An Open-Box Physics-Based Neural Network for Modeling Shortwave Radiative Transfer

Abstract We model shortwave radiative transfer using a neural network that assigns physical meaning to the components within its structure. Separate components represent transmissivity, scattering, multilayer interreflection, and the spectral decomposition of radiation, where each of these contains computational paths for direct and diffuse radiation. This approach is an “open-box” alternative to a black-box neural network. It not only exposes the network’s internal variables to physical interpretation but also facilitates a synthesis of physical knowledge within the neural network. Beer’s law, the adding–doubling algorithm, conservation laws, the nonnegativity of physical variables, and physical independence are hardcoded into the network architecture. The resulting network contains just 3475 weights. We train it as a single system from input to output, jointly learning all weight values under the constraints of the embedded physical models and physical laws. Training and testing data were generated using the ecRad radiation scheme on input reanalysis data for eight atmospheric constituents from the Copernicus Atmosphere Monitoring Service. The network was trained on a dataset from 2008 and tested on datasets from 2009, 2015, and 2020, with error rates no worse than 0.026 K day −1 root-mean-square error (RMSE) in heating rate and 0.098 W m−2 RMSE in radiative flux, improving upon the prior state of the art in machine learning–based shortwave radiative transfer. Significance Statement Traditional physics-based modeling and data-driven machine learning often appear to be incompatible approaches for representing physical processes. We propose a synthesis that leverages the unique strengths of each. We overcome incomplete physics-based models by selectively incorporating data-driven neural network elements. Conversely, physical knowledge guides the design of the network’s architectureand its data-driven elements. The resulting network is not a typical black box but an “open box,” where its internal elements have well-defined physical functions and abide by physical laws. We demonstrate this novel approach by applying it to shortwave radiative transfer, a vital component of weather and climate forecasting models.