Among the issues most commonly discussed are individuality, the rights of the individual, the limits of legitimate government, morality, history, economics, government policy, science, business, education, health care, energy, and man-made global warming evaluations. My posts are aimed at thinking, intelligent individuals, whose comments are very welcome.

"No matter how vast your knowledge or how modest, it is your own mind that has to acquire it." Ayn Rand

28 May 2017

A Critical Lesson from the NASA Earth Energy Budget

The essence of the argument that an increase in the concentration of carbon dioxide, an infrared-active or greenhouse gas, causes the Earth's surface to become warmer lies in a radiation-dominant viewpoint in the transport of energy between the surface and the atmosphere.  This viewpoint is depicted in the NASA energy budget shown below:

If the Earth's surface is simply viewed as a black body radiator at temperature T as though it were isolated in space with no other energy loss mechanisms, then the rate of energy loss by means of radiation would be

P = 398.2 W/m2 = σ T4 = (5.6697 x 10-8 W/m2K4) T4, and T = 289.5 K

Since the Earth's average surface temperature is usually said to be about 288 K, this means that the Earth's surface is assigned an emissivity of 1.02, making it a super black body radiator.  Real objects generally have an emissivity less than 1 and never more than 1.

Let us note a result discussed in my post mgh, Not Greenhouse Gases, Provides a Warm Earth because I do not want this critical observation to be lost among other observations.  I want to discuss its implications more here.

Of the 398.2 W/m2 of infrared radiation emitted from the surface in this NASA Earth energy budget, 358.2 W/m2 is absorbed by the atmosphere.  The atmosphere only absorbs infrared radiation at the wavelengths that water vapor and carbon dioxide absorb, aside from very minor absorption by other infrared-active gases.  It does not act like a black body absorber and it does not act like a black body emitter.  But we can establish upper and lower bounds on what the atmosphere is capable of doing if we treat it as though it were a black body radiator.  When dealing with complex physics problems, it is always good to know when the answers you provide are within the physically possible bounds.

Doing so, and taking Ta to be the temperature of the black body absorber and Ts the temperature of the surface, we have 

σ (Ts)4 -  σ (Ta)4 = 358.2 W/m2 ,

which is the maximum electromagnetic radiation the absorber can absorb from the higher temperature emitter black body.  We know that for the NASA Earth energy budget that the first term on the left is 398.2 W/m2 , albeit with an emissivity of 1.02, so we calculate that 

Ta = 163.0 K.

Now this is a very interestingly low temperature.  There is no temperature this low in the U.S. Standard Atmosphere Table of 1976.  The temperature with altitude drops approximately linearly in the troposphere, stabilizes at the minimum temperature of 216.65 K in the tropopause, and then increases with altitude through the stratosphere until there is essentially no atmosphere left to do any absorbing of infrared photons.  But we can make an approximate calculation of where in the solar system we could place a black body absorber at a temperture of 163.0 K that could absorb such a large fraction of the power irradiated from the NASA Earth surface.  A black body radiator at temperature 163.0 radiates 40.0 W/m2 , which matches the power of the infrared radiation that NASA says escapes the Earth's atmosphere without absorption.  

So we ask where does a sphere around the Sun in radiative equilibrium with the Sun have an energy output rate of 40.0 W/m2 ?  This will be where the product of the power output per unit area of the photosphere of the Sun times the surface area of the sphere at the radius of the photosphere equals 40.0 W/m2 times the surface area of the sphere at that distance around the Sun.  We have:

Temperature of the sun on the photosphere = 5772 K
Radius, R, of the sun at the photosphere = 6.957 x 105 km

We calculate the power output per unit area on the Sun's photosphere using the Stefan-Boltzmann Law to be:

Power output at the solar photosphere radius = 6.293 x 107 W/m2 

For the solar photosphere radius R, the distance r at which the solar power will be reduced to 40 W/m2 , will be 

r2  = [(6.293 x 107 W/m2 ) / ( 40 W/m2 )] R2   = [(6.293 x 107 W/m2 ) / ( 40 W/m2 )] [6.957 x 105 km]2  

and so r = 8.726 x 108 km.

The mean radius of the Earth's orbit is 1.496 x 108 km, so according to the NASA Earth energy budget, 358.2 W/m2 of power radiated as infrared radiation from the Earth's surface is dumped into the Earth's atmosphere at a distance from the Sun which is minimally 5.83 times further from the Sun than is the Earth.  Actually, the distance from the earth that portions of the surface emitted radiation is absorbed in space varies from 4.83 to 6.83 times the mean radius of the Earth's orbit.

NASA has a most interesting definition of the Earth's atmosphere.  What is more, how does that energy absorbed in the distant portions of our solar system manage to return to the Earth's atmosphere in any way that might increase the temperature of the Earth's surface?  Of course it does not.  This NASA Earth Energy Budget is a complete farce, as are the many similar Earth energy budgets used by the UN IPCC reports to justify their claims that adding carbon dioxide to the atmosphere will cause catastrophic warming problems for mankind.

