UNESCO-IHP Water Programme for Environmental Sustainability - WPA II
The CATchment HYdrology (CATHY) Model
Working Group:
Claudio Paniconi and Mauro Sulis
INRS-ETE, University of Quebec, Canada
Mario Putti and Matteo Camporese
University of Padova, Italy
Stefano Orlandini, Giovanni Moretti, Maurizio Cingi and Alice Cusi
University of Modena & Reggio Emilia, Italy
First “Climate Change...” Project Meeting, May 29 – June 4, 2009, Brazil
Context
Surface and subsurface waters are not
isolated components of the hydrologic system,
but interact in response to topographic, soil,
geologic, and climatic factors.
Groundwater seepage can take the dual role of
source and sink:
• Groundwater may seep out from shallow
aquifer and feed networks of irregular
channels.
• Surface water may seep back into the
ground, possibly depleting streams until they
run dry.
Context
The interaction of groundwater and surface flow is a key focus of interest for:
• Water resources management (under the effects of climate and land use and
demographic changes)
• Water quality (e.g., role hyporheic fluxes in aquatic habitats)
• Geomorphology (e.g., action of groundwater seepage on channel initiation)
A number of modeling tools and approaches have been developed for studying
coupled surface water-groundwater systems: Three-dimensional equation for
variably saturated subsurface flow, i.e., Richards equation, coupled with a one- or
two-dimensional approximation of the Saint-Venant equations for overland and
channel flow, represent the current state-of-the-art in catchment-aquifer models.
Outline
1. Model description:
•
Mathematical formulation
•
Numerical discretization
•
Surface–subsurface interactions
•
Surface flow conceptualization
2. Test cases and applications
3. Data Requirements
Model description: Mathematical formulation

 ( Sw )
    K s K rw ( Sw )(  z )   qs ( h)
t
Q
Q
 2Q
 ck
 Dh 2  ck qL (h, )
t
s
s

Sw

s
Ss
f

t
Ks
Krw
z
general storage term [1/L]:
 = SwSs + f(dSw/d)
water saturation = /s [/]
volumetric moisture content [L3/L3]
saturated moisture content [L3/L3]
specific storage [1/L]
porosity (= s if no swelling/shrinking)
pressure head [L]
time [T]
saturated conductivity tensor [L/T]
relative hydraulic conductivity [/]
zero in x and y and 1 in z direction
z
qs
h
s
Q
ck
Dh
qL
(1)
(2)
vertical coordinate +ve upward [L]
subsurface equation coupling term
(more generally, source/sink
term) [L3/L3T]
ponding head (depth of water on
surface of each cell) [L]
hillslope/channel link coordinate [L]
discharge along s [L3/T]
kinematic wave celerity [L/T]
hydraulic diffusivity [L2/T]
surface equation coupling term
(overland flow rate) [L3/LT]
(1) Paniconi & Wood, Water Resour. Res., 29(6), 1993 ; Paniconi & Putti, Water Resour. Res., 30(12), 1994
(2) Orlandini & Rosso, J. Hydrologic Engrg., ASCE, 1(3), 1996 ; Orlandini & Rosso, Water Resour. Res., 34(8), 1998
(1)+(2) Bixio et al., CMWR Proceedings, 2000 ; Putti & Paniconi, CMWR Proceedings, 2004
Model description: Numerical discretization
Surface:
• PDE of the kinematic wave solved by a
finite difference (FD) scheme
• Numerical dispersion arising from the
truncation error of the scheme is used to
simulate the physical dispersion
• Unconditional stability reached by
matching numerical and physical
diffusivities through the temporal
weighting factor used to discretize the
kinematic wave model
Model description: Numerical discretization
Subsurface:
• PDE solved by a three-dimensional finite element (FE)
spatial integrator and by a weighted finite difference (FD),
i.e. Euler or Crank-Nicolson, scheme in time
• Nonlinearity arising from the storage (Sw) and
conductivity Krw(Sw) terms are handled via a Picard or
Newton linearization scheme
• Time varying boundary conditions: prescribed head
(Dirichlet type) or flux (Neumann type), atmospheric fluxes,
source/sink terms, and seepage faces
Model description: Surface–subsurface interactions
The coupling between the land surface and the subsurface is handled by an
automatic boundary condition (BC) switching algorithm acting on the source/sink
terms qs(h) and qL(h,).
The coupling term is computed as the balance between atmospheric forcing
(rainfall and potential evaporation) and the amount of water that can actually
infiltrate or exfiltrate the soil.
The switching check is done surface node by surface node in order to account for
soil and topographic variability.
The switching check is done at each time the surface equation is solved
(according to the values of ponding heads at the surface) and at each subsurface
time or iteration.
Model description: Surface–subsurface interactions
Unified Flow Direction Algorithm
The mathematical formulation implemented is based on the use of:

Triangular facets introduced by Tarboton (1997, WRR)

Path-based analysis introduced by Orlandini et al. (2003, WRR)

Plan curvature computation introduced by Zevenbergen and Thorne (1987, ESPL)
Unified Flow Direction Algorithm
Orlandini et al. (2003, WRR)
Orlandini and Moretti (2009, JGR)
Unified Flow Direction Algorithm
Orlandini and Moretti (2009, WRR)
Validation Using Contour Elevation Data
Moretti and Orlandini (2008, WRR)
Drainage Basin and Drainage Slope
Orlandini and Moretti (2009, WRR)
Prediction of the Drainage Network
Hydraulic Geometry (Leopold and Maddock, 1953)
W  a Qb
Ym  cQ f
U  k Qm
S f  t Qz
kS  r Q y
Parameterization of Stream Channel Geometry
(Channels and Hillslope Rivulets)
b
W  a Q

