Do Global Energy budgets make sense. ???

[Terry Oldberg]

Derek:

I'd like to assist you in your project of casting the description into layman's terms. The math concepts could be a barrier to comprehension. This barrier could be overcome by explaining these concepts in layman's terms. I attempt to do so below.

A mathematical idea that is a key to understanding is that of a vector. A "vector" is a mathematical entity that has a direction and a magnitude. Velocity is an example of a vector; the magnitude of this vector is the "speed."

The sign of the magnitude of a vector can be positive or negative. Changing the sign of a vector makes this vector point in the opposite direction.

There are rules for the addition of two or more vectors. In discussing the existence or non-existence of the greenhouse effect, all one needs to know about these rules is that if two vectors A and B are pointed in the same direction and are added, the resulting vector C points in the same direction as A and B while the magnitude of C is the sum of the magnitudes of A and B.

Flows can be represented as a vector field; such a field assigns a vector to every point in space. For example, flows of water can be represented by a field of vectors where each vector represents the velocity of a small chunk of the water at the point (x, y, z) in the space whose coordinates are X, Y and Z.

A heat flow can be represented by a vector. The magnitude of such a vector has the unit of measure of watts per meter squared.

Now suppose the heat flow vectors A, B and C point toward Earth's surface and are perpendicular to this surface. C is the vector sum of A and B.

Let a, b and c designate the magnitudes of the heat flow vectors A, B and C. By the rules of vector addition

c = a + b (1)

Equation (1) is an example of a heat balance. At Earth's surface, the sums of the magnitudes of downward heat flows must equal the sums of the magnitudes of upward heat flows for the heat flows to balance. This simply means that the downward flowing heat equals the upward flowing heat.

Now if one stands at Earth's surface and aims a radiometer up into the sky, one measures a property of electromagnetic radiation that is called its "intensity." The intensity has the unit of measure of watts per meter squared.

A heat flow and a radiation intensity have the same unit of measure: watts per squared meter. Thus, one might take them to represent the same concept. However, there is a crucial difference. As Gerlich and Tscheuschner point out on page 20 of their paper, "In classical radiation theory radiation is not described by a vector field assigning to every space point a corresponding vector. Rather, with each point of space many rays are associated (Figure 3)." To get an idea of what G&T mean, you should take a look at Figure 3. Because a radiation field is not described by a vector field, it does not participate in a heat balance.

The Kiehl-Trenberth diagram represents the "back-radiation" by a vector. As the tail of this vector rests in the relatively cold matter of the troposphere while the head rests in the relatively hot matter in Earth's surface, one can be sure that this vector does not represent a heat flow, for if it were a heat flow it would violate the second law of thermodynamics. The obvious alternative is that it represents a radiation intensity but a radiation intensity does not participate in a heat balance.

UCAR, NASA-GISS and the IPCC err in assuming that the radiation intensity participates in a heat balance. Thus, they add the radiation intensity of the "back radiation" into the heat balance of the Earth below its surface. In doing so, they take the "back-radiation" to be a vector that is pointed downward toward Earth's surface; one can see this vector graphically represented in the Kiehl-Trenberth diagram or in the equivalent diagram of Schmidt's essay. In order for the heat flows to balance, the sum of the magnitudes of the upward heat flows must equal the sum of the magnitudes of downward heat flows at this surface.

The radiation intensity increases with the addition of greenhouse gases to the troposphere. Thus, when UCAR, NASA-GISS and the IPCC add the radiation intensity into their heat balance, they find the heat flowing downward as back-radiation rises with the concentrations of the greenhouse gases. Let r designate the amount of the rise at a particular time. In order for the heat flows to balance, the sum of the magnitudes of the heat flows going upward must rise by r. The only way in which this can happen is for Earth's surface temperature to rise. This is the effect which UCAR and NASA-GISS call "the greenhouse effect." A heat balance is simply an expression of the law of the conservation of energy. On this basis, believers in "the greenhouse effect" express great confidence in the existence of their effect.

However, the thinking of UCAR, NASA-GISS and the IPCC is erroneous. By the second law of thermodynamics, the heat flowing downward as "back-radition" is nil. Thus, the contribution to the heat balance from the greenhouse gases is nil. It follows that the addition of greenhouse gases to the troposphere has no effect on Earth's surface temperature. That this is true falsifies "the greenhouse effect" of UCAR and NASA-GISS." Their "greenhouse effect" results from their mistake of representing a radiation intensity as a vector.