One must also take note that without the absorption of this 358.2 W/m2 of power from the surface, the idea that the atmosphere can back radiate 340.3 W/m2 to the surface becomes impossible.  It is the absorption of the surface radiated power coupled with the back radiation of a nearly as great power that is the very basis of the claim that adding more greenhouse gases to the atmosphere will cause the Earth surface temperature to rise.  And no, there is no way that water vapor, carbon dioxide, and methane gas can absorb and emit more infrared radiation than can a black body absorber.  They fall well short of being as effective as absorbers and emitters compared to a black body absorber/radiator.

According to the U.S. Standard Atmosphere of 1976 table, the coldest temperature within the Earth's atmosphere is the 216.65 K of the tropopause, the layer of the atmosphere between the troposphere and the stratosphere.  A black body layer placed there could at most absorb a power of infrared emitted from the surface of 

P  = σ T4 = (5.6697 x 10-8 W/m2K4) (216.65K)= 124.9 W/m2

This upper limit absorption of 124.9 W/m2 is vastly less than the claimed absorption of 358.2 W/m2 . Even if the theoretical limit of absorption did occur in the tropopause, one would still have the insurmountable problem of finding a way to return any significant portion of this energy to the surface to provide any significant warming of the surface.  Equally important, such a violation of such an easily calculated upper limit on the fraction of the surface infrared emission which can be absorbed wipes out any confidence one can reasonably have in any of the NASA science used to create this Earth energy budget.  Indeed, there are many other errors in this fanciful creation.

This upper limit as defined by the Stefan-Boltzmann Law of Electromagnetic Radiation is itself much too high an upper limit for the following reasons:

1)  The surface of the Earth does not emit the 398.2 W/m2 as claimed by NASA because this surface is not emitting radiation at a vacuum interface and has competing energy loss mechanisms cooling at least local submicroscopic areas of the surface briefly.  This is a matter dictated by the Law of Conservation of Energy.  Since less energy is emitted from the surface as infrared radiation, the atmosphere cannot absorb as much either.

2)  As noted earlier, water vapor, carbon dioxide, methane, and other infrared-active molecules can each absorb only a fraction of the wavelengths of infrared radiation that a black body absorber/radiator can.  These gas molecules also have many cases of overlap of those wavelengths they do absorb. Therefore, once again, the fraction of the wide spectrum of infrared radiation that the surface emits that can be absorbed by the atmosphere is much reduced.

3)  The mean free path for the absorption of such infrared as the infrared-active molecules absorb is much too short for surface emitted infrared radiation that can be absorbed to reach the tropopause before it is absorbed.  Indeed, in most areas of the Earth, the absorption mean free path for water vapor is many, many times too short for this to happen.  Even that for carbon dioxide at present concentrations is much too short for this to happen.  This means the temperature differentials are much reduced and consequently much less energy is absorbed.

In short, the NASA Earth Energy Budget is based on nonsense physics.  This, we are told, is the settled science of the climate.  Is it any surprise that computer models based on nonsense physics have been making wrong predictions of climate warming for 19 years now? Garbage physics in means no reality out.

23 May 2017

mgh, Not Greenhouse Gases, Provides a Warm Earth

According to the usual viewpoint, the surface of the Earth is 33K warmer than the 255K temperature of the Earth as seen from its thermal radiation temperature in space because of greenhouse gases. This is claimed on the basis of the NASA Earth Energy Budget shown below:

According to this federal government story, infrared radiation emitted by our atmosphere provides a surface warming power flux of 340.3 W/m2 compared to 163.3 W/m2 of radiation (UV, visible light, and infrared) directly absorbed from the sun.  In the official pronouncements of the United States of America federal government, so-called back radiation from our cooler atmosphere provides 2.084 times as much heat to the warmer surface as does the sun directly.

In this viewpoint, commonly claimed to be the consensus viewpoint of 97% of all scientists, the Earth does not have a gravitational field which acts upon air to to provide a temperature gradient in accordance with simple physics which has been well-know for a very long time.  This article will explain this very simple, well-known, yet now completely ignored physics in relatively simple terms.  If one is to understand the equilibrium climate of the Earth's surface and its lower atmosphere, the troposphere, that understanding requires that we understand how gravity acts upon our atmosphere.
Yet we cannot ignore the role of radiation in developing this understanding either.  Let me reprise some considerations from my earlier article The Simple Physics Explaining the Earth's Surface Temperature by way of introduction.

NASA says that the Earth emits 239.9 W/m2 of longwave infrared radiation into space.  This implies an effective Earth system radiative temperature T:

P = 239.9 W/m2 = σ T4 = (5.6697 x 10-8 W/m2K4) T4

so T = 255.0K, by application of the Stefan-Boltzmann equation for black body radiation.

Now we can go a step further, since NASA says that 40.1 W/m2 of longwave infra-red radiation emitted from the surface passes through the atmospheric window without absorption by the atmosphere directly into space. This allows us to calculate the effective radiative temperature of the atmosphere alone.  Consequently, the effective radiative temperature of the atmosphere as a black body is found to be:

P = (239.9 - 40.1) W/m2 = σ T4 = (5.6697 x 10-8 W/m2K4) T4,

so T = 243.7 K, the effective radiative temperature of the atmosphere alone as seen from space.

