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 -
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