  Monitoring water stage and discharge at hydrometric stations is essential for
flood characterization and prediction. Continuous measurement is feasible for
stage records, whereas discharge must be calculated, typically using a rating
curve. Several methods have been developed, such as surface velocity
measurement or rating curve methods. Nevertheless, hydrometric stations may be
influenced by tidal fluctuations, leading to transient flow conditions that can
disrupt the stage-discharge relation, complicating the accurate estimation of
discharge. In the case of a quasi-unsteady flow, the dynamic can be managed by
a relationship between water level, elevation, and discharge based on the
Manning-Strickler formula and measurements of water level and slope of the
waterline. However, in unsteady flow, when tidal effects are pronounced, these
types of relationships and their variations have proven to be less effective.
To capture the complex flow dynamics, including flow reversal, an approach via
a 1D hydrodynamic model is proposed. Here, model estimation refers to
estimating the posterior distribution of parameters and the structural error
model.To set up the model, the cross-sectional geometry, friction coefficient,
upstream discharge(s), and downstream water level are necessary. In
hydrodynamic modeling, the friction coefficients, often represented through a
set of Strickler coefficients, are the main calibration parameter, but manual
calibration is difficult due to spatial variations in roughness combined with
unsteady flow. Furthermore, understanding and quantifying uncertainties
associated with data and the model are an important step in the calibration
process. Therefore, automatic calibration of friction coefficients is proposed
through Bayesian inference.In terms of numerical tools, the 1D hydrodynamic
code used here is Mage, developed by INRAE, which solves the 1D Saint-Venant
equations for river flows and transients. However, the proposed method is not
specific to a given simulation code: it can be applied to any usual 1D
hydrodynamic code. Bayesian calibration is performed using the software BaM!
(Bayesian modeling: https://github.com/BaM-tools), which allows specifying
prior information on model parameters (in this case, friction coefficients) to
then estimate them with associated uncertainties, using observations themselves
with their uncertainties (not only water levels but also gauging campaigns).
