The Flat Universe Society

While it is clear that the earth is sort of round, rather like a baseball that has absorbed too many home runs, to the best of our understanding, the universe is flat.

By flat, we do not mean that you could walk to the edge and fall off, like pre Columbian notions of the earth. Rather, we mean that despite all of Mr. Einstein’s distortions of spacetime, at the largest scales we can manage, the universe follows the geometry of Euclid drawn flat in the sand.

If the old Greek guys had done their geometry on a sphere or a saddle (ignoring the impracticality of sand on these shapes for the sake of argument), the sum of angles in a triangle would not be 180 degrees. The same is true for any surface not perfectly flat.

Astronomers measure the distances to stars and such and can calculate the angles of triangles connecting them. Always 180 degrees.

This seems as peculiar as energy being a function of the speed of light squared.

Nevertheless, the flatness of the universe has become as embedded in our cosmology as pre Columbian notions of the earth. The critical density to achieve flatness is the cornerstone of many equations.

If you could fall off the edge of the universe, would you have found the multiverse?

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Energy and Matter

An interesting upshot of Mr. Einstein’s famous equation is that in units of the speed of light, energy and mass are equal. Mr. Poincare once observed that mathematics is the exercise of making different things the same (equal), and sophistry above with the square of the speed of light might be just the sort of trick he was referring to.

Nevertheless, the human concept of squareness derives from carefully drawn figures in the sand, subdivided and counted. A square divided in two each way yields four smaller squares, so it is natural to say that four is two “squared”. In this frame of reference, when you don’t subdivide your square at all, each side remains one, and you have but one square. That one squared equals one is unassailable.

We have noted before that equating energy to matter times the speed of light squared seems peculiar. Here we explore an alternate notion that the huge asymmetry between energy and mass in units smaller than the speed of light, disappearing to unity at the speed of light, is precisely why the equation works.

Mr. Einstein did not know about fermions. Fermions are subatomic particles that take up space, have mass, and constitute the matter in the universe. Electrons, quarks, and the triplets of quarks we call protons and neutrons are fermions.

Mr. Einstein knew about photons. He was instrumental in their discovery. Photons have no mass, take up no space, represent force rather than matter, and travel at the speed of light. In our standard model photons are bosons, and we see the difference between fermions and bosons as a fundamental division of the universe.

Complicating the picture, the divide between fermions and bosons is not about mass. The divide is about the ability (even propensity) to condense into or occupy the same space. Many bosons have mass derived from Mr. Einstein’s equation because they do not travel at the speed of light. Of the bosons, only photons, gluons (carriers of the force holding quarks into protons and neutrons), and the (as yet) hypothetical gravitons have no mass and travel at the speed of light.

This brings us to an important distinction between mass and matter, often loosely interchanged as the “m” in E=mc^2. All matter has mass, but not all mass is matter. While we can write E=f(ermions)c^2 and the expression is true, we cannot write E=mb(osons)^2.

If we use units of the speed of light, in some sense we pose our subject energy, mass, and matter to be travelling at the speed of light. This is not possible, as mass and matter cannot travel at the speed of light. There is still something the matter with our conception.

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Entropy and Watermelons

What is the entropy of a watermelon? This question is not entirely fair, because living things are singularities swimming upstream against the tide of entropy. We can’t merely count the ways the invisible molecules in a watermelon can be rearranged and still be a watermelon. We don’t even know all of the molecules in a watermelon.

We do know that a watermelon is usually over 90% water. We can weigh the watermelon and calculate the number of water molecules with 90% accuracy. We can then take the ideal gas constant and divide it by Avogadro’s number (this is the Boltzmann constant), multiply this by the log of the enormous number of ways we could exchange water molecules throughout the watermelon without changing its appearance, and derive a number for the entropy of 90% of the watermelon. This would be foolishness, because the reason a watermelon can swim upstream against the tide of entropy to exist at all is a result of information; the information in its DNA. Information can create singularities of negative entropy.

