Penumbra: A spatially distributed, mechanistic model for simulating ground-level incident solar energy across heterogeneous landscapes.

Landscape solar energy is a significant environmental driver, yet it remains complicated to model well. Several solar radiation models simplify the complexity of light by estimating it at discrete point locations or by averaging values over larger areas. These modeling approaches may be useful in certain cases, but they are unable to provide spatially distributed and temporally dynamic representations of solar energy across entire landscapes. We created a landscape-scale ground-level shade and solar energy model called Penumbra to address this deficiency. Penumbra simulates spatially distributed ground-level shade and incident solar energy at user-defined timescales by modeling local and distant topographic shading and vegetative shading. Spatially resolved inputs of a digital elevation model, a normalized digital surface model, and landscape object transmittance are used to estimate spatial variations in solar energy at user-defined temporal timesteps. The research goals for Penumbra included: 1) simulations of spatiotemporal variations of shade and solar energy caused by both objects and topographic features, 2) minimal user burden and parameterization, 3) flexible user defined temporal parameters, and 4) flexible external model coupling. We test Penumbra's predictive skill by comparing the model's predictions with monitored open and forested sites, and achieve calibrated mean errors ranging from -17.3 to 148.1 μmoles/m2/s. Penumbra is a dynamic model that can produce spatial and temporal representations of shade percentage and ground-level solar energy. Outputs from Penumbra can be used with other ecological models to better understand the health and resilience of aquatic, near stream terrestrial, and upland ecosystems.