integrated hydrology model (inhm): development, testing ...€¦ · integrated hydrology model...
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Integrated Hydrology Model (Integrated Hydrology Model (IInnHMHM):):Development, Testing, and Development, Testing, and
ApplicationsApplications
DYNAS Workshop ``Numerical Modeling for Hillslope Hydrology'' INDYNAS Workshop ``Numerical Modeling for Hillslope Hydrology'' INRIA RIA RocquencourtRocquencourt ---- 6 to 8 December 20046 to 8 December 2004
Joel VanderKwaak Joel VanderKwaak 1,21,2
Keith LoagueKeith Loague 22, Christopher Heppner, Christopher Heppner 22, Adrianne Carr, Adrianne Carr 22, , QihuaQihua Ran Ran 22, , Brian Brian EbelEbel 22, , Benjamin MirusBenjamin Mirus22
11 ARCADIS G&M, San Francisco, CaliforniaARCADIS G&M, San Francisco, California22 Stanford University, Stanford, CaliforniaStanford University, Stanford, California
The Real WorldThe Real World
OutlineOutline
MotivationMotivationNumerical ModelNumerical ModelLaboratory scale exampleLaboratory scale exampleField scale exampleField scale exampleSubSub--catchmentcatchment scale examplescale example
MotivationMotivationHydrologyHydrology
Spatial/temporal distribution of recharge and seepageSpatial/temporal distribution of recharge and seepageDynamics of variable source areas for stream flow generationDynamics of variable source areas for stream flow generation
Solute TransportSolute Transportsubsurface subsurface vsvs overland pathways (mining, agriculture, urban overland pathways (mining, agriculture, urban runoff, atmospheric deposition, etc) runoff, atmospheric deposition, etc) chemicallychemically--based hydrograph separationbased hydrograph separation
Landscape evolutionLandscape evolutionErosion/depositionErosion/depositionDam removalDam removalHillslopeHillslope stability, pore pressuresstability, pore pressuresHigh conductivity features (fractures, High conductivity features (fractures, macroporesmacropores))
Have to get the hydrology Have to get the hydrology ‘‘rightright’’ in order to simulate in order to simulate transport processestransport processes
Research PhilosophyResearch PhilosophyApply code to real problemsApply code to real problemsUse real data, avoid calibrationUse real data, avoid calibrationHonestly evaluate resultsHonestly evaluate resultsLearn what doesnLearn what doesn’’t work (and why)t work (and why)Experiment with alternative Experiment with alternative conceptualizationsconceptualizationsOpen source the code so others can test, Open source the code so others can test, learn and contribute (see www.inhm.org)learn and contribute (see www.inhm.org)
IInnHM HM -- Integrated Hydrology ModelIntegrated Hydrology Model(insert (insert namename here model)here model)
Numerical model of flow and transport in multiple interacting coNumerical model of flow and transport in multiple interacting continuantinuaRichards equation in subsurface (1d/2d/3d)Richards equation in subsurface (1d/2d/3d)
•• Optional dual continua to represent fractures/Optional dual continua to represent fractures/macroporesmacropores•• Optionally includes water/matrix compressibilityOptionally includes water/matrix compressibility•• LeverettLeverett scaling of characteristic relationshipsscaling of characteristic relationships
Diffusion wave equation on land surface (1d/2d)Diffusion wave equation on land surface (1d/2d)•• Include depression storage (immobile water)Include depression storage (immobile water)
AdvectionAdvection--dispersion equations (multiple species)dispersion equations (multiple species)•• SorptionSorption•• Chain decayChain decay•• Air phase partitioning and diffusionAir phase partitioning and diffusion
Robust, general and efficient solution methodsRobust, general and efficient solution methodsControl volume finite element with mixed element typesControl volume finite element with mixed element typesOptionally drop diagonal terms in finite elementsOptionally drop diagonal terms in finite elementsNodal properties (can be time variable)Nodal properties (can be time variable)Primary variable switching for flowPrimary variable switching for flowNonlinear flux limiters for transportNonlinear flux limiters for transportImplicit flow, Implicit/central transport, Implicit flow, Implicit/central transport, Optional adaptive implicit/explicit solutionOptional adaptive implicit/explicit solution
