then from there what the movement of the material within the outer core might have been in order to generate the magnetic field we've observed. This is thanks to (math heavy :( ) frozen-flux theorem, that essentially says magnetic field is "frozen" into the iron-rich fluid at the surface of the Earth's outer core, so acts like a tracer for the fluid movement at the top of the outer core.

For an idea of what the flow (labelled "|U|") of material at the surface of the core might look like during the last 20 years to produce the field (labelled "Br", note the flipped color scheme), here are stills from the same model cited by the publication's authors of the field and flow at the core surface in 1999 and 2017. The Canadian "blob" gets stretched out and weaker relative to a strengthening Siberian "blob", as the flow speeds up under Canada:

(Source: https://geodyn.univ-grenoble-alpes.fr/, play with the great visualisations, but the animations are enormous files!)

So yes, you can map the distinct location of these "blobs" of strong field (though only outside the core), but bear in mind the maps are plotted with largely irrelevant choices of contour levels -- the field is continuous and varies smoothly, it's been drawn like this to highlight the "blobs" more clearly.

(Edit: added images of field and flow at the core surface to clarify, and make this answer a bit long...)


Have there ever been any islands that disappeared due to rising sea level?

Definitely, there are lots.

As you say, sea-level is rising in most (but not all) coastal areas. Indeed, at the end of the last ice age ca. 12,000 years ago, sea-levels rose about 120 m. Many islands and land bridges — such as Beringia across the Bering Strait, and Doggerland across the North Sea — drowned.

I can't find any lists of drowned islands, but here are some places you will find them today and in the geological past:

'Banks' on the eastern seaboard of North America would have been emergent during the ice age — Georges Bank and the Grand Banks for example. As they drowned, they would have formed islands — lots, in the case of Grand Bank.
The Hawaiian archipelago is part of a famous chain of drowned islands, but the change in sea-level is not the only thing that's drowning them. As the plate moves over an upwelling in the mantle — the same thing that's causing the volcanism there — it subsides and cools. I'm sure there are many drowned islands in other extinct and active volcanic provinces and seamount chains: the Zubairs, Canaries, Azores, Iceland, the South Pacific, etc. Sometimes life keeps up for a bit as a coral reef grows around the sinking island, perhaps forming an atoll.
Near-sea-level islands like atolls abound in places like the Maldives. These atolls are volcanic and actively subsiding. Sea-level may or may not inundate them, depending on whether the coral growth can keep up. Another fragile island is Sable Island off Nova Scotia — clinging to the edge of the continental shelf.
Volcanos can explode as well as sink slowly into the sea. Krakatau Island is probably the best example. This one has nothing to do with sea-level.
Rift basins start as mountainous tears in the crust, then subside and flood. Global sea-level change will often act to accelerate this. An example might be the various island groups on the shores of the Red Sea. These will likely sink into the sea eventually.
Salt-domes in Louisiana (e.g. Avery Island) form hills, but the domes continue offshore for hundreds of kilometres. Many of them would have been exposed in the past, some even more recently than the last ice age.

Maybe others can chip in some other scenarios; I'm sure there are dozens.

The point is that sea-level is not the only factor — subsidence, sediment accumulation rate, and erosion also play their rôles. But sea-level always plays some part, and can change quickly relative to the other factors.


Is the whole San Francisco Bay Area essentially one giant fault?

Much of western California is composed of small lighter landmasses scraped off of the Pacific Plate as the heavier mantle sank under the North American Plate, and the San Francisco Bay Area is no exception. Here's an illustration of how some of CA was formed as the Pacific Plate was subducted under the North American Plate:

As these separate landmasses were scraped off the Pacific Plate, they formed distinct rock types, with the boundary of each forming a distinct fault.  Here's a good illustration of what that looks today:Of course, these faults and rock types will be different depending on what cross section you're looking at.I know this isn't a complete description, but I think it's a good starting point. These illustrations came from USGS bulletin 2195, which can be found here. It's an interesting read in and of itself.


Why did the Laki eruption of 1783 produce so much fluorine?

First things first about Laki: it's in Iceland, which means its source is a combination of an ocean ridge and a mantle plume. The plume contribution means that the source composition is relatively undegassed (unlike the source for most mid-ocean-ridge basalts (MORBs)!) and very basic, so contains relatively high concentrations of sulphur and other volatiles.

Secondly, it was actually a pretty high-volume eruption: per Gudmundsson (2011) it has been estimated that it produced 14 km3 of lava - compare with the estimated average global rate of magma emplacement and volcanic output of 26-34km3 per year.

The eruption style during the Laki eruption - not dissimilar to other Icelandic eruptions - is believed to have promoted volatile emissions during the eruption, including liberating up to 50% of F originally dissolved in the melt:

  The high degree of degassing at the vents is attributed to development of a separated two-phase flow in the upper magma conduit, and implies that high-discharge basaltic eruptions such as Laki are able to loft huge quantities of gas to altitudes where the resulting aerosols can reside for months or even 1–2 years.

Thus the significant fluorine release at Laki seems to have been due to a large-volume eruption degassing halogens extremely efficiently, with a relatively high initial fluorine concentration in the melt (~400ppm).


Continental collision as Indian Plate with Eurasia one finish in a merge, but the process is slow. An example of merged plates is Iberian Subplate that is presently considered Eurasian Plate.

The collision creates mountain chains as Himalaya. Presently Indian Plate is a separated system because it has still a big granite root under the mountains. While erosion happens, the new geophysical echillibrium bounces new relief to the chain and the root starts to be sutured. There is stil some decenes of kilometers of granite root under the Himalaya, so the chain is still a plate limit.


Why is the elevation of the Iberian Peninsula so high?

I don't know for sure, but my guess is that at least a part of the high Iberian elevation is due to NNE-SSW compression in northeast Spain, caused by rotation of the Iberian block. That is,the same rotation that opened up the Bay of Biscay deep basin, whilst compressing the Pyrennean mountains. The gentle dip of most of Iberia towards the southwest would fit well with such an explanation.
But then you may ask: 'Why is there a low elevation sedimentary basin just southwest of the Pyrenees?' Check the age of sediments in this trough. I would bet they are pretty recent, and I suspect that there may well be some late-stage counter-rotation caused by the  relative east-west displacement along the Rif-Betic arc.


What's the prospect of air quality forecasting based on machine learning?

While the prospects are more of an economic question, I can answer that there is at least one study using machine learning methods (https://etda.libraries.psu.edu/catalog/13561nvb5011).

