I can only recommend Bejan’s work regarding the Constructal Law, as it has a number of applications in hydrology. Some of them are listed here, including Bejan’s textbook, “Convection in Porous Media”.

All the best,

w.

]]>Willis, I do not know much about the maximization principle of the Constructal Law but I am somewhat reluctant to use notions such as this one or the self organized criticality or the scaling as a postulation, before we explore if these could be derived by other well established physical and mathematical principles. Certainly nature optimizes (extremizes) some quantities and optimization laws are much more powerful than preservation laws. Well established optimization principles are in my opinion Fermat’s principle of least (in fact extremal) time for the light propagation, the principle of least (extremal) action for the motion in classical and in quantum physics and the principle of maximum (extremal) entropy for the macroscopic states of complex systems.

]]>That’s why I do not think that this particular way (the use of the “generalised entropy”) is promising or even correct to found the stochastical theory of scaling or Hurstlike dynamics.

OK, but as I said in #524, I did **not** use generalized entropies at all to derive the Hurst-like dynamics. I used only the **standard (Boltzmann-Gibbs-Shannon)** definition of entropy. Therefore the interesting references you link are irrelevant to this discussion. In any case, your references demonstrate that there is an ongoing dialogue about the generalized entropy. In my opinion, a dialogue with different scientific opinions should not worry us; rather it is very healthy and a necessary condition for scientific progress.

Thank you very much for drawing attention to my paper “Nonstationarity versus scaling in Hydrology, 2005” and for your kind comment about it.

]]>Below I have linked to the images of the plots for anomaly trend, residual plots and residual autocorrelation (AR1) for the monthly, annual, January and June GISS NH temperature series for the time periods 1880-2007 and 1979-2007. That gives 6 graphs for each month, annual, etc.

This links to monthly: http://img149.imageshack.us/img149/7098/anomresidualsmonthlydc3.gif

I am presenting the data with links as I have heard comments that displaying the graphs directly into a longer thread will slow it down.

]]>Any result is not inconsistent when there are floor to ceiling CIs. Sharpshootingâ€¦

Hardly sharpshooting! Miss-the-barn-shooting, I think.

]]>If that’s true, then their predictions are not falsifiable by observations.

Not unlike Gavin claiming the current stall, or even decline, is “not inconsistent with the models.” Any result is not inconsistent when there are floor to ceiling CIs. Sharpshooting…

Mark

]]>I don’t want to quibble about semantics or seem argumentative, but just to observe that if a prediction is not credible, it’s not a prediction. It’s something else. Modelers have been very remiss in publishing physically valid CIs about their projections. It seems likely they don’t at all know the magnitude of the physical CI of their models. If that’s true, then their predictions are not falsifiable by observations. That makes model outputs more like guesstimates. Even in Demetris’ recent work, showing GCM mean projections do not match observations, can not really falsify GCMs if the true-but-unknown physical CI about the GCM temperature projection (for example) was about, say, (+/-)5 C. With a CI like that over 20 years, GCM outputs would be consistent with *any* trend in temperature.

This sort of result would just indicate that more basic physics needs to be done on climate itself so as to eventually bring sufficient theoretical precision into GCMs, that they might make a testable prediction. I.e., climate models as prediction machines are a premature birth of (a beautiful) climate physics. More gestation is needed to make the child viable.

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