Scale Effects in Large Scale Watershed Modeling
Mustafa M. Aral and Orhan Gunduz
Multimedia Environmental Simulations LaboratorySchool of Civil and Environmental Engineering
Georgia Institute of TechnologyAtlanta, GA USA
Precipitation
2-D Overland Flow Model
1-D Channel Flow Model
1-D UnsaturatedZone Model
2-D SaturatedZone Model
SCHEMATIC OF AN INTEGRATED SCHEMATIC OF AN INTEGRATED WATERSHED MODELWATERSHED MODEL
COMPLEXITIES.........COMPLEXITIES.........
MultiMulti--pathway flow and contaminant pathway flow and contaminant transport problem.transport problem.Integrated modeling of all pathways is the Integrated modeling of all pathways is the key.key.Each process pathway has its own Each process pathway has its own characteristic scale.characteristic scale.What should be the optimal scale of a What should be the optimal scale of a fully integrated model?fully integrated model?
MODELING TOOLSMODELING TOOLS
Lumped parameter modelsLumped parameter models
Distributed parameter modelsDistributed parameter models
MAP ALGEBRAMAP ALGEBRA
Precipitation data map
Runoff data map
0
10
20
30
40
50
60
70
Precipitation
RUNOFF
Regional Response Curve
DEM data Precipitation data
Land use map
Concentrationmap
Accumulated load
Function
Function
Function
Groundwaterdata
Lumped Par. Models
Runoff
WHAT IS A SCALE?WHAT IS A SCALE?
Spatial or temporal dimensions at Spatial or temporal dimensions at which entities, patterns, and which entities, patterns, and processes can be observed and processes can be observed and characterized to capture the characterized to capture the important details of a important details of a hydrologic/hydrologic/hydrogeologichydrogeologic process.process.
SCALINGSCALING
The transfer of data or information The transfer of data or information across scales or linking subacross scales or linking sub--process process models through a unified scale is models through a unified scale is referred to as referred to as ““scaling.scaling.””
FRAME OF REFERENCEFRAME OF REFERENCE
Absolute and Relative frame of Absolute and Relative frame of referencereference
Precipitation
2-D Overland Flow Model
1-D Channel Flow Model
2-D SaturatedZone Model
1-D UnsaturatedZone Model
SCALE EFFECTSSCALE EFFECTS
Heterogeneity.Heterogeneity.
SubSub--process scales.process scales.
Nonlinearity.Nonlinearity.
SCALING PROBLEMSSCALING PROBLEMS
When largeWhen large--scale models are used to scale models are used to predict smallpredict small--scale events, or when smallscale events, or when small--scale models are used to predict largescale models are used to predict large--scale events, problems may arise.scale events, problems may arise.
Problems also arise when integrated Problems also arise when integrated models are used across scales.models are used across scales.
FUNCTIONAL SCALEFUNCTIONAL SCALE
At what spatial and temporal scale At what spatial and temporal scale does the final model performs does the final model performs optimally; and,optimally; and,
What scale should be selected to What scale should be selected to implement the final integrated implement the final integrated model? model?
SUBSUB--PROCESSESPROCESSES
Integrated river channel flow and groundwater flow.
Integrated overland flow, unsaturated and saturated groundwater flow.
Integrated watershed model.
COUPLED SURFACE WATER AND COUPLED SURFACE WATER AND GROUNDWATER FLOW MODELGROUNDWATER FLOW MODEL
0)(=−
∂∂
+∂+∂ q
xQ
tAAs oc
0)/( 2
=+⎟⎠⎞
⎜⎝⎛ ++∂∂
+∂
∂+
∂∂ LSS
xhgA
xAQ
tQs
efrm β
( ) ( )t
hSIQ
yh
Kzhyx
hKzh
xg
y
n
kw
gybg
gxbg
w
k ∂
∂=+∑+⎥
⎦
⎤⎢⎣
⎡∂
∂−
∂∂
+⎥⎦
⎤⎢⎣
⎡∂
∂−
∂∂
=1
Channel flow
Groundwater flow
Interaction parameterbetween two domains
Key parameters of interest
zbDatum
hg
hr
mr
zr
AQUIFER
Impervious Layer
RIVER
wr
COUPLING OVER THE INTERFACECOUPLING OVER THE INTERFACE
Type-3 boundary condition of the groundwater flow model couples with the lateral inflow/outflow term in the stream flow equation
q
?