There are problems such as the attribution of error to physical processes are not feasible, the spatial extent of the model is very limited, the accuracy of the model is dependent on the history and integrity of the data, etc. Perhaps a hybrid, some sort of Model Output Statistics could be formed, but this would be doubly expensive.


Are there secondary causes of sea level change?

Yes, there are lots of other factors.

Factors affecting sea levels are no different from other natural processes: there is a large number of coupled, non-linear effects, operating on every time scale, and at every length scale, and across many orders of magnitude.

The Wikipedia page Current sea level rise lists many of the known processes. And I wrote a blog post, Scales of sea-level change, a couple of years ago with a long list, mostly drawn from Emery & Aubrey (1991). Here's the table from it:

Reference
Emery, K & D Aubrey (1991). Sea-Levels, Land Levels and Tide Gauges. Springer-Verlag, New York, 237p.


How to calculate 'real-world' geometric height from ERA reanalysis data

If I understood the question right:
CDO can interpolate from model level to height level with the operator

ml2hl infile.nc outfile.nc

additionally, for the lower atmospheric levels, you can add an extrapolation option.
BUT I don't recommend it since its extrapolation performance is questionable.


How isotropic is the Earth's inner core boundary?

Some recent geophysical observations by Dai et al. (2012) (1) showed that compressional seismic waves reflected off the inner core boundary (ICB) exhibit significant variations in:

travel time, of the order of -2 to 2.5 seconds.
amplitude, by up to a factor greater than 4 (up to a factor of 6 oberved by Li et al. 2014 (2)).

These observations, according to Dai et al. (2012) (1) suggest that the ICB is irregular, with possible height differences of up to 14 km, across a distance of 6 km, and 4-8 km over a distance of 2-4 km.

Dai et al. (2012) (1) suggest that these variations are indicative of thermochemical deformation of the ICB. An alternative explanation presented by Li et al. (2014) (2), after numerical analyses of seismic traces, taking into account the effects of shallower structures, suggest that the ICB being a several-kilometre-thick 'mushy' layer indicative of a gradual transition between the inner and outer core.

The actual nature of the ICB is not completely understood, a recent theory by Vamos and Suciu (2014) (3) suggest that the anisotropy of seismic observations could be a result of a de-centred core due to interactions with the flow and the magnetic field inside the outer core.

Observations by Wen (2006) (4) found that seismic traces from the same location taken at different times posessed different return times in the space of ~10 years, suggesting that deformations (as later described by Dai et al (1)) occur on a differentially rotating inner core, alternatively, Wen (4) suggests that the size of the inner core changes with time.

References

(1) Dai et al. 2012, Irregular topography at the Earth’s inner core boundary, PNAS

(2) Li et al. 2014, Notes on the variability of reflected inner core phases, Earthquake Science

(3) Vamos and Suciu 2014, Geophysical implications of a decentered inner core, arXiv.org

(4) Wen 2006, Localized Temporal Change of the Earth's Inner Core Boundary, Science


What is the difference between lunar and earth soil

The single biggest difference is the lack of chemical weathering in lunar soils which are subject to physical weathering almost exclusively. If you exclude biological processes, terrestrial rocks undergo significant weathering from water and atmosphere, which the moon lacks.

For example, both earth and moon contain feldspar-rich rocks, however, clays, the result of chemically altered feldspars, are not found on the moon. Neither are oxidized minerals, as the moon has no oxygen-rich atmosphere to speak of.


How far above sea level can you get on the equator?

I would assume that's the highest point on the equator you talking about, so The highest point on the Equator is at the elevation of 4,690 metres (15,387 ft), at 0°0′0″N 77°59′31″W, found on the southern slopes of Volcán Cayambe [summit 5,790 metres (18,996 ft)] in Ecuador. This is slightly above the snow line and is the only place on the Equator where snow lies on the ground.


Do our continents lay on the mantle because solid silicon dioxide is less dense than its liquid form?

Even if the mantle was pure silica, it wouldn't melt at great depth because of the pressure and paucity of volatiles at that depth (which would act like fluxes, depressing the melting point). So it wouldn't behave like a solid phase floating on a chemically similar liquid phase.

For the most part the crust is not silica but a mix of silica and alumino-silicates of calcium, sodium and potassium, with traces of a whole lot of other stuff. The average specific gravity is about 2.8. On the other hand the mantle is predominantly a mixture of magnesium-iron silicates, with a little calcium, nickel, chromium, etc, and an average specific gravity of about 3.2.  So it is a case of silica-rich (not pure silica) rocks floating on much denser silicates, depleted in aluminium, and relatively depleted on silica. The biggest difference is the high iron content of the mantle.

I suspect confusion arises because many people are not clear about the distinction between quartz silica, which always has a specific gravity of 2.65, and silicates, where the density is highly variable between about 2.0 and 4.7.


What is this strange formation near Râmnicu Vâlcea?

My guess is streams fed by mountains that have been tectonically compressed and is undergoing some rotation. Near Italy are 3 tectonic boundary. Convergent, transform, and divergent. Due to the plate motion of the Eurasian plate, to the African plate, and the Arabian plate, it is causing compression and what I can describe as some rotation the land. It appears to be an involved relationship. I used Google Earth to create this map:

I hope I helped or gave you a direction to look. As you can see by the arrows, there are areas of convergence that are oblique and related in a way, that his geologic feature is not at all impossible.

Other sources

Google search
Earthquakes in Italy


Is the gulf stream both a wind-driven current and part of thermohaline circulation?

Yes.Thermohaline circulation is dependent on differences in water density, caused by differences in temperature and salinity between different bodies of water. It therefore requires deepwater areas, of which the northern and middle Atlantic have the most, for these differences or "gradients" to form. These are influences on the Gulf Stream.

In addition, the Gulf Stream is wind driven, as is true of most currents. So it depends on both influences.


What type of yellow-green stone is this?

I think your mineral specimen is smithsonite based on texture and the dark metallic specks that appear to be galena.


Is the difference in 'Summer tanning' in the Southern Hemisphere related to the Ozone hole or are there other factors?

Tanning is the skin's response due to the dose of UV radiation that the person is exposed to  [Wikipedia].

One major factor for the differences in tanning between the two hemispheres is that the Earth's orbit is not circular - and is at aphelion (furthest distance from the sun) during the Northern Hemisphere summer and is at perihelion (closest distance from the sun) during the Southern Hemisphere summer.  See the diagram below:

Source: NASA

Hence, a greater amount of solar radiation reaches the Earth's surface during the southern hemisphere summer.

