WRF output grid is smaller than input definition

Your model grid is an Arakawa C grid:

Image from Skamarock et al. A description of the Advanced Research WRF Version 3

It appears the geogrid grid generation uses the 25x25 as the furthest extents of the grid (and this is backed up by the grid maximum needing to be a multiple of the grid ratio +1).  As a result, only the u and v variables will see 25 grid points and each only in one direction, east/west and north/south respectively.  All other variables are located horizontally on the $\theta$, or scalar points in the middle of the grid boxes and there will only be 24 of these points in your setup leaving most of your grids having a horizontal dimensions of 24x24.


How did these dark lenticular features form? (Near Hoganekkal Falls India.)

It's hard to tell (don't you have other photos?), but it looks like magma lenses.

The area is known for the Hogenakkal Carbonatite Complex, where lenses of carbonatite (a carbonate-rich magma) are found in pyroxenite dykes. See for instance this paper:

  The carbonatites form a series of discontinuous bodies within two nearly parallel NNE-SSW trending pyroxenite dykes intruding Precambrian chamockites. [...] Each carbonatite body consists of discrete veins and lenses emplaced in pyroxenite which has been permeated and soaked to various degrees by the carbonatites.

But it is hard to say if this is the geological formation that you saw without more information.


How did a tropical storm starting with "D" end up next to a typhoon starting with "T"?

The naming of typhoons, in the north west pacific region, is different to that used by other parts of the world. According to accuweather,

  For typhoons, there is one list with 140 names submitted from nations in the region such as China, Japan, Vietnam and Cambodia. There is no restrictions to how many can be used in a calendar year.

  “Unlike hurricanes, lists are not year-specific, so they scroll through the whole list irrespective of calendar

  The Philippines are also a part of the list of nations which submit names. However, according to the Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA), they will use local names whenever a cyclone is within the Philippine Area of Responsibility (PAR).

NOAA has a list of the names for the north west pacific region. At the end of the webpage, in column V of the last table you will see Talim followed by Doksuri, then Khanun. This is why you are seeing Tropical Storm Doksuri just after Tropical Storm Talim.

It appears that Doksuri, which means eagle, Korean, is the replacement name for Nabi. South Korea submitted the name Nabli to the list of typhoon names, but the name Nabi was retired when Typhoon Nabi hit Japan in 2005.

Tropical Storm Doksuri (2017) was initially named Maring by the Philippine authorities.


What visual wave behaviour help to tell if a tide is going in or out?

As SimonW points out strong tidal currents will modify the wave shape and significant height.  The Wolf & Prandle (1999) study provides a neat summary description of the effects of currents (of any kind) on waves:

  (i) Wave generation by wind—the effective wind is that relative to the surface current, and the wave age (cp/U*) and effective surface roughness may be important, e.g., Janssen (1989). Here cp is the wave phase speed and U* is the friction velocity of the wind. The effective fetch also changes in the presence of a current.

  (ii) Wave propagation—the effects of depth refraction are easy to spot, turning the mean wave direction towards shore-normal. Current refraction has a more subtle effect, dependent on the spatial variation of currents, whether decreasing or increasing towards the coast. Generally shoaling depths will increase the tidal amplitude towards the coast until friction reverses this trend. The waves will tend to turn towards the direction of the current axis.

  (iii) Doppler shift—the effect of a steady current on intrinsic (relative) wave frequency. Waves of the same apparent (absolute) period will have a longer intrinsic period in a favourable (following) current and a shorter intrinsic period in an opposing current.

  (iv) Steepening of waves on an opposing current (related to (iii)), due to shorter wavelength and increased wave height from wave action conservation.

  (v) Modulation of absolute frequency by unsteady currents and modulation of intrinsic frequency by propagation over spatial gradients of current. If the current is steady the absolute frequency should be constant, if the current is homogeneous the intrinsic frequency should be constant. If both intrinsic and absolute period show a tidal modulation, the currents must be effectively inhomogeneous and unsteady.

  (vi) Wave–current bottom stress. Various empirical theories for wave–current interaction in the bottom boundary layer suggest that the friction coefficient experienced by waves in a current regime will be larger than in no current. This also applies to the effective current friction factor in the presence of waves.

  (vii) Effect of vertical current shear on wave breaking. Wind-driven surge currents would be relevant to this, the tidal currents have no surface shear.

I think the most "observable" of this effects from a "brief rainy day observation" will be their #4 effect. The steepening of waves as they oppose the current can be observed relatively easily. Care must be taken though when interpreting item #4: In steady (constant in time) and homogeneous (constant in space) current, the wavenumber remains unchanged, only the apparent (absolute) frequency and phase speed change:

$$
\omega = \sigma + \mathbf{k}\cdot\mathbf{U}\\
$$

$$
C_p = C_{p0} + U
$$

where $\omega$ and $\sigma$ are the apparent and intrinsic frequencies, respectively, $k$ is the directional wavenumber vector and $U$ is the current vector. $C_{p}$ and $C_{p0}$ are apparent and intrinsic phase speeds, respectively. Due to the conservation of wave crests that says:

$$
\dfrac{\partial k}{\partial t} + \dfrac{\partial\omega}{\partial x} = 0
$$

wavenumber, and thus the steepness of the wave can change only in unsteady or non-homogeneous current field, in absence of other effects.

However, visually, steepness is not the only property of the waves that can reveal strong underlying current. For example, in absence of swell and in presence of strong Eulerian currents and light intermittent wind, small wind-generated ripples can be observed to form on the surface. These waves are almost capillary, very short and low, and propagating slowly. The direction of their propagation can be identified visually because the front face of the wave is steeper than the rear. In presence of strong Eulerian flow against the direction of wind, the whole patch of these short waves can be observed to move backward, rather than forward, thus revealing the direction of the underlying current.

In a similar but different effect, underlying Eulerian flow can be identified in a situation where the current increases to the point where it equals the opposing group velocity of the waves. Since the wave energy is advected with group velocity, they cannot propagate beyond this point, and usually a line the divides the two regimes can be seen: one side with smooth surface without waves, and the other where waves are present, propagating toward the line but steepening and whitecapping when reaching the line. This physical process is known as wave blocking.

Another classic example is the mouth of the Columbia River, where the waves during ebb tide become so steep they often break along the Columbia River Bar. During strong ebb tides, large ocean waves, especially swells, become larger, steeper, and also they come closer together. The resulting dangerous conditions change rapidly as the tide turns to flood with waves being smaller and less steep.

.

One study that looked at the effect on wave height is Gemmrich & Garrett (2012). The attached figure from their paper 2 shows how the significant wave height is affected (modulated) by the normalized tidal speed. Larger waves occur during times of larger tidal currents. . The theoretical considerations can be found in Tolman (1990) where a thorough explanation of the changes in surface wave amplitude, direction, and frequency caused by currents. Other studies looking at wave height modulation include Thornton & Kim (2012) and Wolf & Prandle (1999).


What exactly are singular biomes as units?

I guess it depends on which biome classification you use (there are several), but yes, usually tropical forests of Amazonia, Africa & Asia are classified within the same biome. For instance if you take the WWF classification made by Olson et al. (2001), which has 14 terrestrial biomes, they all fall in the "Tropical and subtropical moist broadleaf forests" biome, in green in their figure 1:

The ecoregions are categorized within 14 biomes and eight biogeographic realms to facilitate representation analyses.

It means they share some global characteristics in terms of climate, vegetation... (described here), but they also have some differences. To see these differences, you have to go to a lower level than biomes: ecoregions. The same study divided the world into 867 ecoregions, that are mostly based on the distribution of species.


How much of the ice on earth is floating?

A first-order estimate is about 5%.

This is a trickier question than it first appears because of ice shelves. Quoting from Kusky (2014):

  Ice shelves form where ice sheets move over ocean waters and form a thick sheet of ice floating on the water and attached to the land on one, two, or three sides. Their seaward sides are typically marked by a steep cliff up to 1500 ft (500 m) high, where many glaciers calve off from forming icebergs.

So they are floating, and they can be up to 2000 m thick, according to antacticglaciers.org. So they definitely make a substantial contribution to the world's sea ice fraction.

Continuing with Kusky:

  Ice shelves are found in Antarctica, Greenland, and along the polar seacoasts of the Canadian Arctic Islands. The largest ice shelves are contained in Antarctica, which contains 91% of the world's glacial ice, around 7% of which is contained in ice shelves. These ice shelves cover 50% of the coast of Antarctica, forming an area 1/10th the size of the continent.

If you don't take ice shelves into account, and only think about pack ice, you end up with about 0%, because pack ice is generally thinner than about 4 m, and so makes up a tiny fraction of global ice volume, in spite of its extensive area.

But if you do account for ice shelves, especially the southern ones, the answer must be much greater. I have not done the research to find the numbers, but the text I quoted suggests something less than 7%, so I'm going with 5% as a first-order, round-number guess.

Reference

Kusky, T M (2014), Encyclopedia of Earth Science, New York Academy of Sciences, 529 pp. In Google Books.


What was the Earth's continent's positions 10000 years ago, or 11700 years ago, AKA when the late Pleistocene epoch was coming to an end?

The reason that you have not seen any diagram showing the position of the continents 10K years before present (ybp) is that the plates move so slowly that there would not be a perceptual difference on the scale of a world map. The Atlantic is spreading about a half centimeter per year. So 10,000 years will have moved Europe away from North America by 5000 cm, or 50 meters.

An additional reason is that most models of continental drift have the sub-oceanic magnetic banding due to geomagnetic reversals as their guide for "recent" positions of the plates.  The latest geomagnetic reversal, the Brunhes–Matuyama reversal, occurred 780K ybp.  This is long before your 10K ybp point of interest and so any interpolated data would be suspect.


Here is an excellent explanation of the math as related the stresses represented by the Moh'r circle.

http://www.geology.sdsu.edu/visualstructure/vss/htm_hlp/mor_cir.htm


Timeline of Himalayas/Tibetan plateau formation

Drying out of North Africa is likely the result of something far more local. I've never heard of the either the Tibetan Plateau or the growing Himalaya as causing changes to Africa's monsoons and always understood the connection between Milankovich cycles and the consequences of glaciation. According to this study, which modelled weather patterns of the time:

Aridification of the Sahara desert caused by Tethys Sea shrinkage during the Late Miocene

The drying of Africa started much earlier and was likely related to orbital cycles of glaciation-induced drying of the Mediterranean region.