•• Dynamically partition equations, solve reduced systemDynamically partition equations, solve reduced systemAggressive adaptive time steppingAggressive adaptive time steppingNode based assemblyNode based assemblyFull Newton solution using numerical derivativesFull Newton solution using numerical derivativesEfficient iterative matrix solverEfficient iterative matrix solver
FirstFirst--order coupling relationshipsorder coupling relationshipsEach system of coupled nonlinear discrete equations solved simulEach system of coupled nonlinear discrete equations solved simultaneously taneously
Coupled ContinuaCoupled Continua
Water and SoluteExchange
Flow and Transporton Land Surface
SurfaceStorage
MacroporeStorage
Flow and Transportwithin Macropores
PorousMediumStorage
Flow and Transportwithin
Porous Medium
Porous MediumSource/Sink
SurfaceSource/Sink
MacroporeSource/Sink
Example Coupled MatrixExample Coupled Matrix
2
4
9
6
7
1
5
3
8
Surface Element
Porous Medium Elementq9d3xxxX9
q8d2xxxX8
q7d1xxxX7
q6h6xxxx6
q5=h5xxxxx5
q4h4xxxx4
q3h3Xxxxx3
q2h2Xxxxx2
q1h1Xxxxx1
987654321
Discrete Exchange Relationships Discrete Exchange Relationships
( )D D Dp s
e e es sp s p pQ C C Q−= Λ − =
( ) *pD
p
es ee e s
sp w w wss s
Q AS DA a
α φ τ Λ = +
Flow:
Transport:
( )p s
ee es sp s p pQ Qψ ψ −= Γ − =
e e zzw ssp rw p
w s
g Ak ka
ρµ
Γ = As: interface area
as: characteristicinteractiondistance
3D porous medium continuum
2D surface continuum(depth integrated)
First Order CouplingFirst Order CouplingReqiresReqires definition of interface flux functions. definition of interface flux functions.
1D Darcy equation1D Darcy equation1D advection1D advection--dispersion equationdispersion equation
Coupling coefficientsCoupling coefficientsConsistent with coupling used in dual subsurface continuaConsistent with coupling used in dual subsurface continuaLarge values make pressure head at land surface equal water deptLarge values make pressure head at land surface equal water depthhUpstream weight interface relative permeabilityUpstream weight interface relative permeabilityHarmonic weight interface saturationHarmonic weight interface saturationCoupling coefficients go to zero when there is no Coupling coefficients go to zero when there is no pondedponded waterwater
Our coupling coefficients functions of:Our coupling coefficients functions of:interface geometry (e.g. thickness and area)interface geometry (e.g. thickness and area)system state (e.g. saturation)system state (e.g. saturation)physical properties (e.g. permeability)physical properties (e.g. permeability)
Eliminates iteration between separate model components.Eliminates iteration between separate model components.Interface fluxes determined as part of solutionInterface fluxes determined as part of solution
Need to backNeed to back--calculate to get valuecalculate to get valueNot defined a prioriNot defined a prioriEvolve with spatially and temporally variable hydrodynamicsEvolve with spatially and temporally variable hydrodynamics
ExperimentalExperimental Surface FunctionsSurface Functions
min 1,max 0,rel s shψ ψ =
rw wk S≡
Relative Water Depth:
Pseudo-Saturation:
Pseudo-Relative Permeability:
ψs
hs
( )2 1 relw relS ψψ −=
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Relative Water Depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SurfaceSaturation
linearfunctional
Flow Boundary ConditionsFlow Boundary ConditionsTemporally and spatially variableTemporally and spatially variableImplemented as generic source/sink termImplemented as generic source/sink termMultiple boundary conditions can be simultaneously Multiple boundary conditions can be simultaneously activeactiveAll continuaAll continua
Specified flux (both rainfall and evaporation)Specified flux (both rainfall and evaporation)Specified head or water depthSpecified head or water depth
Subsurface continuaSubsurface continuaDrainageDrainageSpecified gradientSpecified gradientExtrapolated gradientExtrapolated gradientSeepageSeepage
Surface ContinuaSurface ContinuaCritical depthCritical depthTabulated depthTabulated depth--dischargedischarge
ImplementationImplementation
Modular, structured, extensibleModular, structured, extensibleFortran95Fortran95
Derived data typesDerived data typesDynamic memory managementDynamic memory managementModules defined by functionModules defined by functionPhysics isolated from numerical methodsPhysics isolated from numerical methods