As for the ozone 'hole', as can be seen in the image below, it only really affects Antarctica and surrounding oceanic waters to any great extent:

Source: NASA

Taking Australia as an example (as you mentioned it in your question).

According to the Australian Bureau of Meteorology FAQ about ultraviolet radiation:

  Does the Antarctic Ozone Hole ever come over Australia?
  No. The ozone hole has only ever been observed to be well south of the Australian mainland and Tasmania. In fact, during springtime, when the hole is in existence, ozone levels over southern Australian cities are at their highest.

  However, after the ozone hole has broken up parcels of ozone depleted
  air mixed with mid latitude air move northwards. These parcels can
  move over the southern part of Australia and cause a reduction in
  total ozone values.

Australia's SunSmart FAQ about UV radiation sums it up nicely:

  Why does Australia have high levels of UV radiation?

  Australia experiences some of the highest levels of UV radiation in
  the world because we are close to the equator and have a lot of clear
  blue-sky days. The Earth's orbit also takes countries in the southern
  hemisphere (Australia included) closer to the sun in their summertime
  than countries in the northern hemisphere during their summer.


Will Lithium batteries mean we have to exploit Co-Mn-Ni nodules from the seafloor?

No it is not inevitable that the production and continued used of lithium batteries will mean the exploitation of cobalt, manganese and nickel nodules from the sea floor.
Sufficient quantities of these metals are obtained from conventional land based mines.
Nickel
Two types of nickel mineralization are currently mined: sulphides and oxides (laterites).
Sulphide nickel is easier to treat metallurgically than oxide nickels. Once mined nickel sulphides are initially processed using flotation plants. Nickel oxides usually need to be treated in autoclaves (high pressure cookers for minerals) and depending on secondary mineralization the autoclaves use either acid or ammonia.
The top ten nickel producing countries are:

The major laterite producers are: Indonesia, Philippines, New Caledonia, Brazil and Cuba.
The major sulphide producers are: Canada, Australia & Russia.
Australia also has significant reserves of nickel laterites (oxides).
The top nickel mining companies are:

There is plenty of land based nickel available before sea bed nodules need to be mined for nickel.
Manganese
Manganese is the 12th most abundant element in the Earth’s crust. About 18.5 million tonnes of manganese are produced globally annually, from
South Africa   6.2 Mt
Australia      3.0 Mt
China          2.9 Mt
Gabon          1.8 Mt
Brazil         1.0 Mt

There are significant known resources of land based manganese for many years to come.
Cobalt
Cobalt is currently mined by eight countries, with the Congo being the main producer:
Congo           100.0 kt
Russia            6.1 kt
Australia         5.1 kt
Philippines       4.6 kt
Cuba              3.5 kt
Madagascar        3.3 kt
Papua New Guinea  3.1 kt
Canada            3.0 kt

Again, there is sufficient production and resources of land based Cobalt to not require the exploitation of sea bed nodules.


Climate on Venus after it becomes tidally locked

While Venus is not tidally locked to the sun, it rotates slow enough that you might as well consider it tidally locked.
However you have to disentangle the slow rotation from the superrotating atmospheric motion. The fast atmospheric rotation (as reaction of the atmospheric gases to the intense solar radiation) redistributes heat very efficiently in the upper atmosphere.
In the lower atmosphere, no significant winds are observed, but the atmosphere has a large density, which through heat conduction again makes redistribution of heat efficient.
All in all, Venus' atmosphere has therefore a horizontally uniform temperature. Said differently, next to no dayside-nightside temperature gradients exist. Nothing will precipitate.
Furthermore the $CO_2$ at the surface is superfluid due to the intense pressure, and this state doesn't seem to form droplets, it IS a sort of highly-viscous $CO_2 $-ocean.


Does the gravitational pull of the moon affect the composition of Earth's atmosphere?

The atmosphere is continuously mixed by turbulence, so no sorting of its  ordinary components can occur easily and rapidly. Twice a day change, anyway, is far too fast for anything but some tidal effect on pressure and thus on temperature. Ok, these might indirectly slightly modify some thresholds and balance e.g. between states change (water) and some atmospheric chemistry, by a fraction of what day/night change does. I wouldn't call that "change of composition", though.


How many mole of oxygen gas is there in the atmosphere?

It is easier to calculate:

The pressure of air on the ocean level is $\approx 100 \rm {kPa}$.
Thus, its weight is $\approx$ 100000N over $1 \rm m^2$.
Considering that the overwhelming majority of the atmosphere is below some km over the surface of the Earth, we can ignore the decrease of the gravity with height.

Now calculate the mass of the air above a square meter (ten tons). And multiple it with the surface of the Earth (in square meters). Then, divide it with the mean molar mass of air and multiple with the partial pressure of $\ce{O2}$ in it ($\approx$ 29%).


How to calculate specific humidity with relative humidity, temperature, and pressure

It looks like your program is using an approximation based on
$q \approx w = w_s*RH$ with an approximation of Clausius-Clapeyron to find $w_s$.  Looking at a few values of RH,T and P, your approximation is pretty close (+/- 5%) to an analytic answer.  Based on the output you quoted it looks like you are providing incorrect values of RH.  Note in the comments to your routine it says:

@param rh relative humidity (proportion, not %)

This means you need to provide the RH proportion, not the percentage.  E.g. divide by 100 -- RH=1 for 100%, RH=0.5 for 50%, etc.

If you adjust your input data you should be able to use your code as-is.  If you wish to compare it to something, you can reference the solution below.

If you are given $RH$ (in the range [0,1]), $T$ (K) and $p$ (Pa) you can proceed as follows.

Knowing that $$RH = \dfrac{e}{e_s},$$ $$w = \dfrac{e\ R_d}{R_v(p-e)},$$ and $$q = \dfrac{w}{w+1}$$

Then we can solve for specific humidity $q$.

Rather than combining this into a single formula and solving, it is more straightforward to present this incrementally.

First, find $e_s(T)$ where $$e_s(T) = e_{s0}\exp\left[\left(\dfrac{L_v(T)}{R_v}\right)\left(\dfrac{1}{T_0}-\dfrac{1}{T}\right)\right]$$ and then find $e$ from the first formula ($e = RH*e_s$).  Then plug $e$ into the formula for $w$ and then that result into the formula for $q$.

