## 1. Introduction

[2] In the past decades, General circulation models (GCMs) have become central tools for the study of the Earth climate and operational weather forecast. Because those numerical tools are mainly based on physics laws, they can be in principle adapted quite easily to various planetary atmospheres, by changing in particular fundamental parameters such as the planetary radius, the gas heat capacity, etc. Some specific processes must also be included depending on the planet such as the presence of ocean and of vegetation on Earth, the CO_{2} condensation on Mars, or the presence of photochemical haze surrounding the atmosphere on Titan [*Hourdin et al.*, 1995; *Forget et al.*, 1999; *Richardson et al.*, 2007]. However, a major step in this process is generally the development of a radiative transfer code. Because of the complexity of radiative transfer computation, and because heating rates must be computed typically a few times per hour for simulations covering decades or centuries, at each mesh of a grid of typically a few tens of thousands of points, such codes (named radiative transfer parameterizations) must be based on highly simplified algorithms that are generally specific to the particular atmosphere.

[3] From this point of view, the case of Venus is quite challenging. With its deep atmosphere of CO_{2} (92 bars at the surface), its huge greenhouse effect (735 K at surface), its H_{2}SO_{4} clouds which in some spectral regions behave as pure scatterers, allowing to “see” through the clouds in some near infrared windows [*Allen and Crawford*, 1984; *Bézard et al.*, 1990], and because part of the spectral properties are not measured or constrained in the conditions encountered there, Venus is even a problem for making reference computations with line-by-line codes.

[4] A full description of the energy balance of the atmosphere of Venus can be found in the work of *Titov et al.* [2007]. A large fraction of the solar flux is reflected by the clouds, allowing the absorption by the atmosphere of only approximately 160 W m^{−2} on average. Only 10% of the incident solar flux reaches the surface. Because of the thickness of the atmosphere in most of the infrared, most of the outgoing thermal radiation comes from the cloud top. Below clouds, the deeper atmosphere can only radiate to space in the near-infrared windows. The huge infrared opacity in that region induces a strong greenhouse effect that can explain the extremely hot surface temperature. In this region, energy is radiatively transported through short-range radiative exchanges. Convection, essentially located in the lower and middle clouds (from roughly 47–50 km to around 55 km altitude), has been identified thanks to the stability profiles measured by Pioneer Venus and Venera entry probes [*Schubert*, 1983]. This convection certainly plays a role in transporting energy from the base of the clouds (heated from below by the deep atmosphere) to the upper clouds, where infrared radiation is able to reach space. This one-dimensional description of the energy balance is a global average view, and its latitudinal variations is related to the dynamical structure of the atmosphere, the description of which is the main goal of a General Circulation Model.

[5] In order to perform reference infrared computations and to develop a fast algorithm suitable for a GCM, we make use of the Net Exchange Rate (NER) formalism based on ideas originally proposed by *Green* [1967] and already used to derive a radiation code for the LMD Martian GCM [*Dufresne et al.*, 2005], or to analyze the radiative exchanges on Earth [*Eymet et al.*, 2004]. In the NER approach, rather than computing the radiative budget as the divergence of the radiative flux, this budget is computed from the radiative net exchanges between all the possible pairs of elements *A* and *B*, defined as the difference of the energy emitted by *A* and absorbed by *B* and that emitted by *B* and absorbed by *A*. Using the plane parallel approximation, net radiative exchanges to be considered are those between two atmospheric layers, between a surface and an atmospheric layer (space being considered as a particular “surface” at 0 K) or between the two surfaces (ground and space). This formalism insures some important properties such as the reciprocity principle and the energy conservation whatever the retained numerical assumptions [*Dufresne et al.*, 2005]. Thus drastically different levels of approximation can be applied to various terms of the computation, without violating those fundamental physical principles.

[6] Within the GCM, the radiative transfer is divided in solar radiative forcing, and thermal radiation energy redistribution (and cooling to space). This paper describes exclusively how we use the NER formalism to compute thermal radiation, and how this computation is parameterized for use within the GCM. This is only a first step, since we need also to compute the solar radiative forcing with consistent input parameters (essentially the cloud structure and optical properties) to get a fully consistent radiative scheme in the GCM. However, for the moment, the solar forcing in the GCM is taken from computations by *Crisp* [1986], or by *Moroz et al.* [1985] and *Tomasko et al.* [1980]. The development of a parameterization of solar forcing is a work in progress, and will be published in a future paper.

[7] In section 2, a set of referenced optical data is chosen and briefly described for all components of Venus atmosphere, and these optical data are used to perform reference net exchange simulations. The corresponding net exchange matrices are then physically interpreted, in order to highlight the features that will serve as start basis for the parameterization design. This parameterization is described and validated in section 3. In the validation process, accuracy is checked against reference Monte Carlo simulations assuming that all optical data are exact. This means that, at this stage, the parameterization methodology (the retained physical pictures, the formulation choices) is validated. In particular, we can confidently extrapolate that no further technical developments will be required if we want to include more accurate optical data that may arise from a better knowledge of the spectral characteristics and composition of the atmosphere of Venus. However, we need to discuss the level of confidence associated to our present optical data against available observations in order to allow an immediate use of the proposed parameterization in Venus GCMs [*Lebonnois et al.*, 2005, 2006]. This discussion is the object of section 4, in which a particular attention is devoted to the collision induced continuum model and the composition and vertical structure of the cloud.