Original development on Unix (Original development on Unix (SGiSGi, HP, IBM), HP, IBM)Development currently on Windows and LinuxDevelopment currently on Windows and LinuxExtending code to utilize potential of Linux clustersExtending code to utilize potential of Linux clusters
IInnHM ComponentsHM ComponentsInputInput
Finite element grid (internally or externally generated)Finite element grid (internally or externally generated)Physical constants and properties (can vary in time)Physical constants and properties (can vary in time)Boundary conditions (variable in time and space)Boundary conditions (variable in time and space)Solution parametersSolution parametersGenerates an HDF5 input file Generates an HDF5 input file
ModelModelReads HDF5 input fileReads HDF5 input fileSolves specified steady state or transient problemSolves specified steady state or transient problemWrites results to HDF5 data fileWrites results to HDF5 data file
Output Output Reads HDF5 input and data filesReads HDF5 input and data filesPerforms statistical analysesPerforms statistical analysesConverts and normalizes unitsConverts and normalizes unitsWrites visualization files (Writes visualization files (TecPlotTecPlot, GMS, etc), GMS, etc)
HDF5HDF5
General purpose library and file format for General purpose library and file format for storing and sharing scientific datastoring and sharing scientific data
C/C++/F95/Java interfacesC/C++/F95/Java interfaces
Efficient storage and I/OEfficient storage and I/OCross platform compatibleCross platform compatibleStructured and self describingStructured and self describingLarge and varied user communityLarge and varied user communityOpen source (free!) Open source (free!) http://hdf.ncsa.uiuc.edu/HDF5/http://hdf.ncsa.uiuc.edu/HDF5/
Illustrative Examples (Testing)Illustrative Examples (Testing)
Flow and transport at increasing spatial Flow and transport at increasing spatial and temporal scalesand temporal scales
Laboratory (Laboratory (‘‘GillhamGillham’’ box )box )Small field site (Borden)Small field site (Borden)Shallow slope 1Shallow slope 1stst--order order catchmentcatchment (R5)(R5)
Laboratory Scale TestingLaboratory Scale Testing
0 20 40 60 80 100 120 140(cm)
0
20
40
60
80
100
(cm)
MonitoringLocation
' Rainfall' for 20 min across land surface (4.3 cm/hour)Bromide Tracer
0 0.2 0.4 0.6 0.8 1Saturation
-40
-20
0
PressureHead(cm)
0 10 20Time (min)
0
20
40
60
80
100
Discharge(cm3 /min)
0
0.2
0.4
0.6
0.8
1
C/C
0DischargeC/C0
Finite Element MeshesFinite Element MeshesFine GridBase Case Grid
Coarse Grid
0 20 40 60 80 100 120 140
Distance (cm)
0
20
40
60
80
100
Elevation(cm)
Nodes: 3621Subsurface Elements: 7000Surface Elements: 70
0 20 40 60 80 100 120 140
Distance (cm)
0
20
40
60
80
100
Elevation(cm)
Nodes: 14241Subsurface Elements: 28000Surface Elements: 140
0 20 40 60 80 100 120 140
Distance (cm)
0
20
40
60
80
100
Elevation(cm)
Nodes: 936Subsurface Elements: 1750Surface Elements: 35
HydrographsHydrographs
0 5 10 15 20 25Time (minutes)
0
10
20
30
40
50
60
70
80
90
100
Discharge(cm3 /min)
Coarse GridRefined GridMeasured Base Case
Hydraulic HeadsHydraulic Heads
0 20 40 60 80 100 120 140(cm)
76
78
80
25 Minutes
7678
80
82
84
86
88
9092
94
9698
100102
100 Seconds
0
20
40
60
80
100
(cm)
78
80
82
84
86
88
90
9294
96
50 Seconds
0 20 40 60 80 100 120 140(cm)
0
20
40
60
80
100
(cm)
7880
82
84868890
92
94
96
98
100102
20 Minutes
Surface Water Surface Water
-3
-2
-1
D(log 10)
0
0.5
1
S
100 seconds
-3
-2
-1
D(log 10)
0
0.5
1
S
20 minutes
0 20 40 60 80 100 120 140(cm)
-3
-2
-1
D(log 10)
0
0.5
1
S
D (log10)S
25 minutes
-3
-2
-1D(log 10)
0
0.5
1
S
50 seconds
Refined GridMeasured
Coarse Grid
0 5 10 15 20 25Time (minutes)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
C/C
0
Base Case
Tracer ConcentrationsTracer Concentrations
Lab Scale ConclusionsLab Scale ConclusionsSimulation of coupled surfaceSimulation of coupled surface--subsurface hydrologic subsurface hydrologic response relatively easy.response relatively easy.Simulation of Simulation of conservativeconservative tracers relatively difficult.tracers relatively difficult.Surface tracer concentrations sensitive to Surface tracer concentrations sensitive to
11stst order coupling relationshiporder coupling relationshipDiscrete subsurface mixing volume.Discrete subsurface mixing volume.Likely moreLikely more……..
