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Water Quality Modeling Water Quality Modeling Workshop, HWorkshop, H--GAC:GAC:M d li F d t lM d li F d t lModeling FundamentalsModeling FundamentalsTim Cox, Ph.D., P.E.Tim Cox, Ph.D., P.E.
CDMCDM
June 30, 2010June 30, 2010
Session OutlineSession Outline
Modeling Overview
Stream Water Quality Modeling
Lake Water Quality Modeling
Estuary Modeling
Watershed Modeling
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Modeling OverviewModeling Overview
Modeling OverviewModeling OverviewWhy do we use models?Why do we use models?
To predict the future
To quantify things that are difficult (or expensive) to directly measure
To gain a better understanding and interpretation of existing measured data.
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Modeling OverviewModeling OverviewTypical Applications of Water Quality ModelsTypical Applications of Water Quality Models
TMDLs
BMP assessment
Compliance demonstration
Data interpretationData interpretation
Modeling OverviewModeling OverviewModel Limitations and Sources of ErrorModel Limitations and Sources of Error
Measurement error data inputscalibration
Numerical errorstability t titruncation error
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Modeling OverviewModeling OverviewModel Limitations and Sources of ErrorModel Limitations and Sources of Error
Structural errornot comprehensive enoughmissing key processes or structures
Operator errorbad model selectionbad calibrationbad calibrationbad application or extension
Modeling OverviewModeling OverviewModel CategoriesModel Categories
Mechanistic
Qin = CIA + baseflow
Cin = EMC, Cbase
Qout = Qin
[Chl a]
fd fp Evap
[N1]Qsup , Csup
kd
[P1]
Phytoplankton = F(N1, P1, d1, V1 )
Qrecirc
vS
[N2] ,[P2] [N3],[P3]kd3
kd2
Linternal = D *AdzdC
d2
kdz
V2= ρ*d2*A
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Modeling OverviewModeling OverviewModel CategoriesModel Categories
Empirical
7 Day Low Flow vs Total Water Year Precip:
y = 10.97e0.05x
R² = 0.8480
100
120
140
160
180
7Q (cfs)
7 Day Low Flow vs. Total Water Year Precip: Kaweah River
0
20
40
60
0 10 20 30 40 50 60
7
total precipitation (in.)
Modeling OverviewModeling OverviewModel CategoriesModel Categories
Deterministic
C XC1 = XC2 = Y...
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Modeling OverviewModeling OverviewModel CategoriesModel Categories
ProbabilisticDistributions of 7Q10 Low Flows:
15
20
25
307Q
10 (cfs)
Kaweah River, 3 Rivers CA
Historical Data 7Q10 = 18 cfs
0
5
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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Risk of Lower 7Q10
A2 Climate Change B1 Climate Change Historical Distribution Bootstrapping
Modeling OverviewModeling OverviewModel CategoriesModel Categories
Probabilistic
a.) Modeled Exceedance Probability CDF:24-hour Storm Events
0 4
0.6
0.8
1
of e
xcee
danc
e
10 yr Post 10 yr Pre5 yr Post 5 yr Pre2 yr Post 2 yr PreAcute Standard (160.3) *
0
0.2
0.4
0 2000 4000 6000 8000 10000 12000
C (ug/l)
prob
abili
ty
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Modeling OverviewModeling OverviewModel Calibration and VerificationModel Calibration and Verification
1 6
Machado Lake Phosphorus
M-1 M-2 M-3 modeled
0 6
0.8
1.0
1.2
1.4
1.6
TP (m
g/l)
0.0
0.2
0.4
0.6
9/25/2007 1/3/2008 4/12/2008 7/21/200810/29/2008 2/6/2009 5/17/2009 8/25/2009 12/3/2009date
Modeling OverviewModeling OverviewModel SelectionModel Selection
Intended Use
Relative, Current Absolute, Current Relative, Future Absolute, Future
single param
multiple params
single param
multiple params
single param
multiple params
single param
multiple params
Model Complexity1D -> 3D
Simple, Empirical
Multi-Variate, Empirical
Lumped, Mechanistic
Distributed, Mechanistic
1D > 3D
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Modeling OverviewModeling OverviewModel SelectionModel Selection
Model ParameterizationModel Parameterization
Site Specific Measured Inputs
Internal Parameter Calibration
Internal Parameter Calibration + Verification
Estimated or Regional Measured Inputs
Modeling OverviewModeling OverviewModel SelectionModel Selection
Intended Use
Relative, Current Absolute, Current Relative, Future Absolute, Future
single param
multiple params
single param
multiple params
single param
multiple params
single param
multiple params
Model Complexity1D -> 3D
Simple, Empirical
Multi-Variate, Empirical
Lumped, Mechanistic
Distributed, Mechanistic
1D > 3D
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Modeling OverviewModeling OverviewModel SelectionModel Selection
Model ParameterizationModel Parameterization
Site Specific Measured Inputs
Internal Parameter Calibration
Internal Parameter Calibration + Verification
Estimated or Regional Measured Inputs
= high cost + high data requirements!
