The Lozano Closure: A TOA-Normalised Spectral Mapping Between Broadband Shortwave Radiation and PAR

Abstract. Accurate reconstruction of photosynthetically active radiation (PAR) from broadband shortwave (SW) measurements remains central to biosphere–atmosphere studies and ecosystem modelling. Most existing approaches rely on empirical regressions, machine-learning techniques, or site-specific calibration, often treating global and diffuse PAR separately. Here, we introduce the Lozano Closure, a physically constrained transmissivity framework that links broadband shortwave radiation and PAR through a top-of-atmosphere (TOA)-normalised spectral mapping.

The formulation expresses global PAR transmissivity as a power-law function of broadband transmissivity via a spectral exponent α, and diffuse PAR through an additional partition exponent β. Both exponents are derived from log–log transmissivity relations rather than fitted directly to PAR. Across multiple climatic regimes, the non-trivial solution yields pooled r² ≈ 0.98–0.99 for global PAR and 0.92–0.98 for diffuse PAR without site-specific calibration or auxiliary meteorological inputs.

The exponent α exhibits quasi-stationary behaviour consistent with its interpretation as a band-integrated optical-depth ratio, whereas β reflects the greater regime sensitivity of diffuse partitioning. Sensitivity analysis demonstrates that α depends structurally on the adopted extraterrestrial spectral normalisation, highlighting the importance of coherent TOA definitions for universal implementation.

The Lozano Closure provides a minimal, spectrally consistent alternative to empirical and machine-learning approaches, achieving competitive performance while maintaining cross-site transferability and physical interpretability. The framework is extensible to other spectral bands and offers a pathway toward spectrally coherent sub-band reconstruction within broadband radiation models.