Analysis domain
Groundwater flow discretizationChannel network
Channel flow discretization
COUPLED SYSTEMCOUPLED SYSTEM
2-Dgroundwaterdomain elements
1-Driver domain elements
River nodeGroundwater node
DISCRETIZATION OF DOMAINDISCRETIZATION OF DOMAIN
APPLICATIONAPPLICATION
Simulation scenarios:
• Two set of runs are done to simulate:lateral flow from stream to groundwater and from groundwater to streamTime lag between the timing of stream flow peak and groundwater head peakFlow reversal conditions
RUN-1: Lateral flow towards groundwater flow domainRUN-2: Lateral flow towards stream flow domain
Groundwater flow modelGroundwater flow model
• Initial conditions: RUN-1: hg = 32 m
RUN-2: hg = 35 m
APPLICATIONAPPLICATION
• Boundary conditions:
No flux boundary, q = 0
No flux boundary, q = 0
Fixed head boundaryRUN-1: h = 32 mRUN-2: h = 35 m
Fixed head boundaryRUN-1: h = 32 mRUN-2: h = 35 m
Head-dependent boundary
APPLICATIONAPPLICATIONBoundary and Initial Conditions:
Stream flow modelStream flow model
• Upstream BC: Trapezoidal discharge hydrograph
• Initial conditions: Uniform flow discharge Q = 100cms Uniform flow depth d = 3.57m
• Downstream BC: Single-valued rating curve that maps the discharge to its uniform flow depth
t (days)
Q (cms)
10
100
350
11
River DischargeGroundwater HeadRiver Stage
9/1/97 0:00 9/7/97 0:00 9/13/97 0:00 9/19/97 0:00 9/25/97 0:00 10/1/97 0:00Time
30
32
34
36
38
Gro
undw
ater
Hea
d an
d R
iver
Sta
ge (m
)
0
100
200
300
400
500
River D
ischarge atUpstream
Boundary
(cms)
-2000 -1000 0 1000 2000Distance from River Centerline (m)
31
32
33
34
35
Gro
undw
ater
Hea
d (m
)
t=0 dayst=5 dayst=10 dayst=15 dayst=20 dayst=25 dayst=30 days
River DischargeGroundwater HeadRiver Stage
9/1/97 0:00 9/7/97 0:00 9/13/97 0:00 9/19/97 0:00 9/25/97 0:00 10/1/97 0:00Time
30
32
34
36
38
Gro
undw
ater
Hea
d an
d R
iver
Sta
ge (m
)
0
100
200
300
400
500
River D
ischarge atUpstream
Boundary
(cms)
-2000 -1000 0 1000 2000Distance from River Centerline (m)
34
34.4
34.8
35.2
35.6
36
Gro
undw
ater
Hea
d (m
)
t=0 dayst=5 dayst=10 dayst=15 dayst=20 dayst=25 dayst=30 days
Soil surface
Groundwater table
SaturatedFlow Zone
UnsaturatedFlow Zone
OverlandFlow Zone Overland flow surface
Impervious layer
Note: Figure not to scale
Key parameters of interest
o o oox oy
h h hK K R It x x y y
⎛ ⎞∂ ∂ ∂∂ ∂⎛ ⎞= + + −⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠
( ) ( ) IQyh
zhKyx
hzhK
xth
Sw
k
n
kw
gbggy
gbggx
gy +∑+⎟⎟
⎠
⎞⎜⎜⎝
⎛∂
∂−
∂∂
+⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂−
∂∂
=∂
∂=1
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ +∂∂
∂∂
=∂∂
+∂∂ 1s z
Kztt
SS uwψθψ
COUPLED OVERLAND FLOW AND COUPLED OVERLAND FLOW AND SAT/UNSAT GROUNDWATER MODELSAT/UNSAT GROUNDWATER MODEL
2-D
2-D
1-D
INTEGRATED MODELINTEGRATED MODEL
Two dimensional finite element modeling
One dimensional finite difference modeling
Two dimensional finite element modeling
Dynamicwater table
Staticground surface
Imperviousstrataz
yx
2-D Overland flowdiscretization
2-D Saturatedgroundwater flowdiscretization
1-D Unsaturatedgroundwater flow discretization
OVERLAND, UNSATURATED and SATURATED OVERLAND, UNSATURATED and SATURATED GROUNDWATER MODEL STRUCTUREGROUNDWATER MODEL STRUCTURE
COUPLING OVER INTERFACESCOUPLING OVER INTERFACES
• At the ground surface, overland flow and unsaturated zone models are coupled via the infiltration flux.
