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Comparative assessment of empirical and hybrid machine learning models for estimating daily reference evapotranspiration in sub-humid and semi-arid climates

202537 citationsOpen accessAbdelmalek Essaâdi University

In plain language

Accurate estimation of daily reference evapotranspiration is necessary for agricultural water planning and irrigation scheduling, especially when complete weather data are unavailable. A study conducted in the Gharb and Loukkos irrigated perimeters in Morocco evaluated eight empirical formulas and four standalone machine learning models, as well as four hybrid computational models. The tested algorithms included Random Forest, M5 Pruned, eXtreme Gradient Boosting, and Light Gradient Boosting Machine, using varying combinations of temperature, relative humidity, solar radiation, and wind speed. When benchmarked against the standard Penman-Monteith method, the Valiantzas 2013 model proved to be the most accurate empirical option. Among computational approaches, the hybrid configurations combining eXtreme Gradient Boosting with Light Gradient Boosting Machine, and Random Forest with Light Gradient Boosting Machine, achieved the highest precision. These hybrid models offer strong potential to improve water resource management across sub-humid and semi-arid agricultural landscapes.

Key takeaways

  • The Valiantzas 2013 model demonstrated the highest accuracy among eight tested empirical equations for estimating daily reference evapotranspiration.
  • Hybrid machine learning models combining eXtreme Gradient Boosting or Random Forest with Light Gradient Boosting Machine delivered the lowest prediction errors overall.
  • The tested models successfully estimated reference evapotranspiration across sub-humid and semi-arid climatic conditions using limited meteorological inputs.

Why it matters

Farmers and water authorities need accurate information on crop water requirements to avoid waste and manage limited supplies. Standard calculation methods frequently fail because local weather stations lack full sensor equipment. Testing data-driven models with reduced weather variables helps water managers schedule irrigation efficiently, preserving critical water supplies in dry and climate-stressed agricultural regions.

Commercialisation angle

The tested hybrid machine learning models could be integrated into precision agriculture software, digital irrigation advisory tools, and regional water management systems. Expected users include irrigation managers, agricultural tech providers, and agronomic advisors. As an applied analytical study tested on regional meteorological data, the algorithms represent an applied research stage that requires software integration and field trials before commercial operational deployment.

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Abstract

Abstract Improving the accuracy of reference evapotranspiration (RET) estimation is essential for effective water resource management, irrigation planning, and climate change assessments in agricultural systems. The FAO-56 Penman-Monteith (PM-FAO56) model, a widely endorsed approach for RET estimation, often encounters limitations due to the lack of complete meteorological data. This study evaluates the performance of eight empirical models and four machine learning (ML) models, along with their hybrid counterparts, in estimating daily RET within the Gharb and Loukkos irrigated perimeters in Morocco. The ML models examined include Random Forest (RF), M5 Pruned (M5P), eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), with hybrid combinations of RF-M5P, RF-XGBoost, RF-LightGBM, and XGBoost-LightGBM. Six input combinations were created, utilizing T max , T min , RH mean , R s , and U 2 , with the PM-FAO56 model serving as the benchmark. Model performance was assessed using four statistical indicators: Kling-Gupta efficiency index (KGE), coefficient of determination (R 2 ), mean squared error (RMSE), and relative root squared error (RRSE). Results indicate that the Valiantzas 2013 (VAL2013b) model outperformed other empirical models across all stations, achieving high KGE and R 2 values (0.95–0.97) and low RMSE (0.32–0.35 mm/day) and RRSE (8.14–10.30%). The XGBoost-LightGBM and RF-LightGBM hybrid models exhibited the highest accuracy (average RMSE of 0.015–0.097 mm/day), underscoring the potential of hybrid ML models for RET estimation in subhumid and semi-arid regions, thereby enhancing water resource management and irrigation scheduling.

Research topics

  • Plant Water Relations and Carbon Dynamics
  • Hydrology and Watershed Management Studies
  • Irrigation Practices and Water Management

Sustainable Development Goals

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DOI: 10.1038/s41598-024-83859-6

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