Modeling of subsurface agricultural drainage using two hydrological models with different conceptual approaches as well as dimensions and spatial scales

Figures & data

Figure 1. Location of tile-drained plot of interest in the Bras d’Henri micro-watershed (the star indicates the outlet).

Figure 2. Different scenarios of saturated hydraulic conductivity (KsXY) configurations for soil dynamics models assessment: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; (d) Scenario 4; (e) Scenario 5; (f) Scenario 6; (g) Scenario 7; and (h) Scenario 8.

Table 1. CATHY soil hydraulic parameters in the porous media.

Layers	Depth (m)	Thickness (m)	KsXY (cm/h)	KsZ (cm/h)	Ss (m^−1)	ϕ (-)
01–03	0.00–0.25	0.25	16.25	3.25	6.0 x 10^−4	0.48
04–05	0.25–0.75	0.50	97.60	32.5	1.8 x 10^−4	0.48
06–10	0.75–1.25	0.50	16.25	3.25	6.0 x 10^−4	0.41
11–15	1.25–5.45	4.20	25.90	5.18	3.5 x 10^−4	0.45
VGN (-): 4.85 VGRMC (-): 0.105 VGPSAT (-): −0.25

Table 2. DRAINMOD soil input values.

Layer bottom depth (cm)	KsXY (cm/h)	Tension (cm)
		0	50	100	333	15,000
		Volumetric moisture content (cm^−3 cm^−3)
25	16.25	0.50	0.37	0.33	0.30	0.13
75	92.70	0.40	0.10	0.07	0.05	0.02
125	16.25	0.50	0.37	0.33	0.30	0.13
545	6.47	0.45	0.23	0.20	0.17	0.08

Table 3. List of drainage design input parameter values.

Parameter	DRAINMOD	CATHY
Depth from soil surface to drain (cm)	110	115
Spacing between drains (cm)	1825	2000
Effective radius of drains (cm)	1.02	-
Actual distance from surface to impermeable layer (cm)	545	545
Equivalent depth from drain to permeable layer (cm)	111.73	-
Drainage coefficient (cm day^−1)	0.63	-
Kirkham’s coefficient	10.81	-
Initial depth to water table (cm)	60	60
Maximum surface storage (cm)	0.50	-
Kirkham’s depth for flow to drain (cm)	0.25	-

Table 4. Calibration and validation procedure periods.

Year	Season	Days of interest (Julian day)	Crop	Procedure
2010	Fall	18 October–1 November (291–305)	Corn	Validation
2011	Summer	4–18 July (185–199)	Soybean	Calibration
	Fall	17–31 October (290–304)
2012	Fall	19 October–3 November (292–307)	Oat	Validation

Table 5. Model performance statistics.

Objective	Statistic (unit)	Symbol and expression
Soil dynamics model assessment	Percent error in peak (%)
	Percent error in volume (%)
Model evaluation	Total predicted drain flow (mm) Total observed drain flow (mm)
	Coefficient of determination (-)
	Coefficient of efficiency (Nash) (-)
	Modified coefficient of efficiency (-)

Note:

n = number of observations during the simulated period, i = Julian day, O = observed drain flow, P = predicted drain flow,  = arithmetic mean of observed drain flow,  = arithmetic mean of predicted drain flow. Assuming a 20% error on tile-drain flow observed values, J is defined as follows (Bessiere 2008):

Table 6. Model maximum and total predicted drain flows and their PEP and PEV values.

Model	Scenarios	1	2	3	4	5	6	7	8
DRAINMOD	Max.(mm/d)	3.1	4.9	3.0	3.0	3.1	4.9	2.4	2.9
	TPDF (mm)	29.3	19.8	26.3	26.3	29.4	19.8	38.9	40.5
CATHY	Max.(mm/d)	2.5	1.2	2.5	0.9	2.2	2.5	1.4	1.5
	TPDF (mm)	12.1	6.3	16.5	9.0	11.5	9.5	7.1	8.7
Statistic	|PEP| (%)	19	75	16	71	27	50	49	48
	|PEV| (%)	59	68	37	68	61	52	82	78

Figure 3. DRAINMOD and CATHY simulated tile-drain flow under soil dynamics models assessment using 2012 meteorological data: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; (d) Scenario 4; (e) Scenario 5; (f) Scenario 6; (g) Scenario 7; and (h) Scenario 8.

