Jérôme Monnier

An intercomparison of remote sensing river discharge estimation algorithms from measurements of river height, width, and slope

The Surface Water and Ocean Topography (SWOT) satellite mission planned for launch in 2020 will map river elevations and inundated area globally for rivers >100 m wide. In advance of this launch, we here evaluated the possibility of estimating discharge in ungauged rivers using synthetic, daily ‘‘remote sensing’’ measurements derived from hydraulic models corrupted with minimal observational errors. Five discharge algorithms were evaluated, as well as the median of the five, for 19 rivers spanning a range of hydraulic and geomorphic conditions. Reliance upon a priori information, and thus applicability to truly ungauged reaches, varied among algorithms: one algorithm employed only global limits on velocity and depth, while the other algorithms relied on globally available prior estimates of discharge. We found at least one algorithm able to estimate instantaneous discharge to within 35% relative root-mean-squared error (RRMSE) on 14/16 nonbraided rivers despite out-of-bank flows, multichannel planforms, and backwater effects. Moreover, we found RRMSE was often dominated by bias; the median standard deviation of relative nresiduals across the 16 nonbraided rivers was only 12.5%. SWOT discharge algorithm progress is therefore encouraging, yet future efforts should consider incorporating ancillary data or multialgorithm synergy to improve results.

Identification of equivalent topography in an open channel flow using Lagrangian data assimilation

We present a Lagrangian data assimilation experiment in an open channel flow above a broad-crested weir. The observations consist of trajectories of particles transported by the flow and extracted from a video film, in addition to classical water level measurements. However, the presence of vertical recirculations on both sides of the weir actually conducts to the identification of an equivalent topography corresponding to the lower limit of a surface jet. In addition, results on the identification of the Manning coefficient may allow to detect the presence of bottom recirculations.

Superposition of local zoom models and simultaneous calibration for 1D-2D shallow water flows

We address the problem of coupling 2D shallow water equations with 1D shallow water equations (St-Venant equations), as applied to river-floodplain flows. Mathematical coupling conditions are derived classicaly from the 3D Navier-Stokes equations by integrating over the vertical wet section, when overflowing occurs. It leads to extra source terms in the 1D equations. Next we assume to be in a variational data assimilation context, then the optimal control process allows to couple both models and assimilate data simultaneously (Joint Assimilation Coupling algorithms). Two different versions of JAC algorithms are presented and compared. In a numerical test case, we superimpose the local 2D model on the 1D global model. The results show the efficiency of the present simultaneous superposition-assimilation approach.

Shape Optimal Design Problem with Convective and Radiative Heat Transfer: Analysis and Implementation

We present a study of an optimal design problem for a coupled system, governed by a steady-state potential flow equation and a thermal equation taking into account radiative phenomena with multiple reflections. The state equation is a nonlinear integro-differential system. We seek to minimize a cost function, depending on the temperature, with respect to the domain of the equations. First, we consider an optimal design problem in an abstract framework and, with the help of the classical adjoint state method, give an expression of the cost function differential. Then, we apply this result in the two-dimensional case to the nonlinear integro-differential system considered. We prove the differentiability of the cost function, introduce the adjoint state equation, and give an expression of its exact differential. Then, we discretize the equations by a finite-element method and use a gradient-type algorithm to decrease the cost function. We present numerical results as applied to the automotive industry.

Hydraulic visibility: Using satellite altimetry to parameterize a hydraulic model of an ungauged reach of a braided river

What hydraulic information can be gained from remotely sensed observations of a river’s surface? In this study,we analyze the relationship between river bed undulations and water surfaces for an ungauged reach of the Xingu River, a first-order tributary of the Amazon river. This braided reach is crosscut more than 10 times by a ENVISAT (ENVironmental SATellite) track that extends over 100 km. Rating curves based on a modeled discharge series and altimetric measurements are used, including the zero-flow depth Z0 parameter, which describes river’s bathymetry. River widths are determined from JERS (Japanese Earth Ressources Satellite) images. Hydrodynamic laws predict that irregularities in the geometry of a river bed produce spatial and temporal variations in the water level, as well as in its slope. Observation of these changes is a goal of the Surface Water and Ocean Topography satellite mission, which has a final objective of determining river discharge. First, the concept of hydraulic visibility is introduced, and the seasonality of water surface slope is highlighted along with different flow regimes and reach behaviors. Then, we propose a new single-thread effective hydraulic approach for modeling braided rivers flows, based on the observation scales of current satellite altimetry. The effective hydraulic model is able to reproduce water surface elevations derived by satellite altimetry, and it shows that hydrodynamical signatures are more visible in areas where the river bed morphology varies significantly and for reaches with strong downstream control. The results of this study suggest that longitudinal variations of the slope might be an interesting criteria for the analysis of river segmentation into elementary reaches for the Surface Water Ocean Topography mission that will provide continuous measurements of the water surface elevations, the slopes, and the reach widths.

CONVECTIVE AND RADIATIVE THERMAL TRANSFER WITH MULTIPLE REFLECTIONS. ANALYSIS AND APPROXIMATION BY A FINITE ELEMENT METHOD

We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and twodimensional numerical results of thermal exchanges under a car bonnet are presented.

FREE CONVECTION WITH RADIATIVE THERMAL TRANSFER OF GREY BODIES: ANALYSIS AND APPROXIMATION BY FINITE ELEMENT METHODS

We study a steady-state free (or mixed) convection model in two- or three-dimensions of space, taking into account radiative thermal transfer of grey bodies separated by a nonparticipating media. The existence of a weak solution is proved and the uniqueness is obtained when the viscosity and thermal conductivity of the fluid are large enough. Then, we discretize the model using classical finite element schemes and prove in detail the existence, uniqueness and the convergence of the discrete solution (when the viscosity and the thermal conductivity are large enough and the step size is small enough).

Four-field finite element solver and sensitivities for quasi-Newtonian flows

A computationally efficient finite element algorithm for power-law fluid is elaborated in view of extensive direct and inverse simulations. We adopt a splitting technique to simplify the nonlinear structure of the fluids equations and derive a four-field saddle-point formulation for which we prove the existence of a solution. The resolution of the corresponding variational inequalities is based on an augmented Lagrangian method and a mixed finite element discretization. The resulting iterative solver proves to be fast and robust with low memory consumption. The time-saving provided by the algorithm compared to the standard algorithms of fixed point and Newton increases with the number of degrees of freedom and the nonlinearity of the problem. It is therefore well suited for the solution of large problems with a great number of elements and for corresponding adjoint-based computations. Bidimensional numerical experiments are performed on two realistic situations of gravity flows: an experimental viscoplast...