Thursday, October 20, 2011

Another Shot at Explaining the Atmospheric Effect

I found a dedication quote in response to this question:
Dallas: "Do you actually believe that down welling long wave radiation is nearly twice solar?

"Yes, I do, because that’s what the measurements show and that’s what’s required to close the energy balance. See SURFRAD data, for example ( )."

That's what's required? A perfect display of biased perception. The reason I am stating what should be obvious to inquisitive minds.

Carbon dioxide in the atmosphere both warms and cools. This is nothing new. The fear has been it will warm more than cool. At times it will. The relationship is complex.

While I would prefer to move on to other interests, I am asked why and how I may know this. The truth is the Kimoto equation is a very valuable tool for quickly testing relationships between radiant, conductive and latent thermal fluxes in the atmosphere. Simply, it works. How well, I am still working on that.

With the equation dF/dT=4(0.33Fc+1.09Fl+0.825Fr)/T, where Fc is the conductive, Fl is the latent and Fr is the radiant thermal fluxes from the surface at 288K, it is easy to use the standard values available from NASA to do “what ifs” to your heart’s content. That and a basic understanding of thermodynamics, is all it takes to see what is happening.

The basic thermodynamics should be obvious. If surface warming is due to Fr being restricted, the other two fluxes will increase as temperature increases. Water vapor increase is well known, but the increase in conduction seems to have been over looked. It will increase. That is a cooling effect.

Perhaps, the confusion is in the values, 0.33, 1.09 and 0.825? These are the values determined from the steady state condition of the Earth at 288K and 390Wm-2 associated with the 288K by the relationship of a black body’s radiant energy via Stefan’s Law. If the steady state values, 24Wm-2 for conductive, 79Wm-2 Latent and 390-24-79=287 radiant are equal to 0.33Fc, 1.09Fl and 0.825Fr are correct, be my guest and check my work, then you can determine roughly what and how much each value will change. It is easier to see if you consider what would change.

Fr, is the total of all surface radiation after allowing for conductive and latent cooling. Fr, includes both the energy absorbed by the atmosphere with greenhouse gases, and the energy eventually lost directly to space through the atmospheric window, and the matching up welling energy for the down welling atmospheric effect, or greenhouse effect. The radiant energy absorbed by the atmosphere is approximately 80 Wm-2 that can be determined by looking at the NASA Earth Energy Budget drawing where they have clearly shown how incoming solar energy is matched by outgoing combined conductive, latent and radiant flux. The remainder, 287-80=207 is the approximate greenhouse effect. Depending on which source drawing you use, NASA or the Keihl & Trenberth drawings, the 207 varies to approximately 220 Wm-2. Small change, but the values are approximate.

The coefficients are "Effective” values in that they, effect the atmospheric absorption. The 207 to 220 is a balancing force that would vary only if the effects of the three thermal fluxes increase the surface temperature. Then the 207-220 would increase to balance the atmospheric effect.

If you look at the top of the atmosphere, you will see that the solar absorbed by the atmosphere and clouds plus the solar absorbed by the surface is roughly 240Wm-2, The total absorbed by the atmosphere OLR from the surface and incoming solar equals roughly 240Wm-2 and the total leaving from the atmosphere is equal to roughly 240Wm-2. That is the energy balance. The 207 to 220 is the value of the greenhouse effect and is internal to the system.

This value is different from the classic top of the atmosphere value of 390-240=160Wm-2 sometimes noted as 155Wm-2 depending on the initial values used. That flux value corresponds to the 33C warmer the Earth is considered to be because of the combined atmospheric effects, conductive, latent and radiant energy transferred to the atmosphere from the surface to become the potential energy holding the atmospheric gases above the surface in opposition to the gravity attempting to pull them back to the surface. It is higher because the efficiency of the work done and the opacity of the atmosphere varies with pressure.

Everything balances, which is the desired result if you are attempting an Energy Balance of the Earth. The surface, the atmosphere, the top of the atmosphere and the potential energy of the atmosphere, the atmospheric effect, all of these are considered with these values. There are of course small differences due to rounding and uncertainty, but everything is in reasonable balance.

If there is more warming of the atmosphere, the greenhouse effect is getting warmer, the coefficients of surface fluxes, Fc, Fl and Fr increase. That would add to the potential energy of the atmosphere and have to be balanced by an increase of the 207-220 Wm-2.

The hard part for some to grasp, is that increased atmospheric absorption reduces the potential energy difference between the surface to the atmosphere, reducing heat transfer to the atmosphere, with some exceptions, causing interesting feedbacks. These are the rather complex feedbacks to the warming surface. Clouds both absorb more from the surface and reflect more solar from above. CO2 above the clouds retain more heat which warms the cloud tops first, which tends to increase convection at the upper troposphere. More CO2 improves the conductivity which allows more efficient heat transfer from the surface to the lower troposphere. The impacts of these feedbacks vary from region to region.

