What does this research mean for the field?

Locally calibrating empirical reference evapotranspiration equations, particularly the Mahringer model using monthly varying coefficients, provides highly accurate ET₀ estimates with limited meteorological data in Mediterranean climates. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to evaluate and calibrate empirical reference evapotranspiration models for the Mediterranean climate in İzmir.

June 21, 2026Journal of Hydrology and Hydromechanics0 citationsOpen Access

Monthly and fixed coefficient calibration of empirical reference evapotranspiration equations: A case study for a Mediterranean climate (Izmir Province)

BKBirol KayaDokuz Eylül University MAMaryam AdhamiTarbiat Modares University CUCeren UstabasDokuz Eylül University

Key Points

The aim is to evaluate and calibrate empirical reference evapotranspiration models for the Mediterranean climate in İzmir.
Used daily meteorological data from 40 stations (2000–2020) for calibration evaluation.
Applied least squares regression and gradient-based optimization for model calibration with fixed and monthly coefficients.
Assessed model performance using various statistical metrics including R², MAE, and RMSE.
Before calibration, the Priestley–Taylor model had R² = 0.932, MAE = 0.68; after calibration, Mahringer model achieved R² = 0.995, MAE = 0.05 with monthly coefficients.
Calibration resulted in substantial accuracy improvements across all models, particularly with monthly coefficients.
Missing sunshine duration data was reconstructed, maintaining calibration accuracy and resulting in more representative datasets.

Abstract

Abstract Accurate estimation of reference evapotranspiration (ET₀) is essential for efficient irrigation and water resource management, particularly in water-scarce regions. Although the FAO56 Penman–Monteith (PM-FAO56) equation is widely accepted as the standard method, its application is often constrained by the requirement for comprehensive meteorological data. This study provides a regional evaluation and calibration of three widely used empirical ET₀ models Hargreaves and Samani (temperature-based), Priestley and Taylor (radiation-based), and Mahringer (mass transfer-based) under Mediterranean climatic conditions in İzmir, Türkiye. Daily meteorological data from 40 stations covering the period 2000–2020 were used. Model performance was assessed against PM-FAO56 using the coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), percentage error (PE), Nash–Sutcliffe efficiency (NSE) and mean bias error (MBE). Calibration was performed using least squares (LS) regression and a gradient-based optimization approach, with both fixed and monthly varying coefficients. Before calibration, the Priestley–Taylor model showed the best performance among the empirical equations (R² = 0.932, MAE = 0.68, RMSE = 0.92, PE = 7.32, NSE=0.796, MBE=− 0.65). After calibration, all models improved substantially, with the Mahringer equation achieving the highest accuracy when monthly coefficients were applied (R² = 0.995, MAE = 0.05, RMSE = 0.154, PE = 1.41, NSE=0.992, MBE=0.022). The LS and gradient-based optimization approaches produced nearly identical results. In addition, the reconstruction of missing sunshine duration (ADS) data using a regression-based approach enabled the inclusion of a more spatially representative dataset without introducing significant bias into the calibration results. The findings demonstrate that locally calibrated empirical equations, particularly when temporal variability is accounted for through monthly coefficients, can provide highly accurate ET₀ estimates with relatively limited data requirements. This study provides practical monthly and fixed calibration coefficients for the İzmir region and supports the use of monthly calibrated empirical models for irrigation planning in Mediterranean environments.

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