Daily in situ river discharge observations were obtained from the National Hydrological and Rainfall Information System of the Ministry of Water Resources of China, which integrates national and regional monitoring networks spanning major rivers, lakes, and reservoirs. We compiled daily discharge records from 1196 gauging stations across 2014–2024 to construct the CDR² dataset (Fig. 2a). To minimize redundancy, when multiple gauges were located within 100 m of one another, only the gauge with the longest observational record was retained. The resulting gauge network spans nearly all major river basins in China, with the Southwest Rivers Basin being the only exception because discharge records were unavailable from the source platform. Mean discharge among the selected gauges ranges from 0.5 to 30 000 m³ s⁻¹, with each gauge containing an average of 1945 observations. In terms of temporal coverage, more than 80 % of the gauges contain observations beginning in or before 2015, while over 90 % include records extending back to 2018 or earlier (Fig. 2c).

Compared with existing publicly available global discharge datasets, CDR² substantially improves both the spatial coverage and observational availability of river discharge records across China. The GRDC, currently the most comprehensive global archive of in situ discharge observations, contains records from only 31 gauges in China, many of which predate 2004 and have relatively short observational periods, including some with only a single year of data. Similarly, the Chinese Hydrology Project (CHP) dataset provides discharge records from 141 gauges, primarily spanning 1953–1987 (Henck et al., 2010; Schmidt et al., 2011). In contrast, CDR² incorporates approximately 8.5 times as many gauges as CHP and 38.6 times as many as GRDC (Fig. 2d), while also offering substantially more recent observations at a daily temporal resolution.

To identify gauges suitable for satellite-based discharge reconstruction, we employed the Surface Water and Ocean Topography River Database (SWORD) (Altenau et al., 2021) as the reference river network. SWORD provides a globally consistent river centerline dataset with connected topology, in which river systems are segmented into predefined reaches and nodes. To minimize the influence of non-channel water bodies, river reaches linked to lakes and reservoirs were excluded using the SWORD lakeflag attribute. For each gauge, all river nodes located within a 2 km buffer radius were extracted to establish the spatial correspondence between in situ discharge observations and satellite-observed river width. To improve robustness, outlier nodes were removed using a median-based relative deviation criterion, whereby nodes with width deviations exceeding 100 % of the median width were considered anomalous and excluded. A gauge was retained only if it satisfied two conditions: (1) the presence of at least three valid matched nodes, and (2) at least one node with a mean river width of ≥100 m, as defined in SWORD. These criteria ensured that the river channel could be reliably detected by optical satellite imagery and that the extracted width measurements were sufficiently representative for discharge reconstruction. Following the screening procedure, 401 gauges were identified as suitable for satellite-based river discharge reconstruction (Fig. 3). The mean discharge of these gauges ranges from 1.66 to 27 797.46 m³ s⁻¹, with a median of 217 m³ s⁻¹ and a mean of 1090 m³ s⁻¹. The corresponding river widths range from 69 to 3504 m, with a median of 191 m and a mean of 277 m.

The at-a-station hydraulic geometry (AHG), first introduced by Leopold and Maddock (1953), describes the power-law relationship between river width and discharge at a specific cross-section: 4W=aQb where a and b are empirically derived coefficients representing the scaling relationship between river width and discharge. This relationship has been widely applied to characterize the nonlinear response of river width to discharge variations and has demonstrated strong applicability for satellite-based discharge estimation (Gleason and Wang, 2015; Riggs et al., 2023). Accordingly, the instantaneous river widths derived from satellite imagery (Sect. 2.2) were paired with concurrent in situ daily discharge observations at each gauge (Sect. 2.1). Among the 401 candidate gauges, only those with at least ten valid width–discharge pairs (N≥10) were retained, yielding 358 gauges for subsequent evaluation of the width–discharge relationship.