A watermelon is not a gas. Most gasses are invisible to us even at the macroscopic levels we chunk their molecules up, like pressure, temperature, and wind. Our conceptions of thermodynamics were really developed for steam engines, machines designed to extract work from the disequilibrium of pressurized gas. The molecules in a gas want to spread out. The molecules in a watermelon do not, at least not as quickly. The watermelon seems content, as if it has reached some (temporary) quantum of negative entropy equilibrium.

Steam is the gas phase of 90% of a watermelon. Not the steam we think we can see, that is actually liquid water that has condensed from the invisible gas phase. Most of the water in a watermelon is liquid or bound up in solid organic molecules. Solids, by definition, do now want to spread out as much as liquids or gasses.  The very property of being solid constrains the spread. The information coding for particularly the solid rind of the watermelon temporarily defeats the tendency to spread out.

Boltzmann entropy was the intellectual beginning of the notion that a probability field extends through the universe from the point human perception fails. The existence of the watermelon in negative probability phase space makes the value of W (the number of ways the invisible components can be rearranged without perceptible difference) negative. The fundamental reason for this negative entropy is information. Information implies purpose.

Entropy is perplexing because while we easily understand why it increases toward the future, since all the fundamental laws of physics seem reversible, entropy should also increase toward the past. Boltzmann wrote this off to probability, simply maintaining as a brute fact that probability flows to the future. Yet probability fails to explain why an entire universe should evolve with billions of galaxies each containing billions of stars, just to get to a human brain. It is far more likely that a human brain, whose perceptions reputedly define the line between the classical and the probabilistic, would randomly fluctuate into existence.

So while we can derive a number for the entropy of a watermelon based on the statistical mechanical properties of the high proportion of water it contains, we really have no way to evaluate the probability of the information it contains. In some sense all living things are watermelons. In some sense our planet is a watermelon.

 

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God and Dice

We don’t spend much time thinking about what God does for recreation these days, but the great scientists from Newton to Einstein who have framed our Western cosmology were often deeply religious men. It is understandable that when they found three term equations that explained nearly everything, they believed these were insights to the mind of God.

1/r^2 Newton’s inverse square diminution of gravity.

F=ma Newton’s second law. Describes the relations between force, mass, and acceleration.

S=klogW Boltzmann’s formula for entropy.

E=hv Planck-Einstein energy of a photon, Planck’s Constant x  frequency.

E=mc^2 Einstein’s General Relativity. In units of the speed of light, energy=mass.

These are a few famous examples, and except Boltzmann, they are classical mechanics. In classical mechanics there is no need for probability, and there is no margin of error (except in measurement). The rules are absolute. Space is a field, or reference frame with fixed Cartesian coordinates, x,y, and z. Even today, you need nothing but classical mechanics to send a rocket to the moon. Except for a small deviation in the orbit of Mercury, classical mechanics describes the motions of the planets in our solar system.

The flamboyant Monsieur Laplace seems to have been the first to observe that using Newton’s laws, if you knew the position and momentum of every particle in the universe in the present moment, you could extend this information indefinitely into both the past and the future. You would know everything there was to know. (Momentum is a vector quantity that includes direction). Asked by Napoleon why his work contained no mention of God, he replied that he had no need.

In Special Relativity Einstein argued the concept of spacetime, where every xyz coordinate becomes a clock that is inseparable from the point. He showed that in a curved trajectory different observers would record different amounts of time passing. Space and time are relative.

In General Relativity Einstein argued that spacetime itself is warped by gravity, and that not only space and time, but energy and mass are relative. The only constant is the speed of light.

Newton’s and Einstein’s theories are classical, there is no probability, no statistics, and no dice. The title of this post refers to a quote from Albert Einstein made in a letter discussing statistical mechanics with Max Born. He said (in German),  that he believed God does not play dice with the universe. We will argue in favor of Einstein in this regard. We will argue that Boltzmann’s introduction of probability in his study of entropy set the stage for probabilistic notions in quantum mechanics. We will argue that both probabilistic approaches founder on an anthropocentric philosophical error.

