SSolar-GOA v1.0: a simple, fast, and accurate Spectral SOLAR radiative transfer model for clear skies

Abstract

The aim of this work is to describe the features of and to validate a simple, fast, accurate, and physically based spectral radiative transfer model in the solar wavelength range under clear skies. The model, named SSolar-GOA (the first “S” stands for “spectral”), was developed to evaluate the instantaneous values of spectral solar irradiances at ground level or at a given altitude of the atmosphere. The model requirements are designed based on the simplicity of the analytical expressions for the transmittance functions in order to be easily replicated and applied by a wide community of users for many different applications (atmospheric and environmental research studies, satellite remote sensing, solar energy, agronomy and forestry, ecology, and others). Although spectral, the model runs quickly and has sufficient accuracy for the evaluation of solar irradiances with a spectral resolution of 1–10 nm. The model assumes a single mixed molecule–aerosol scattering layer where the original Ambartsumian method of “adding layers” in a one-dimensional medium is applied, obtaining a parameterized expression for the total transmittance of scattering. Absorption by the different atmospheric gases follows “band model” parameterized expressions. The input parameters must be realistic and easily available since the spectral aerosol optical depth (AOD) is the main driver of the model. The validation of the SSolar-GOA model has been carried out through comparison with simulated irradiance data from the libRadtran package and with direct and global spectra measured by spectroradiometers. Thousands of spectra under clear skies have been compared for different atmospheric conditions and solar zenith angles (SZA). The SSolar-GOA is validated by a quantitative comparison with libRadtran, showing that it underestimates direct normal, global, and diffuse spectral components with relative differences of +1 % (RMSE % = 4.6–8), +3 % (RMSE % = 5.3–8), and 8 % (RMSE % = 9.3–9.6), respectively, when the SZA varies from 6 to 60∘. Compared with the measured irradiance data of the LI-1800 and ASD spectroradiometers, the relative differences of direct normal and global components are within the overall experimental error, about ±2 %–12 % (RMSE % = 5–8.3), with underestimated or overestimated values. The diffuse component presents the highest degree of relative difference that can reach ±20 %–30 % and RMSE of 25 %–50 %. The relative differences depend strongly on the spectral solar region analysed and the SZA, but the high values of RMSE are due to the artifice generated by the different spectral resolution of the absorption coefficients of both models. Model approach errors combined with calibration instrument errors may explain the observed differences. The SSolar-GOA v1.0 is implemented in Python and open-source licensing.