## New Computer Fund ## Friday, November 30, 2012

### Thermodynamic Reference Layers - A Visual Aid

When discussing the Greenhouse Effect, radiant energy tends to dominate the discussion and most folks have  some difficulty visualizing some of the concepts.  This visual aid will not be perfect, but hopefully, will resolve some of the problems.  The numbers in Watts per meter squared correspond to temperatures if each of the colored layers were ideal radiant surfaces.  Radiant energy emits isotropically, or in all directions equally.  Since the drawing is in two dimensions you have to imagine that each of the colored layers are emitting towards, away, up, down and to each side.  The arrows for the red 500 Wm-2 point to what would be the poles of the Earth.  From the Equator, the center of the red, temperature drops by about one degree for each degree as you get closer to the points of the arrows.  316Wm-2 is the energy of a surface at 0 degrees Celsius, the freezing point of fresh water.  240Wm-2 is about -18 C degrees which is what the temperature of the Earth looks like from space.  200 Wm-2, about -30 C degrees (28.4 C actually, but 30 is a nice round number) is approximately the effective radiant layer of the atmosphere and 65 Wm-2 is roughly the effective temperature of the tropopause, which may require some explanation.

Since the coldest temperature ever measured in the Antarctic is about -90 C degree (~65Wm-2)  it is a good reference temperature in my opinion.  In my opinion just means it is an assumption, there is no known physical property that restricts the tropopause to any fixed temperature.  The -30 C degrees is an approximation based on the Stephens energy budget estimates which tend to make reasonable sense.  The 240 Wm-2, -18 C is used often in the literature as the no greenhouse gas temperature of the surface of the Earth based on what it would appear to be from space.  The freezing point of water is a solid physical standard.  Even the freezing point of water can vary, so all these layers are just rough references.

Below the red layer is supposed to be the deep oceans.  334Wm-2 is roughly the radiant energy of a surface at 4 C degrees, the approximate average temperature of the oceans.  The oceans though are liquid and much denser than the atmosphere.  Because of the density of the characteristics of liquid water, radiant energy is not typically used in liquid energy flow calculations.  Water has a density of about 1 kilogram per liter at sea level.  Air has a density of roughly 1 kilogram per meter cubed.  Since there are 1000 liters in a cubic meter, the density of air at sea level is about 1/1000 of the density of water.  As altitude increases, the density of the air decreases which causes a great deal of the confusion.  Density and heat capacity are related.  Lower density, lower heat capacity.

As density decreases, the utility of radiant energy transfer makes more sense.  There is less conduction and convective energy transfer because there are few molecules to collide with each other transfer energy by contact, conduction.  Since convection is driven by differences in density, the lower the density the less difference there can be, so convection decreases.  The only means to transfer energy in a vacuum is through radiant energy.

The effective radiant layer of 200 Wm-2 is at an average altitude of about 7 kilometers but if you live near the poles you know that it can be -30C (-22F) in your backyard in the winter and even in the summer if you vacation in the Antarctic.  Adding CO2 to the atmosphere will cause a shift in that layer by about 3.7Wm-2 per doubling of CO2.  Since temperature and effective radiant energy are related by the Stefan-Boltzmann relationship, the new temperature at a doubling would be about [(200+3.7)/5.67E-8]^.25 or 243.7K or about 1.1C warmer.  The average radiant layer near the poles would move by about 120 kilometers.  Since the density of the atmosphere at about 7 kilometers is less, the effective radiant layer would rise by about  100 meters.

This drawing is the same with vertical "Walls" inserted at roughly the freezing point of water, 0C 316 Wm-2. Since there is a temperature difference across those walls, energy would flow from the warmer portion to the the colder polar regions.  Since air has a lower density than water, the 4C, 334 Wm-2 region of the oceans extends beyond the approximate 0 C air wall.  In discussions of the Greenhouse Effect, the Earth is modeled as a flat disc with only the up/down portion of energy transfer used for simplicity.  If the oceans and atmosphere had a uniform density or if the Earth were uniformly heated, there would be nothing wrong with that simple model.  However, the real world is not as simple.  The internal energy flow has to be considered to determine the ultimate impact of a doubling of CO2.  With the approximate temperature and energy of the Effective Radiant Layer being -30C and 200Wm-2 and using the rough 4C 334 Wm-2 of average ocean temperature with that much larger energy density, 334-200 or 134 Wm-2 is a reasonable estimate of the energy flow one would expect through the "Walls" at the higher latitudes of the Earth.  Since the solar energy that determines the 240Wm-2 layer is assumed to be constant, even though it is highly variable with respect to 3.7Wm-2 of CO2 "forcing", the location of the vertical walls with ~134Wm-2 passing through can expand or contract with internal changes in heat capacity which increases with density.  As density increases, the role of conductive and convective (advective if heat flow is not vertical) increases.

Since the Earth is a sphere, the area impacted by an increase in total heat capacity decreases as the walls expand toward the poles.  The decrease in area and heat capacity, there is less mass to heat, would have to cause a shift in energy flow by increasing the average altitude of the poleward Effective Radiant Layers or by increasing the rate of energy flow into a warming higher density surface.  At some point, the conductive and convective means of energy transfer would limit the degree of warming possible since the area available to absorb the additional energy decreases with the increase in total energy.

To add to the complexity, the heat capacity of the northern "wall area" is less than the southern "wall area".  In order to transfer energy internally, conduction or advection in the form of ocean currents would have to transfer energy through or below the higher temperature tropical surface and atmospheric temperatures, the 500Wm-2 red zone.  The rate of that conductive and convective (advective) heat transfer is extremely slow, on the order of thousands of years, much like the variation in temperatures indicated for the past million of years in the paleoclimate reconstructions.  Global average surface temperature depends on the efficiency of internal heat transfer dominated by conductive and convective (advective) transfer.