On the Relationships between Clear-Sky Indices in Photosynthetically Active Radiation and Broadband Ranges in Overcast and Broken-Cloud Conditions

Several studies proposed relationships linking irradiances in the photosynthetically active radiation (PAR) range and broadband irradiances. A previous study published in 2024 by the same authors proposes a linear model relating clear-sky indices in the PAR and broadband ranges that has been validated in clear and overcast conditions only. The present work extends this study for broken-cloud conditions by using ground-based measurements obtained from the Surface Radiation Budget Network in the U.S.A. mainland. As expected, the clear-sky indices are highly correlated and are linked by affine functions whose parameters depend on the fractional sky cover (FSC), the year, and the site. The previous linear model is also efficient in broken-cloud conditions, with the same level of accuracy as in overcast conditions. When this model is combined with a PAR clear-sky model, the result tends to overestimate the PAR as the FSC decreases, i.e., when fewer and fewer scattered clouds are present. The bias is equal to 1 W m⁻² in overcast conditions, up to 18 W m⁻² when the FSC is small, and 6 W m⁻² when all cloudy conditions are merged. The RMSEs are, respectively, 5, 24, and 15 W m⁻². The linear and the clear-sky models can be combined with estimates of the broadband irradiance from satellites to yield estimates of PAR.