4.2 Bayesian-based Rating Curve (RC) estimation The derivation of rating curves from altimetric water surface elevation (WSE) and in situ or simulated discharge (Q) relies on a Bayesian framework, which allows for robust parameter estimation while accounting for uncertainty (Figure 3). Figure 3: Rating curve computation methodology 4.2.1 Bayesian approach The Bayesian method is a robust statistical approach used for constructing a rating curve, frequently applied in hydrology when the goal is to estimate unknown parameters from observed data, while considering their associated uncertainty (Gelman et al., 2013). The core of the method relies on Bayes’ theorem: (Eq.1):
P(θ D) = P(D) P(D θ) P(θ) Eq.1 Here: P(θ D) is the posterior probability distribution of the model parameters θ, which are the parameters of the rating curve we aim to estimate. P(D θ) is the likelihood of observing the data D, given a specific set of parameters θ, usually based on a probabilistic model. P(θ) is the prior probability distribution of the parameters, which incorporates existing knowledge or assumptions. P(D) is the marginal likelihood of the data, serving as a normalizing constant to ensure the posterior is a valid probability distribution. According to this, the estimation of the rating curve using the Bayesian method involves several steps: D.3 River Discharge ATBD.
Reference: RD_CCI-0006-ATBD - Issue 2.0 – 31/07/2025 Open/Public © 2019 CLS. All rights reserved. Proprietary and Confidential. 13/31