Is it possible for Earth to experience Polar Shift?

Yes, and it has happened before.

In the past 80 million years it happened over 150 times. The last time this happened was around 800 thousand years ago. A quick note about what a polar shift is, more properly termed a geomagnetic reversal. Earth's magnetic is such that a compass points to a certain direction. For example, a modern compass would point north. In a reversal, it would point south instead because the poles are reversed. Without going too much into detail, this occurs not by spinning of the poles but rather by decreasing in intensity until it becomes negative, thus reversing the poles.

Another important thing is the intensity. A strong magnetic field shields Earth's from some kinds of radiation, for example the stuff you can see in Gordon's answer. However, a reversed but strong magnetic field is just as fine. What you should be worried about is the change in the intensity of the field, and this is going up and down all the time, quite rapidly as you can see in the following figure:

The black bit (called Brunhes) is now - when the magnetic field is "normal". The white field in the bottom is more than ~780 thousand years ago, when it was reversed (called Matuyama). As you can see, even though the magnetic field has been normal though this entire time, the intensity went up and down. So yes, a reversal would mean that at one point the intensity would be very low, but this can happen even without a reversal.

  What would be the possible effect to human beings if this happens?

In contrast to what some people on the Internet claim, there would be no earthquake or volcanoes or other scary stuff related to it. This is simply not how this works. Also, mass extinctions from the geological history are not correlated with geomagnetic reversals, so you can take that worry off your mind. What can happen is detailed in a good way in Gordon's answer. Nothing too scary.

  Magnetic Field of the earth is seriously degrading for the past centuries and we are currently in the process of the so called Polar Shift

Not necessarily. It seriously degraded many times before without associated geomagnetic reversals.


Are the elements of an averaging kernel matrix always centered on the diagonal, or can they be exclusively off-diagonal in rare cases?

This statement from Geophysical Data Analysis: Discrete Inverse Theory: William Menke should make things clear for you

  The diagonal elements of the covariance matrix are a measure of the
  width of the distribution of the data, and the off-diagonal elements
  indicate the degree to which pairs of data are correlated.

Regarding the second part of your doubt whether a situation is possible where ds = 0 ; this would imply some error in measurement(for example - some noise) and would not have any implication on the geophysical nature of the data . It would be advisable to take multiple readings at different locations in this kind of situation.

Finally ds provides some insight into the quality of data collected but no true information about the "information content of measurement".


Could an earthquake create a design in a sand pendulum?

Interesting images, thanks for sharing them.

I think its quite likely that a sand pendulum would act as a type of seismograph.  I'm more in geochemistry than geophysics side of things but this kind of pattern does not seem at all inconsistent with seismic shaking.  The linear nature of a recording seismograph is because it is designed to record against a time scale which is perpendicular to the "movement" scale.  Even if movement had a stronger direction in the ground, the table and building this sand pendulum is in would translate the shaking movement into additional directions.  There were multiple movements to make the pattern shown.  It defiantly looks like more than just a truck or subway going by!


Could the Grand Canyon be flooded by the ocean if it got deep enough?

It is unlikely just from erosion. There are a couple reasons for this but because of the time scale over which this process would occur, other phenomenons might change the geologic picture completely.

The reason the canyon formed in the first place is because of tectonics that uplifted the rocks. From this page:

  Uplift of the Colorado Plateau was a key step in the eventual formation of Grand Canyon. The action of plate tectonics lifted the rocks high and flat, creating a plateau through which the Colorado River could cut down.

Erosion is much quicker when the slope is steeper so the carving of the canyon slows down as the river flow gets gentler. So the deeper the canyon carves, the more potential force it loses. From the same source as the earlier quote, a stratigraphic profile:

Another reason erosion has slowed down significantly is that the type of rock the water has to carve through is much different the deeper it gets. The river has now reached metamorphised layers that are much harder than the limestones and sandstones from the upper layers. The Vishnu Group is practically bedrock. This page has a nice explanation:

  The steeper the slope, the faster the runoff flow and the more force it will have to move material. The less vegetative (plant) cover and leaf material on the ground, the more open the soil will be to the flowing runoff water. Four things cause slope erosion: the amount and rate of rainfall, the steepness or gradient of the slope, the amount and nature of plant cover, and the type of soil and bedrock underneath.

Regarding this question:

  why don't we see the mouth of the Colorado (or any river for that matter) gradually move upstream, with ocean filling in where the river once was?

Erosion takes material away but this material has to go somewhere. Sediments are carried downstream and deposited at the mouth of those rivers, becoming what we call river deltas. The deltas usually advance into the sea as the mass of sediments is incredibly huge. Take a look at this picture:

This is the eastern end of Lake Mead where the Colorado river would flow when the reservoir level was higher. The entire flat brownish area is deposited silt from around 50 years of flow. I rafted through that now exposed silt and the walls on either side of the new channel were over 30 feet high. The same thing occurs in the oceans, but over much longer timescales.

So, to summarize:

There is much less water flowing through now than in the past. If Colorado winters become too mild and dry, then the river's power will be even further diminished.
The slope gradient of the river can only get gentler, so erosion will slow down.
The river has reached much harder rock that resists erosion much better.


why we don't have solar eclipse every month?

The moon's orbit is at a slight angle from the plane of earth's orbit around the sun, so it doesn't always hit the right spot, as described on NASA's Total Solar Eclipse 2017 site:

  Eclipses only occur if the Moon is located within 0.5 degrees of the
  plane of the ecliptic, on a line that passes through the center of the
  Sun and the Earth. The Moon travels along an orbit that is inclined by
  5 degrees to the ecliptic plane, so there are only two opportunities
  each month when it passes through the plane of the ecliptic. These
  points are called the ascending and descending nodes. Eclipses of the
  Sun only occur if new moon occurs when the Moon is near of one of
  these nodes. A similar argument explains why lunar eclipses do not
  occur every full moon at the node opposite the Sun from the Earth.


Are the Olympic Mountains (in Washington state) geologically unique?

Short answer: yes, there are other mountains which contains oceanic crust in their lithologies.

The process you described as "the upthrust of ocean crust" is called obduction. The resulting rock sequence is called an ophiolite. As you can see here, there is quite a lot of them around the world! One of the most studied is the Oman ophiolite. I have seen the Chenaillet ophiolite in the French Alps, it's quite spectacular.

Note that ophiolites usually include not only basalts (often in form of pillow lavas, typical of emplacement under the ocean), but also other oceanic crust lithologies such as gabbros, and even the underlying lithospheric mantle, often as serpentinite (a peridotite altered by water).

Edit:

I found a  Guide to the Geology of Olympic National Park on the USGS website. Unfortunately some links are dead, but you can still find lots of information on the range's lithology and formation. The page on "basalt and its associated rocks" mentions the presence of gabbro (a magmatic rock with the same composition as basalt but a crystalline texture due to slower cooling), but not that of any mantle rock. According to this other page on "colliding plates and Olympic rocks", the basalt is not from the oceanic crust itself but rather from a submarine volcano emplaced avove the plate (fig. 26). So, the Olympic Mountains would not be an ophiolite per se, but rather an accretionary wedge, i.e. "a thick wedge of rocks produced by the progressive offscraping of ocean floor sediments during subduction and their accretion to the continental margin" (excerpt from the guide's preface).


The other answers are correct that you need to know the soil depth to convert from mass units (kg m-2) to volumetric units (m3 m-3).  However, when comparing these variables you should also be aware that satellite soil moisture is typically measured only over the top few centimetres of soil. Total column soil moisture from a climate model will typically be the sum over several metres, so the dynamics of these two variables are likely to be quite different (contrast the red and light blue lines in the upper plot).

It's more common to compare satellite data with top-layer soil moisture and even then to normalize each dataset in some way, e.g,

$$NWI = \frac{SM - SM_{min}}{SM_{max} - SM_{min}}$$

or as normalised anomalies,

$$NWI = (SM - \overline{SM}) / \sigma_{SM}$$

I've used the latter to normalize the lower plot.  Normalization gets around the units problem, but doesn't get around the fact that you're comparing physically different quantities.


The temperature of the ocean below 1000 m

General Information

One major operational system for the measurement of deep sea temperature, salinity and pressure is the Argo program. Individual Argo floats are distributed in the worlds oceans. Their measurement data are scientifically evaluated and are available for public download. Additionally, several research institutions own gliders. However, I am not sure if they are also used operational for deep sea measurements.

Argo floats

Argo floats are large submerged buoys. They are made for profiling the top 2000 m of the world's oceans. The common depth of an Argo floater is approximately 1000 m. Approximately in 10-day intervals they sink to 2000 m depth and afterwards rise to the sea surface, from where broadcast their position and measurement data. Currently, more than 1000 Argo floats are active in the worlds oceans.

The official Argo homepage is here. Here you find a more detailed description of the function of Argo drifters and here you can download drifter measurements.

Gliders

Gliders are one tool for measuring temperature and salinity on vertical transects (actually not a purely vertical transect). Some gliders can go below 1000 m. The disadvantage of a glider is that it needs considerable horizontal space available straight ahead of his direction of motion.

A nice explanation and applications are given here and here.

This is the homepage of the global scientific glider community.


With fires, the forest cover and climate generally control what are the worse seasons for fires, add to this the human factor, accidental and prescribed burning.  For purposely ignited fires spring and fall are the major seasons, spring because the ground is often still damp but the fine fuels on the surface are dry enough to burn, making the fire easier to control, fall because the fuel is generally dry but the weather is getting colder and wetter with winter approaching making the fire easier to extinguish and reducing the time required to monitor the fire.

In the case of the Smoky mountains, it appears that the weather is more damp, humid, in the winter and summer, additionally, summer has more moderating green moist vegetation that is not present in the spring or fall.  The following excerpt from the Great Smokey Mountains Fire management plan directly mentions the spring and fall seasons (See page 16).  Great Smoke Mountains Fire Management Plan

  The annual fire weather cycle is more a function of seasonality and temperature than
  precipitation. Warm temperatures and exposed fuels during the dormant seasons of spring and
  fall condition the fuels for easy ignition and spread. In contrast, during the winter, cold
  temperatures prolong the wetting effect of the precipitation, and in the summer, heavy sheltering
  of fuels by tree foliage (coupled with high humidity) makes for poor ignition conditions under
  normal circumstances. Exceptions to the norm have occurred. Atypical dry spells in any
  season can result in more fires and/or unusually higher fire intensities. In 1987, and again in
  2007, extreme summer-time droughts made the normally fire-resistant hardwood forest
  susceptible to fire. Numerous lightning- and human-caused fires in and near the Park burned
  thousands of acres during summer months in those years.


