A TOA-consistent transmissivity-based mapping of global and diffuse PAR from broadband shortwave radiation

Surface solar radiation is a key driver of land–atmosphere interactions and ecosystem processes, yet photosynthetically active radiation (PAR) is often approximated from broadband shortwave radiation using simplified empirical relationships or fixed ratios. These approaches do not explicitly account for spectral differences in atmospheric attenuation or for the partitioning between direct and diffuse radiation, limiting their applicability across varying atmospheric conditions.

Here we introduce a physically constrained, top-of-atmosphere (TOA)-consistent mapping that links broadband shortwave radiation and PAR through a transmissivity-based framework. The formulation is grounded in the Beer–Lambert representation of atmospheric attenuation and expresses PAR as a spectrally integrated transformation of broadband shortwave radiation. This allows the reconstruction of both global and diffuse PAR using only broadband radiation inputs, without site-specific calibration or auxiliary predictors.

The approach is evaluated using multi-site radiometric observations spanning contrasting climatic regimes. Results show that global PAR can be reproduced with coefficients of determination up to r² ≈ 0.99, while diffuse PAR achieves r² values between ≈0.92 and 0.98 across sites. The formulation captures both the magnitude and variability of PAR and its diffuse component with a consistent parameterisation across environments, demonstrating robustness under different atmospheric conditions.

These findings indicate that PAR can be interpreted as a spectrally constrained extension of broadband shortwave radiation, rather than as an independent variable requiring empirical parameterisation. The proposed framework provides a physically consistent alternative to empirical and machine-learning approaches and is directly applicable to surface radiation datasets, reanalysis products, and observational networks. It offers potential for improving radiation inputs in ecosystem, land-surface, and climate modelling, particularly in contexts where only broadband measurements are available.