  Through a set of experiments, we demonstrate that the African summer monsoon was drastically weakened by Tethys Sea shrinkage, allowing arid, desert conditions to expand across north Africa. Not only did the Tethys shrinkage alter the mean climate of the region, it also enhanced the sensitivity of the African monsoon to orbital forcing, which subsequently became the major driver of Sahara extent fluctuations.


Should RTM amplitudes (pre- and post-stack) be related to rock physics properties?

It depends on the implementation, but bare-bones reverse time migration is usually not amplitude friendly.

The problem is that the ideal imaging condition — deconvolution — is difficult to apply or unstable in the time domain. So cross-correlation is used instead, and this loses the relative amplitude information... so amplitudes are no longer necessarily related to reflection coefficients. Since this is the assumption of inversion (e.g. AVO inversion), an RTM volume could give spurious results.

Several vendors have devised ways to compensate for this. For example, Zhang & Sun (2009; First Break, vol 26) described one of CGG's methods. Zhang et al. have written more recently (2013; EAGE London) about how this processing has evolved. Cogan et al (2011; SEG Annual Meeting) have written about Schlumberger's normalization algorithms, which aim to achieve the same goal.

Those papers also contain nice explanations of why RTM is not ordinarily amplitude friendly.

My advice is to talk at length to your vendor about the processing applied, and the attention paid to phase and amplitude. Ask lots of questions. Most processors (generalizing horribly) are either over-enthusiatic about treatments, especially new and/or proprietary ones, or ignorant of your needs as an interpreter–analyst. So if you're actually in the middle of processing now, test everything, ideally against geological data (like a synthetic).

Lots of processing steps can hurt amplitudes, and inversion can work in surprisingly poor data... so assume nothing, and never give up!


We define rain events in terms of the probability of reccurrence. For example, we call a certain rainfall the "10-year rain event," meaning that this amount of rain would only be expected to occur once every 10 years. We usually like to have at least 30 years of data before calculating recurrence intervals.

Note: Just because we call something the 100-year storm event does not mean that it will only occur every 100 years.  Sometimes they occur much more frequently.  Sort of like winning the lottery twice in a row when the odds of winning at all are quite low.  Unlikely, but possible.

The 100-year storm also changes with the available data.  If we were to have several "100-year storm events" in the span of 10 years, we might need to go back and determine a new 100-year event that takes recent data into account.  This is especially important with respect to climate change.  In Boston, the 100-year flood event is projected to occur every 2-4 years by 2050 or so.  Obviously we then need to go back and calculate what a new 100-year event is.

USGS Q&A on flooding

NE Aquarium Climate Change page


Permeability of well screen as a limitation to a slug-in test

High permeability (K) values for rock /sediment would be 1x10+2 to 1x10+5 (darcy)
The table below shows permeability values for sand/gravel packs placed around the well screen.  Well Screen itself would have even higher K values.

I would say, that well screen itself (not including the sand and gravel pack around the well screen) will not limit the results of slut test results.

Essentially, for the well screen to limit slug test results, you need to place the well into a large cave or min void and the use a very large slug volume if you hope to measure the screen itself.

Note: Permeability values can approach very large values in limestone with caves.

Note: my answer assumes that the well construction materials and methods are known that were used to install the well being tested.  I am also assuming the well has a manufactured well screen not a piece of pipe with 3 hack saw cuts to allow water to flow. Not knowing the well configuration, can reduce the accuracy of slug test results.

Source: Petrowiki


Why are the Great Lakes not considered a sea?

"Sea" versus "lake" versus "just part of the ocean" is a bit fuzzy, but there are two things that are universal about seas:

They are saline.
They are either endorheic or have a sea-level (tidally-influenced) connection to the ocean.

Now, let's see how the Great Lakes look under these criteria.

Saline?  No, salinity is 0, give or take measurement error.  Even the Baltic Sea, the least-salty of the generally-recognized seas, is far more saline, at 0.5%.
Endorheic?  No, they're connected to the ocean by way of the Saint Lawrence River, and have been for at least 10,000 years.
Sea-level connection?  No, the Saint Lawrence River has about 500 km of non-tidal flow below the outlet of Lake Ontario, over which it descends 75 meters.

Score: 0 out of 3.  Not surprising that the Great Lakes are considered lakes, not seas.


Is it normal for a cyclonic storm to form at the latitude of New York, USA?

A cyclone is nothing more than a low-pressure system. It can surely form in the North Atlantic; in fact, most low-pressure systems that reach Europe form in the North Atlantic.
You are probably thinking about a tropical cyclone, which indeed cannot form that far north. Among others, a tropical cyclone needs high sea temperatures (>27 C), which are usually not present at such high latitudes.

About the present cyclone south of Nova Scotia: I think it is a cold core cyclone, as 500 hPa temperature are lower than in surroundings (which is e.g. not the case for tropical storm Dorian, which is currently east from the Lesser Antilles). Therefore, it's not a tropical cyclone but an ordinary extra-tropical cyclone, which can perfectly form at those latitudes.


Has Earth's geological activity calmed down in the past 250 million years?

The large-scale volcanic eruptions you mention are called Large Igneous Provinces (LIPs) and are probably linked to mantle plumes. They have been investigated for quite some time now. Ernst & Buchan (2001) built a database of 300+ LIPs and used it to analyse their temporal distribution, among other things. Here is the age spectrum they obtained:

... ‘well-established’ and ‘probable’ plume head events occur
throughout the geological record since at least 3500 Ma, and probably
since 3800 Ma, with no plume-free intervals greater than about 200 Myr
since 3500 Ma. Plume head arrival does not follow any obvious
periodicity...

If you look at the cumulative frequency diagram, there seems to be a increase in event frequency over the last 150 Ma:

There are periods when plume activity appears to be more intense than
at other times. These intervals are identified by steeper slopes on a
cumulative plot of LIP frequency. The most prominent are at
2800–2700, 2200–1800, 150–0 Ma and more speculatively at 1300–1100 Ma.

But as the authors explain, this is a bias due to the fact that the recent record preserves both oceanic and continental LIPs. However, the oceanic crust is consistently recycled (it's nowhere older than ~200 Ma), thus older events are continental LIPs only. If corrected to include only continental LIPs in the recent (< 150 Ma) record, the trend seems "normal" (dotted line).


How stable is the Gulf Stream? Could it stop suddenly?

There's a pretty good rundown of this issue over at RealClimate, and a wikipedia article dedicated to the topic.

A summary of the main points from there:

The Gulf Stream is part of the Meridional Overturning Current (global ocean conveyor), which is primarily wind-driven, and secondarily thermohaline-driven. The Gulf Stream itself is also primarily wind-driven.
There has been some reduction of the thermohaline drivers in the north Atlantic, due to increased temperatures, and influxes of fresh water, largely from melting of the Siberian permafrost. This part of the system does fluctuate (as do most parts), but there does appear to be a trend.
These changes are not enough threaten the Gulf Stream, and there hasn't really been any observations of an over-all slow down that couldn't be otherwise explained by natural variation.
It is likely that the Gulf Stream will slow down over the next few centuries (slow downs appear in some of the IPCC models out to 2100).
A complete shut-down is possible (it has happened before, notably during the Younger Dryas), but it is hard to predict, as causes are not very well understood. But it seems unlikely to happen any time soon.


Why is the Atlantic Hurricane Season defined as being between June 1 and November 30?

The hurricane season is set by the National Hurricane Center.  They use statistics to determine the dates.  Specifically:

  The Atlantic hurricane season is officially from 1 June to 30 November. There is nothing magical in these dates, and hurricanes have occurred outside of these six months, but these dates were selected to encompass over 97% of tropical activity.  June 1st has been the traditional start of the Atlantic hurricane season for decades. However, the end date has been slowly shifted outward, from October 31st to November 15th until its current date of November 30th

  NHC

As for why the dates are spreading out (from October to November), it appears that the dates of the hurricanes themselves are spreading out. (per James P. Kossin [1])

So, the dates are getting wider because the hurricanes are spreading out throughout the season.  So, the NHC widens the dates throughout the years to correctly cover the majority of the hurricanes.

[1] James P. Kossin - Is the North Atlantic hurricane season getting longer? GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L23705, doi:10.1029/2008GL036012, 2008
James P. Kossin


What was the highest temperature ever recorded on the surface of Earth?

The record the article is referring about seems to be the same as registered at Guiness World Records:

  On 13 September 2012 the World Meteorological Organisation
  disqualified the record for the highest recorded temperature, exactly
  90 years after it had been established at El Azizia, Libya, with a
  measurement of 58°C. The official highest recorded temperature is now
  56.7°C (134°F), which was measured on 10 July 1913 at Greenland Ranch, Death Valley, California, USA.

Those records are usually well researched, and in this case it matches what is reported by the WMO. Since 2007, the WMO Commission for Climatology (CCl) has maintained the Archive of World Weather and Climate Extremes. In that archive, the same record is reported as the current highest temperature ever recorded:

More details about the record are described here.
The official WMO press release about the invalidation of the 1922 El Azizia record can be found here.

It is surprising however, that with most the hottest years on record happening in the last few decades, the maximum recorded temperature is still from 1913.

Some people have questioned the reliability of those old measurements. More recent and much more reliable measurements seem to top-up at about 54.0°C as pointed out by a very interesting article brought up by @Plutor in the comments.

Note that you are mixing temperature and heat index in your question. Make sure you understand the difference.

PS: "Greenland" Ranch... a rather sarcastic name for such a place.

Photograph of old Greenland Ranch Station, California, USA (source)


Why is the ocean paleotemperature trend downwards?

