Explicit uncertainty quantification, with posterior distributions computed separately for each mission. This refined treatment enhances both the accuracy and continuity of discharge estimates across the altimetric record. 4.2.3 Method 1 – Bayesian estimation using overlapping dataset – preferred approach When a temporal overlap exists between the altimetric water surface elevation (WSE) time series and discharge data (either in situ or simulated), a Bayesian approach can be applied to the paired WSE–Q observations to derive a rating curve.
This method is applicable regardless of whether the WSE data comes from a single altimetry mission (WSE mono-mission) or a merged multi-mission time series (WSE- merged), provided that enough synchronous data pairs are available. To define the sufficient number of synchronous observations needed to compute the rating curve, we base the requirement on the ability to represent seasonal coverage. Specifically, we require data spanning at least 10 distinct months, with each month containing at least 3 points. This criterion ensures that the rating curve is based on a dataset with adequate temporal coverage and density to reliably capture seasonal variability.
The rating curve parameters (commonly denoted as a , b , and z0 ) are estimated using Markov Chain Monte Carlo (MCMC) sampling, allowing the derivation of predictive discharge values along with associated confidence intervals. This approach assumes the WSE measurement location is hydraulically consistent with the discharge reference (e.g., colocated or in a reach with stable morphology), and that river conditions remain relatively stationary during the calibration period.
This method has been widely adopted in recent literature (e.g., Garambois et al., 2017; Domeneghetti et al., 2014; Paris et al., 2022) and is well suited to rivers without major non-stationarities such as ice cover or abrupt morphological changes. However, in real-world applications, river dynamics may not always support the direct application of this method due to seasonal ice effects or non-uniform flow behaviors. To address these situations, we define three specific cases for the construction of the rating curve: 4.2.3.1 Case 1 – General rivers In this case, a standard Bayesian rating curve is computed directly from all available overlapping WSE–Q pairs.
No filtering of the time series is needed, and the full dataset is assumed representative of the hydraulic behavior. This case applies to rivers without significant freeze/thaw effects or strong interannual variability in seasonal patterns. 4.2.3.2 Case 2 – Partial ice cover rivers In some river systems, particularly in temperate cold climates, ice cover appears only intermittently, typically during winter months (e.g., December to March), and varies from year to year. This irregular freezing can create outliers or distortions in the WSE–Q relationship during those periods. To mitigate this, the overlapping dataset is filtered using a temperature threshold:
WSE–Q pairs associated with monthly mean air temperatures below 0°C are excluded. For instance, at the Near- Brookings station, the river was frozen in some winters, producing anomalies in the WSE–Q scatter plot. 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. 16/31