The tropics are virtually saturated for all three heat fluxes. More radiant warming above the clouds increases convection which increases latent cooling, winds increase and precipitation tends to cool the surface, offsetting warming. The southern pole is temperature limited due to angle of inclination, increased conduction balances increased radiant forcing resulting in little surface temperature change. It is in the Northern polar and subtropical region where radiant forcing impacts the surface temperature the most.

Since increased CO2, impacts a relatively small portion of the radiant spectrum at the surface, the radiant energy flux in the atmospheric window to space increases, which does increase surface warming somewhat, but is limited by near saturation of the CO2 portion of the surface radiant window. Higher in the troposphere, the atmospheric window helps cool the cloud tops warmed by CO2 forcing.

It is a complex system with many more feedbacks than commonly discussed in the literature. The conductive impact and the downward opacity to increased infrared forcing are virtually ignored and crucial for understanding the atmospheric effects. Minimum Local Emissivity Variations are just being evaluated to improve the accuracy of satellite telemetry and surface down welling radiation monitoring plagued with inaccuracy.

Sometimes simple equations are much more valuable for analyzing a complex problem than millions of hours of computer modeling.

Now, try the equation and look out the window.

What? Need more information?

Then let us start at the beginning.

The Earth’s Virgin atmosphere.

If the Earth had no atmosphere, if it were just floating in space minding its own business, the surface temperature would be about 278 degrees K or about five degrees above zero on average. That is because the sun warms the Earth half the time with 340 Wm-2 of energy. If the Earth had snow on the surface that reflected a portion of this energy it would be colder as less solar energy would be absorbed.

So if 30% of the sunlight were reflected, the average temperature would be about 255K which is 18 degrees C below zero. The Earth though has an abundance of nitrogen and oxygen, gases that have a small but significant thermal coefficient 0f 0.025W/m-2.K at 20 degrees C and about 0.024W/m-2.K at -18 degrees C. So even at the colder temperature, the virgin Earth would have surface heat transferred to the atmosphere by conduction. We would have an atmosphere, even without greenhouse gases. Those interested may wish to read up on the ideal gas laws and visit the Engineering Toolbox dot com.

This poses a bit of a challenge for what the virgin albedo of the Earth would be, would the energy be reflected from the surface, the atmosphere or both? Both, is the obvious answer. Why, because nitrogen and oxygen scatter some electromagnetic radiation, absorb some and certain wavelengths cause chemical changes, like O2, oxygen, being split by ultraviolet light and recombining as O3, ozone. This is a little more complicated, but the Engineering Tool box has the information, which should be common knowledge for scientists involved in atmospheric physics.

In addition, the Earth has plenty of water which at the equator would not only be liquid, but evaporate, adding water vapor to the atmosphere. Even if the water vapor had no interaction with outgoing longwave radiation from the surface, it would still interact with incoming solar. The virgin Earth would have a Tropopause, or an inversion if atmospheric temperature cooled from below by the release of radiant energy from the water vapor and conductive energies dissipating to space and warmed from above by solar interaction with oxygen and ozone.

With part of the albedo or reflection of solar energy being in the virgin atmosphere, the surface temperature would be approximately 2 degrees C different, depending on the ratio of surface to atmospheric absorption. This is what a no greenhouse gas Earth atmosphere would be, not a rock in space with no atmosphere at all, a planet with a simple atmosphere that obeys the principals of physics.

The Surface-Atmosphere Solar Absorption Ratio

Without getting into too much detail, the ratio of the solar energy absorbed by the atmosphere versus the surface defines the atmospheric effect. This balance or ratio varies to control the surface temperature. Change the radiant energy forcing, throws that balance off requiring the Earth and Atmosphere to seek a new equilibrium state. This is “Enhanced” Greenhouse Effect aka Global Warming, aka Climate Change aka Climate disruption. Understanding starts with the natural ratio and how it will be changed.

Readers with some experience in thermodynamics will have noted that the description of the Virgin Atmosphere provides three main frames of reference, the surface, the Tropopause and the Top of the Atmosphere (TOA). Properly balanced from one frame of reference, all frames of reference can be described. That is a simple check to verify the accuracy of your solution, Thermo 101 stuff.

The Solar Ratio and Impact of Conductive Heat Transfer

The basic model of the Virgin Earth Atmosphere is very educational. Conductive heat transfer is responsible for most of the atmospheric effect, latent cooling balances the conductive heat transfer and generates indirectly the clouds that maintain the solar absorption ratio. A beautifully simple and elegant relationship. The Radiant component of heat transfer enhances the conductive/latent relationship, it does not dominate the relationship.

