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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2025-03-01
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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. |
| format | Article |
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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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