Combining the independent pixel and point-spread function approaches to simulate the actinic radiation field in moderately inhomogeneous 3D cloudy media

Abstract

Field observations and three-dimensional (3D) radiative transfer (RT) simulations of the actinic flux density show strongly pronounced local variations in the presence of inhomogeneous cloud fields which depend on the spatial distribution of the clouds and their optical properties. While exact three-dimensional RT models like, for example, Monte-Carlo techniques or the Spherical Harmonics Discrete Ordinate Method (SHDOM), despite their large computational burden are fully capable of resolving the observed 3D structures of the actinic radiation field, the often employed independent pixel approximation (IPA) for RT can not treat this situation realistically. For inhomogeneous 3D optical property fields of clouds this lack of horizontal photon transport may lead to significant local errors with up to 30% in the present study. Therefore, a very fast method was developed which realistically reproduces the actinic radiation field for 3D cloud fields having moderate spatial variability. This method employs a combination of the IPA, including an exact 3D treatment of the direct sunlight, and a Gaussian point spread function (PSF) to mimic the smoothing properties caused by 3D diffuse radiative transport. As a post-processing step the effect of horizontal photon transport is approximated by means of a Gaussian smoothing filter which accounts for characteristic optical properties of the medium under consideration. Compared to exact 3D RT simulations, the new method delivers more realistic results than the pure IPA approach in all cases analysed. Local deviations of the actinic flux density from 3D RT simulations are significantly reduced in comparison to IPA RT simulations. Depending on the inhomogeneity of the treated cloud fields, the computing time is reduced by a factor of about 20 relative to a full 3D RT simulation. Due to the employment of the IPA in which the RT is handled independently in each column, the size of the simulated model domain is practically unlimited. We also illustrate how this method can improve IPA RT simulations over orographically structured terrain.