Developing an Analytical Model for Neighborhood-Scale Urban Surface Bidirectional Reflectance Incorporating Three-Dimensional Structure

The bidirectional reflectance factor (BRF) is a key parameter for understanding the radiative transfer process within cities, influenced by the sun-target-sensor geometry. Simulating urban BRF poses significant challenges due to the complex three-dimension (3-D) structures of urban landscapes. Previous attempts have been facing significant hurdles, either inadequately addressing the complexities of real-world urban structures or consuming too many computing resources. To overcome these challenges, this study introduces an analytical model—urban bidirectional reflectance analytical model (UBRAM), which takes advantage of landscape-level geometric and radiometric parameters incorporating 3-D urban structures to simulate the BRF of neighborhood-scale urban landscapes ( $100\times 100- 1000\times 1000$ m). UBRAM underwent verification using simulations from the well-known radiative transfer model (discrete anisotropic radiative transfer, DART) under various solar-illumination geometries and diverse urban morphologies. Results demonstrated a good agreement between UBRAM and DART, with an overall ${R} ^{2}$ ranging from 0.829 to 0.983 and the shape similarity index exceeding 0.99 in most scenes, underscoring the effectiveness of UBRAM. Notably, leveraging a modular design, UBRAM enables independent processing of 3-D urban scenes and radiative transfer simulation, ensuring efficiency and scale applicability. This study establishes UBRAM as a viable model, offering a novel approach for quantifying BRF of neighborhood-scale urban surfaces. Moreover, UBRAM requires a limited number of easily obtainable parameters, facilitating its straightforward adaptation for application in other urban areas. UBRAM facilitates the simulation of radiative transfer processes based on real-world 3-D urban models, thereby enhancing the accuracy of scene rendering and downstream applications such as urban heat islands and environment monitoring.