What causes the beautiful Auroras on the north and south magnetic poles?

Straight from wikipedia:

  Auroras are associated with the solar wind, a flow of ions
  continuously flowing outward from the Sun. The Earth's magnetic field
  traps these particles, many of which travel toward the poles where
  they are accelerated toward Earth. Collisions between these ions and
  atmospheric atoms and molecules cause energy releases in the form of
  auroras appearing in large circles around the poles. Auroras are more
  frequent and brighter during the intense phase of the solar cycle when
  coronal mass ejections increase the intensity of the solar wind.

  Auroras result from emissions of photons in the Earth's upper
  atmosphere, above 80 km (50 mi), from ionized nitrogen molecules
  regaining an electron, and oxygen atoms and nitrogen molecules
  returning from an excited state to ground state. They are ionized
  or excited by the collision of solar wind and magnetospheric particles
  being funneled down and accelerated along the Earth's magnetic field
  lines; excitation energy is lost by the emission of a photon, or by
  collision with another atom or molecule:

  oxygen emissions: green or brownish-red, depending on the amount of energy absorbed.
  nitrogen emissions: blue or red; blue if the atom regains an electron after it has been ionized, red if returning to ground state from an excited state.

  Oxygen is unusual in terms of its return to ground state: it can take
  three quarters of a second to emit green light and up to two minutes
  to emit red. Collisions with other atoms or molecules absorb the
  excitation energy and prevent emission. Because the very top of the
  atmosphere has a higher percentage of oxygen and is sparsely
  distributed such collisions are rare enough to allow time for oxygen
  to emit red. Collisions become more frequent progressing down into the
  atmosphere, so that red emissions do not have time to happen, and
  eventually even green light emissions are prevented.

  This is why there is a color differential with altitude; at high
  altitude oxygen red dominates, then oxygen green and nitrogen
  blue/red, then finally nitrogen blue/red when collisions prevent
  oxygen from emitting anything. Green is the most common of all
  auroras. Behind it is pink, a mixture of light green and red, followed
  by pure red, yellow (a mixture of red and green), and finally, pure
  blue.


Why is more carbon in the atmosphere good, up to a certain level?

If plants were growing poorly when atmospheric CO2 was 200ppm, it was probably because Earth was in the middle of an ice age and covered with glaciers, not because plants were starved of carbon dioxide.

All things being equal, increasing the amount of carbon dioxide available in the atmosphere can benefit some plants, but the problem is that all things do not remain equal.

CO2 is only a fertilizer in environments where CO2 is the limiting input for a plant; plants in the outdoors may receive too little moisture, too much warmth, or too little sun for additional CO2 to make much difference.
Adding CO2 to the atmosphere also changes global and regional climates, reducing precipitation and increasing temperatures in ways that offset benefits from CO2 fertilization.

The authors of Plant growth enhancement by elevated CO2 eliminated by joint water and nitrogen limitation in Nature Geoscience found that

  the presence of a CO2 fertilization effect depends on the amount of
  available nitrogen and water. Specifically, elevated CO2 levels led to
  an increase in plant biomass of more than 33% when summer rainfall,
  nitrogen supply, or both were at the higher levels (ambient for
  rainfall and elevated for soil nitrogen). But elevated CO2
  concentrations did not increase plant biomass when both rainfall and
  nitrogen were at their lower level. We conclude that given widespread,
  simultaneous limitation by water and nutrients, large stimulation of
  biomass by rising atmospheric CO2 concentrations may not be
  ubiquitous.

Scientific American tackled the question in Ask the Experts: Does Rising CO2 Benefit Plants?, concluding that "Climate change’s negative effects on plants will likely outweigh any gains from elevated atmospheric carbon dioxide levels."

Researchers cited in that article pointed out that added CO2 provides diminishing returns, with Samuel Myers, principal research scientist in environmental health at Harvard University, noting that “We know unequivocally that when you grow food at elevated CO2 levels in fields, it becomes less nutritious."

The second part of your question was what would happen if CO2 levels fell to 200 ppm. This is unlikely to happen on human timescales; the current CO2 level is about 410ppm, rising 3-5 ppm per year. CO2 levels were at about 280ppm for most of human civilization, only increasing substantially when fossil fuel use became widespread in the 1800s. CO2 has a residence time in the atmosphere of several centuries.


How much distance does $0.001^\circ$ in latitude or longitude represent?

I don't understand the last sentence about decimal places, but I can tell you about the relationship between lat, long and distance.

Over two centuries ago, the meter was defined as one ten-millionth (1/10 000 000) of the length of a quadrant along the Earth's meridian; that is, the distance from the Equator to the North Pole. So, for latitude the number of degrees from the pole to the equator is $90^\circ\!$, and the number of meters is 10 million (or 10,000 kilometers). That means $1^\circ\!$ of latitude is $10,000/90 = 111$ kilometers, and $0.001^\circ = 0.111$ kilometers or $111$ meters, essentially an American football field plus both endzones.

The total length of the Equator is about equal to four times the distance from a Pole to the Equator. (Slightly more because the Earth's figure is a little oblate, like a slightly flattened ball.) Think of a great circle going from the North pole, to the Equator, to the South pole, to the Equator on the opposite side of the world, then back to North Pole ($360^\circ\!\!$ of a circle). That would be (almost) equivalent to the great circle ($360^\circ\!\!$ of longitude) of the Equator. So, at the Equator, $0.001^\circ\!$ of longitude will also be $111$ meters. But...

The other circles of latitude are smaller than the great circle of the Equator, yet still have $360^\circ\!$, so those degrees cover less than $111$ kilometers.

In fact, the size of a degree of longitude as a function of latitude scales as the cosine of the latitude. So $0.001^\circ\!$ of longitude change at $30^\circ\!$ latitude would be $111 \times \cos (30^\circ\!) = 111 \times 0.866 = 96$ meters.


Does this paper, using neural nets, prove industrialization is irrelevant to global warming?

The paper is deeply flawed from both the climate science and machine learning perspectives.  The most obvious being the most eye-catching claim that equilibrium climate sensitivity is approximately 0.6C, which if true would overturn our understanding of the climate system.  However the paper doesn't actually explain how this figure of 0.6C is obtained from a "largest deviation" of 0.2C, it is basically just a hand-wave.  Also the largest deviation is not 0.2, this is the largest average (mean absolute) deviation seen in the proxies, and you can have a mean absolute deviation without there being a trend that you could relate to increased GHG concentrations and hence estimate ECS.  More importantly, this would give an estimate of transient climate sensitivity, not equilibrium climate sensitivity, and you can't reliably estimate ECS (which is global) from regional or sub-regional proxy records.

Approaches such as the one taken in this paper, which seek to see how much of the data can be attributed to "climate cycles" with the remainder being taken as the anthropogenic component are inherently biased towards low estimates of ECS.  This is because of omitted variable bias; because the anthropogenic forcing signals are not included in the model, if the net effect of independent changes in the forcings is correlated with a sinusoidal component, they will be wrongly attributed to these climate cycles, when in fact they are produced by the forcings.  Models like this can only be used to estimate lower bounds on ECS, likewise if you make a model using the forcings as inputs and treat the residual as being "natural variability" it will tend to over-estimate ECS, giving an upper bound estimate.  The  Abbot and Morahasy paper cites a similar paper by Loehle, but sadly does not also cite the comment paper (of which I was the lead author, note the corregendum).  This is poor scholarship, and sadly  Abbot and Morahasy have gone on to make many of the same basic mistakes (but with a more complicated model), which is a shame.

Rather than using the original datasets (many of which are freely available) the authors chose to digitise images of the datasets instead.  This seems somewhat bizarre, and Gavin Schmidt points out via twitter that in at least one case the dataset has not been scaled or aligned correctly (andends at 1965, and so does not include the recent warming where anthropogenic contributions are most evident).  It also transpires that Figures 5 and 9 are identical.

The paper says "However, superior fitting to the temperature proxies are obtained by using the sine wave components and composite as input data. This was established by comparing the spectral analysis composite method versus the ANN method for the training periods.".   Evaluating performance on the training data is a classic error in the use of machine learning that people used to make all the time in the late 1980s and 90s, but is rarely seen today.  If you have two nested models (one can be implemented as a special case of the other) of different complexities, then the more complex model will always have a lower training set error, if only because it has more capacity to memorize the random noise in the data, but that doesn't mean it is the more accurate model.  For that you need out-of-sample comparisons, which are absent from the paper.

There is no handling of uncertainty in the model (for instance the periods of the cyclic components are not known exactly, cycles with slightly different periodicities will explain the observations almost as well), and likewise there will be uncertainty in the parameters of the neural net, but none of this is propagated through to give the uncertainty in the estimate of ECS.  As seen in the comment on the Loehle paper, this can be substantial.

Table 13 seems to suggest that paleoclimate studies give lower ECS estimates than GCMs, which suggests a rather selective view of the paleoclimate studies, which generally indicate high ECS IIRC.

The study also has problems with too many degrees of researcher freedom (e.g. how was the particular subset of proxies chosen?) and there is a lot of (automated) exploration of model architectures and feature selection, which is often a recipe for over-fitting in model selection.  It is also not clear why the observation should be a non-linear function of the cyclic variables (especially given that the cycles were obtained from the data by linear analysis).


Latent heat is released when water vapor turns to liquid\solid water.  So latent heat is released where there is precipitation.  So you're looking primarily at places where there is lots of moist convection... the ITCZ near the equator and then the midlatitudes.

I would believe that all of that latent heat release aloft should mean more heat is moved Poleward in the upper atmosphere branches of global circulation than would be moved by dry convection.  And would therefore make the circulation more efficient, perhaps having a long-term effect of allowing reduced horizontal wind magnitudes in comparison to a dry world (the resulting reduction in instability means weaker updrafts and the better transport Poleward means smaller temperature\pressure imbalances and thus less wind than a world without moisture).

