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

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 t...

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Main Authors: Apolinario Lujano, Miguel Sanchez-Delgado, Nestor Montalvo-Arquiñigo, Absalon Vasquez-Villanueva, Abel Mejia-Marcacuzco, Efrain Lujano
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Atmosphere
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Online Access:https://www.mdpi.com/2073-4433/16/4/408
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author Apolinario Lujano
Miguel Sanchez-Delgado
Nestor Montalvo-Arquiñigo
Absalon Vasquez-Villanueva
Abel Mejia-Marcacuzco
Efrain Lujano
author_facet Apolinario Lujano
Miguel Sanchez-Delgado
Nestor Montalvo-Arquiñigo
Absalon Vasquez-Villanueva
Abel Mejia-Marcacuzco
Efrain Lujano
author_sort Apolinario Lujano
collection DOAJ
description 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>H</mi></mrow></semantics></math></inline-formula>) and empirical exponent (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>H</mi></mrow></semantics></math></inline-formula>) 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>H</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>H</mi></mrow></semantics></math></inline-formula>, 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.
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spelling doaj-art-8aea3a403d144515b6a754b2ca761b0e2025-08-20T02:17:24ZengMDPI AGAtmosphere2073-44332025-03-0116440810.3390/atmos16040408Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude AreasApolinario Lujano0Miguel Sanchez-Delgado1Nestor Montalvo-Arquiñigo2Absalon Vasquez-Villanueva3Abel Mejia-Marcacuzco4Efrain Lujano5Programa de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, PeruPrograma de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, PeruPrograma de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, PeruPrograma de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, PeruPrograma de Maestría en Riego y Drenaje, Universidad Nacional Agraria La Molina, Lima 15024, PeruEscuela Profesional de Ingeniería Agrícola, Universidad Nacional del Altiplano, Puno 21001, PeruThe 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>H</mi></mrow></semantics></math></inline-formula>) and empirical exponent (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>H</mi></mrow></semantics></math></inline-formula>) 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>H</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>H</mi></mrow></semantics></math></inline-formula>, 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.https://www.mdpi.com/2073-4433/16/4/408calibrationinterpolationPenman-Monteithmultiple linear regressionPeruvian Altiplanovalidation
spellingShingle Apolinario Lujano
Miguel Sanchez-Delgado
Nestor Montalvo-Arquiñigo
Absalon Vasquez-Villanueva
Abel Mejia-Marcacuzco
Efrain Lujano
Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
Atmosphere
calibration
interpolation
Penman-Monteith
multiple linear regression
Peruvian Altiplano
validation
title Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
title_full Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
title_fullStr Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
title_full_unstemmed Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
title_short Regionalization of the Hargreaves-Samani Coefficients to Estimate Reference Evapotranspiration in High-Altitude Areas
title_sort regionalization of the hargreaves samani coefficients to estimate reference evapotranspiration in high altitude areas
topic calibration
interpolation
Penman-Monteith
multiple linear regression
Peruvian Altiplano
validation
url https://www.mdpi.com/2073-4433/16/4/408
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