Comment on ”Can we distinguish Richards’ and
Boussinesq’s equations for hillslopes?: The Coweeta
experiment revisited” by T. S. Steenhuis et al.
Christine Michel
To cite this version:
Christine Michel. Comment on ”Can we distinguish Richards’ and Boussinesq’s equations for
hillslopes?: The Coweeta experiment revisited” by T. S. Steenhuis et al.. Water Resources
Research, American Geophysical Union, 1999, 35 (11), pp.3573-3573. .
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WATER
RESOURCES
RESEARCH,
VOL. 35, NO. 11, PAGE 3573, NOVEMBER
1999
Comment on "Can we distinguish Richards' and Boussinesq's
equations for hillslopes?: The Coweeta experiment revisited"
by T. S. Steenhuis et al.
Claude
Michel
Water Quality and HydrologyDivision,Cemagref,Antony, France
In their paper,Steenhuis
et al. [1999]showthat Boussinesq's Let V denotethe volumeof water remainingin the slope:V and Richards'equations,when appropriatelysimplified,yield Mo• - M, Vo - Mo•, and Q = dM/dt, then
one and the sameanalyticaldescriptionof the flow througha
dM
I/2
sloping shallow soil hillside. However, both models cannot
Q
=
dt
=
properly allow for the cumulativeoutflow as measuredduring
the Coweeta experiment. More surprisingly,when using a
From a lumpedpoint of view a quadraticreservoirbetter fits
more precisenumericalintegration,they get farther from the the data than the Darcy-derivedequations.It is interestingto
actual cumulative
curve.
The discrepancy
betweenpredictedand actualhydrographs
is wide and cannot easilybe explainedwithout rejectingthe
Darcy law. Yet the form of the hydrographis easyto describe
analytically.If M(t) is the cumulativedrainageandMo• is the
total drainage (same notationsas given in Steenhuiset al.
[1999]),the followingrelationshipbetter fits the actualcumulative outflowthan (14) or (22) of Steenhius
et al. [1999]:
note that Benturaand Michel [1997] showedthat a similar
conclusioncould be held for the Saint-Venant'sequation
which could be replaced,for a whole reach of channel,by a
quadraticreservoir(and an additionaltime lag). Consequently,
one may questionwhether all these facts do not support a
lumped approachof flow dynamicsat the hillslopescale.Is it
necessaryto revert to a nonlinear partial derivativeequation
that would allowone to derive,after numericalintegration,the
samesimplebottom-lineresult?
References
where z is a parameterthat couldbe equal to about32 hours. Bentura,P. L. F., and C. Michel, Flood routingin a wide channelwith
a quadraticlag-and-routemethod,Hydrol. Sci. J., 42(2), 169-189,
When derivingwith respectto time, one gets
1997.
Moo
dM
dt
Eliminatingt betweenthe two precedingequationsyields
aM
(Moo- M) 2
dt
,Moo
Steenhuis,T. S., J.-Y. Parlange,W. E. Sanford,A. Heilig, F. Stagnitti,
and M. F. Walter, Can we distinguishRichards'and Boussinesq's
equationsfor hillslopes?:The Coweetaexperimentrevisited,Water
Resour.Res.,35(2), 589-593, 1999.
C. Michel, Water Quality and HydrologyDivision, Cemagref,Parc
de Tourvoie, BP 44, 92163 Antony cedex,France. (claude.michel@
cemagref.fr)
(ReceivedMarch 31, 1999;revisedJuly 21, 1999;
acceptedJuly 23, 1999.)
Copyright1999 by the American GeophysicalUnion.
Paper number 1999WR900228.
0043-1397/99/1999 WR900228509.00
3573