Extremal principle of entropy production in the climate system

Paltridge found reasonable values for the most significant climatic variables through maximizing the material transport part of entropy production by using a simple box model. Here, we analyse Paltridge's box model to obtain the energy and the entropy balance equations separately. Derived expressions for global entropy production, which is a function of the radiation field, and even its material transport component, are shown to be different from those used by Paltridge. Plausible climatic states are found at extrema of these parameters. Feasible results are also obtained by minimizing the radiation part of entropy production, in agreement with one of Planck's results, Finally, globally averaged values of the entropy flux of radiation and material entropy production are obtained for two dynamical extreme cases: an earth with uniform temperature, and an earth in radiative equilibrium at each latitudinal point

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Estimating 750 years of temperature variations and uncertainties in the Pyrenees by tree-ring reconstructions and climate simulations.

Past temperature variations are usually inferred from proxy data or estimated using general circulation models. Comparisons between climate estimations derived from proxy records and from model simulations help to better understand mechanisms driving climate variations, and also offer the possibility to identify deficiencies in both approaches. This paper presents regional temperature reconstructions based on tree-ring maximum density series in the Pyrenees, and compares them with the output of global simulations for this region and with regional climate model simulations conducted for the target region. An ensemble of 24 reconstructions of May-to-September regional mean temperature was derived from 22 maximum density tree-ring site chronologies distributed over the larger Pyrenees area. Four different tree-ring series standardization procedures were applied, combining two detrending methods: 300-yr spline and the regional curve standardization (RCS). Additionally, different methodological variants for the regional chronology were generated by using three different aggregation methods. Calibration verification trials were performed in split periods and using two methods: regression and a simple variance matching. The resulting set of temperature reconstructions was compared with climate simulations performed with global (ECHO-G) and regional (MM5) climate models. The 24 variants of May-to-September temperature reconstructions reveal a generally coherent pattern of inter-annual to multi-centennial temperature variations in the Pyrenees region for the last 750 yr. However, some reconstructions display a marked positive trend for the entire length of the reconstruction, pointing out that the application of the RCS method to a suboptimal set of samples may lead to unreliable results. Climate model simulations agree with the tree-ring based reconstructions at multi-decadal time scales, suggesting solar variability and volcanism as the main factors controlling preindustrial mean temperature variations in the Pyrenees. Nevertheless, the comparison also highlights differences with the reconstructions, mainly in the amplitude of past temperature variations and in the 20th century trends. Neither proxy-based reconstructions nor model simulations are able to perfectly track the temperature variations of the instrumental record, suggesting that both approximations still need further improvements.