Variables used:

$q$ specific humidity or the mass mixing ratio of water vapor to total air (dimensionless)
$w$ mass mixing ratio of water vapor to dry air (dimensionless)
$e_s(T)$ saturation vapor pressure (Pa)
$e_{s0}$ saturation vapor pressure at $T_0$ (Pa)
$R_d$ specific gas constant for dry air (J kg$^{-1}$ K$^{-1}$)
$R_v$ specific gas constant for water vapor (J kg$^{-1}$ K$^{-1}$)
$p$ pressure (Pa)
$L_v(T)$ specific enthalpy of vaporization (J kg$^{-1}$)
$T$ temperature (K)
$T_0$ reference temperature (typically 273.16 K) (K)


Weather forecast based on pressure, temperature and humidity only (for implementation in Arduino)

Such simple algorithms are empirical and for the same reason very local, so depending on your location they can have very bad performance. In the other hand, some people argue that properly calibrated they can be over 90% accurate.

Most of them are based in the Zambretti algorithm or some variant of it. This algorithm was originally implemented in a forecaster device produced by the firm Negretti and Zambra in the early XX century.

It considers the absolute value of the pressure, the trend of the pressure, the season and the wind direction (although wind direction and season have a small impact in the output). The algorithm is well described and translated to formulas in this article, but in summary it works calculating a tabulated forecast number $Z$ as follows:

From your measured pressure $P$, temperature in Celsius $T$ and the altitude in meters $h$ compute the atmospheric pressure reduced to sea level $P_0$. There are many formulas for this, a common one is:

$P_0=P\left(1-\frac{0.0065 h}{T + 0.0065 h+ 273.15}\right)^{-5.257}$

Compute the pressure trend and

If the pressure is falling compute the forecast number as $Z = 130-\frac{P_0}{81}$
If the pressure is steady compute the forecast number as $Z = 147 -\frac{5 P_0}{376}$
If the pressure is rising compute the forecast number as $Z = 179-\frac{2 P_0}{129}$

Adjust $Z$ for wind direction:

For Northerly winds adjust $Z=Z+1$
For Southerly winds adjust $Z=Z-2$

Adjust $Z$ for the season:

If Winter adjust $Z=Z-1$
If Summer adjust $Z=Z+1$

Look up for the forecast from the following table:

This was made for the UK, and many people have developed modified version to work in other areas. You will find many implementations online with downloadable code, as this one in javascript, or this one in C for Arduino UNO, an explanation of this Arduino UNO implementation can be found here.


What is the difference between radiation balance and the global energy balance?

Radiation balance only account for energy transfers trough electromagnetic radiation. Something very useful for the Earth as a whole. As it is the only (or most important by far) way of energy exchange between the Earth and the outer space.

Energy balance in the other hand, account for energy transfers trough all possible processes, namely radiation, conduction, sensible heat, latent heat, convection, etc. That are very important to account for the energy transfers within the atmosphere and between it and the surface.

In this case your global energy balance includes evaporation and convection (thermals), that are forms of energy exchange not mediated by electromagnetic radiation.


Difference in surface temperature between the Northwest Atlantic and Northeast Atlantic

The main reason is that the Gulf Stream transports warm surface water from the tropics, driven by the thermohaline circulation. The tropical trade winds push surface water towards Western Atlantic and build up stress. Further north the dominant wind direction is towards the east. The Coriolois force also helps to move the warm water masses towards the east.

The Labrador Current, on the other hand, brings cold water down West Atlantic Ocean. The thermohaline turnover is further south in West Atlantic Ocean.


How much of the Earth's heat is caused by the hot centre?

Given the insulating effect of 6370 km of rock (the average radius of the Earth) & its low thermal conductivity, if the temperature at the center of the earth was 18 °C it contribution to warming the atmosphere would be negligible.

The temperature at the center of the Earth is about 7000 °C, while the average temperature of the surface is about 10 °C. So if the temperature at the Earth's center was 18 °C its contribution to the surface temperature would be exceedingly small.


Is the poleward migration of the maximum intensity of cyclones a result of tropical expansion or are there some other contributing factors?

You will find the full text of Jim Kossin's migration paper here.
http://www.ssec.wisc.edu/~kossin/articles/nature13278.pdf
In it he describes his findings only as an empirical observation.  He does state that the migration is consistent with tropical expansion but he does not attribute the migration to the expansion. In fact he does not get into the subject of attribution at all. Perhaps attrbution will be the subject of a future paper. You may wish to check his list of publications from time to time to see if he has written an attribution paper. His (vey impressive) publication list may be found at http://www.ssec.wisc.edu/~kossin/pubs.html


Why is the colour gradient in the sky at sunset on an angle?

Looking at your picture I would say it was most likely not taken facing in the direction of the setting sun, but perpendicular to it. What you see as a colour gradient is most likely the shadow of the Earth. I suspect if you took a series of pictures you'd see the shadow (your gradient) moving upwards and becoming steeper while the sun sets deeper behind the horizon.


Could the current climate change events cause long-term problems in the viability of Earth to sustain life?

There is one scenario in which climate change could render the Earth inhospitable to life in general, which would be a runaway greenhouse effect.  In a runaway greenhouse effect, the Earth would get so hot that the oceans start to evaporate, adding more water vapour (powerful greenhouse gas) to the atmosphere, which will make it hotter yet, until Earth ends up like Venus.
However, the current scientific consensus is that a runaway greenhouse effect as a consequence of anthropogenic global warming is not possible.

Life in general will almost certainly go on, and most consider it unlikely that the survival of humanity itself is at risk as a direct consequence of climate change.  Many other species, however, will likely disappear, as has been widely documented in the scientific literature.  As an example, complicated ecosystems depend on coral reefs, and as things stand, there may not be any coral reefs left by the end or even the middle of the century.  This will be disastrous for significant subpopulations of humanity (I've heard in a talk last week than 400 million people depend on fish supported by ecosystems around coral reefs), but it will not by itself cause the extinction of mankind.


How Good is The Evidence For Snowball Earth?

Paul Hoffman's argument for Snowball Earth

So, first off, I'm just a guy with access to JSTOR and an interest in geology, so perhaps I'm not really qualified to assess "how good" the evidence is. But, I can read through the papers and summarize some stuff for you, which perhaps is sufficient to answer the question.

So, as suggested in the title, serious consideration of the Snowball Earth theory started with a Paul Hoffman paper in 1998, free copy linked here. The evidence in the initial paper is thus:

Inorganic $\delta^{13}$C showed decreases during glacial periods between 750 and 550 Ma that were 'enormous in comparison' with variation seen at other times in the Earth history. This references previous stratigraphic work by Alan Kaufman, a co-author on the paper we are discussing.
Based on a theory by Kirschvink (the geologist who proposed the Snowball Earth theory), an ocean completely sealed by sea ice would quickly become anoxic, leading to chemical reactions that would cause the observed changes in carbon deposition.
New stratigraphic work in the Otavi Group formation in Namibia confirms the drop in inorganic carbon, as well as providing evidence of glaciation on land at a latitude of ~12 S (latitude determined by paleomagnetic data; age determined by radiometry).
The geological evidence suggests that the proportion of organic carbon in total carbon burial drops to "virtually zero" immediately after the glaciation begins.
The paper then presents evidence that a large volcanic event with C)$_2$ levels > 300 times the present could "undo" the Snowball Earth event.

