Development of multiple linear regression models for annual reference evapotranspiration estimation under limited data conditions

Development of Multiple Linear Regression Models for Annual Reference Evapotranspiration Estimation under Limited Data Conditions

Accurate estimation of reference evapotranspiration (ET₀) is essential for agricultural water management, particularly in regions with limited data availability. The aim of this study was to evaluate multiple linear regression (MLR) models to estimate ET₀ at the annual scale. Meteorological data from the Kuhdasht synoptic station, Iran for a 25-year period (1998–2022) were used. ET₀ was calculated using the FAO-56 Penman-Monteith method implemented through the CROPWAT 8.0 software. A total of 31 MLR models were developed using the Regression option from the Analysis ToolPak of Microsoft Excel 2019 to quantify the relationship between ET₀ and climatic variables. Seven statistical indices were used to evaluate the performance of the MLR models in estimating ET₀. Results showed that 16 models achieved very high accuracy, with coefficients of determination (R²) greater than 0.92. Among single-variable models, wind speed (MLR4) was the most significant predictor of ET₀ (R² = 0.92, P-value = 0), followed by minimum temperature (MLR1, R² = 0.39, P-value = 0) and maximum temperature (MLR2, R² = 0.39, P-value = 0). Relative humidity (MLR3, R² = 0.1, P-value = 0.12) and sunshine (MLR5, R² = 0, P-value = 0.79) were not statistically significant predictors. Several two-variable models achieved R² = 0.92 to 0.96, and most three-variable models reached R² = 0.93 to 0.97. Four-variable models also performed strongly (R² ≈ 0.95 to 0.97), while the five-variable model yielded R² ≈ 0.97, similar to simpler models. Wind speed emerged as the most influential factor, highlighting that well-chosen two- or three-variable models can estimate ET₀ as effectively as more complex alternatives.

Development of Multiple Linear Regression Models for Annual Reference Evapotranspiration Estimation under Limited Data Conditions



Accurate estimation of reference evapotranspiration (ET₀) is essential for agricultural water management, particularly in regions with limited data availability. The aim of this study was to evaluate multiple linear regression (MLR) models to estimate ET₀ at the annual scale. Meteorological data from the Kuhdasht synoptic station, Iran for a 25-year period (1998–2022) were used. ET₀ was calculated using the FAO-56 Penman-Monteith method implemented through the CROPWAT 8.0 software. A total of 31 MLR models were developed using the Regression option from the Analysis ToolPak of Microsoft Excel 2019 to quantify the relationship between ET₀ and climatic variables. Seven statistical indices were used to evaluate the performance of the MLR models in estimating ET₀. Results showed that 16 models achieved very high accuracy, with coefficients of determination (R²) greater than 0.92. Among single-variable models, wind speed (MLR4) was the most significant predictor of ET₀ (R² = 0.92, P-value = 0), followed by minimum temperature (MLR1, R² = 0.39, P-value = 0) and maximum temperature (MLR2, R² = 0.39, P-value = 0). Relative humidity (MLR3, R² = 0.1, P-value = 0.12) and sunshine (MLR5, R² = 0, P-value = 0.79) were not statistically significant predictors. Several two-variable models achieved R² = 0.92 to 0.96, and most three-variable models reached R² = 0.93 to 0.97. Four-variable models also performed strongly (R² ≈ 0.95 to 0.97), while the five-variable model yielded R² ≈ 0.97, similar to simpler models. Wind speed emerged as the most influential factor, highlighting that well-chosen two- or three-variable models can estimate ET₀ as effectively as more complex alternatives.

Development of Multiple Linear Regression Models for Annual Reference Evapotranspiration Estimation under Limited Data Conditions



Accurate estimation of reference evapotranspiration (ET₀) is essential for agricultural water management, particularly in regions with limited data availability. The aim of this study was to evaluate multiple linear regression (MLR) models to estimate ET₀ at the annual scale. Meteorological data from the Kuhdasht synoptic station, Iran for a 25-year period (1998–2022) were used. ET₀ was calculated using the FAO-56 Penman-Monteith method implemented through the CROPWAT 8.0 software. A total of 31 MLR models were developed using the Regression option from the Analysis ToolPak of Microsoft Excel 2019 to quantify the relationship between ET₀ and climatic variables. Seven statistical indices were used to evaluate the performance of the MLR models in estimating ET₀. Results showed that 16 models achieved very high accuracy, with coefficients of determination (R²) greater than 0.92. Among single-variable models, wind speed (MLR4) was the most significant predictor of ET₀ (R² = 0.92, P-value = 0), followed by minimum temperature (MLR1, R² = 0.39, P-value = 0) and maximum temperature (MLR2, R² = 0.39, P-value = 0). Relative humidity (MLR3, R² = 0.1, P-value = 0.12) and sunshine (MLR5, R² = 0, P-value = 0.79) were not statistically significant predictors. Several two-variable models achieved R² = 0.92 to 0.96, and most three-variable models reached R² = 0.93 to 0.97. Four-variable models also performed strongly (R² ≈ 0.95 to 0.97), while the five-variable model yielded R² ≈ 0.97, similar to simpler models. Wind speed emerged as the most influential factor, highlighting that well-chosen two- or three-variable models can estimate ET₀ as effectively as more complex alternatives.