Additional screening procedures were applied to remove gauges exhibiting weak or physically unrealistic width–discharge relationships. First, the Spearman rank correlation coefficient (ρ) was calculated to assess the monotonic association between river width and discharge. Compared with linear correlation metrics, Spearman correlation is less sensitive to outliers and nonlinear behavior and is therefore more suitable for hydraulic geometry analysis (Patidar et al., 2025). Gauges with ρ<0.25 were discarded. Such weak or negative correlations generally indicate that river width does not reliably respond to discharge variability, often due to strong channel confinement, backwater effects, reservoir regulation, or other anthropogenic disturbances (Eggleston et al., 2024; Wang and Smith, 2025). Second, the fitted hydraulic geometry exponent b was evaluated for physical plausibility. In natural river systems, b typically ranges between 0 and 0.59, reflecting realistic channel width adjustments under varying flow conditions (Park, 1977; Yuan et al., 2024). Gauges with fitted exponents outside this range were removed to avoid incorporating unstable or physically implausible hydraulic relationships into the discharge reconstruction framework. After applying all screening criteria, a total of 310 gauges were retained for river discharge reconstruction.

To quantitatively evaluate the performance of the satellite-based discharge reconstruction, four commonly used metrics were employed: the Pearson correlation coefficient (CC), normalized root mean square error (NRMSE), relative bias (rBias), and Kling–Gupta efficiency (KGE). These metrics assess different aspects of model performance, including correlation, error magnitude, systematic bias, and overall hydrological consistency. Their formulations are defined as follows: 5CC=∑i=1NQiobs-Qobs‾Qiest-Qest‾∑i=1NQiobs-Qobs‾2∑i=1NQiest-Qest‾26NRMSE=1N∑i=1NQiest-Qiobs2Qmaxobs-Qminobs7rBias=∑i=1NQiest-Qiobs∑i=1NQiobs where Qiobs and Qiest denote the observed and estimated discharge (m³ s⁻¹) at time step i, respectively. Qobs‾ and Qest‾ represent the corresponding mean discharge values, and N is the total number of paired observations. 8KGE=1-(r-1)2+(α-1)2+(β-1)29r=CC,α=σest/σobs,β=μest/μobs where σobs and σest represent the standard deviations of the observed and estimated discharge, respectively, while μobs and μest denote their mean values.

To quantify uncertainty in the fitted AHG parameters and the reconstructed discharge series, a nonparametric bootstrap procedure was applied independently to each gauge. This approach is well suited to hydrological applications because it does not require prior assumptions about the error distribution of the remote sensing observations (Hesterberg, 2011; Rodrigues et al., 2015). For each bootstrap realization, N pairs of width–discharge observations were sampled with replacement from the original set of N observations, and the AHG relationship in Eq. (4) was refitted using nonlinear least squares. Repeating this procedure 1000 times yielded empirical distributions of the coefficient a and exponent b. Their relative uncertainties, RUa and RUb, were defined as the ratio of the half-width of the 95 % confidence interval to the median of the corresponding bootstrap distribution: 10RUa=(a97.5-a2.5)2a50×100%11RUb=(b97.5-b2.5)2b50×100% where a2.5, a50, and a97.5 denote the 2.5th, 50th, and 97.5th percentiles of the bootstrap distribution of coefficient a, respectively, with analogous definitions for b2.5, b50, and b97.5 corresponding to exponent b.

For each remotely sensed river width observation (Wt) at time step t, the 1000 bootstrap parameter sets were then used to derive the corresponding discharge distribution: 12Qt^(i)=Wta(i)1/b(i),i=1,2,…,1000

The 2.5th, 50th, and 97.5th percentiles of this distribution, denoted as Qt,2.5, Qt,50, and Qt,97.5, respectively, were used to calculate the relative discharge uncertainty at time step t: 13RUQ(t)=(Qt,97.5-Qt,2.5)2Qt,50×100%

Finally, the median RUQ(t) across all available time steps was used to represent the overall uncertainty in discharge reconstruction at each gauge. All uncertainty measures are expressed as dimensionless percentages, enabling direct comparison among gauges with different discharge magnitudes and across geographic regions.

Following the screening criteria, a total of 310 gauges were retained for discharge reconstruction, each with sufficient width–discharge observations (10–529 pairs; median = 108) and a physically consistent hydraulic geometry relationship (Fig. 5). The ρ between river width and discharge ranges from 0.26 to 0.99, with a median value of 0.88 and a mean of 0.84 (Fig. 5a, c). The interquartile range (IQR) spans 0.78–0.92, and approximately 70 % of the gauges exhibit strong correlations (ρ>0.8), whereas only 1.3 % show correlations below 0.5. Additionally, nearly 90 % of gauges fall within the range of 0.59–0.96. Spatially, strong width–discharge correlations are widely distributed across diverse hydroclimatic regions of China, whereas weak correlations show no clear geographic clustering (Fig. 5a). These results indicate that river width at the selected gauges responds sensitively and consistently to discharge variability, thereby satisfying a key prerequisite for satellite-based discharge estimation.

