Author(s): M. Mahdade; N. Le Moine; R. Moussa

Linked Author(s):

Keywords: River geometry; At-many-stations hydraulic geometry; Periodic approach; Pool-riffle sequences; Shallow water equations

Abstract: The geometry of river cross-sections is known to vary at the scale of a hydrographic network, with a strong dependence on drainage area, but also at much shorter scales within a reach (e.g. pool-riffle sequences). We propose a simplified, periodic approach to this high-frequency variability. The high frequency variability of river geometry is not easily taken into account in hydraulic models at the scale of a large hydrographic network, in many cases we have to make crude assumptions such as geometrical parameters correlated with large scale descriptors (e.g. upstream drainage area) as in DHG (downstream hydraulic geometry). However, a higher frequency variability is superimposed on these trends, with facies or alternating morphological units: shallow portions with fast flow velocity (e.g. riffles, or crossings between two meanders) alternate with deep portions, with low flow velocity (pools, e.g. the outside of the meander curves). Such sequences occur at intervals of 5 to 10 times the bank-full width. In addition, the irregularity of the stream geometry for a given flow rate (considered constant at the reach scale) generates a variability of the hydraulic variables (width, depth, hydraulic radius, velocities, the energy slope, etc.). Therefore, any geometric variability “smoothed out” by a uniform approach will come back in the form of a bias in effective friction parameters, thus reducing the robustness of the model. This variability represented in the rating curves at the scale of some morphological sequences, coined “At-Many-stations Hydraulic Geometry” (AMHG), is a new research topic. However, very few approaches based on the simple 1-D steady-state flow equation (backwater curve) have attempted to explain the emergence of AMHG and the longitudinal variability of rating curves at the reach scale. Nonetheless, it is likely that the AMHG is the result of a coevolution of geometrical bed parameters, and of an emerging covariance structure between these parameters at the reach scale. We can take advantage of this covariance structure to reduce the dimensionality of the bathymetric model, without smoothing out the high frequency variability as in the uniform approach. At the end, it can be represented by strictly periodic functions, which allows at the same time a quasi-analytical resolution of the backwater curve equation (Fourier transform, the resolution in the frequency domain, and inverse transform), sending upstream and downstream boundary conditions at ±∞. For this, we established our approach on the Shallow Water Equations (SWE) that requires data such as along-stream channel and floodplain bathymetry, friction parameters, and reach boundary conditions (typically, upstream inflow hydrograph and downstream rating curve). Generally, these data are difficult to recover at sufficient spatial resolution, but the use of the periodic resolution will decrease the system’s degrees of freedom (elimination of boundary conditions). In our case, we worked on a dataset of 17 reaches of small French rivers extensively studied. In our approach, a reach is modeled as a succession of pools and riffles in trapezoidal cross-sections, with periodic series for the thalweg depth anomaly, the bankfull width and the bankfull depth, the banks slope and floodplain lateral slope. Furthermore, we put in the interactions between the bank and floodplain using the “Debord” formulation. The mean spatial period of the sequences is obtained using wavelet analysis. The spectral treatment of AMHG on this dataset allowed us to reproduce a 1-D model of variability in rating curves at successive cross-sections by solving the SWE, with a periodic.

DOI: https://doi.org/10.3850/978-981-11-2731-1_235-cd

Year: 2018