According to the U.S. Standard Atmosphere Table of 1976, this is the temperature at mid-latitudes at an altitude of 6846 meters by interpolation of table data.  Now, the U.S. Standard Atmosphere Table of 1976 may not be a great representation of the average Earth atmosphere, but it gives us something concrete to work with and is certainly intermediate between the properties of the atmosphere over the tropics and over arctic regions.  Our effort here is to develop a physical sense of the size of the gravitational effect on the temperatures of the lower atmosphere and of the Earth's surface.  We are not trying to displace the need for future worldwide computer models to address climate issues more accurately.  But, at this time, essential physics is not going into the computer models in use. Let us investigate whether it makes sense to ignore the effect of gravity upon our atmosphere.

This effective atmospheric temperature is important because it is at an altitude at which the atmosphere is in equilibrium with radiation into it and out of it with respect to space.  This is an effectively pinned temperature in our atmosphere from the standpoint of radiation. Changes in the water vapor concentration and those of other infrared-active gases may move this point somewhat, but there is such a point given any such changes in infrared-active molecule concentrations which serves as a reference point for an equilibrium temperature of the atmosphere as seen from space.  Where this altitude is is mostly determined by water vapor in the atmosphere.

The total energy of an air molecule in the Earth's gravitational field is E = KE + PE, where KE is the kinetic energy and PE is the potential energy.  Let us take the PE at the Earth's surface to be zero and the potential energy at a height h to be mgh, where m is the mass of the average air molecule and g is a slowly decreasing value with altitude.  At the Earth's surface, g is 9.8066 m/s2 in the US Standard Atmosphere Table and by interpolation of the values in that table for 6500 m and 7000 m, it is 9.7856 m/s2 at h = 6848 m.

An equilibrium atmosphere will have a constant energy throughout.  The system of air molecules will equilibrate at a nearly constant total energy everywhere.  The real atmosphere will have sufficient disturbances that this will not be the case, but those disturbances will tend to operate around this equilibrium condition on average.  Consequently, the total energy of an air molecule at zero altitude will be the same as one at an altitude of 6846 m. This is actually an application of the 2nd Law of Thermodynamics.

The temperature of an ideal or perfect gas is proportional to its kinetic energy.  Air molecules are very nearly perfect or ideal gas molecules.  Consequently, the temperature of an air molecule is given by KE = C T, where C is the heat capacity (at constant pressure), or the amount of energy required to increase the temperature of the molecule by 1 Kelvin.

We can calculate the temperature difference between an air molecule at the surface (h=0) and at h = 6846 m altitude by calculating the kinetic energy difference between the molecules and using the heat capacity of the air molecule to convert the kinetic energy difference into a temperature difference.  So we have

KE (h=0) - KE (h = 6846m) = mgh = m(9.7856 m/s2  ) (6846 m) = m (66992.2   m2/s2 )

According to the U.S. Standard Atmosphere Table of 1976, the average air molecule has a mass of 0.028964 kg/mol.  So the kinetic energy difference of one mole of air molecules at the surface and at an altitude of 6846 m is 

KE (h=0) - KE (h = 6846m) = (0.028964 kg/mol) (66992.2   m2/s2 ) = 1940.36 J/mol

The heat capacity at constant pressure for a mole of the average air molecule is 29.07 J/K mol.  So we have 

T(h=0) - T(h=6846 m) = (1940.36 J/mol) / (29.07 J/K mol) = 66.75K

This is a temperature gradient per km of altitude of 9.75 K/km, which is a bit less than the more frequently given 9.8 K/km because we took into consideration the fact that the gravitational constant is not really quite constant and decreases slightly with altitude.

Now comes the important lesson of this exercise.  We can now calculate the equilibrium surface temperature of the Earth due to the temperature gradient in the troposphere resulting from gravity acting on the atmosphere.  Recall that at 6846 m altitude, the temperature interpolated from the US Standard Atmosphere Table of 1976 is 243.7 K.  With a gravitational temperature gradient of 9.75 K/km, the surface temperature is 

T (h=0) = 243.7K + (6.846 km) ( 9.75 K/km) = 310.4 K

The air temperature at the bottom of the atmosphere, where the molecules of the atmosphere are bombarding the surface, should be about 310 K were it not for the existence of cooling effects.  This is much higher than the 288 K average temperature of the Earth's surface.

In fact, given that the surface is said in the Earth Energy Budget above to be absorbing 163.3 W/m2 of direct radiation from the sun, the surface should be much hotter than 310 K. The problem is still greater if the surface is also warmed by back radiation from the atmosphere of 340.3 W/m2 , despite the exaggerated surface infrared emissions of 398.2 W/m2 of that energy budget.  I discussed why the surface infrared emissions are greatly exaggerated recently in Infrared Radiation from the Earth's Surface and the So-Called Scientific Consensus.  The claim of a large back radiation from the atmosphere was needed because even without an exaggerated cooling by radiation of the surface, there was no way to achieve an average temperature of 288 K at the surface without the gravitational effect being taken into account.