The hydraulic geometry exponent b derived from the AHG relationship further supports the physical realism of the width–discharge relationship (Fig. 5b, d). The fitted b values range from 0.039 to 0.530, with a median of 0.217, a mean of 0.243, and an IQR of 0.177–0.303. Approximately 92 % of gauges exhibit b values between 0 and 0.4, consistent with previous large-sample hydraulic geometry studies. For example, Park (1977) reported a median b value of ∼ 0.23 based on 139 gauges, while Yuan et al. (2024) found a median value of 0.213 using 436 global gauges, with 94 % of gauges falling within the 0–0.4 interval. Notably, relatively high b values (e.g., 0.44 and 0.53) are primarily associated with gauges located in multi-threaded or laterally unconfined river systems (Fig. 5e, f). In these environments, increasing discharge often induces substantial lateral inundation across multiple channels, bars, and floodplain surfaces, thereby enhancing the sensitivity of river width to discharge fluctuations. Such amplified width responses are characteristic of braided and morphodynamically active river systems (Ashmore and Sauks, 2006; Yuan et al., 2024). Overall, these results demonstrate that satellite-derived river widths effectively capture river discharge dynamics and provide a physically robust basis for reconstructing discharge records at daily temporal resolution across the selected gauges.

Given the limited sample size at individual gauges and the fact that evaluating the predictive capability of the AHG relationships is not the primary objective of this study, the in-sample fitting (ISF) approach was adopted for final parameterization to maximize the calibration sample size and thereby ensure the robustness of the long-term discharge reconstruction. Building upon the robust width–discharge power-law relationships established at 310 gauges, we reconstructed and extended river discharge records at daily temporal resolution for 1990–2024 and evaluated performance using four complementary metrics. The satellite-extended discharge exhibits strong agreement with in situ observations (Fig. 6). The median values of the CC, NRMSE, rBias, and KGE are 0.80, 12.67 %, 6.56 %, and 0.66, respectively. Approximately 73 % of gauges exhibit strong correlation (CC > 0.7), while 79 % achieve NRMSE values below 20 %, indicating that the reconstructed discharge reliably captures both the temporal variability and magnitude of observations across diverse hydrological regimes. Notably, KGE values exceed -0.41 at 96 % of gauges, suggesting that the reconstructed discharge consistently outperforms a simple mean discharge benchmark and retains meaningful predictive skill (Knoben et al., 2019). Moreover, 91 % of gauges show positive KGE values, demonstrating that the reconstructed records generally reproduce observed discharge dynamics with acceptable overall fidelity. Spatially, gauges with high predictive performance are broadly distributed across China's major river basins, with no obvious concentration in any specific hydroclimatic region. This consistent performance across diverse river systems demonstrates the robustness and scalability of the proposed framework and highlights the strong potential of integrating satellite-derived river widths with AHG relationships to reconstruct river discharge records at daily resolution over large spatial domains.

To assess the robustness of the performance evaluation, a leave-one-out cross-validation (LOOCV) analysis was performed (Kim et al., 2014). Compared with the ISF results, LOOCV exhibited only marginal reductions in performance, with median decreases in CC and KGE of 0.01–0.04, while differences in NRMSE and rBias remained below 0.7 % (Fig. A1 in the Appendix). These minor discrepancies indicate that the ISF approach introduces little overfitting and that the reconstructed discharge estimates are robust to the choice of calibration strategy.