I recommend you read the original paper Lear et al. (2000). In it they explain that the results are controlled by processes in polar regions and likely associated with the polar surface temperature. The surface temperature will vary considerable depending on the proximity and extend of the deep water formation areas. As these areas are fairly local, relatively small changes in the location and extend of deep water formation can result in deep water temperature being altered. The uncertainty associated with using single cores to estimate global temperatures is thus quite large. What the authors suggest is a predominantly ice-free world during most of the Paleocene and Cretaceous periods and several ice-sheet expansion events during the Oligocene, Miocene and Pleistocene. If there is no ice, the polar and sub-polar deep-water formation is limited and the water temperatures in the deeper part of the ocean is much warmer.

The temperature record shows a general cooling trend for the past 50 My, but its resolution is too low to define abrupt temperature extremes. Assuming that the process of deep water formation at high latitudes prevailed throughout the past 50 My, these deep-ocean temperatures can be inferred to represent polar surface temperatures (1). The temperature trend (Fig. 1C) appears to comprise four main cooling phases separated by periods of more stable temperatures. These cooling phases occur during the early Middle Eocene, the Late Eocene through Early Oligocene, the late Middle Miocene, and the Plio-Pleistocene.
Alternative evidence supports the existence of these principal cooling phases. A sharp cooling in the early Middle Eocene has been invoked to explain the abundance of siliceous sediments of this age (20). The Early Eocene warm climate is thought to have promoted in- tense chemical weathering of siliceous rocks at
high latitudes, which resulted in high concentrations of dissolved silica in the oceans. The subsequent cooling stimulated upwelling of nutrient-rich water and intense biosilicification. The cooling over the Late Eocene through Ear- ly Oligocene is coincident with the transition from “Paleogene” to “transitional” benthic foraminiferal faunas and high extinction rates in planktonic and terrestrial faunas. The initiation of this deep water cooling also coincides with a reduction in the extent of tropical rainforests on land (21, 22). The cooling in the late Middle Miocene is marked by a narrowing of tropical and warm subtropical biotic provinces in terrestrial and marine environments (23). Warmwater diatom assemblages were replaced by cold-water species at this time (24). The Plio-Pleistocene cooling is not represented by an extinction phase in benthic foraminiferal faunas; instead, faunal groups adapted to the changing bottom water conditions by migration (21).

When you use data from other regions, you get a much different result. For instance, Elderfield & Ganssen (2000) showed how different the temperature changes can be for different species and locations.
Their data are much more recent and suggest an increase in temperature over the last 20,000 years. As always, everything depends on the temporal scales. One issue that tends to be true is that estimates for periods long time ago tend to have larger uncertainties.


There are indeed a lot of positive feedback mechanisms, i.e. a warm climate leads to a warmer climate. From this Wikipedia article, they are:

Carbon cycle feedbacks
Cloud feedback
Gas release
Ice-albedo feedback
Water vapor feedback

However, there are also a few negative feedbacks (same source):

Blackbody radiation
Carbon cycle
Lapse rate
Impacts on humans

Now the question is: what is the net budget between positive and negative feedbacks? To assess this, climatologists use some metrics, the main ones being "transient climate response" (TCR) and "equilibrium climate sensitivity" (ECS). From Knutti et al. (2017):

TCR is defined as the global mean surface warming at the time of
doubling of CO$_2$ in an idealized 1% yr$^{−1}$ CO$_2$ increase
experiment, but is more generally quantifying warming in response to a
changing forcing prior to the deep ocean being in equilibrium with the
forcing. Based on state-of-the-art climate models, and instrumentally
recorded warming in response to CO$_2$ and other anthropogenic and
natural forcings, the Intergovernmental Panel on Climate Change's
Fifth Assessment Report (IPCC AR5) assessed that the transient climate
response is 'likely' (>66% probability) to be in the range of 1 °C to
2.5 °C.
By contrast, the equilibrium climate sensitivity (ECS) is defined as
the warming response to doubling CO$_2$ in the atmosphere relative to
pre-industrial climate, after the climate reached its new equilibrium,
taking into account changes in water vapour, lapse rate, clouds and
surface albedo. [...] The estimated range of ECS has not changed much
despite massive research efforts. The IPCC assessed that it is
'likely' to be in the range of 1.5 °C to 4.5 °C.

Which basically means that the climate will get warmer in the future, until it will eventually reach some kind of equilibrium.


How reanalysis data influence our research/results?

Welcome to StackExchange SE!

I don't think I fully understand your question, but I'll try to answer it. Reanalysis data is the use of weather models and data assimilation to piece back the weather. It is a 4-dimensional dataset (Latitude, longitude, pressure levels, and time). You can do whatever you wish with that data (provided you follow the legal guidelines with using the ERA dataset), but know that it isn't perfect; it usually is at a coarse resolution, and doesn't always contain everything you may want. Often reanalysis data can be used as input into other meteorological models, such as the WRF model.

As far as a random forest model, it really depends on what your intentions and design are. Admittedly, I don't know much about random forest model or your experimental design. To answer the question of whether the data could be used as explanatory variables, sure if you have some data that isn't within the dataset. But be aware of the limitations. There are other highly used reanalysis datasets, such as the CFSR and MERRA-2 and a variety of other reanalysis datasets, but those have similar limitations too.


Why doesn't the earth become superheated?

A body has to emit as much thermal energy as it absobs to remain in thermal equilibrium. The Earth has been doing the same since  its formation, i.e, it absorbs solar  shorwave radiation by its atmosphere, solid earth and water body, and releases it in the form of longwave radiation. The amount that is released has to be equal to the amount that is absorbed to maintain same temperature. However, due to much emission of greenhouse gases in to the atmosphere (or according to sceptics of such concept due to solar activity, volcanic emission), some amount that the Earth has to release is absorbed by the gases in the atmosphere and are causing the Earth to warm by few degrees every year.


What makes the conditions at the core/mantle boundary ideal for aluminum to combine with other elements besides oxygen?

A reason found experimentally is that the pressure and temperature conditions at the mantle-core boundary result in the reduction of aluminium oxides.  According to the Nature article Chemical interaction of $\ce{Fe}$ and $\ce{Al2O3}$ as a source of heterogeneity at the Earth's core–mantle boundary (Dubrovinsky et al. 2001) through their experiments simulating the thermochemical conditions at the boundary, that one of the main factors in the core-mantle boundary region is

  that iron is able to reduce aluminium out of oxides at core–mantle boundary conditions, which could provide an additional source of light elements in the Earth's core and produce significant heterogeneity at the core–mantle boundary.

Further, from the ESRF Highlights 2001 webpage Chemical Interaction of Iron and Corundum at High Pressure and Temperature: Implication for the Earth's Deep Interior, experimentally found that the following reaction, forming iron-aluminium compounds (amongst other alloys) occurred at temperatures that are believed to exist at the mantle-core boundary:

$$\ce{($2+3x$)Fe + $x$Al2O3 -> 2FeAl_{$x$} + $3x$FeO}$$

Where $x$ varied between 0.02-0.03 to 0.25


Why high tides occur simultaneously on opposite sides of the Earth?

First of all, tides are not as simple as the "two-bulge" simplification. In reality, the diagram shown is misleading. The two bulges appear assuming an ocean of constant depth covers the entire surface of Earth. Clearly that is not the case and in the diagram you can see the continents. Considering the different sizes of the basins and the distinct frictional characteristics in each location, the resulting tidal effect is much more complex. The difference in phase and amplitude is shown here and it clearly shows that the the tide varies for the same longitude. That wouldn't be the case in the simple explanation above.

Source Wikipedia.
Looking at this tidal animation from TPXO is also illustrative.

The simple "two-buldge" explanation would result in a pure two peak daily tide. That is certainly not the case in places like the Gulf of Mexico.
As mentioned in Camilo Rada's answer, the bulges are a consequence of the tidal force. This  apparent force result from the difference in strength in the gravitational field. The result is that Earth's body is stretched toward and away from the center of mass of the Earth-Moon system. The water thus adjust to this difference in geopotential giving rise to the tides.
A more intuitive explanation is given in Project Earth Science: Physical Oceanography

The explanation of the two-bulge tide comes from the fact that the Moon and Earth form a two-body system that rotates about an axis located within Earth.
The bulge of water on the side of Earth that faces the Moon is easily explained. It is due to the gravitational attraction between the Moon and Earth, including the water on Earth. This attraction pulls water toward the Moon and creates a “bulge” on the surface of Earth. The bulge on the other side of Earth is due to inertia. Inertia is the tendency of an object at rest to stay at rest and the tendency of a body in motion to continue its motion in a straight line.
There is an inertial tendency resulting from the rotation of the Earth-Moon system for objects (water among them) to move away from both sides of Earth—the side facing toward the Moon and the side facing away. The model demonstrates that the effect of things moving away from Earth is much greater on the side facing away from the Moon.
Many textbooks and other sources use the concept of “centrifugal force”— which is actually a preconception—to explain the effects of inertia. According to this preconception, there is a force that acts on all objects that are in circular motion, and this force pushes or pulls the object out from the circle. There is no such force. The preconception arises from our own experience with circular motion.

The gravitational forces of Earth, Sun and Moon cause a bulge of water on the nearest side and an equal bulge on the other side. Thus, in this simple scenario, the tide is composed of two bulges of water (four, in fact), traveling around the world as the world spins. When Moon and Sun aligned, their respective bulges add together to form "spring tides" every two weeks. When the Moon and Sun are at right angles, we encounter "neap tides", as the bulge of the sun adds to the low lunar tide, resulting in higher low tides but lower high tides.
The limitations of this model are:

It cannot explain that there are places without tides, with one daily high, and most with two tidal highs each day.
Tidal height is not maximal at the Equator (and minimal at the poles) as the simplification suggests.
High tide is not associated with the position of the Moon. It occurs at different times of the lunar cycle depending on the location.
If continents are included, the tidal wave would reflect off the continental shelf as it reaches a continent. A tidal wave of almost equal magnitude will be propagating in the opposite direction, which is not observed.
The tidal waves required for this model would have to travel at much faster speeds that are possible in reality.

