Geoscience Reference
In-Depth Information
capability of the radar system to penetrate vegetation to the underlying water surface.
Given the radar design, both SWOT and AirSWOT are expected to penetrate vegetation
through canopy openings.
4 Inferring Remaining Unknown Variables Using DA
As noted above, no current or planned future satellite system is capable of measuring either
river bathymetry or discharge directly, and to determine discharge from space requires that
the river bathymetry and friction are known (see, for example, Smith
1997
; Bjerklie et al.
2003
). Discharge is a key variable for surface water science, for which we currently have
no globally consistent and comprehensive data. However, by combining dynamical
information on changing water level and flood extent derived from remote sensing with a
suitable hydraulic model, it may be possible to infer the unknown bathymetry and friction
and hence estimate discharge from space. Data assimilation provides the mathematical
framework for this analysis as it allows for optimal estimation of the unknown variables
given the observed data and the constraints provided by the physical laws encoded by the
model. To first order the problem of estimating, discharge from space can be illustrated by
the well-known Manning equation:
Q
¼
AR
2
=
3
S
1
=
2
f
ð
2
Þ
n
where Q is the discharge; A is the channel cross-sectional area; R is the hydraulic radius;
S
f
is the water surface slope; and n is the Manning resistance coefficient which describes
all the frictional losses. Clearly, only S
f
is observable from space, yet to estimate dis-
charge,wealsoneedtoknowA, R and n. Early research in this area showed that if either
frictionorbathymetrywasassumedtobeknown,itwasrelativelyeasytoestimatethe
remaining unknown variable (see, for example, Andreadis et al.
2007
;Durandetal.
2008
; Neal et al.
2009
; Biancamaria et al.
2011
;Yoonetal.
2012
). However, Eq.
2
clearly shows that A, R and n trade-off against each other, which complicates the joint
estimation problem. Joint estimation therefore requires considerably more dynamical
information to isolate the differing effects of bathymetry and friction on water level
dynamics. However, recent research (e.g., Lai and Monnier
2009
;Hostacheetal.
2010
;
Durand et al.
2010
, submitted) is beginning to show that such joint estimation may
indeed be possible because friction and bathymetry vary in distinctive and different ways
in space and affect the various terms in the Saint-Venant equation (Eq.
1
)indifferent
ways. Changing friction or bathymetry has different ''signature'' effects on water surface
height and slope change in time and space, and only a few combinations of both can fully
explain observations of floods with different wave speeds or water surface slopes.
Physically, water surface slopes respond only gradually to changing friction, whereas a
sudden change in channel capacity or bed slope can have a much more immediate effect
on the flow and wave propagation. Data assimilation methods can be developed to exploit
these differences and hence estimate unknown bathymetry and friction simultaneously
based only on repeated observations of water level and slope and an appropriate
dynamical model to obtain discharge. Key research questions are therefore exactly how
much water elevation and slope data are required and how much dynamical variation in
the observations is necessary to obtain a (near) unique solution.
