- Standard deviation: 5 meters, accommodating variation in channel depth across different rivers (up to ~30 m of flow depth) S (slope): - Treated as observed input data from SWOT; uncertainties in slope measurements can be incorporated into the likelihood model or modeled as error terms. These prior distributions are crucial, particularly when dealing with limited or noisy datasets, as they influence the convergence and stability of the estimation process. 4.2.1.3 Posterior estimation and uncertainty quantification: The final step is the estimation of the posterior distributions of the parameters using Markov Chain Monte Carlo (MCMC) sampling techniques.
These distributions provide both point estimates (e.g., posterior means or medians) and credible intervals (e.g., 95% intervals) for each parameter, offering a probabilistic interpretation of the rating curve and its uncertainty. For this study, the No-U-Turn Sampler (NUTS) algorithm (Hoffman et al., 2014) was selected due to its efficiency in high-dimensional spaces and its adaptive step-size tuning. This advanced variant of the Hamiltonian Monte Carlo (HMC) method ensures faster convergence and better exploration of the parameter space compared to traditional algorithms like Metropolis-Hastings (Robert et al., 2004). 4.2.2 WSE data type 4.2.2.1 WSE merged-mission:
When the water surface elevation (WSE) time series is constructed by merging data from multiple altimetry missions, the rating curve computation is restricted to the calibration period, defined as the last two-thirds parts of the time window where both WSE and discharge data are available (see previous section for details). This period is selected to ensure greater stability in the rating relationship and to avoid early data with potentially lower quality or non-stationary behavior. If enough paired WSE–Q observations are available within this calibration period, Method 1 (see section 4.2.3) is applied. If not, Method 2 (see section 4.2.4) is used as a fallback.
This approach ensures that the resulting rating curve is based on a coherent, hydraulically consistent subset of the data, improving the reliability of the discharge estimates during the selected period. 4.2.2.2 WSE mono-mission: In contrast, when WSE data are treated mission by mission, as implemented in Phase 2 of the project, all available common data between each altimetry mission and the discharge series are used, without restricting to a specific calibration window. This approach acknowledges the sensor-specific nature of each mission and allows for the full exploitation of available paired observations.
For each mission (e.g., Topex/Poseidon, Jason-2, Envisat, Sentinel-3), a separate rating curve is derived. Depending on data availability, either direct pairing (Method 1) or quantile matching (Method 2) is applied individually per mission. This mission-specific strategy offers several advantages: Reduced inter-mission bias, by accounting for the unique characteristics of each sensor; Improved temporal resolution, by leveraging the full extent of available WSE–Q pairs for each mission; 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. 15/31