To further investigate the influence of river dynamics on reconstruction performance, the selected gauges were stratified into five equal-frequency groups (G1–G5) according to the coefficient of variation of river width (CV_w), with group mean values ranging from 6 % to 23 % (Fig. 7). Performance metrics were then compared across the CV_w gradient. The results reveal a clear positive relationship between discharge reconstruction performance and river width variability. Specifically, both NRMSE and rBias decrease with increasing CV_w (Fig. 7b, c), while KGE increases correspondingly (Fig. 7d), with all trends statistically significant (p<0.05). These findings are physically consistent with expectations, as rivers exhibiting greater morphological variability generally respond more sensitively to discharge fluctuations. Such enhanced hydraulic responsiveness improves the detectability of width changes in satellite observations and strengthens the robustness of width-based discharge estimation (Durand et al., 2023; Lin et al., 2023; Scherer et al., 2024). Although CC does not exhibit a statistically significant monotonic trend (p=0.11), the relatively high coefficient of determination (R2=0.62) still suggests a moderate positive association with CV_w (Fig. 7a). However, CC values remain consistently high (>0.75) across all groups, with only limited intergroup variability, indicating that the temporal dynamics of river discharge are effectively captured regardless of river width variability. Notably, even within the low-CV_w groups, where predictive performance is comparatively weaker, the reconstruction framework retains satisfactory skill, with median CC, NRMSE, rBias, and KGE values of approximately 0.76, 15.97 %, 9.65 %, and 0.55, respectively. These results demonstrate that reliable discharge reconstruction can still be achieved in rivers with relatively limited width variability, highlighting the robustness and broad applicability of the proposed framework across diverse channel morphologies and hydrological conditions.

Although the reconstructed discharge records agree well with in situ observations, uncertainties in the parameters fitted from the AHG relationships may accumulate and propagate through the discharge retrieval process. To quantify this effect, we employed bootstrap resampling to estimate the propagation of AHG parameter uncertainty in the reconstructed discharge series across 310 gauges (Fig. 8). The median relative uncertainties of the coefficient a and exponent b (RU_a and RU_b) were 14.36 % and 13.24 %, respectively (Fig. 8a, b). Approximately 68 % of gauges exhibited RU_a below 20 %, and about 80 % showed RU_b below 20 %, indicating robust parameter estimation for the majority of gauges, with the half-widths of their 95 % confidence intervals all less than one-fifth of the median parameter estimates. The median relative uncertainty in reconstructed discharge attributable to parameter propagation (RU_Q) was 11.89 %, and approximately 83 % of gauges had RU_Q below 20 % (Fig. 8c), suggesting that the influence of parameter estimation errors on discharge reconstruction is generally acceptable. Fewer than 2 % of gauges exhibited RU_Q exceeding 40 %, all of which had fewer than 25 width–discharge paired samples, implying that limited calibration data are the primary source of elevated discharge uncertainty. Spatially, gauges with higher parameter and discharge uncertainties were mainly located in the Yangtze and Pearl River basins (Fig. 8a–c). Frequent cloud cover in these regions may reduce the availability of effective optical observations and seasonal representativeness, thereby weakening the statistical constraints on AHG parameters and amplifying discharge uncertainty.

Moreover, RU_Q showed a significant positive correlation with the exponent b (R2=0.40, p<0.001), but no significant correlation with coefficient a (R2=0.01, p>0.05) (Fig. 8d). This divergence is consistent with the AHG equation, in which uncertainty in the exponent b is amplified through its reciprocal exponent. The exponent b therefore exerts a stronger control on uncertainty propagation, supporting the necessity of filtering out gauges with physically unreasonable b values, as described in Sect. 3.1. Overall, the CDR² dataset exhibits relatively constrained parameter-induced uncertainty for most gauges, providing a data foundation with quantitative confidence bounds for subsequent analyses of long-term discharge change across China. However, RU_Q only characterizes the propagation of AHG parameter uncertainty under given satellite-derived river widths and does not account for other sources of uncertainty, including remote sensing observation errors, model structural errors, or changes in external hydrological processes.

Using the satellite-extended discharge estimates with daily temporal resolution from 310 gauges spanning 1990–2024, we quantified the long-term trends and observational characteristics of rivers across China (Fig. 9). Trend detection was performed using the non-parametric Mann-Kendall test (Mann, 1945) in combination with Sen's slope estimator (Sen, 1968), applied to annually aggregated discharge series. Relative annual rates of change (% yr⁻¹) were calculated by normalizing Sen's slope with the multi-year mean discharge, thereby facilitating comparison among rivers with varying discharge magnitudes. To improve the robustness of trend estimation, only years containing at least three observations separated by a minimum intra-annual interval of six months were retained. Furthermore, trend analysis was restricted to gauges with more than 15 valid years of records. After quality filtering, 309 gauges were included in the final analysis, with an average effective record length of 32.5 years.