Offhand I don't know the literature well... Google Scholar helps though you run into a lot of climate model parameterization articles using most terms.

The nature of the global circulation of the atmosphere should be fairly stalwart, as Lorenz was pretty big in the field I believe.  It talks about how latent heat in the tropics enhances the updraft winds in the ITCZ on page 17 a small bit.  The paper seems to suggest it would increase the global circulation strength by increasing those velocities.

Response of the Hadley Circulation to Convective Forcing in the ITCZ
looks like it might have potential too.

My most successful search term set seemed to be
"global circulation" "latent heat" -simulation -co2
though it still wasn't amazing.  But probably some other good articles to find if you thumb through them.

I'm certainly not a top expert in the field, but hope these thoughts and links add at least a little potential help or a starting point for you.


Why is colored seismic inversion called 'colored'?

Colored inversion is designed to approximately match the average spectrum of inverted seismic data with the average spectrum observed impedance (Lancaster and Whitcombe, 2000). The earth’s reflectivity can be considered fractal, and the resulting amplitude spectrum favors high frequencies (spectral blueing). If there was no preferred frequency, then you would have a "white spectrum", but as there are some frequencies with more energy, then it is called "colored".

Figure 4 from Lancaster and Whitcombe: Acoustic impedance from 4 sites in the North Sea


I found the picture with a small write up on a JPL site.

It's a picture of the Aine Corona with pancake domes.

  P-38340 MGN-48
  5/21/91

  This Magellan radar image shows a region approximately 300 kilometers (180 miles) across, centered on 59 degrees south latitude, 164 degrees east longitude and located in a vast plain to the south of Aphrodite Terra. The data for this image were obtained in January 1991.The large circular structure near the center of the image is a corona, approximately 200 kilometers in diameter and provisionally named Aine Corona. Just north of Aine Corona is one of the flat-topped volcanic constructs known as "pancake" domes for their shape and flap-jack appearance. This pancake dome is about 35 kilometer (21 miles) in diameter and is thought to have formed by the eruption of an extremely viscous lava. Another pancake dome is located inside the western part of the annulus of the corona fractures. Complex fracture patterns like the one in the upper right of the image are often observed in association with coronae and various volcanic features. They are thought to form because magma beneath the surface follows pre-existing fracture patterns. When eruptions or other movements of the magma occur, the magma drains from the fractures and the overlying surface rock collapses. Other volcanic features associated with Aine Corona include a set of small domes, each less than 10 kilometers (6 miles) across, located along the southern portion of the annulus of fractures, and a smooth, flat region in the center of the corona, probably a relatively young lava flow. The range of volcanic features associated with coronae suggests that volcanism plays a significant role in the formation of coronae.

Apparently, pan cake domes are on found on Venus.


Converting grid resolution from degrees to kilometers

Assuming spherical shape, Earth's circumference is about $40,000\mathrm{km}$. These are split into $360^\circ$, so one degree is a bit more than $100\mathrm{km}$. This is true for latitudes. For longitudes, the circles of constant latitude are shorter as you move away from the equator. Therefore you need to multiply that number by $\cos(latitude)$. To summarize, if $R_e$ is Earth's radius, we got

$$\Delta y=2\pi R_e\frac{\Delta lat}{360^\circ}$$

and

$$\Delta x=2\pi R_e\cos(lat)\frac{\Delta lon}{360^\circ}.$$
Note that here I am using $\Delta x$ and $\Delta y$ for the resolution in a cartesian frame with $y$ pointing south-north and $x$ pointing west-east. For your numbers, think about it as around $50\mathrm{km}$ resolution.


How can daily brightness be quantified or measured?

It can be measured in units of energy per surface area, for example, kWh/m2.  The official SI name would be radiant exposure but I haven't seen that phrase used in a climate or weather context.

For example, here is a map by NREL of average radiation per day in the US for July:

(Source: National Renewable Energy Laboratory)

And here is a map for Sweden for the same quantity per year (hence the much larger numbers):

(Source: SMHI)


Estimating the permeability tensor of an oil field by remote sensing

I remember a comment on this by Rodney Calvert in the video lecture version of his SEG Distinguished Instructor Lecture "Insights and Methods for 4D Reservoir Monitoring and Characterization":
http://shop.seg.org/OnlineStore/ProductDetail/tabid/177/Default.aspx?ProductId=1842

The comment was referring to the possibility of observing a pressure change front moving through the reservoir (as opposed to a fluid staturation change front) if one were to perform very closely repeated time lapse seismic surveys (down to probably days instead of months between surveys) AND in the very early stages of development. Costly of course but it would allow far superior well placement in complex reservoirs.

There's some reference to this in Chapter 2 of the book:
http://library.seg.org/doi/book/10.1190/1.9781560801696

but if I recall, the comment in the video lecture was far more specific. It is worht a try, the course is great to take anyways.

UPDATE

Following comments below and a review of some reference material.
The problem of permeability is that this is a multiscale property. You get different estimates (and different relationships, for example to porosity) at different scales (e.g. pore, lamina, bed, geobody, formation, and reservoir scales). The challenge is to link permeability at all scales and it is compound mainly by two facts: 1) at some scales you measure permeability statically, at other scales dynamically; and 2) at some scales permeability is not well captured/represented by any measurement (for example bedset scale, which is larger than core scale but often not well captured by wireline log data).

My advice to you would be to get this book by Patrick Corbett, the go-to guy in the field: http://library.seg.org/doi/book/10.1190/1.9781560801597. It is about 90 pages and it guides you through the whole process, with measurements, modeling, testing at all scales, topped by an excellent example of integration at all scales in chapter 6. I worked through the book and several of the reference papers 3 years ago, for personal knowledge, and it was great.

From a quick review last night I'd say one very important tool is Petrotyping, as defined in the book. The full work is in reference paper Corbett and Potter, 2004, Society of Core Analysts paper SCA2004-30. This paper defines Hydraulic Units as representative volume elements where geological, petrophysical, hydraulic properties are predictable and different from those in other units. Each unit is defined by a Flow Zone Indicator (FZI) (defined in the paper). A relationship is intorduced in the paper relating permeability to porosity via FZI. With this relationship a set of lines of constant FZI can be used as a template in a porosity (decimal) - permeability (log) plot to assess Global Hydraulic Elements in the reservoir. A Global Hydraulic Element is an element where the relationship between porosity and permeability is unique. If you are lucky your reservoir (for example a chalk reservoir, one of the examples in Corbett's book) has a single Global Hydraulic Element, in essence a single rock type of uniform properties. In this case you could go relatively easily from a static geomodel of reservoir facies modeled at the reservoir scale (and constrained with seismic inversion for acoustic impedance or porosity, ideally stochastically) to permeability at the scale of your lab measurements - you would be using also well tests (drill stem tests, production tests) and Lorentz plots. In the case of a developed field you may also integrate dynamic simulations and time laps (4D) seismic data (linekd to saturation and/or geomechanic changes introduced  in the reservoir by production).

If there are multiple GHEs, then the work of predicting at core plug scale, upscaling, validating with dynamic testing, and extending to the reservoir scale is more complicated (but still possible).

I really recommend the book.


How have levels of outgoing longwave and incoming shortwave radiation changed over the last 20-30 years?

Have we seen any changes in the flux associated with the recent "slowdown" in global warming?

There is no evidence for such a slowdown, nor for a change in the associated flux.  Atmospheric warming has not been significant in the past 15 years (nor can we significantly state that it hasn't warmed), ocean warming has continued.  As the oceans absorb the vast majority of the excess heat, this net flux probably has not significantly changed during the "slowdown".  Note that 15 years is in any case too short to state anything about global climate change.

As for your other questions: estimates of the flux have certainly changed over the past 20 years. but estimates vary quite a bit, so I don't think we can significantly state that there has been a change in the fluxes over the past 20 years.  Nor can we state the reverse; it appears further research is needed.

For an excellent and still somewhat recent overview article on the topic, see:

Trenberth et al., Earth's Global Energy Budget, BAMS 2009


How to relate the backward trajectories with offline particular samples?

Most atmospheric science researchers use back-trajectory analysis in qualitative sense to explain source of a pollutant. And as pointed out by the questioner, it is not possible to associate trajectories calculated at a particular time to the measurement that is average of say several hours.

However, quantitative analysis of observed concentration with back-trajectories is possible and is used to identify emission sources and their strength.

For the quantitative analysis, a large number of back-trajectories are simulated (of the order of 100000) from the place of measurement, however each trajectory is initiated with slightly different initial condition.

Let me explain with an example. Suppose PM2.5 concentration was measured on a certain date as 24 hour average at location given by co-ordinates x, y and z. Assuming that air was well mix in region surrounding x, y and z given by x-dx to x + dx, y-dy to y+dy and z-dy to z + dy, backtrajectories will be simulated, each with slight different x,y and z but within volume given by 2dx*2dy*2dz. Also, the number of trajectories simulated will be equally distributed in the volume and time period (24 hours in this example) to which observation represents. The simulation will result in distribution of trajectory with some grid-boxes visited by several trajectories whereas others may have no trajectory or very few trajectories. Emissions in the grid-boxes which are more frequently visited, have more potential to contribute to observed concentration. In other words, the concentration being measured at x, y, z will be proportional to sum of amount of time spent by each trajectories multiplied by emission flux in that grid box.

More detailed description of backtrajectory analysis and its application to related to observed quantity are available in following articles.

Gadhavi et al., 2015, Evaluation of black carbon inventories using a Lagrangian dispersion model - a case study over Southern India, Atmos Chem Phys, vol. 15, 1447-1461, doi: 10.5194/acp-15-1447-2015.
Seibert and Frank, 2004, Source-receptor matrix calculation with a Lagragian particle dispersion model in backward mode, Atmos. Chem. Phys., vol. 4, 51-63, doi:10.5194/acp-4-51-2004


Why do ooids not grow larger than 0.5 mm?

I was unaware of a 0.5 mm maximum rule with ooid size. The Sam Boggs Jr. book on Principals of Sedimentology and Stratagraphy indicates that ooids can grow up to 2 mm. Grains larger than this are pisoids.  The size limitation may depend on how you define an ooid. To me, an ooid carbonate grain with a nucleus and concentric layers of calcite or aragonite.

