Rene TherrienLaval University, Quebec, Canada
NiCA Meeting May 31, 2011
HydroGeoSphereA Three-dimensional Numerical Model
Describing Fully-Integrated Subsurface andSurface Flow and Solute Transport
Integrated Physically-Based Modelling
• Attempt to account for all interactions between surface and subsurface flow regimes
• Conceptually superior to linked simulators or iteratively coupled simulators
Complex (more processes, highly nonlinear)
Challenges
Disparate time frames between (atmosphere) surface/subsurface flow and transport regimes, myriad of processesVery large unstructured grids, irregular topography, complex boundary conditions, surface properties & geological featuresStrong nonlinearities in governing equationsData availability and upscaling issues
Some Issues• How well can we represent all the relevant
processes in a scientifically plausible, physically-based manner?
• How big can we go in 3D, and over what time frames?
• Do we have the needed input data and, if not, how do we acquire it?
• What linkages should be made to other disciplines (atmospheric science, agriculture, geomorphology, biology, ecology, economics, policy & decision making…)?
Waterloo-Laval HydroGeoSphere Model(Group of Ed Sudicky)
• Physically-based, fully-integrated surface and subsurface flow
• 2D overland flow and solute transport on the land surface, and 3D variably-saturated flow and transport in the subsurface, including porous media, fractures, macropores, ET, etc.
• Can be executed in either Control-Volume Finite Element mode or Finite Difference mode.
• Sub-gridding, sub-timing and thermal transport were recently added.
• Parallelization of HGS completed.• Has been successfully applied to multiple spatial and
temporal scales of problems.• Mostly academic users
Flow Equations
Porous Medium (3D):Richards’ Equation
Surface Water Flow (2D):Diffusion Wave Equation
o oo o o o o
hd q d Qt
∂φΓ∂
−∇⋅ − ± =v
−∇⋅ + Γ ± =∑v s wm ex m
Sq Q
t∂θ
ω ω∂
Manning Equation (2D):
Darcy Equation:
( )2 3
1 2o
o ro o odq k d z
nΦ=− ∇ +v rv
( )rq K k zψ=− ⋅ ∇ +rv
,,,
o
w
s
m
r ro
o
ex o
dz
S
Kk kQ Q
n
ψ
θω
Γ Γ
Φ
==
==
=
=
==
=
==
=
r
v
r
pressure headwater depthelevationsaturation porositypm volume fraction
permeabilityrel. perm.source/sink rateexchange fluxes
roughness sw gradient
Flow Equations: Integrated Solution
os w
m mSq Qt
∂θω ω∂
−∇⋅ + ±Γ =vinteract via water exchange relationsfeed-back SW-GWconvergence difficulties reducedexchange relationships need explicit definition
o oo o
o o ohq Qddt
Γ ∂φ∂
−∇⋅ − ± =v
( )o o rso so od k K h hΓ = −
so
rso
Kk
=
=
surface/subsurface conductance coupling rel. perm./rill storage
Coupled Equations:
First-Order Exchange (head difference):
c
Transport Equations: Integrated Solution
[ ]s wm s w m s w p
o
ar
c
S RC S R C qC S D C R Ct
Q
∂θω θ λ ω θ∂
Ω
λ⎡ ⎤ ⎡ ⎤+ =−∇⋅ − ∇ +⎣ ⎦⎢ ⎥⎣ ⎦± +
vv
[ ]
o o o oo o o o s o o o o o o
o o o o cop o oar
h R C h R C q C D h Ct
h R C Q d
∂φ φ λ ψ φ∂φ λ Ω
⎡ ⎤+ = −∇⋅ − ∇⎣ ⎦
+ ± −
vv
( )o ups o o oC C CΩ Γ α= + −
Coupled Advection-Dispersion Equations:
Advective-dispersive Solute Exchange Flux (e.g.):
• interact via advective and diffusive transport processes
• feed-back SW-GW• distinct surface and
subsurface concentrations
• exchange relationships need explicit definition
Heat Transport Equations: Integrated Solution
• interact via convective and diffusive transport processes
• feed-back SW-GW• distinct surface and
subsurface temperatures
• exchange relationships need explicit definition
[ ]( )b bw w b b b oT
cT q c T k c D T Qt
∂ρ ρ ρ∂
Ω⎡ ⎤=−∇⋅ − + ∇ ± +⎢ ⎥⎣ ⎦
[ ]( )w w o oo w w o b o w w o o oTo o
c h T q c T k D c d T dQt
∂ρ ρ ρ∂
Ω= −∇⋅ − + ∇ ± −
( )o w w ups o o w w oc T c T TΩ ρ Γ α ρ= + −
Coupled Advection-Dispersion Equations:
Thermal Exchange Flux (e.g.):
Evapotranspiration• PET from empirical relationships (Penman-Monteith, Thornthwaite)• Interception storage
