The Canonical Solar Photosynthesis Geometry Model (CS-PGM): A Deterministic Framework for Quantifying the Absolute Physical Limits of Crop Yield Efficiency
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Abstract
Global agricultural output is constrained by the efficiency with which crops convert solar radiation into biomass through Photosynthetically Active Radiation (PAR). Existing crop models, often empirical, frequently incorporate confounding atmospheric and environmental variables, obscuring the fundamental physical limitation imposed by solar geometry. This research introduces the Canonical Solar Photosynthesis Geometry Model (CS-PGM), a deterministic, zero-external-data mathematical framework designed to calculate the Theoretical Maximum Potential Yield (TMPY) for any location on Earth. The CS-PGM rigorously integrates celestial mechanics ( ), a postulated Canonical Atmosphere (Ttotal 0.72), and the established Light Use Efficiency (LUE) principle (LUEmax = 4.8 g MJ-1 PAR for C4 plants). These canonical constants represent the absolute thermodynamic limits and optimal clear-sky transmittance, stripping away empirical weather noise. The model's primary contribution is the establishment of a universal, non-empirical benchmark for yield potential, enabling the precise quantification of the Theoretical Yield Gap (TYG). The results confirm the mathematical phenomenon of Isophotic Peak Shifting, showing that TMPY peaks at mid-latitudes (e.g., 74.6 t ha-1 at 16° (N/S) for a 120-day season), significantly higher than at the equator (69.0 t ha-1). This demonstrates mathematically that the absolute physical ceiling for biomass is not located at the equator. This transparent, physics-based framework provides policymakers and agricultural researchers with a powerful diagnostic tool for strategic resource allocation, by isolating the maximum potential yield from environmental variability.
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