Revised Parameterization of Atmospheric Transmittance for Clear-Sky Direct Normal Irradiance

Abstract

Despite the significant progress achieved in recent years, there is still room for improving the accuracy of atmospheric transmittance estimation under clear-sky conditions. This study introduces a new parameterization of atmospheric transmittance for estimating direct normal irradiance (DNI). The model equations are derived by integrating the spectral transmittances of the main atmospheric extinction processes into broadband formulations. New empirical corrections are introduced for uniformly mixed gas and water vapor transmittances to reduce systematic deviations from ground measurements. The resulting model, called GM-DNI, was evaluated against high-quality ground measurements collected at eight radiometric stations located on five continents and spanning four climate zones. For the entire test dataset, GM-DNI achieved an nRMSE of 1.84% and an nMBE of 0.22%. The analysis of individual errors showed consistently high accuracy across the investigated conditions, with the best performance at high solar elevations and under low aerosol loading, while no evident dependence on atmospheric water vapor content was observed. Comparison with a reference model places GM-DNI among the most accurate broadband parametric models for clear-sky DNI estimation. The proposed parameterization provides a simple and accurate framework for clear-sky DNI estimation, supporting solar resource assessment and applications requiring reliable direct-normal irradiance data.