In the conclusion, the authors say that a Snowball Earth explains the evidence from carbon isotope excursions, but no alternative hypothesis does. This is discussed more in detail in Hoffman, et al., 1998a (an article by the same authors, the same year) and Hoffman and Schrag, 2002. Among hypotheses rejected include a period of ocean stagnation and overturn; the Earth having a larger axial title until the end of the Proterozoic, true polar wander, a major bolide impact, deep ocean anoxia and others.

The point I want to make here is that the questions that you ask in the OP don't fit into the original explanation for why there might have been a Snowball Earth episode. It is true, that without accurate fossil dating, radiometric methods can't prove that near-equatorial glaciers occured in multiple places at the same time. But, that isn't really a required proof. Evidence for Snowball Earth is "good" as long as it is the most likely explanation for the observed paleomagnetic, stratigraphic, and carbon isotope data.

That last is the part that I am perhaps not qualified to speak on; you'd have to do a full literature review on both Snowball Earth and alternate theories to determine which has the best evidence supporting it. But, clearly there are many geologists who thing that Snowball Earth is the "best" hypothesis.

Answers to specific questions

Although at the beginning of this period, there were, so far as we know, no advanced invertebrates able to leave easily identifiable fossils, there were by the end of it, so how were they able to thrive and evolve under the ice?

From Kirshvink, et al., 2000,

  Finally, we speculate that the predicted severity of climate and
  geochemical change during the snowball event and its aftermath may
  have forced enormous biological adaptation and left recognizable
  signatures in the phylogenies of extant organisms and their genes.

The extreme geochemical conditions include significant changes oxygen and iron availability. Thought the above article specifically addresses an earlier Snowball Earth episode, the suggestion is that the few organisms that did survive the glaciation had novel geochemical adaptations that allowed them to explode into the much more friendly world environment that existed after glaciation.

Indeed, the Ediacara fauna appeared after the glaciations had passed; from Hofmann, et al., 1990 (not the same Hoffman/Hofmann; also couldn't find a free full copy):

  The Ediacara fauna generally regarded as containing the oldest
  metazoan fossils, has been described from about 25 localities around
  the world; all occurances to date place it above the highest
  Proterozoic tillites of the Varanger glacial epoch.

The Varanger glacial epoch is what is now theorized to be the Cryogenian period, divided into two glaciations, the Sturtian and Marinoan.

So, overall, the explosion of evolution and diversity happened after the glaciation passed, and it happened because radial new biochemical processes had to be evolved to survive in the radically divergent marine chemistry of the frozen ocean.

There must also have been early marine plants under the ice (there were none on land), so how did they survive?

Eukaryotic algae (like red and brown algae) existed before the Cryogenian, and survived until after. There are many mechanisms for them to have survived. Firstly, algae do live on the snow on the terrestrial surface of Antarctica; such "snow algae" could have survived on Snowball Earth.

Secondly, there is no consensus that the surface of the Ocean was uniformly thick. Some modeling, for example from Pollard and Kasting, 2005 indicates that the sea ice was on the order of meters thick in the equatorial regions. In that case, algae could have easily survived on the underside of ice sheets, as it does in the modern arctic and antarctic. A thin, cracking, and periodically melting (under tropical solar radiation) state would be consistent with conditions in the polar regions today, and is quite capable of supporting life.

Couldn't there be other explanations for these apparent glacier tracks, apart from Snowball Earth? For example, Australia may have been closer to the S.Pole then, and some of the locations where evidence of glaciers was found might have been much higher above sea level than they are today.

I haven't done a deep dive, but the latitude of various points of the Earth's surface can be estimated by paleomagnetic data. Note that the many of the alternate explanations (such as increased axial tilt and true polar wander) also include mechanisms for explaining why the magnetic record is wrong (i.e. the magnetic poles were not where we though they were).

However, this is something of an Occam's Razor situation. In order to explain tropical glaciers without Snowball Earth, you have to explain how the Earth was physically rotating on a different axis. While possible, it takes a lot of energy to make the Earth move from one axis of rotation to another. Snowball Earth is a simpler explanation from the energy physics point of view.

As mentioned earlier, there are two links to papers where Hoffman and company dismiss various alternate explanations.


Why is satellite imagery data delivered as signed 16 bit integers?

Because the surface or top-of-the-atmosphere products are not raw data. Atmospheric corrections have been applied to the raw data and those corrections have been done with a precision that can't be properly captured in 8-bit numbers. You can round data outputs to 8-bits, but there would be information loss.
Some bands, like atmospheric opacity can be calculated by the model with high precision, and you need a 16-bit number to store such precise values.
Although the values are stored as 16-bit integers they are floating point numbers, and the scale factor is provided in the same table you mention.

I also think that it have to do with having a coherent data format across all the Landsat derived products, including Landsat 8 that have the OLI sensor with a spectral resolution (or bit depth) of 12-bit, that means that the intensity of each pixel is recorded with a number between 0 and 4095, something that provides much more information than the traditional 8-bit (Used by Landsat 7 and before), were intensity is recorded with values between 0 and 255.
Additional bits give more information and is specially useful to distinguish details in areas with low contrast, like shadows, water or snow fields. For example, all the shades of white in a snow field that corresponded to just one color in Landsat 7, can correspond to 16 different colors in Landsat 8.

Data is distributed in 16-bit files because computers are optimized to deal with 8, 16 or 32 bit numbers, and most software reads images with those bit depths. Therefore, a 12-bit file would not be very compatible, and the smaller standard file that can store all the information of a 12-bit image is a 16-bit data file.

The bands that use 8-bits in the table 6-1 that you mention are quality control bands, that contain information that can be stored in 8 bits without any loss in performance.


Is the Amazon rainforest resistant to fires?

Most fires are probably in the periphery because they are started by humans.

They encroach on the jungle from the outside, where they already live, and there are roads instead of impenetrable jungle.


What ore minerals are likely to be found in a thin section like this? What can we deduce from the structure?