It is ironic that the probabilistic approaches to entropy and quantum mechanics both begin with a wildly improbable assumption: that what humans can perceive somehow matters at a fundamental level in the universe. The basic problem is that the nanoscale world of molecules, atoms, and sub-atomic particles is largely invisible to us.

For Boltzmann, the solution was to count the ways the invisible components can be arranged and remain visibly the same. Entropy becomes the log of this number of ways the invisible components can be arranged (w) multiplied by Boltzmann’s Constant (k); which is the ideal gas constant divided by Avogadro’s number. Boltzmann’s insight was that the behavior of gasses well understood at a practical level by engineers of the industrial revolution, was dictated by the interactions of the invisible molecules and atoms.

We can see above that it works very well for the density of the earth’s atmosphere. The molar concentrations of the invisible (to us) gasses in the atmosphere are well-known. If we suddenly developed the ability to see the different gasses, and they became distinguishable to us, nothing would change. Entropy here is the separation between the molecules in the air, density–regardless if we can see the molecules or not. Is it simply more probable that the spaces between molecules seek a higher entropy equilibrium as pressure is relieved, or is it certain they will do so?

Probability is a tool for the blind. If we can see it, it is classical; if not, we would have God play dice. We are blind at the scale of particles, atoms, and most molecules. Quantum mechanics is fundamentally the notion that the energy of electrons is not a smooth linear progression, but rather a stairway with discrete intervals or steps; quanta. Our efforts to locate electrons and other subatomic particles are hindered by the unfortunate circumstance that when we ping them we unavoidably alter them. Werner Heisenberg formulated this as his uncertainty principle. We can know either the positions or  momenta of invisible particles, but not both. This quandary evolved into the probabilistic notion of a wave function, where waves of probability are our only information until we collapse the wave to a particle by pinging it. It is even maintained that there is no such thing as where the particle actually is until it is observed.

Can you imagine anything more anthropocentric? If a tree falls in a forest and nobody hears it, did it really fall? Of course it did. It is not a matter of phase space between probability waves. It is easy to go and see many fallen trees that very likely nobody heard. Trees fall and  particles have positions and momenta regardless the perceptions of naked apes, or even – aliens capable of somehow garnering information on both position and momentum.

Take a macroscopic object, a watermelon. They differ somewhat in color, size, and skin pattern. These differences arise from somewhat different arrangements of components, but people will generally agree that a watermelon is a watermelon. A watermelon is composed of all manner of quarks held together in Protons and Neutrons by the strong nuclear force. These may be surrounded by electrons in quantized shells held to the protons by the electromagnetic force (and to both neutrons and protons weakly by gravity). These atoms may be bound to others by ionic or covalent bonds in complex molecules. Add these layers up and you sometimes get a watermelon.

When we observe a watermelon, we change the universe. Photons of visible light reflect from the surface of the watermelon and our retinas absorb these photons, which otherwise would have travelled to a different fate. Did the watermelon exist before we observed it? Did the photons exist before our retinas absorbed them, or were both the watermelon and the photons mere probability waves before we intervened? When we turn our back to the watermelon, our eyes no longer absorb the photons. Some may be reflected from our clothing, and others may be absorbed by our skin without sending information about the watermelon to our brain. We change the universe even when we don’t observe the watermelon, but the watermelon is still there.

Imagine that our vision deteriorates and we can no longer see individual watermelons, but can barely discern a large pile of watermelons. We will have lost a lot of information. Our degraded retinas absorb a different set of photons.We could then argue that the positions of the watermelons in the stack is a probability function, and there is no such thing as exactly where a watermelon is in the pile until we reach in blindly and grab one. This would be foolishness, but it is exactly what the probabilistic  Copenhagen Interpretation of quantum mechanics would have us do. If the pile of watermelons is subject to gravity and forms a cone, we could even develop formulas that determine the probability of grabbing a watermelon as being much higher when we reach blindly toward the bottom of the pile rather than the top.