Of the 240Wm-2 of solar absorbed by the Earth system, approximately 175Wm-2 is absorbed by the surface and 65 Wm-2 is absorbed by the atmosphere. This is an important ratio, 0.37 approximately. If you are curious, you would notice that the ratio of conductive to latent surface flux is 24/79 or approximately 0.30. If you are rally curious you would investigate the sensible portion of latent cooling, combine that with the conductive flux which is a sensible heat transfer, and find that( 24+5)/74 = 0.39. The surface response attempts to balance the solar impact. How these two ratios vary with respect to each other would determine if the surface is warming or cooling, GHGs enhances this relationship. The values used are approximations, but accurately calculated, the relationship would hold true.

So how does CO2 enhance the atmospheric effect?

At the surface, CO2 is a more efficient conductor of thermal energy both as a radiant absorber and as a conductive gas. Co2 readily absorbs surface thermal energy and transfers that energy to the nitrogen and oxygen in the atmosphere. It is the inefficient heat transfer of nitrogen and oxygen that causes the atmospheric effect. Thermo 101 again, if nitrogen and oxygen were perfect conductors of thermal energy there would be no energy transferred to the atmosphere. CO2 improves the conductivity, but does not make it perfect. Also, CO2 has a non-linear thermal conductivity, at 20C it is 0.09, nearly four times as conductive as N2 and O2 and at -20C it is 0.12, that is nearly a full order of magnitude greater than N2 and O2. Not an insignificant difference even at trace gas quantities. While this conductive impact is often assumed to be negligible, the Antarctic temperature response appears to believe otherwise.

Why is this the right way?

Starting at on a solid thermodynamic base allows for double checking all values. Then differences, even subtle differences can have meaning. Something missed, something new or some silly mistake that is confusing the issue. The conductive portion of the atmospheric effect is fairly constant with temperature with a stable humidity. Conductive flux is directly related to surface pressure, a solid base value that would be simple to determine globally. The latent energy is more variable, but extensively monitored by satellite and surface stations. With solid data for conductive and latent, radiant flux can be accurately calculated, far more accurately that direct measurement by satellite and ground stations. This provides a method to check methods, which is very important in a dynamic system.

So why are the satellites and surface stations measuring radiant down welling flux so far off?

Because temperature is related to radiant flux and neither are stable in the atmosphere, they are dynamic. Changes in humidity, and conductive efficiency impact already limited accuracy of direct measurement of thermal flux. The infrared pyrometers are designed to read temperatures by the approximation of the black body temperature of the object being tested. Atmospheric gases change temperature, density, composition continuously with the weather, why would their radiant energy flux be easy to measure? It is much easier to measure the average temperature of a layer of the atmosphere than it is to measure its energy flux emitted in all directions.

Where the satellites and ground stations are inaccurate is more informative than where they are accurate. Anomalies are the teachers.

Why am I so excited by the Flux measurement anomalies?

The anomalies appear to be indications of relativistic effects in the atmosphere! That is exciting if true. Effects typically only measurable under strict laboratory conditions may be apparent in the petaWatt per sec surface and atmosphere energy exchanges involving peta^n collisions and absorptions of photons as they travel from the surface to space. Something lost so far to science because of a silly erroneous assumption that data must fit preconceived notions. An interesting possibility.


The most obvious is that the potential temperature of air at 600mb is a good indicator of changes in radiant forcing versus atmospheric response, aka feedbacks. With 600mb as a base value, the potential temperatures at varying altitudes would be a simple metric for modeling changes in thermal flux interaction at various atmospheric layers. Simple, IF, the base pressure has a physical relationship to Down Welling Long Wave Radiation.

Since the ratio of surface to atmospheric absorption of incoming solar irradiance is an indication of the atmospheric effect, comparisons of solar reconstructions with surface temperature reconstructions can be more informative. Now that it is known that the spectral bands of solar irradiance change more at ends of the spectrum than uniformly across the spectrum, the impact of the individual spectral changes on the atmosphere and surface, (read Oceans) can better explain the solar to temperature relationship.

Conductivity changes, though small, can be better studied to evaluate the Antarctic versus Arctic discrepancy, which is a valuable clue, not an instrumentation anomaly.

In short, the correct frame of reference can make a huge difference in understanding a complex system.


Brian H said...

An interesting side issue: treating the CO2 atmosphere of Venus as a planet-wide radiative short-circuit, which keeps day/night temps almost identical, despite very slow rotation.

Dallas said...

Brian H,

I don't think there can be any side issues. There correct explaination of the atmospheric effect should work with any conditions. It is all interesting though.

Blog Archive