Sulfide ore petrography is reflected light is even harder than transmitted light. Unlike transmitted light, colour is actually a very important characteristic feature. But the perception of colour can vary between different light sources, quality and time since polish, microscope lens, and cameras. Therefore, from an image like that it is extremely challenging to tell what the minerals are.

In my opinion you have two of either chalcopyrite, pyrite, pentlandite, pyrrhotite. It is very hard to tell. My guess would be pyrite (the bright one) and chalcopyrite/pentlandite (the golden one).

In cases like this, as a way to move forward, do one or both of the following:

Have thin sections where you know the identity of the minerals so you can compare with your unknown, on exactly the same analytical conditions.
Get access to an EDS-SEM system. I know it's easier said than done, but nowadays these instruments are extremely common in almost every research institution, and once you're experienced it takes literally minutes to identify the minerals.


How is carbon distributed among the atmosphere, the oceans, the biomass and the unburnt fossil fuels?

1.How much carbon is there on Earth?

Taken as whole, the Earth is estimated to be 730 parts per million carbon by mass.

So $4.4 \times 10^{21} kg$

http://quake.mit.edu/hilstgroup/CoreMantle/EarthCompo.pdf

  How much carbon is there in the atmosphere (in the form of CO2 and CO)?

$3.1 \times 10^{15} kg$ CO2 and insignificant CO, so $8 \times 10^{14}$ kg of C.

  How much carbon is there in the oceans in the form of CO2 and CO?

Carbon of all forms in the the ocean is $4 \times 10^{16} kg$

http://ioc-goos-oopc.org/documents/oosdp/oosdp_br5.pdf

  How much carbon is there currently in the biomass?

$8 \times 10^{14}$ kg (not including soil)

$2 \times 10^{15}$ kg (if soil is included)

  How much carbon is there left in the form of fossil fuels?

$5 \times 10^{15} kg$

http://www.gcrio.org/CONSEQUENCES/vol4no1/carbcycle.html

(This could be an underestimate, depending upon what you consider to be "fossil fuel"; methane clathrates are estimated to hold $10^{16}$ kg of carbon)

  If possible, i would also like to know how this distribution has changed, for example, over the last 100 years (in particular, how much carbon from the fossil fuels has been burnt over the last 100 years).

The amount of carbon in the atmosphere has increased about 30% since pre-industrial times, and the amount in biomass, not including soil, has decreased about 10%.  Amount in the oceans has not changed significantly.


What is the mechanism behind changes in oxidation state (of iron, for example) as magma rises?

My question is a more fundamental one, being, if this equilibrium (#11) governing the changes in oxidation states becomes more prevalent as the pressure decreases rapidly, what are the governing equations for when the magma is deeper in the earth?

My interpretation is that at the volcano being studied, the right side of equation 11 is favored at low pressure, and the left side is favored at high pressure (greater depth).  Deep magma there contains sulfide ($\ce{S^2-}$) in accordance with equation 11, rather than sulfate ($\ce{SO4^2-}$) which would involve equation 12.  So equation 11 applies to all depths being studied and equation 12 does not apply to this volcano at any depth.


What model best describes the alignment of the Sun and Moon during a lunar eclipse?

It's difficult but not impossible to model the Earth, Moon and Sun, but the scale is a bit tricky to get right if you try to build or draw it.

If we call the Moon's diameter = 1 moon unit, then, Earth's diameter is about 4 moon units.   Distance between Earth and Moon, about 110 units, Sun's diameter, about 400 units, and the big one, the Sun's distance to the earth, about 43,000 moon diameter units.

So if the Moon is big enough to see, but still very small, say 1 mm, then the sun needs to be 40 cm in diameter (about 33% larger than a basketball) and 43 meters away.


How much atmoshphere is there compared to land and water

71% of Earth's surface is covered with water and 29% land.

Thinking in that regard, that's saying that on 29% of Earth's "surface" locations you have land below your feet, and in 71% of the locations, you have water.  So to continue in such terms, you'd then ask... ok, what percentage of Earth's surface locations would have air above them!?!  Well that's all of them.  So to if you're comparing it with those percentages, I guess you'd have to say it's another 100%.  Or, if we put them together into a full 3-dimensional surroundings at the surface, well it'd basically be 50% air, 36% water, 14% land.

But to compare how much of each there REALLY is, you need to include depth, getting some sort of 3 dimensional understanding of it.  But the picture that reveals is certainly not the picture we are used to from daily experience.  From the values I was able to find:

In terms of the room each takes up, the volume:

Surface water (oceans+lakes+rivers, glaciers, etc) is 1.4 billion km³
The inside of the Earth is about 1 trillion = 1000 billion km³
For the atmosphere, as mentioned in comments, it's a little more difficult, as the gases only gradually give way to space.  You find less and less gas as you go up, but there's no set spot where there is none, as some tiny amount is always floating off into space.  So where do you draw the line?  A commonly used boundary between the atmosphere and space is the Karman line.  This would lead to a volume of 53 billion km³ (using Earth's radius = 6371 km).  Note that only about half of that is in the troposphere and stratosphere, which are perhaps the familiar zones of the atmosphere where weather and the ozone layer (and 95% of air molecules) reside.

To compare these directly, the volume of land is 20+ times larger than the atmosphere (or 40+ times larger than the troposphere+stratosphere), and 750+ times larger than the Earth's water.

Or as percentages, the volume is:

Land 95.3%
Air 5.6%,
Ocean 0.1%

Another useful way to look at is mass.  In terms of how much mass there is of each (from NASA):

Atmosphere: $5.1\times10^{18}$ kg
Hydrosphere: $1.4\times10^{21}$ kg
Geosphere: $6.0\times10^{24}$ kg

So there is 500+ times more water than air... and 4000+ times more "land" than water.

Or in percents, the mass is:

Land: 99.98%
Water: 0.02%
Air: 0.00008%

You could also look at the comparison in other ways, such as with the number of molecules.  But to save time, the answers will still typically boil down to the same idea: though land is the least of what we see around us on the surface (if you're a true global traveler), it is by far and away the greatest part of our planet overall.

One final visualization that looks interesting is considering if we made giants balls of the air and water at Earth's surface... they'd actually be about the same size...  and nowhere close to the size of Earth (and that's even neglecting the fact that for fair comparison, the Earth, if somehow all of it could be brought to surface conditions, would be even larger due its current internal compression).

As to whether the amount of oxygen is changing, remember no element can be created or destroyed (aside from nuclear processes).  So the only way oxygen can change is if it is tied up in a compound or is removed into the ground or space.  In our lifetimes, there is very insignificant change overall, though it sounds like a notable amount is being used up each day in combustion reactions (see the part about oxygen depletion further down) [oxygen decreases from that, but since carbon dioxide has more mass, the overall atmospheric mass actually increases, just not the stuff you can breathe!].  If you're looking for a much longer history, it appears this Britannica article gives a more thorough discussion of the factors in play and some of the changes that have occurred.

