## Definition of Reference Evapotranspiration

The primary purpose for developing ET0 equations is to estimate a reference ET by which a crop coefficient is multiplied to obtain an estimate of crop ET. In many instances, the ET0 equation has represented a hypothetical living crop reference in order to provide for a complete record of ET0 during the development of crop coefficients and during calibration or analysis of other ET equations. Wright and Jensen [53] and Wright [71] utilized a hypothetical alfalfa ET0; Jensen [54] and Jensen et al. [2] used an equation to represent "lysimeter ET"; George et al. [72], Pruitt and Swann [56], and Feddes [73] used an ET0 equation to represent a hypothetical grass ET0; and Martin and Gilley [74] also assumed a hypothetical grass reference crop.

Allen etal. [21] and Jensen etal. [2] supported the use of the PM equation to represent both alfalfa and grass ET0. The PM method was ranked high among all methods evaluated in the American Society of Civil Engineers' (ASCE) study [2], both as a grass and as an alfalfa reference. Based on results of studies reported here, the Food and Agriculture Organization (FAO) Expert Consultation on Revision of FAO Methodologies for Crop Water Requirements [75] recommended the PM method as the primary ET0 method for defining grass ET0 and for determining crop coefficients. A hypothetical grass reference crop with constant height and surface resistance was selected to avoid problems with local calibration that would require demanding and expensive studies.

The surface resistance [Eq. (5.6)] of a grass crop can be well estimated because it is commonly accepted that the average minimum daytime value of stomatal resistance for a single leaf is approximated as rl = 100 s m-1; the LAI effective for transpiration can be appropriately calculated using LAIf = 0.5 LAI; and the LAI for a clipped grass with height not larger than 0.15 m can be approximated as LAI = 24 h. The above approximations produce the following relationship for the surface resistance:

If a constant h = 0.12 m is assumed hypothetically [75], Eq. (5.10) yields a constant LAI = 2.88, which produces the constant value rs = 70 s m-1. These characteristics, with the additional standard crop reflectivity factor (albedo), fully characterize a hypothetical grass reference crop as discussed by Allen et al. [59].

The same assumption is adopted in the Soil Conservation Service (SCS) Handbook [74], where the clipped grass reference crop is considered with constant height h = 0.125 m. This results in also adopting a constant rs = 66 s m-1.

The selection of constant height and bulk surface resistance parameters is a compromise and may not represent reality in all climatic regimes. However, this selection provides consistent ET0 values in all regions and climates and among research locations. The PM equation is a close, simple representation of the physical and physiological factors governing the ET process. By using the PM definition for ET0, one may calculate crop coefficients at research sites where ET0 is not measured simultaneously with measured ET from other crops. In addition, various crops may exhibit variations in rs with climate that are different from those exhibited by grass. In the Kc ET0 approach, the variations in rs and ra relative to the reference crop are accounted for within the crop coefficient, which serves as an aggregation of the physical and physiological differences between crops (see Pereira et al. [14]). The aggregation of various differences and the development of crop coefficients should be simplified by using the constant rs in the ET0 definition [76, 77].

Therefore, the reference ET (ET0) is defined as the rate of ET from a hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 sm-1, and an albedo of 0.23, closely resembling the ET from an extensive surface of green grass of uniform height, actively growing, completely shading the ground, and having adequate water.

## Growing Soilless

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