Abstract
Is it possible to estimate river discharge from satellite measurement of river surface variables (width L, water level Z, surface slope Is, surface velocity Vs) without any in situ measurement ? Current or planned satellite observation techniques in the hydrology-hydraulic domain are limited to the measurement of surface variables such as river width L (optical and SAR imagery), water level Z (radar and Lidar altimetry), river surface longitudinal slope Is (cross-track interferometry) and surface velocity Vs (along-track interferometry). On the opposite, river bottom parameters such as river bottom height (Zb), river bottom longitudinal slope (Ib), Manning coefficient (n), vertical velocity profile coefficient (α the ratio between mean water velocity and surface velocity), that are key data for discharge estimate and modeling, cannot be measured by satellite. They require in situ measurement (Zb, Ib, α) and model calibration (n). We present here a method to derive river bottom parameters from satellite measured river surface variables in the absence of any in situ measurement. This will then allow us to estimate river discharge for any set of surface variables. The method relies on a set of hydraulic hypothesis (for instance rectangular section, constant Manning coefficient n and constant velocity profile coefficient α). It consists of solving an equality constraint between two formulations linking the river discharge Q to the surface variables and the unknown parameters (Q1 and Q2 obtained from the mass conservation equation and the energy conservation equation): Q1=L.α.Vs.h Q2=L.h^(5/3).Is^(1/2) .[n^2+g^(-1).h^(1/3).(Is-Ib)] where h=Z-Zb Given a river section, estimating the river bottom parameters (α, Zb, Ib, K) is achieved by using a set of surface variables (L, Z, Is, Vs)i=1 to N, measured on this section at various times ti throughout the hydrological cycle, and by determining the set of river bottom parameters that minimizes a deviation criteria between (Q1)i and (Q2)i. This minimization is achieved by iterative or direct methods, depending on the type of criteria and on additional hypothesis (ex. a uniform regime hypothesis leads to an analytical solution). Several simulations have shown the efficiency of theses methods on exact simulated data set (i.e. for which (Q1)i=(Q2)i). We have assessed the robustness of these methods to measurement noise on river surface variables. We proposed several modifications to increase this robustness and the ability to provide acceptable river discharge estimates (error