## ET0 Equations

Methods for computing ET0 from weather data of Doorenbos and Pruitl [55] may be utilized when validated or calibrated against the FAO-PM. However, they lose importance.

• The FAO-PM relies on a conceptual approach—the original Penman method— which has been modified into a new and more solid approximation of the evaporation from vegetated surfaces, the PM approach. The use of the original Penman requires a locally calibrated wind function [14], which would require appropriate data sets, available only in very few locations. Therefore, the Penman approaches definitely should be replaced by the PM (FAO-PM) method.

• The FAO-radiation (FAO-Rad) equation corresponds to an approximation of the radiation term [A ( Rn - G)/(A + y *)] in the FAO-PM equation, but uses an adjustment factor c for daytime wind U2 and mean RH. The FAO-Rad requires observations of temperature and sunshine, and the use of regional estimates for RH and U2. The FAO-PM can be utilized when T^ replaces Tdew and when regional U2 values are imported to the location where they are missing. Therefore, the use of FAO-Rad is not considered to be an alternative to FAO-PM when U2 and RH data are missing.

• The FAO Blaney-Criddle (FAO-BC) method estimates ET0 from temperature data only and requires correction for RH, wind speed, and relative sunshine using regional values of these variables. However, the FAO-BC has been shown to overestimate ET0 for a large number of locations, particularly for the nonarid ones. Thus, as indicated earlier (in "Comments on Using ET0 PM with Estimates of Missing Data"), when only temperature data are available, there is no advantage in using an alternative to the FAO-PM equation with estimates of missing weather data.

• The Hargreaves method [82, 84] not only has shown good results as a temperature method when applied in a variety of locations but, despite being empirical, it has the appropriate conceptual foundation to be utilized and represents a great improvement in relation to the FAO-BC method. It can be expressed as

ET0 Harg = C0(Tmax - Tmin)05 ( Tmean + 17.8) Ra, (5.50)

where EToHarg is the estimate of grass reference ET (mm day-1), Tmax and Tmin are the maximum and minimum daily air temperatures (°C), T^,^ is the mean daily air temperature (°C), Ra is the extraterrestrial radiation (MJm-2 day-1), C0 is the conversion coefficient = 0.000939 (= 0.0023 when Ra is in mm day-1) and 17.8 is the factor for conversion of °C to °F.

The temperature difference (T^hx - Tmin) allows for an approximation to the amount of radiation available at the surface as analyzed for Eq. (5.44). The difference (Tmax - Tim) is also an indicator for VPD, which is normally higher for clear sky (high Tmax - Tmin) and lower for overcast conditions (low Tmax - Tmin).

However, because the equation can underestimate ET for locations where high wind speed is associated with high VPD, and because it may overestimate if humidity is high, validation or calibration of the equation is recommended for such regions [see Eqs. (5.48) and (5.49)].

The Hargreaves equation can be computed on a monthly or a daily basis. However, the best use of daily estimates is made when summed or averaged for a week or 10-day period, as is usual for irrigation scheduling computations.

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