By having God play dice, we elevate probability to the status of a force of nature, joining the strong, weak, electromagnetic, and gravitational forces. The field and waves are established in the form of the wave function. A probability particle can’t be far behind.

 

 

 

 

 

 

 

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Entropy and the Grand Canyon II

We left off in the last post having boated 78 miles, about five days on a typical trip, and having encountered the last of the suite of three books that comprise the geological story revealed in the Grand Canyon. We also concluded that the fluctuations in the altitudes of land and sea evident in the story appears to be the breathing of a great beast deep within our planet.

In the 78 miles we have navigated 16 rapids with holes big enough to turn our 18′ rafts upside down. These holes result from the water’s defiance of gravity and momentum to curl back upstream to fill voids in the flow when the water is forced to pass around rocks. It curls back upstream to reduce the gradient in potential energy from the disturbance of the water’s cohesive force, and increase the entropy.

Fortunately, age and experience can influence luck, and this was our first trip where nobody was even out of the boats in a rapid.

The Vishnu metamorphic complex brings us to a really staggering unconformity, called the Great Unconformity. We may recall that the Tapeats sandstone began to be deposited about  545 mya, just slightly before the Cambrian period, the first period of the Paleozoic era 540 mya.

The Tapeats was deposited variously on top of late Proterozoic Super Group members where they occur, and on top of  the early Proterozoic Vishnu complex where the Supergroup is absent in much of the canyon. We may also recall that the Vishnu complex includes both highly metamorphosed sedimentary rocks and magmatic plutons which injected and overprinted any age information in the sediments. Our best overall dates for last crystallization are 1.7 billion years ago.

Where the Tapeats sits on the Vishnu, a little arithmetic reveals that the Great Unconformity spans 1.16 billion years. This is almost exactly 1/4 of the time since our planet is thought to have coalesced from stardust 4.6 billion years ago.

Above is the unconformity in Blacktail Canyon. The bedding within the Tapeats above the unconformity is highlighted by the different lime content and erosion resistance. If you look carefully, you will see some very thin bedding just above the contact, that based on color, seems to be erosion from the Vishnu. These redder bands alternate with lighter material from a different source, possibly the same source as the lighter bedding seen generally in the Tapeats above.

Really though, the Great Unconformity between the Tapeats and Vishnu overstates the case a bit. The Supergroup is absent here, but it exists elsewhere in the Grand Canyon. The Vishnu was folded nearly vertical at some point. The Supergroup was tilted against the Vishnu at some point, and both were eroded to a nearly flat surface during the Great Unconformity. This flat surface eventually received the Tapeats, and the Tapeats therefore overlies the Vishnu and each of the tilted layers of the Supergroup in turn.

Above we show a more fair representation of the Grand Canyon unconformities. These were assembled using date ranges for members from Wikipedia and Macrostrat. The two sources do not always agree, so a measure of our own judgement was required. This cannot be considered the last word, but the general trend for longer unconformities the further we go back in time is clear.

It may be that as you go back in time, the probability of having had a long unconformity that erases a lot of little ones increases. Or it may be that the breathing of the great beast has sped up.

Ludwig Boltzmann was the pioneer of statistical mechanics, a notion that although some important things are unknowable to us, like the position and velocity of every atom in a watermelon; we are not entirely powerless. He showed us that in situations where we can count the possible ways the atoms could be rearranged and still appear to be a watermelon, we can calculate the probability of a watermelon. Unfortunately, neither watermelons nor great breathing beasts are among these situations.

Unconformities are the most fundamental and largest scale changes evident in the Grand Canyon, but they are by no means alone. Every layer shows some level of fluctuation between more marine, calcerous, well sorted periods; and more terrestrial, silicious, and poorly sorted periods.

