نوع مقاله : مقاله پژوهشی

• اقلیم‌شناسی- اقلیم

عنوان مقاله English

Evaluation and Calibration of the Makkink Model in Estimating Reference Evapotranspiration in Windy Areas of Iran

نویسندگان English

کلیدواژه‌ها English

Extended Abstract

1. Introduction

Accurately determining the amount of irrigation water is crucial for improving agricultural water use efficiency, and this largely depends on properly estimating evapotranspiration (ET0). The Food and Agriculture Organization (FAO) of the United Nations recommends the Penman-Monteith (PM) model as the most reliable method for calculating ET0. However, the PM model has a drawback: it requires a wide range of climatic variables, such as solar radiation, wind speed, relative humidity, and air temperature. This complexity has led researchers to develop simpler empirical equations that rely on fewer meteorological parameters, making them more practical for use in diverse climatic conditions. Among these, temperature- and radiation-based models have become some of the most widely used methods for estimating ET₀ globally. One such model is the Makkink (MK) model, which is both simple and popular due to its reliance on just two key factors: solar radiation intensity and air temperature. These are, of course, the primary meteorological drivers of ET0. However, in certain regions, particularly windy areas, wind speed also plays a significant role. This is because wind influences horizontal advection and sensible heat transfer, which can substantially affect ET0 rates. Therefore, the objectives of this study are, first, to investigate the impact of wind speed on the accuracy of the Makkink model in Iran's windy regions, and second, to improve the performance of this simple model by developing a coefficient for the Makkink model using average wind speed values.

2. Materials and Methods

Based on a review of the literature, the meteorological stations of Ardabil, Aligoodarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil were selected. The reason for choosing these stations is their high and consistent wind speeds compared to other synoptic stations in the country. The meteorological data used include air temperature, solar radiation, relative humidity, sunshine hours, and wind speed on a daily scale for the time period from 2000 to 2024. The PM model was used as the standard method to evaluate and calibrate the Makkink (MK) model. The MK model was first developed in the Netherlands and later successfully applied in the United States. This model can be considered a simplified version of the Priestley-Taylor equation, as it similarly requires only radiation and temperature as input variables. The difference is that instead of using net radiation (Rn) and temperature, the Makkink model uses shortwave radiation (Rs) and temperature. The Makkink model can provide reliable estimates of ET0. Various researchers have modified the model proposed by Makkink (1957) for different regions. Therefore, in this study, four different versions of the Makkink model were utilized. To calibrate the MK model, three common methods proposed in previous studies were also employed.

3. Results and discussion

The ET0 values were estimated using the Makkink (MK) model group for the selected stations and compared with the standard method. Interestingly, the results varied significantly across stations. Overall, the Zabol station showed the least agreement with the standard model, with an NRMSE higher than 5.5 and a d-index lower than 0.65 for all evaluated models. This discrepancy is likely due to Zabol’s high average wind speed, which seems to have a notable impact on the model’s performance. On the other hand, the Ardabil station stood out as an exception, with d-values exceeding 0.97 for all models. This suggests that, even without calibration, the MK model group provides ET0 estimates that are remarkably close to those of the standard model at this location. For all the examined stations except Ardabil, based on the provided statistical indices (highest r and d values, as well as the lowest RMSE and MBE), the MK4 model demonstrated the highest agreement with the standard model. This is while, for the Ardabil station and based on statistical indices, the MK3 model showed the highest agreement with the standard model, albeit by a slight margin. Among the MK group models for each station, the model that provided the best results according to the statistical indices was selected, and its correction coefficient was adjusted using three methods. For the Torbat-e Jam, Rafsanjan, Zabol, and Manjil stations, the best results were obtained by establishing a regression relationship between the parameter α and wind speed, achieving negative MBE values of 0.019, 0.001, 0.017, and 0.003, respectively, and r values nearly equal to 1. However, for the Ardabil, Aligoodarz, and Bijar stations, no suitable regression relationship was found between the parameter α and wind speed. In these stations, the coefficient of the selected model was optimized by minimizing the sum of squared errors, yielding the best results with MBE values of 0.015, 0.126, and 0.100, and r values equal to 1, with only minor differences compared to the first correction method. Overall, the adjusted MK method demonstrated a very high level of agreement with the ET0 values obtained using the PM method. This suggests that, with appropriate calibration, the MK model can be a reliable alternative for estimating ET0, even in regions with varying climatic conditions.

4. Conclusion

The results of this study indicated that the MK model, before calibration, did not provide a satisfactory estimate of ET0 compared to the standard PM model for the stations of Aligoodarz, Bijar, Torbat-e Jam, Rafsanjan, Zabol, and Manjil. The largest discrepancy was observed for the Zabol station, which also had the highest wind speed among all the examined stations. However, for the Ardabil station, satisfactory results were obtained even before calibration. After applying corrections, the results significantly improved for all stations. Among the correction methods, for the Torbat-e Jam, Rafsanjan, Zabol, and Manjil stations, the best results were achieved by establishing a regression relationship between the parameter α and wind speed. For the Ardabil, Aligoodarz, and Bijar stations, the coefficient of the selected model was optimized by minimizing the sum of squared errors, yielding the best results with only slight differences compared to the first correction method. These estimated coefficients have proven to provide reliable estimates across all stations and are highly adaptable to local climatic conditions.

5. Acknowledgement & Funding

This article is derived from a master's thesis conducted with the financial and spiritual support of the University of Zabol and the Islamic Republic of Iran Meteorological Organization.

6. Conflict of Interest

The authors declare no conflict of interest.