Hydraulic visibility and effective cross sections based on hydrodynamical modeling of flow lines gained by satellite altimetry

Abstract:

Hydrodynamic laws predict that irregularities in a river bed geometry produce spatial and temporal variations in the water level, hence in its slope. Conversely, observation of these changes is a goal of the SWOT mission with the determination of the discharge as a final objective. In this study, we analyse the relationship between river bed undulations and water surface for an ungauged reach of the Xingu river, a first order tributary of the Amazon river. It is crosscut more than 10 times by a single ENVISAT track over a hundred of km. We have determined time series of water levelsat each of these crossings, called virtual stations (VS), hence slopes of the flow line. Using the discharge series computed by Paiva et al. (2013) between 1998 and 2009, Paris et al. (submitted) determined at each VS a rating curve relating these simulated discharge with the ENVISAT height series. One parameter of these rating curves is the zero-flow depth $Z_0$. We show that it is possible to explain the spatial and temporal variations of the water surface slope in terms of hydrodynamical response of the longitudinal changes of the river bed geometry given by the successive values of $Z_0$. Our experiment is based on an effective, single thread representation of a braided river, realistic values for the Manning coefficient and river widths picked up on JERS images. This study confirms that simulated flow lines are consistent with water surface elevations (WSE) and slopes gained by satellite altimetry. Hydrodynamical signatures are more visible where the river bed geometry varies significantly, and for reaches with a strong downstream control. Therefore, this study suggests that the longitudinal variations of the slope might be an interesting criteria for the question of river segmentation into elementary reaches for the SWOT mission which will provide continuous measurements of the water surface elevation, the slope and the reach width.