Lapse Rate vs Radiative Forcing vs CO2 Alarmism

In Basic Thermodynamics of the Atmosphere I give an argument connecting lapse rate to radiative heat forcing, indicating that increased radiative forcing of the thermodynamics, e.g. from increased CO2, is compatible with a non-increased lapse rate and thus global non-warming.

The lapse rate is the drop in temperature with altitude, observed to be 6.5 C/km.

The argument is thus that more CO2 will not cause warming. If this is true CO2 alarmism collapses.

The atmosphere is a thermodynamic system subject to radiative heat forcing and thus

thermodynamics may have an answer:

We start from the 2nd Law of Thermodynamics in the form

• dE = -W + D + Q, dP = W - D, (thus dE + dP = Q),

with (assuming the kinetic energy is small)

• E = heat energy
• P = potential energy = int Rho U g dx dt
• Rho density, U convective velocity
• W = work
• D = turbulent dissipation
• Q = heat forcing = 120 W/m2 (observation)
• dE rate of change of E, dP sim.

We consider a column of (rising) air above a squaremeter at the Equator reaching to the top of the atmosphere (at 5 km). Let L be the lapse rate which can vary from 0 (isothermal atmosphere) to 10 C/km (isentropic). Balancing potential energy (increase of altitude of rising air) with loss of heat according to the lapse rate, we have dE/dP = - L/10 and thus recalling that dE + dP = Q,

• dP x (1 - L/10) = Q
• with Q = 120 and L = 6.5 we get dP = 350 (W/m2)

With Q = 0 (no heat forcing) it is natural to assume L = 10 and thus (1 - L/10) = 0 and dP is not determined. If now Q is increased to the observed 120 W/m2, then L decreases to an observed 6.5 C/km and dP settles at 350 W/m2.

The key question is what happens with the lapse rate L if Q is further increased reflecting increasing effective radiative forcing of the thermodynamics from the presence of more atmospheric CO2 (more heat to be transported by thermodynamics). We have

• L = 10 x (1 - Q/dP )

1. We see that if dP stays constant, then increasing Q will decrease L and thus cause cooling.

2. If dP increases like Q (increasing rising velocity U) then L may stay constant without cooling or warming.

3. Including also phase change (evaporation/condensation), we have that increased forcing will

lead to increased evaporation/condensation which will tend to reduce the lapse rate by

lowering temperature at low altitudes and increasing temperature at high altitudes. The lapse rate will thus react to increased forcing in a battle between

• possibly increasing dP by increasing vertical convection
• decreasing L from phase change.

Case 1-2 gives no warming, while 3 may cause warming depending on the balance between

convection and phase change.

Observation indicates that out of a forcing of Q = 120 W/m2 the major part of 100 W/m2 gets allocated to phase change, which may give an indication of what sets the lapse rate: convection or phase change. Benchmark computations are on the way. Stay tuned...

Note that CO2 alarmism is based on a postulate of a "greenhouse effect" from radiation without thermodynamics, which by definition leads to warming by increased CO2. But science

by definition is empty science, and so is global climate without thermodynamics.

There is substantial evidence that the lapse rate is determined primarily by thermodynamics, not by radiation, and thus that the basic postulate of CO2 alarmism lacks scientific value.

The above connects to interesting observations of temperature (lapse rate) for regions

below sea level (The Dead Sea and deep in mines) brought to the light by Charles R. Anderson in NOAA's U.S: Standard Atmosphere Tables: Who Needs Greenhouse Gas Warming?

upon suggestion from Marty Hertzberg and Alan Siddons.