Discussion of “Case Study on the Accuracy and Cost/Effectiveness in Simulating Reference Evapotranspiration in West-Central Florida” by Michael Grant Exner-Kittridge and Mark Cable Rains

The authors evaluated various alternative reference ET equations based on various combinations of measured meteorological data for their accuracy in conjunction with their corresponding cost. The evaluated equations concern various reduced-data versions of the ASCE-PM standardized procedures (Allen et al. 2005), versions of the Priestley-Taylor equation, the Abtew (1996) radiation-type empirical formula, and the Hargreaves temperature-based equation. The various combinations of measured meteorological data examined are ( $R_s$ , $G$ , $U$ , RH, $T$ ); ( $R_s$ , $G$ , $T$ ); ( $R_s$ , $U$ , RH, $T$ ); ( $R_s$ , $T$ ); ( $T$ ) ( $R_s$ , $G$ , $T$ ); and ( $R_s$ ). However, the authors did not examine the case where the only measured data are ( $R_s$ , RH, $T$ ). This combination of measured data approaches economically more closely the ( $R_s$ , $T$ ) and ( $R_s$ ) combinations than the ( $R_s$ , $U$ , RH, $T$ ) combination (Tables 1 and 4 of the original paper) because the cost of an anemometer is more than that of an RH sensor.

For places where wind data, $U_2$ , are not readily available, a reduced-to-wind-data ET formula was recently suggested (Valiantzas 2006), which is a simplified version of the Penman-1963 scheme with $U_2=2\mathrm{m}/\mathrm{s}$ (average wind speed value over the globe). The reduced ET formula suggested by Valiantzas (2006) is the following:where $R_A$ ( $\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$ ) = extraterrestrial radiation; $R_s$ ( $\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{day}$ ) = solar radiation; $T$ (°C) = air temperature; RH(%) = relative humidity; and the albedo value is taken equal to $\alpha =0.23$ .

To test the performance of the approximate REF-ET formula, Eq. (1), using the ( $R_s$ , RH, $T$ ) combination of measured data, the daily weather data selected from two representative weather stations of the California Irrigation Management Information System (CIMIS) database were used. The formula, Eq. (1), is also compared with the reduced-to-wind-data $U_2$ ASCE Penman-Monteith procedure as detailed in Allen et al. (2005) and reported here as ASCE-PM ( $R_s$ , RH, $T$ ), and with the reduced ASCE-PM ( $R_s$ , $T$ ) method already evaluated by the authors. The ASCE-PM ( $R_s$ , $U$ , RH, $T$ ) scheme (Allen et al. 2005) is considered the standard reference method for the estimation of the evapotranspiration from a hypothetical reference crop (grass) surface ${\mathrm{ET}}_0$ . The two data sets used came from measurements of daily weather data (minimum and maximum temperatures, minimum and maximum relative humidity values, solar radiation, and wind speed) from the climatological stations of Davis, California (Station No. 6), characterized by a semiarid climate [with a long-term average value of wind $U_2(\mathrm{\text{average}})=2.7\mathrm{m}/\mathrm{s}$ ], and Novato, California (Station No. 63), characterized by a humid climate [with a long-term average value of wind $U_2(\mathrm{\text{average}})=1.05\mathrm{m}/\mathrm{s}$ ]. The selected data concern a 6-year period from January 1, 1994, to December 31, 1999, for Davis and a 4-year period from January 1, 1998, to December 31, 2001, for Novato. The REF-ET values ( ${\mathrm{ET}}_0$ ) obtained by the three approximate methods were compared with the values of the standard method, and the SEE was calculated:where SEE = standard error of the estimate; $Y$ = reference values obtained by the standard method; $X$ = correspondence estimates by the comparison method; and $n_O$ = total number of observations. Linear regression analysis was performed between the standard and the approximate estimates. Because the $Y$ -intercept did not differ statistically from zero, the regression was forced through the origin, i.e.,  $Y=SX$ , where $S$ = regression coefficient (slope of the linear curve passing through the origin). The traditional coefficient of determination, $R^2$ , was also used.

The long-term average ratio was also computed for each comparison method:where $X_{\mathrm{av}}$ = long-term average value of approximate estimates; and $Y_{av}$ = long-term average of standard estimates.

The results of comparison of the three methods with the standard method for the two regions are presented in correlation graphs in Figs. 1(a-f). Among the three reduced-data methods, the simplified formula Eq. (1) produced sufficiently good estimates closest to the standard ASCE-PM ( $R_s$ , $U$ , RH, $T$ ) scheme for both locations. The systematic error of Eq. (1) is the lowest among the three methods, the coefficient of determination, $R^2$ , is more than its counterpart ASCE-PM ( $R_s$ , RH, $T$ ) method and much more than the ASCE-PM ( $R_s$ , $T$ ) method, and the value of the standard error of the estimate, SEE, is less than the ASCE-PM ( $R_s$ , RH, $T$ ) method and much less than the ASCE-PM ( $R_s$ , $T$ ) method.