The size is likely a function of the availability of calcium and carbonate ions in the water (calcite or aragonite saturation).  I think that microbial action also contributes to large grain size, but if microbes are involved, then you might call it an oncoid instead.

The similarity of ooid size is a function of similarities in the environment of deposition.

Microfacies of Carbonate Rocks by Erik Flugel is a great book that discusses these features in detail.


Are there ways stormwater attenuation can be quantified for comparison between different systems or conditions?

A typical ratio calculated to quantify this type of response, especially at larger scales (such as for land use changes) is the runoff ratio:

$$R = Q/ P$$

where $R$ is the runoff ratio [mm/mm or dimensionless], $Q$ is the annual flow volume [mm], and $P$ is the annual precipitation [mm]. The runoff ratio is usually calculated for a given data period (multiple years of data) or on an annual basis. It is tricky to calculate for individual events since the antecedent conditions play a large role, but on an annual basis this would be a decent metric to compare different basins or the same basin in time. This is assuming you have a number of years of data to calculate the ratio from.


How much water gets consumed by residential use versus all other uses?

Dams are hydroelectric, thermoelectric is something else.

Thermoelectric refers to water extracted to boil to power a generator or used to cool the fluid used in said generator, In the US mostly coal, gas, and fuel oil plants but other ones like geothermal, nuclear, and mass solar also count, basically if it works off heat it consumes water (thermo- literally means heat). Much of this water of course evaporates. And yes it is quite high. About the same as we extract for irrigation.

 https://water.usgs.gov/watuse/wuto.html

Public water (purple), can be further divided, the USGS estimates public use as follows. You'll note no differentiation is made between commercial and industrial.

Wikipedia actually has a decent entry with further EPA estimate breakdowns, if you want to dive further.


Incised valleys and hydrocarbon potential

Sandstone bodies in incised valleys can be good hydrocarbon reservoirs.

Incised valleys form on the coastal plain and/or continental shelf during a fall in relative sea-level by a combination of fluvial and marine processes (e.g. fluvial erosion, headward erosion). Here's some coastal plain incision by the Orari River in New Zealand — look at those sand bars!

With the caveat that incised valleys can be filled with mud (non-reservoir) too, there are a few reasons why lots of hydrocarbon fields have been discovered in incised valleys:

Incision spatially focuses sediment delivery to the shelf-edge and slope. So if coarser sediment (needed for porosity preservation and therefore a reservoir) is stranded on the shelf, there'll be more of it the incision.
Sediment only stays where there is 'accommodation'. A big hole that wasn't there before (like a new valley) is accommodation.
The valley acts as a container, so channels tend to have a high ratio of thickness to width.
For these reasons, valleys sometimes fill with multi-storey sand/mud successions. Lots of reservoirs!
After the sea-level fall comes sea-level rise, or 'transgression'. Everything is flooded, and you're back to a marine environment. There's mud everywhere and so now you have a top seal.
It's relatively easy to connect a valley to a marine source rock, either directly updip via porosity, or via faults or other conductors.
Unlike basin-floor fans, which can also be good reservoirs, incised valleys are on the shelf and might still be beneath the modern shelf. This means there are many more options for drilling wells targeting them, and it's much cheaper and easier.
Compared to unincised systems, incised valleys are relatively easy to spot in well logs and even on seismic. So they are conspicuous, and easily diagnosed.
Since the start of the incised valley craze in the 1990s, incised valleys have been deliberately targeted, so there's probably some sample bias: lots of wells means lots of discoveries!

The last little gem is that, even if there's no luck exploring on the shelf, incised valleys might mean that coarse sediment has been delivered to the basin floor, opening up a promising play there too.


Why are there no CO2 snowfalls on Earth?

There is more to phase change than just what you see on that graph.  At temperatures and pressures that support multiple states (e.g. solid and gas) you have to look at the saturation vapor pressure of the gas and the actual vapor pressure (partial pressure) of the gas -- the line on the graph represents equilibrium between the states.  The differences between the two will tell you if you have net sublimation or net deposition and determine whether you end up with a solid or a gas. For solid CO2 to form you need to have more deposition (transition from gas to solid) than sublimation.  The transition to solid may also need help nucleating, though I'm not familiar enough with CO2 to say for sure.

To summarize, in your example Vostok at -90 C and 1000 hPa you have a rate of CO2 molecules depositing and a rate of CO2 molecules sublimating.  The partial pressure of CO2 in the atmosphere is low enough that there is more sublimation than deposition, e.g. net sublimation.  To deposit CO2 ice on the ground and have it stay there you would need atmospheric CO2 concentrations at least at saturation, which we do not have.

@Tristan provided some numbers in the comments that atmospheric CO2 vapor pressures (partial pressure) are <1 mm Hg (or less than about 133 Pa).  To get net sublimation you need to either reach saturation via increasing the vapor pressure (add more CO2) or reducing saturation vapor pressure (lower the temperature).  He provided an estimate that given CO2 partial pressures temperatures approaching -140 C would be needed for net deposition and CO2 snow.


Conditions at the bottom of a VERY deep hole

If it is enclosed and undisturbed there would be a risk of the heavier gasses collecting at the base of the hole, with carbon dioxide, argon, neon and xenon displacing the nitrogen and oxygen. Hence the danger of asphyxiation for any organism at that depth. Mixing, to keep the air homogeneous would also have the effect of heat transfer to further up the hole, so you will need artificial mixing and cooling. There are likely to be traces of helium and hydrogen at such depth, but not enough for the upward flow of such light gasses to have any significant mixing effect. However, hydrogen will be a potentially explosive problem at the enclosed surface environment. At these temperatures water rock reaction at the exposed base of the hole would be rapid. It is not clear whether your hole would have punched through to the mantle. I'm assuming it would, in which case there will be water vapour - hartzburgite reaction to yield more hydrogen. Serpentinization of the rock will proceed, involving about a 17% rock expansion. The rate of such a reaction will be limited by the amount of water vapour in the hole. A by-product of the reaction will be moisture at pH12 which will rapidly react with the high partial pressure of CO2 to produce carbonate encrustation. So it will be a problem to keep the hole clean - unless you prevent any moisture entering the hole from the surface control area.


Question about the sign of the shearing deformation terms

Did you try to sketch one of those situations? Try a square grid, define x and y, and then put $U$ and $V$ components onto one of the grid points, which you choose as starting point.

Now proceed to implement a). For example, from your starting arrows, go to the next grid point eastwards, and implement $\frac{dV}{dx}<0$, i.e. the upwards pointing arrows become smaller as you go eastwards. Do the same for U. Repeat for enough grid points until you see a pattern. Now connect $U$ and $V$ components into the final, two-dimensional velocity vector $\vec v$.

In this way you will possibly self-answer your question. I don't know if I can help you more, because I don't know what you mean with \

  I would like to know what does it mean to have

The end result will be the graphical representation of a vector field. The shear tensor simply measure the amount of shear in each vector field. You will discover that some field structures surprisingly possess shear, while others don't.


How long does it take for a stone to alter?

Mountains and rock do decompose or weather into sediment.  A basic rock cycle overview shows the possible pathways between all three rock types (igneous, metamorphic, and  sedimentary) how one type can be transformed into another. After a rock is weathered into sediment, that sediment can become a rock again.

Weathering rates of rock vary widely regional based on the following factors:

Mineral composition of the rock  (some minerals are less stable at surface conditions than others)
Amount of plant life growing on the rocks and mountains. (Plant roots can be powerful chemical and physical weathering agent)
Amount of precipitation (Chemical dissolution due to rainfall is a significant weathering factor for some rock types (carbonate rocks)
Seasonal freezing periods.  (Ice expansion in cracks and fractures can weaken rocks over very short periods of time.
Temperature range of the region.  (I believe diurnal temperature differentials specially in high mountain deserts has a specific weather impact on some rock types).
Local earthquakes and volcanic activity.
Erosion due to water (streams, rivers, lakes, and oceans).
Erosion due to glaciers and ice flows.

You can get an estimate of weathering rates of different rock types for a local region by careful examination of cemetery gravestones.


The answer is no, yes and then, perhaps, no.

No: water vapour is not "dissolved" in the oceans, rather it becomes part of the oceans through a phase change from vapour to liquid (possibly via an intermediary stage as ice). The process of "dissolving" refers to a substance entering a "solution", which is defined as stable mixture of two or more substances in which the state of the solution is determined, generally, by the solvent (the liquid water in this case). For example, see the wikipedia article on "solution". When water vapour enters the ocean, it is just adding to the volume of liquid water. Water vapour bubbles suspended in the ocean is another issue. When a gas is dissolved in a liquid, it ceases to be a gas. So we do not have "O2 gas" dissolved in the ocean, we have O2, which is a gas in the atmosphere, present in the ocean as a solute.

Yes: on the other hand, there is continuous exchange of water between the atmosphere and the ocean: sometimes water passes from the atmosphere to the ocean, sometimes the other way around, depending on the weather conditions. This is nothing to do the the process of being "dissolved", but, if the question is motivated by an interest in the exchange of compounds between the atmosphere and the ocean, this cycling of water between the two, which is described more below, will be of interest.

Finally, perhaps, no: the water vapour in the atmosphere is not in equilibrium with liquid water in the ocean (see wikipeadia foe discussion of equilibrium between liquid and gas phases). Generally speaking, the partial pressure of water vapour above the ocean will be below equilibrium, so there will be an evaporative flux of water from the ocean into the atmosphere. The steady evaporation of water from the surface of the oceans is balanced by precipitation (rain, sleet and snow) out of the atmosphere which falls on the oceans or falls on land and then drains into the oceans (see The Fundamentals of the Water Cycle).


Can we separate a sandy, clayey & salt layer on basis of their rheological properties?

In your question I think you are mixing up metamorphic conditions such as the conditions that gneiss forms from sedimentary rock with the formation of diapirs.  Diapirs occur where a less dense layer of a relatively plastic rock has denser overlying formations create sufficient pressure so that the less dense substance deforms and rises over time.

Diapirs of salt occur where thick salt deposits over overlain by dense sedimentary shales and sandstones.  Because of the slowness with which salt deforms the sedimentary deposits will be buried sufficiently deeply that they will have lithified, turning to rock and becoming more dense.  The salt layer will have some trapped water in it that helps the salt to recrystallize as a response to a pressure gradient.