More Resistant Lighter Layers Form Cavern “Cieling”

We saw the fluctuations in the Redwall above in the last post.

Muav Cycles, ~1,000 year Clastic Intervals

Above is some detail of the Cambrian Muav from National Canyon. If you measure the average distance between the bands and factor the section thickness and duration of the Muav you can calculate the intervals. This is a crude exercise. It can tell you it is probably not  100,000 years, and probably not 10 years.

One Chock too many for wet feet

Above is some context of the finely bedded Muav.

If you measure the spacing of these fluctuations within the Muav, or the Redwall or any other large scale stratum, you discover that despite the appearance of regularity, the spacing is never exactly the same.

One could take a section of aside creek like the one above that cuts through only the Muav, and imagine it as a miniature Grand Canyon. Sequences could be identified , grouped, and dated, and possibly unconformities could be found. This has been done for the more wildly varying members like the Supai.

Ultimately our groupings, and how sharply we focus our scope becomes somewhat arbitrary. It is our nature to rationalize and categorize, but at some point we are always left like Ludwig Boltzmann; trying to count the possible ways this all could have happened to assign a probability, when all we can see is the apparent result a great breathing beast.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Entropy and the Grand Canyon

It has been our good fortune to row 280 miles of the Colorado River through the Grand Canyon twice in the last seven months. This is rare for private boaters limited to one trip per calendar year and subject to a lottery system where a decade can pass between successful applications.

Carved very recently, by many accounts within the last six million years, the river has exposed a section of the earth’s crust that provides a rare opportunity to study the ways our planet worked in the past. The clear message of this section through the crust is change. Constant and unremitting change; change working simultaneously on different time scales. Change working differently in different parts of the Canyon.

A boat trip down the Grand Canyon begins a few miles below Glen Canyon Dam and Lake Powell, at a place called Lee’s Ferry. Faulting has resulted in the canyon being eroded back here, allowing access by road. The next road access is 226 miles downstream. The red formation in the middle background is the Moenkopi formation, deposited above sea level in a low energy delta and braided stream setting. Moenkopi is of earliest Mesozoic age, the age of dinosaurs, but dinosaurs had not yet evolved. Tracks of Therapsids, the reptilian branch that would eventually lead to mammals can be found in the Moenkopi mud. Below Lee’s Ferry, you bid farewell to the Mesozoic, and enter a realm where older Paleozoic rocks form the canyon rim.

Conformity in geology is when sediments are deposited in an uninterrupted sequence. The most fundamental changes in the Grand Canyon are the unconformities, where a time interval is missing. The first such unconformity is between the Mesozoic Moenkopi and the underlying Paleozoic Kaibab limestone. It is difficult to know if sediments were simply not laid down during the interval of unconformity, or if they were laid down and later eroded away.

The missing time between the Moenkopi and the Kaibab means that the Grand Canyon section does not speak to the greatest extinction in the history of life. This extinction marks the end of the Paleozoic and the beginning of the Mesozoic eras. Fortunately for us, our Moenkopi Therapsid relatives survived this extinction. Unconformities, missing time intervals, mark most layers, and all layer groups in the Grand Canyon.

Above is the configuration of continents 250 million years ago at the Mesozoic/Paleozoic boundary according to Christopher Scotese’s Paleomap Project. The supercontinent Pangea was beginning to break up, and a seaway had formed between North America and Africa.

Above is the configuration 260mya during the formation of the Kaibab Limestone that forms the rim of the Grand Canyon. The 250mya continents remain in tan beneath and it can be seen that Pangea tightened up and rotated as we progress backward in time. The Kiabab was very much an inland sea, and as the river cuts quickly through the upwarp visible in the first photo, the Toroweap formation beneath the Kaibab formed in an arid inland lake like the current Great Salt Lake. By mile 4 the river has already cut to the underlying Coconino sandstone, laid down as vast dunes like the current Sahara Desert covered large areas of western North America. You may have guessed that the Coconino and Kaibab are separated by an unconformity.