It is important to understand that under equilibrium conditions, the gravitational field is not transferring heat through the atmosphere or to the surface.  The gravitational field effect on the temperature of the atmosphere is trying to stabilize the temperature gradient in the atmosphere and at the surface and heat transfer only occurs when heat transferring effects such as radiation, water evaporation and condensation, and thermals upset the balance.  In this sense, the gravitational field effect does not belong in the Earth Energy Budget.  But, the fact that it does not belong there points out that the Earth Energy Budget is inadequate to understand equilibrium temperatures and is actually misleading.

While it is wrong to think of the gravitational effect as a power input in the system, it is still instructive for the sake of comparison to those factors that do put power into the Earth system to calculate its effective power input.  Using the Stefan-Boltzmann equation this would be given as

P = σ T4 = (5.6697 x 10-8 W/m2K4) (310.4 K)4 =  526.3 W/m2 

If one adds to this the 163.3 W/m2 of direct solar radiation and subtracts the 18.4 W/m2 of cooling thermals and the 86.4 W/m2 of cooling water evaporation power, the Earth's surface temperature would be given by

P = 584.8 W/m2 = σ T4 = (5.6697 x 10-8 W/m2K4) T4

so T = 318.7 K.

Clearly, the main question we should be addressing as scientists is not why is the Earth's surface as warm as 288 K, but why is it as cool as 288 K.  The mechanisms cooling the Earth's surface must be much more robust than those of the NASA Earth Energy Budget. Thermals and water evaporation must be more powerful than depicted and/or the effects of infrared active molecules must not only be less warming, but most likely must provide a net cooling of the Earth's surface.

Looking at the NASA Earth Energy Budget, the infrared-active gases emit all but 40.1 W/m2 of the 239.9 W/m2 of outgoing infrared radiation into space, making this a cooling effect of 199.8 W/m2 for the entire Earth system.  But if we look at the effects on the surface temperature, then the 77.1 W/m2 of solar radiation absorbed by the atmosphere is a cooling mechanism with respect to the surface.  Much of the 77.0 W/m2 due to cloud and atmospheric reflection owes to the so-called greenhouse gas water vapor, which again is a cooling mechanism.  Another important cooling mechanism for the surface is the evaporation of water to produce water vapor which removes 86.4 W/m2 of heat.  Adding these three surface cooling effects together gives us a surface cooling effect due to infrared-active or greenhouse gases of 240.5 W/m2 , which is much more than the 163.3 W/m2 of direct solar radiation absorbed by the surface.

Already, one should be able to see that the only way to support the idea that infrared-active gases are warming the surface is to believe in the reality of the 340.3 W/m2 of back radiation shown in the diagram.  This back radiation requires that a black body radiator be at a temperature of 278.34 K, which in the U.S. Standard Atmosphere Table of 1976 occurs at an altitude of 1510 m.  The infrared radiation from such a black body would have to travel 1510 m to reach the surface without any absorption by the infrared-active molecules in that path. In reality, because water vapor and carbon dioxide only emit a portion of the spectrum of a black body radiator, to emit so much radiation they would have to be at a much cooler temperature than 278.34 K, which means that the radiation they emitted exclusively at the wavelengths that they also want to absorb would be emitted at a very much higher altitude than 1510 m.  This would require a much longer mean free path for their emitted radiation than 1510 m.  In reality, the mean free path is very much shorter than 1510 m.  This makes this large back radiation from the atmosphere a fiction.

Note that adding still more CO2 to the atmosphere will actually further reduce the mean free path for infra-red radiation and reduce the temperature differentials that are required to transport much heat between areas at different temperatures by radiation.  Because of the T to the fourth power dependence of radiative emissions, smaller temperature differentials yield rapidly decreasing radiative heat transport back from the atmosphere to the surface. Most of the time, when an infrared-active molecule absorbs a photon, it transfers almost all of that energy to other infrared-inactive molecules such as nitrogen, oxygen, or argon during many collisions with them.

The large back radiation of the NASA Earth Energy Budget is a fiction inserted because they have failed to acknowledge the critical role of gravity in providing us with a warm surface.

There is much more that is very odd about the NASA notion of back radiation here.  Let us do a little accounting.  Note that the atmosphere absorbs energy at the following rates:

77.1 W/m2 from incoming solar radiation
358.2 W/m2 of radiation from the surface
18.1 W/m2 from thermals rising from the surface
86.4 W/m2 from the condensation of water evaporated at the surface
Total atmospheric energy flux input is 540.1 W/m2 .

Note that the atmosphere radiates the following energy fluxes:

(239.9 - 40.1) W/m2 = 199.8 W/m2 into space
340.3 W/m2 to the surface
Total atmospheric energy flux output is 540.1 W/m2 .

