69th SWCS International Annual Conference July 27-30, 2014 Lombard, IL

1. 1
D. N. Moriasi, P.H. Gowda, J. G. Arnold, D.J. Mulla, S. Ale, J.L.
Steiner, and M. D. Tomer
NEW SWAT TILE DRAIN EQUATIONS: MODIFICATIONS,
CALIBRATION, VALIDATION, AND APPLICATION

2. 2
Outline
 Introduction
 Tile drainage
 New tile equations
 Modifications
 What and why
 Calibration and validation (1983-1996)
 Results
 Application
 Sensitivity analyses (1983 -1996)
 drainage systems and N application rates on tile drain NO3-N losses
 Long-term (1915 – 1996) effects of precipitation, drainage design, and N
application rates on tile drain NO3-N losses
 Conclusions

3. 3
Subsurface Tile Drainage
 agricultural practice
 ↑nitrate-nitrogen (NO3-N) to surface waters

4. 4
 Alternative method – depth, size, and space
 3-step approach for computation of drainage flux (q)
Hooghoudt (1940) steady-state equation
wtd below surface
Kirkham (1957) equation
ponded depths
If q > design drainage capacity (DC), q = DC
Hooghoudt and Kirkham Equations
Skaggs, 1978; Moriasi et al., 2007, 2012, 2013a,b

5. Modifications
 Parameters g and HDRAIN – 2 new input parameters
 Why? Based on preliminary sensitivity analysis of SDRAIN on flow.
 Initially f(space, size, and height of tile above impervious layer
 Modified soil water content method used to estimate
retention parameter (S) – over-prediction of surface runoff
 ∗ ∗
.
 Smax is the maximum value the retention parameter can achieve on any given day (mm)
 SW is the soil water content of the entire profile excluding the amount of water held in
the profile at wilting point (mm H2O)
 w1 and w2 are shape coefficients
 SAfctr is the retention parameter adjustment factor (≥1) for a given HRU, which is a
function of the effective soil profile drainable porosity (Sands et al., 2009), slope,
drainage system design
 CN procedure (SCS, 1972)

.
.
Neitsch et al., 2011; Moriasi et al., 2013a,b

6. Curve Number Method: CN2
 Soil’s permeability
 Land use
 Antecedent soil water conditions
 Slope (5%)
 Not a function of tile drainage
Neitsch et al. (2011)
Cover
Hydrologic Soil Group
Land Use Treatment or practice
Hydrologic
condition A B C D
Fallow Bare soil - - - - 77 86 91 94
Crop residue cover Poor 76 85 90 93
Good 74 83 88 90
Row crops Straight row Poor 72 81 88 91
Good 67 78 85 89
Straight row w/ residue Poor 71 80 87 90
Good 64 75 82 85
Contoured Poor 70 79 84 88
Good 65 75 82 86
Contoured w/ residue Poor 69 78 83 87
Good 64 74 81 85
Contoured & terraced Poor 66 74 80 82
Good 62 71 78 81
Contoured & terraced w/ residue Poor 65 73 79 81
Good 61 70 77 80
Small grains Straight row Poor 65 76 84 88
Good 63 75 83 87
Straight row w/ residue Poor 64 75 83 86
Table 2:1-1: Runoff curve numbers for cultivated agricultural lands (from SCS Engineering Division, 1986; Neitsch
et al. (2009 )
 Crop residue cover applies only if residue is on at least 5% of the surface throughout the year.

