Evidence of linear relationships between clear‑sky indices in photosynthetically active radiation and broadband ranges

Abstract

This study provides empirical relationships between photosynthetically active radiation (PAR) and broadband clear‑sky indices at ground level for both the PAR global irradiance and its direct component. Once multiplied by the irradiance in clear‑sky conditions, the clear‑sky index provides the irradiance under cloudy conditions. The relationships are developed by the means of radiative transfer simulations of various realistic atmospheric states including both ice and water cloud phases. For the direct component, the PAR clear‑sky index is equal to the broadband clear‑sky index. For global irradiance, several linear relationships are proposed depending on the availability of cloud properties namely cloud phase and cloud optical depth. The developed relationships are validated numerically and experimentally by using ground-based measurements from the SURFRAD network in the U.S.A. Overall, it has been found, a squared correlation coefficient R 2 $R^{2}$ close to 1.00 and a relative bias (relative root mean square error) in absolute value less than 3 % (6 %) with respect to the means of the relevant measurements, demonstrating a high level of accuracy of the proposed relationships.