These sums are in balance, as one expects in a system without gravity.  However, one has to note that of the total atmospheric infrared radiation, only 37% is radiated to space, while 63% is somehow radiated back to the surface.  As each infra-red active molecule absorbs an infrared photon, it is equally likely to subsequently emit an infrared photon in any direction according to the ideas of photon emission to which the scientists who created this vision of the Earth's energy budget ascribe.  If so, because the atmosphere becomes less dense with altitude and because beyond the altitude at which water vapor condenses there is much less absorbing water vapor, more infrared radiation should escape the atmosphere to space than should be returned to the surface.  The reality is that in the lower troposphere, the transport of energy or heat as radiation is small compared to the transport by convection.  The transport by convection is much greater because the rate of molecular collisions is much greater than is the rate of photon emission by the infrared-active molecules in the lower, very dense atmosphere.  But even if radiative transport of energy were the dominant means of energy transport in the lower troposphere, one could not have more than half of the energy transported downward.

Here is still another unphysical oddity:  According to NASA and the many similar energy diagrams adopted by many other governmental organizations such as the UN and the European Union, all but about 10% of the infrared radiation of the surface is absorbed by the atmosphere.  Here, the surface emits 398.2 W/m2 and the atmosphere absorbs 358.2 W/m2 of that.  If the surface temperature is Ts and the effective atmospheric temperature is Ta, then one has

σ (Ts)4 -  σ (Ta)4 = 358.2 W/m2 

and we know that for the NASA Earth energy budget that the first term on the left is 398.2 W/m2 , so we have 

Ta = 163.0 K

Now this is a very interestingly low temperature.  There is no temperature this low in the U.S. Standard Atmosphere Table of 1976.  The temperature with altitude drops in the troposphere, stabilizes at 216.65 K in the tropopause and then increases with altitude until there is essentially no atmosphere left to do any absorbing of infrared photons.

In order to get enough energy flux to return a large back radiation to the surface to replace the role of gravity, NASA has to find a way to absorb almost all of the infrared radiation emitted from the surface in the atmosphere and to do that they have to make the atmosphere very cold.  They have to make it colder than it is.  Even if it were cold enough in its upper reaches and dense enough to absorb the radiation, how then could it actually return that radiation to the surface and also appear to be a black body radiator with a temperature of 378.3 K, which we calculated above?  And note that this problem only becomes worse when we recognize that none of the infrared-active gases are black body absorbers or emitters.

Having more infra-red active molecules in the upper portion of the troposphere provides more emitters of radiation into space, which will lower the temperature of the altitude whose temperature is in radiative equilibrium with space, but will do so without moving that equilibrium altitude very much at all.  This is because water vapor already has a very low concentration in the upper troposphere, after decreasing in concentration rapidly at altitudes colder than the condensation temperature of water.  CO2 even doubled does little to shift the equilibrium altitude given water vapor dominance in the emission spectrum and given the temperature uniformity in the tropopause.  The net effect is simply more heat emission to space and little change in the distance to the surface over which the gravity-induced temperature gradient works.  The net effect of adding carbon dioxide is a cooling effect in terms of the atmospheric radiation of infrared to space.

The infrared active molecules speed the upward transport of solar insolation which has warmed the surface by short hop radiation from a warmer layer of air to a cooler layer just above it. The mean free path for the reabsorption of emitted infrared is short, so the amount of energy transported this way is small.  But, this effect is a cooling effect in that the energy transport at the speed of light is much faster than the velocity of air molecules traveling upward in convection currents.

The primary infrared active molecule, water vapor, has a mass to heat capacity ratio less than that of the average air molecule, so it reduces the temperature gradient created by gravity in accordance with the calculation performed above.  Because the water molecule is lighter than the average air molecule, it also has a tendency to increase updrafts of air at higher humidity and thus speed up heat dissipation from the surface by carrying heat to the altitude at which water condenses.  The Earth is also cooled by plant growth and the absorption of water and carbon dioxide by minerals, which increases with more carbon dioxide and water vapor in the atmosphere. 

All of these factors are candidates for being underestimated by the NASA Earth Energy Budget and provide mechanisms in which infrared-active molecules actually cool the surface of the Earth and, ultimately, the atmosphere.

The fact that the greater part of the surface temperature of the Earth is due to our gravitational field acting on air molecules goes a long way to explain why our day to night temperature differences are relatively moderate.  If the electromagnetic spectrum of radiation played as big a role as that implied in the usual greenhouse gas warming hypothesis, this relative moderation of day and night temperatures is difficult to explain. Very difficult. The fact that the direct solar absorption at the surface is only 27.9% of the effective net energy in and out the surface helps to explain this beneficial stability of the surface temperature.  The surface and atmospheric radiative emissions over the daily cycle act to increase the day to night temperature differences and also the seasonal differences.

We are very fortunate to have a dense atmosphere in a substantial gravitational field composed mostly of infrared inactive molecules with enough water to dissipate heat adequately by evaporation at the surface and enough infrared active molecules to dissipate heat from the upper troposphere.  It is also critically important that the mean free path length for the absorption of infrared radiation emitted by our infrared-active molecules is short so that heat near the surface is not immediately and directly dissipated to space, but must instead rise slowly through the troposphere to the top portion of the troposphere before it is lost to space.  The infrared-active gases play a critical role, but they do so in conjunction with the powerful effect of our Earth's gravitational field acting on our air molecules.

