Agricultural Water Management 152 (2015) 188–197 Contents lists available at ScienceDirect Agricultural Water Management jou rn al hom epage: www.elsevier.com/locat e/agwat Solar radiation and relative humidity based, empirical method, to estimate hourly reference evapotranspiration C.D. Chatzithomas ∗ , S.G. Alexandris Laboratory of Agricultural Hydraulics, Department of Natural Resources Management & Agricultural Engineering, Agricultural University of Athens, Iera Odos 75, 118 55 Athens, Greece a r t i c l e i n f o Article history: Received 15 September 2014 Accepted 21 January 2015 Keywords: Two-variable formula Penman–Monteith equation Multiple linear regression Semi arid climate Theoretical daylight duration a b s t r a c t A new empirical method which estimates hourly reference evapotranspiration is proposed, that utilizes two meteorological variables, namely incoming solar radiation and relative humidity. It also utilizes a term that combines both variables. The inverse of the natural logarithm of relative humidity and the vapor pressure deficit of the atmosphere were investigated and were found to correlate quite well. The equation was calibrated in a semi arid environment, using data from Davis station (year 2000), of the CIMIS network. The estimations of both, the empirical method and the ASCE PM method, were compared. Validation of the method was performed with hourly data from the same station for 8 years, using various statistical indices. The hourly empirical equation was investigated for the whole period, for each year separately and for the summer period. It was found that it performed satisfactorily in all cases. Yearly RMSE ranged from 0.036 to 0.045 mm/h with an average for the whole period 0.042 mm/h. For the summer period RMSE ranged from 0.040 mm/h to 0.055 mm/h with an average for all the values of the summer period 0.047 mm/h. It was also validated with data from the grass reference meteorological station in the experimental field of the Agricultural University of Athens in Copais, Greece and was found to perform satisfactorily with RMSE equal to 0.043 mm/h. The deviations of the new empirical method from the ASCE PM method were investigated for various ranges of wind speed and vapor pressure deficit data values. It was found that the empirical method estimates were acceptable for practically all cases when 0.073 mm/h was considered as the threshold RMSE value. The proposed hourly empirical equation is recommended for use in semi arid climates. © 2015 Elsevier B.V. All rights reserved. 1. Introduction The largest part of the total amount of water resources con- sumed goes to agriculture. The consumption can be reduced with improved irrigation efficiency which in turn depends on accurate knowledge of reference evapotranspiration (ET o ). ET o can be either measured e.g. with the use of lysimeters or it can be estimated. Lysimeter measurements in most cases are used to compare the estimations of the various methods and assess their accuracy and true reliability (Abtew, 2007; Allen et al., 1989; Hargreaves, 1994; Hargreaves and Allen, 2003; Jensen et al., 1990; López-Urrea et al., 2006; Makkink, 1957; Snyder et al., 2005; Ventura et al., 1999). There are few sites maintaining lysimeters and therefore only few data are available. Furthermore, proper mainte- nance of a lysimeter is costly and demanding. Poor data may result ∗ Corresponding author. Tel.: +30 1 210 529 4076. E-mail addresses: Costas@aua.gr, lhyd7hak@gmail.com (C.D. Chatzithomas). as a consequence of mismanaging a lysimeter, (Allen et al., 1994; Allen et al., 2011). In such cases methods for estimating ET o from meteorological data, may give better results. Combination methods for estimating ET o , are the most accurate and data intensive. They are based on theoretical considerations which combine the aerodynamic and the energy balance meth- ods. Penman (1948) first introduced such a method which needed data only from the air above an open water surface, bypassing the need for surface measurements. Various forms were later devel- oped, e.g. FAO 24 Penman (Doorenbos and Pruitt, 1977), CIMIS Penman, (George et al., 1985; Snyder and Pruitt, 1985; Snyder and Pruitt, 1992), Kimberly Penman (Wright and Jensen, 1972; Wright, 1982). Monteith (1965) introduced the properties of the canopy and proposed a new more complete form of the equation, the Penman–Monteith (PM) equation. It was further modified with the FAO56 PM, Allen et al. (1998) and ASCE-EWRI PM (ASCE-EWRI, 2005) equation. Combination methods can estimate ET o for any period of time e.g. hourly, daily, monthly etc. The reliability of these methods makes them suitable for benchmarks against which other http://dx.doi.org/10.1016/j.agwat.2015.01.019 0378-3774/© 2015 Elsevier B.V. All rights reserved.