7. Impact of Tile Drainage and Slope
on Hydrology
 Drainage increases storage capacity in the soil - “sponge
effect”
 removal of excess water
 improved soil structure
 Lower slopes (0.1% for Waseca)
 increase infiltration, reduce surface runoff

8. 8
Study Area and Data
 Three continuous corn plots located
in the University of Minnesota’s
Agricultural Experiment Station near
Waseca, southern Minnesota
 These plots were designed to
simulate a tile drain spacing of 27 m.
Tile drains were installed at a depth
of 1.2 m; with a gradient of 0.1%. Tile
drain diameter of 100 mm.
 Plots were tilled using moldboard
plow.
 Field measurements of soil and crop
data were made as a part of a tile
drainage study
 Tile drain flows were measured daily
and summed to calculate monthly
and yearly values – April – August
(1983 -1996).
 Weather data recorded at a weather
station located 0.5 km from the
experimental plots was used in the
simulation
Davis et al. (2000)

9. 9M
Results: Budget and Statistical Measures
Table 1. Observed/reported and simulated average annual water and nitrogen budgets. *Moorman et
al. (1999); **Nangia et al. (2010a); ***Meisinger and Randall (1991). ET is evapotranspiration
Water Budget
Obs./Literature Revised SWAT
Nitrogen
Budget
Annual Average
Obs./Literature
Revised SWAT
Depth
(cm)
Percent of
Precipitation
(%)
Depth
(cm)
Percent of
Precipitation
(%)
Nitrogen
(kg ha-1)
% of
Applied
Nitrogen
Nitrogen
(kg ha-1)
% of
Applied
Nitrogen
Precipitation 52.8 100 52.8 100
Applied
Fertilizer 200 100 200.0 100
ET 64 – 70* 37.1 70
Total Crop
Uptake 143 73 140.6 70
Tile Drainage 20.7 39 20.5 39
Drainage 33.5 17 34.0 17
Runoff 0.4 5** 0.4 1
Denitrification 10 - 25*** 26.5 13
Component
Calibration Validation
NSE PBIAS (%) RSR RMSE NSE PBIAS (%) RSR RMSE
Tile flow 0.84 -1 0.39 2.4 mm 0.76 3 0.49 2.1 mm
NO3-N Losses in tile flow 0.74 -4 0.51 5.7 (Kg ha-1) 0.66 1 0.58 5.5 (Kg ha-1)
Corn yield:8.6 metric tons ha-1
Table 2. Monthly calibration and validation statistics. NSE is the Nash-Sutcliffe efficiency, PBIAS is
percent bias, RMSE is root mean square error, and RSR is the ratio of RMSE and standard deviation
of the observed data.

10. 10
Methods – Sensitivity and Long-term
 Sensitivity Analyses (1983-1996) on flow and NO3-N
losses
 Depth (DDRAIN), spacing (SDRAIN), N application rates (Davis et al., 2000)
 Calibrated and validated Revised SWAT model
 Calibrated and default values were baseline and kept constant while during
parameter being investigated was varied
 Long-term average effects (1915 – 1996) on flow and
NO3-N losses
 Effect of precipitation
 linear regression models were developed using the predicted NO3-N losses data (April-August)
for 82 years (1915-1996) for each N application rate
 Probability of exceedance of target flow and NO3-N losses in any given year
 P is defined as the probability that a simulated value of equal or greater magnitude will occur in
any single year
 predicted tile flow and NO3-N losses were ranked in decreasing order
 P is prob. of exceedance; N is rank; n = total number of annual predicted values

11. 11
Results: Sensitivity Analyses
 DDRAIN (3 depths: 0.9, 1.2, 1.5 m)
 NO3-N losses decreased by 14% (from 34.0 to 29.4 kg ha-1) when
DDRAIN was decreased by 40% (1.5 to 0.90 m).
 Tile flow decreased by 8% (from 207 to 191 mm) over the same
DDRAIN range.
 SDRAIN (6 spacings:15, 27, 40, 80, 100, 200 m)
 NO3-N losses decreased by 16% (from 33.8 to 28.4 kg ha-1) when
SDRAIN was increased by 122% (27 to 60 m).
 Tile flow decreased by 11% (from 205 to 182 mm) over the same
SDRAIN range.
 N Application Rates (6 rates: 100, 125, 150, 175, 200, 225
kg ha-1)
 NO3-N losses decreased by 67 % (from 33.8 to 11.1 kg ha-1) when
application rate was decreased by 50% (from 200 to 100 kg ha-1).