18 May 2017

Prof. Walter E. Williams Explains What Our Trade Deficit with China Really Means

Trade Ignorance and Demagoguery
     When we discuss international trade and balance of payments, there are two types of accounts. There is the current account, which includes goods and services imported and exported and receives the most political attention. In 2016, the American people imported $479 billion worth of goods and services from Chinese producers, and we sold $170 billion worth of goods and services to Chinese customers. That made for a $309 billion current account deficit. In other words, we purchase more goods and services from Chinese producers than Chinese consumers purchase from American producers.
     How much of a problem is it when there is a deficit, or a negative imbalance, on current accounts? Let's look at it.
     I buy more from my grocer than he buys from me. Our Department of Defense buys more from General Dynamics than General Dynamics buys from our Department of Defense. With just a bit of thought, one could come up with thousands of examples in which one party buys more from another than that party buys from it -- creating deficits in current accounts. But a current account deficit is always offset by a surplus somewhere else.
     That somewhere else is known as the capital, or financial, account. This account consists of direct foreign investment, such as the purchase or construction of machinery, buildings or whole manufacturing plants. The capital account also consists of portfolio investment, such as purchases of stocks and bonds. In our capital account, the U.S. has a huge surplus with China. That means money is flowing into our country from China. In other words, Chinese people are investing more money into the U.S. -- in the forms of home and factory purchases, stocks, and bonds -- than Americans are investing in China. Of necessity, the deficit that we have with China on our current account, ignoring timing issues, must equal the surplus we have with China on our capital account.
     It turns out that foreigners own $30 trillion worth of U.S. assets, such as stocks, Treasury bonds, manufacturing plants and real estate. One of the reasons that foreigners hold so much U.S. capital is that our country is one of the world's most attractive places to invest. Secondly, our capital markets, unlike our goods markets, are open to foreigners. Foreigners can buy and sell any U.S. asset in any quantity, except in cases in which national security is an issue. One of the troubling aspects of foreign confidence in America is that foreigners invest so much in U.S. Treasury bonds. That in turn gives the U.S. Congress greater latitude to engage in profligate spending. Japan owns $1.1 trillion worth of U.S. Treasury bonds, and China owns $1 trillion.
     What about President Donald Trump's call to reduce our current account trade deficit? By the way, we know that we're being deceived when a politician talks only about the current account deficit, without a word about the capital account surplus. If foreigners sell us fewer goods, they will earn fewer dollars. With fewer dollars, they will be able to make fewer investments in America. But that's fine with politicians. The beneficiaries of trade restrictions are visible. Tariffs on tires, clothing and electronics will mean more profits and jobs and more votes for politicians. The victims of trade restrictions, such as people in the real estate market and other areas where foreigners are investing, are less visible. Last year, Chinese citizens alone purchased record amounts of residential and commercial real estate, bringing their five-year real estate investment total to more than $110 billion (
     Let's put trade deficits into historical perspective. If trade deficits were something for a president to fret about, every U.S. President from 1790 to today ought to have been fretting. For most of our history, we have had current account deficits ( I should say every president except Herbert Hoover and Franklin D. Roosevelt, whose administrations ushered in the Great Depression. Nine out of the 10 years of the economic downturn of the 1930s, our nation had a current account trade surplus. Should we reproduce the economic policies of that era and re-create the "wonderful" trade surplus?

17 May 2017

Infrared Radiation from the Earth's Surface and the So-Called Scientific Consensus

In the catastrophic man-made global warming hypothesis, the solar radiation absorbing surface area of the Earth is assumed to be the same as the infrared-emitting surface area of the Earth.  Let us rigorously examine this important assumption.  Of course in light of the claims by many advocates of catastrophic man-made global warming that there is a consensus among scientists that their theory is correct and this opinion is so justified with a thorough rational understanding of the applicable science, an interested person should have seen many discussions of the matters I am about to discuss in this article already.  So, keep asking yourself how often you have seen this discussion before as you read my discussion of these supposedly settled issues.

Most of the absorption of the solar radiation is by the surface directly illuminated in line-of-sight with the sun.  In comparison to the infrared-emitting surface area, this is reasonably consistent with the general models used by the catastrophic man-made global warming hypothesis.

The heat-emitting surface area is actually larger than is the absorbing, line-of-sight surface area.  This is especially the case in land areas.  A rough, rocky surface has a much higher surface area than does the surface of the perfectly smooth sphere used in the models.  A vegetated area has heat emission from the ground and from every part of every plant on that surface.  The stems and trunks emit heat. Both sides of every leaf emit heat.  Let us say that the 71% of the Earth's surface which is water has a surface area about equal to that of the round, smooth surface as a simple base for further discussion, though even its surface area is slightly larger.  This leaves 29% of the surface and those areas with vegetation may have a surface area which is 2 or 3 times the surface area of the smooth sphere in a given bordered area in 2-dimensions as viewed from space.  Desert and arctic areas may only have an area 1.3 times as large.  Every surface mineral particle in the desert with an air-exposed area will have a surface area much greater than the portion of the surface of a sphere covering the same periphery.

