Altimetric Rating Curves (ARCs) parameters from "Global Scale River Discharge and Mean Depth from Radar Altimetry and Model"

Abstract

Corresponding peer-reviewed publication This dataset corresponds to the rating curves produced in the study reported in: Paris, A., Garambois, P.-A., Gal, L., Cerbelaud, A., Larnier, K., David, C. H., Juca Oliveira, R. A., Wongchuig, S., Tourian, M.-J. and Calmant, S., Global scale river discharge and mean depth from radar altimetry and model. Nat Commun (2026), https://doi.org/10.1038/s41467-026-78275-5. When making use of any of the files in this dataset, please cite both the aforementioned article and this dataset. Dataset description This dataset provides calibrated power-law rating curve parameters and associated discharge statistics at over 32,000 river virtual stations (VS) distributed across the globe. It is the primary output of a study combining nadir satellite altimetry water surface elevation (WSE) time series from the Hydroweb-Next database with a 30-year global monthly river discharge reanalysis (MeanDRS; Collins et al., 2024, Nature Geoscience), bias-corrected through long-term inverse routing at approximately 1,000 gauging stations worldwide. Rating curves follow the power-law form Q = a⋅(WSE - z₀)b where Q is river discharge (m³/s), WSE is the Water Surface Elevation (m), and a, b, z₀ are station-specific calibrated parameters. Two calibration approaches are represented in the dataset: the Monthly Mean Rating Curve (MMRC), applied when WSE and discharge records overlap in time, and the Quantile-Quantile Rating Curve (QQRC), used in the majority of cases (~93%) where no temporal overlap exists. Prior to calibration, anomalous hydroclimatic years were identified and removed using CHIRPS v2 precipitation data (1981–2009 reference period), reducing the influence of extreme ENSO-driven events on the fitted relationships. Parameter estimation was performed via Bayesian Markov Chain Monte Carlo (MCMC), yielding both optimal values and uncertainty estimates (standard deviations) for each parameter. Rating curves performance metrics (KGE, NSE, nRMSE, pBIAS) are computed by comparing rated discharge against the MeanDRS monthly climatic mean discharge used for calibration, and therefore reflect goodness of fit rather than independent validation accuracy. Independent validation strategy against in situ gauge networks is presented in the associated paper. The effective mean river depth can be approximated at each station as heq = Z̄(t) − z₀, where Z̄(t) is the long-term mean WSE. The global distribution of these depth estimates constitutes, to the authors' knowledge, the first near-global satellite-derived map of mean river depth. The dataset covers the six continents and spans a wide range of river sizes and hydroclimatic regimes. Performance varies geographically, with generally stronger results in large to very large rivers (discharge > 100 m³/s) and in basins where the MeanDRS reanalysis has been bias-corrected. Lower scores are observed in arid or semi-arid regions, areas with strong human regulation of river flow (dams, diversions), and rivers with non-perennial flow regimes. Files included in this version of the dataset 1. Rating curve parameters — ARCs_summary.csv Semicolon-delimited text file. One row per virtual station. Column Units Description basin — Basin name station — Virtual station identifier (reach name and river reach ID) rivid — River reach identifier from MeanDRS / MERIT-Basins used for discharge calibration lon ° Longitude of the virtual station lat ° Latitude of the virstual station a — Scaling coefficient of the power-law rating curve b — Exponent of the power-law rating curve z0 m Effective cease-to-flow elevation (reference riverbed elevation) a_sd — Posterior standard deviation of a b_sd — Posterior standard deviation of b z0_sd m Posterior standard deviation of z₀ zmin m Minimum observed WSE in the altimetry time series NSE — Nash–Sutcliffe Efficiency KGE — Kling–Gupta Efficiency PBIAS % Percent bias between rated and modelled discharge NRMSE % Normalized root mean square error R2 — Coefficient of determination approach — Calibration method: quantile (QQRC) or monthlymean (MMRC) first_date UTC Start date of the WSE time series (YYYY-MM-DD HH:MM:SS) last_date UTC End date of the WSE time series (YYYY-MM-DD HH:MM:SS) Q_mean m³/s Mean discharge from MeanDRS Q_median m³/s Median discharge from MeanDRS Qmin m³/s Minimum discharge from MeanDRS Qmax m³/s Maximum discharge from MeanDRS Q_quantile25 m³/s 25th percentile discharge from MeanDRS Q_quantile75 m³/s 75th percentile discharge from MeanDRS mission — Altimetry mission (e.g., J2, S3A, S6A) Note: Performance metrics (KGE, NSE, NRMSE, PBIAS, R²) in this file are computed by comparing rated discharge against the MeanDRS monthly climatic mean discharge used for calibration. They reflect goodness of fit, not independent validation accuracy. 2. Independent validation statistics — validation_ARCs.csv Semicolon-delimited text file providing independent validation of the rated discharge time series against in situ streamflow records from global and national gauge networks (GRDC, SCHAPI, and others). Each row corresponds to one virtual station–gauge pair. Validation is performed by comparing rated discharge against in situ monthly mean discharge computed over the overlapping observation period. Column Units Description basin — Basin name station — Virtual station identifier Provider — Source gauge network (e.g., GRDC, SCHAPI) GaugeID — Gauge identifier in the source network lon ° Longitude of the virtual station lat ° Latitude of the virtual station R2 — Coefficient of determination NSE — Nash–Sutcliffe Efficiency KGE — Kling–Gupta Efficiency Pbias % Percent bias NRMSE % Normalized root mean square error obs_median m³/s Median observed discharge from in situ gauge sim_median m³/s Median rated discharge from the rating curve Classes_obs — River size class based on observed discharge (e.g., S = small, M = medium, L = large) Note: Unlike the calibration metrics, all scores here are computed by comparing rated discharge against in situ monthly mean discharge not used during calibration, and therefore constitute a true out-of-sample evaluation of rating curve performance. 3. Independent validation statistics (daily) — validation_ARCs_daily.csv Semicolon-delimited text file providing independent validation of the rated discharge time series against in situ streamflow records from global and national gauge networks (GRDC, SCHAPI, and others). Each row corresponds to one virtual station–gauge pair. Validation is performed by comparing rated discharge against in situ monthly mean discharge computed over the overlapping observation period. Column Units Description basin — Basin name station — Virtual station identifier Provider — Source gauge network (e.g., GRDC, SCHAPI) GaugeID — Gauge identifier in the source network lon ° Longitude of the virtual station lat ° Latitude of the virtual station R2 — Coefficient of determination NSE — Nash–Sutcliffe Efficiency KGE — Kling–Gupta Efficiency Pbias % Percent bias NRMSE % Normalized root mean square error Note: Unlike the calibration metrics, all scores here are computed by comparing rated discharge against in situ daily discharge not used during calibration, and therefore constitute a true out-of-sample evaluation of rating curve performance.