A gradient-based 3D nonlinear spectral model for providing components optical properties of mixed pixels in shortwave urban images

Unmixing optical properties (OP) of land covers from coarse spatial resolution images is crucial for microclimate and energy balance studies. We propose the Unmixing Spectral method using Discrete Anisotropic Radiative Transfer (DART) model (US-DART), a novel approach for unmixing endmember OP in the shortwave domain from mono- or multispectral remotely sensed images. US-DART comprises four modules: pure pixel selection, linear spectral mixture analysis, gradient iterations, and spectral correlation. US-DART requires a surface reflectance image, a 3D mock-up with facets’ group information, and standard DART parameters (e.g., spatial resolution and skylight ratio) as inputs, producing an OP map for each scene element. The accuracy of US-DART is evaluated using two types of scenes (vegetation and urban) and images (Sentinel-2 surface reflectance and DART-simulated pseudo-satellite images). Results demonstrate a median relative error of approximately 0.1 % for pixel reflectance, with higher accuracy for opaque surfaces compared to translucent materials. Excluding co-registration errors and sensor noise, the median relative error of OP is typically around 1 % for opaque elements and 1–5 % for translucent elements with an accurate a priori “reflectance-transmittance” ratio. US-DART enhances our ability to derive detailed OP from coarse-resolution imagery, potentially enabling more accurate modeling of spatial resolution conversions, and energy dynamics, including albedo and shortwave radiation balance, across diverse environments. • 3D radiative model nonlinear unmixing for element optical properties. • It considers the 3D structure and illumination effect in urban areas. • Median relative error of approximately 0.1 % for pixel reflectance. • Ideal experimental conditions: Median OP error: ∼1 % opaque, 1–5 % translucent. • It incorporates computer graphics, deep learning, geostatistics, physics.