A Two Stream Radiative Transfer Model for Vertically Inhomogeneous Vegetation Canopies Including Internal Emission

Abstract

Two stream models of radiative transfer are used in the land surface schemes of climate and Earth system models to represent the interaction of solar and terrestrial radiation with vegetation canopies. This is done both to model the surface energy balance and the photosynthetic flux of carbon into the terrestrial biosphere. Two stream models are especially attractive for inclusion in large complex models of the Earth as they allow for an analytical and computationally cheap solution to the radiative transfer problem, whilst accounting for all orders of photon scattering and hence preserving energy balance. As the vegetation processes described in land surface models become more complex, new two stream formulations are required to correctly represent radiative components. For example, as ecosystem demography becomes more prevalent in land models, the need to represent canopies with vertically varying structure becomes more important, but an analytical, efficient solution to the transfer problem is still desirable. Here we describe a two stream scheme constructed from layers with independent optical properties. It is physically consistent with the existing radiative transfer schemes in many current land surface models, with typical differences in the order of $10^{-14}$ in normalized flux units, and its solution is analytical. The model can be used to represent complex canopy structures and its formulation lends itself to modeling the canopy leaving flux arising from internal emissions, for example, longwave radiation or fluorescence. We also discuss the parameterization of two stream schemes and demonstrate that this could be improved in existing models.