Abstract
Reference evapotranspiration (ET0) plays a crucial role in the management and optimal use of water resources, climate studies, and the water cycle. Among the various approaches used to estimate ET0, the FAO Penman-Monteith (PM) model is recognized as the standard method. However, the requirement for extensive data limits the application of this method. Hybrid models show good performance in estimating ET0, among which the Penman Group (PG) models, by separating the contributions of aerodynamic and energy balance components, are widely used for calculating ET0. This study was conducted with the aim of evaluating and calibrating the Penman Group (PG) model for windy regions of Iran. For this purpose, long-term meteorological data from seven weather stations, Ardabil, Aligoudarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil—were utilized. The results indicated that the Penman (P) model has the highest level of agreement with the standard model. Therefore, to improve the results, the mentioned model was calibrated for the studied stations, and the contribution of each of the aerodynamic and energy balance components was calculated using the calibrated model. The findings revealed that as wind speed increases, the contribution of the aerodynamic component rises for all the examined stations, and this increase is more pronounced for the Zabol station, which experiences higher wind speeds. Considering the significant impact of air flow and wind speed on the low values of ET0 in windy areas, implementing strategies such as installing windbreaks—both natural and artificial—can significantly help reduce ET0 values and, consequently, contribute to better water resource management.
Keywords: Combination models, Penman-Monteith, water resources management, wind function.

Introduction
Reference evapotranspiration (ET₀) is a key indicator of crop water requirements, and its accurate estimation is essential and necessary for water resource management. The Food and Agriculture Organization of the United Nations (FAO) recommends the FAO Penman-Monteith (PM) model as the standard method for estimating reference evapotranspiration (ET₀). However, its application is not always feasible due to high data requirements. Previous studies indicate that combination-based models demonstrate the best performance in estimating ET₀. Solar radiation and air temperature are the primary meteorological factors influencing ET₀ (Ghiat et al., 2021). Nevertheless, in certain locations such as windy regions, wind speed also plays a significant role. Therefore, the objective of this study is to investigate the contribution of the aerodynamic component and the energy balance component to ET₀ in windy regions of Iran. For this purpose, the Penman-Monteith model was selected as the standard model, along with three combination models Penman, Penman-Kimberly, and Allen-Pruitt which separately estimate the contributions of the aerodynamic and energy balance components (Wright, 1996). Additionally, improving the performance of the selected models through calibration and adjustment for windy regions of Iran is another goal of this research. To achieve these objectives, daily meteorological data from seven synoptic stations across the country Ardabil, Aligoudarz, Bijar, Rafsanjan, Zabol, and Manjil were used (Mohamadi et al., 2021).
Methodology
For this purpose, based on a review of available sources, the meteorological stations of Ardabil, Aligoudarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil were selected. The main reason for selecting these stations is their prolonged periods of high wind speed compared to other synoptic stations across the country. The meteorological data used include daily-scale parameters such as air temperature, solar radiation, relative humidity, sunshine hours, and wind speed over the time period from 2000 to 2024 (Table 1). In this study, the Penman-Monteith (PM) model was used as the standard method for evaluation and calibration. The general form of the Penman (P) model allows for separate calculation of the aerodynamic component γ/(∆+γ) F_w (e_s-e_a ) and the energy balance component ∆/(∆+γ) (R_n-G) (Wright, 1996). The dimensionless wind function (Fw) represents the effect of wind speed on the advection of sensible heat in ET₀ estimation. Various researchers have proposed different values for the wind function coefficients (aw and bw). In the original Penman equation (P), aw and bw are equal to 0.1 and 0.537, respectively; in the Penman-Kimberly (PK) model, they are 0.75 and 0.993, respectively; and in the Allen-Pruitt (AP) model, they are 0.1 and 0.862, respectively (Table 2). Therefore, in this study, three different versions of the Penman model were used. To calibrate the investigated models, the sum of squared errors (SSE) method was employed.

Results and Discussion
ET₀ values were calculated using the Penman group models (P, PK, and AP) for the selected stations and compared with the standard method. The results showed that, for all studied stations, all Penman group models overestimated ET₀ compared to the standard method. The highest agreement was observed for the P model (Penman, 1963), with agreement coefficients of 0.95, 0.98, 0.98, 0.99, 0.97, 1.00, and 0.97, respectively, for Ardabil, Aligoudarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil. The lowest agreement belonged to the PK model (Penman-Kimberly, 1972), with agreement coefficients of 0.91, 0.88, 0.90, 0.90, 0.88, 0.89, and 0.85 for the same stations. Therefore, the P model was selected as the best-performing model for all stations and was calibrated by adjusting the wind function coefficients (Fw) through the error minimization method (least squares). After calibration, the ET₀ values estimated by the adjusted Penman model (Adjusted-P) became closer to those estimated by the standard method. The model efficiency (EF) also improved after calibration, reaching values of 0.99, 0.98, 0.99, 1.00, 1.00, 0.99, and 1.00 for Ardabil, Aligoudarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil, respectively. The relationship between average wind speed and the average contribution of energy balance and aerodynamic components at the daily scale was also plotted for the studied stations. Results indicated that, for all stations, as wind speed increased, the contribution of the aerodynamic component clearly and significantly increased. Subsequently, the contributions of the aerodynamic and energy balance components were calculated for the calibrated Penman model. The contribution of the aerodynamic component was found to be considerable across all stations, particularly pronounced at Zabol station, which has the highest average wind speed. Therefore, the role of this component—which reflects airflow and wind speed—in determining ET₀ values cannot be ignored. Consequently, using simplified alternative models for ET₀ estimation that do not account for wind speed, such as radiation-based or temperature-based models, should be accompanied by appropriate calibration and adjustment of their coefficients to ensure accuracy in windy regions.
Conclusion
The results indicate that as the average wind speed increases, the contribution of the aerodynamic component rises across all investigated stations. Overall, the contribution of the aerodynamic component is considerable compared to that of the energy balance component at all studied stations, with this effect being particularly pronounced at Zabol station, which has the highest average wind speed. Therefore, given the significant influence of airflow and wind speed on the magnitude of ET₀ in windy regions, implementing measures such as installing natural or artificial windbreaks in these areas could substantially contribute to reducing ET₀ and, consequently, improving water resource management. However, the effectiveness and practical implementation of such measures require further extensive investigation.