Bathymetry reconstruction based on the zero-inertia shallow water approximation

Inference of effective river properties from remotely sensed observations of water surface

“…A high-order Runge-Kutta numerical scheme is a good candidate to solve accurately these systems of differential equations. Remark that the low Froude model has been used and inverted in [23] (and called the zero inertia shallow water equation).…”

“…1 km reach length). It is shown that the most complete physical model which allows to separate the bathymetry from the roughness coefficient is the low Froude model (the so called zero inertia SW in [23]). The inverse models built in this study tackle the question of flow representation given the scale of observation grid.…”

“…a single smooth bump) are identified from extremely dense measurements of water levels by inverting an explicit time-step scheme, while the roughness is supposed to be known. For the same kind of bathymetries, an analytical expression of the bathymetry is proposed in [23] in the case of one in-situ observation. This original analytical approach is revisited and re-analyzed in the present study.…”

“…As demonstrated below, this possibility can be very interesting in practice since it leads at the end to a more accurate inversion of A 0 ; K; Q ð Þ . The idea of bathymetry identification without roughness coefficient and based on vanishing advection terms has been introduced by [23]. The authors called the equations ''zero-inertia'' shallow water approximation (the present so-called low Froude model), and they obtained directly Eq.…”

“…(2.4)), below, which allows to calculate explicitly the bed bathymetry from free surface elevation data. Recall that in [23], the inverse problem is solved in two spatial dimensions using the method of the characteristics. The test cases considered are basic, with very smooth geometry and very dense observations of water surface elevation.…”