By mile 8 the river has cut through to the Coconino to the Hermit shale, separated by an unconformity. The Hermit was laid down in low angle braided streams on land. By mile 12, separated by another unconformity, the Supai group is exposed. The Supai group is characterized by alternating marine limestone cliff forming units and stream deposits laid down on land that are less resistant to erosion and form slopes.

A typical river trip makes its first camp in the Supai. It has been a busy day cutting through 50 million years!

At 300mya the continents are shown in purple with 250mya as tan background. Remember that the tan areas were ocean 300mya.

Entropy is a fundamental force of nature that acts to minimize all gradients. It is universal, working from molecular scale to the forces that move continents. Rocks fall from the canyon walls to the river because the gradient of altitude is reduced. The river flows to the Sea of Cortez because the gradient of altitude is reduced. “Ah”, you say, “this is just gravity.” The river shows us it is not just gravity. When the water is forced to separate around an obstruction, usually a rock, the water curls back upstream, defying gravity, to fill the void and reduce the gradient in its own cohesion. We call these “holes” and try to avoid the big ones as they can turn your boat upside down when the water curls back upstream.

The Supai has an unconformity within it that separates the Permian, the youngest period of the Paleozoic era, from the older Pennsylvanian.  Besides the “icehouse” period we currently live in, the Pennsylvanian/Permian transition about 300mya marks the center of the mist recent “icehouse”, a long period of glaciation that extended well into the Permian. The Pennsylvanian is notable for the highest atmospheric Oxygen levels in our planet’s history.

It takes the river 11 miles to chew through the Supai, and at mile 23 the Redwall limestone that defines the older Mississippian period in the canyon is first exposed at river level. Of course, an unconformity separates it from the overlying Supai. The Mississippian period saw the first  amphibians crawl on to land to live, but in the Grand Canyon the Redwall Sea resulted in the deposition of carbonate shells of foraminifera, corals, et al 800 feet deep. The resulting limestone is resistant to erosion and forms imposing cliffs above the river.

We can see above that even the massive Redwall has striations. Despite its name, the Redwall limestone is not naturally red. It is painted red by color from above. The lighter bands have higher carbonate concentration, are more resistant to erosion, and stick out from the wall further than the softer intervening bands. The softer bands are more porous and hold the paint better.

 

More Resistant Lighter Layers Form Cavern “Cieling”

Above is detail of Redwall Layering from the near the bottom of the Redwall section at the famous Redwall Cavern.

The layers get tighter toward the bottom of the Redwall sequence, and some folding aided the river in undercutting this cavern.

Above is the current distribution of Pennsylvanian (lower Supai) and Mississippian (Redwall) surface rocks in the western United States. These are broad categories chosen by individual State Geologists, and some Permian rocks are included, but it can be seen that shallow ocean covered large areas. These are all sedimentary rocks except some minor volcanics in central Nevada. These volcanics and the folding at the bottom of the Redwall are probably related to the Antler overthrust in Nevada where sediments were pushed over what was then a continental shelf.

Above are the continents 360mya, the transition between the Mississippian Redwall and the older Devonian Temple Butte Formation. Dominant ocean floor spreading was sweeping the continents into a pile we call Pangea. The Temple Butte is really not encountered at river level by boaters because it thins out against higher terrain at the time in the eastern Grand Canyon. There are a few lenses of Temple Butte between miles 38 and 48. The Temple Butte thickens to the west and becomes a significant layer in the western Grand Canyon, but above river level.

For boaters, the Redwall sits atop the Cambrian Muav Limestone, first seen at mile 36. The unconformity between these two spans three periods, the Ordovician, Silurian, and Devonian. The missing 120 million years between the  Redwall and the Muav is an awfully long time, considering that complex multi-cellular life forms have only been around for 600 million years. Even the 100 million years between the Muav and Temple Butte, where it occurs further west, is a very long time. The magnitude of this unconformity can be appreciated by comparing the continents at 360mya above and 500mya below.

