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Net Exchange Reformulation of Radiative Transfer in the CO2 15-μm Band on Mars

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  • 1 Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, CNRS, and Université Pierre et Marie Curie, Paris, France
  • 2 Laboratoire d’Energétique, Université Paul Sabatier, Toulouse, France
  • 3 Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, CNRS, and Université Pierre et Marie Curie, Paris, France
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Abstract

The net exchange formulation (NEF) is an alternative to the usual radiative transfer formulation. It was proposed by two authors in 1967, but until now, this formulation has been used only in a very few cases for atmospheric studies. The aim of this paper is to present the NEF and its main advantages and to illustrate them in the case of planet Mars.

In the NEF, the radiative fluxes are no longer considered. The basic variables are the net exchange rates between each pair of atmospheric layers i, j. NEF offers a meaningful matrix representation of radiative exchanges, allows qualification of the dominant contributions to the local heating rates, and provides a general framework to develop approximations satisfying reciprocity of radiative transfer as well as the first and second principles of thermodynamics. This may be very useful to develop fast radiative codes for GCMs.

A radiative code developed along those lines is presented for a GCM of Mars. It is shown that computing the most important optical exchange factors at each time step and the other exchange factors only a few times a day strongly reduces the computation time without any significant precision lost. With this solution, the computation time increases proportionally to the number N of the vertical layers and no longer proportionally to its square N 2. Some specific points, such as numerical instabilities that may appear in the high atmosphere and errors that may be introduced if inappropriate treatments are performed when reflection at the surface occurs, are also investigated.

*thinsp;Current affiliation: Laboratoire d’Océanographie Physique, Museum National d’Histoire Naturelle, Paris, France

Corresponding author address: Jean-Louis Dufresne, Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, Université Pierre et Marie Curie, Boite 99, F-75252 Paris Cedex 05, France. Email: dufresne@lmd.jussieu.fr

Abstract

The net exchange formulation (NEF) is an alternative to the usual radiative transfer formulation. It was proposed by two authors in 1967, but until now, this formulation has been used only in a very few cases for atmospheric studies. The aim of this paper is to present the NEF and its main advantages and to illustrate them in the case of planet Mars.

In the NEF, the radiative fluxes are no longer considered. The basic variables are the net exchange rates between each pair of atmospheric layers i, j. NEF offers a meaningful matrix representation of radiative exchanges, allows qualification of the dominant contributions to the local heating rates, and provides a general framework to develop approximations satisfying reciprocity of radiative transfer as well as the first and second principles of thermodynamics. This may be very useful to develop fast radiative codes for GCMs.

A radiative code developed along those lines is presented for a GCM of Mars. It is shown that computing the most important optical exchange factors at each time step and the other exchange factors only a few times a day strongly reduces the computation time without any significant precision lost. With this solution, the computation time increases proportionally to the number N of the vertical layers and no longer proportionally to its square N 2. Some specific points, such as numerical instabilities that may appear in the high atmosphere and errors that may be introduced if inappropriate treatments are performed when reflection at the surface occurs, are also investigated.

*thinsp;Current affiliation: Laboratoire d’Océanographie Physique, Museum National d’Histoire Naturelle, Paris, France

Corresponding author address: Jean-Louis Dufresne, Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, Université Pierre et Marie Curie, Boite 99, F-75252 Paris Cedex 05, France. Email: dufresne@lmd.jussieu.fr

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