Empirical formulae for Et and EP

Previous editions of Hydrology in Practice have summarised a number of different empirical formulae for estimating potential and actual evapotranspiration. The main reason for using such formulae is when the data required for using, say, the Penman-Monteith equation as set out above, are not available (Xu and Singh (2006), e.g. compare the performance of seven different simplified formulae). In data-sparse situations, e.g. it may be possible to obtain data on daily maximum and minimum temperatures, but there may not be a nearby meteorological measurement station (or FLUXNET site) that will give wind speed and humidity data (or direct estimates of Et). However, the cost of obtaining the relevant variables has, with the availability of modern automatic weather stations, been greatly reduced. There are even recent experiments where large numbers of weather measurements are being made using cheap sensors linked by wireless network technology, such as the SensorScope program at EPFL, Lausanne.2 Thus, it is suggested that, wherever possible, the Penman-Monteith equation now be used for point estimates of actual and potential evapotranspiration in preference to any of the empirical equations.

It has been shown how the Penman-Monteith equation can be used to estimate Et directly. Over a long period, however, and in particular a long dry period, this does require information about how canopy resistance for a given type of surface will change with water availability. There have been many studies with different crops and natural vegetation canopies to suggest the nature of this relationship, but it is also possible to use the Penman-Monteith equation to estimate potential evapotranspiration and then use a functional relationship between the ratio of actual to potential evapotranspiration and soil moisture to estimate Et. One thing should be noted in taking this approach. From the derivation of the Penman-Monteith equation, it is expected that the canopy resistance rc will only be zero for a canopy that is wet. When the canopy is dry but transpiring at the potential rate for the prevailing conditions, rc may be greater than zero even if the water supply is non-limiting (Table 10.1).

For this reason, the Food and Agricultural Organisation of the United Nations (FAO) use the term reference crop evapotranspiration, ETo, when water is not limiting rather than potential evapotranspiration (Allen et al., 1998, 2005). The FAO now recommend the Penman-Monteith equation for estimating ETo but has taken an empirical approach to determining Et from ETo and has tabulated crop coefficients relating Et to ETo for a wide variety of crops under different cropping patterns during a production season. Et for a given crop is then calculated from estimates of ETo as:

Some examples of crop coefficients are shown in Table 10.2.3 They will vary with the stage of growth of the crop (see Allen et al. (1998), who outline procedures for constructing seasonal crop coefficient curves). Given some information about Eto in

Table 10.2 Single (time-averaged) mid-growing season crop coefficients, Kc, for non-stressed, well-managed crops in sub-humid climates (relative humidity >45%, wind speed >2 m s) for use with the FAO Penman-Monteith Et0

Crop Kc

Small vegetables 1.05

Roots and tubers 1.10

Legumes (Leguminosae) 1.15

Perennial vegetables (with winter dormancy and initially bare or mulched soil) 1.00

Fibre crops 1.15

Oil crops 1.15

Cereals 1.15

Turf grass - cool season 0.95

Sugarcane 1.25

Banana 1.05

Coffee - bare ground 0.95

Rubber trees 1.00

Berries (bushes) 1.05

Apples cherries pears active ground cover 1.20

Citrus no ground cover (70% cover) 0.65

Citrus with active ground cover or weeds (70% canopy) 0.70

Conifer trees 1.00

a given region and these crop coefficients for typical cropping patterns, the water requirements for different crops can be estimated.

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