Jumping into the Klotzbach

As the innocent little bunnies may have observed there is a rather teapotish tempest going on about Roger Pielke Sr.'s work. For the most part the way science deals with stuff no one believes or cares about (pick one) is to ignore it, and a lot of what RPS has published fits into that category which irritates the old guy no end. Recently he and Jr. published a paper, Klotzbach, et al. which purports to show that there should be a significant (as in measured) difference between GLOBAL surface temperatures and those higher up. This would be a real difference, not an instrumental effect.

The idea is that nighttime inversion layers form near the surface limiting near surface cooling. As has been pointed out, first by Michael Tobis, the edifice rests on Pielke papers all the way down

That, of course, was only the beginning. Since then we have the prequel
e Pur Si Scalda - MT (8/3)

Enter the protagonists
Evidence that global temperature trends have been overstated - RPJ
Warm bias in the surface temperature trend - RPS at his "Climate for Dummies" site
New Paper Documents a Warm bias in the Calculation.... - RPS (8/13)

and the follow-on
Pielkes all the Way Down - MT (8/14)
Klotzbach in the Blogosphere - MT (8/17)
Evidence for Bias in Atmospheric Temperature Trends - JEB (in Stoat speak) (8/17)
An Exchange with Gavin Schmidt on Klotzbach - RPJ at his new lemonade stand (8/17)
Speeding through Haldane's Four Stages - RPJ (8/18)
Curiouser and Curiouser - JEB (8/19) where James swallows a Pielke and goes down the Rabett hole
The Global Average Temperature Warming Really Is Overstated - RPS (8/20)
The Paper “Heat Balance In The Nocturnal Boundary Layer During CASES-99″ By Sun Et Al 2003" - at the New Pielke Sr. Times
My Final Word on Klotzbach - MT (8/20)
Comment on MT's Final Word on Klotzbach - RPS (8/20)
Pathologies in Climate Science - RPJ (8/20)
PM05 Resolved - JEB
Pielke and Matsui Revisited - JEB (8/22)
Major Errors in James Annan's Post PM 05 Revisited - RPS (8/23)
Oh dear - JEB (8/23)
Comments on an Email Exchange with James Annan - RPS (8/23)
Does Gavin Schmidt Understand Boundary Layer Physics - RPS (8/23)
My Craven Rave - MT (8/24)
The Issue that James Annan and Gavin Schmidt Should Focus On - RPS (8/24)
A Bizarre Rewriting of History - JEB (8/25)
The Santer, et al View of The Importance of Error in the Surface Record - RPS (8/28)
Comments on a New Post by James Annan - RPS (8/28)
Scientific Arguments as Climate Science - RPJ (8/29)
Remarkable Admission by James Annan on Klotzbach, et al - RPS tag teaming (8/29)
But they Also Laughed at Bozo the Clown - JEB (8/31)

Well, now that the class has RTFR, Eli would like to drive a carrot truck through the procedings. As MT first, and later James, point out, Klotzbach's rests on Pielke and Matsui 05 which is connected to Eastman, Coungenour and Pielke, and so on.

Let us, as James did, get off at the first stop, Pielke and Matsui, 2005, which is an attempted refutation of Parker 2004. PM05 claims that there should be different trends in temperature records at different heights

Long-term climate trends of surface air temperature should not be expected to have the same trends for light wind and stronger wind nights, even if the trends in the boundary layer heat fluxes were the same. Parker (2004) segmented observed surface temperature data into lighter and stronger wind terciles in order to assess whether the reported large-scale global-averaged temperature increases are attributable to urban warming. We conclude, however, that trends at an individual height depend on wind speed, thermodynamic stability, aerodynamic roughness, and the vertical gradient of absolute humidity. We present an analysis to illustrate why temperature values at specific levels will depend on wind speed, and with the same boundary layer heat content change, trends in temperature should be expected to be different at every height near the surface when the winds are light, as well as different between light wind and stronger wind nights.

So Eli went and read the paper, which is really a thin thing that comes down to calculating the potential temperature profile at a height z (more or less quoting here) Δθ(z) for a "continually turbulent stable clear night boundary layer over a flat surface"

Δθ(z) = Δθ_s exp(-z/H_e)

where H_e is a scale length approximately equal to

H_e ~ a (V_RL)^0.75t^0.5

a is a constant, V_RL the wind speed and t the time from when the inversion is established (not quite, but close enough). Also

θ_s = Q_AK/H_e

Q being the cumulative heating. They calculate the profiles, lapse rates, etc for wind speeds from 1 - 10 m/s and different cumulative heating, but the rubber meets the road in that formula for θ_s.

Drive the wind speed to zero and you end up with a zero thickness scale length, an infinite temperature difference between ground and the layer a micron up. In other words, at some point this little model fails. It probably is not too bad for the upper range of the wind scale used, but, of course, in that case the scale length will also be larger, e.g. the layer thicker and the lapse rate not as extreme.

This calculation, borrowed from Stott's text, by itself is inappropriate for at least some of the conditions Pielke and Matsui are trying to model. Perhaps more kindly put, it may be right about the part of the system it is trying to model, but something is missing. The near ground lapse rates for windless conditions are too high and the scale height for the layer in contact with the surface too small. It is trivial (Eli does not do hard work) to reduce PM05 to an absurdity as a complete description of a real surface inversion layer and if it is not a complete description it is inappropriate and wrong as a refutation of the observation based work of Parker.

UPDATE: Having thought about this while watering the carrot patch, it must be that the estimate of the scale length H_e ~ a (V_RL)^0.75t^0.5 must have a minimum value and not go to zero when the wind velocity does. This basically means that the temperature differences between the 2 m surface temperature measurements and the satellite measurements are smaller than PM05 would imply.

Comments?