• Function of Leaf Area Index (LAI)• Infiltration
• After interception is full• Total PET first met from interception storage• Remaining PET from transpiration and evaporation
• Transpiration is a function of:• LAI• Moisture Content• Root Zone Distribution Function
• Evaporation is a function of:• Moisture Content• Evaporation Distribution Function
Second continuum
11
- Same input parameters as porous medium- Interaction with porous medium : Γd
- Example (Fractured clay till, Denmark)Porous medium equation : clay matrixSecond continuum : macropores
3D flow equation
Discrete fractures
12
2D Variably-saturated flow equation (modified Richards' equation) for fracture of aperture wf
Storage term
Darcy flux
Numerical formulationControl volume finite element method (CVFE)
Local conservation of massEfficient computation of Jacobian matrix for Newton-Raphson method (non-linear equations)Easy to modify advective flux weighting
upstream weightingflux limiter
Influence coefficient method for computing elemental matrices
avoids numerical integration (faster)allows easy switch to finite difference discretization
13
Discretization
• Not required to identify location of streams
• Discretization of topography to capture surface flow
Discretized equation
15
Simplified flow equation
- Discretized flow equation CVFE - Mass balance for volume associated to node i:
- LHS : Mass stored- RHS : Flow in/out of volume- Implicit time weighting - Element-wise assembly- λ : k at interface (upstream)- γij : K and element dimensions
Element types
16
- 3D Rectangular prisms (blocks), 8 nodes- 3D Triangular prisms, 6 nodes- Internal decomposition of prisms into tetrahedra (deformed meshes)- 2D rectangles and triangles-1D line elements- Finite element / finite difference switch (modify γij in discretized equation)
Superposition 3D/2D
17
For example, matrix node 2 has same coordinates as fracture node 1• Common approach: h and c are same in matrix and fracture (1 unknown)• Dual approach: h and c are different in matrix and fracture (2 unknowns)
FracturesPossible geometriesPossible geometries
Obstruction
h oh s
Retention
Flow zone
h d
0
HFlow depth
Volumestorage
Soil surface
Microtopography and Vegetation
Horizontal flow if water depth > hdSurface relative permeability kro = 0 at hd, kro = 1 at hd + h0SW-GW transfer term (krso) goes from 0 (soil surface) to 1 at hd
Sub-Catchment of Laurel Creek Watershed(17 km2)
Land Use
Soil Series
Hydrostratigraphy
Physical System Geometry
Total of 179740 nodes
Simulated vs. Observed Hydrograph
CalculatedObserved
Observed vs. Computed Drainage Network
Observed Drainage Network Computed Surface Water Depths
Duffins Creek Watershed286 km2 in areaHydro-eco concerns due to urban development
Geology and HydrogeologyBedrock shale: Whitby Formation (Late Ordovician)Quaternary sediments 0 m (absent) to 200 m thickEight hydrostratigraphic units including three aquifers
Discretization(700 000 nodes)
Calibration Results: Steady-State Subsurface Heads
Simulated hydraulic head (m)
Mea
sure
dhy
drau
liche
ad(m
)
50 100 150 200 250 300 35050
100
150
200
250
300
350 Oak Ridges MoraineThorncliffeScarborough
RMS error: 14 m
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Easting (m)
Nor
thin
g(m
)
640000 645000 650000 655000 660000
4850
000
4860
000
4870
000
4880
000
Lake Ontario
+ Well Screens in ORMWell Screens in Thorncliffe Formation
* Well screens in Scarborough Formation
Calibration Results: Steady-State Streamflows
Simulated stream flow (m /s)M
easu
red
stre
amflo
w(m
/s)
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
F
CB
P
EA
3
3
D
JN
G,I,O
Mean error: 0.0024 m3/s
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+
Easting (m)
Nor
thin
g(m
)
640000 645000 650000 655000 660000
4850
000
4860
000
4870
000
4880
000
Lake Ontario
G I J O N
F
D
C B
PA E
