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Abstract. Topography exerts significant influences on the incoming solar radiation at the land surface. A few stand-alone regional and global atmospheric models have included parameterizations for sub-grid topographic effects on solar radiation. However, nearly all Earth system models (ESMs) that participated in the Coupled Model Intercomparison Project (CMIP6) use a plane-parallel (PP) radiative transfer scheme that assumes that the terrain is flat. In this study, we incorporated a well-validated sub-grid topographic (TOP) parameterization in the Energy Exascale Earth System Model (E3SM) Land Model (ELM) version 1.0 to quantify the effects of sub-grid topography on solar radiation flux, including the shadow effects and multi-scattering between adjacent terrain. We studied the role of sub-grid topography by performing ELM simulations with the PP and TOP schemes over the Tibetan Plateau (TP). Additional ELM simulations were performed at multiple spatial resolutions to investigate the role of spatial scale on sub-grid topographic effects on solar radiation. The Moderate Resolution Imaging Spectroradiometer (MODIS) data was used to compare with the ELM simulations. The results show that topography has non-negligible effects on surface energy budget, snow cover, snow depth, and surface temperature over the TP. The absolute differences in surface energy fluxes for net solar radiation, latent heat flux, and sensible heat flux between TOP and PP exceed 20, 10, and 5 W m−2, respectively. The differences in land surface albedo, snow cover fraction, snow depth, and surface temperature between TOP and PP exceed 0.1, 0.1, 10 cm, and 1 K, respectively. The magnitude of the sub-grid topographic effects is dependent on seasons and elevations and is also sensitive to the spatial scales. Although the sub-grid topographic effects on solar radiation are larger with more spatial details at finer spatial scales, they cannot be simply neglected at coarse spatial scales. When compared to MODIS data, incorporating the sub-grid topographic effects overall reduces the biases of ELM in simulating surface energy balance, snow cover, and surface temperature, especially in the high-elevation and snow-covered regions over the TP. The inclusion of sub-grid topographic effects on solar radiation parameterization in ELM will contribute to advancing our understanding of the role of the surface topography on terrestrial processes over complex terrain.

Rugged terrain, including mountains, hills, and some high lands are typical land surfaces around the world. As a physical parameter for characterizing the anisotropic reflectance of the land surface, the importance of the bidirectional reflectance distribution function (BRDF) has been gradually recognized in the remote sensing community, and great efforts have been dedicated to build BRDF models over various terrain types. However, on rugged terrain, the topography intensely affects the shape and magnitude of the BRDF and creates challenges in modeling the BRDF. In this paper, after a brief introduction of the theoretical background of the BRDF over rugged terrain, the status of estimating land surface BRDF properties over rugged terrain is comprehensively reviewed from a historical perspective and summarized in two categories: BRDFs describing solo slopes and those describing composite slopes. The discussion focuses on land surface reflectance retrieval over mountainous areas, the difference in solo slope and composite slope BRDF models, and suggested future research to improve the accuracy of BRDFs derived with remote sensing satellites.