The unsaturated zone MetaSWAP-package

Paul van Walsum

Wageningen Environmental Research

Overview

1. Introduction

2. MetaSWAP concept for the unsaturated zone

3. Coupling to MODFLOW

4. Verification of MODFLOW-MetaSWAP <-> Richards model SWAP

5. Conclusions

2

Introduction

Why MetaSWAP?

Simple MODFLOW packages for unsaturated zone:

EVT, ETS – extinction function for capillary rise; soil water dynamics ?

UZF1 – kinematic wave for infiltration; capillary rise ?

Advanced MODFLOW packages:

VSF/REF1 – Richards Equation Flow ; computation time ?

3

MetaSWAP

Water balance of 1D-Richards equation:

θ : moisture content (m3 m-3)

q : vertical flux (m d-1)

τ : source term (m3 m3 d-1)

4

𝜕θ

𝜕𝑡+𝜕𝑞

𝜕𝑧= 𝜏

MetaSWAP

Water balance of Richards equation:

θ : moisture content (m3 m-3)

q : vertical flux (m d-1)

τ : source term (m3 m3 d-1)

Solution procedure in two steps:

Generate steady state profiles, store in database

Combining steady state profiles with water balance during simulation coupled to groundwater model

5

𝜕θ

𝜕𝑡+𝜕𝑞

𝜕𝑧= 𝜏

MetaSWAP

Steady state profiles: detailed vertical resolution

6

q (mm d-1) 1 0 -1 -2 -5

m3

m-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

root zone

h

T > 0 I > 0

Metafunction for the verticale flux q

7

q(pr,h):

● pr : mean pressure head root zone

● h : groundwater level

Aggregation boxes for water balances

Subgrid computational method

8

Aggregation box 1

(root zone)

Aggregation box 2

Swap compartments

Aggregation box 3

Aggregation box 4

Metafunction for storage in root zone

9

sr(pr,h):

● sr : storage in root zone (m)

● pr : mean pressure head root zone(m)

● h : groundwater level (m)

s2(pr,h) or second box, etc

Simulation of percolation

10

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

q = 0

Simulation of percolation

11

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

q0 = - 16 mm d-1

Simulation of percolation

12

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

qr

Δsr

q0 = - 16 mm d-1

Schematisation:

Sharp transition of profiles at box boundary

No influence on gradient at box boundary

q (mm d-1) 1 0 -1 -2 -5

m3

m-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

root zone

h

T > 0 I > 0

Simulation of percolation

13

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

qr

Δsr

q0 = - 16 mm d-1

Integration of Richards equation over root zone box:

→ Δsr / Δt + (q0 – qr) = 0 → Δsr – qr Δt = - q0 Δt 𝜕θ

𝜕𝑡+𝜕𝑞

𝜕𝑧= 𝜏

Simulation of percolation

14

Σ = Δsr − qr∙ Δt

pr pe

∙ Δt = -q0 Δt = 16.0 Δsr qr −

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0 -1

h

qr

Δsr

q0 = - 16 mm d-1

Simulation of percolation

15

Σ = Δsr − qr∙ Δt

pr pe

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

qr=

-3.8 mm d-1

Δsr = 12.2 mm

q0 = - 16 mm d-1

pr j+1

16.0

Simulation of percolation

16

root zone

m 3 m

-3

0.00 0.30 0.32 0.34 0.36 0.38 0.40 0.42

z (m)

-2.0

-1.5

-1.0

-0.5

0.0

h

qr=

- 3.8 mm d-1

Δsr = 12.2 mm

q0 = - 16 mm d-1

Δs2 = 3.4 mm

q2=

- 0.4 mm d-1

p (m)

-0.8 -0.6 -0.4 -0.2 0.0

z (m)

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

4 d

3 d t = 2 d

box 1 (root zone)

box 2

box 3

17

q

(mm

d-1)

qtot

(mm)

Simulation of percolation:

comparison with SWAP

Coupling to MODFLOW

Two possible options for balances:

System Control

volumes volume

18

Groundwater

Unsaturated zone

Unsaturated zone

Groundwater

Coupling to MODFLOW

Balance equation for communal control volume

Implementation with Control volume

dynamic

storage coefficient μ (sc1)

μ (hn – ho) =

(qmsw + qmod) ∆t

19

Unsaturated zone

Groundwater

20

Storage (m)

h (m)

-5

-4

-3

-2

-1

0

1

Coupling to MODFLOW

Storage table for the control volume, use latest value of root zone pressure head

21

MODFLOW returns hn and qmodn

Options for new μn:

Head-based

Balance based

Coupling to MODFLOW (from 2nd cycle on)

21

hmod

Storage (m)

h (m)

-5

-4

-3

-2

-1

0

1

S~

ho

hn

Sn

qmodn Δt

22

MODFLOW returns hmodn and qmod

n

Head-based μ:

μh = (Sh – S~)/(hn – ho)

Coupling to MODFLOW (from 2nd cycle on)

22

hmod

Storage (m)

h (m)

-5

-4

-3

-2

-1

0

1

S~

ho

hn

Sh

23

MODFLOW returns hn and qmodn

Head-based μn :

μhn = (Sh – S~)/(hn – ho)

Balance-based μn :

μqn = (Sn – S~)/(hS – ho)

Coupling to MODFLOW (from 2nd cycle on)

23

hmod

Storage (m)

h (m)

-5

-4

-3

-2

-1

0

1

S~

ho

hS

Sn

qmodn Δt

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MODFLOW returns hn and qmodn

Head-based μn :

μhn = (Sh – S~)/(hn – ho)

Balance-based μn :

μqn = (Sn – S~)/(hS – ho)

Most used:

μn = (μhn + μq

n )/2

Coupling to MODFLOW (from 2nd cycle on)

24

hmod

Storage (m)

h (m)

-5

-4

-3

-2

-1

0

1

S~

ho

hS

Sn

qmodn Δt

Verification of coupling MODFLOW-MetaSWAP

Comparison MODFLOW-MetaSWAP with SWAP

MODFLOW-dummy : only drainage flux

25

-2,5

-2

-1,5

-1

-0,5

0

3655 4020 4385 4750

SWAP

MF-MSW

h

(m)

Model N (mm/j ETact (mm/j) R (mm/j)

SWAP 809 484 325

MF-MSW_1d 809 485 324

Computational performance

Conclusions

MetaSWAP, the pro’s:

fast (10-50X SWAP) emulator of Richards model water balance and groundwater dynamics

stable and efficient coupling to MODFLOW

Limitations:

hill slope situations (1D instead of 2D)

deep groundwater when timing of infiltration front is critical (cf. UZF1)

27

Questions ?

28