Surface Water Depths
Steady-state Surface Drainage Network & Surface/Subsurface Exchange Fluxes
Surface/Subsurface Exchange Fluxes
Transient Model: Hydrographs
Influence of Climate Change on Water Resources in Regional-Scale Watersheds: An example in the Grand River Watershed
Water Budget Parameter Value (mm/year)
Precipitation 930Evapotranspiration 605
Surface Flow Out of GRW 313.5Infiltration 465Exfiltration 170Recharge 186
Groundwater Flow Out of GRW ~ 0
Groundwater Pumping 11.5
6800 km2
Population:900 000
Layers
Wells
Calibration for Long-Term Averages
Surface Drainage NetworksSimulatedObserved
y = 1.0304xR2 = 0.9959
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Observed Flow (m3/s)
Cal
cula
ted
Flow
(m3 /s
)
Brantford
Galt
West Montrose
Stream Discharge
R² = 0.997
150
200
250
300
350
400
450
500
150 200 250 300 350 400 450 500Cal
cula
ted
Subs
urfa
ce H
ead
(m)
Observed Subsurface Head (m)
1:1 …
Subsurface Head
Synthetic Climate Change Scenarios
Scenario
Change in actual precipitation throughout
simulation, relative to 1960-1999 levels
1 -5%2 +5%3 +10%4 +15%5 +20%
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Dundalk
Marsville
Below Shand D
am
West M
ontrose
Galt
Brantford
Grand River Gauge Stations
Dis
char
ge (m
3 /s) Observed
1961 to 1999 average
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario Nodally-averaged change in depth-to-water table (m)
Base 0.01 +0.482 -0.363 -0.644 -0.885 -1.08
Scenario Recharge (mm/year)
Change relative to base case (mm/year)
Base 186 -1 176.5 -9.52 198 123 207 214 216.5 30.55 226 40
Scenario 1: Driest Scenario 5: Wettest
Depth to Water Table [m]: Driest vs. Wettest Scenarios
Drainage galleries
Meuse River
Geer River Basin
N
S
• Area = 465 km²
• Sub-catchment of the Meuse River
• Intensive agriculture (65% of the basin)
• Aquifer intensively exploited
→ Extraction of 30 millions m³/year for drinking water
(~600,000 people)
Impact of climate Change – Geer Basin (Goderniaux, PhD)
(up to 20 m)
(locally)
(from a few meters up to 70 m)
Quaternary Loess
Sands
Chalk
Impermeable clays
Flint conglomerate
Geology
Water exchanges between nodes
at each time step
SUBSURFACE DOMAIN
3D variably-saturated flow
(Richards' equation)
(10 000 nodes)
SURFACE DOMAIN
2D surface water flow
(1000 nodes)
Precipitations Actual ET• ET = f (PET, soil moisture, root depth,
evaporative depth, LAI, Canopy storage)
• Computed at each time step and node
Discretization - Parameterization
• Precipitation – PET
• Draining galeries – pumping wells
Surface parameters
• Soil map ↔ coupling coef.
• Land use map ↔ ET, friction coef.
• Hydrogeologic data
↔ Variably saturated properties
Subsurface parameters
Specified stresses
Discretization - Parameterization
Simulated and observed groundwater levels
Simulated and observed flow rates
Subsurface saturation
Water depth (Surface)
Calibration
Uncertainty related to the natural variability of the weather• Climate change scenarios from :
- 6 RCMs
- CO2 emission "Medium-High" (A2)
Monthly mean temperature change (°C) – 2070-2100
Mean monthly precipitation change (%) – 2070-2100
Weather
Generator
2010 2040 2070 2085
2010 2040 2070 2085
T
WL
August temperatures (RCAO_E)
February temperatures (RCAO_E)
August precipitations (RCAO_E)
February precipitations (RCAO_E)
• For the Geer basin :
- 100 climate change scenarios for each RCM
Uncertainty related to the natural variability of the weather
• Application of stochastic climate change scenarios as input of the Geer model
Evolution of groundwater levels
RCM :
Arpege_h
RCM :
RCAO_E
All 6 RCMs
Evolution of MEAN groundwater levels
Uncertainty related to the natural variability of the weather
• For the Geer basin hydrological model :
- 95 % confidence intervals around absolute predicted variables and predicted
decreases
- Calculated over 4 years of HIRHAM_H (2071-2100)
