The Ångström–Prescott model, extended to practical use by John Prescott in 1940, estimates global solar radiation, the total shortwave energy arriving at the surface, from the ratio of actual bright sunshine hours to the maximum possible daylight hours. Its two coefficients, conventionally labelled a and b, translate the fraction of clear-sky sunshine into a fraction of extraterrestrial radiation. The Food and Agriculture Organization’s influential FAO-56 handbook, which underpins crop water requirement calculations worldwide, suggests default values that assume a relatively clean, stable atmosphere. India’s atmosphere, as the new study demonstrates, is anything but that.

Led by Ashutosh Kumar Misra of the India Meteorological Department in Pune, with colleagues from the department’s regional centres in Guwahati and Chennai, the team derived station-specific coefficients from collocated daily radiation and sunshine-duration records. The network-wide means came out at a = 0.336 with a standard deviation of 0.079, and b = 0.364 with a standard deviation of 0.122. Those averages alone would not be alarming, but the spatial pattern is striking: the largest departures from FAO-56 defaults occurred precisely at stations burdened with heavy aerosol loading across the Indo-Gangetic Plain, Rajasthan, and the western coast, where dust, smoke, and industrial pollution scatter and absorb incoming sunlight in ways the default coefficients never anticipated.

To judge how well the calibrated model performed, the authors deployed a demanding seven-metric evaluation framework rather than relying on a single goodness-of-fit statistic. They computed the coefficient of determination, mean absolute error, root mean square error, normalised RMSE, Willmott’s index of agreement, mean bias error, and the Kolmogorov–Smirnov integral, then synthesised all seven into a Global Performance Index. This composite approach matters because different metrics capture different failure modes: a model can correlate well with observations yet carry a systematic bias, or track the shape of the seasonal cycle while missing its amplitude. Collapsing the picture into one number risks hiding exactly the flaws that matter for irrigation scheduling or solar farm siting.

The headline numbers are respectable. Across the network, the calibrated model achieved a mean coefficient of determination of 0.75, a root mean square error of 1.75 megajoules per square metre per day, a normalised RMSE of 9.95 percent, and Willmott’s index of agreement of 0.92, a value close to the theoretical maximum of one. For a model that requires nothing more than a sunshine recorder and a table of extraterrestrial radiation, that level of skill explains why the Ångström–Prescott formulation has survived a hundred years of competition from far more elaborate schemes, including neural networks and satellite retrievals.

But the seasonal breakdown tells a more nuanced story, and it is here that the study becomes genuinely useful for practitioners. The pre-monsoon months of March through May produced the weakest correlations, with a network-mean R² of just 0.50, even though the RMSE of 1.75 megajoules per square metre per day matched the annual figure. The culprit is day-to-day aerosol variability superimposed on transient convective cloud development. In the hot dry season, dust storms, crop residue burning, and the first thunderstorms of the year can transform the atmospheric transmission of sunlight within hours, decoupling the sunshine-duration record from the radiation actually measured at the surface. A pyranometer responds to every attenuating process; a sunshine recorder, by contrast, only registers when direct beam irradiance exceeds a threshold, so the two instruments can disagree most dramatically exactly when the atmosphere is most turbulent.

The monsoon season posed a different problem. There the model recorded its largest root mean square error, 2.02 megajoules per square metre per day, alongside a systematic positive bias of 0.88 megajoules per square metre per day, meaning the model overestimated the radiation reaching the ground. During the southwest monsoon, thick stratiform and cumuliform cloud decks, elevated humidity, and aerosol-cloud interactions suppress surface radiation far below what the sunshine fraction alone would suggest. For hydrologists computing evapotranspiration during the very season when Indian agriculture depends most critically on accurate water balance estimates, that bias is not a statistical curiosity but a potential source of systematic error in crop water demand calculations.

Beyond calibration, the study turned its attention to the long-term trajectory of surface solar radiation itself, applying the Mann–Kendall nonparametric trend test to annual mean values at each qualifying station. The verdict was sobering: statistically significant downward trends emerged at the majority of stations examined. This finding aligns India with the broader global phenomenon of solar dimming documented in the early 2000s, when researchers first showed that declining surface radiation across many continents was linked to increasing anthropogenic aerosols. Over the Indo-Gangetic Plain, where aerosol optical depths are among the highest in the world and continue to be fed by urbanisation, industrial emissions, and seasonal biomass burning, the dimming signal appears firmly entrenched in the observational record.

The implications ripple outward across several domains. Agricultural water management in India relies heavily on FAO-56 evapotranspiration methods, which use solar radiation as a key input; using uncalibrated default coefficients in aerosol-laden regions risks misestimating irrigation demand by meaningful margins. Solar energy resource assessment, a sector expanding rapidly as India pursues ambitious photovoltaic deployment targets, likewise depends on accurate historical radiation records to rank candidate sites and forecast plant output. And climate modellers have long noted that global models tend to underestimate the direct radiative effects of aerosols over India, a discrepancy that ground-based calibration studies like this one help to quantify and ultimately correct.

What makes the study particularly valuable is its provenance. The data come from the India Meteorological Department’s own operational network, the same institution whose 150-year history of observation underpins much of South Asian climatology, and the daily radiation records are available through the department’s data service portal in Pune for researchers who follow the prescribed procurement procedure. By grounding a century-old empirical relationship in four decades of modern measurements and testing it with a rigorous multi-metric framework, the authors have delivered both a practical toolkit, regionally tuned coefficients that any Indian water manager or solar planner can adopt, and a warning written in the language of statistics: the sunlight reaching India’s surface is fading at many stations, and the models we use to track it must be recalibrated to see that clearly.

Subject of Research: Calibration of the Ångström–Prescott solar radiation model and long-term surface solar radiation trends across India

Article Title: Calibration and long-term trends of the Ångström-Prescott model for surface solar radiation across India

Article References: Misra, A. K., Ghosh, K., Karale, M., & Kumar, A. (2026). Calibration and long-term trends of the Ångström-Prescott model for surface solar radiation across India. Theoretical and Applied Climatology, 157(10), Article 639. https://doi.org/10.1007/s00704-026-06567-3

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06567-3

Keywords: Ångström–Prescott model, solar radiation, India, sunshine duration, aerosols, solar dimming, FAO-56, Mann–Kendall trend test, India Meteorological Department, evapotranspiration, Indo-Gangetic Plain, Global Performance Index