Abstract: The objective of the investigation was to determine a semi-empirical formula that relates the reference evapotranspiration with the vapor pressure deficit, wind speed, temperature range and extraterrestrial radiation using data from the Puno meteorological station. Multiple linear regression was applied in the calibration and then the formula was validated by comparing its results with the class A tank method, Penman-Monteith, Hargreaves, and Serruto. The multiple linear regression coefficients are statistically significant (p<0.05), a correlation coefficient of 84% and determination of 71% was determined. The formula has a physical basis because the terms wind speed and vapor pressure deficit represent the aerodynamic factor; the temperature and extraterrestrial radiation terms include the energy balance factor. The formula better estimates the reference evapotranspiration than the methods with which it was compared and has a lower mean square error with respect to values obtained with a class A tank. The variation of values obtained with the formula is statistically equal to the variation obtained with a class A tank The formula slightly overestimates the mean because the reference evapotranspiration values in the calibration are higher than those in the validation.

Keywords: Formula, semi-empirical, evapotranspiration, reference, regression, Puno.

| DOI: 10.17148/IARJSET.2023.10206