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

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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

kwaak@pangea.stanford.edukwaak@pangea.stanford.eduGet the code Get the code --> > www.inhm.orgwww.inhm.org

Keith Keith LoagueLoaguekeith@pangea.stanford.edukeith@pangea.stanford.edu

www.pangea.stanford.eduwww.pangea.stanford.edu/hydro//hydro/