Variational Principles in Thermodynamics

[mathjax]Let’s start with a telling quote :

James Annan: “There’s so little interesting stuff going on in climate science these days.”

… well of course, if we don’t have anything worthwhile to say.   But then we also find this:

Peter Ván: “The basic mystery in thermodynamics is the universality. The validity of thermodynamic equations and theories regularly exceed the expectations.” [1]

The CSALT model of the global temperature anomaly has no right to work as well as it does. After all, it solves no dynamical behavior and requires little information with regards to the complexity of the earth’s surface. Yet, it still captures all the useful detail in the historical temperature record, leaving behind a residual close to being in the white noise regime.

Fig. 1 : Residual noise of the CSALT model is flat and close to white noise

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CSALT with CW Hybrid

The correction to the HadCRUT4 global temperature series as described by Cowtan and Way [1] and applied to the CSALT model is evaluated by the following fit:

Fig 1 : The top panel shows the original HadCRUT4 CSALT fit and the bottom panel is the CW Hybrid correction. No filtering was applied to the data. Note the narrowing of the gap in recent years

The previous post predicted that the recent diverging decrease in warming was an artifact of not taking measurements of the rapidly warming Arctic region, and since energy is balanced over the earth a decrease was to be expected.  But once estimates of the Arctic and other regional warming was taken into account, this divergence would close up.

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CSALT Ju-Jutsu

Cowtan and Way’s hybrid correction to the HadCRUT global temperature series [1]  has provoked expected interest by auditor Steve McIntyre.  This is always welcome, because as with the majority of of these nosy irritants, the more that they try to find something wrong with a well-reasoned comprehensive analysis, the more that they lay out a cookie trail for us to follow.   So guys like McIntyre make our job easier because what they try to expose backfires on them and it just gives climate scientists further substantiation of their own models — not exactly what McIntyre had in mind.

This case is no different, starting with McIntyre’s figure below:

Fig 1: Delta between CW Hybrid (basis 1961-1990) and HadCRUT4. From McIntyre  Note the divergence in recent years.

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CSALT and SST corrections

According to the CSALT model, which fits the temperature series data over the last 100+ years, the most significant anomaly encountered is a warming peak that occurred over the WWII years.  This spike is only weakly associated with a SOI peak and is suspicious as it corresponds to missing temperature readings during the war years (see Figure 1 below from IPCC).

Fig 1 : The geospatial distribution of surface temperatures. The interval from 1940 to 1945 shows the Northern Hemisphere dual warming spikes along with an ENSO El Nino event in the Southern Hemisphere. These regions do show warming but they may also have a common warming bias.

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Convergence in Temperature Time Series

Climate science investigators Cowtan and Way [1] updated the HADCRUT4 global temperature time series to properly account for areas that had little representation, incorporating regions such as Africa and the Arctic using geospatial kriging techniques . The Arctic in particular has shown considerable anomalous warming that hadn’t been captured in that time series.  They have a methods page that contains details here.

This impacts the CSALT model by adjusting the temperatures upward in the last few years to better match the movement out of the “pause” regime that the fluctuation components plus relentless CO2 forcing have been predicting would occur. See Figure 1.

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Simple models of forced warming

Caldeira and Myrhvold [1] attempted the obvious by compiling various global warming models to try to extract simple thermal behavioral patterns, see their online paper.
They succeeded in my opinion.

What is most important about their work is that they placed diffusional models of warming, as pioneered by James Hansen [2], on an equal footing with first-order kinetics model. The first-order models use damped exponentials and are favored by analysts that want to keep the math simple. Caldeira and Myrhvold understand this and provide mixed exponential models that will piece-wise map to the diffusional responses normally seen in the numerical simulations.

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