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Jerg, Matthias (2006): Solar radiative transfer parameterizations for three-dimensional effects in cloudy atmospheres. Dissertation, LMU München: Faculty of Physics
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Abstract

This thesis addresses two major problems in the field of radiative transfer (RT) in the earth’s atmosphere. The first problem is linked with the need for significant computational resources of RT in a three-dimensional (3D) atmospheric model. Although only highly efficient one-dimensional (1D) RT models are employed for each pixel of the model domain separately and independently, it is still not possible to utilize these models on a frequent basis, compared to the rate at which meteorological variables are computed. That means that the calculated radiative properties (RP) are held constant for a longer period of time, while the prognostic meteorological variables are updated at a rapid rate. Even though there is no detailed study about the consequences of this disproportion, an attempt was made to develop an RT model which permits the fast computation of basic radiative transfer properties which could be used in the future to update this information more frequently. The developed model is based on the application of the radiative transfer perturbation theory to realistic cloud fields column by column. It turned out that the application, intended to replace the Independent Pixel Approximation (IPA), see below, is possible and promising within the assumptions and constraints of the utilized methods. It could be demonstrated that, depending on the actual case, errors in the pixel transmission and reflection stay bounded to values of up to 10%−15%. In one case the achieved acceleration could be investigated. It was about a factor of four compared to the direct application of the usual forward variant of the model, although no numerical optimization was carried out. The second problem concerns the realistic treatment of the 3D interactions of clouds and solar radiation. As implied in the above paragraph, 1D RT models are usually employed column by column which suppresses the exchange of radiation between those columns. Thus, fundamental 3D effects are neglected by this so-called Independent Pixel Approximation (IPA). These comprise not only small scale contributions due to diffuse radiative transport, but also large scale patterns like geometric effects of the inclined solar illumination. Examples are blurred radiative structures due to radiative smoothing and the shifted location of shadows and bright areas. To parameterize those effects strong efforts have been undertaken during the last couple of years. However, no method has proven to be completely satisfactory and ready for implementation. To carry this research one step further two approaches have been adopted and extended. The first is the concept of the Tilted Independent Pixel Approximation (TIPA). In contrast to the IPA, which ignores the solar geometry, this method correctly accounts for the slant illumination due to the correct tracking of the direct beam. As a result, the optical parameters in the slant columns are arranged in a more realistic order and the attenuation and the positions of the RP are less erroneous. To further improve this method a transformation has been developed which yields 3D resolution of the RP in the original grid. Since the TIPA still does not include any diffuse radiative exchange as another approach the Nonlocal Independent Pixel Approximation (NIPA) has been explored. This technique uses 1D results and carries out a convolution product to distribute RP across column boundaries. In order to arrive at a fully independent treatment of this method a simplified derivation of the convolution parameters was developed. Finally, TIPA and NIPA are combined to form NTIPA. These approaches have proven to be superior to IPA with respect to several aspects. The improvement ranges from several percent to 50% if maximum errors of the transmitted and reflected light are considered. Criteria like the distribution of the errors or the vertical profiles of the RP are also more preferable than their counterparts derived by IPA.