Updating the Coupling Algorithm in ‘HYDRUS Package … · HMG-IITM Introduction: HYDRUS Package...
Transcript of Updating the Coupling Algorithm in ‘HYDRUS Package … · HMG-IITM Introduction: HYDRUS Package...
HMG-IITM
Updating the Coupling Algorithm in ‘HYDRUS
Package for MODFLOW’
SAHILA BEEGUM
Guided by
Dr. K P Sudheer, Dr. Indumathi M Nambi & Dr. Jirka Šimunek
19 January 2018
Hydrologic Modeling Group
Department of Civil Engineering, Indian Institute of Technology Madras
HMG-IITM
Introduction: HYDRUS Package for MODFLOW (HPM)
Seo et al. (2007) and Twarakavi et al. (2008)
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HYDRUS 1D Šimůnek et al., 2016
1D Richards equation
MODFLOW Harbaugh et al., 2000
3D Groundwater flow
HMG-IITM
HPM: Spatial discretization
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HYDRUS- 1D MODFLOW
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HPM: Temporal discretization
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Stress period 1 Stress period 2 Stress period 3
MODLFOW
step 1 step 2 step 1 step 1 step 2 step 3 Time Time Time Time Time Time
Sta
rt o
f si
mula
tio
n
En
d o
f si
mula
tio
n
Time step 1 Time step 2 Time step 1 Time step 1 Time step 2 Time step 3
Stress period 1 Stress period 2 Stress period 3
HYDRUS-1D
MODFLOW
WT
WT
WT
WT
WT
WT
RF
RF
RF
RF
RF
RF
Multiple time
steps in
HYDRUS-1D
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HPM: Limitations
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10 m
1 m
Inflow = 0.001 m/day
1 m
No flow boundaries: Sides and bottom
0
1
2
3
4
5
6
7
8
9
10
-5 -4 -3 -2 -1 0 1 2 3 4 5
Dep
th (
m)
Initial pressure head (m)
600 days
No. of time steps: 6, Duration of each time step: 100 day
Sta
rt o
f si
mula
tio
n
En
d o
f si
mula
tio
n
HMG-IITM
0
1
2
3
4
5
6
0-100 100 -200 200 -300 300 - 400 400-500 500-600
Wat
er tab
le e
levat
ion (
m)
Time (days)
HPM: Limitations
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-0.04
0.06
0.16
0.26
0.36
0.46
0 100 200 300 400 500 600
Bott
om
flu
x (
m/d
ay)
Time (days)
-0.4
-0.3
-0.3
-0.2
-0.2
-0.1
-0.1
0.0
0 100 200 300 400 500 600
Cum
ula
tive
bott
om
flu
x (
m)
Time (days)
Cumulative bottom flux in the HYDRUS-1D profile.
The water table elevation after every MODFLOW time step. The flux at the bottom of the HYDRUS-1D profile. Eliminate the sudden variation in the
bottom flux from HYDRUS-1D
HMG-IITM
Objectives
To update the coupling algorithm between HYDRUS-1D and MODFLOW to eliminate sudden fluxes when the groundwater table depth changes.
To verify the coupling algorithm using HYDRUS-2D/3D and analytical solution
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HMG-IITM
h1 h2= WT from h2
MODFLOW
Updating the coupling algorithm between HYDRUS-1D and MODFLOW
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8
Stress period 1 Stress period 2 Stress period 3
step 1 step 2 step 1 step 1 step 2 step 3 Time Time Time Time Time Time
Sta
rt o
f si
mula
tio
n
En
d o
f si
mula
tio
n
Update pressure head profile in the HYDRUS-1D column
Pressure head profile Steady state pressure Pressure head at the end of T1
at the end of T1 head profile adjusted before moving to T2
q1 q1
Dep
th o
f so
il
WT
WT WT
Steady-state nodal fluxes
compared with the nodal fluxes
at T1
If (relative difference between
these two fluxes > 0.1% of the
flux);
• Pressure head values below
this node = pressure heads
obtained by the steady-state
profile
• Pressure head values above
this node = pressure heads
at T1
- - -
+ + + q1
HMG-IITM
Steady state pressure head profile obtained using Darcy-Buckingham law
The above equation has to be solved for hi+1, while the value hi is known and q is equal to the bottom flux.