In reality, the tides instead of running east to west as Earth rotates, tidal waves propagate around in circles around islands, and certain points in the sea, called tidal nodes or amphidromic points. These nodes can be seen in the first figure from this answer.
Thus, the tidal patterns in the ocean are a set of rotating standing waves. These waves have periods that represent the natural resonance periods of the ocean basins. These waves can be considered modes of "vibration" and can be decomposed using a Fourier decomposition. That is the source of the different tidal constituents that are used currently for tidal prediction.


How can I find the nearest point on the coast from an ocean location?

There are public databases with the coastline in lon,lat format. You just need to find the point closest to your coordinates in that coastline. For that you need the formula of the distance between two lon,lat points on an ellipsoid. In this article you can find that and an idea of how to do it:
Garcia-Castellanos, D., & U. Lombardo, 2007. Poles of Inaccessibility: a calculation algorithm for the remotest places on Earth. Scott. Geogr. J., 123, 227-233. doi:10.1080/14702540801897809
available here: https://web.archive.org/web/20140629230429/http://cuba.ija.csic.es/~danielgc/papers/Garcia-Castellanos,%20Lombardo,%202007,%20SGJ.pdf


What is a breadboard (retrieval) algorithm in the context of geophysical satellite retrievals/remote sensing?

When determining the retrieval algorithm for a spectrometer that will be built, it is first done on highly mathematical software platforms.  The software allows to the best curve approximation fitting equations to be derived (across all detected wavelengths) that will work for the proposed optics.  This is important because the diffracted light that is detected will interfere with itself very uniquely, depending on the geometry of your optical setup.   The data from the spectrometer's detector needs to be interpreted with a good curve fitting function so that you can get good wavelength resolution from your instrument.

When building a spectrometer for operational use on a satellite, it is ideal to be able to process the retrieval algorithm using hardware, rather than software.  The hardware processor allows real time function that isn't dependent on an operating system that requires lot's of computational overhead.  So, you build a breadboard that you can connect to your spectrometer so that your retrieval algorithm is processed using integrated circuits that can be programmed.  You essentially hard-code your algorithm into hardware.

Search for "breadboard spectrometer" in Google and you will find many examples.

Now, to answer your question.  A breadboard algorithm is developed using software that is used to help engineer the actual breadboards to be built in the future.  The software allows you to predict the response of your proposed circuitry to the spectrometer detector without having to actually build the breadboard yet.  Once your breadboard algorithm is setup properly (confirmed by testing the software version of your needed hardware) you can go about building the actual breadboard spectrometer model.

Once a breadboard spectrometer model is built and passes quality control checks, you can evaluate the spectrometer performance and see if its worth optimizing and fabricating a standalone instrument payload that can be deployed in the field (or in space).


What is the earliest tropical cyclone in record?

Japanese legend claims that typhoons twice save Japan from attempted invasions by Kublai Khan, once in 1274 and seven years later 1281. These divine winds ("kamikaze") are mixed in Japanese mysticism and are perhaps apocryphal.

The Chinese were meticulous record keepers and recorded disasters of all kinds. Liu et al. scoured written Chinese history for records of typhoons. T earliest unequivocal report of a typhoon they found was in the “Official History” of the Song Dynasty:

  In the tenth lunar month of the eighth year of the reign of Kai Bao [i.e., November AD 975], the city of Guangzhou was struck by a jufeng [typhoon]. Two zhang [a traditional Chinese measurement unit that equals about three meters] of rain fell within a day and night. The sea rose. Some boats were blown away and lost.

The Mayans were also meticulous record keepers and their homeland, the Yucatan, suffers a high rate of hurricane landfalls. There are two problems, however. One is that the Spanish conquistadors and the priests they brought with them were extremely meticulous about hunting down and destroying Mesoamerican writings. The other issue is that those writings were inextricably interwoven with the bizarre religion of the Mayans.

The Popol Vuh, written by the Dominican priest Francisco Ximénez around the turn of the 18th century, records some aspects of Mayan mythologies. The translations are a bit challenging. The Popol Vuh describes the ball court (which was very important to the Mayans), describes many of the Mayan deities, describes the Mayan creation story. One translation of this creation story follows.

  Heart of Sky arrived here with Sovereign and Quetzal Serpent in the darkness, in the night. He spoke with Sovereign and Quetzal Serpent. They talked together then. They thought and they pondered. They reached an accord, bringing together their words and their thoughts. Then they gave birth, heartening one another. Beneath the light, they gave birth to humanity. Then they arranged for the germination and creation of the trees and the bushes, the germination of all life and creation, in the darkness and in the night, by Heart of Sky, who is called Huracan. First is Thunderbolt Huracan, second is Youngest Thunderbolt, and third is Sudden Thunderbolt. These three together are Heart of Sky.

Note the name of the Heart of Sky, Hurucan. Others translate that name as Juracán, yet others, Hurricane. That Mayan god may well be the source of the word "hurricane". Then again, that god might have been given that name based on an already existing word. Similar sounding words were used throughout Mesoamaerica and the Caribbean to describe what we now call hurricanes, and also to describe the god of the sky.

Heart of Sky was a blood-thirsty god (many of the Mayan gods were blood-thirsty.) Two surviving Mayan stelae (carved stone monuments) depict a destructive event dated on one of the stelae as having occurred on June 3, 544 that depict whirling winds and pools of blood. That might well have been a hurricane. Then again, it might have been the ascension of a powerful king who aligned himself with Heart of Sky.

Stephen Houston, "Hurricane!", http://www.mesoweb.com/articles/houston/hurricane.pdf

Kam‐biu Liu, Caiming Shen, and Kin‐sheun Louie. "A 1,000‐Year History of Typhoon Landfalls in Guangdong, Southern China, Reconstructed from Chinese Historical Documentary Records." Annals of the Association of American Geographers 91.3 (2001): 453-464.


Characterizing earthquakes using accelerometer data

Yes, you can measure seismic energy with accelerometers. Most people do.

There are three ways to measure seismic energy: by displacement $x$, velocity $\dot{x}$, or acceleration $\ddot{x}$. Loose-spring devices like geophones measure velocity; stiff-spring devices like MEMS and relative gravimeters measure acceleration: they are accelerometers. Those used in seismology and exploration geophysics are very precise.

I wrote about the various instruments used to measure seismic energy in a blog post a while back. An excerpt about seismometers:

  Seismometers [are] precision instruments not used in exploration
  seismology because they are usually quite bulky and require careful
  set-up and calibration. [Most modern models] are accelerometers, much
  like relative gravimeters, measuring ground acceleration from the
  force on a proof mass. Seismometers can detect frequencies in a very
  broad band, on the order of 0.001 Hz to 500 Hz: that's 19 octaves!

Short story: When digital seismic receivers arrived on the scene in Calgary in the early 2000s, there was a lot of skepticism. We spent a lot of time comparing them to traditional geophones. The conclusion: they were about the same. Here's one comparison by Michael Hons at CREWES, and here's another; here's yet another from one of the big manufacturers, Sercel (now CGG). Finally, here's a presentation more oriented around earthquake seismology.

Okay, but I was talking about the accelerometers in iPhones!

Oh, sorry. As @Fred points out in his answer, consumer-grade MEMS accelerometers (as you might find in a phone or latop) may not have the sensitivity or calibration that a researcher would want, but one might compensate somewhat for this with multiple measurements, e.g. an array of devices. In other words: quantity, not quality. (This is perfectly legit: we do it in exploration seismics too.)

Dashti et al. (2013) in Earthquake Spectra Journal found you could get useful measurements (e.g. for emergency response) from networks of phones with a few tricks:

The more measurements the better.
Horizontal orientation is best.
Prefer high-friction phone covers.
Don't expect to get great data for small quakes.
Treat small groups of phones as arrays.
Don't use data for phones that fell off a table!


How do the slow and fast carbon cycles influence climate change?

One example of the slow carbon cycle: Surface uplift of Tibet and Cenozoic global cooling

  Continental weathering on a global scale influences ocean chemistry and imposes a net drawdown of atmospheric CO2 that modulates global climate ... . This observation, in addition to seawater Sr records that suggest an increase in continental weathering after ca. 40 Ma, led researchers to suggest that the uplift and erosion of the Himalayan-Tibetan orogen over the past 40 m.y. has drawn down atmospheric CO2 and cooled the globe, leading to the glacial climate that persists today


How, exactly, do scientists know location of earliest continents?

Well, the really earliest continents, the answer is we don't. As you go further back the uncertainties get larger and larger. It has been speculated that there have been around 4-5 super continents like Pangaea. Before Pangaea there was Rodinia, but before that it gets more and more sketchy.

The oldest ocean floor is only Jurassic. So ocean palaeomagnetism is only good back to the Jurassic, but can be extrapolated a bit beyond that. You have continental magnetism and this helps place the palaeo-latitude - for example, we know the UK was just south of the Equator in the early Palaeozoic. That doesn't give you relative location but is an important piece of the jigsaw.

The other is stratigraphy. Yes that includes palaeontology, but before the Palaeozoic, palaeontology is limited (eg. do Ediacaran species have global or regional distribution? what about earlier single celled organisms?). It can also include rock correlations, isotope signatures, etc. For example, the Lewisian Gneiss is a piece of Archaeon craton in NW Scotland that has some well studied dyke sequences. If you find similar gneisses elsewhere with the same dates and dykes with the same chemical signatures, then you can hypothesise they were a part of the same unit and they split after the dyke intrusion.


Does the increasing number of significant earthquakes relate to increasing population density in earthquake zones?

The only possible linkage between moderate earthquakes and population is that more people create increased groundwater extraction, and hence near-surface fault planes tend to dry out. This effectively increases the friction so that there are less frequent but more violent quakes. However, this would only affect near-surface earthquakes which seldom exceed about magnitude 3 or 4. The really big earthquakes originate at plate tectonic interfaces at depths from about 10 km to hundreds of kilometres. There is nothing that humanity can do to influence processes on this scale.

Another issue is that micro-seismicity occurs all the time - millions of small quakes that go un-noticed every year. Some of these can certainly be caused by humans - but does this really count?


Why are the south, the west and the north of the Caspian sea lush but its east completely dry?

The mountains.