• Infiltration flux becomes a sink/source term in overland flow model.
• The top boundary condition for the unsaturated column depends on the presence of overland flow.
Present Not present
Head condition Flux condition
APPLICATIONAPPLICATIONSimulation scenarios:
• Response of clay and sand soils to a two-peaked precipitation event to simulate:
Response of overland flow generation to different soil typesResponse of groundwater recharge to different soil typesResponse of unsaturated column moisture migration to intermittent rainfallResponse of groundwater levels to arbitrary precipitation events over different soilsInteractions between different pathways
RUN-1: Clay soilRUN-2: Sand soil
APPLICATIONAPPLICATIONPhysical Setup:
• 40 m wide X 500 m long hypothetical rectangular plot0 < x < 500 m and 0 < y < 40 m
• Uniform slope in x-direction, Sox = 0.001 m/m• No slope in y-direction, Soy = 0.0 m/m• Essentially one-dimensional flow• Response to a two-peaked precipitation event:
0 2000 4000 6000Time (sec)
0
2E-005
4E-005
6E-005
8E-005
0.0001
Rai
nfal
l Rat
e (m
/s)
RESULTSRESULTS –– Overland flow depth time seriesOverland flow depth time series
0 4000 8000 12000 16000 20000Time (sec)
0
0.04
0.08
0.12
0.16
Ove
rland
Flo
w D
epth
(m)
CLAY SOIL
Node 13Node 123Node 243
0 4000 8000 12000 16000 20000Time (sec)
0
0.02
0.04
0.06
0.08
0.1
Ove
rland
Flo
w D
epth
(m)
SANDY SOIL
RESULTS RESULTS –– Groundwater head time seriesGroundwater head time series
0 4000 8000 12000 16000 20000Time (sec)
89.2
89.6
90
90.4
90.8
GW
hea
d (m
)
SANDY SOIL
Node 13Node 123Node 243
0 4000 8000 12000 16000 20000Time (sec)
89.2
89.6
90
90.4
90.8
GW
hea
d (m
)
CLAY SOIL
RESULTSRESULTS –– Unsaturated zone moisture Unsaturated zone moisture distributiondistribution
-0.6 -0.4 -0.2 0 0.2Pressure Head (m)
89.2
89.6
90
90.4
90.8
Elevation
(m)
NODE 243
Both soils, t=0secSandy soil, t=9000sec Clay soil, t=9000secSandy soil, t=18000secClay soil, t=18000sec
-0.6 -0.4 -0.2 0 0.2Pressure Head (m)
89.2
89.6
90
90.4
90.8
91.2
Elevation
(m)
NODE 13
SCALES OF IMPORTANCESCALES OF IMPORTANCE
10103 - 1010610103 - 10106Saturated GW Saturated GW zonezone
10102 - 1010510103 - 10106River Channel River Channel flowflow
0.1 0.1 -- 1010210 10 -- 10104Overland flowOverland flow
0.1 0.1 -- 101020.01 0.01 -- 1010Unsaturated Unsaturated GW zoneGW zone
Time (sec)Time (sec)Space (cm)Space (cm)
HYBRID MODELS ARE THEHYBRID MODELS ARE THE
SOLUTION TO INTEGRATEDSOLUTION TO INTEGRATED
WATERSHED MODELING WATERSHED MODELING SYSTEMSSYSTEMS
APPLICATION:APPLICATION:
Analysis of Coastal Georgia EcosystemStressors Using GIS Integrated RemotelySensed Imagery and Modeling:A Pilot Study for Lower Altamaha River Basin
http://groups.ce.gatech.edu/Research/MESL/research/altamaha/index.htm
Georgia Sea Grant College Program of the National Sea Grant Program.
