A novel multi-scale parameter estimation approach to the Hargreaves-Samani equation for estimation of Penman-Monteith reference evapotranspiration

Abstract

The main focus of this study is to develop a multi-scale surrogate model for the FAO-56 Penman-Monteith (PM) evapotranspiration (ETo) using Hargreaves-Samani (HS) equation, which uses only temperature as a hydrometeorological variable to estimate ET. This feature is particularly useful for scarce data regions and climate change impact assessment studies, where the direct estimation of ETo from the PM equation can be problematic. As the parameters of the HS equation may vary across space, a Bayesian approach was adopted to estimate (or recalibrate) them rather than relying on the fixed values as suggested in the traditional model. The Bayesian approach allows a sound development of our model in a multi-scale temporal framework, where the ETo at daily, monthly and annual scales are jointly used to estimate the HS equation parameters. The proposed and reference models are applied and tested using meteorological data from 17 stations located across the Han river basin in South Korea. The results indicate that the traditional HS equation with fixed parameters and without recalibration tends to overestimate the reference ET for all stations. The locally recalibrated approach to the HS equation at a daily temporal scale can effectively reduce the systematic bias associated with the use of the traditional HS equation but fails to reproduce the underlying distribution of ETo at different temporal scales (e.g., monthly and annual). This leads to a large systematic bias in ETo at these scales. In contrast, the proposed multi-scale surrogate model offers a more precise estimation of the reference ET at a daily timescale as well as at the aggregated monthly and annual temporal scales. This is particularly useful to minimize the systematic bias often observed when using traditional surrogate models for the reference ET in hydrological studies such as rainfall-runoff modeling and assessment of climate change impact on water resources.