2.3: Soil Water Content
- Page ID
- 44328
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The amount of water in a soil can be expressed in many ways, including a dry soil basis (mass water content), a volumetric basis (volumetric water content),fraction of the available water remaining, and fraction of the available water depleted. With so many different terms, confusion is bound to arise. Irrigation managers must understand all of these terms to interpret soil water status correctly.
The mass water content or gravimetric water content (θm) is the ratio of the mass of water in a sample to the dry soil mass, expressed as either a decimal fraction or as a percentage. Mass water content is determined by weighing a field soil sample, drying the sample for at least 24 hours at 105°C, and then weighing the dry soil. The decrease in mass of the sample due to drying represents the mass of water in the soil sample. The mass of the sample after drying represents the mass of dry soil. The mass water content is found by:
\(θ_m=\dfrac{M_w}{M_s}\) (2.3)
where: θm = mass water content,
Mw = mass of water lost during drying (g), and
Ms = mass of dry soil (g).
Figure 2.3 illustrates the relationship between the weight of the water in the soil and the dry weight of the soil when determining mass water content.
Figure 2.3. Concept of mass water content.
The volumetric water content (θv) represents the volume of water contained in a volume of undisturbed soil. The volumetric water content is defined as:
\(θ_v=\dfrac{V_w}{V_b}\) (2.4)
Figure 2.4. Concept of volumetric water content.
\(θ_v=\dfrac{ρ_b}{ρ_w}θ_m\) (2.5)
where: ρw = density of water, which is 1 g/cm3.
When comparing water amounts per unit of land area, it is frequently more convenient to speak in equivalent depths of water rather than water content. The relationship between volumetric water content and the equivalent depth of water in a soil layer is:
\(d=θ_v L\) (2.6)
where: d = equivalent depth of water in a soil layer (cm)
L = depth increment of the soil layer (cm).
Figure 2.5 illustrates the concept of equivalent depth of water per depth of soil. This calculation is very useful in irrigation scheduling which will be discussed in Chapter 6. In Figure 2.5, π is a constant equal to 3.14 and r is the radius of the cylindrical sample.
Figure 2.5. Concept of depth of water contained in a soil layer.
A field soil sample prior to being disturbed has a volume of 80 cm3. The sample weighed
120 grams. After drying at 105°C for 24 hr, the dry soil sample weighed 100 grams. What
is the mass water content? What is the volumetric water content? What depth of water
must be applied to increase the volumetric water content of the top 1 ft of soil to 0.30?
Given: Ms = 100 g
Mw = 120 g – 100 g = 20 g
Vb = 80 cm3
Find: θm
θv
d
Solution
\(θ_m=\dfrac{M_w}{M_s}=\left(\dfrac{20\text{g}}{100\text{g}}\right)=0.20\)g of water/g of soil
\(ρ_b=\dfrac{M_s}{V_b}=\left(\dfrac{100\text{g}}{80\text{cm}^3}\right)=1.25\) g/cm3
\(θ_v=\dfrac{ρ_b}{ρ_w}θ_m=\left(\dfrac{1.25\text{g/cm}^3}{1.00\text{g/cm}^3}\right)\times0.20=0.25\) cm3 of water/cm3 of soil
The current depth of water in 1 ft of soil is:
d = θv L = (0.25)(12 in) = 3 in
The depth of water in 1 ft of soil when θv = 0.30 will be:
d = θv L = (0.30)(12 in) = 3.6 in
Thus, the depth of water to be added is 0.6 in (3.6 in – 3.0 in).