Modeling OverviewModeling OverviewModel SelectionModel Selection
Intended Use
Relative, Current Absolute, Current Relative, Future Absolute, Future
single param
multiple params
single param
multiple params
single param
multiple params
single param
multiple params
Model Complexity1D -> 3D
Simple, Empirical
Multi-Variate, Empirical
Lumped, Mechanistic
Distributed, Mechanistic
1D > 3D
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Modeling OverviewModeling OverviewModel SelectionModel Selection
Model ParameterizationModel Parameterization
Site Specific Measured Inputs
Internal Parameter Calibration
Internal Parameter Calibration + Verification
Estimated or Regional Measured Inputs
= low cost + medium data requirements!
Stream Water Quality ModelingStream Water Quality Modeling
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Stream Water Quality ModelingStream Water Quality ModelingSolute TransportSolute Transport
U, D1200
1600
2000
2400
trat
ion advection, dispersion
0
400
800
1200
0:20:00 0:30:00 0:40:00 0:50:00
time (min.)
conc
ent
Stream Water Quality ModelingStream Water Quality ModelingSolute TransportSolute Transport
CCQCA ∂∂∂∂ )()(LLCq
xCAD
xxCQ
tCA
+∂∂
∂∂
+∂
∂−=
∂∂ )()()(
QCQCCQ ni
ni
ni
ni
n −∂ 11)( Error ~ Δx
xQCQC
xCQ iiii
Δ=
∂∂ −− 11)( Error Δx
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Stream Water Quality ModelingStream Water Quality ModelingDissolved OxygenDissolved Oxygen
DISSOLVEDDISSOLVEDOXYGENOXYGEN
Stream Water Quality ModelingStream Water Quality ModelingDissolved OxygenDissolved Oxygen
HydraulicsHydraulics
ReRe--aerationaeration
DISSOLVEDDISSOLVEDOXYGENOXYGEN
SODSOD Plant / AlgaePlant / Algae
TemperatureTemperature
NutrientsNutrients
BOD/TKNBOD/TKNOxidationOxidation
Plant / Algae Plant / Algae Photosynthesis & Photosynthesis &
RespirationRespiration
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Stream Water Quality ModelingStream Water Quality ModelingDO, Nutrients, Plants (Eutrophication)DO, Nutrients, Plants (Eutrophication)
ModelsWASP = dynamicWASP = dynamicQUAL2E / QUAL2K = steady stateHSPF / WARMF = dynamic watershed WQ models with instream modules
http://www epa gov/ceampubl/swater/http://www.epa.gov/ceampubl/swater/
http://www.epa.gov/waterscience/basins/
http://www.epa.gov/ATHENS/wwqtsc/html/warmf.html
Stream Water Quality ModelingStream Water Quality ModelingDO, Nutrients, PlantsDO, Nutrients, Plants
Model Calibration
Typical calibration parameters:– Kinetic rates– SOD– Plant growth rates– Must have hydraulics/transport first!
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Stream Water Quality ModelingStream Water Quality ModelingPlantsPlants
Phytoplankton (floating algae)Larger rivers lakesLarger rivers, lakesChl a (mg/L)
Periphyton (attached algae)Smaller/shallower streamsChl a (mg/m2), Dry wt. (mg/m2)
Macrophytes (rooted plants)Shallower streams = emergentLarger rivers/lakes = submerged, floatingDry wt. (mg/m2)
Stream Water Quality ModelingStream Water Quality ModelingPlantsPlants
Phytoplankton
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Stream Water Quality ModelingStream Water Quality ModelingPlantsPlants
Periphyton
Stream Water Quality ModelingStream Water Quality ModelingPlantsPlants
Macrophytes
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Stream Water Quality ModelingStream Water Quality ModelingNitrogenNitrogen
NITROGEN CYCLEAIRAIR
PlantsPlants
WATERWATER
Nitrate (NO3
-)DissolvedOrganic N
ParticulateOrganic NAmmonia
(NH4+)
Nitrogen
TKNTKN
Nitrification/Nitrification/OxidationOxidation
SEDIMENTSSEDIMENTS
ParticulateNNitrate Pore Water
SRPPore WaterAmmonia
Pore WaterAmmonia
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NITROGEN CYCLEWATERWATER
SEDIMENTSSEDIMENTS
ParticulateNNitrate Pore Water
Ammonia
(Aerobic)(Aerobic)
DEEP SEDIMENTSDEEP SEDIMENTSN2 Gas
(Anaerobic)(Anaerobic)Nitrate Pore Water
Ammonia
DenitrificationDenitrification
Bacteria Bacteria in in StreamsStreams
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SourcesSources
WWTPs
Wildlife, CAFOs, AFOs
Septic Systems SSO/CSO
Sediment
SSO/CSO
OUTPUT(t t h)
InIn--stream Fate and Transport stream Fate and Transport –– Planktonic Planktonic BacteriaBacteria
• WWTPs• SSOs
INPUT (From Watershed)
Bacterial removal through:• Settling• Die-off
In-StreamINPUT(Point)
(to next reach)
• Sed-associated bacteria• Runoff
Wildlif• SSOs• CSOs• CAFOs
Die off
Addition of Bacteria from:• Regrowth
• Wildlife• Septic Systems• Boat Discharge