The results reveal a subtle but widespread decline in river discharge across China, with approximately 65 % (n=201) of gauges exhibiting negative trends and a median relative change rate of -0.21 % yr⁻¹ (Fig. 9a). Spatially, declining trends are concentrated in northern and central China, particularly within the Haihe, Liaohe, and Yellow River basins, as well as parts of the middle Yangtze River basin. This pattern is consistent with recent assessments, suggesting that discharge reductions in these regions are primarily driven by geomorphological alterations, further intensified by anthropogenic water management activities such as water abstraction, inter-basin diversion, and reservoir regulation (Yang et al., 2022; Wang et al., 2025a). In terms of trend magnitude, most declining gauges (n=180) exhibit relatively modest decreases of less than 2 % yr⁻¹, whereas 21 gauges show declines exceeding this threshold. Importantly, a persistent decrease greater than 2 % yr⁻¹ corresponds to a cumulative reduction exceeding 40 % over the past three decades, indicating substantial long-term discharge loss at these locations. Statistical significance testing identifies monotonic trends at 141 gauges (46 % of all analyzed gauges, p<0.1), among which 61 % exhibit declining discharge. Within the significantly declining subset, 66 gauges decrease by less than 2 % yr⁻¹, while 20 gauges decline by more than 2 % yr⁻¹. Conversely, 108 gauges exhibit increasing discharge trends, approximately 51 % of which are statistically significant. These increasing trends are primarily concentrated in the northwestern and middle-to-lower Yangtze River basin, the northern Pearl River basin, and the upper Yellow River basin. Overall, the spatial heterogeneity of discharge trends reflects the diverse and complex hydrological responses occurring across China's distinct geographical and hydroclimatic regions.

The temporal sampling characteristics of the satellite-extended discharge dataset were further examined (Fig. 9b). The median number of observations per gauge is 375, corresponding to approximately 11 observations per year, while about 42 % of gauges contain more than 420 observations (≥12 observations per year). Despite this generally dense temporal coverage, observation frequency exhibits substantial spatial heterogeneity across China. Gauges with fewer than 300 observations are predominantly concentrated in the middle Yangtze and Pearl River basins. This reduced sampling density is primarily associated with persistent cloud cover, frequent precipitation, and complex topography, which limit the availability of high-quality optical satellite imagery and consequently reduce the number of usable observations. Nevertheless, even under irregular observational intervals, the reconstructed discharge records preserve key hydrological dynamics. For example, the reconstructed time series at the Dalai (Fig. 9c) and Longmenzhen (Fig. 9d) gauges successfully capture transitions from baseflow to peak-flow conditions while maintaining coherent multidecadal variability and long-term discharge trends. These examples demonstrate that the satellite-based reconstruction framework can resolve both short-term hydrological fluctuations and long-term discharge despite the discontinuous sampling inherent in optical remote sensing observations. Overall, these results indicate that the satellite-extended discharge dataset provides sufficient temporal depth and observational frequency to support robust gauge-scale trend analysis, offering valuable insights into the long-term hydrological evolution of China's major river systems.

To better contextualize the contribution of the CDR² dataset, we conducted a comparative assessment against several representative global remotely sensed river discharge products, including RSEG (Elmi et al., 2024), SAEM (Saemian et al., 2025), and the datasets developed by Lin et al. (2023) and Riggs et al. (2023). Although these datasets have substantially expanded the spatial coverage of global river discharge observations, their representation within China remains extremely limited (Fig. 10 and Table 2). Specifically, the number of gauges in China ranges from only one in Riggs et al. (2023) to 62 in SAEM. In all cases, Chinese gauges account for less than 1 % of the total stations included in these global products, reflecting both the scarcity of publicly accessible in situ discharge observations and the challenges of satellite-based discharge retrieval in this region. In contrast, CDR² expands the number of gauge-constrained discharge records available for China by approximately 5–300 times relative to existing global datasets, providing discharge estimates at daily temporal resolution for 310 gauges distributed across diverse hydroclimatic and geomorphological settings (Fig. 10). The dataset encompasses rivers spanning a wide range of discharge magnitudes and channel sizes, thereby substantially improving the representation of China within global river discharge archives.

