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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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

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Flo

w D

isch

arg

e m

3/d

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1200800

400

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Inflo

w t

o U

pper

Rai

n G

ard

en (

m3 /

d)

Outflow From Upper Rain Garden

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Flo

w D

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3 /dOutflow From Lower Rain Garden

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Soi

l Mo

istu

re (

%)

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S8

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Soil Moisture Upper Left Column

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Soi

l Mo

istu

re (

%)

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Soil Moisture Upper Middle Column

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Soi

l Mo

istu

re (

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Soil Moisture Upper Right Column

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Soi

l Mo

istu

re (

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Soil Moisture Lower Left Column

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Soi

l Mo

istu

re (

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Soil Moisture Lower Middle Column

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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: massoudieh@cua.edu