Soil Hydraulic models
Van Genuchten model
Modified van Genuchten (Vogel and Cislerova)
Brooks and Corey
Van Genuchten with air entry value of 2 cm
Log-normal (Kosugi)
12 1
11
ii
iiii
zz
hhhKhKq
Coupling algorithm
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HMG-IITM
Verification of the updated coupling algorithm
Constant boundary condition
Varying boundary conditions
Different soil types
Comparison with HYDRUS 2D/3D
Comparison with Analytical solution
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HMG-IITM
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-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0 100 200 300 400 500 600
Cum
ula
tive
bott
om
flu
x (
m)
Time (days)
Without pressure head
modification
With pressure head
modification 0
1
2
3
4
5
6
7
8
0 - 100 100 -
200
200 -
300
300 -
400
400 -
500
500 -
600
Wat
er t
able
ele
vat
ion (
m)
Time (days)
With pressure head modification
Without pressure head modification
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
0 100 200 300 400 500 600
Wat
er t
able
ele
vat
ion (
m)
Time (days)
6 TS, modified
6 TS, unmodified
60 TS, modified
60 TS, unmodified
600 TS, modified
600 TS, unmodified
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0 100 200 300 400 500 600
Cum
ula
tive
bott
om
flu
x (
m)
Time (days)
6 TS, modified
6 TS, unmodified
60 TS, modified
60 TS, unmodified
600 TS, modified
600 TS, unmodified
Verification of the coupling algorithm: Constant surface flux
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0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 50 100 150 200 250 300 350
Wat
er t
able
ele
vat
ion (
m)
Time (days)
10 TS, modified
20 TS, modified
20 TS, unmodified
30 TS, modified
30 TS, unmodified
365 TS, modified
365 TS, unmodified
Verification of the coupling algorithm: Variable surface flux
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-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0 50 100 150 200 250 300 350
Cum
ula
tive
bott
om
flu
x (
m)
Time (days)
10 TS, modified
10 TS, unmodified
20 TS, modified
20 TS, unmodified
30 TS, modified
30 TS, unmodified
365 TS, modified
365 TS, unmodified
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0 50 100 150 200 250 300 350
Pre
cip
itat
ion / P
ote
nti
al
evap
otr
ansp
irat
ion (
m/d
ay)
Time (day)
Precipitation (m/day)
Potential evapotranspiration (m/day)
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Verification of the coupling algorithm: Different soil types
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0.078 0.43
3.6
1.56 0.2496 0.5 0.057 0.41
12.4
2.28 3.502
0.5 0.045 0.43
14.5
2.68
7.128
0.5
0
2
4
6
8
10
12
14
16
18
20
Residual moisture content [-]
Saturated soil moisture content [-]
Parameter alpha in the soil water
retention function [L-1]
Parameter in the soil water retention
function
Saturated hydraulic conductivity [LT-1]
Tortuosity parameter in the conductivity
function [-]
Loam Loamy sand Sand
HMG-IITM
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-0.05
-0.03
-0.01
0.01
0.03
0.05
0 5 10 15 20 25 30 35 40 45 50
Bo
tto
m f
lux
(m
/day
)
Time (days)
50 TS_unmodified
25 TS_unmodified
10 TS_unmodified
50 TS_modified
25 TS_modified
10 TS_modified
-0.06
-0.01
0.04
0.09
0.14
0.19
0 5 10 15 20 25 30 35 40 45 50 B
ott
om
flu
x (
m/d
ay)
Time (days)
50 TS, unmodified
25 TS, unmodified
10 TS, unmodified
50 TS, modified
25 TS, modified
10 TS, modified
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0 5 10 15 20 25 30 35 40 45 50
Bo
tto
m f
lux
(m
/day
)
Time (days)
50 TS, unmodified
25 TS, unmodified
10 TS, unmodified
50 TS, modified
25 TS, modified
10 TS, modified
Sand (K=7.128 m/day)
Loam (K=0.2496 m/day)
Loamy sand (K= 3.502 m/day)
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Verification of the modified HPM with HYDRUS 2D/3D
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5.000
5.050
5.100
5.150
5.200
5.250
5.300
0 100 200 300 400 500 600
Wat
er t
able
lev
el (
m)
Time (days)
HYDRUS-2D
HPM
-0.0012
-0.0010
-0.0008
-0.0006
-0.0004
-0.0002
0.0000
0 100 200 300 400 500 600
Bo
tto
m f
lux
(m
/day
)
Time (days)
HPM HYDRUS-2D
HMG-IITM
Comparison with analytical solution
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Department of Civil Engineering, Indian Institute of Technology Madras 16
5.00
5.05
5.10
5.15
5.20
5.25
5.30
0 25 50 75 100 125 150 175 200
Wat
er t
able
ele
vat
ion
(m
)
x (m)
Analytical solution
HYDRUS (2D/3D)
HPM
2 22 2 22 1
1
( ) ( )( ) ( ) ( )
H H WH x H x lx x
l K
H1 H2
(Bear, 1972)
HMG-IITM
Summary and Conclusion
The coupling algorithm between HYDRUS-1D and MODFLOW is updated in HPM
The algorithm is verified for its functionality for Different boundary condition
Different soil types
HPM is verified by comparing the HPM results with the results obtained using HYDRUS-2D/3D and analytical solution
19 January 2018
Hydrologic Modeling Group
Department of Civil Engineering, Indian Institute of Technology Madras 17