A Model to Estimate Global Radiation in Complex Terrain

Global radiation is an important parameter necessary for most ecological models. However, in situ data barely meets the needs of modelling mountainous ecosystems since most field stations are located in flat areas. Consequently, it is usually necessary to extrapolate radiation measurements obtained from an adjacent flat area to the complex terrain of concern. The distribution of radiation in complex terrain depends upon two factors: the local atmospheric conditions, which determine the radiation potentially available to a supposed flat surface in a given location, and the topographic effects on this possible radiation. The latter have been included in detail in most radiation models for complex terrain, but the former are often only simply treated as constant or estimated by over-simplified empirical algorithms. In this paper we propose a novel model that uses a parametric atmospheric model to calculate the potential radiation for a supposed flat surface in a given location, and then account for topographic effects. Direct radiation, diffuse radiation and reflected radiation are calculated separately in the model due to the distinctive characteristics of and the effects by topography. Based on the parametric model, this paper has investigated the relationship between radiation transmittance, clearness indices and altitude under a series of water vapour content and turbidity conditions. This combines three ratios, Rb, Rd, and Rr, defined as the direct radiation, diffuse radiation and reflected radiation received by the arbitrary surface, respectively, to their counterparts in the horizontal surface, to estimate the global radiation for any given location. The model has been validated with data from measurements in National Park Berchtesgaden, Germany, where six measurement sites with various altitudes and topographic characteristics have been deployed. The r2 of modelled and measured hourly global radiation are greater than 0.90 in all six sites, with RMSE varies from 16 to 100 W m−2. Sensitivity analysis revealed that the model was not sensitive to change in water vapour content, which suggests the possibility to use an exponential algorithm of water vapour content when there is no in situ water vapour content information in complex terrains. The NRMSE was only reduced by 0.04, on average, in five of the six sites when water vapour content information was calculated from the in situ air temperature and relative humidity measurements.