It is not really clear why The Grand Canyon region would have remained elevated and not received sediments; or why these sediments could have been laid down and later eroded away. From the Mid-Cambrian above to the Mississippian Redwall at 260mya, North America moved from west to east, and not very much compared to the other continents.

Just for fun and to recap the quarter billion years from the Kaibab to the Muav we have traversed in ~50 river miles, the continents are shown above at 250mya in tan and 500mya in violet. It can be seen that North America moved comparatively little as Pangea formed, and the other continents basically self assembled around North America, the oldest continental craton.

Above we show the current surface rocks deposited during the time between the Muav and Redwall in the western US. There seems to have been a broad seaway to the west in Idaho, Utah, Nevada, and California. Not just the Grand Canyon, but the entire Colorado Plateau seems to have missed out on deposition during this time. Perhaps it was elevated like it is today.

The Muav is the youngest member of the Tonto group, a group of three periods taken to represent a classic marine transgression.

S=KlogW is Boltzmann’s formula for entropy. S is entropy, K is Boltzmann’s constant of nature, and W is the number of possible ways invisible components can be arranged without changing the appearance of what we see. W is the tricky one. Unless we can somehow count the invisible things, we are out of luck. What we can’t see are the physical interactions that give rise to the impression that there is a giant beast breathing deep within our planet.

At mile 51 we encounter the Bright Angel shale at river level. The Bright Angel is the middle member of the Tonto group, and represents a transition from the sand dunes of the underlying Tapeats (mile 58) sandstone to near shore sediments. The Bright Angel is like the Moenkopi or the Hermit shale, except that it interfingers and grades into the Muav from west to east, following the marine transgression. As encountered by river runners, The Muav, laid down in marine conditions, begins younger.

Wouldn’t it be too simple if the Grand Canyon could just be read like a book with a few pages torn out?  The Grand Canyon Supergroup is first encountered just before mile 69. The unconformity between the Tapeats and the Supergroup, as first encountered by boaters as the Dox formation is half a billion years! This is basically the amount of time from the Muav to the present day.

The Supergroup strata are inclined at about 15 degrees compared with the essentially level Paleozoic section above, and the Supergroup pinches out against even more steeply inclined Vishnu basement below, so the Supergroup does not even exist many places in the Grand Canyon. The Dox, the first unit encountered on the river, is not even the youngest member of the Supergroup, the younger strata having pinched out.

If we think of books, The Grand Canyon is really three books. The first book is the Paleozoic section. It is relatively level, has a few pages missing, and basically extends from the “Cambrian Explosion” of multicellular life forms to the Permian Therapsids (funky lizards)–from the Tapeats sandstone to the Kaibab limestone. This first book encompasses ~300 million years from 544 to 245mya.

The second book is the Supergroup. It is twice as thick, both physically and in time, but it is inclined and does not extend to much of the Grand Canyon. In the history of life, the Supergroup extends from the evolution of sexual reproduction in single celled creatures through the Marinoan glacial period or “Cryogenian”. This second book encompasses ~600 million years from 1250 to 650mya.

The third book is nearly illegible. The Vishnu metamorphic complex has been squished, stomped, and injected. Many of what were once level strata are now vertical in the inner gorge. Many areas were never sedimentary pages at all, but blobs of ascending magma called plutons. The isotopic information we use to date rocks gets overwritten each time the rock is melted or metamorphosed, so we can’t really know how old the sediments were. The dates of last crystallization range from 1.85 to 1.7 billion years ago. This is about the center of the period when the most advanced life forms were single cells that had learned to keep their DNA in a nucleus (Eukaryotes).

