Global scale river discharge and mean depth from radar altimetry and model

TL;DR

This paper presents a near-global dataset of altimetric rating curves (ARCs) and effective mean river depths at more than 26,000 virtual stations, built by combining satellite radar altimetry water surface elevations with a 30-year monthly discharge reanalysis. The calibrated power-law stage-discharge relationships yield median KGE 0.41 against modeled discharge and provide space-based discharge estimates and mean depth fields across diverse hydroclimates.

Key findings

• The ARC dataset was generated for 26,000+ virtual stations using Hydroweb-Next water surface elevation and MeanDRS discharge; calibration across 32,000 virtual stations yielded median KGE 0.41, nRMSD 33%, and pBIAS 6.91%, with top-quartile KGE 0.65. Table 1 reports median KGE 0.52 for QQRC on the research database (6,764 samples) and 0.38 on the operational database (26,055 samples), and median KGE 0.43 for MMRC on the research database (1,402 samples) and 0.67 on the operational database (970 samples).
• Validation against 3,378 in situ gauges for 2010–2024 showed daily global median KGE greater than zero and upper-quartile KGE 0.53; performance improved with discharge magnitude, reaching median daily KGE 0.38 for high-magnitude rivers (1,000–10,000 m³/s), while very low and low classes had daily KGE −4.62 and 0.09. Overall median KGE was 0.18 across diverse climatic and hydrological settings.
• Effective mean river depth, derived as mean altimetric water surface elevation minus calibrated z₀, was mapped from 32,819 virtual stations, highlighting deep channels such as the Amazon and lower Congo. Log-linear a–b relationships were consistent with at-many-stations hydraulic geometry, with a median 1/b exponent of 0.67.
• Multi-mission altimetry produced continuous discharge time series dating back to 1993, with up to 10 monthly discharge estimates for some rivers since 2018.

Methods

• Hydroweb-Next WSE time series (34,843 at the study time, spanning Topex/Poséidon to Sentinel-6A, 1993–2025) were paired with the MeanDRS monthly discharge reanalysis (bias-corrected with 1,000 gauges over 1980–2009; approximately 3 million MERIT-Basins reaches).
• Rating curves were fitted with the power law Q = a(Z − z₀)^b using Bayesian Markov Chain Monte Carlo (Metropolis-Hastings), with priors a ∈ [0, 3000], b ∈ [0, 5], and z₀ constrained below all WSE observations. Monthly Mean Rating Curves were used when temporal overlap existed; Quantile-Quantile Rating Curves were used for no-overlap cases (almost 93% of virtual stations). Climatic anomaly filtering with CHIRPS v2 and HydroBASINS level 5 excluded 91,720 of 387,912 observations, about 23%.
• Validation used 3,378 in situ gauges from ANA, GRDC, and SCHAPI for 2010–2024, paired by drainage area with a ±5% threshold, and evaluated with KGE, NSE, nRMSD, and pBIAS at daily and monthly scales.

Limitations

• The paper states that the static power law assumes steady, uniform flow and cannot resolve dynamic hysteresis or backwater effects, and that a single exponent cannot fully represent transitions between low-stage section control and high-stage overbank floodplain flow, especially in regulated rivers and extensive floodplains.
• The paper states that ARC parameters remain linked to calibration-data errors from global hydrological reanalyses and from historical LRM versus modern SAR altimetry tracking precision, so inferred parameters represent effective rather than directly observed hydraulic properties. It also states that comprehensive global validation of effective river depth is hindered by scarce in situ bathymetry, and that discharge validation intersects gauge-rich regions where the reference model was already bias-corrected, so uncertainty in completely unmonitored basins may be higher.
• The paper states that filtering for anomalous hydroclimatic years was not applied outside 50°N–50°S due to lack of long-term precipitation data, less-constrained modeled discharge, and ice/freeze-thaw contamination, with lower ARC performance in eastern Australia, northern Africa, central Asia, and the southwestern U.S. Evident from the reported validation, very low and low discharge classes show poor skill (daily KGE −4.62 and 0.09), and the validation database is unevenly distributed, mostly in Europe, North America, South America, and Australia.