12. 12
Results: Effect of Precipitation on
Tile drain NO3-N Losses
Moriasi et al. (2013b)
Tile flow
Tile flow model†
Slope (m) Intercept (b) R2
0.64 -12.67 0.69
Nitrate N loss model‡
N application rate (kg ha-1) Slope (m) Intercept (b) R2
100 0.30 -3.15 0.21
125 0.56 -7.58 0.35
150 0.83 -12.71 0.43
175 1.10 -17.73 0.46
200 1.40 -23.15 0.48
225 1.64 -27.66 0.49

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Results: Exceedance Probability - Depth
• P is defined as the probability
that a predicted value of equal
or greater magnitude will occur
in any single year
0.45 (45%) at 1.2 or 1.5 m
0.32 (32%) at 0.9 m

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0.48 (48%) at 15 m
0.14(14%) at 200 m
Results: Exceedance Probability -
Spacing

15. 15
0.44 (44%) at 200 kg ha-1
0.05 (5%) at 125 kg ha-1
Results: Exceedance Probability –
N Application Rate

16. 16
 Modifications made to the new Hooghoudt and Kirkham equations –
were successfully made
 New input parameters – Kirkham g and HDRAIN based on preliminary sensitivity
analysis of SDRAIN on tile flow
 Incorporated the retention parameter adjustment factor (SAfctr ≥1) – improve
simulation surface runoff and tile flow – useful for both tile drain methods in SWAT
 Calibration and validation
 important to ensure that budgets of simulated components and yields are validated to
ensure right statistical performance values for the right reasons
 Sensitivity analysis
 of physically based parameters and measurable inputs on outputs of processes of
interest is essential
 Helps validate model algorithms or recommend modifications for pertinent processes
 Shallower depth yields relatively larger reductions in tile flow and corresponding NO3-
N losses than with wider spacing
 However, reduction of N application rate has a much more impact on reduction of
NO3-N loses and is more practical
 From cost-reduction perspective
 Shallower depth and/or wider spacing lead to reduction in crop yields due to plant stress caused by excess
water in the root zone
 Trafficability issues
Conclusions

17. 17
 Long-term impacts
 Precipitation has a significant impact on NO3-N losses
 Generated probability of exceedance curves can help extension specialists determine
reasonable drainage systems and N application rates depending on their defined
target NO-N losses.
 Results show potential of the new tile drainage equations in SWAT to:
 determine optimum tile drain depth and spacing combinations that reduce NO3-N
losses while optimizing the crop yield
 Simulate impacts of N-application rates and the climate on NO3-N losses
Conclusions Cont’d

18. 18
Thank You!
Questions?
E-mail: daniel.moriasi@ars.usda.gov
References
Moriasi, D.N., C.G. Rossi, J.G. Arnold, and M.D. Tomer. 2012. Evaluating hydrology of the Soil and
Water Assessment Tool (SWAT) with new tile drain equations. Journal of the Soil and Water Conservation
67(6):513-524.
Moriasi, D.N., P. H. Gowda, J.G. Arnold, D.J. Mulla, S. Ale, J.L. Steiner, and M.D. Tomer. 2013a.
Evaluation of the Hooghoudt and Kirkham tile drain equations in the Soil and Water Assessment Tool to
simulate tile flow and nitrate-nitrogen. J. Environ. Qual. 42(6):1699–1710.
Moriasi, D.N., P. H. Gowda, J.G. Arnold, D.J. Mulla, S. Ale, and J.L. Steiner. 2013b. Modeling the impact
of nitrogen fertilizer application and tile drain configuration on nitrate leaching using SWAT. Agricultural
Water Management 130:36– 43.
Neitsch, S.L., Arnold,J.G. Kiniry, J.R. and Williams, J.R., 2011. Soil and Water Assessment Tool
theoretical documentation version 2009. Texas Water Resources Institute Technical Report No. 406.
College Station, Texas
Skaggs, R.W. 1978. A water management model for shallow water table soils. Report No. 134. Chapel Hill,
NC: Water Resources Research Institute of the University of North Carolina.