The Vishnu is first encountered at mile 78. There are still over 200 miles yet to run, but the entire geological sequence has been revealed. Due to undulations in the strata, the river will actually “climb” out of the Vishnu gorge into younger strata again, before cutting a second Vishnu “lower gorge” further west.

 

 

 

 

 

 

 

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CERES and MODTRAN VII, Clouds

MODTRAN deals only with infrared light, and at least the version we are using includes only low level cloud types.

 

Above is a screen shot of the menu. It can be seen that the highest altitude is three kilometers. This is unfortunate. The atmosphere radiates at the Planck curve like a brick below one kilometer. Significant deviations from the Planck curve begin at about a kilometer in the CO2 bands, and two kilometers in the water bands.

The extent of MODTRAN cloud limitation can be seen above. Oh well, we will just have to work within the MODTRAN limitations and parse out the CERES deep convective data to get a direct comparison.

The CERES data has Cloud Area Fraction by latitude, and when latitude is sorted to our prior zonal criteria, you get the result above. The general decline in boreal cloud fraction is interesting. It shows a steep decline from the millennium to 2012, and then a partial recovery. Tropical cloud fraction possibly shows a small increase, and mid latitude fraction seems steady.

What we must do to compare CERES and MODTRAN is multiply this cloud area fraction by the percentage of cloud types in the MODTRAN menu. For that, we need cloud type data, and fortunately ISCCP has this data from 1983 to 2009.

It can be seen above that the period shows a steady decline in cumulus, interrupted by the eruption of Mt. Pinatubo in June 1991 shown as a vertical line. Interesting that other cloud types were not impressed with the volcano. The CERES data we will be comparing with MODTRAN begins in 2001. Over the 2001-2010 period we see a decline and increase in annual variation of stratocumulus; a modest increase and plateau in altocumulus; and an increase and increase in annual variability of Nimbostratus. This annual variability seems peculiar, and we may return to this. Stratus clouds seem not to have changed much over the entire period.

Notice that the low level clouds have the lowest percent coverage globally, at about 5%.

We realized at the beginning that this exercise of comparing CERES and MODTRAN would be difficult. We are integrating data from three different and uncoordinated formats (CERES, MODTRAN, ISCCP). The differences in formats and data ranges allows only nine years (2001 to 2009) of direct comparison, as the ISCCP cloud type data ends in 2009. Differences in ranges of latitude between the different formats had to be normalized, adding uncertainty.

MODTRAN ignores deep convective clouds, which are imbedded in the CERES coverage data. Since MODTRAN is the source of the radiance data by cloud type, it is not possible to subtract deep convective clouds from CERES coverage rigorously. ISCCP cloud types are for daylight only, and CERES data is day and night.

Nevertheless, the cloud integrated MODTRAN result is interesting.

We can see that MODTRAN predicts far more variation than CERES measures. Any analysis of trend over nine years would be overreaching, particularly as MODTRAN variation wildly exceeds any apparent trend.

The 2006/7 spike predicted by MODTRAN results from modest increases is several cloud types (notably altocumulus in the IPCC graph above), probably from the weak El Nino of those years.

We can recall from earlier in this series that the 2006/7 period showed high total precipitable water without any corresponding increase in atmospheric temperature. It seems that MODTRAN falls victim to this discrepancy.

The MODTRAN global prediction is heavily influenced by the tropics, which cover 50% of the planet as defined here.

Mid Latitude Winters show the 2006/7 spike far more than summers.

Boreal summers and winters differ little and show little response 2006/7.

At the end of this seven post series, we cannot say that MODTRAN integrated for clouds shows the same divergence in trend from CERES that the two show for clear skies. For clear skies, MODTRAN predicts a steady decrease in LW radiation to space, while CERES measurements show a small increase.

If cloud type data could be found after 2009, this project could be extended, and perhaps reveal a divergence. All we can say at this point is that MODTRAN overreacts to the clouds, which according to CERES cover ~65% of the planet at any given time.

 

 

 

 

 

 

 

 

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