Diapirs can also occur where water saturated sands are overlain by muds (sand volcanoes) or where water saturated clay layers are overlain by dense silts (mud lump islands).  In these cases the layers are relatively shallow and the sands and clays are not lithified.

In conditions of deep burial and high pressure differentials the sedimentary rocks will recrystallize into denser rocks and will deform, producing folds in some lithologies and faults in other rock types.  The slow speed of the deformations and high pressures and temperatures (mostly due to deep burial) give the mineral grains the rocks are made of time to recrystallize and move around each other.  Only if this sub-microscopic recrystallization is not happening fast enough will there be faulting in a layer.


Role of radiation parametrization update frequency in Tropical Cyclone simulation

Parameterizations are not usually updated at every time step, generally speaking. Radiation parameterization, in particular, is the most computationally expensive parameterization, since it calculates the integral of an exponential of an integral.

So what happens is you set a frequency to update the radiation parameterization, say every 30 minutes. So your model wiil find the diabatic heating tendencies from the initial state and use that for the first 30 minutes of model-time. After the first 30 minutes of model time, the parameterizations recalculate the diabatic tendencies based on the model values (such as clouds, etc). The shorter the timestep, the more you will account for changing model conditions. In short, it is how frequently the radiation parameterization is invoked.

So for example, if you are modeling your tropical cyclone, and you have the update frequency for too long of a time, you could be heating a place like the eye is passing over it, but the eye has already moved.

The shorter the frequency, the more the radiation will adapt to the model state, but at the cost of computational time.


The youngest and oldest source rock for hydrocarbons in economic quantities

According "The youngest natural oil on earth" Doklady Chemistry vol. 438, pages 144-147:

Prior to this paper, it was known that oil of the Guaymas basin is from young sediments and is 5000 years old.

However, their work shows that oil in the Kamchatka volcanic area is "less than 50 years old".  Oil is shown through carbon dating to have formed between 1962 and 1973.

At the opposite extreme, this 1986 New York times article reports:

  A team of geologists working for the Australian Government's Bureau of Mineral Resources reports in the journal Nature that it has discovered oil formed from the decayed remains of organisms that lived 1.4 billion years ago, when the earth was young. After the group drilled a 1,100-foot-deep test hole beneath the McArthur Basin in northern Australia, the oldest oil of its kind ever found bubbled to the surface.

Tiny amounts of oil as old as 3.2 billion years have been found more recently.


Is COMSOL Multiphysics good for subduction CFD modelling? Are there alternatives?

numerical modelling is a vast field and the tool to address your problem depends strongly on ... your problem and your approach!
Are you a master student? a PhD student with very short time to wrap up your thesis? A plumber with an intelectual interest in plate tectonics?
In short: Comsol may be an adequate tool. However, with large displacements (larger than the element volumes), you may want to avoid Finite Element method and probably better to have a look at other methods.
You can find a nice description of alternative methods in the book "Introduction to Numerical Geodynamic Modelling" from Professor Taras Gerya. He sugests to use Matlab, but you can probably follow all the book simply with Python.


What caused the Younger Dryas cold event?

The most accepted theory is that the Younger Dryas was caused by a large reduction or shutdown of the North Atlantic "Conveyor" because of a sudden influx of fresh water from Lake Agassiz and deglaciation in North America.
(Although evidence for such an event is thus far lacking.) The global climate would then have become locked into this new state until freezing removed the fresh water "lid" from the north Atlantic Ocean.

Another theory suggests that the jet stream shifted northward in response to the changing topographic forcing of the melting North American ice sheet, which then brought more rain to the North Atlantic which freshened the ocean surface enough to slow the thermohaline circulation.

http://geosciencesocietysio.wordpress.com/2014/05/04/paleoclimate-what-caused-the-younger-dryas-event/


Are the length of seasons the same globally?

As has been noted in a comment, it depends on how you define seasons (see https://earthscience.stackexchange.com/a/2603/111).

If seasons are defined in astronomical terms, then they have the same length everywhere on the planet. This is simply down to geometry.

However, the effects of astronomical seasons vary geographically in a number of ways. The magnitude of seasonal changes, for example changes in day/night lengths, is more pronounced in higher latitudes, so the effect of (for example) winter might be noticeable for a shorter time period in the tropics than the arctic, and hence some people might reasonably consider winter to be shorter there. There are other, less systematic variations that depend on local climate and weather. In weather terms, not everywhere in the world has the same 4-season cycle that temperate zones tend to experience - so when defining seasons in terms of observable effects one often has,  for example, a wet season and a dry season rather than spring /summer /etc.


Is silicon dioxide (silica) found in all types of soil on the planet?

tl;dr

Silica is everywhere, in everything. The amounts can be close to 100% in quartz sand, or less than 1% in things like peat or limestones (and derived soils). Finding completely pure soils (let's say less than 0.1%) is wishful thinking.

Silicon dioxide (or silica, or silicon oxide, it's all the same thing) can exist in two "forms":

As the compound, most commonly known as quartz, but also all kinds of other materials such as chert, agate, jasper, opal, etc.
As the chemical component in other materials (think oxygen in water). Most of the hard and brittle solid materials you know have silica as a chemical component in them. This includes most rocks, clay minerals, concrete, bricks, ceramics, etc.

Silica the compound (as quartz and others) is one of the most abundant materials on the surface. Sand (the white-yellow stuff) is commonly 99% quartz. Silt and clay are actually definitions of grain size, not chemical composition. Most soils that are silt or clay size also have abundant quartz in it. Quartz is a component of dust. This stuff gets everywhere.

For soils that don't have quartz proper in them, most will have silica as a chemical component. Clay minerals, pyroxenes, amphiboles, micas, feldspars, and all silicate minerals (which are the most common rock forming minerals on Earth).

It is easier to talk about the rocks and soils that don't have any silica in them.

Peat and other organic soils (coal?). These form by decay of plant material, and should not have any silica in them. However, since silica is a component of dust, and dust accumulates when these soils form, there will be some amount of silica. The amount can vary from a few percent to as little as a tenth of a percent, but it will be there.
Evaporites. Things like salt, gypsum, etc. These are chemically precipitated rocks which should not have silica. Then again, dust. There will be some amount.
Carbonates. Limestone is calcium carbonate. Limestones are rarely pure though, and the most common contaminant is - you guessed it - silica. Because of dust. Or just silicate sediments floating in the sea when the limestones form.


When GCMs are calibrated do they use 'corrected rainfall' input?

Precipitation is the results of physical processes. As each model implement convective and thermodynamic processes differently (mainly through parametrization or imposed by different grid cell resolution), each model will produce different precipitation. Hence, in other words, you can't tune precipitation, but you can tune the parameters that will produce precipitation. As rainfall is not an easy observable, especially in the period usually used for tuning (~1850-1900), climate modelers does not use such information for their tuning.

Mauritsen et al. (2012) gives an interesting overview of this subject. The abstract is given below. From this article, it states (emphasis are mine) :

"[...] Formulating and prioritizing our goals is challenging. To us, a global mean temperature in close absolute agreement with observations is of highest priority because it sets the stage for temperature-dependent processes to act. For this, we target the 1850–1880 observed global mean temperature of about 13.7 \deg C [Brohan et al., 2006]. Beyond that, we prioritize having globally averaged TOA shortwave absorption and outgoing longwave radiation in good agreement with satellite observations, along with a representation of important climate variability modes. [...]"

Abstract

"During a development stage global climate models have their properties adjusted or tuned in various ways to best match the known state of the Earth’s climate system. These desired properties are observables, such as the radiation balance at the top of the atmosphere, the global mean temperature, sea ice, clouds and wind fields. The tuning is typically performed by adjusting uncertain, or even non-observable, parameters related to processes not explicitly represented at the model grid resolution. The practice of climate model tuning has seen an increasing level of attention because key model properties, such as climate sensitivity, have been shown to depend on frequently used tuning parameters. Here we provide insights into how climate model tuning is practically done in the case of closing the radiation balance and adjusting the global mean temperature for the Max Planck Institute Earth System Model (MPI-ESM). We demonstrate that considerable ambiguity exists in the choice of parameters,and present and compare three alternatively tuned, yet plausible configurations of the climate model. The impacts of parameter tuning on climate sensitivity was less than anticipated."

Citation

Mauritsen, Thorsten, Bjorn Stevens, Erich Roeckner, Traute Crueger, Monika Esch, Marco Giorgetta, Helmuth Haak, et al. 2012. “Tuning the Climate of a Global Model.” Journal of Advances in Modeling Earth Systems 4 (3): n/a – n/a. doi:10.1029/2012MS000154.


I have found this fossil tooth, could it be pliosaur ? Or maybe theropod?

Most likely plesiosaur. That fluted structure is indicative of marine reptile teeth. My first guess was mosasaur but their are a lot of plesiosaurs from that formation so I would go with that. It is obviously a shed tooth which makes it harder. shark teeth flare out at the base becasue they attach differently than marine reptile teeth, sharks need more surface area for a strong connection.  Hopefully a marine reptile person can give you a tighter identification, I mostly work on dinosaurs.


Dynamic meteorology - calculating air temperature based off falling air

Well.. W/kg = J/(kgs) = Nm/(kgs) = (kgm/s^2)m/(kgs) = m^2/s^3 So, J and wg have same unit, and also your final answer has correct unit, Kelvin per second. Your final answer says the parcel`s temperature will drop, even without cooling term J(you will find this strange because it should be heated by adiabatic heating). It is because you set w=0.5 instead of w=-0.5. I hope this helps you :)


Typically seismic data should oscillate around 0 amplitude in the time domain, i.e. there should be just as much positive amplitude as there is negative (otherwise the ground would have had a net displacement in some direction). This is the energy at 0 Hz in the amp spectrum. It is like a bulk shift (DC shift) on the data.

So... unless the ground was permanently displaced by your seismic source, this is probably just an artifact. It could be as simple as: you used too few data to calculate your amplitude spectrum (e.g. small window, etc). Or it could be a super low frequency artifact coming from data processing.


Why is there a line of volcanoes along the northwest coast of North America?