Absolute groundwater levels and 95 % confidence intervals
Change in groundwater levels and 95 % confidence intervals
Uncertainty related to calibration of hydrological model
Calibration
uncertainty
(95% conf. interval)
February
August
'Quantile Mapping Bias Correction'
(2071-2100)
'Weather Generator'
Stochastic scenarios (2085)
(95% conf. intervals)
Surface flow rates (m³/s)
Groundwater levels (m)
Summary of all uncertainty
(mm/yr)1002003004005006007008009001000150020003000
precipitation
Legend (m)< 2526 - 5051 - 100101 - 200201 - 300301 - 400401 - 500501 - 750751 - 1,0001,001 - 1,5001,501 - 2,0002,001 - 3,0003,001 - 5,0005,001 - 8,000> 8000
sediment thickness
Legendinland water bodiesAcrisolsCambisolsChernozemsPodzoluvisolsRendzinasFerralsolsGleysolsPhaeozemsLithosolsFluvisolsKastanozemsLuvisolsGreyzemsNitosolsHistosolsPodzolsArenosolsRegosolsSolonetzAndosolsRankersVertisolsPlanosolsXerosolsYermosolsSolonchaksMisc. Land Units
soil type
Legendinland water bodies> 75% crops> 75% forest> 75% pasture and browse> 75% barren and sparsely vegetated50 - 75% crops50 - 75% forest50 - 75% pasture and browse50 - 75% barren and sparsely vegetated> 50% artificial surfacemixed
land use
Legend (mm/yr)0 - 200201 - 400401 - 600601 - 800801 - 1,0001,001 - 1,2001,201 - 1,4001,401 - 1,6001,601 - 1,8001,801 - 2,0002,001 - 2,2002,201 - 2,4002,401 - 2,6002,601 - 2,8002,801 - 3,000
ETgeology
3D Simulations over the Canadian Landmass(10 000 000 km2, UWaterloo)
Continuous permafrostDiscontinuous permafrostUpper unconsolidated sediment
Lower unconsolidated sedimentSedimentary rockFractured basement rocksBasement rocks
HydroGeoSphere Model(ca. 1 800 000 elements,1 000 000 nodes)
Summary: Fully-integrated ModelSolves one system of discrete CFVE equations
Eliminates iteration between separate models or model components and need for “artificial” boundary conditions (e.g. seepage face BC)
Does not a priori assume rainfall-runoff generation mechanisms
Transport intimately linked to surface/subsurface hydrodynamics
Water and solutes not “lost” from system in fully-integrated modelling framework
Equations are highly nonlinear, computationally expensive
Variably-saturated flow : Saturation / relative permeability functions
Sub-timing (variable Δt for a single time step)
Uncertainties in process representation and quantification
Coupling surface / subsurface flow and transport
Important parameters (calibration)
Dealing with heterogeneity, spatio-temporal up-scaling issues (reach to catchment to basin scales)
Lumped approaches for small-scale features
Sub-gridding methods
Challenges
It is inevitable to use relatively large grid sizes when simulating at these large scales given the current level of computing hardware performance.Two legitimate questions rise:
What does the coarse-grid simulation result really represent?
i.e. same as the average of fine-grid simulation?How to maximize the similarity between the coarse-grid result and the fine-grid result?
Challenges
2
4
6
8
Spe
edup
(-)
2 4 6 8Number of CPU
Newton-RaphsonTotal
a)
Parallel HGS : Integrated surface and subsurface flow
• Maximum speedup : 6.5 (newton‐Raphson) and 4.8 (total)
• Parallel efficiency : 82 % (newton‐Raphson) and 60 %(total)
Multi-component reactive chemistry
Linking hydro(geo)logy and ecology with feedback
Linking with atmospheric models
Data issues
Management (amount)
Quality Assurance
Processing
Visualization
Applications : building a library of examples
Challenges
Monthly Water Balance
Month
Vol
umet
ricra
te(m
/s)
4 5 6 7 8 9 10 11 12-10
-5
0
5
10
15
20
25PrecipitationRunoffSubsurface storage changeSurface storage changeET
1986
Apr
il
May
June
July
Aug
.
Sep
t.
Oct
.
Nov
.
Dec
.
3
Month
4 5 6 7 8 9 10 11 12-10
-5
0
5
10
15
20
25PrecipitationRunoffSubsurface storage changeSurface storage changeET
1987
Apr
il
May
June
July
Aug
.
Sep
t.
Oct
.
Nov
.
Dec
.