FutherFuther work:work:Analysis of coupling sensitivity to form of 1Analysis of coupling sensitivity to form of 1stst--order coupling.order coupling.Expansion of spatial scale and the physical meaning of Expansion of spatial scale and the physical meaning of parameters.parameters.
Borden Field ExperimentBorden Field Experiment
0
2
4
0
10
20
30
40
50
60
70
80
Distance(m
)
0 5 10 15
Distance (m)
43210
Elevation (m)
•• Rainfall containing a Rainfall containing a conservative tracer conservative tracer applied for 50 applied for 50 minutes at 2 cm/hrminutes at 2 cm/hr
•• Hydrologic response Hydrologic response observed and observed and measuredmeasured
•• Capillary fringe Capillary fringe intersects land intersects land surface along stream surface along stream axis (initial head axis (initial head about 22 cm below about 22 cm below stream)stream)
3
4
(m)
0
20
40
60
80
(m)
0 5 10 15
(m)
Lab Experiment(Abdul, 1985)
Borden Field Experiment(Abdul, 1985)
FieldField--Scale TestingScale Testing
FieldField--Scale TestingScale Testing
Simulate field experiment with two Simulate field experiment with two different finite element meshes:different finite element meshes:
dzdz == 2 cm (lab scale) for 1== 2 cm (lab scale) for 1stst 50 cm 50 cm dxdx, , dydy >> lab scale>> lab scale•• 11stst mesh == [20 mesh == [20 –– 50 cm]50 cm]•• 22ndnd mesh == [5 mesh == [5 –– 12 cm]12 cm]
All other parameters available measured All other parameters available measured or derived from lab experiment.or derived from lab experiment.
0
2
4Z
0
20
40
60
80
X
0 5 10 15
Y
0
2
4
Z
0
20
40
60
80
X
0 5 10 15
Y
Nodes :194184Subsurface Elements: 371140Surface Elements: 10604
Nodes :21952Subsurface Elements: 39765Surface Elements: 2651
Finite Element MeshesFinite Element Meshes
HydrographsHydrographs
0 25 50 75 100Time (min)
0
10
20
30
40
50
60
70
80
90
Discharge(L/min)
Simulated (coarse)
Measured
0 25 50 75 100Time (min)
0
10
20
30
40
50
60
70
80
90
Discharge(L/min)
Simulated (fine)
Tracer ConcentrationsTracer Concentrations
0 25 50 75 100Time (min)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
C/C
0
Simulated (fine)
0 25 50 75 100Time (min)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
C/C
0
Simulated (coarse)
Measured
Tracer Mass FluxTracer Mass Flux
Measured
0 25 50 75 100Time (min)
0
10
20
30
40
50
60
70
80
90
C/C
0
Simulated (fine)
0 25 50 75 100Time (min)
0
10
20
30
40
50
60
70
80
90
C/C
0
Simulated (coarse)
Field Scale ConclusionsField Scale ConclusionsHighly nonlinear hydrologic response (another Highly nonlinear hydrologic response (another presentation)presentation)Surface discharge fairly easy to simulate. Surface discharge fairly easy to simulate. Tracer concentrations in discharge water fairly Tracer concentrations in discharge water fairly difficult to simulate.difficult to simulate.Concentration discrepancy appears to be Concentration discrepancy appears to be greatest at low surface flows.greatest at low surface flows.Mass flux (Q*C) is simulated reasonably well. Mass flux (Q*C) is simulated reasonably well. Horizontal spatial Horizontal spatial discretizationdiscretization relevant, but relevant, but ‘‘coarsecoarse’’ mesh captured the essential physics.mesh captured the essential physics.
