A finite element–spherical harmonics model for radiative transfer in inhomogeneous clouds: Part I. The EVENT model

Abstract

We present a new numerical radiative transfer model for application to solar radiation transport in three-dimensional (3D) cloudy atmospheres. The code uses the finite element–spherical harmonics (FE– P N ) approximation to solve the second-order even-parity form of the transport equation. It is validated by comparison with solutions from two well-established, deterministic radiative transfer models, the one-dimensional (1D) DISORT code and the spherical harmonics discrete ordinates method (SHDOM). The cases solved show generally good agreement, but also reveal some differences. EVEn-parity Neutral particle Transport (EVENT) is very efficient at performing 1D calculations quickly and, even for quite high angular resolutions, is faster. EVENT also has a competitive speed for the simpler, less-heterogeneous multidimensional cases but it is slower than SHDOM for more variable cases. However, there is significant potential to improve the performance of EVENT; it has not yet been optimised for speed and, as such, is not a finished product. Even as it is, EVENT could be used to produce fast, lower-resolution estimates for applications where this would be sufficient, or at lower-spatial resolutions with partial homogenisation. Another difference between the models is that the SHDOM algorithm is designed for small-scale inhomogeneous cloud fields in which the grid spacing is comparable to the mean free path. Problems arise from the use of larger grid cell optical depths, with an increase in the number of iterations required and a lack of flux conservation. Neither of the models is specifically constrained to conserve flux, but the conservation of flux gives an indication of the accuracy of the solution. Increasing the spatial and angular resolution can improve the accuracy but this is not always possible for very large 3D scenes. The grid-point method of property definition in SHDOM means that it performs best for cases with a continuous variation in extinction as this avoids discontinuities in the source function. The finite clouds used in our tests have sharp boundaries that are easily defined in EVENT but the difficulties caused by these in SHDOM are evident in excesses of up to 10 fluxes. The EVENT mesh resolution is determined by the local optical depth; it has no problem in dense areas but has more trouble in coping with voids or optically thin regions. These conditions are easily handled in SHDOM through streaming of photons along discrete ordinates but EVENT must implement methods such as a ray-tracing algorithm. Cases with extreme values of the extinction coefficient are probably best avoided with EVENT, but slightly larger-scale cases with greater optical depths, not suitable for SHDOM, may be solved more easily. These factors should be considered when selecting the most appropriate method for a particular application.