It is not at all unlikely that the average land area whose solar absorbing surface area is A, would have a heat-emitting surface area of about 1.6 A.  Thus, the heat-emitting area including the 71% of the Earth's surface which is water and the nominal 29% which is land could readily be:

0.71 A + 0.29 (1.6) A = 1.17 A

Now, I am not claiming to know this effective emission area accurately.  I most certainly do not know it accurately.  But, if the science of the so-called greenhouse effect and its consequences for man-made global warming is a scientific consensus, as opposed to a political consensus, then this effective area is a well-known parameter and should be readily available to all interested parties.

As a scientist interested in the effects of carbon dioxide and other infrared gases upon the climate, I would have to know this effective Earth emission surface area to be a member of any scientific consensus of those effects on the Earth's climate.  As a benevolent human being, I would also have to be very sure of this before I would become an advocate of killing off the many conveniences and life securing benefits of the use of fossil fuels, not to mention the jobs of those dependent upon the use of these forms of energy.

This issue of the effective Earth infrared emission surface area does not end here.  No, it gets much more complex yet.

We have to remember, as far too few scientists seem to do, that infrared emission occurs because electric charges are accelerated with respect to one another, thereby creating dipole, quadrapole, and other higher order electromagnetic fields.  The dipole field created by oscillating electric charges at the molecular level is the primary source of the resulting electromagnetic field, so I will just refer to these oscillating electric charge pairs henceforth in this discussion to keep things a bit simpler.  The higher the temperature, the greater the acceleration and deceleration applied to the electric charges in each oscillating electric dipole because the frequency of the oscillation increases as the temperature increases.  The greater these changes in acceleration are, the greater the strength of the dipole electromagnetic field created.  The greater the strength of the electromagnetic dipole field, the greater the photon emission.  At the temperature of the Earth's surface, the photon emission is in the mid infrared wavelength range.  At the temperature of the surface of our Sun, the photon emission is in the higher energy and shorter wavelength range of ultraviolet, visible, and near infrared radiation.

Now if the Earth's surface interfaced directly with space and there were no water on the surface either evaporating or sublimating and there were no atmospheric molecules bombarding it, all of the Earth's surface area would emit infrared radiation in accordance with the Stefan-Boltzmann equation which is often utilized in the semi-scientific climate science discussions of infrared radiation from the Earth's surface.  Of course as discussed above, the Earth's real surface area for that emission is not taken into account.  No, in those discussions the Earth is replaced by a perfect sphere.

Our Earth has a surface which is not only not a perfect sphere, but 71% of it is liquid water and additional portions are ice.  This portion of the Earth's surface has obvious cooling mechanisms other than the emission of infrared radiation.  Most of the land surface covered by vegetation, animals, soil, and minerals also has considerable water present.  Consequently, evaporation of water from these surfaces is a significant cooling effect.  Plants and animals are mostly water.  Soil and minerals absorb considerable water on the surfaces of the particles of which they are composed.  Many of the minerals common in the Earth's surface have lamellar structures at the atomic level and absorb water and carbon dioxide between the layers of atoms of which they are composed and can be more or less hydrated depending on the humidity and time between rains.  The evaporation of water provides a powerful cooling effect on almost every part of the Earth's surface.

Where does the energy come from that causes a water molecule to evaporate and become water vapor in our atmosphere?  It has to come from the nearby atoms of the surface at the site of the evaporating water molecule.  This is a clear requirement of the Conservation of Energy.  In what form was that energy which has been taken up in the evaporation of our water molecule?  It was the vibrational energy in the nearby atoms that was the same vibrational energy that caused them to create their contribution to the dipole electromagnetic field.  As that energy is soaked up by the evaporating water molecule, the frequency of the oscillations of the nearby dipoles is reduced and the strength of the local electromagnetic field is decreased.  The temperature of the local atoms is effectively reduced for a brief time before energy from the surrounding surface materials can flow into the local atomic area that just lost energy to the evaporation process.  During this time, any infrared emissions from those lower frequency oscillating electric dipoles are those characteristic of a material at a lower temperature.  To be sure, this time of reduced infra-red radiation energy loss is short, but then in many cases the time to the next case of a local water molecule evaporation may also be short.  And what is very important here, the real surface area emitting infrared radiation characteristic of the Earth's surface temperature according to the Stefan-Boltzmann equation is reduced on the macroscopic level.

Yes, those local atomic environments within the macroscopic area where no water molecule has evaporated will emit radiation in accordance with the Stefan-Boltzmann equation.  But other local atomic environments having just given up energy to the evaporation of a water molecule cannot do so, at least not at the normal temperature of the Earth's surface.  At any given time, the fraction of the area of the Earth's surface emitting radiation in accordance with the Stefan-Boltzmann equation for the average Earth temperature of 288K, must be less than 1.  And of course, any scientific consensus in favor of the catastrophic man-made global warming hypothesis would include knowledge of just what this fraction is.  At some point, this would have been a hot topic of discussion.  This issue having been resolved, every advocate of the truth of catastrophic man-made global warming will be able to discuss this intelligently with any inquirer.