The south has a steep relief, as well as the west. That means that there is much precipitation. The clouds throw every drop on these mountains, so almost nothing is left. The east is pretty low, so the remaining clouds (not much left) just fly over. In fact, deserts are generally not steep and they are usually behind the mountains. That is right what happens here. On the north, the effects of the west are still felt, so it isn't so dry, but it is pretty low, too. Also, I wouldn't say that it's lush : )


What affects the surface characteristics of cumulus clouds?

No, clouds don't really have a 'surface' that could have tension like a body of water. The different looks in these two examples (left Cumulonimbus Calvus and right Cumulus Humilis) are greatly dependent on how they have formed and how are they evolving now.

The large Cumulonimbus is still growing in a relatively rapid speed. The cloud is reaching higher and higher upwards carrying moist air. The moist air due to turbulent flows and expanding of the rising air gets mixed with the cold air and instantly forms/extends cloud as it reaches saturation (saturation is reached with less water in colder air and air is colder in higher altitudes). If there wasn't the expansion then flows of dry air to the cloud would desaturate the cloud and more small scale variation could be seen as in the Cumulus Humilis. Also the Cumulonimbus being much larger and further away looks different just due to distance. The steady state like situation of the Cumulus Humilis where it isn't growing (perhaps a little on the top) and the fact that the lower atmosphere has stronger turbulent motions equals to the appearance where more cotton candy pieces 'drift' from the cloud.

Neither of these are ice droplet clouds (they look different just because they are made of ice and not water droplets), but all clouds that are in freezing temperatures have some very small percentage of ice in them too. The Cumulus Humilis might be below 0 Celsius and the Cumulonimbus definitely is at some height. A crude estimate is that temperature drops 6 Celsius every kilometer. The base of both clouds is probably somewhere between 1 and 2.5 kilometers and the Cumulonimbus might reach over 10 kilometers.


Are there water molecules in the oceans which will almost never fall down as rain?

Never is a very, very long time.  Almost never is a vague term.

The age of deep ocean water has been studied with both models and observations, and both indicate a lower limit age in the order of thousands of years, rather than decades.  Here, age is defined as elapsed time since contact with the surface, which would be the only opportunity for evaporation.

On a geological timescale, all ocean water has ample opportunity to evaporate and fall back as rain again and again.  On a human timescale, not so much: for some water in the ocean, it has been well over a thousand years since the last time it was near the surface.

For an example of a recent study into the topic:

  Gebbie and Huybers (2012): The Mean Age of Ocean Waters Inferred from Radiocarbon Observations: Sensitivity to Surface Sources and Accounting for Mixing Histories.  in: Journal of Physical Oceanography.  http://dx.doi.org/10.1175/JPO-D-11-043.1

From the abstract (emphasis mine):

  A number of previous observational studies have found that the waters of the deep Pacific Ocean have an age, or elapsed time since contact with the surface, of 700–1000 yr. Numerical models suggest ages twice as old. Here, the authors present an inverse framework to determine the mean age and its upper and lower bounds given Global Ocean Data Analysis Project (GLODAP) radiocarbon observations, and they show that the potential range of ages increases with the number of constituents or sources that are included in the analysis.
  (...)
  The authors find that the North Pacific at 2500-m depth can be no younger than 1100 yr old, which is older than some previous observational estimates.
  (...)
  Subject to the caveats that inference of the mixing history would benefit from further observations and that radiocarbon cannot rule out the presence of extremely old waters from exotic sources, the deep North Pacific waters are 1200–1500 yr old, which is more in line with existing numerical model results.


Solution for the coexistence of overpopulated human species with nature

It's important to understand that this problem is a bit more nuanced.
Population growth in every species is exponential (as much as exponential growth can exist, in reality almost nothing is proven to grow infinitely, therefore at some point stops growing exponentially).
Check out this for a description of carrying capacity. In a lot of ways it shows that human population growth is not much different than any other species... but we do it on such a grand scale, and that is something to consider. https://en.wikipedia.org/wiki/Carrying_capacity#:~:text=The%20carrying%20capacity%20of%20an,water%2C%20and%20other%20resources%20available.
The biggest problem in the future may not be our exponential growth, but our increase in carrying capacity for our specific environment (which for humans is the entire Earth). The most significant cause of this is the Green Revolution (agricultural improvements, not environment).
https://en.wikipedia.org/wiki/Green_Revolution
We certainly don't want to see that carrying capacity drop.


The caption under the image on the Digital Globe website identifies the location as Fiery Cross Reef.

Multiple sites identify what's going on as the Chinese government building an airstrip and related facilities on the site to solidify its claim to the South China Sea.

According to this 2015 BBC story:

  China claims almost the whole of the South China Sea, resulting in
  overlapping claims with several other Asian nations including Vietnam
  and the Philippines.

That story is based on a Jane's 360 analysis of satellite images:

  The 23 March images show a paved section of runway 503 m by 53 m on
  the northeastern side of Fiery Cross Reef, which China began to turn
  into an island in late 2014. Paving and ground preparation of other
  sections of the runway has also begun further along the island. In
  addition, workers have paved about 400 m by 20 m of apron.

According to the Permanent Court of Arbitration on the wider South China Sea territorial dispute between China and the Philippines: (PDF)

  ...China had caused severe harm to the coral reef environment and
  violated its obligation to preserve and protect fragile ecosystems and
  the habitat of depleted, threatened, or endangered species.

But it didn't seem that the reef in question was explicitly protected by any governmental action, especially given the dispute over which country governed the territory. China does not recognize the jurisdiction of the court.


The state of Nitrogen, Phosphorous and Potassium during Anaerobic Digession

You're the man who grows coconuts and had a small problem with mimosa plants which you now intend to compost. Don't forget that coconut fronds blown down by the wind and any other waste products from the palms can all go into your compost. In England, earthworms are highly valued in the compost heap, as they help the vegetation break down more efficiently, but I'm not sure how available worms are in Mangalore. If you have a machine that can chop your mimosa cuttings into tiny pieces, that will also help them to compost. Some of the nitrate produced by their roots will find its way to your coconut palms if they are nearby.

Yes, there will be nitrate, phosphate and sulphate in your compost, especially nitrate manufactured by the roots of your mimosa plants. Anaerobic composting still leaves nitrates, phosphates etc in the final product, but also creates methane, which is a very potent greenhouse gas best not released into the atmosphere. The compost also requires an airtight container, so your worms would be suffocated. If your compost is of sufficient quantity to make it worth while, you could tap off the methane and use it as a fuel for cooking.

I think the aerobic process would be best suited to your needs, therefore your compost heap will need to be well aerated. Make a bed of twigs to  build your compost heap on, and that will let air in underneath. You will also need to turn the compost over occasionally to let more air in. Aerobic composting does not produce methane. If you see a thriving population of worms in your compost, things are going well.


There are few known mechanisms that lead to the generation of Rogue waves, such as the ones you mentioned, but essentially all Rogue waves are the due to the nonlinear wave dispersion characteristics of large groups of waves.

I can imagine one approach to predicting the emergence of such waves is to simulate the evolution of initial wave states with Navier-Stokes based wave models that capture the nonlinear dynamics involved in real time. However, with the limited computational power and numerical techniques we have today, that is currently impossible.

So I think the question is: Do we know of specific signatures in the ocean wave climate, which ultimately give rise to these so called "walls of water"? Presumably these wave patterns could serve as early warning indicators of an upcoming rogue wave event.

There is indication that the emergence of solitons from modulational instability or dispersion of wave packets occurs in consonance with nonlinear effects and nonlocal coupling giving rise to Roge waves. Thus, an approach based on the spectral analysis of the sea-state as a whole or of particular envelopes of propagating waves may hint at particular wave-field patterns that originate Rogue waves. Please see the sources below for more information on the current state of the art. However, at the moment the answer is that forecasting Rogue waves is still much of an unknown.

  Akhmediev, Nail, et al. "Rogue Waves: Early Warning vs Forecast."
  (2011).

  Akhmediev, N., et al. "Early detection of rogue waves in a chaotic
  wave field." Physics Letters A 375.33 (2011): 2999-3001.

  Onorato, Miguel, et al. "Rogue waves and their generating mechanisms
  in different physical contexts." Physics Reports 528.2 (2013): 47-89.


what is the best way to actually make the Earth lose heat?

What is the best way to actually make the Earth lose heat?

TL;DR: Stop pumping so much carbon dioxide into the atmosphere.

The easiest approach in terms of human effort would be to let the Earth warm up a tiny bit. Thanks to the Stefan-Boltzmann law, a tiny increase in the Earth's effective temperature will easily rectify the ~0.6 watts/meter2 imbalance in the Earth's energy budget. If the Earth was a perfect black body radiating at an effective temperature of 252 kelvins, all that would be needed would be a 0.17° Celsius increase in the effective temperature to make that energy imbalance disappear. Easy, right?

Wrong.

Thanks to feedbacks, that small increase in the Earth's effective temperature requires a significantly larger increase in the Earth's surface temperature, and that's ignoring the fact that humanity is currently making the energy imbalance worse. Temperatures are currently rising and will continue to rise for a while due to the large amount of CO2 humanity has already pumped into the atmosphere.

Continuing to pump ever increasing amounts of CO2 into the atmosphere (the "business as usual" scenario) will result in a 4° to 9° C increase in the Earth's surface temperature by the end of the century, with the uncertainty of the increase depending largely on the climate sensitivity to a doubling in CO2 levels. Even the bottom of that range represents a disaster. The only way to avoid this disaster is to stop pumping so much CO2 into the atmosphere.

  Can we have thermoelectric (Seebeck) generators powering infrared spotlights pointing out into space or something?

You wouldn't want to use infrared spotlights. You'd want the radiation to be in the visible range. The atmosphere is opaque in the infrared.

Playing "what if", suppose every last bit of energy currently consumed by humanity (18 terawatts) is used to power massive air conditioners, with lasers venting the generated heat into space. Suppose we somehow manage to get 17 times as much cooling as energy consumed out of the system, resulting in 300 terawatts of cooling. Dividing that by the Earth's surface area results in 0.6 watts per square meter -- i.e., the current energy imbalance.

