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)

19 January 2018


Department of Civil Engineering, Indian Institute of Technology Madras 2

HYDRUS 1D Šimůnek et al., 2016

1D Richards equation

MODFLOW Harbaugh et al., 2000

3D Groundwater flow

HMG-IITM

HPM: Spatial discretization

19 January 2018



HYDRUS- 1D MODFLOW

HMG-IITM

HPM: Temporal discretization

19 January 2018



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


HYDRUS-1D

MODFLOW

WT

WT

WT

WT

WT

WT

RF

RF

RF

RF

RF

RF

Multiple time

steps in

HYDRUS-1D

HMG-IITM

HPM: Limitations

19 January 2018



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

19 January 2018



-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

19 January 2018



HMG-IITM

h1 h2= WT from h2

MODFLOW

Updating the coupling algorithm between HYDRUS-1D and MODFLOW

19 January 2018



8


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

19 January 2018



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

19 January 2018



HMG-IITM

19 January 2018



-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

HMG-IITM

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

19 January 2018



-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)

HMG-IITM

Verification of the coupling algorithm: Different soil types

19 January 2018



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

19 January 2018



-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)

HMG-IITM

Verification of the modified HPM with HYDRUS 2D/3D

19 January 2018



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

19 January 2018



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



updating the coupling algorithm in ‘hydrus package … · hmg-iitm introduction: hydrus package...

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