SubSub--CatchmentCatchment Scale testingScale testing
Borden Field Site
400
405
(m)
100200
300400
(m)0
100
200
300
400
(m)
R5 Catchment
R5 in the 80sR5 in the 80s
R5 TodayR5 Today
DataData
RunoffRunoff
390
400
410
100
200
300
400
Distance (m) 100
200
300
400
Distance
(m)400
403
4 05
402
395 400 405 410
Elevation(m)
Total Head
Event 68: Initial ConditionsEvent 68: Initial Conditions
R5 HydrographsR5 Hydrographs0
50
100
(mm/hr)
RainfallIntensity
Phase IIIPhase IIPhase ILVVL
Time (hours)
Streamflow(L/s)
20 22 24 260
50
100
150
200
250
Observed
390
400
410
100
200
300
400
Distance (m) 100
200
300
400
Distance
(m)400
403
4 05
402
395 400 405 410
Elevation(m)
Total Head
Event 68: Conditions at Peak DischargeEvent 68: Conditions at Peak Discharge
Example Coupled Response Example Coupled Response (animation)(animation)
(b) (c) (d)
(f) (g) (h)
Time (hours)
Streamflow(L/s)
20 22 24 260
20
40
60
80
100
120
140
160
b h
gc
d f
e
(a)
1
0.95
0.9
(e)
Saturation
Surface Saturation through TimeSurface Saturation through Time
Runoff GenerationRunoff Generation
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(a) (b) (c)
Exchange Rate (qe) / Rainfall Rate (qb)
0 1 2 3 4 5
Permeability (m2 x 1012)
R5 ConclusionsR5 ConclusionsUsed all measured dataUsed all measured dataGuessed at initial water table locationGuessed at initial water table locationActive rainfallActive rainfall--runoff mechanisms form a continua runoff mechanisms form a continua between infiltrationbetween infiltration--excess (Dunne) and rainfallexcess (Dunne) and rainfall--excess excess (Horton)(Horton)Contributing area is a hysteretic function of rainfallContributing area is a hysteretic function of rainfall--runoff historyrunoff historyHydrograph not perfect, but pretty goodHydrograph not perfect, but pretty goodLow flow simulated less accurately Low flow simulated less accurately Hydrologic response sensitive toHydrologic response sensitive to
representation of topographyrepresentation of topographyinitial conditionsinitial conditions
Continuous SimulationsContinuous Simulations
0 100 200 300Time (days)
100
200
300
400
500
Discharge(L/s)
Event 68
CatchmentCatchment Scale TestingScale Testing
0
100
200
300
400
(m)
0
2000
4000
(m)
40005000
60007000
(m)
R5 CatchmentMystery Catchment
Sediment TransportSediment Transport
Multiple suspended Multiple suspended ‘‘speciesspecies’’ on land on land surfacesurfaceSolves reduced system of transport Solves reduced system of transport equations utilizing solution to fully coupled equations utilizing solution to fully coupled flow problemflow problem
Sediment Transport Component TestSediment Transport Component Test
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000Time (seconds)
0
0.2
0.4
0.6
0.8
1
Dis
char
ge(m
3 /s)
0
10
20
30
40
50
60
70
80
90
100
110
Sed
imen
tDis
char
geR
ate
(kg/
s)
Water Discharge (m3/s)Sediment Discharge (kg/s)Rate (0.25 mm)Rate (0.05 mm)Rate (0.005 mm)
0
0.2
0.4
0.6
0.8
1
Dis
char
ge(m
3 /s)
0
10
20
30
40
50
60
70
80
90
100
110
Sed
imen
tDis
char
geR
ate
(kg/
s)
Water Discharge (m3/s)Sediment Discharge (kg/s)Rate (0.25 mm)Rate (0.05 mm)Rate (0.005 mm)
Kineros
InHM
Questions?Questions?Joel Joel VanderKwaakVanderKwaak
[email protected]@pangea.stanford.eduGet the code Get the code --> > www.inhm.orgwww.inhm.org
Keith Keith [email protected]@pangea.stanford.edu
www.pangea.stanford.eduwww.pangea.stanford.edu/hydro//hydro/