a flexible framework for forward and inverse modeling of stormwater lids arash massoudieh mahdi...
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A FLEXIBLE FRAMEWORK FOR FORWARD AND INVERSE MODELING OF STORMWATER LIDS
Arash Massoudieh
Mahdi Maghrebi
The Catholic University of America
Washington, DC
Overview• Why a new framework?• Governing Equations
• Hydraulic• Particle Transport• Contaminant transport• Numerical method
• Demonstration cases• Bioretention (hydraulic)• Infiltration basin (hydraulic)• Permeable pavement (hydraulic)• Wetland/stream (hydraulic + reactive transport)• Small catchment (hydraulic, transport)
• Conclusions
Green Infrastructure modeling• Diverse system configurations• Need to choose/adjust the levels of complexity• The importance of particular processes depends on:
• the goal of simulation• contaminant of concern• time scale of interest
• Inverse Modeling/Uncertainty assessment
Pond
Substrate
Pipe Storage
Native Soil
Ground water
Block-Connector conceptualization
789101112
012345
141516171819
Inflow
A=85.71A=61.67 A=207.14
613 2024
24” Engineered soil
15” Aggregate6” PVCSlope=0.5%
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3138 45
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24” Engineered soil
15” Aggregate
12” PVCSlope=0.5%
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Z=155.05
Z=154.67
Z=0
Z=155.86
Z=157.37
Z=156.99
Z=0
Z=158.13
Z=156.53
Z=0
A=98.00A=182.14 A=20.97
Z=158.06Z=157.98
Z=156.02
Z=155.72Z=155.66
Z=157.22Z=157.18 Z=157.08
Z=157.0
Z=154.9Z=154.78 Z=154.82
Z=154.78
Z=154.73A=100, Depth=10000
A=5, Depth=1000
Governing Equations - Hydraulics
, ,1 1
nj nsi
ij s j ij j
dSQ Q
dt
• Water Balance
• Head-Storage constitutive theory
• Head-Flow constitutive theory
;i ih f S other factors
, ;ij i jQ f h h other factors
Constitutive Equations
+user-defined blocks
Constitutive Equation (hydraulics) • Constitutive relations are not hard-coded. Default relationships for known elements are available
• S-H relationships
Soil Pond Storage Catchment Manhole Darcy Stream
Soil N/A Pipe N/A
Pond
Storage Pipe N/A
Catchment N/A N/A
Manhole Pipe Pipe Pipe Pipe Pipe
Darcy N/A Pipe
Stream N/A N/A Pipe
2
1/1 1m i jm
s e e
h hAK S S
d
2
1/2 1 1m i jm
s e e
h hAK S S
d
21/ 2
2 1 1m i i i im
s e e
H h z h zAK S S
d
21/2 1 1
m i jms e e
h hAK S S
d
2
1/2 1 1m i jm
s e e
h hAK S S
d
5/3
2i j i jh h y yW
dn d
i js
h hK
d
5/3
5/3
( )
( )
i ji
j ij
pos h hWy
dn d
pos h hWy
dn d
5/3( )j jj
pos h zWy
dn d
5/3( )i ii
pos h zWy
dn d
2 i js
h hAK
d
5/3
2i j i jh h y yW
dn d
21/
21/
22 1 1
2 1 1
m i i i ims e e i j
m i jms e e
H h z h zAK S S if z z
dh h
AK S S elsed
i js
h hK
d
i j
s
i is
h hK horizontal
dh z
K verticald
5/3( )j jj
pos h zWy
dn d
( )j is
i js
pos h hK A horizontal
dh h
K A verticald
5/3
5/3
( )
( )
i ji
j ij
pos h hWy
dn d
pos h hWy
dn d
5/3( )i ii
pos h zWy
dn d
5/3
5/3
( )
( )
i ji
j ij
pos h hWy
dn d
pos h hWy
dn d
5/3( )i ii
pos h zWy
dn d
5/3( )j jj
pos h zWy
dn d
5/3( )i i
i
pos h zWy
dn d
2
1/2 1 1m i jm
s e e
h hAK S S
d
2 i js
h hAK
d
( )i j
s
i js
pos h hK A horizontal
dh h
K A verticald
i js
h hAK
d
i js
h hAK
d
5/3
2i j i jh h y yW
dn d
5/3( )j jj
pos h zWy
dn d
5/3( )j j
j
pos h zWy
dn d
5/3
5/3
( )
2
( )
2
i j i j
j i i j
pos h h y yW
dn d
pos h h y yW
dn d
Soil Pond Storage Catchment Manhole Darcy Stream
1//(1 )11 /
nn ne s sz S S
/ sS A
/
/s s n
s
S AS V
/s sS A/s sS A /s sS /s sS A
Particle Transport
, ,, ,
1 1
, , , ,1 1
( . . )
capacitymobility
nj nji k i k
k ij ij j k ij ij i kj j
Advection
nk nk
k k i k k k i kk k
massexchangebetween phases e g mobile phase and attached phase
d S GH Q Q G H Q Q G
dt
G G
K K
, , ,
, ,1
/
njs i j k
k j k i kj ij
dispersion diffusion
DG G
d
• User-specified number of particle types
• User-specified number of phases
Coupled dissolved/particle facilitated constituent fate, reaction and transport
c
, , , ,, , , , , ,
1 1
, , , , , , , ,1 1
capa ity
nj nji k i k l i k
k ij ij j k l j k ij ij i k l i kj j
