Simplified Version of the METRIC Model for Estimation of Actual Evapotranspiration

ABSTRACT

The remote sensing approach of Mapping Evapotranspiration with the Internalized Calibration (METRIC) model is one of the accurate evapotranspiration models but the its complexity motivated us to seek for a simplified version of the original model. This study was designed to propose and evaluate the performance of a new methodology called Simplified Mapping Evapotranspiration with the Internalized Calibration (S-METRIC) model to estimate Actual Evapotranspiration (AET). S-METRIC is a simpler technique to implement while it requires relatively limited input data without losing tangible precision. Thanks to the simpler equations, it is faster computationally. The election of the mathematical form of this formula is mainly based on two purpose: first, it was upon the simplification of the formulas and then, their precision to approximate the formulas of METRIC. Polyfitn function and the synthetic meteorological data were used to fit corresponding curves for the four formulas of S-METRIC ($R_{\mathrm{s}\downarrow }$, ${\tau }_{\mathrm{s}\mathrm{w}}$, $\mathrm{C}\mathrm{o}\mathrm{s}{\theta }_{\mathrm{h}\mathrm{o}\mathrm{r}}$ and $\mathrm{C}\mathrm{o}\mathrm{s}{\theta }_{\mathrm{r}\mathrm{e}\mathrm{l}}$). The monthly AET calculated by S-METRIC was compared using a number of statistics indexes, including mean absolute error (MAE), root-mean-square error (RMSE), BIAS, relative error (RE), coefficient of determination (R²) and Nash-Sutcliffe efficiency coefficient (NSE). The results of the monthly AET comparison suggested that both models had similar performance to estimate monthly AET in the Vanak Basin with R² = 0.97–0.99, NS = 0.90–0.99, MAE = 0.49–8.7 mm month⁻¹ and RMSE = 0.8–13.1 mm month⁻¹. Also, the results of the monthly estimated $R_{\mathrm{s}\downarrow }$METRIC and $R_{\mathrm{s}\downarrow }$S-METRIC values comparison suggested that both models had showed a similar performance to estimate monthly $R_{\mathrm{s}\downarrow }$with R² = 0.97–0.99, MAE = 5.9–11.38 W m² and RMSE = 7.17–13.12 W m².

Disclosure statement

No potential conflict of interest was reported by the author(s).