As to the mass of the atmosphere over eons, I naively thought maybe less would be known about that... but articles in Scientific American and Nature both hint the atmosphere was at much different pressures once upon a time (albeit reaching conclusions in opposite directions!)  Such changes in pressure would likely come with large differences in mass and/or volume of the atmosphere as well, but until someone shows me otherwise, those estimates would seem to be quite speculative.

And if we're going that direction, maybe we should just turn to What-If XKCD!


What kind of data is best shown in a rose diagram?

Rose diagrams, also called polar bar plots, are useful for showing azimuthal (directional) data. Any dataset consisting of lots of measurements of direction or orientation could be visualized this way.

A common application in sedimentology is visualizing measured cross-bedding azimuths. This can help work out the palaeocurrent direction (that is, the direction of the prevailing wind or current at the time). This paper by Sengupta and Rao has some examples and some data.

The rose diagram display is also often used by structual geologists, to visualize the measured orientations of folds, faults, or other strain indicators. Here's an example (on page 10 of the PDF) from Twiss & Moores's Structural Geology book.

One way to generate a lot of data yourself would be to find a geological map with lots of faults or dip/strike indicators on it, and then measure their angles (clockwise from N).

I'm not sure which came first, but I suspect the design was originally conceived for wind data.


Are these plane trails seen from satellite

Under the right conditions (in a basic sense, locally high relative humidity; see also this discussion on this site regarding contrail formation), the clouds initially formed by contrails may persist for hours and spread outwards to form larger areas of cirrus cloud. Additionally, NASA's Contrail Education Project website has some specific examples here showing the evolution of contrails and associated clouds over the course of a day, with extremely similar visual properties to those shown in the question. They also provide some discussion describing how large these clouds must be compared to what a typical weather satellite "sees":

  In order to be seen, a contrail must be wide enough (and long enough) to change the brightness of a satellite pixel. Each pixel covers a portion of the Earth. The size of that area is determined by the resolution of the satellite instrument. Typical weather satellites, such as you see on the news, have pixels that might be 8 km, 4 km, or 1 km on a side. To show up in such an image, a contrail must be nearly 1 km wide!

In other words, yes, they are contrails (or more accurately, persistent clouds originating from contrails) as observed by satellite.


The sea floor has been mapped using sonar from ships as shown here, and radar. But the fact was first discovered long before these technologies existed by sailors who got stuck in the ice. The entire ice sheet is floating and spinning at a relatively high rate of speed. When they got stuck, they could see, from the stars, that they were moving. I cannot find it now, but I remember reading on project gutenburg a terrifying historic first hand account of being stuck up there, and seeing that they were moving away from Europe and civilization and could not move their ship.


What physical measurement / elevation is used to define Earth's radius?

Originally, the concept of a reference ellipsoid was an ellipsoid that best approximated mean sea level. This concept predates satellite-based geodesy by hundreds of years. There are now better ellipsoids in terms of providing a better fit to mean sea level than the WGS84 ellipsoid. Yet the WGS84 ellipsoid is used worldwide (including the ridiculously over-precise flattening value).

The WGS84 reference ellipsoid is now just that, a reference ellipsoid (that is, it's the ellipsoid used as a reference by GPS and related systems). In 1993 the WGS84 governing committee voted, with one exception, to retain the 1984 defining values, despite improvements to those defining values. The one exception: The flattening in the original definition of WGS84 was a calculated value, based on the Earth's second dynamic form factor as determined from satellite orbits ($\bar C_{2,0}$ in WGS84, $J_2$ in GRS80). This calculated value became a defining value in 1993. The reason for keeping those older values was GPS. It's better to have a reference ellipsoid that is constant over time than it is to have an ever improving best fit ellipsoid.

Besides, not all of the changes in the best fit ellipsoid represent a reduction in measurement errors. The best fit ellipsoid truly does change over time as the Earth continues to recover from the last glaciation and as the Earth's rotation rate slows down. There are very few applications where a best fit ellipsoid truly is needed while there are many applications where a constant reference ellipsoid is the "best fit".


How and when was the $\mathsf{CO_2}$ scrubbed when Earth was still primordial?

As you probably realise, the Earth's early atmosphere was mainly composed of CO2, as are the atmospheres of Mars and Venus to this very day. You are right in thinking that most of this CO2 was removed by biological activity; if all the earth's fossil fuels and limestone rocks were converted back into CO2, we would have an atmosphere similar to that which existed nearly 4 billion years ago. It was this same biological activity which built up the oxygen level to its present 21 percent. The process continues right up to the present day. The CO2 content of the atmosphere is to some extent self regulating: the higher the levels, the more vigorously plants and photosynthetic micro-organisms grow, extracting more and more carbon dioxide from the atmosphere, but this natural process could be swamped if the build-up of CO2 exceeded the capacity of plants to remove it. It is not generally known that algae and phytoplankton in the sea remove more CO2 and generate more oxygen than all the rainforests.


Are we consuming more oxygen than the world is producing due to fossil fuels?

Yes, atmospheric oxygen is being depleted by fossil fuel burning.
From https://cdiac.ess-dive.lbl.gov/trends/oxygen/modern_records.html -

Oxygen concentrations are currently declining at roughly 19 per meg
per year, or about 4 ppm per year. One "per meg" indicates one
molecule out of 1,000,000 oxygen molecules, or roughly one molecule in
4.8 million molecules of air.

And -

fossil fuel burning is depleting atmospheric oxygen at a rate of almost 1000 tons per second. There are about 32 million seconds in a
year, so that somewhere around 30 billion tons of O2 are being
converted to CO2 annually.

Because the quantities of O2 are very large the reduction is small in comparison. From same source -

There are about 1,200,000 billion metric tons of O2 in the atmosphere,
so we can keep burning fossil fuels at the present rate for 40,000
years before we run out of oxygen. By then, all of the world's fossil
fuel supply will have long since been exhausted.


Is the Arctic sea ice disappearing in a linear or non-linear way?

The box in the lower left of the bottom chart is key to understanding what is presented. Five attempts of a line of best fit have been presented. From the chart, the linear fit (yellow line) is the least best fit, so the loss of Arctic ice not a linear relationship. The other lines are different modeling scenarios the author has attempted.

When testing for lines of best fit, one is trying to find a mathematical equation that will neatly describe something - in this case Arctic ice loss over time.

