Observing Rivers with Varying Spatial Scales

Abstract:

The NASA/CNES Surface Water and Ocean Topography (SWOT) mission
will estimate global river discharge using remote sensing.
Synoptic remote sensing data extends in situ point measurements,
but, at any given point, is generally less accurate. We
address two questions: 1)What are the scales
at which river dynamics can be observed, given spatial sampling and
measurement noise characteristics? 2) Is there an equation
whose variables are the averaged hydraulic quantities
obtained by remote sensing, and which describes the dynamics
of spatially averaged rivers? We use calibrated hydraulic models to examine the power
spectra of the different terms in the momentum equation, and conclude
that the measurement of river slope sets
the scale at which rivers
can be observed. We introduce the reach-averaged
Saint-Venant equations, that involve only observable hydraulic
variations, and which parametrize within-reach variability with
a variability index that multiplies the friction coefficient and
leads to an increased "effective" friction coefficient. An exact expression
is derived for the increase in the effective friction coefficient,
and we propose an approximation that
requires only estimates of the hydraulic parameter variances. We
validate the results using a large set of hydraulic models and
find the approximated variability index is
most faithful when the river parameters
obey lognormal statistics. The effective
friction coefficient, which can vary from a few percent to more than
50% of the point friction coefficient, is proportional to the
river bed elevation variance and inversely proportional to the depth.
This has significant implications for estimating discharge from SWOT data.