Reduction Coeficient for Limited Soil Water Ks

The Kcb in Eq. (5.53) and Kc in Eq. (5.54) are reduced when soil water content of the plant root zone is too low to sustain transpiration at potential levels. The reduction is made by multiplying Kcb or Kc by the water stress coefficient Ks. Ks can be predicted from [90]

when 9 < 9t, where Ks is the dimensionless ET reduction factor (0-1), 9 is the mean volumetric soil water content in the root zone (m3 m-3), 9t is the threshold 9 for the root zone, below which transpiration is decreased because of water stress (m3 m-3), and 9ll is the soil water content at the lower limit of water extraction by plant roots (m3 m-3). By definition, Ks = 1.0 for 9 > 9t. Parameter 9ll is synonymous with the term wilting point.

The threshold soil water content 9t is predicted as

where Fns is the average fraction of available soil water that can be depleted before water stress occurs (0-1), and 9jjl is the soil water content at the drained upper limit of the soil profile (field capacity) (m3 m-3). Fns represents the depletion fraction for no stress, and is equivalent to the p term of Doorenbos and Pruitt [55] and Doorenbos and Kassam [90] and is similar to the term "management-allowed depletion" (MAD), introduced by Merriam [103]. However, values for MAD may be influenced by management and economic factors in addition to physical factors influencing Fns. Generally, MAD < Fns when there is risk aversion or uncertainty, and MAD > Fns when plant water stress is an intentional part of soil water management.

Values for the 6 parameters in Eqs. (5.82) and (5.83) represent averages for the effective root zone. Fns normally varies from 0.30 for shallow-rooted plants at high rates of ET0 (>8 mm day-1) to 0.80 for deep-rooted plants at low rates of ET0 (<3 mm day-1). Values for Fns are given in Table 5.1. Values listed need to be adjusted for climate as indicated in footnoted of the same table.

The determination of Ks requires a daily balance of soil water content.

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