This is of course utterly unrealistic.  We aren't plowing or harvesting our fields, manufacturing products, transporting goods, driving to and from work, heating or cooling our houses. To make this unrealistic "what-if" scenario worse, the hydrocarbons used to produce that energy are exacerbating the energy imbalance.

The best way to make the Earth lose heat is to stop pumping so much carbon dioxide into the atmosphere.


Climate on an Earth without an Axial Tilt

Just throwing  some thought on the subject, it is easy to me to understand that there is a big pump moving large amount of water from one pole to the opposite one along the year, that is during summer in north hemisphere the ice melts at Arctic and mix to the sea; at the same time water start precipitating more and more on the Antarctica, piling up as snow and ice.  During the other six months the pump reverts, moving water from Antarctica to the Arctic.

In this hypothetical situation this pump will behave differently.   The water will evaporate from the sea, and precipitate towards the poles.   Those rain in midway to the pole would provide vegetation life, erosion, and all sort of things rain water does.   That water falling in the north and south pole would have no reason, in principle, to melt and reinsert in the oceans.

If the rain started to fall mostly on high latitudes, possibly the region around equator would be more exposed and deserter, increasing the heat, evaporation, and the convection of the air at high speed.   Possibly very intense winds blowing everything, moving quickly the clouds and vapor to higher latitudes, where the rain would fall.   Anyway, the hotter atmosphere should increase the loss of the lighter gases to the space due to kinetic energy gain, decreasing the atmosphere pressure little by little while becoming hotter.  In this loss there could be even some water vapor.

Then I think that in the long run the water would tend to move all the way to the poles draining drastically the remaining of the planet.  If we think of an ocean as salty (3.5%) as ours, possibly there would be deposition of large layers of salt, most of it sodium chloride. I don't really know if there would be a "life zone" around some high latitude.  Certainly tropic would have no meaning in this configuration.

That is the "big picture", but not all the story.

We have different wind flow in atmosphere and water flow in the oceans due to others factors.   One of those being the tides that move water in waves half circumference of the planet.   The main component being that from the moon, but we have other of smaller intensities like the solar influence.  Other factors are the convection due difference temperatures and pressures, and Coriolis force making it go round in its trip across latitudes.

Another factor is that we have a non homogeneous distribution of mass on planet surface, the removal of large amount of water, moved to the poles, possibly would increase the amount of wobbling, then the precession ( https://en.wikipedia.org/wiki/Axial_precession) of the planet.   Perhaps this wobbling would be responsible to a certain amount of melting at the poles, keeping the pumping working longer and, who knows, preserving some life in the planet.

A hotter atmosphere could increase the amount of clouds, if it covers all the planet we could have a very long freezing of the planet.

If we think on a dry planet with water moved to poles as ice, we could perhaps include sublimation of ice in the figure, adding the loss of water to space due to  heating of the atmosphere.   I don't think we would become a Mars, our gravity is about three times Mar's gravity.

HTH


How is abundance of elements in the Earth's crust estimated?

can he also say how accurate this estimations are?

Let's begin by saying that the crust is heterogeneous. There is no one "composition of the crust". If you go to a place rich with limestones, then Ca and C are the most common elements (excluding O), if you go to a place rich with granites then Si and Al are the most common. Go to places with abundant basalt and you get lots of Mg. That means that the accuracy is irrelevant. If you have the average of an entire continent, there is no one rock or one area that has this composition. And if there is, it is by pure coincidence.

what methods exist and were used to estimate this?

One way to find an average is to know how much of each rock you got (which is easy if you have geological maps of everything) and what's the composition of each rock. However, there is a more clever way of doing it. You can sample sediments. Take major rivers that have huge areas in their drainage basin. These rivers transport the fragments of those rocks as sediments and deposit them in one place. All you have to do is to analyse those sediments. Surprisingly (or not), when you actually do this for rivers in Europe, America, Australia, etc, the composition of them turns out to be almost identical! So that's one way to derive an approximation.

up to 50km deep

You can't directly probe that deep. Our deepest drill hole was just over 10 km, and that was almost impossible (and extremely expensive to do). Fortunately, we have an indirect method of sampling rocks from 50 km and even deeper. Sometimes magma erupted from depth tears away pieces of rock from the walls of the conduit. This rock is then embedded in in the volcanic rock. Here's an example:

Source: James St. John, flickr
You have the black basalt and in it a rock that came from several tens of km below the surface (or more). By collecting a lot of those deep-seated rocks from volcanic rocks, we can get a good idea of what the lower crust and the upper mantle look like.


What is this upside-down transparent funnel-shaped item on a weather monitoring station?

The upside down funnel-shaped attachment is used to prevent rain-water getting inside the inlet of instruments which analyse ambient air. Usually, these instruments are air pollution monitoring instruments like ozone analyser, carbon monoxide analyser, particle concentration analyser, etc.

One may think why can't just use U-shaped tube (inlet). In case of U-shaped inlet, rainwater falling on inlet will eventually roll down near the entrance and will be pulled in with air due to strong flow. Funnel shape will have smaller flow near the wider opening and prevents water from getting into the air stream.


What is meant by Monte-carlo simulation? (would like an elaborated answer with some references)

There are times when any realistic 'answer' has to incorporate some degree of randomness. For example, when interpolating missing data in a rainfall time-series. You can do this 'informally', or through a slightly more rigorous 'Monte-Carlo' approach - there are several possible ways to deal with such problems. J.E. Gentle's book; Random Number Generation and Monte Carlo Methods, is a good read, although being 2003, it's starting to look a bit dated. But it's more than enough to get you started, and then the rest you can do with off-the-shelf software.

Alternatively, as Farrenthorpe points out, the Wikipedia reference may give you all you need to know.


The Quaternary is definitely a good guess. But it is difficult to answer your question because the "age of a fjord" is a rather ambiguous concept.
Also, I'll asume you are interested in the bedrock topography associated  to the fjords, and not only the sea inlets (as in that case they would have formed very recently, just when the glaciers receded enough to allow the ocean water to take their place). With that said let's try to answer the question:

The fjords of western Patagonia are a feature created by the Pleistocene glaciations, therefore you can definitely say that the fjords as a feature of the landscape were formed during the Quaternary. However, they are in constant evolution, so you can arguably also say that the fjords as you see them today, were formed today.

Glacier erosion rates in Patagonia range roughly from a few tenths of millimeters to a few centimeters per year. Faster rates probably happening at the edges of the ice sheets were glacier basal sliding velocities are higher. Long term averages (~10 ka) are probably between 0.5 mm/yr and 1 mm/yr, meaning that in the 2.6 Ma of the Quaternary you would erode just about one to two kilometers. As some fjords can be much deeper than that (when measured from the mountain tops), it is clear that the fjords as a geographical feature are not in steady state, and they are now more dramatic than ever throughout the Quaternary.

Erosion rates measured in outlet glaciers in Patagonia and other areas in different timescales. From figure 2.a in "The relative efficacy of fluvial and glacial erosion over modern to orogenic timescales" 2009, Nature Geoscience 2(9):644-647.

The reason that explain why Fjords can become deeper than that one kilometer estimate, is the concentrated erosión in outlet glaciers at the edge of the ice sheet. For example, the most visited glacier in the Northern Patagonian Icefield: the San Rafael glacier, show erosion rates of 0.83 mm/year. And as shown in the figure above, outlet glaciers can erode up to ~5 cm/yr at shorter timescales.

Sumarizing:

Northern Patagonian Ice Field's fjords started to form with the first Pleistocene glaciation at the begin of the Quaternary about 2.6 million years ago, but they have become deeper after each successive glaciation and they are still forming today. Current glaciers are eroding their bedrock at rates on the order of one to a few centimeters per year.


Is there a maximum size for a single snowflake?

According to Caltech physics professor Kenneth G. Libbrecht's site SnowCrystals.com

  This monster is, to my knowledge, the largest snow crystal ever photographed. It measures 10.1 mm (0.4 inches) from tip to tip (averaged over the three axes). ... Note that this is a snow crystal: a single crystal of ice ... Larger snowflakes have been reported, but those were puffballs made of huge numbers of individual snow crystals stuck together. During very calm conditions, these puffballs can grow into pancake-shaped agglomerations as large as a dinner plate

He has a paper Physical Dynamics of Ice
Crystal Growth, but I don't see any discussion of theoretical maximum sizes of crystals or agglomerations.


What are Ordovican trace fossils, and what do they look like?

Trace fossils are marks or things left behind by living things do their thing,  they are indirect remains of organisms, coprolites (poop), footprints, egg shells, ect. If we found a fossilized beehive or beaver dam those would also be trace fossils. Bioturbation is a specific type of traces fossil, marks of disturbances of the sediment itself animals leave behind, trackways and burrows are the classics.
Identifying bioturbation is tricky in a lot of cases, there are thousands of kinds which makes it worse, there is no way to give a direct answer. Your best bet is to find out what particular bioturbation they are referring to.  Burrows, trackways, feeding trails, nest, hold marks the list is endless. there are nearly as many trace fossils as there are organisms that crawl or dig.  Worse they are often very contextual and need examination of  micro-structure.  What is obvious a trace fossil in one formation will look identical to the naked untrained eye to something that is obviously not a trace fossil in a different formation. Generally you want to a specialized experts opinion before if saying something might be bioturbation someplace you don't expect it.
Even from a single location you can have a wide variety of forms,  here are a few examples from the ordovician, ...the second of six periods of the Paleozoic Era, 485.4–443.8 million years ago.
Bioturbation

The photos from mars are not likely to be bioturbation but are almost certainly differential erosion of normal chemical variation in rock. They do not have any of the characteristics that scream "this has to be biological activity" like cross cutting bedding planes or parallel patterns. Sedimentary rocks are rarely homogenous and chemical processes combine with erosional ones can produce some weird results. for comparison here are a few things that are definitely NOT fossils.
**Pseudofossils AKA Leaverite **

Pseudofossils are things lake look like fossils to the untrained eye but are just rocks, usually the leftovers of a chemical or erosional process. the term leaverite comes from geologists telling others "just leave're there"


What is the reason why there are radiosonde measurements in the atmosphere?

