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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
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𝜕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
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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
24
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
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-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
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