The Cascades (the volcanic range that Mt. St. Helens and Mt. Ranier are a part of) are "arc volcanoes" (a.k.a. "a volcanic arc", etc).

Volcanic arcs form at a regular distance (and fairly regular spacing) behind subduction zones.  Subduction zones are areas where dense oceanic crust dives beneath more buoyant crust (either younger oceanic crust or continental crust).

The down-going oceanic plate begins to generate fluids due to metamorphic reactions that occur at a particular pressure and temperature.  These fluids cause partial melting of the mantle above the down-going slab.  (Contrary to what's often taught, the oceanic crust itself doesn't melt at this point - it's the mantle above it that does.)

This causes arc volcanoes to form at the surface at approximately where the down-going oceanic slab reaches ~100km depth (I may be mis-remembering the exact number).

However, there's an interesting story with the Cascades, the San Andreas Fault, and the Sierra Nevada.

Basically, Sierras are the old volcanic arc before an oceanic spreading ridge tried to subduct off the coast of California. (Search for the Farallon plate.) The ridge was too buoyant to subduct, so subduction stopped, shutting off the supply of magma to the volcanic arc.  Because the motion of the Pacific Plate (on the other side of the spreading ridge that tried to subduct) was roughly parallel to the margin of North America, a strike slip boundary formed instead: The San Andreas Fault.  Northward, there's still a remnant of the Farallon plate that's subducting beneath Northern CA, OR, WA, and BC.  Therefore, the Cascades are still active arc volcanoes, while the Sierras are just the "roots" of the old arc.


Specific Chemical Composition of Nero Marquina Marble

To a first order approximation, the black stuff and white stuff are the same. Both are calcite (CaCO3).

The only information I could find online was that it contains some impurities of Mg (as dolomite maybe?) and of Al2O3. This shouldn't matter too much to you. The black stuff is black because it is very fine grained, and of organic origin. This is a limestone - made from millions of dead animals. The mass of the rock is their shells, made of calcium carbonate. However, you need just a little bit of organic material and heat, and it all turns to graphite. Graphite is an excellent material in making stuff black. Even a small percentage of fine grained graphite dispersed in the rock will make it black. The white stuff is pure calcite. Dissolved and reprecipitated in fractures as coarse grained crystals without any graphite or other impurities. That's why it's white.

I'm not sure what do you mean by "manipulating". This rock (as all limestones) is very sensitive to acids: vinegar, lemon juice, carbonated drinks, etc. Put it out in the rain for several decades and you will see the damage. It's also very soft. Unlike granite, which can hardly be scratched, limestone will be scratched very easily.


Why is mass fraction always abbreviated wt% and not ma%?

This is because of historical inertia.

Yes, you are correct that "mass" is technically more correct than "weight". However, because these are percentages, it does not matter. There are no units. A rock that has 50 weight% SiO2 also has 50 mass% SiO2, regardless of the planet (i.e. g) you are in.

Regarding using "ma%" - I have never seen it and it would be confusing, especially since "ma" will probably be interpreted as the unit "milliannum" which is weird. Using "mass%" would be better, but "wt%" is only 3 characters compared to 5 so there's the issue of laziness. I have seen papers using "mass%" and that's fine, and I wouldn't object to such usage if I were to review a paper.

That said, geologist often weigh rocks. Yes, the numbers are mass. But the action itself is "weigh". Go figure.


You need a model. You could try to use Bayes theorem to build a model based upon conditional probabilities. See this reference from NOAA about weather forecasting: Probability Forecasting - Primer .

If I were to try to build a Bayesian model for weather forecasting, with the intention of using a limited data set of observations I had collected myself, I would look into existing software frameworks to see if I could use one of these. For example, the Infer.NET framework is available for free, and has several examples which would be a good starting point for learning about probabilistic modeling.


Did the impact event that caused the Chicxulub-Crater definitively and single-handedly cause the Cretaceous-Paleogene extinction?

No, it did not definitively single-handedly cause the KT mass extinction event. Around the same time, the Deccan Traps Large Igneous Province (India) was being emplaced. Flood volcanism has been associated with other mass extinctions, due to the impact on climate, sunlight at the surface, etc, of the output of huge volumes of sulphur-based gases.

The Chicxulub impact probably didn't hurt the extinction, but the large particulate material it distributed in the atmosphere would have sedimented out again entirely within a handful of years. Meanwhile, the Deccan Traps contain sediment layers intercalated between lava flows, some of which contain fossilised dinosaur eggs.

The reasons for mass extinctions (and whether they actually occur at all, as distinct identifiable events) remain poorly understood, but we're pretty sure the meteorite impact wasn't the only thing that did for the dinosaurs.


How do seismologists locate the epicenter and focus of an earthquake?

Earthquake epicenters are located using triangulation, this is possible once seismograms of the earthquake - coming from at least three locations - have been analyzed properly. Here is a good explanation on a site for seismology students at Michigan Tech which takes its seismogram illustrations from Bolt's textbook on earthquakes (1978). Read this page and you will have a good explanation of how seismologists determine the location of an earthquake epicenter.

How Do I Locate That Earthquake's Epicenter?


There is no strict definition of ammonites

Ammonites are not strictly defined. One can reffer to ammonites as to the whole group of ammonoids (Ammonoidea, ammonites sensu latto). This is common, but not supported by most researchers. Researchers use the term "ammonoid" for paleozoic ammonoidea and "ammonite" for Jurassic and Cretaceous Ammonoidea (ammonites sensu stricto). Ammonites sensu stricto reffer to ammonoids with complex (ammonitic) sutures, which are typical for Jurassic and Cretaceous ages. However, complex ammonitic sutures are not exclusive for Jurassic and Cretaceous ammonoids. Ceratitic sutures are not exclusive for Triassic either and occur in Jurassic ammonoids, too.

  So caution must be exercised when using suture lines as a means of classification. To obviate some of the problems posed by this
  simplistic classification, Wedekind, in 1918, introduced the terms
  palaeo-, meso- and neoammo-noids to classify ammonoids better.

(PDF) Goniatites. Available from: https://www.researchgate.net/publication/262048294_Goniatites [accessed May 10 2019].


Why do some places have rain frequently?

The factors contributing to such differences between any given 2 locations are simply too numerous to be specific. From the top of my head : Hadley cell, local topography, source of humidity upstream (oceans, lakes, ...), etc...

In the case you are referring (i.e. Cherrapunji), this is mostly due to a combination of Himalaya (topography forcing), Indian Ocean (source of humidity), Walker circulation and the strong tropical evaporation at those latitudes (among other things).


How to compute du/dx and dv/dy in moisture flux convergence?

I imagine you have a horizontal grid (x,y) and wind components u(x,y) and v(x,y).

Normally we do 1-degree of latitude constant (y-dimension) and equal to 110000 m. So your dy depends on how many degrees per grid point you have (yresolution). However, dx will vary according to the latitude.

dy=110000*yesolution;

Now, we may use centered finite differences to compute what you want. (Below is a Matlab code, but I believe generic enough to be reproducible in other languages).

for y=2:length(lat)-1
     dx=abs(110000*cos(latx(y)*(2*pi/360))*xresolution);
     for x=2:length(lon)-1
          div(x,y,1)= (u(x+1,y,1)-u(x-1,y,1))/(2*dx) + (v(x,y+1,1)-v(x,y-1,1)/(2*dy);
     end
 end

Note that you will have an empty frame around your divergence field when x=1, x=max(x), y=1 and y=max(y), once they do not have two neighboors to compute the differences. The same is observed when you do this with hdivg function in Grads, for example.

By the way, this is based on and yields the same result as Grads (I have checked!) using cdiff to reproduce hdivg.

Also note that the cosine function here works with radians, so if you compute cosines in degrees directly (i.e. cosd function in Matlab), you should omit the term scaling by (2*pi/360), which is just a conversion.

Hope it helps!


Does WRF simulation use sigma or eta vertical coordinate system?

WRF is using the sigma (terrain-following) vertical coordinate. However, as @gansub has already referred, in WRF V3.9 you can now select a hybrid sigma-pressure vertical coordinate. The advantage of this is that the coordinate is terrain-following near the surface, but it 'converts' to pressure levels at higher levels, which improves the accuracy of the calculation of the pressure gradient. Over very steep terrain the sigma coordinate extends this steepness throughout the atmosphere which is not very ideal.

For sigma coordinates, you still define the eta-levels. (Note that it sigma coordinates is just a normalisation of pressure)
$$
\sigma = \frac{p-p_t}{p_s-p_t}
$$
where $p$ is specified through
$$
p=A+Bp_s.
$$
It has been a few years since I played around with WRF, so I don't know how this change affects computational efficiency. If you get any results on this that will be interesting to hear.


How much of earth's molecular oxygen in the atmosphere is due to plants?

The oxygen in the atmosphere was produced by cyanobacteria during the Great Oyxgenation Event, around 2.3 billion years ago. Cyanobacteria produced & still, produces, to a lesser extent, oxygen by photosynthesis. Plants did not exist during the Great Oxygenation Event, but these day plants replenish atmospheric oxygen by removing carbon dioxide by photosysnthesis, like cyanobacteria. According to David Biello, The Origin of Oxygen in the Earth's Atmosphere the production of oxygen by cyanobacteria during the Great Oxygenation Event took one billion years.

During the Carboniferous period, about 350 million years ago, the amount of oxygen in the atmosphere increased to 30% because the rate of burial of organic matter prevented it from reacting with atmospheric oxygen, History & Significance of Oxygen in the Atmosphere

According to Wallace S. Broecker our atmospheric oxygen supplies are vast:

  Simply put, our atmosphere is endowed with such an enormous reserve of this gas that even if we were to burn all our fossil fuel reserves, all our trees, and all the organic matter stored in soils, we would use up only a few percent of the available $\ce{O2}$. No matter how foolishly we treat our environmental heritage, we simply don't have the capacity to put more than a small dent in our $\ce{O2}$ supply.

From Atmospheric oxygen - Broecker


How to find SMAP Satellite acquisiton plan?

