CONTROL OF

COUPLING MASS BALANCE ERROR IN THE CATHY MODEL

Department   of   Engineering   “Enzo   Ferrari,”   University   of  Modena  and  Reggio  Emilia    

Marcello Fiorentini Stefano Orlandini, Claudio Paniconi

Workshop on Coupled Hydrological Modeling

23-24 September 2015 (Padua)

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

CATchment Hydrology (CATHY) model University of Modena and Reggio Emilia, University of Padua, University of Quebec

Subsurface water flow •  3D solver of Richards equation for variably saturated porous media •  pressure head based formulation

Surface water flow propagation •  quasi-2D (path-based) surface routing

Coupling algorithm •  node-to-cell and cell-to-node interpolation algorithm •  sequential iterative coupling strategy (Dagès et al., 2012)

•  Develop criteria to measure the

sources of error in the model

•  Run systematic tests to assess

model error

•  Propose improvements (e.g.,

information passing and time

stepping schemes)

Objective:

Explore the nature of mass balance errors in a coupled distributed hydrological

model (CATHY)

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Mass balance errors

•  Subsurface error ( )

•  Surface error ( )

•  Coupling error ( )

)1()1()1( +++ +Δ−= kssw

kssw

kssw VSε

)1()1()1()1( ++++ −+Δ−= kout

ksw

ksw

ksw VVSε

)1()1()1()1()1( +++++ Δ−Δ−−= kssw

ksw

kout

ka

k SSVQε

sswε

swε

cε

)1()1()1()1( ++++ −−= ksw

kssw

kkc εεεε

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Dimensionless indices

•  Saturation index (SI)

•  Degree of coupling index (CI)

b

sat

AASI =

exf

SAexf

SA

VV

VVCI

+

+=

inf

inf

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Case studies

•  Sloping plane (Sulis et. al., 2010)

•  Tilted v-catchment (Sulis et. al., 2010)

•  Enza River drainage basin

•  Atmospheric forcing (step functions)

•  Hortonian effect

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Case studies

•  Sloping plane

•  Tilted v-catchment

•  Enza River drainage basin

•  Atmospheric forcing (step functions) •  Hortonian effect •  Dimensionless indices

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Sloping plane •  Sensitivity of subsurface and coupling error to time step size •  Sensitivity of surface error to mesh size

Sensitivity of mass balance errors to recession limb

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

⎪⎩

⎪⎨

⎧

≥+Δ

<≤Δ

<−Δ

=Δ +

2)(

21)(

1)(

)1(

,,

,

ititatmititittititstm

tk

m

k

kr

k

( )( )( )

( )⎪⎩

⎪⎨

⎧

≥+Δ−

<≤Δ−

<−Δ−

=Δ +

2)()(

21)()(

1)()(

)1(

,,,1min,

ititatWmititittWm

ititstWmt

kkCIm

kkCIm

kkCIr

k

)1(

)()( 1

+−= k

kkCI CI

CIW

Heuristic time step size control

Normalized variation of the degree of coupling index

Modified time step size control

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

•  interpolation of exchange fluxes

•  surface water propagation

•  cell water balance

•  reconstruction of ponding heads

)()( kL

celltonodeks qq ⎯⎯⎯⎯ →⎯ −−

)1()1()1( +−−++ ⎯⎯⎯⎯ →⎯→ knodetocellkksw hhS

sqQIdtdS

LΔ+−=

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Interpolation exchange fluxes

•  geometric interpolation

•  new interpolation algorithm

⎪⎩

⎪⎨

⎧

=

>Δ= ∑

=

0,0

0,41

),(

),(4

1

),()(),(

ik

ik

jj

jkswiik

L

S

SwQsq )(S

jjj NNw =

∑=Δ

=4

1

),()(

),(

41

j

jkswi

ikL Q

sq

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

CATHY modifications: •  original code (O) •  modified time step control strategy (TC) •  new node-to-cell interpolation algorithm (IA) •  combination between TC and IA (IT)

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

CATHY modifications: •  original code (O) •  modified time step control strategy (TC) •  new node-to-cell interpolation algorithm (IA) •  combination between TC and IA (IT)

Results: •  Reduction of surface error (up to 97%) •  Faster recession limbs

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -

Conclusion

•  Sources of mass balance errors in CATHY were analyzed •  Global indices were presented to describe the hydrologic response of water basins

•  Modified algorithms to control the time step size were presented •  A new interpolation algorithm to pass exchange fluxes from surface to subsurface compartment was introduced

•  Mesh size with local refinements will be investigated

•  Application to real water basins

Workshop on Coupled Hydrological Modeling

- Control of Coupling Mass Balance Error in the CATHY model -