The other four lines of best fit that were considered were: the exponential curve, Gompertz fit, logarithmic fit and a second order polynomial fit. Visual examination of these curves shows they are very close in describing the data and are close to each other.

The important thing to consider in such curve fits is the value of R2, sometime denoted as r2. A value of 1 means a perfect fit and a value of zero means absolutely not fit.

All four curved lines have a fit greater or equal to 0.902. That is a good result.

The Gompertz fit has an R2 of 0.917 which is the highest value of the options presented. It means that for the data analyzed and evaluated in this study the Gompertz fit is the one that best describes the data. However, given the closeness of R2 values, the other options also give good results, but not as good as the Gompertz fit.


Is it possible to have a busier tropical storm season in the eastern Pacific basin than in the western Pacific basin?

There are many determinants of tropical storms. The most important is to have sea surface temperatures of >27 deg C. Obviously, this will increase in extent, though not necessarily in frequency, with global warming, and increased incidence of El-Nino events. Shallow sea, as in the western Pacific, warms up faster than deep sea, as in the eastern Pacific. Hence there are always likely to be more tropical storms in the west Pacific.
The second determinant is for the air mass to have a 'start-up' rotation, which is a function of latitude. That is, almost no tropical storms at the equator, but many in the tropics, as air masses pick up Coriolis rotation.


How to identify a predator's coprolite from an herbivore's?

If it is a predator's coprolite you should expect to see bone fragments. Coprolites from herbivores? I would expect them to be pretty rare as there is almost nothing likely to fossilize.
As for meteorites, they come in many forms: stones, irons, palasites, chondrites. The candidates need a good description. A weathered heat ablation surface is the most obvious characteristic to look for. In all cases the rock identification is best achieved with a polarizing microscope, unless it is something very obvious like an iron meteorite.


When metamorphic rocks undergo pressure, how are they changed?

Metamorphic rocks are formed when a rock (sedimentary, igneous or a previous metamorphic rock) comes under high pressure and/or temperature. Pressure and temperature forces the atoms to form new minerals and thereby a new kind of rock. It's not necessary fragmented, but the rock rather morph through recrystallization into a new state in response to the pressure and temperature as the material reorganize.

Recrystallization doesn't remove any material, it's only a physical reorganization to compact the rock. If some change of the chemical composition occurs, it's called metasomatism. In metasomatism atoms are actually moved from one part of the rock or formation, often with water involved.

A good petrologist can usually determine what kind of parent rock, protolith, that have been metamorphosed and to what degree, but sometimes it can be difficult do recognize the difference. At lower degrees of metamorphism, features of the original rock is preserved. E.g. you can see ripples and even fossils in slates or deformed structures from the source rock, but at higher degrees of metamorpism it's increasingly difficult to imagine how the parent material looked like. Gneiss formed from sandstone and granite can look very similar as the lihology represents the conditions of metamorphism, not the protolith.

It can also be difficult to recognize a metamorphic rock. A weathered slate and shale or even granite and gneiss can appear very similar in the field. However, the processes to form the rocks are different and with a closer look at the minerals it can be possible to understand what kind of process that formed the rock.

    (1, Blueschist facies
    2, Eclogite facies
    3, Prehnite-pumpellyite-facies
    4, Greenschist facies
    5, Amphibolite-facies
    6, Granulite facies
    7, Zeolite facies
    8, Albite-epidote-hornfels facies
    9, Hornblende-hornfels facies
    10, Pyroxene-hornfels facies
    11, Sanidinite facies)

The temperature and pressure determine what metamorphic rock you get, but the chemical composition is inherited from the protolith. Degrees of metamorphism are called metamorphic facies. This diagram shows at what depth and temperature a particular rock is formed.

Igneous rocks are formed when a melt hardens to crystals and sedimentary rocks are formed from sediments. All rocks weather if exposed to water and air, and weathered material is transported by rivers to oceans where sandstone can be formed from the sand at the beach and shale from the finer sediments further away from the coast. Igneous rocks can be formed as hot magma intrudes the crust and slowly cools down and minerals are formed or form lava at volcanoes. This is known as the rock cycle and is one of the fundamental, but complicated, concepts in geology. You can read more about the rock cycle e.g. here to learn more about rock types and how they are formed.


Why is the lithostatic pressure gradient 1 psi/ft? How is it derived from density?

Lithostatic pressure might be roughly 23 kPa/m (about 1 psi/ft) in young basins dominated by siliciclastic rocks, but it varies substantially. Pressure has a linear relationship to density. Let's explore the relationship, and the variance.

First some definitions:

Lithostatic pressure — vertical pressure due to the weight of rock and fluid.
Hydrostatic pressure — vertical pressure due to the weight of fluid only.
Fracture pressure — the pressure at which the rock fractures.
Pore pressure — the pressure in the pores of a rock; usually close to hydrostatic.

There's a lot of jargon in this field — lithostatic pressure is sometimes called confining pressure, overburden pressure, vertical stress, total stress, and various other things. I hadn't heard of geostatic pressure before, and a quick bit of research revealed that some people call the pressure due to rock and fluid 'lithostatic' and some call it 'geostatic', reserving 'lithostatic' for the pressure due to the dry rock only. In my experience, it doesn't pay to be pedantic about these inconsistencies, all you can do is spell out what you mean.

We'll do a quick derivation (there's a more comprehensive one here). Pressure $P$ is force $F$ per unit area, and Newton told us that $F = ma$, where $m$ is mass and $a$ is acceleration. Since we're interested in vertical pressure, acceleration is due to gravity so we can use $g$. We know the mass of a rock normalized to volume as density $\rho$, and we're interested in a depth $d$, so:

$$P = \rho d g$$

The units are $[\mathrm{kg/m}^3] \times [\mathrm{m}] \times [\mathrm{m/s}^2]$ or newtons per square metre, N/m$^2$, which we call pascals, Pa, for convenience (10 kPa is 1.45 psi). Note that in the real world density varies with depth, so you'll need to integrate.

Because the pressure increases roughly linearly with depth, it's often convenient to talk about the pressure gradient, which is usually expressed in units of kPa/m, and of course is just the gradient of a line on a pressure–depth plot, like in the example below from a fictional offshore well.

So where does 23 kPa/m come from? If we take an approximate average density of sedimentary rock as 2300 kg/m$^3$, then $P = 2300 \times g$ Pa/m, or about 23 kPa (we often round $g$ to 10). Different mineralogies, different porosities, different fluids — all these will change the lithostatic pressure gradient.