Reference evapotranspiration, abbreviated ETo, represents the water loss from a standardized grass surface under given weather conditions. Because directly measuring evapotranspiration with lysimeters or micrometeorological towers is expensive and technically demanding, hydrologists and agronomists rely on ETo as a proxy for atmospheric demand. The internationally accepted way to compute it is the Penman–Monteith equation as standardized by FAO-56, a physically based formula that combines an energy term, driven by net radiation, with an aerodynamic term, driven by wind speed and the vapor pressure deficit between the surface and the air. The equation’s multivariate structure is its strength, but it also raises a critical question: which of these meteorological ingredients matters most, and does the answer change from place to place and season to season?

That question motivated a team led by Lucas da Costa Santos of the Federal University of the Jequitinhonha and Mucuri Valleys. The researchers assembled thirty years of daily meteorological records, from 1990 to 2019, for six Brazilian municipalities chosen to represent sharply contrasting climate typologies under the Köppen–Geiger classification: Belém in the Amazon with an equatorial monsoon climate, Salvador with a tropical rainforest regime, Petrolina in the hot semi-arid northeast, Pirenópolis with a tropical savanna climate, and Franca and São Luiz Gonzaga in the humid subtropical south. The sites span a remarkable range, from mean annual temperatures of about 21.4 degrees Celsius in São Luiz Gonzaga to 27.7 degrees in Belém, and from mean solar radiation of 16.69 megajoules per square meter per day in the subtropical south to 23.19 in Petrolina.

To disentangle the influences, the team turned to path analysis, a statistical technique that decomposes simple correlations between weather variables and ETo into direct and indirect effects. Direct effects capture the independent contribution of each variable, while indirect effects reveal how variables interact with one another through their mutual correlations. The researchers first checked for multicollinearity among predictors using variance inflation factors, retaining mean air temperature as the thermal variable because maximum and minimum temperatures introduced redundancy that destabilized the regression models. They also ran Mann–Kendall trend tests to check whether the predictor variables themselves were changing over the study period, finding significant long-term trends in at least one variable at five of the six locations.

The results were striking in their consistency and their variability at the same time. The path models explained between 97.7 and 99.5 percent of the annual variability in ETo across all six locations, an extraordinarily high proportion. Yet the identity of the dominant driver shifted from site to site. In São Luiz Gonzaga, Franca, Salvador, and Belém, solar radiation carried the largest direct effect, with standardized coefficients reaching 0.812 in Franca, indicating that in these places evaporative demand is primarily limited by the energy available at the surface. In Pirenópolis and Petrolina, by contrast, wind speed took the lead, with a coefficient of 0.711 in the semi-arid Petrolina, pointing to a regime in which the aerodynamic removal of vapor, rather than energy supply, sets the pace of evaporation.

The decomposition of indirect effects added a layer of nuance that simple correlation studies miss entirely. In Franca, the seemingly dominant direct effects of radiation and wind were substantially offset by negative indirect pathways, cutting their total effects to a fraction of their direct coefficients. In humid Belém, the positive direct effect of wind speed was overwhelmed by a strong negative indirect effect mediated through solar radiation, so that wind’s net association with ETo actually turned negative. In Petrolina, the opposite occurred: positive indirect effects reinforced the direct dominance of wind, pushing its total effect to 0.837. In other words, the same meteorological variable can be amplified, muted, or even reversed in its apparent influence depending on the interaction structure of the local atmosphere.

Seasonality compounded the picture. When the team repeated the analysis for each meteorological season of the Southern Hemisphere, the hierarchy of controls reconfigured systematically through the year. Solar radiation ranked among the top drivers during the high-insolation summer and spring months, while wind speed gained prominence during autumn and especially winter, when energy availability declines but atmospheric ventilation remains strong, particularly at inland and semi-arid sites. Relative humidity, meanwhile, displayed negative direct effects at every location and in every season, a physically coherent signal of the vapor pressure deficit that governs the aerodynamic term of the Penman–Monteith equation. Drier air pulls water from the surface more aggressively, and the humidity coefficients, reaching −0.469 in São Luiz Gonzaga and −0.374 in Petrolina, quantify that pull.

Perhaps the most consequential finding concerns what did not dominate: temperature. Mean air temperature ranked among the three strongest drivers at only half of the locations at the annual scale, and even there its coefficients were systematically smaller than those of radiation or wind. This challenges the widespread reliance on temperature-based empirical methods such as Hargreaves–Samani, which implicitly assume that thermal proxies can capture evaporative demand. The authors argue that temperature functions mainly as a thermodynamic state variable, signaling the energy content of the atmosphere, while the actual fluxes of vapor depend on radiation balance, humidity gradients, and wind. In regions with strong ventilation or high radiative variability, temperature-only models risk systematic underestimation of water demand, with tangible consequences for irrigation scheduling and water resource planning.

The practical implications extend into a warming future. As global temperatures rise, the atmosphere’s water-holding capacity increases, and vapor pressure deficit tends to grow disproportionately, intensifying evaporative demand in ways that temperature records alone do not reveal. The study’s authors are careful to note the limitations of their approach: ETo is not an independently observed quantity but a deterministic product of the same variables used as predictors, so the path coefficients should be read as indicators of relative contributions within the FAO-56 framework rather than as evidence of independent causation. Solar radiation was estimated from sunshine duration rather than measured directly, each municipality was represented by a single weather station, and the significant long-term trends in several predictors mean the reported hierarchies describe dominant tendencies over the study period rather than fixed relationships.

Even with those caveats, the diagnosis is clear and actionable. There is no universal driver of evaporative demand; the balance between radiative and aerodynamic control is a property of each climate and each season. For water managers in aerodynamically dominated environments like Petrolina, monitoring wind speed and humidity is essential, and neglecting them can mean underestimating irrigation requirements during dry periods. In radiatively controlled regions such as Belém, Salvador, Franca, and São Luiz Gonzaga, cloud cover and seasonal insolation set the agenda, and models that ignore radiation do so at their peril. The study makes a strong case that the era of one-size-fits-all, temperature-based evaporation estimates should give way to multivariate, physically consistent approaches capable of tracking how the atmosphere’s thirst is truly regulated across a changing planet.

Subject of Research: Meteorological controls on reference evapotranspiration across contrasting Brazilian climate typologies

Article Title: Energy versus aerodynamic controls of reference evapotranspiration: a multi-regional assessment across Brazilian climate typologies

Article References: da Costa Santos, L., Capuchinho, F. F., do Patrocínio Figueiró, L. S., José, J. V., dos Reis, E. F., Bonfá, C. S., Araujo, J. E., & Nhongo, E. J. S. (2026). Energy versus aerodynamic controls of reference evapotranspiration: a multi-regional assessment across Brazilian climate typologies. Theoretical and Applied Climatology, 157(10), Article 646. https://doi.org/10.1007/s00704-026-06580-6

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06580-6

Keywords: reference evapotranspiration, Penman–Monteith, solar radiation, wind speed, relative humidity, vapor pressure deficit, path analysis, Brazil, climate typologies, irrigation management, FAO-56, hydrology

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