Statistical Modeling of Reference Evapotranspiration for Areas of the Peruvian Altiplano with Lack of Insolation Data

Empirical methods have been developed in the literature to estimate evapotranspiration from climatic elements which require rigorous local calibrations and have shown limited global validity; in addition, proving their accuracy requires much time and money. The objective of this research was to perform statistical modeling of reference evapotranspiration for highland areas with a lack of insolation data. The Puno altiplano has 42 meteorological stations; however, only 09 stations measure sunshine hours and only in these stations is it possible to determine the reference evapotranspiration (ETo) with the Penmam-Monteith (PM) method. In the present research, the relationship between ETo obtained with PM and the methods of Hargreaves-Samani (HS) and class "A" tank. Then, homogeneous zones were determined by cluster analysis where the relationship obtained between ETo by PM and H-S and tank "A" can be applied. An empirical model was also developed relating the ETo obtained with PM with an energy term (TE) and an aerodynamic term (TA) through multiple regression. The advantage of this model is that it does not need sunshine hours, since instead of net radiation it uses extraterrestrial radiation. The regression was examined for spuriousness with the Durbin-Watson < r2 statistic, then detected for heteroscedasticity with White's test and corrected with weighted least squares estimation. The Hargreaves-Samani method was found to estimate PM ETo very well with r2 ranging from 0.70 to 0.88 at several stations. With the cluster analysis, 10 homogeneous zones were determined to apply the empirical models obtained; the relationship between ETo and the TE and TA terms is significant with r2 varying from 0.648 to 0.912, with statistically significant coefficients (p ≤ 0.05) for several stations. The models with corrected heteroscedasticity have r2 from 0.80 to 0.99 and statistically significant coefficients (p ≤ 0.05). It is recommended to investigate the behavior of sunshine hours in the highlands since it is an under-measured variable