fw V fs J i where (We)i and (We)i-1 are the depths of water (mm) depleted from the evaporating soil upper layer at the end of days i and i - 1[0 < (We)i < Wx], P is the precipitation on day i (mm), (Qr)i is the runoff from the soil surface on day i (mm) [0 < (Qr) < Pj], (In is the net irrigation depth on day i (mm) that infiltrates the soil [Eq. (5.58)], (KeET0/ fs)i is the evaporation from the fs fraction of the exposed soil surface on day i (mm), and (Ts )j is the transpiration from the fs fraction of the evaporating soil layer on day i (mm).

To initiate the water balance [Eq. (5.77)], the user can assume that (We)j = 0 immediately following a heavy rain or irrigation or, if a long period of time has occurred since the last wetting, the user can assume that (We)j = Wx. An example of application of the basal crop coefficient approach is presented in Fig. 5.7.

When Pi < 0.2 ET0, P\ usually can be ignored. Estimation of (Qr)j can be performed using the curve-number method as described by Martin and Gilley [74]. In most applications, (Qr)t = 0. For the majority of crops, except for very shallow rooted crops

(maximum rooting depth <0.5 m), the amount of transpiration from the evaporating soil layer is small and can be neglected [i.e., (Ts) = 0]. This applies, for row crops, where little or none of (Tsdepletes the fs portion of the surface soil layer [(Ts= 0]. When the complete soil surface is wetted as by precipitation or sprinkler, then fs is essentially defined as 1 - C, where C is the average fraction of ground covered by vegetation.

However, for irrigation systems where only a fraction of the soil surface is wetted, fs is calculated as fs = min(1 - C, fw), (5.80)

where C is the average fraction of ground covered (or shaded) by vegetation (0-0.99), and fw is the average fraction of soil surface wetted by irrigation or precipitation (0.01-1) [see Eq. (5.58)]. In days when precipitation occurs, fw = 1. The min(-) function selects the lowest value of the 1 - C and fw.

Where it is not observed, the parameter C (0-0.99) can be estimated from

cmax c

where Kcb is the value for the basal crop coefficient for the particular day or period; Kcmin is the minimum Kc for dry, bare soil with no ground cover (^0.15-0.20), commonly the same as Kcbini; Kcmax is the maximum Kc immediately following wetting [Eq. (5.77)], and h is the mean plant height (m). The 1 + 0.5h exponent in Eq. (5.81) represents the effect of plant height on shading of the soil surface and on increasing the value for Kcb, given a specific value for C. The user should limit the difference Kcb - Kcmin to >0.01 for numerical stability. The value for C will change daily as Kcb changes. Therefore, Eq. (5.81) is applied daily.

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