Sensitivity Analysis of Several Potential Evapotranspiration Equations to Climatic Variables in the Basetime and Future Periods Using the Sobol Method

Document Type : Research Paper

Authors

• mahdi vaziri ¹
• NOZAR GHAHREMAN ²

¹ Department of Irrigation and Reclamation Engineering, Faculty of Agriculture-University of Tehran -Karaj-Iran

² Department of Irrigation and Reclamation Engineering-Faculty of Agriculture- University of Tehran-Karaj-Iran

Abstract

Keywords

• Potential evapotranspiration
• Sobol
• PyET
• Climate change
• CMIP6

Main Subjects

• ...

Introduction

Potential evapotranspiration (ET_P) represents a key component of the hydrological cycle and is a major determinant in water resource management, irrigation planning, and climate impact assessments. Accurate estimation of ET_P requires understanding its dependence on multiple meteorological variables such as air temperature, humidity, wind speed, and net radiation. However, these variables interact in complex and nonlinear ways, resulting in uncertainty in ET_P estimation, especially under changing climate conditions. Sensitivity analysis is therefore an essential tool to identify which input parameters exert the greatest influence on ET_P, allowing researchers to prioritize data accuracy and model calibration efforts. Among global sensitivity analysis methods, the Sobol variance-based approach is one of the most robust techniques, as it quantifies both the individual and interaction effects of input variables on model outputs (Sobol, 2001; Saltelli et al., 2010). This study aims to evaluate the sensitivity of several ET_P equations to key climatic parameters across Iran’s diverse climatic zones using the Sobol method. Three empirical and physically based ETP models FAO-56 Penman–Monteith, Romanenko, and Thom-Oliver were applied to assess and compare parameter sensitivities during a historical baseline period (2001–2024) and a projected future period (2025–2100) under climate change scenarios derived from CMIP6 global climate models.

Method

Meteorological data for the baseline period, including mean, minimum, and maximum temperature, relative humidity, wind speed, and shortwave and longwave radiation components, were obtained from the NASA POWER database with a monthly temporal resolution. Future climate data (2025–2100) were extracted from two CMIP6 models CNRM-ESM2-1 and INM-CM5-0 under two shared socioeconomic pathways, SSP2-4.5 and SSP5-8.5, from the Copernicus Climate Data Store. Eight representative meteorological stations were selected to capture the climatic diversity of Iran, including Sari, Tehran, Kermanshah, Tabriz, Mashhad, Kerman, Ahvaz, and Bandar Abbas. These stations represent a broad range of climatic conditions, from humid coastal zones in the north to arid and semi-arid environments in the central and southern regions.

The ET_P was computed using three different models available in the open-source Python package PyET (Vremec et al., 2024):

1- FAO-56 Penman–Monteith, a physically based method recommended by FAO for semi-arid regions;

2- Romanenko, an empirical temperature–humidity model suitable for data-scarce and dry environments;

3-Thom–Oliver, which emphasizes the role of net radiation and energy balance, making it suitable for humid and coastal areas.

Sensitivity indices were computed using the Sobol method implemented in the Python libraries SALib and NumPy. The Sobol first-order index (Si) quantifies the direct effect of each variable on ETP, while the total-order index () includes all interaction effects among variables. These indices were calculated for each ETP model, climate scenario, and time period to capture how the importance of meteorological drivers may evolve under climate change.

Results

The Sobol sensitivity analysis highlighted significant spatial and temporal differences in how climatic variables affect potential evapotranspiration (ET_P) across Iran. During the baseline period, ET_P in humid and coastal regions (e.g., Bandar Abbas and Sari) was mainly controlled by net radiation, reflecting high energy inputs, while in arid and continental areas (e.g., Kerman, Mashhad, Ahvaz), maximum temperature and relative humidity were the dominant factors. Mountainous regions (Kermanshah, Tabriz) showed sensitivity to both net radiation and maximum temperature due to solar exposure and large diurnal temperature ranges.

In future periods, ET_P became more sensitive to thermal variables, with temperature-driven vapor pressure deficits increasingly dominating over radiation and wind contributions. Humidity gained importance in arid regions, highlighting the role of atmospheric dryness in ET_P increases, while in coastal areas, temperature and wind effects slightly intensified due to land–sea thermal contrasts. Mountain stations exhibited reduced sensitivity to minimum temperature, reflecting smaller diurnal temperature variations under warmer nights. Humid northern stations shifted from radiation- to temperature-dominated control, indicating thermal forcing increasingly shapes surface energy balance.

Overall, maximum temperature and relative humidity were the most influential variables historically and in future scenarios, with net radiation and wind playing secondary roles. The findings underscore that local factors such as elevation, proximity to water, and surface characteristics modulate ET_P sensitivity, stressing the need for regional assessments. These results align with global studies showing enhanced ET_P sensitivity to temperature and humidity under climate change, while emphasizing spatial variability across Iran.

Conclusions
The Sobol sensitivity analysis provided a comprehensive quantitative framework for evaluating how different meteorological variables influence ET_P under current and future climate conditions in Iran. The results confirm that future ET_P dynamics are likely to be governed by enhanced temperature sensitivity and increased atmospheric dryness, particularly in arid and semi-arid regions. Conversely, in humid regions, the controlling mechanisms may shift from radiative to thermal dominance. The observed inter-station variability revealed the necessity of considering local climatic characteristics when modeling evapotranspiration across Iran’s diverse environments. The combination of three selected ET_P models Penman-Monteith, Romanenko, and Thom-Oliver allowed for a robust assessment of both energy-driven and humidity-driven processes. Furthermore, this study highlights the relatively limited application of global sensitivity analysis techniques such as Sobol in Iranian hydrological studies and demonstrates their potential for improving ET_P modeling accuracy. In summary, climate change is expected to intensify thermal controls on evapotranspiration while diminishing the influence of radiation and wind, reshaping the surface energy balance and water demand across Iran. The findings of this research can aid in refining evapotranspiration models, improving irrigation planning, and guiding adaptation strategies for sustainable water management under future climatic conditions.

Author Contributions

M.V.: Data Analysis, programming, results synthesis, draft preparation

N.G.: Visualization, Supervision, Manuscript editing, Conceptualization, Methodology

Data Availability Statement

No datasets are available

Acknowledgements

We would like to express our sincere gratitude to the University of Tehran for the logistical supports and Iran Meteorological Organization for providing required data.

Ethical considerations

The study was approved by the Ethics Committee of the University of ABCD (Ethical code: IR.UT.RES.2024.500). The authors avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

The author declares no conflict of interest.