A method of calibration and variance analysis with respect to the Penman-Monteith equation for the Turc, Hargreaves and Abtew potential evapotranspiration models

Introduction: The full ASCE/FAO-56 Penman-Monteith evapotranspiration (PM-ET) equation and crop coefficients are often employed for irrigation scheduling of open-field crops. To obtain PM-ET derived water-use figures requires access to full weather station datasets, which includes radiation, air temperature, wind-speed, and relative humidity measurements.

Over the years there have been many studies aiming to create (and evaluate) simpler models with fewer measurements that are easier to use and less costly to implement than a full weather station facility. In this paper we have focussed on the Turc, Hargreaves and Abtew models which employ daily averages of: solar radiation, air temperature and relative humid to determine daily ET.

Daily PM-ET values were obtained from a WS-GP2 weather station located at the Quinta de São Pedro study centre on the Setúbal peninsula in Portugal. The WS-GP2 is based around the programmable GP2 Data Logger and Controller, whose software (controlled by a script editor) can create step by step operations to control complex processes or recording requirements.

The Turc, Hargreaves and Abtew models were integrated into the WS-GP2 (using the GP2’s script editor) enabling direct daily comparisons with PM-ET values. Daily average values of: solar radiation, air temperature and relative humidity were recorded for model recalibration purposes. Data was collected over 12-months from May 2018. Dataset comparisons between the Turc, Hargreaves and Abtew models and the PM-ET equation indicated that all three potential ET models overestimated ET and benefitted from recalibration. In each case the Bland-Altman method of variance analysis was applied, resulting in the following 2-sigma confidence level accuracies against PM-ET of: Turc ± 0.43 mm/day, Hargreaves ± 0.46 mm/day, and Abtew ± 0.88 mm/day.

For the Abtew and Turc models, recalibration consisted of the application of an offset whilst retaining the originally published coefficients, the Hargreaves model required adjustment to one of the two published coefficients. Following recalibration, the comparison of ET from the Turc and Hargreaves models follows a 1:1 relationship.

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