As @gerrit pointed out, the Pytroll project has a couple of package which could be useful.
To answer your question and get the next overpasses for the next twelve hours above a given location, you can use Pyorbital (https://github.com/pytroll/pyorbital):

from pyorbital.orbital import Orbital
from datetime import datetime
orb = Orbital("SMAP")
orb.get_next_passes(datetime.now(), length=12, lon=16, lat=55, alt=0.05)

with length in hours, lon and lat in degrees, alt in km. And this will display (at the time of writing this):

[(datetime.datetime(2020, 2, 24, 13, 14, 54, 147587),
  datetime.datetime(2020, 2, 24, 13, 23, 23, 955297),
  datetime.datetime(2020, 2, 24, 13, 19, 8, 924860)),
 (datetime.datetime(2020, 2, 24, 14, 48, 41, 249324),
  datetime.datetime(2020, 2, 24, 15, 1, 24, 171709),
  datetime.datetime(2020, 2, 24, 14, 55, 1, 725148)),
 (datetime.datetime(2020, 2, 24, 16, 25, 14, 798347),
  datetime.datetime(2020, 2, 24, 16, 39, 0, 109628),
  datetime.datetime(2020, 2, 24, 16, 32, 5, 434271)),
 (datetime.datetime(2020, 2, 24, 18, 5, 14, 617775),
  datetime.datetime(2020, 2, 24, 18, 15, 43, 280401),
  datetime.datetime(2020, 2, 24, 18, 10, 27, 671621))]

Each tuple is (rise, fall, highest point).

Now we also have the pytroll-schedule package, in case you need to make a full acquisition plan, that will allow you for example to put priorities on satellites:
https://github.com/pytroll/pytroll-schedule


Temperature as a function of luminosity and greenhouse gas concentrations

You need a radiative transfer model and global climate model to do it with greenhouse gases.  you can derive the temperature without greenhouse gases as discussed below:

The absorption is highly variable depending on wavelength and can be seen in this graphic:

Radiative transfer through the atmosphere is specific to pressure, temperature, and wavelength. So in order to calculate the contribution of greenhouse gases you need to know their concentration distribution both vertically and horizontally not to mention an accurate representation of the atmospheric conditions. It's not one general function... it's millions of functions that all get integrated together and vary dynamically in time and space. I suggest you look at the HITRAN database for the complexities in absorption potential of different greenhouse gases.

You may also be interested in climate sensitivity paramaters.
From wikipedia http://en.wikipedia.org/wiki/Climate_sensitivity :

"For coupled atmosphere-ocean global climate models (e.g. CMIP5) the climate sensitivity is an emergent property: it is not a model parameter, but rather a result of a combination of model physics and parameters. By contrast, simpler energy-balance models may have climate sensitivity as an explicit parameter.
 (ΔTs) = λ (ΔRF)
The terms represented in the equation relate radiative forcing (RF) to linear changes in global surface temperature change (ΔTs) via the climate sensitivity λ."

This is convenient because if you know the change in concentration of a gas and the corresponding RF you can compute a change in surface temperature.  Though, I believe the climate sensitivity parameters are particularly for certain time and concentration regimes.


What equation should I use in this isostasy problem?

As this is a homework problem I don't think I can answer what you have posted.

I think you have confused Airy's stress function with his concept of isotasy.  For some helpful information to get you pointed in the right way try the Wikipedia article on isostasy:

https://en.wikipedia.org/wiki/Isostasy


What is the difference between an inertial instability and a symmetric instability?

Inertial instability is similar to the centrifugal instability in that we are looking at the stability of parcels to horizontal perturbations.  In the inertial case, however, the initial state is geostrophic balance rather than cyclostrophic balance.

Symmetric instability is the case where a parcel is inertially stable to horizontal perturbations and statically stable to vertical perturbations but unstable to perturbations between the horizontal and vertical.  An additional constraint is that the flow is symmetric and only varies in two dimensions.  This instability was also first examined as centrifugal instability, but with added baroclinity.  Conditional symmetric instability (CSI) is related to symmetric instability with the difference being that $\overline{\theta}^*_e$ rather than $\overline{\theta}$ surfaces are used to asses the instability.

For more information on these mesoscale instabilities, you can find information on them in Markowski and Richardson (2010) pages 49 (inertial instability) and 53 (symmetric instability).  Holton (4th ed, 2004) treats these instabilities on pages 204 (inertial oscillations) and 279 (symmetric instability).

Markwoski, P., and Y. Richardson, 2010: Mesoscale meterology in midlatitudes. Wiley, 430 pp.
Holton, J. R., 2004: An introduction to dynamic meteorology. Elsevier, 4th ed., 535 pp.


Mark's answer is correct, but in my opinion is not clear enough. Let's make it a bit simpler:

  Is it possible that the geomagnetic field reversal led to the extinction of Dinosaurs?

NO, DEFINITELY NOT

Here's why:

The cause for the K-Pg extinction event (in which many living species, including dinosaurs, died) is well known: volcanic eruptions (the Deccan Traps) and an impact (Chicxulub). It's still debated which one contributed more to the event, or whether one is the result of the other, but that's not the point. It's not related to magnetism.

In fact, all big five extinction events in Earth's history are well linked to increased volcanic activity (including the Siberian Traps at the time of the largest extinction, the P-T extinction event aka the "great dying").

On the other hand, magnetic reversals happen all the time. Yet, there are no extinctions related to them. Your question also lists several incorrect assumptions:

  continuous meteor bombardment

Incorrect: Geomagnetic reversals have no effect on whether we are bombarded by meteors or not.

  raised volcanic and tectonic activities

Incorrect: Geomagnetic reversals are not linked to raised volcanic or tectonic activity.

  Between Matuyama Epoch of 243 million ya to 68 million years ago to Brunhes-Matuyama current epoch

These are recent magnetic epochs from the Pleistocene, only a few million years ago. Thus unrelated to the K-Pg extinction event (or any event for that matter).


As far as I know; no. Lightning can either come from large amounts of friction in the atmosphere, or from a discharge of built up energy sourced from space (primarily solar radiation) captured by Earth's magnetosphere. The same energy that causes the Auroras.

That said, clouds will probably be present regardless of the source of the energy.


What would happend in distant future if we didn't extract fossil fuels

Obviously if all fossil fuels had been left in the Earth it would greatly lessen the climate warming problem. You ask what would happen to these fossil fuels in the course of time if we left them alone. The coal would remain inert and fairly well behaved; some would be exposed by erosion, but would do no harm. Some would be buried even deeper as new deposits of sediment were laid on top of them.

Most of the oil would remain buried out of harm's way, but some would be exposed by erosion and geological faults to form tar pits or asphalt lakes (which are both much the same thing). Oil seepages are a nuisance, because they pollute the sea and fresh water on land. Fortunately they do not occur very often. On land, the volatile fraction evaporates quickly and leaves a thick, sticky residue called tar or asphalt, the latter being slightly thicker.

Well known examples are the La Brea tar pits in Los Angeles, famous for the fossils of extinct animals trapped by the tar, and the asphalt lake in Trinidad which has long been mined for surfacing roads etc. There are several other tar pits in California, and a large asphalt lake in Venezuela.

Looking into the future, a few more oil reservoirs would be caused to leak in the course of time by geological faults, but most would stay safely in the ground. Meanwhile the old processes would be at work, transforming vegetable matter into peat, peat and wood into lignite, and lignite into coal. Plankton and vegetable matter in the ocean would form more oil reservoirs.

Present fossil fuel deposits will become buried more and more deeply in the course of millions of years, when man has vanished from the scene, with new layers of sediment and new fossil fuels laid down on top of them, but they will never be buried deep enough to reach the asthenosphere, never mind the centre of the Earth. They will just, in some cases, have another kilometre or two of rock placed on top of them.


What causes 'positive' lightning to be rarer, higher charged, and longer lasting than 'negative' lightning?

Positive lightning is indeed very interesting. According to the National Weather Service, the reason why it has a higher amperage and voltage is due to the due to the amount of air it must get through to reach the ground. Otherwise, it would never reach the ground.

  Since it originates in the upper levels of a storm, the amount of air
  it must burn through to reach the ground usually much greater.
  Therefore, its electric field typically is much stronger than a
  negative strike. Its flash duration is longer, and its peak charge and
  potential can be ten times greater than a negative strike; as much as
  300,000 amperes and one billion volts!

This would also account for the brightness of positive lightning and the extended duration, as a higher amperage & voltage strike would appear brighter and take longer to dissipate.

This page talks about why positive lightning occurs. It says:

  "Positive lightning" is a simple process of completing an electrical
  circuit from the cloud to the ground and back to the cloud.  As
  negative lightning strikes the ground, the ground becomes negatively
  charged over a wide area.  As the storm moves over this area and past
  it, the H+ in the upper reaches of the cloud feels this potential
  difference from the ground and sends out a positive streamer which,
  for all intents, looks like normal negative lightning.  The ground
  sends up a negative streamer and once these two join, electrons from
  the ground flow upwards to the H+ in the top of the cloud. The ground
  then becomes neutral once again.  The ground will hold the negative
  charge of dozens of negative strikes, building up a huge potential,
  before positive lightning will occur.   This is why positive lightning
  is so powerful.

Positive lightning is probably so rare because it takes so many negative strikes in order for enough energy to build up to cause a positive lightening strike.

There are quite a few interesting facts about positive lightning:

  Some interesting properties of positive lightning:

  Positive lightning can be the dominate type of cloud-to-ground during the winter months and in the dissipating stage of a
  thunderstorm.
  Positive lightning has been identified as a major source for the recently discovered sprites and elves. Sprites and elves are most
  likely lightning discharges but occur from 18-60 miles (30-95 km) in
  altitude, well above the parent thunderstorm.
  Positive lightning is usually composed of one stroke (negative lightning typically consists of two or more strokes)

Another NOAA site says that positive lightning can strike "near the edge of a cloud", or even 10 miles away from the cloud! This means that a positive lighting strike could occur somewhere where the sky is blue, and it's not raining.

In addition, there is also a type of lightning called "bipolar" lightning, which changes its polarity.


Does a mountain top have higher gravity than a nearby sea-level surface?

I gave this one some thought and ran some numbers.

The real answer to your question is that you would be lighter because the material that makes up continental plates is lighter than the basalt rock under it.  It might not look that way but continents, mountains and oceans are actually balanced with about equal weight under them.  Continents are above sea level because of larger amounts of crust which is lighter than basalt.  The earth, which is pretty malleable as a whole, adjusts for significant unbalanced changes in mass, it's still rebounding from the melted glaciers from the last ice age for example.

