ATTP and Eli have been exploring the carbon cycle, with a few simple, but illustrative models. ATTP's attention was drawn to a recent submission to Earth System Dynamics A simple model of the anthropogenically forced CO2 cycle by Weber, Lüdeke and Weiss, which is not even wrong, worse, it is misleading. Hans Joachim Lüdeke, the S. Fred Singer of the German denialist set seems to be making a retirement project of such things. If you doubt your friendly bunny and Eli knows none of the readers of Rabett Run would stoop so low, there is this comment from Neven about an earlier attempt at misdirection by Herr Lüdeke-Singer
I do not dismiss them because they belong to a certain political group. I dismiss them because I have seen them lie and distort repeatedly, and never be right about anything, and never retract allegations, and never admit or correct mistakes.and this analysis of the attempt (published in E&E and Int J. Mod Phys B, who would have guessed, not Eli to be sure), by Richard Tol during one of his rational periods. Tol points out that
Lüdeke concludes that there is no trend in the global temperature record of the past century or so, after he removed the trend by So far so good. Unfortunately, fluctuation analysis does not work on trending variables. Therefore, LLE use DETRENDED fluctuation analysis. That is, they first fit a polynomial of order two to the data, remove this trend, and study the deviations from the trend.
Having removed the trend from their data, LLE cannot answer the question: What caused the warming? They eliminated from their analysis the very thing in which they are interested.This trick, of course is one of Tamino's top ten on this list of statistical flim flam but there is a lot more.
The abstract of the Weber paper claims that
From basic physical assumptions we derive a simple linear model of the global CO2 cycle without free parameters. It yields excellent agreement with the observations reported by the carbon dioxide information analysis center (CDIAC) as time series of atmospheric CO2 growth, of sinks in the ocean and of absorption by the biosphere. The agreement extends from the year 1850 until present (2013). Based on anthropogenic CO2 ; emission scenarios until 2150, future atmospheric CO2 concentrations are calculated. As the model shows, and depending on the emission scenario, the airborne fraction of CO2 begins to decrease in the year ∼ 2050 and becomes negative at the latest in ∼ 2130. At the same time the concentration of the atmospheric CO2 will reach a maximum between ∼ 500 and ∼ 900 ppm. As a consequence, increasing anthropogenic CO2 emissions will make the ocean and the biosphere the main reservoirs of anthropogenic CO2 in the long run. Latest in about 150 years, anthropogenic CO2 emission will no longer increase the CO2 content of atmosphere.Now some, not Eli to be sure, might fight their war through the mathturbation, including a freshman level reprise of Euler's method for solving a simple differential equation. Eli is a visual bunny and he always looks at the figures first. His attention was drawn to Figure 5b, which purported to show the response of the atmosphere to a pulse of CO2
The Weber model fails because it does not consider reverse interchanges from the biosphere and the surface ocean into the atmosphere. According to Weber, et al the adjustment time is 100 years and the grey shaded regions are the responses of 15 models considered by Joos et al., 2013. One immediately notices that their atmospheric CO2 concentration declines rapidly to zero. This is possible for sequential reactions, a --> b + s but not for opposing reactions (a = b and a = s) where there are both forward and backwards reactions. A simple, straightforward kinetic model for the flow of carbon between the three reservoirs would be
Where kxy is the rate constant for moving carbon from reservoir x to y and Nx is the amount of carbon in reservoir x. n is the CO2 injected into the atmosphere at time t. If No is the total amount of CO2 in the system, at equilibrium where a steady state approximation can be applied (in other words set each of the derivatives to zero because the concentrations are not changing, the system is in equilibrium)
By inspection Weber et al’s result can only be obtained if the rate constants for transfer between the biosphere, kba, and surface ocean, ksa, to the atmosphere are zero. Nope
And then there is physics and chemistry. Even if one denies the analysis of the carbon cycle as shown above, if, as Weber, et al, claim, all of the excess carbon injected into the atmosphere is totally sequestered into biological materials after a hundred years or so, for it to stay there as required by their analysis would mean that decomposition of biological materials would not be increased by the increased amount of material. Similarly for excess CO2 sequestered in the surface oceans. If the partial pressure of CO2 in the surface ocean is increased physics requires that the out gassing of the surface ocean would be increased.
Finally, if Weber et al, are going to try and claim that they were talking about a rapid descent of the atmospheric carbon dioxide into the deep oceans, well, there is a lot of information about that interchange, and one of the reviewers, Fortunat Joos, buries that one
Can transport processes within the ocean be approximated with a single time scale? There is the GLODAP data base on CDIAC which includes CFCs and radiocarbon data sampled over the pastdecades (Key et al., 2004). These data show that mixing time scales for the upper thermocline are decadal and mixing time scales for the deep ocean are multi-centennial. The lowest radiocarbon ratios of dissolved inorganic carbon are found in the deep Pacific with values that are about 240 permil or so lower than the atmosphere or about 200 permil lower compared to the surface ocean. This corresponds to a water age of roughly 1800 years.