Now this is not the end of the surface area of infrared emission story.  To this point, we have not considered the bombardment of the Earth's surface by air molecules.  According to the usual theory of the large greenhouse gas effect on the climate, the primary reason the Earth's surface has an average temperature of about 288K is the absorption of radiation from the sun directly and the absorption of an even larger amount of radiation energy from the atmosphere.  See the viewpoint expressed in the Earth energy budget below:

All of the energy that warms the surface is in the form of these two radiation sources, with the back radiation from the atmosphere being 2.08 times the direct solar radiation absorption according to this NASA Earth energy budget.  This is entirely false, which I have explained many times.  This viewpoint is based on the wrongheaded idea that the Earth's entire surface emits radiation as though it were in a vacuum and absorbs massive radiant energy from a generally cooler atmosphere which is even greater than the energy absorbed from the Sun.  In reality, the Earth's surface emission is much, much less than shown in this diagram and the back radiation is much, much, much, much less than is shown.  In fact, back radiation is actually limited to those cases of atmospheric temperature inversions, which do occur in a dynamic atmosphere, but have a much smaller effect than that claimed.  The principal the Earth's surface is as warm as it is is due to being in equilibrium with the temperature of the warm air molecules that bombard it.

Why are these air molecules warm enough to establish an equilibrium temperature with the surface which is much higher than that of the Earth system equilibrium temperature as seen from space? Primarily because of the action of the Earth's gravitational field on the molecules of the atmosphere. At the altitudes from which the Earth's atmosphere emits infrared radiation into space from water molecules, carbon dioxide, and other infrared-active molecules, the atmosphere is much cooler than is the surface of the Earth.  The Earth's surface also emits a large fraction of the infrared radiation it does emit directly into space, because much of its spectrum of radiation is not absorbed by the infrared-active molecules of the atmosphere. The fraction of the Earth's surface emission absorbed by the atmosphere is much smaller than is shown in the NASA Earth energy budget above.

The temperature of the atmosphere at the altitudes from which its infrared emission into space occurs is fixed by that process and depends upon the concentration of the infrared-active molecules with altitude.  The energy of an air molecule at that altitude is given by E = Kinetic Energy + mgh, where g is the gravitational constant (actually very slightly reduced with altitude from the surface value) and h is the altitude.  The gas molecules in our atmosphere are very nearly perfect or ideal gases in their behavior, Consequently, the temperature of those gas molecules is proportional to the Kinetic Energy of those molecules.  This is a property of ideal or perfect gases.

Of course every good scientist knows both that the gas molecule kinetic energy in the atmosphere varies with altitude due to the potential energy term mgh and every one of them knows that the temperature of a perfect or ideal gas molecule is proportional to its kinetic energy.  Consequently, any respectable scientist understands that the temperature of an air molecule at the surface of the Earth is much higher than its temperature at an altitude of say 7000 meters where atmospheric radiation into space largely occurs.  Do we not see this discussed all the time in the consensus viewpoint supposed to back the catastrophic man-made global warming hypothesis?

In fact, simply due to this gravitational action on gas molecules in our atmosphere, the temperature of gas molecules on average at the Earth's surface and in equilibrium with the Earth's surface raises the surface temperature more than does the directly absorbed radiation from the Sun.  It is only when the Earth's surface temperature is higher than the temperature of gases at the bottom of the atmosphere that heat flows from the surface to the atmosphere.  This happens when the surface is warmed by sunlight.  At night, as thermal radiation from the surface cools the surface, it is kept from cooling very much because the air molecules bombarding it tend to maintain the temperature the gravitational field imparts to them.  These effects on the surface temperature are not indicated in the NASA Earth energy budget.  The only role that the Earth's molecules striking the surface plays in the NASA "consensus" viewpoint is the loss of heat by the subsequent creation of thermals.  The primary reason for the Earth's high surface temperature is converted into a minor heat loss.

If the only effect of gas molecules bombarding the Earth's surface were a heat loss, then each instance of a gas molecule striking the surface would remove heat locally and act much like the evaporation of a water molecule described above.  Each such event would locally lower the surface temperature and reduce the energy loss due to the emission of infrared photons.  This would reduce the effective area emitting radiation in accordance with the Stefan-Boltzmann equation.  And, being conscientious scientists, those claiming they were part of the scientific consensus on catastrophic man-made global warming would have come to a conclusion, known to all of them and available to every interested inquirer, about the effect on the fraction of the surface emitting energy in accordance with the average temperature by Stefan-Boltzmann radiation and the fraction emitting infrared radiation characteristic of lower temperatures due to energy loss to bombarding air molecules.

So, I ask you if those scientists who ascribe to what has been frequently claimed to be a scientific consensus have indeed considered the critical scientific issues I have discussed above?  It is not as though these are difficult issues to recognize as critical if one has both some understanding of very basic principles of science and a scientific mind.  It would be a terrible travesty of science and good government if the United States government has spent many tens of billions of taxpayer dollars on backing catastrophic man-made global warming and yet has not considered the basic science I have tasked them with here.

Interestingly enough, in the the 1950s through the 1970s, the U.S. government funded the computation of tables for the U.S. Standard Atomsphere which did recognize the gravitational source of the temperature of the lower layer of the Earth's atmosphere, the troposphere.  How odd that the government has forgotten that science.  I have been reminding people about this since 2010, with little effect.