This happens with Mountains too, also slowly, but mountains are formed over millions of years so the adjustment has time to take place.  Mountains are formed when two continental plates push against each other, one slides under the other, so both what forms the mountain, and what goes under the mountain is lighter than basalt under the Earth's crust.   When you climb a mountain, you're not actually on top of more mass because much of the rock under you is lighter rock.  Mountains are actually puffy (I always wanted to say that).    If mountains were actually greater mass relative to the (relatively) spherical Earth, then they'd sink into the Earth, which they do to some extent, but, as I said above, Mountains are puffy buoyant compared to the Earth's crust, so the mass is pretty much the same on top of the mountain and at the foot of the mountain.

That's not to say the Earth is perfectly balanced, it's definitely not, but the imbalance doesn't appear to follow mountain ranges.  Google "Earth Gravity Map" for more on that.  Article with pretty picture here.

But I suspect, your question wasn't just real world but also a mathematical query, so, moving on.   If we create a cone shaped mountain, a large flat one, lets say it's 6.371 km tall (reason I picked that number will become clear soon), and lets give it 4 times that as a radius or 25.484 km radius to it's base and a specific density of 2.7, the mass of our mountain, using 1/3 base times height is:  3.1416 * .333333 * 2.7 * 25,484^2 * 6,371 * 1000  (the 1,000 is for density of 1,000 KG per cubic meter at specific density of 1) = about 1.17x10^16 KG.

So, on top of this artificial mountain that, if it was actually added to the earth, it would push the earth down and the earth would adjust it's mass around it over time, but ignoring that, the mountain is 1/1000th the radius of the earth so the distance from the Earth's center is increased by 0.1%

The mass of the mountain, 1.17E16kg is about 1/510,000,000 the mass of the Earth, 5.97E24kg, So we have a mass increase of about 0.0000002% and a corresponding reduction in gravitation by increased distance to the center of the earth (the square of 0.1%), or 0.0001.   or, 510 times as much is lost by the higher altitude than is gained by the increase in mass.  Now if you make the mountain flat enough, you'd probably be able to increase gravity the tiniest bit, but past a certain point the foot of the mountain is so spread out that the calculation grows inaccurate.  The short answer is simply, no, as the other two posters have said.  The mass of any mountain is simply insufficient to increase the force of gravity more than it loses by what's lost in the higher altitude.

A 3rd real factor, completely unrelated to your question is air density.  Heavier air does create some buoyancy which reduces our weight and the gravity we feel, this effect varies with high and low pressure and temperature, but on an average day at sea level air buoyancy reduces our mass by about .12%, so if you weighed yourself in a vacuum chamber vs your regular bathroom routine, you'd find you weigh about 2 or 3 ounces more for an average person.   Climb a mountain, the thinner air, you might gain an ounce due to loss of air buoyancy and that more than makes up for any small changes in gravity, so if you measure gravity by a scale and a weight, things weigh more on top of a mountain, because of thinner air, even though the G force is slightly lower.

The rotation of the earth and the centrifugal force also decreases mass, depending on how close the mountain is to the equator, (see picture).  as does the bulge of the Earth around it's equator, but all these changes are tiny.


Where can I find broadband seismic reflection data?

It depends on what purpose you need the data for.

This site https://wiki.seg.org/wiki/Open_data gives several sources of data. If it must be land acquisition (as opposed to marine) data then the Poland 2D, Teapot dome 3D, or Stratton 3D surveys might be of interest.

These free data sets are for pedagogical/research purposes, so if you'd like to 'strike-it-rich' these are not the droids you're looking for.

Hope this helps,
-D


A cylindrical projection with a vertically oriented cylinder which is tangent to the Equator produces a map that you are looking for. In this kind of map projection, all the points on the same latitude (all the points that are at the same distance from Equator) stays on the same horizontal line on the projected map.


How to convert Relative humidity (%) or Specific humidity (kg/kg) to Air humidity (mb)?

I guess what you need is water vapour pressure - that is one way of expressing humidity as the partial pressure of water vapour - in mb or hPa (they are equal).
According to World Meteorological Organization (WMO No.8 Guide to Instruments and Methods of Observation, Vol 1 Measurement of Meteorological Variables, ANNEX 4.B. FORMULAE FOR THE COMPUTATION OF MEASURES OF HUMIDITY), saturation vapour pressure - ews(t) - in hPa may be derived by the following formula, where t is temperature in degrees Celsius:
ews(t) = 6.112 exp [17.62 t/(243.12 + t)]

in hPa and degrees C, for liquid pure water (–45 °C to 60 °C)

This is the saturation water vapour pressure - a kind of "maximum" water vapour that can normally exist at a certain temperature t.
To know what the actual water vapour pressure - ew(t) - is, you must multiply it by the relative humidity (Rh) (and divide by 100 if Rh is in percentage):
ew(t) = ews(t) * Rh(%) / 100
So,
ew(t) = 6.112 exp [17.62 t/(243.12 + t)] * Rh(%) / 100
This is your "humidity" in mb, if you use Celsius for t.


Does the image of the pushbroom scans a path perpendicular to the direction of satellite travel?

Not really. There is no "scanning" in a push broom sensor. A push broom sensor does not have any moving parts; compare with the related whisk broom sensor which does indeed scan a path perpendicular to the satellite's motion. The difference between the two is that a push broom sensor has multiple identical sensors arranged in a line (orthogonal to the nominal direction of travel) while a whisk broom sensor has but one sensor. The line of sensors in a push broom sensor eliminates the need for scanning.

Both types of sensors form an image by forming image lines and then pasting those image lines, one after another, into an image buffer. A push broom sensor forms an image line by exposing all of the sensors to light simultaneously. A whisk broom sensor forms an image line by taking a series of snapshots, rotating the sensor a bit between each snapshot. With both kinds of sensors, the satellite's motion between capturing individual lines is what enables an image to be formed.


What causes some plates to move faster than others?

The driving forces of plate tectonics has long been debated. Several mechanisms have been proposed, mainly ridge push, mantle drag, and slab pull (see this page from the British Geological Survey). However, there is now a good agreement that slab pull is the main driving force of plate tectonics. It means that it is the subducting plate which controls the velocity of the plate's movement. And the rate at which a plate sinks depends mostly on its age/temperature/density: older plates are cooler/denser, thus they sink at a higher velocity than younger plates.


Why is Earth's inner core made of an iron-nickel alloy?

The first thing you should think about is how the accretionary disk cooled and the cosmochemical constraints this put on Earth (But I am not going into details here). From studying meteorites it is apparent that the oldest meteorites don't show signs of chemical differentiation (e.g. melting, ...) and are thought to represent the solids that formed from the accretionary disk. Because of their characteristic round structures, chondrules, they are called Chondrites. The most chemically primitive Chondrites (e.g. https://en.wikipedia.org/wiki/Allende_meteorite) roughly have the same composition as Earth. This is why it is thought that Earth formed by accretion of these smaller chondritic objects.

There are also other meteorites called "achondrites", meaning "no chondrules". They show signs of chemical differentiation (we can find stony-, stony-iron-, and iron-achondrites). For this chemical differentiation to happen it is necessary to think of the meteorite as having a parent body, on which this differentiation took place. These parent bodies differentiated similar to earth into an iron-nickel core (iron-achondrites), an olivine-rich mantle (stony and stony-irons) and a silicate crust (stony-achondrites). Because differentiation takes time, it is somewhat unlikely that a parent body formed, was destroyed and the iron-core was recycled to nucleate Earth (Earth has roughly the same radiometric age as many meteorites). So your suggestion C would take quite some explaining. Also suggestion B is not temporally possible, because the magnetic field needs a liquid iron core to work and therefore only came into existence after the iron migrated to the core.

A few words about iron-nickel. This has something to do with the abundance of elements in the accretionary disk (http://upload.wikimedia.org/wikipedia/commons/e/e6/SolarSystemAbundances.png). Iron and Nickel are very common elements. They are also siderophile, which means, that when a chondrite melts, the iron will try to separate from the sulfide- and silicate-melt. Because of the larger density of this melt, it will try to move towards the core of a planet. But it is very likely that other elements form a certain percentage of the core's chemical composition and it can be reckoned that this will be similar to some of the compositions of iron-meteorites.

If you get more interested in this I can fully recommend "McSween, Harry Y. (1999). Meteorites and their parent planets (2. ed. ed.). Cambridge [u.a.]: Cambridge University Press. ISBN 978-0521583039." which is very enjoyable to read and because of its descriptive approach not outdated. The newer book is also very good "Huss, Harry Y. McSween, Jr., Gary R. (2010). Cosmochemistry. Cambridge: Cambridge University Press. ISBN 978-0521878623.".


Can atmospheric conditions cause carbonated beverages to fizz more?

This is physics rather than Earth Sciences, but differential pressure between tinned liquid and atmosphere is by far the dominant factor. In Scotland I remember opening a can of 7-up at sea level with almost no effervescence. Then I climbed Ben Nevis, 1344 metres, and celebrated reaching the summit with another can. The resulting 'geysir' ejected about half the can in spectacular fashion. Temperature also has an effect in that the solubility of CO2 on a cold day, say 10 deg C, is about 30% more than on a hot day of ~30 deg C. So if the outside temperature is warmer than at the time the drink was canned, then there will be an excess of free gas that has come out of solution, but is still in the can waiting to be released. If we say two grams of excess CO2 in the can, that will yield about a litre of gas at one atmosphere and 21 deg C.

I'm wondering what the effect of a high sugar content would be. Could large organic molecules act as foci for gas bubble formation? Maybe a fun  school experiment!


Moon tilt against the horizon in a single day

Mooncalc.org offers a pretty comprehensive set of tools for viewing the moon.  Click on the location you want, then drag the slider on top through the day to see which direction's sky the moon will be in (or times where it will not be visible).  And it shows the moon's shape you will see (I presume that's as viewed with nearest horizon down?)
(For those interested, suncalc.org is their sister site for the sun.)

I'm not an astronomer, but this article from Goddard Space Flight Center looks like it offers a very solid discussion of libration, and the causes due to moon's orbit, the relative location of the moon from different viewing locations, and the tilt of the Earth in relation to the sun.