Figure 4. DRAINMOD and CATHY predicted and observed tile-drain flow comparison during calibration process: (a) summer 2011 and (b) fall 2011.

Table 7. Statistical comparison between simulated and observed tile-drain flow for the calibration periods. (TPDF: total predicted drain flow, TODF: total observed drain flow, R²: coefficient of determination, NSE: coefficient of efficiency (Nash), NSEm: modified coefficient of efficiency).

Period	Summer 2011		Fall 2011
TODF (mm)	5.85		11.52
Model	DRAINMOD	CATHY	DRAINMOD	CATHY
TPDF (mm)	5.66	5.28	12.88	10.18
TPDF/TODF (-)	0.98	0.90	1.12	0.88
R^2 (-)	0.36	0.02	0.96	0.76
NSE (-)	−0.50	−8.32	0.67	0.34
NSEm (-)	0.90	−0.32	0.99	0.96

Figure 5. DRAINMOD and CATHY predicted and observed tile-drain flow comparison during validation process: (a) fall 2010; and (b) fall 2012.

Table 8. Statistical comparison between simulated and observed tile-drain flow for the validation periods. (TPDF: total predicted drain flow, TODF: total observed drain flow, R²: coefficient of determination, NSE: coefficient of efficiency (Nash), NSEm: modified coefficient of efficiency).

Period	Fall 2010		Fall 2012
TODF (mm)	4.29		10.46
Model	DRAINMOD	CATHY	DRAINMOD	CATHY
TPDF (mm)	4.47	4.21	13.67	7.67
TPDF/TODF (-)	1.04	0.98	1.31	0.73
R^2 (-)	0.31	0.10	0.97	0.87
NSE (-)	−0.25	−1.41	0.79	0.73
NSEm (-)	0.61	0.22	0.95	0.92

Figure 6. DRAINMOD and CATHY predicted tile-drain flows and the uncertainty range (in gray) with an error of ± 20% on observed tile-drain flows: (a) summer 2011; (b) fall 2011; (c) fall 2010; and (d) fall 2012.

Figure 7. Cumulative PET and cumulative AET simulated by DRAINMOD and CATHY: (a) summer 2011; (b) fall 2011; (c) fall 2010; and (d) fall 2012. (PET: Potential Evapotranspiration, AET: Actual Evapotranspiration).

Table 9. Model performance in simulating actual evapotranspiration.

Criteria	R^2 (AET versus PET) (-)				(TPET-TAET)/TPET (%)
Model	S 2011	F 2011	F 2010	F 2012	S 2011	F 2011	F 2010	F 2012
DRAINMOD	0.84	0.94	0.97	0.95	19.97	25.54	40.03	38.73
CATHY	0.96	0.95	0.98	0.97	15.32	18.50	27.54	23.46

S: summer; F: fall, PET: Potential Evapotranspiration, AET: Actual Evapotranspiration, TPET: Total Potential Evapotranspiration, TAET: Total Actual Evapotranspiration.

Figure 8. Impact of lateral saturated hydraulic conductivity (KsXY) change in each layer (variation of value of layer 1 (L1), 2 (L2), 3 (L3), 4 (L4)) of the porous media one at a time with respect to the cumulative tile-drain flow: (a) 1/10 KsXY – DRAINMOD; (b) 10 KsXY – DRAINMOD; (c) 1/10 KsXY – CATHY; and (d) 10 KsXY – CATHY.

Bessiere, H. 2008. Variational data assimilation for distributed hydrological modeling of fast kinetic flood. Thèse de doctorat, Université de Toulouse, Institut National Polytechnique de Toulouse, 321.

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