Nasseri et al. (2026) Exploring Accuracy and Uncertainty in Watershed-Scale Estimation of Actual Evapotranspiration: Comparing Conceptual Budyko Framework and Machine Learning Methods

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-04-01
• Authors: Mohsen Nasseri, Yousef Kanani-Sadat, Hassan Naghavi, Mohammad Salimi
• DOI: 10.1007/s11269-026-04564-9

Research Groups

• School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran
• School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran
• Iran Water Resources Management Company, Tehran, Iran

Short Summary

This study compared Budyko-like conceptual frameworks with Random Forest and XGBoost machine learning models for actual evapotranspiration (Eₐ) estimation across 598 sub-basins in Iran. Machine learning models significantly outperformed conceptual approaches in accuracy and robustness, with dryness index and basin slope identified as dominant controls, while also providing more comprehensive uncertainty quantification.

Objective

• To quantify the influence of key hydro-climatic and physiographic factors (precipitation, slope, vegetation condition, geographic location) on Eₐ predictions and model residuals.
• To compare predictive accuracy and uncertainty characteristics between conceptual Budyko-like formulations and data-driven machine learning approaches (Random Forest, XGBoost).
• To examine how topographic gradients regulate hydrological partitioning across contrasting landscape types (Plain and Highland basins).

Study Configuration

• Spatial Scale: 598 sub-basins across Iran, categorized into 293 "Plain" and 305 "Highland" basins, representing diverse physiographic and climatic conditions (arid to temperate Köppen–Geiger climate classes).
• Temporal Scale: Long-term mean annual water balance components, with data adjusted for a 20-year period (2000–2020).

Methodology and Data

• Models used:
  • Conceptual Budyko-like functions (e.g., Schreiber, Oldekop, Budyko, Turk, Pike, Milly, Zhang, Zhou et al. 2015).
  • Machine Learning (ML) algorithms: Random Forest (RF) and Extreme Gradient Boosting (XGBoost).
  • Optimization: Particle Swarm Optimization (PSO) for ML model hyperparameter tuning.
  • Explainable ML: SHapley Additive exPlanations (SHAP) for feature importance analysis.
• Data sources:
  • National hydro-climatic dataset for basin-scale annual precipitation (P), actual evapotranspiration (Eₐ), and potential evapotranspiration (Eₚ).
  • Eₐ estimated using an annual water balance equation: Eₐ = P - Qs - ΔSg + Wu - R (where Qs is observed streamflow, ΔSg is change in groundwater storage, Wu is water withdrawals, and R is return water).
  • Ancillary variables: basin-mean elevation (meters), average long-term mean Normalized Difference Vegetation Index (NDVI), average Curve Number (CN), mean slope (dimensionless), geographic coordinates (latitude and longitude in degrees) of the region’s centroid, and a topographic classification variable (Plain/Highland).
  • Renewable water sources from Iran’s Third National Water Resources Surveys (TNWRS) by Iran Water Resources Management Company (IWRMC).

Main Results

• Machine learning models significantly outperformed conceptual Budyko formulations in predictive accuracy, bias control, and residual behavior.
• XGBoost achieved the highest validation accuracy (NSE = 0.61, RMSE = 0.091), followed by RF (NSE = 0.58, RMSE = 0.096) for the Eₐ/P ratio.
• Sensitivity and explainability analyses (Mean Decrease in Impurity, SHAP) consistently identified the dryness index (Eₚ/P) and mean basin slope as the most influential predictors for both ML models. Highland/Plain classification and basin centroid latitude were also highly influential.
• Mean basin slope showed a strong negative correlation with Eₐ/P (Pearson correlation coefficient = -0.60), while the dryness index showed a moderate positive correlation (Pearson correlation coefficient = 0.32).
• Uncertainty analysis revealed that ML models, despite having wider normalized uncertainty bounds (higher Average Relative Interval Length, ARIL), achieved higher prediction levels (P level), indicating a superior ability to capture the true variability of hydrological processes compared to conceptual models.
• Among Budyko formulations, Zhou’s curve displayed the broadest uncertainty bounds, while Turk and Zhang models showed the narrowest, but these were associated with lower predictive accuracy and higher bias.
• Highland regions exhibited a persistent positive bias in Budyko residuals, suggesting systematic overestimation of evapotranspiration or underestimation of runoff in mountainous terrain.

Contributions

• Conducted the first comprehensive national-scale assessment comparing Budyko-like conceptual models with optimized machine learning approaches (Random Forest and XGBoost) for actual evapotranspiration estimation across 598 hydro-climatically diverse watersheds in Iran.
• Systematically assessed the role of topographic complexity (slope and elevation) in shaping Budyko residuals and parameter uncertainty across a large and diverse region.
• Integrated sensitivity analysis, explainable machine learning techniques (SHAP), and ensemble-based uncertainty assessment to provide a holistic comparison of conceptual and data-driven frameworks beyond traditional accuracy metrics.
• Provided new insights into water-energy balance behavior in data-scarce and ungauged basins by bridging conceptual hydrology with explainable and uncertainty-aware ML modeling.
• Demonstrated the practical utility of ML-based evapotranspiration estimates for improving national water accounting systems and informing risk-informed water management policies in water-stressed regions.

Funding

The authors did not receive support from any organization for the submitted work.

Citation

@article{Nasseri2026Exploring,
  author = {Nasseri, Mohsen and Kanani-Sadat, Yousef and Naghavi, Hassan and Salimi, Mohammad},
  title = {Exploring Accuracy and Uncertainty in Watershed-Scale Estimation of Actual Evapotranspiration: Comparing Conceptual Budyko Framework and Machine Learning Methods},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-026-04564-9},
  url = {https://doi.org/10.1007/s11269-026-04564-9}
}