5.3.6: Chemical Leaching Losses
- Page ID
- 44399
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Deep percolation losses not only decrease irrigation efficiency, but also result in chemical movement or loss below the root zone. The volume of deep percolating water due to nonuniformity can be designated Vdp1. For an adequacy of 90% and a normally distributed (in a statistical sense) water application depth, the Vdp1 is given by:
Vdp1 = Vz (1 – F1)
where: Vz = dz A = volume of water infiltrated,
dz = average depth of water infiltrated,
A = total irrigated area, and
F1 = factor (Table 5.1).
| CU | F1 |
|---|---|
| 70 | 0.46 |
| 71 | 0.48 |
| 72 | 0.49 |
| 73 | 0.51 |
| 74 | 0.53 |
| 75 | 0.55 |
| 76 | 0.57 |
| 77 | 0.58 |
| 78 | 0.60 |
| 79 | 0.62 |
| 80 | 0.64 |
| 81 | 0.66 |
| 82 | 0.67 |
| 83 | 0.69 |
| 84 | 0.71 |
| 85 | 0.73 |
| 86 | 0.75 |
| 87 | 0.77 |
| 88 | 0.78 |
| 89 | 0.80 |
| 90 | 0.82 |
| 91 | 0.86 |
| 92 | 0.86 |
| 94 | 0.89 |
| 96 | 0.93 |
| 98 | 0.96 |
Deep percolation due to excessive average irrigation depths and/or irrigating too frequently (excessive application) is denoted Vdp2 and:
If \(d_{LQ} < SWD\), then \(V_{dp2} = 0\)
If \(d_{LQ} > SWD\), then \(V_{dp2} \approx 0.95 A (d_{LQ} - SWD)\) (5.15)
Total deep percolation, Vdp, is given by:
Vdp = Vdp1 + Vdp2 (5.16)
The depth of deep percolation, dp , is:
\(d_p = \frac{V_{dp}}{A}\) (5.17)
The amount of chemical lost with the leachate can be calculated by:
\(C_l = 0.226 \, C \, d_p\) (5.18)
where: Cl = chemical loss (lb/ac),
C = concentration of the chemical in the leachate (deep percolation) (ppm), and
dp = depth of deep percolation (in).
Find the nitrate leached (lb/ac) for the field illustrated in Example 5.1 if the average concentration of nitrate-nitrogen in leachate is 20 ppm and SWD = 1.2 in.
Find: Determine the amount of nitrate-nitrogen leached from the field during each irrigation.
Solution: Since we need to calculate this in lb/ac, assume that A = 1 ac. From Table 5.1, F1 = 0.71 for a CU of 84%. Using Equations 5.14, 5.15, 5.16, 5.17, and 5.18:
Using Equations 5.14, 5.15, 5.16, 5.17, and 5.18:
Solution
Vdp1=dz A (1=F1) (Eq. 5.14)
Vdp1=(2.0 in) (1ac) (1=0.71)
Vdp1=0.58 ac=in
Vdp2=(0.95 A (dLQ-SWD) (Eq. 5.15)
Vdp2=(0.95) (1 ac) (1.5 in-1.2 in)
Vdp2= 0.29 ac-in (Eq. 5.16)
Vdp= Vdp1 + Vdp2
Vdp=0.58 ac-in 0.29 ac-in 0.87 ac-in
\(d_p = \frac{V_{dp}}{A}\) (Eq. 5.17)
\(d_p = \frac{0.87 \text{ ac-in}}{1 \text{ ac}} = 0.87 \text{ in}\)
Ci = 0.226 C d p (Eq. 5.18)
Ci = 0.226 ( 20 ) ( 0.87 ) 3.9 lb/ac
Thus, 3.9 lb/ac of nitrate-nitrogen are lost to leaching for each irrigation.
Another approach for finding the average dp, if data from a uniformity test is available, is to determine the dp at each irrigation catch can and then averaging. From Example 5.1, the dp in Can No. 1 is 0 in (1.2 in caught – 1.2 in SWD). For Can No. 20, it is 0.8 in (2.0 – 1.2). For the 20 cans in Example 5.1, the dp is:
| Can N0. |
Deep Perc. (dp) (in) |
|---|---|
| 1 | 0.0 |
| 2 | 1.4 |
| 3 | 0.6 |
| 4 | 0.9 |
| 5 | 1.0 |
| 6 | 0.5 |
| 7 | 1.7 |
| 8 | 1.5 |
| 9 | 0.4 |
| 10 | 0.8 |
| 11 | 0.9 |
| 12 | 0.5 |
| 13 | 0.7 |
| 14 | 1.2 |
| 15 | 1.2 |
| 16 | 0.8 |
| 17 | 0.4 |
| 18 | 1.1 |
| 19 | 0.6 |
| 20 | 0.8 |
Averaging the 20 depths, we get an average dp of 0.85 in, which compares well with the 0.87 in calculated in Example 5.