The reason is that we need them!  And we could probably do with more of them (e.g. bigger launch budgets).

Surface observations will tell us where fronts are, where low and high pressure is, and how surface temperature and moisture are being advected.  We can also deduce large scale ascent or descent (vertical motion) from surface divergence and convergence.  We might even be able to provide very short term forecasting, though the skill won't be great. To know how the surface will evolve you need to know what is going on above the surface.

If we know what the 500 mb surface looks like, we can combined this information with the surface fields and some quasi-geostrophic theory and do better with short term forecasts.  With just one upper air layer we can see how the feedbacks between the mid/upper-troposphere and the surface will behave and better predict the development and motion of low pressure systems.

To provide more accurate forecasts, have a shot at predicting convection, and provide longer term forecasts we need more information about the vertical structure of the atmosphere.  The current state of models are such that one of the best things we can do to improve them are to provide better initial conditions (better observations and more of them).  Balloon launches are a great way of getting this data.  Ground and satellite based observations can provide parts of this, but we still benefit from being able to directly sample the atmosphere and to calibrate the remote sensing algorithms with the radiosondes.

One example of the necessity of balloon launches is in convection.  Knowing only surface convergence, temperature and moisture is important, but does not tell the whole story.  If the 850 mb temperatures are too warm, it won't matter how good the surface observations look, you won't get convection.  How much energy the storm can tap into depends on the temperatures all the way up to the tropopause (and higher if you want to know how high the cloud tops will be).  Knowing what type of storm to expect depends on knowing the winds in at least the bottom 6 km of the atmosphere.  Having vertical information provided by a radiosonde is the difference in only being able to say "the air is warm and juicy" versus being able to say "expect isolated supercells today with large hail and straight-line wind damage" or "despite the high dew points, the capping inversion and associated CIN will suppress all convection today -- no storms" given the exact same surface observations.

And yes, models can give us the upper air structure to base these kind of statements on, but remember the radiosonde launches are where a lot of the upper-air data comes from that allows the models to work well comes from.


Eclipse, Hurricanes, Earthquake....Related Events?

The occurrences of Hurricanes, Harvey, Irma, Katia and Jose, east of Mexico and a magnitude 8.1 earthquake southwest of Mexico within a few weeks of the American solar eclipse of August 21, 2017 are purely co-incidental.

Hurricane Katrina, which devastated New Orleans in 2005 was not associated with any type of eclipse - solar or lunar.

Likewise the eruption of Mt St Helens in May 1980 was not associated with any type of eclipse, or were  the San Francisco earthquake of April 1906 or the Loma Prieta earthquake of October 1989.

There is a list of every solar eclipse that occurred globally during the 20th Century. From the list, you will see there were one to two solar eclipses every year during the past century. None of these have ever been associated with any natural event such as earthquakes or hurricane/cyclones/typhoons.

Co-incidences in nature occur all the time.


Floods are associated with considerable sediment transport and higher than normal water levels.
Therefore, the study of sediment layers in river banks, lake bottoms or the ocean floor can reveal large sediment deposition events, that could be associated with floods or landslides. The characteristics of the sediments can be used to identify the process that generated it, and the organic matter trapped within the sediments can be used to date the time of the flood.

Here is an example of how a sediment layer from a flood looks like in a sediment core

It is taken for a paper that might be interesting to you: Lake Sediments as Archives of Recurrence Rates and Intensities of Past Flood Events. The image in the left is a picture of the sediment core (with a overlay showing the changes in reflectance along it).


The Tetens coefficents are the empirically derived coefficients of an equation for calculating the saturation vapour pressure of water. From wikipedia:

a very good approximation can usually be made using the August-Roche-Magnus formula (usually called the Magnus or Magnus-Tetens approximation, though this attribution is historically inaccurate):
$e_s(T)= 6.1094 \exp \left( \frac{17.625T}{T+243.04} \right)$
e_s(T) is the equilibrium or saturation vapor pressure in hPa as a function of temperature T on the Celsius scale. Since there is only a weak dependence on temperature of the denominator of the exponent, this equation shows that saturation water vapor pressure changes approximately exponentially with T.


Did global temperature increase or drop in the last 2 years (2017-2018)?

Did global temperature increase or drop in the last 2 years?

Before I answer the question, I need to add the caveat that climate change does not say that every year will be warmer than the previous one. Events such as El Ninos and La Ninas can make the global temperature spike or drop in any one year. The Pacific Ocean dumps huge amounts of pent up heat into the atmosphere during El Nino events.

2014 saw the start of an El Nino event that briefly stalled but then became one of the largest such events ever observed. The 2014-2016 El Nino made 2015 and 2016 the warmest years on record -- so far. 2017 and 2018 were a bit cooler than 2015 and 2016. They were however warmer than every year on record prior to 2015.

2019 most likely will not be warmer than 2016, but it might well beat 2015 as the second warmest year on record. And that is without the help of a massive El Nino event.


How to measure voltage differential across different altitudes

Q1: I imagine you could measure the potential difference using weather balloons. Send one balloon up to 10,000 ft (Balloon A) and one to 20,000 ft (Balloon B) with wires connecting them to a voltmeter. The challenge here is to account for the wire resistance, which, if the potential difference is low, will in all likelihood interfere with the measurement. If the difference is too low to be measured, you would have to amplify the voltage and then account for the amplification and wire resistance.
Q2: I would try using weather balloons again, but obviously Balloon A and Balloon B would be at the same altitude but 10 miles apart from each other.
Q3: Instead of a voltmeter measure with an oscilloscope. There's going to be noise no matter what; what oscillations are produced by noise and what is actual oscillations is a judgment call. I would say that truly oscillating potential difference is likely to be low frequency, so to filter out high frequency noise connect the circuit to a low-pass filter before processing with the oscilloscope.
Another way to determine oscillations is to measure the voltage with a data logger and post-process with computer software; any programming language that can easily manipulate large amounts of data would be sufficient, even excel would work. Plot the voltage vs time using a linear regression model to smooth the noise out. As an example, python's numpy has a regression function called polyfit. With a linear regression model and a moving window you will truncate the beginning and end of the dataset, but that shouldn't matter if you have a lot of data.


How to calculate flow duration curve for a set of 12 year data?

Spreadsheets work well for this.

You have 12×12 observations so use 144+1 = 145 as the number of observations for calculating your probabilities.

Put your discharge data in a column and sort from highest to lowest. Put a column of Rankings next to it and number from 1 up to your maximum (1 to 144). Put a column next to that and calculate your probability of exceeding each discharge value:

P = Ranking×100/145

(P as a percent)

Graph discharge vs. P.

You need to consider your 0 discharge months in determining the number of periods but you don't need to calculate P for them.  That's handy if you don't want errors in plotting log discharge vs. P.


Surace,

Here are two references:

http://www.iup.uni-heidelberg.de/institut/forschung/groups/ts/soil_physics/research/pms/cracks
Coupling analysis of pattern formation in desiccation cracks, [2016, Sayako Hirobe and Kenji Oguni]

Best,
Jannes


What would happen if you hypothetically happened to touch an aurora

Auroras typically happen pretty high. About a century ago, Norwegian scientist triangulated more than 12,000 auroras, and this is the distribution they found:

Figure 1 from Störmer, 1946.

So the fist problem will be to "touch" anything at an elevation of 100 km, where the atmospheric pressure is 0.00006% of the sea level pressure and 0.0002% of the pressure at the top of Mount Everest (pressures estimated using CalcTool).

So let's imagine you use very thin space suit that stop your body from blowing up, and keep you alive.

Even in that case, the air is so thin that its heat capacity and conductivity would be extremely low. Therefore, no matter if the air is at -100°C or +300°C, you wouldn't feel it, and the temperature of your fingers would be dominated by the heat loss through radiation (i.e. your hot fingers would radiate infrared radiation and become very cold pretty soon).

Visually they are diffuse objects, so it will be as disappointing as "touching" a cloud. Where you never really feel you ever get to the "edge" of the cloud and touch it. You just feel that you become shrouded in an increasingly thick fog. That's is at least my experience climbing mountains that from below look like they have their top covered in thick clouds. On airplanes the experience is quite similar. So I think you will just not realize you are at the edge of an aurora and you will just see a subtle glow in the air.

Another important effect would be the radiation. You would get a big dose. I mention a bit of this in my answer to this question, however the formula there is not valid at 100 km. Because radiation increase exponentially the first 10-15 km as you go up, and then flattens (Stozhkov et al, 2001). Under normal conditions, at 100 km you would be receiving approximately 500 times more radiation than in the surface (ref1,ref2), which is pretty much the same dose of outer space. That is not a big deal if you don't stay there very long. But auroras don't happen under normal conditions. However, radiation at surface levels during auroras go up but not by a large amount, so I don't think radiation will kill you.

So, if you get up there with a space suit that keep you alive, I think your quest to touch the aurora will be rather disappointing. However, the view from up there would be amazing.

You might want to see this video of a weather balloon sent up under an aurora. With cameras and radiation sensors. It is pretty cool, but it only got about a fifth of the way towards the aurora. And you can't get much higher with balloons, the world record (unmanned) is 53 km, which is just half way there. These are a couple screenshot from that video:


Global warming has to do with the surface only, and at best involves changes of 20 degrees at the outside extreme, in comparison to the earth's core, which is as hot as the surface of the sun.

For complete accuracy, and to reflect what a commenter has pointed out, the inner core is solid already, but this is because of the extremely high pressure of the overlying layers of the outer core (which IS liquid), and the mantle. See the Wikipedia articles concerning the Inner Core, and the Outer Core.  Note that it is the outer core which creates the earth's magnetic field.

The answer is that the earth's core will never be solid.  And I do mean NEVER.  Now, that being said, there is only one way it could ever happen and that is if the earth happened to get thrown out of its orbit to become a nomad planet.  Then it might have time for its core to cool.

The reason I say this is because it will take longer for the earth's core to turn solid than it will take for the sun to run out of nuclear fuel and expand to engulf the earth.  At that point, the earth will be vaporized as it spirals out of its orbit into the sun.  The core would soon turn into incandescent gas.  This will occur something like 4 to 5 billion years from now.