Beyond its improved spatial coverage, CDR² also demonstrates clear advantages in temporal resolution and predictive performance. While RSEG and Lin et al. (2023) provide monthly discharge estimates, CDR², SAEM, and Riggs et al. (2023) operate at daily time scales. Notably, CDR² achieves a median KGE of 0.66, exceeding the reported global median range of 0.33–0.48 among existing products (Table 2), although these comparisons should be interpreted considering differences in gauge selection criteria and river characteristics. Consistent improvements are also evident in other performance metrics, including a lower median NRMSE (12.7 %) and a higher median CC (0.80), indicating enhanced capability in reproducing both the magnitude and temporal variability of observed discharge.

These improvements are partly attributed to the rigorous screening strategy adopted in this study, whereby only gauges exhibiting stable width–discharge relationships and physically consistent hydraulic behavior were retained (Fig. 5). In contrast, global-scale products often face an inherent trade-off between maximizing spatial coverage and maintaining retrieval quality, frequently incorporating gauges with weaker hydraulic relationships or unstable channel responses, thereby introducing greater uncertainty into discharge reconstruction. Moreover, by integrating observations from both Landsat and Sentinel-2 imagery, CDR² achieves a substantially higher effective sampling frequency than single-sensor approaches. This enhanced temporal sampling improves the detection of short-term discharge fluctuations and mitigates the smoothing effects associated with monthly aggregation, as observed in RSEG and Lin et al. (2023), thereby enabling a more realistic reconstruction of discharge dynamics at daily temporal resolution. Overall, CDR² provides an expanded and higher-resolution characterization of river discharge across China, a hydrologically critical yet globally underrepresented region. Through its greatly expanded gauge density, discharge records at daily resolution, and enhanced reconstruction performance, CDR² fills a major geographic gap in existing global river discharge products.

To investigate the influence of hydraulic geometry on discharge reconstruction accuracy, we evaluated the sensitivity of reconstruction performance to the width–discharge exponent b (Fig. 11). This exponent characterizes the responsiveness of river width to discharge variability and therefore serves as a key hydraulic link between satellite-observed channel dynamics and river discharge behavior. The analysis reveals statistically significant relationships between b and multiple performance metrics (Fig. 11a–c). Specifically, both NRMSE and rBias exhibit significant negative correlations with b (ρ=-0.46 and -0.49, respectively; p<0.001), whereas KGE shows a significantly positive correlation (ρ=0.52, p<0.001). These results indicate that rivers with greater hydraulic sensitivity experience larger width variations under comparable discharge fluctuations, making these changes more readily detectable by satellite observations (Fig. 7) and thereby mitigating the propagation of observational uncertainty into discharge reconstruction.

To identify a robust threshold for hydraulic sensitivity, gauges were first sorted according to increasing b values, after which a sliding-window analysis was applied to evaluate local gradients of each performance metric with respect to b. To facilitate comparison across metrics with different numerical ranges, the gradients were normalized to their respective global ranges. The optimal threshold (bopt) is defined as the point at which the absolute normalized gradient consistently declines below 20 % of its global maximum, indicating that performance stabilizes beyond this value. The intersection of these stabilization regions across all metrics yields a global threshold of b=0.25 (Fig. 11d). Below this threshold, large fluctuations in normalized gradients indicate considerable uncertainty in discharge reconstruction for hydraulically constrained rivers. Once b exceeds 0.25, all gradients converge toward zero, suggesting that width-based discharge estimation becomes substantially more stable and reliable for rivers with stronger hydraulic responsiveness.

The contrasting influence of b on reconstruction performance is clearly illustrated by the Zhangjiajie and Wutongqiao (II) gauges (Fig. 11e, f). At Zhangjiajie, characterized by a low b value, substantial discharge variability corresponds to only marginal changes in river width, often approaching the spatial resolution limit of the satellite sensor (∼30 m). Under such conditions, the inversion from width to discharge becomes mathematically ill-conditioned, whereby small uncertainties in width retrieval propagate into disproportionately large discharge errors, ultimately degrading reconstruction performance (Fig. 11e). In contrast, the Wutongqiao (II) gauge exhibits a high b value, where pronounced width sensitivity to discharge allows satellite observations to effectively resolve discharge variations across the full hydrological spectrum, from low-flow conditions to flood peaks. Together, these findings demonstrate that b provides a physically meaningful and robust criterion for identifying rivers suitable for reliable satellite-based discharge reconstruction, offering important guidance for future large-scale discharge estimation and monitoring efforts.

