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.