If by some chance the earth were to become a nomad planet, free to cool in its own good time, then it would take a long long time.  See Energetics of the Earth by John Verhoogen, available online via Google Books.

The main factor slowing down the cooling is radioactive decay of long living atoms, namely Uranium-238, Uranium-235, Thorium-232, and Potassium-40, with half-lives of roughly 4.47 billion years, 704 million years, 14.1 billion years, and 1.28 billion years, respectively. From the half-lives of these isotopes and a comparison with the age of Earth, you can see that internal heat production via radioactive decay will likely persist at near current levels for quite some time to come. Verhoogen gives 5000 K as the core temperature now, and a 250 K cooling since the formation of the Solar System, 4.5 billion years ago.  If it really does cool at that rate (55 degrees per billion years), it would take something like 91 billion years to cool to 0 Kelvin.

But don't worry, it won't happen, as I said.

Edited to add detail


Can the Bering Sea Rule be used to predict the weather?

There are two papers produced by the NOAA's National Weather Service investigating the claims regarding the Bering Sea Rule (BSR) and the Typhoon Rules for long range forecasts.  Some insite for your immediate questions:

Although not giving a percent reliability of the BSR, the second
study does say that the BSR has forecast skill above climatology for
long range forecasting - see Discussion, Summary and Conclusions
section of study II.
From paper I:

  The Bering Sea (BSR) and Typhoon (TR) rules are two observations used
  by weather forecasters. The former was introduced in 2011, while the
  latter has been used since at least the 1940s and are based on the
  idea of teleconnectivity within the Pacific Ocean region which was
  defined statistically by Wallace and Gutzler (1981). For example, the
  Pacific North American (PNA) pattern will be associated with
  alternating trough-ridge patterns from the Central Pacific to the East
  Coast of the US. A ridge-trough pattern from west to east over the US
  is a positive PNA configuration, while the opposite pattern is
  negative. Teleconnection is thought to be the result of downstream
  propagation of Rossby Wave activity in the North and South Pacific
  basins (e.g., Renwick and Revell, 1999; Wang et al. 2011, and
  references therein). The Bering Sea region is close to one
  teleconnective centers in the PNA pattern, which should make these
  rules useful indicators of weather downstream.

Refer to the Case Studies in study II.

Source (Study I): http://www.nws.noaa.gov/ost/climate/STIP/39CDPW/39cdpw-JRenken.pdf

Source (Study II): http://www.nws.noaa.gov/ost/climate/STIP/40CDPW/40cdpw-JRenken.pdf


It is an extinct volcanic crater.
The location is not listed as one of the active volcanoes in Madagascar.

Simplified geologic map of Madagascar (reference) shows the crater to be mapped as basaltic / Gabbro lava,


How hot the earth will be if we have 20% CO2 in the atmosphere instead of ~0.04? and how cold would it be if doesn't have any CO2?

The concentration of CO2 in the Earth's atmosphere has remained less than 1% in the past 470 million years when land plants first appeared--long before mammals, and long before humans graced the earth.
If we are talking about having a biosphere comparable to the one we know, we need to be talking about CO2 and global average temperatures that are comparable to levels during the relatively stable Holocene epoch of the past 11,000+ years.  Those are the conditions that support life, with the current overshoot beyond 350 ppm being brief (in terms of geological time).
As for 0% CO2 concentration in the Earth's atmosphere, that would remove warming that essential for life on the planet. The goal is to have CO2 levels that are stable and also at a level which provides the warming for which life in the biosphere is accustomed to--which is less than 350 and probably even less than 325 ppm.  An accepted scientific paper is Target Atmospheric CO2: Where should humanity aim? [https://arxiv.org/pdf/0804.1126.pdf].
This discussion should also switch from the concentration of CO2 in the atmosphere to global emissions from a few human activities (roughly 90% being combustion of fossil fuels). The question to ask is how much do those human emissions need to change for the current annual increases in CO2 concentrations to stop rising?  They need to return to emission levels that were essentially zero as they were prior to the Industrial Revolution.  That is when natural global emissions and absorption (aka sinks) cancelled one another out to keep levels stable.  However, cutting global human CO2 emissions by half (or let's say 60% to be safe) will stop the rise in CO2 levels for a few years.  If cuts do not go further within the decade toward 100%, CO2 levels in the atmosphere will start to rise again.  Reference: IPCC AR4 FAQ 10.3 [https://archive.ipcc.ch/publications_and_data/ar4/wg1/en/faq-10-3.html].


Does Earth risk losing its oceans to space due to global warming?

We know that terrestrial hydrogen reaches space because ultraviolet images reveal
  a halo of hydrogen atoms surrounding the Earth (Fig. 2). Some of these atoms are
  escaping while the rest are trapped. The temperature at Earth’s exobase is typically around
  1000 K, although it varies as the Sun’s ultraviolet output cycles up and down every 11
  years or so. At 1000 K, hydrogen atoms have an average speed of 5 km/sec, which is
  below Earth’s escape velocity of 10.8 km/sec at the exobase. Yet hydrogen atoms still
  manage to escape because many move faster than average. This loss of particles from the
  energetic tail of the speed distribution is called “Jeans’ escape” after James Jeans (from the
  University of Cambridge), who described it mathematically in the early twentieth century.

The escape of planetary atmospheres Catling & Zahnle, Scientific American,2009 1

The exobase is the lower boundary of the exosphere.

I guess that two degrees increase in surface temperature would not make much difference to the $~1000K$ at the exobase.


What formed this rock slide formation near Hyndman Peak Idaho (photos)?

It is a normal rock slide, AKA a landslide, they happen all the time.

If a slope is not stable the rock collapses, landslides are very common and can be triggered by almost anything from rain, to imperceptible quakes, to simple erosion.
It could be rotational or translational the two blur together anyway. Most likely just a shallow rotational landslide.
The lower areas of a mountain being made of debris is extremely common, it is called a Scree slope. Where do you think all the rock that is eroded off the upper portions go?


Hyperspectral analysis is being used in mining and exploration extensively as a cheaper and quicker alternative to the likes of x-ray fluorescence, x-ray diffraction and others. Hyperspectral is even being used on an active mining faces with scanners installed on excavators and processed image being fed to a computer display that operator can use to direct digging of ores.

Now, as to the crux of your question - no, or at least very difficult. The problem with hyperspectral for ranged resource detection is that it primarily uses visual and near-infrared parts of spectrum. These wavelengths are very easily absorbed/scattered by everything and, therefore, they lack any penetration.

In most cases Earth's surface on satellite imagery will be covered by vegetation and various recent sedimentary formations which will make it nigh impossible to 'see' the bedrock potentially containing ore-bearing rock types and mineralogies.


Is it possible to form a diamond-sapphire hybrid?

Sapphires and ruby's are both aluminium oxide. sapphire melts at 2000 degrees and diamond synthesis can happen at 600 degrees. To coat around the sapphire, you would have to use multiple diamond seeds, which would make a polycrystal. it's probably humanly acheivable.

The scientists would have to study the adhesion of a transition layer, because the sapphire is trigonal, and makes 6 sided crystals, whereas the diamond is cubic.

They do use vapor deposition already to dope crystals with very colorful metals, for example you can build a home kit for titanium quartz.

Perhaps if they used some kind of force to grow the diamond in a given direction, like a carbon-cannon in the vapor chamber, they can control the diamond and have one structure around the other mineral.


Most likely.

I say that because it is heavily supposed that Mars, which is now tectonically stable, was active in the past. The reason why it has reached equilibrium is still a matter of discussion, and its tectonic history is merely hypothetical. But right away I'd say that the reason why Earth's tectonic activity could end converges on the reason why Mars, possibly, is stable nowadays: lack of internal energy.

You see, the current geological model that explains the movement of the tectonic plates is based in mantle convection. The mantle is strictly solid, but on a large timespan, i.e., on the geological scale, it behaves as a fluid, which (sort of) means it has enough mobility to move, and therefore for convection to happen. But here's the catch - convection is a form of heat transfer. So we can interpret that convection, and therefore plate tectonics, are but a form of heat to be "expelled" from the inside to the outside. And naturally, at some point energy should end. But at which point? In my opinion, for an astoundingly long time (over 1 billion, and perhaps even 10 billion years). Earth's been spitting energy for almost 4 billion years now (before that, it was actually gathering energy through the kinetic energy from the impact of planetesimals, which can be thought of as huge meteorites) and it still has enough energy to heat the inner core to over 4000 Celsius degrees (that temperature is due to pressure & Earth's remaining energy, though).

It is important to note that maybe due to the fact extreme depth is intrinsically associated with increased temperature, that pressure-driven temperature might suffice to generate mantle convection. But we wouldn't have oceanic crust generation (no inner heat - no partial melting next to mid ocean ridges - no oceanic crust generation), or it would be very limited. And besides, Earth is an open system with the universe, so it loses energy, and eventually it has to run out of it.


Free periodical satellite/aerial imagery

There are a wide ranging of publically available satellite images with different spatial and temporal resolutions. Notably Landsat (https://earthexplorer.usgs.gov/) and Sentinel (https://scihub.copernicus.eu/dhus/#/home) come to mind.
If you are interested in analysing remote sensing products at a global or regional scale, Google Earth Engine (https://developers.google.com/earth-engine) may be a useful tool for you. GEE can directly access Landsat and Sentinel products at no cost to the user.
I hope this information is of use to you.


What causes such a narrow slit in a cliff? (see photo)

If you see the other user (Jan Doggen's) google maps link, you can see apparently similar features in different states - this is a particularly neat example of a general phenomenon.

These notches form when headlands are undercut by caves carved out by the sea. They may be initiated where there is a fault or jointing in the rock (northwest Jersey is granite, according to google).

In this particular case, the notch seems to have a rounded termination. Blowholes also form from undercutting of headlands producing caves whose roofs then collapse. It's possible this cave may have collapsed after a blowhole formed, so you get a notch where the inland end of the feature appears rounded. That bit is just speculation though.

I found this Jersey geology trail guide that might have more detail: http://jerseygeologytrail.net/Geomorph.shtml