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Bacteria Survival InBacteria Survival In--StreamStreamFactor ResultSunlight/UV Increased UV leads to die-offRadiationTemperature Temperature outside growth range leads
to die-offSalinity High salinity leads to die-offNutrient Levels Suitable levels of nutrients encourage
bacteria growthSettling/ Adsorption
Reduces numbers of suspended bacteria, can increase bacteria in sediment
Typical DieTypical Die--off Rates off Rates
Location K (day-1)kteCC −Seine River 0.10 – 17.86Seine River 0.11 – 0.81
Houston 0.92 – 2.2Various 0.12 – 8.64
Laboratory 0.39 – 0.76
ot eCC =
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Lake Water Quality ModelingLake Water Quality Modeling
Lake Water Quality ModelingLake Water Quality Modeling
Key differences (compared to streams)Mixing > advection
– wind-induced diffusion– high residence times
2-D (vertical)
Sensitivity to surface fluxes:Sensitivity to surface fluxes:– sediments– water / atmosphere interface
Stratification
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Lake Water Quality ModelingLake Water Quality Modeling
Qin = CIA + baseflow
Cin = EMC, Cbase
Ph t l kt F(N P d V )
Qout = Qin
vS
[Chl a]
fd fp Evap
[N1]Qsup , Csup
kd
[P1]
Phytoplankton = F(N1, P1, d1, V1 )
Qrecirc
[N2] ,[P2] [N3],[P3]kd3
kd2
Linternal = D *AdzdC
d2
kdz
V2= ρ*d2*A
Lake Water Quality ModelingLake Water Quality Modeling
Stratification
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Temperature (oC)DO (mg/L)
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
met
ers)
3/13/2002
6/12/2002
9/25/2002
12/11/2002
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10 11 12
(met
ers)
( g )
9
10
11
12
13
14
15
16
Dep
th (m 9
10
11
12
13
14
15
16
Dep
th (
3/13/2002
6/12/2002
9/25/2002
12/11/2002
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Estuary and Bay Water Quality ModelingEstuary and Bay Water Quality Modeling
Estuary and Bay Water Quality ModelingEstuary and Bay Water Quality Modeling
Key Differences (compared to stream and lake modeling)
Hydrodynamics and solute transportHydrodynamics and solute transport– Tidal advection (flow) rather than gravity advection– Bi-directional– Cyclical– High dispersion
May need to couple more sophisticated hydrodynamic model with WQ model
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Estuary and Bay Water Quality ModelingEstuary and Bay Water Quality Modeling
Key Differences (compared to stream and lake modeling)
SalinitySalinity– Additional stratification effects
Depths and widths may require 2-D or 3-D models
Estuary and Bay Water Quality ModelingEstuary and Bay Water Quality Modeling
1
1.5
‐1
‐0.5
0
0.5
0 1 2 3 4 5 6 7
Q
‐1.5time
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Watershed Water Quality ModelingWatershed Water Quality Modeling
Watershed Water Quality ModelingWatershed Water Quality Modeling
Objectives:Source (load) quantification and identificationWatershed BMP assessmentLanduse / landscape changes
Key Differences (compared to water body modeling)
Dynamic hydrology -> dynamic water qualityDynamic hydrology > dynamic water qualityAdditional model parametersAdditional data requirementsImportance of sediment load
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Watershed Water Quality ModelingWatershed Water Quality Modeling
Hydrologic Modeling Hydrologic Modeling
Watershed Water Quality ModelingWatershed Water Quality Modeling
Mechanistic ModelingMechanistic Modeling
Wash-offBacteria loading fromwildlife, trash, etc.
Stor
age
Time
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Watershed Water Quality ModelingWatershed Water Quality Modeling
Empirical ModelingEmpirical ModelingSite 04 Sager Creek
Event 3 Stream Levels and P Samples
0.8
1
1.2
1.4
1.6
th (f
t)
levels samples
0
0.2
0.4
0.6
3/31/06 4/1/06 4/1/06 4/2/06 4/2/06 4/3/06 4/3/06 4/4/06 4/4/06 4/5/06
dept
date / time
EMC = Ltot/Vtot
Watershed Water Quality ModelingWatershed Water Quality Modeling0
2
45,000
6,000
Rainfall (in)
6
8
10
12
14
161 000
2,000
3,000
4,000
Flow
(cfs
)
18
200
1,000
Simulated Hydrograph Observed Hydrograph Observed Rainfall
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Watershed Water Quality ModelingWatershed Water Quality Modeling1.00
Simulated TP
Observed TP
0.50
0.75
hosp
horo
us (m
g/l)
0.00
0.25
Oct Mar Aug Jan Jun Nov Apr Sep Feb Jul Dec May Oct Mar Aug Jan Jun
Tota
l Ph
Questions and DiscussionQuestions and Discussion