Given the mean values and standard deviations (σ) for each parameter, the uncertainty in discharge (δQ) due to uncertainties in these parameters can be computed as Eq.7 if the slope value is unknow otherwise as Eq.8: Eq.7 Eq.8 Where, σa, σb, σz0, σs and σWSE correspond to the standard deviations of parameters a, b, z0, S and WSE respectively. The standard deviations for a, b, and z0 will be determined using the Bayesian approach through the MCMC algorithms (see section 4.2.1). The standard deviation for the WSE will be, initially, consistent across all stations and for each mission. This value will later be adjusted through updates during the validation process.
The standard deviation for the slope will be define as the standard deviation per month over the 2 years of available data. This formula uses the standard deviations as measures of uncertainty in each parameter and calculates the overall uncertainty in discharge considering the propagation of these uncertainties through the power law equation relating discharge and the parameters a, b, z0, S and WSE .
It is important to notice in one hand, that this equation assume that the uncertainties in the parameters (a, b, z0) and WSE are independent, and in another hand, that the propagation of uncertainties provides an estimate based on the assumption of linearization around the mean values of the parameters.
5 Derive discharge from river-width (RD-width) 5.1 River width estimation using optical satellite imagery Following the methodology introduced by Elmi and Tourian (2023), this algorithm estimates river width from time-series satellite imagery (Landsat 8/9 and Sentinel-2) using water indices, topographic constraints, and a graph-based image segmentation framework that incorporates spatial smoothness and temporal dependency. A river reach is first selected from the SWOT River Database (SWORD) and buffered based on its mean width and standard deviation to define an analysis zone.
Only pixels satisfying slope, elevation, and water occurrence thresholds (from FABDEM (Forest And Buildings removed Copernicus DEM) and Global Surface Water Explorer (GSW) (Pekel et al. 2017)) datasets) are retained for analysis. After applying rigorous cloud masking and computing water indices such as Normalized Difference Water Index (NDWI), the image time series is smoothed and normalized within each step. As in Elmi and Tourian (2023), the water index is combined with a long-term water occurrence map via a sigmoid function to enhance temporal consistency. The result is a probability map representing the likelihood of water presence at each pixel and time step.
Segmentation is then performed using a maximum-flow/minimum-cut algorithm that operates on a graph constructed over each probability map. Each pixel is treated as a node connected to source and sink terminals (representing water and non-water classes), with edge capacities determined by the pixel-wise water probability. 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. 20/31