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Volume 16
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Article

Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas

by
Apolinario Lujano
1,*,
Miguel Sanchez-Delgado
1,
Nestor Montalvo-Arquiñigo
1,2,
Absalon Vasquez-Villanueva
1,
Abel Mejia-Marcacuzco
1 and
Efrain Lujano
3
1
Programa de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, Peru
2
Facultad de Ingeniería Agrícola, Universidad Nacional Agraria La Molina, Lima 15024, Peru
3
Escuela Profesional de Ingeniería Agrícola, Universidad Nacional del Altiplano, Puno 21001, Peru
*
Author to whom correspondence should be addressed.
Atmosphere 2025, 16(4), 408; https://doi.org/10.3390/atmos16040408
Submission received: 28 January 2025 / Revised: 18 March 2025 / Accepted: 26 March 2025 / Published: 31 March 2025
(This article belongs to the Special Issue Observation and Modeling of Evapotranspiration)
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Abstract

The Penman-Monteith (PM) equation is considered the most accurate method for estimating reference evapotranspiration (ETo); however, its application requires a large amount of data that is not always available. This study aimed to regionalize the coefficients of the Hargreaves-Samani (HS) equation to estimate ETo in high-altitude areas, specifically the Peruvian Altiplano (PA). The methodology included (1) evaluation of the original HS equation, (2) calibration and validation of the empirical coefficient (CH) and empirical exponent (EH) at each weather station, and (3) regionalization of the calibrated coefficients using a multiple linear regression approach. The results showed that the original HS equation had NSE values ranging from −0.57 to 0.87, PBIAS from −18.60% to 12.70%, MAE from 0.16 to 0.65 mm/d, and RMSE from 0.20 to 0.67 mm/d. After calibrating CH and EH, performance improved significantly, achieving validation values of NSE ranging from 0.67 to 0.94, PBIAS from −0.55% to 1.37%, MAE from 0.01 to 0.05 mm/d, and RMSE from 0.13 to 0.21 mm/d. Finally, the regionalization of 0.859 and 0.744, respectively. These results indicate that the HS equation, with calibrated and regionalized coefficients, is a viable alternative for estimating ETo in regions with limited meteorological data.
Keywords: calibration; interpolation; Penman-Monteith; multiple linear regression; Peruvian Altiplano; validation calibration; interpolation; Penman-Monteith; multiple linear regression; Peruvian Altiplano; validation

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MDPI and ACS Style

Lujano, A.; Sanchez-Delgado, M.; Montalvo-Arquiñigo, N.; Vasquez-Villanueva, A.; Mejia-Marcacuzco, A.; Lujano, E. Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas. Atmosphere 2025, 16, 408. https://doi.org/10.3390/atmos16040408

AMA Style

Lujano A, Sanchez-Delgado M, Montalvo-Arquiñigo N, Vasquez-Villanueva A, Mejia-Marcacuzco A, Lujano E. Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas. Atmosphere. 2025; 16(4):408. https://doi.org/10.3390/atmos16040408

Chicago/Turabian Style

Lujano, Apolinario, Miguel Sanchez-Delgado, Nestor Montalvo-Arquiñigo, Absalon Vasquez-Villanueva, Abel Mejia-Marcacuzco, and Efrain Lujano. 2025. "Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas" Atmosphere 16, no. 4: 408. https://doi.org/10.3390/atmos16040408

APA Style

Lujano, A., Sanchez-Delgado, M., Montalvo-Arquiñigo, N., Vasquez-Villanueva, A., Mejia-Marcacuzco, A., & Lujano, E. (2025). Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas. Atmosphere, 16(4), 408. https://doi.org/10.3390/atmos16040408

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