4.6.2: Water Stress Effects
- Page ID
- 44378
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)If management or water supply limitations restrict irrigation, the effect of water stress on ET should be considered. For managing irrigation, the effect of water stress on ET can be described using a stress factor Ks which is based on soil water content. A linear function (Figure 4.15) has been used by Hanks (1974) and Ritchie (1973). With this method the stress factor is based on the fraction of the available soil water that is stored in the crop root zone. The stress factor (Ks) is computed as:
\(K_s=\dfrac{f_r}{f_{rc}} \text{ for }f_r < f_{rc}\)
\(= 1 \text{ for }f_r \ge f_{rc}\) (4.13)
where: Ks = stress factor,
fr = fraction of the available soil water that remains, and
frc = critical threshold of fr when stress begins (Table 4.3).
Figure 4.15. Relationship of the soil water stress factor (Ks) to available soil water.
Crops vary in the ability to withstand soil water stress. Some crops are tolerant and maintain ET rates under relatively dry conditions. Other crops are sensitive and ET rates decrease when soil is wetter (Figure 4.15). Values for the soil water stress threshold are in Table 4.3. Threshold values for other crops are available from Allen, et al. (1998).
Stress reduces the rate of crop water use. Utilize the water stress factor method to determine the ET for the soil water conditions listed below. Given: Current volumetric water content of a sandy loam soil = 0.15
Volumetric water content at field capacity = 0.24
Volumetric water content at the wilting point = 0.12
ETo = 0.30 in/day
Kco = 1.20
Critical soil water content (frc) = 0.45
Solution
Assume Kw = 0
\(f_r = \dfrac{\theta_v - \theta_{wp}}{\theta_{fc} - \theta_{wp}} \) (Eq 2.10)
\(f_r = \left(\dfrac{0.15 - 0.12}{0.24 -0.12}\right) = \dfrac{0.03}{0.12} = 0.25 \)
\(K_s = \dfrac{f_r}{f_{rc}} = \dfrac{0.25}{0.45} = 0.56 \)
\(ET = K_s K_{co} {ET}_o = 0.56 \times 1.20 \times 0.30 \text{ in/day} = 0.2 \text{ in/day} \)