advection
nk nk
k k i k l i k k k i k l i kk k
mass exchange duetocolloid exchange
d S G CH Q Q G C H Q Q G C
dt
G C G C
K K
, , ,
, , , , , ,1
/
, , , ,, ,
1
/
njs i j k
k j k l j k i k l i kj ij
Dispersion Diffusion
nrl i k l i k
k k k k rl rrk k
transformation reactionadsorption desorption
DG C G C
d
C Cf R
κ
• User-specified number of chemical species• User-specified reaction network
• Coupled particle-bound aqueous transport is important because the main removal processes in many LIDs is particle settling/filtration
Other processes• Evaporation/Vapor exchange• Build-up (exponential, linear, user-defined) • Wash-off (Diffusive, flow-dependent, user-defined)• Atmospheric Flux (e.g. Aeration)
In progress:• Transpiration and plant uptake • Clogging
Reactions
2 2
2 2
2 3
3 2 3
3 2 3
:
:
AerobicOM decomposition OM O NH
Nitrification NH O NO
Denitrification OM NO
CO H
N
O
CO H O HN
𝑟𝑎𝑒𝑟=−𝜇𝑠
[𝑂𝑀 ][𝑂𝑀 ]+𝐾 𝑠
[𝐷𝑂 ][𝐷𝑂 ]+𝐾 𝑜
𝑟𝑛𝑖𝑡=−𝜇𝑛
[𝑁𝐻 3][𝑁𝐻 3]+𝐾 𝑛
[𝐷𝑂 ][𝐷𝑂 ]+𝐾 𝑜𝑛
𝑟𝑎𝑒𝑟=−𝜇𝑎𝑛𝑜𝑥
[𝑁𝑂3][𝑁𝑂3]+𝐾 𝑛𝑜
[𝑂𝑀 ][𝑂𝑀 ]+𝐾 𝑠
𝐾 𝑜
[𝐷𝑂]+𝐾𝑜
Numerical Algorithm• Implicit, Newton-Raphson with partial Jacobian evaluation• Adaptive time-step• C++• We are working on a GUI
Framework features• User-defined reaction kinetics• User-defined particle-medium interaction/settling• Deterministic (GA) and stochastic (Bayesian-MCMC)
parameter estimation• User-defined atmospheric exchange, build-up, wash-off
Examples: St. Francis Bio-retention basin, Cincinnati, Ohio
6/25/13 7/5/13 7/15/13Date
0
200
400
600
800
1000
Flo
w D
isch
arg
e m
3/d
1600
1200800
400
0
Inflo
w t
o U
pper
Rai
n G
ard
en (
m3 /
d)
Outflow From Upper Rain Garden
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0
400
800
1200
1600
Flo
w D
isch
arg
e m
3 /dOutflow From Lower Rain Garden
6/23/13 7/1/13 7/9/13 7/17/13Date
0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S7
S8
S9
S10
S11
Soil Moisture Upper Left Column
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0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S0
S1
S2
S3
S4
Soil Moisture Upper Middle Column
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0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S14
S15
S16
S17
S18
Soil Moisture Upper Right Column
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0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S32
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S34
S35
S36
Soil Moisture Lower Left Column
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0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S26
S27
S28
S29
S30
Soil Moisture Lower Middle Column
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0
10
20
30
40
50
Soi
l Mo
istu
re (
%)
S39
S40
S41
S42
S43
Soil Moisture Lower Right Column
Permeable Pavement System, Louisville, KT
Lee et al., 2005
Reactive transport in a stream
2 2
2 2
2 3
3 2 3
3 2 3
:
:
AerobicOM decomposition OM O NH
Nitrification NH O NO
Denitrification OM NO
CO H
N
O
CO H O HN
𝑟𝑎𝑒𝑟=−𝜇𝑠
[𝑂𝑀 ][𝑂𝑀 ]+𝐾 𝑠
[𝐷𝑂 ][𝐷𝑂 ]+𝐾 𝑜
𝑟𝑛𝑖𝑡=−𝜇𝑛
[𝑁𝐻 3][𝑁𝐻 3]+𝐾 𝑛
[𝐷𝑂 ][𝐷𝑂 ]+𝐾 𝑜𝑛
𝑟𝑎𝑒𝑟=−𝜇𝑎𝑛𝑜𝑥
[𝑁𝑂3][𝑁𝑂3]+𝐾 𝑛𝑜
[𝑂𝑀 ][𝑂𝑀 ]+𝐾 𝑠
𝐾 𝑜
[𝐷𝑂]+𝐾𝑜
Initial DO: 8.5mg/LInitial NO3: 0
Infiltration Basin and GW recharge
Pond2.5 m
Θ=10̊�
Day 1 Day 3 Day 9
100x100m impervious surface-channel + wash-off
•Initial build-up of 1000mg/m2 of an imaginary contaminant with diffusive wash-off•Depression storage 0.005m/m2
•No infiltration
Summery• LIDMod provide a flexible tool to assess the short-term
and long-term performance of LIDs• User-defined hydraulic relationship• User-defined particle/colloid transport and retention• User-defined reactions• User-defined build-up and wash-off• User-defined atmospheric exchange
• The framework is written to allow easy expansion • Scripting language is liberating but not easy to use for
every user • Different level of complexity can be represented• Inverse modeling need more computational speed
Thank you! • If you think you have some applications for the program
contact: [email protected]