The CATchment HYdrology (CATHY) Model

Working Group:

Claudio Paniconi and Mauro SulisINRS-ETE, University of Quebec, Canada

Mario Putti and Matteo Camporese University of Padova, Italy

Stefano Orlandini, Giovanni Moretti, Maurizio Cingi and Alice CusiUniversity of Modena & Reggio Emilia, Italy

UNESCO-IHP Water Programme for Environmental Sustainability - WPA II

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

2

2( , )k h k L

Q Q Qc D c q h

t s s

( ) ( )( ) ( )w s rw w z sS K K S q ht

general storage term [1/L]: = SwSs + dSw/d)

Sw water saturation = /s [/] volumetric moisture content [L3/L3]s saturated moisture content [L3/L3]

Ss specific storage [1/L]

porosity (= s if no swelling/shrinking)

pressure head [L]t time [T]Ks saturated conductivity tensor [L/T]

Krw relative hydraulic conductivity [/]

z zero in x and y and 1 in z direction

z vertical coordinate +ve upward [L]qs subsurface equation coupling term

(more generally, source/sink term) [L3/L3T]

h ponding head (depth of water on surface of each cell) [L]

s hillslope/channel link coordinate [L]Q discharge along s [L3/T]ck kinematic wave celerity [L/T]

Dh hydraulic diffusivity [L2/T]

qL 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

(1)

(2)

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 and Moretti (2009, JGR)

Orlandini et al. (2003, WRR)

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)

bW aQ

fmY cQ

mU kQ

zfS tQ

ySk rQ

Parameterization of Stream Channel Geometry(Channels and Hillslope Rivulets)

at-a-station relationshipbW a Q

downstream relationshipbfW a Q

given frequency discharge, bankfull dischargewfQ u A

,1 bW W A Q

,1 ,

b w b b

s f f s sW A W A Q Q A A A

Orlandini and Rosso (1998, WRR)

Parameterization of Conductance Coefficients(Channels and Hillslope Rivulets)

at-a-station relationshipySk r Q

downstream relationshipyS fk r Q

given frequency discharge, bankfull dischargewfQ u A

,1 y

S Sk k A Q

,1 ,

y w y y

S S s f f s sk A k A Q Q A A A

Orlandini (2002, WRR)

Diffusion Wave Modeling: Mathematical Model

k k L

Q Qc c q

t s

k

dQc

d

2

2k h k L

Q Q Qc D c q

t s s

f fk

S Sc

Q

1cos

f

h

SWD

Q

Kinematic wave model Diffusion wave model

Diffusion Wave Modeling: Parameterization of the Drainage System

2 3 5 3 1 2 1 ,S f SQ k W S k n W P

2

2 4 3 10 3fS

QS

k W

2

4 32 10 3f

S

QS

k W Q

Gauckler-Manning-Strickler Equation

Incorporating the variationof stream channel geometry

Incorporating the variation of conductance coefficient and stream channel geometry

2

2 4 3 10 3f

S

QS

k Q W Q

Diffusion Wave Modeling: Constitutive Equations

5 1

1 23 1 2 3 2 1 2 3

1 2 3 3 1 2 3,1 ,1 y b y by b y b

S fQ k A W A S

2 1 13 1 2 4 3 2 1 2 4 3 3 1 2 4 3 15 2 35 1 2 3 5 1 2 3 10 1 2 3

5 1,1 ,1 ,1

3 1 2 3

y b y b y b y by b y b y b

k S fc k A W A S A Qy b

1 cos

2 1 2 3 ,1

b

h

f

QD

y b W A S

Flow Rating Curve

Kinematic Celerity

Hydraulic Diffusivity

Diffusion Wave Modeling: Muskingum-Cunge Method with Variable Parameters

1

2

2 1k

k

c t s XC

X c t s

2

2

2 1k

k

c t s XC

X c t s

3

2 1

2 1k

k

X c t sC

X c t s

4

2

2 1k

k

c tC

X c t s

1 1 11 1 2 3 1 4 1j j j j ji i i i LiQ C Q C Q C Q C q

Diffusion Wave Modeling: Muskingum-Cunge Method with Variable Parameters

1 2n kD c s X 1cos

fh

SWD

Q

1

2 cosf

k

SWX

c s Q

n hD D

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