Although the CDR² dataset substantially expands the availability of gauge-constrained river discharge records for long-term monitoring, the reconstruction framework remains subject to inherent limitations and uncertainties arising from both hydraulic assumptions and the constraints of remote sensing observations. First, a critical source of uncertainty lies in the implicit assumption that the width–discharge relationship remains temporally stationary. Model calibration relies on in situ observations acquired during 2014–2024 and is retrospectively applied to reconstruct discharge over 1990–2024. Extending hydraulic relationships calibrated over a decade of observations to multi-decadal discharge reconstruction is a common simplification adopted in satellite-based discharge retrieval and implicitly assumes temporal invariance of the AHG relationship (Pavelsky, 2014; Paris et al., 2016). To assess the uncertainty associated with temporal extrapolation, we quantified the extrapolation ratio for each gauge, defined as the proportion of remotely sensed river widths during 1990–2024 that fell outside the calibration width range (Fig. 12). Extrapolation ratios were generally low across the 310 reconstructed gauges, with a median of 0.81 % and a mean of 2.62 %. Overall, 86.5 % of gauges exhibited extrapolation rates below 5 % and 55.2 % below 1 %, suggesting that historical discharge reconstruction at most gauges remained within the calibrated hydraulic regime and that uncertainties associated with extrapolating AHG relationships beyond observed river states were limited. Nevertheless, even when reconstructed widths fall within the calibration range, hydraulic geometry may evolve over multi-decadal timescales in response to both anthropogenic and natural disturbances, including dam construction, reservoir regulation, channel engineering, sediment erosion and deposition, and sand mining (Mansanarez et al., 2019; Zhang et al., 2015). Such changes may alter the underlying width–discharge relationship and introduce additional uncertainty into long-term discharge reconstruction. For example, downstream channel incision caused by sediment retention in upstream reservoirs may substantially increase water depth and flow velocity without corresponding changes in channel width.

Second, discharge reconstruction relies exclusively on river width as the remotely sensed hydraulic observable. Although river width exhibits strong correlations with discharge across most selected gauges (median ρ=0.88), river discharge is jointly controlled by channel width, flow velocity, bed slope, and hydraulic roughness (Leopold and Maddock, 1953; Singh et al., 2003). These hydraulic controls are not explicitly represented in the current framework and may become particularly important in rivers where channel width responds weakly to discharge variability. This interpretation is consistent with the sensitivity analysis of the hydraulic geometry exponent b, which demonstrates progressively improved reconstruction performance with increasing hydraulic sensitivity (Fig. 11). Additionally, the inherent limitations of optical remote sensing introduce further uncertainty. The temporal continuity of CDR² is inevitably affected by cloud cover, atmospheric aerosols, and seasonal snow and ice (Feng et al., 2022; Langhorst et al., 2024), resulting in substantial spatial variability in observation frequency among river basins (Fig. 9b). More importantly, extreme rainfall events are frequently accompanied by persistent cloud cover, causing optical sensors to miss peak-flow conditions and hindering the characterization of rapidly evolving flood hydrographs.

Future improvements should focus on integrating multi-source satellite observations with multi-dimensional hydraulic information. Incorporating channel morphology, sediment dynamics, and anthropogenic regulation into the reconstruction framework would facilitate the identification of temporal variations in width–discharge relationships and improve the robustness of long-term discharge reconstruction. Integrating optical imagery with synthetic aperture radar (SAR) observations would substantially improve temporal sampling under persistent cloud cover while enhancing the monitoring of extreme flood events. Furthermore, combining river width with complementary hydraulic observations, including water surface elevation and slope from emerging satellite missions such as the Surface Water and Ocean Topography (SWOT) mission, through nonlinear multivariate inversion frameworks offers a promising pathway toward more physically constrained and accurate satellite-based river discharge reconstruction.