Heuristic methods applied in reference evapotranspiration modeling

Abstract

The importance of the precise estimation of evapotranspiration is directly related to sustainable water usage. Since agriculture represents 70% of Brazil’s water consumption, adequate and efficient application of water may reduce the conflicts over the use of water among the multiple users. Considering the importance of accurate estimation of evapotranspiration, the objective of the present study was to model and compare the reference evapotranspiration from different heuristic methodologies. The standard Penman-Monteith method was used as reference for evapotranspiration, however, to evaluate the heuristic methodologies with scarce data, two widely known methods had their performances assessed in relation to Penman-Monteith. The methods used to estimate evapotranspiration from scarce data were Priestley-Taylor and Thornthwaite. The computational techniques Stepwise Regression (SWR), Random Forest (RF), Cubist (CB), Bayesian Regularized Neural Network (BRNN) and Support Vector Machines (SVM) were used to estimate evapotranspiration with scarce and full meteorological data. The results show the robustness of the heuristic methods in the prediction of the evapotranspiration. The performance criteria of machine learning methods for full weather data varied from 0.14 to 0.22 mm d-1 for mean absolute error (MAE), from 0.21 to 0.29 mm d-1 for root mean squared error (RMSE) and from 0.95 to 0.99 coefficient of determination (r²). The computational techniques proved superior performance to established methods in literature, even in scenarios of scarce variables. The BRNN presented the best performance overall.

Comparison of the Reference Evapotranspiration among Empirical Methods and Penman-Monteith in Semiarid Region of Northeastern Brazil

“…Hence, these findings correspond to the higher data dispersion and are represented by the coefficient of determination (Figure 3), 0.66 and 0.58, respectively. These results are according to Althoff et al (2018) that modeling and comparing the ETo from different heuristic methodologies confirmed that Thornthwaite's method resulted in a lower determination coefficient, R 2 = 0.39. Some findings by Sales et al (2018) and Oliveira et al (2020) also obtained similar responses to this study with "good" performance in the ETo estimates, on a daily scale, using the empirical method JH.…”

“…Since agriculture represents 70% of Brazil's water consumption, the correct ETo estimation supports the farmer's decision about the quantity the irrigation depth should be supplied to the soil during crop cycle and irrigation frequency (Oliveira et al, 2020). Consequently, the plant does not suffer from a deficit or excess of water, which in turn causes a reduction in productivity and environmental impacts, such as leaching of nutrients and soil salinization (Althoff et al, 2018).…”

“…However, the use of empirical or semi-empirical ETo equations with fewer meteorological parameters is only recommended under certain situations where complete weather data are lacking. Since also different empirical equations overcome these disadvantages with high precision and accuracy, using few meteorological elements (Lacerda and Turco, 2015;Pandey et al, 2016;Althoff et al, 2018;Oliveira et al, 2020).…”

Crop NDVI Monitoring Based on Sentinel 1

“…In addition, there is also the fact that NRPB aggregates predictive information into the models tested, explaining facts that cannot be elucidated only with the backscatter information. The insertion of the NRPB variable in machine learning models, like rf, helps the results to reach better statistical metrics in the validations, and consequently leads to greater generalization capacity in the models [48,49], since these kinds of models are recognized for having a high capacity for pattern recognition and complex solutions [6].…”

Improvement of reference crop evapotranspiration estimates using limited data for the Brazilian Cerrado

“…From a diverse number of models developed in the literature for estimating ETo, the Penman-Monteith (PM) standardized by FAO 56 (Allen et al, 1998) has been widely used as a reference for calibrating a diverse number of methods (Althoff et al, 2018;Feng et al, 2017;Ferreira et al, 2019;Shiri et al, 2014). Penman-Monteith's ETo is calculated as follows: the mean saturation vapor pressure for a day, kPa; e a = actual vapor pressure, kPa; Δ = slope of saturation vapor pressure curve at air temperature (kPa °C-1 ); and, γ = psychrometric constant (kPa °C-1 ).…”