Symbolic Regression Equations for Calculating Daily Reference Evapotranspiration with the Same Input to Hargreaves-Samani in Arid China

To present an alternative simple equation for reference evapotranspiration (ETo) estimation, the symbolic regression (SR) method was applied to establish equations with the same inputs to simple Hargreaves-Samani (HS) equation in arid China. For most of the equations derived by SR method for each station, their performance increased with an increase in the equation complex index (CI). The most precise equation performed well although it was always complex and greatly varied in form. On the other hand, the simplest one was uniform in equation structure and performed slightly better than the HS equation for all the five stations, and sometimes better than the local calibrated HS equation. A trade-off equation was selected with almost the same equation form for all the five stations and low CI index. The site-specific trade-off equation performed better than the simplest one and the locally calibrated HS equation. Then parameters in the trade-off equation were unified for all the five stations, it did not perform as good as the site-specific one, but performed better than the HS equation and unified local calibrated HS equation. Thus, the SR method is suitable to determine both the site-specific and the unified equation among stations for daily ETo calculation in arid regions.