LOWER OCMULGEE
UPPER OCMULGEEUPPER OCONEE
OHOOPEE
ALTAMAHA
LOWER OCONEE
LITTLE OCMULGEE
0 200 400 Kilometers
ALTAMAHA APPLICATIONALTAMAHA APPLICATION
ALTAMAHA RIVER SYSTEMData Required
• Channel slopes, bottom elevations,cross-section top width vs depth data
• Roughness coefficients• Discharge hydrographs at upstream BCs• Rating curve at downstream exit point• Groundwater BCs data• Unconfined aquifer thickness data• Aquifer conductivity data• Infiltration data• Well data• River bottom sediment conductivity
and thickness data
Data Available
•Topography data
•Gage discharge data
•Precipitation data
•Cross-section data at bridges
BASIN REPRESENTATIONBASIN REPRESENTATIONfor LUMPED PARAMETER PROCESESfor LUMPED PARAMETER PROCESES
Land discretizationLand discretizationBASINS automatic delineation toolBASINS automatic delineation toolNational Hydrographic Dataset (NHD) reach National Hydrographic Dataset (NHD) reach file and Digital Elevation Model (DEM) data file and Digital Elevation Model (DEM) data 89 sub89 sub--watershedswatersheds352 PERLN352 PERLN30 IMPLND30 IMPLND
Basins RepresentationBasins Representation
Land discretizationLand discretizationLand UseLand Use
11.411.472,63172,631Mixed Forest LandMixed Forest Land
0.30.32,1252,125Barren LandBarren Land
%%Area (acres)Area (acres)Land UseLand Use
1.71.710,77610,776Urban or BuildUrban or Build--up Land up Land
30.730.7196,084196,084Cropland and Pasture Cropland and Pasture
44.644.6285,147285,147Evergreen Forest LandEvergreen Forest Land
100100639,272639,272TOTALTOTAL
10.510.567,34567,345Forested WetlandsForested Wetlands
0.80.85,1645,164WaterWater
Meteorological DataMeteorological DataPrecipitation (PREC)Precipitation (PREC)
Stations: Stations: JesupJesup and Dublinand DublinFill in missing data Fill in missing data –– Normal Ratio Method Normal Ratio Method JesupJesup →→ JacksonvilleJacksonville--SavannahSavannah--DublinDublinDublin Dublin →→ MaconMacon
Potential Potential EvapotranspirationEvapotranspiration (PETINP)(PETINP)JesupJesup
Potential Evaporation (POTEV)Potential Evaporation (POTEV)JesupJesup
AltamahaRiver
OhoopeeRiver
USGS 02225000Baxley, GA
USGS 02225500Reidsville, GA
USGS 02226000Doctortown, GA
ALTAMAHA RIVER SYSTEMALTAMAHA RIVER SYSTEM
0
50000
100000
150000
11/14/84 8/11/87 5/7/90 1/31/93 10/28/95 7/24/98 4/19/01
0
10000
20000
30000
11/14/84 8/11/87 5/7/90 1/31/93 10/28/95 7/24/98 4/19/01
0
50000
100000
150000
11/14/84 08/11/87 05/07/90 01/31/93 10/28/95 07/24/98 04/19/01
Ohoopee River at Reidsville, GAUSGS 02223500
AltamahaRiver at Baxley, GAUSGS 02225000
Altamaha River at Doctortown, GAUSGS 02226000
GW CROSS SECTIONGW CROSS SECTION
-1200 -800 -400 0 400 800 1200Distance from river centerline (m)
20
22
24
26
28
Gro
undw
ater
hea
d (m
)t=0dayst=35days
CONCLUSIONSCONCLUSIONS
Order of importance of the subOrder of importance of the sub--process;process;
Domain of importance;Domain of importance;
Functional scales; and,Functional scales; and,
Hybrid modeling concepts Hybrid modeling concepts
CONCLUSIONSCONCLUSIONS
Selection of the smallest scale in an Selection of the smallest scale in an integrated model as functional scale is not integrated model as functional scale is not possible.possible.
Hybrid modeling approach is necessary.Hybrid modeling approach is necessary.
Functional scale based on .....Functional scale based on .....
ACKNOWLEDGEMENTS
This research is partly sponsored by the Georgia Sea Grant College Program.
We would like to express our gratitude to Dr. Mac RawsonDr. Mac Rawson, Director of Georgia Sea Grant College Program for his continuous support throughout this study.
For additional information or For additional information or questions, you may contact:questions, you may contact:
M. M. Aral: [email protected]://groups.ce.gatech.edu/Research/MESL/
MESLMESLMESL