( at-a-station relationship 
W  aQbf ( downstream relationship 
Q f  u Aw ( given frequency discharge, bankfull discharge 
W  W ( A,1 Qb
W ( A,1  W ( As , Q f  Q f ( As 
Orlandini and Rosso (1998, WRR)
 b
(A
As 
w( bb
Parameterization of Conductance Coefficients
(Channels and Hillslope Rivulets)
kS  r Q y ( at-a-station relationship 
kS  rQ fy ( downstream relationship 
Q f  u Aw ( given frequency discharge, bankfull discharge 
k S  k S ( A,1 Q
y
kS ( A,1  kS ( As , Q f  Q f ( As 
Orlandini (2002, WRR)
 y
(A
As 
w( y  y 
Diffusion Wave Modeling: Mathematical Model
Kinematic wave model
Q
Q
 ck
 ck qL
t
s
ck 
dQ
d
Diffusion wave model
Q
Q
 2Q
 ck
 Dh 2  ck qL
t
s
s
S f
ck  

S f
Q
 W S f 
Dh  1 

cos


Q


Diffusion Wave Modeling:
Parameterization of the Drainage System
Gauckler-Manning-Strickler Equation
Q  kS W 2 3 5 3 S f 1 2
Sf 
Incorporating the variation
of stream channel geometry
Sf 
Q2
kS W (Q 
2
4 3

10 3
( kS  1 n ,W  P 
Q2
k S 2 W 4 3 10 3
Incorporating the variation
of conductance coefficient and
stream channel geometry
Sf 
Q2
kS (Q  W (Q 
2
4 3
10 3
Diffusion Wave Modeling: Constitutive Equations
Flow Rating Curve
Q  k S ( A,1
1
1 y  2 3b
W ( A,1
2

3 (1 y  2 3b

5
3 (1 y  2 3b
Sf
1
2 (1 y  2 3b
Kinematic Celerity
2
1 
3 (12 y  4 3b
2 (12 y  4 3b
3 (12 y  4 3b 
 1 y  b 
5
1

5






5
1

y

2
3
b
5
1

y

2
3
b
10
1

y

2
3
b
 W ( A,1 (
 S f ( A,1 (
Q  2 3 
ck 
kS ( A,1 (
3 (1  y  2 3 b
Hydraulic Diffusivity
Dh 
Q
1 b 
cos 
2 (1  y   2 3 b  W ( A,1 S f
1
Diffusion Wave Modeling:
Muskingum-Cunge Method with Variable Parameters
Qi j 11  C1 Qi j 1  C2 Qi j  C3 Qi j 1  C4 qLij11
C1 
ck ( t s   2 X
2 (1  X   ck ( t s 
ck ( t s   2 X
C2 
2 (1  X   ck ( t s 
2 (1  X   ck ( t s 
C3 
2 (1  X   ck ( t s 
C4 
2 ck t
2 (1  X   ck ( t s 
Diffusion Wave Modeling:
Muskingum-Cunge Method with Variable Parameters
Dn  ck s (1 2  X 
Dn  Dh
 W S f 
Dh  1 

cos


Q


S f
1
W
X 
2 ck s cos  Q
The Muskingum-Cunge method with variable parameters is:
• Unconditionally stable (Dn = Dh).
• Accurate for Courant numbers not too far from 1 (∆s ≈ ck ∆t).
• Independent of structural parameters ∆s and ∆t.
(Cunge, 1969, JHR; Ponce, 1986, JHE; Orlandini and Rosso, 1996, JHE)
Test cases and applications
1D sloping plane with homogeneous subsurface*
 Sloping plane catchment (400 m x 320 m)
 S0=0.0005 (slope)
 x=y=80 m (spatial discretization)
 Ts = 300 min (simulation time)
 Tr = 200 min (rainfall time)
 Td = 100 min (recession time)
 qr = 20 mm/h (rainfall intensity)
Saturation excess (Dunnian process):
 Ksat=41.7 mm/h
 Water table heights: 0.5 and 1.0 m
Excess infiltration (Hortonian process):
 Water table height: 1.0 m
 Ksat=0.417 and 4.17 mm/h
* Results in agreement with Kollet & Maxwell, Adv. Water. Res., 29, 2006.
Test cases and applications: Saturation excess
Test cases and applications: Infiltration excess
Test cases and applications
Application of CATHY model in a climate
change frameork to the 720 km2 des Anglais
catchment located in southern Quebec
- Data provided by the Canadian Regional
Climate Model (CRCM V4.2.0)
- Precipitation (rain, snow)
- Temperature (max, min)
- Data provided for a 45-km horizontal
grid-size mesh with a daily temporal
resolution:
- Model calibrated to distributed (water
table) and aggregated (flow rate) data
Test cases and applications
Test cases and applications
Data Requirements: Catchment Properties
Grid-based or contour-based digital elevation models
Soil retention characteristics
• residual and saturated water content
• pore-size distribution index
• saturated soil matrix potential
• hydraulic conductivity
Geologic stratigraphy, bedrock depth
Land cover and use
Channel network
• cartographic blue lines
• cross sections
• roughness coefficients
Man-made hydraulic structures
Data Requirements: Hydrologic Variables
Precipitation
• rainfall
• occult precipitation
• snow
Evaporative demand (estimated using the Penman-Monteith equation)
• solar radiation
• air humidity
• wind speed
• air temperature
• barometric pressure
Streamflow
Soil moisture
Water table depth