The GloFAS-ERA5 provides global gridded daily time series of streamflow reanalysis (Harrigan et al., 2020). There has recently been an upgrade from v2.1 to v4.0 (Table 1), resulting from fundamental changes in model architecture with the spatial resolution improving from 0.1 to 0.05° (Prudhomme et al., 2024). In GloFAS-ERA5 v2.1, the OS LISFLOOD hydrological model is primarily utilized for channel routing, forced by surface and sub-surface runoff data from the Hydrology Tiled ECMWF Scheme for Surface Exchanges over Land (HTESSEL) within ERA5 (Zhao et al., 2024). By contrast, the GloFAS-ERA5 v4.0 is forced directly by atmospheric variables from ERA5, enabling the LISFLOOD to internally simulate the entire rainfall-runoff and routing processes (Prudhomme et al., 2024).

The streamflow observations corresponding to reanalysis are sourced from the CAMELS dataset (Addor et al., 2017; Newman et al., 2015). This dataset comprises 671 catchments across the contiguous United States, characterized by minimal anthropogenic disturbances and a wide range of hydroclimatic conditions. Streamflow observations from stations and catchment-mean meteorological forcing data from Daymet, Maurer and NLDAS are provided at the daily timescale. This dataset also provides static attributes related to climate, soils, vegetation, topography and geology (Addor et al., 2017). To align the gridded GloFAS-ERA5 reanalysis with station observations, the Kling–Gupta efficiency (KGE) is calculated between observations and the reanalysis data from the nine nearest grid cells. Then the time series from the grid cell with the highest KGE is selected as the corresponding reanalysis data for that station (Zhao et al., 2022).

The climate reanalysis of precipitation, as well as temperature, is sourced from the ERA5 dataset (Table 2) (Hersbach et al., 2020). It integrates global observations with model output based on data assimilation (Ishida et al., 2024). The ERA5 provides spatiotemporally complete and consistent reanalysis data of global climate, including hourly estimates of a wide range of atmospheric, ocean-wave and land-surface variables from January 1940 to the present. In the analysis, the daily catchment-mean precipitation and temperature are extracted from the raw ERA5 reanalysis of 0.25°×0.25°.

The observations of precipitation, as well as temperature, are sourced from the Daymet dataset (Thornton et al., 2016). By interpolating and extrapolating ground-based observations, it generates long-term, continuous, gridded estimates of daily meteorological variables over continental North America, Hawaii and Puerto Rico. Due to its high resolution of 1 km × 1 km, the Daymet is widely utilized in hydrological modeling (Frame et al., 2023; Newman et al., 2015). As provided in the CAMELS dataset, the catchment-mean Daymet precipitation and temperature are used in the analysis.

The root mean square error (RMSE) is used to quantify the overall discrepancies between reanalysis products and observations (Huang and Zhao, 2022; Liu and Lei, 2026; Li and Zhao, 2026a). The streamflow data of the GloFAS-ERA5 dataset are converted from discharge (m³ s⁻¹) into runoff depth (mm d⁻¹) based on the catchment area. For each catchment, the RMSE values of streamflow (eQi), precipitation (ePi) and temperature (eTi) are calculated as follows: 1eQi=1Ki∑k=1KiQi,k-Q^i,k2ePi=1Ki∑k=1KiPi,k-P^i,k2eTi=1Ki∑k=1KiTi,k-T^i,k2 where Q^i,k, P^i,k and T^i,k denote the streamflow, precipitation and temperature reanalysis for catchment i, respectively; Qi,k, Pi,k and Ti,k represent the corresponding observations, respectively; Ki is the total number of data pairs for catchment i.

To capture the temporal variability of reanalysis errors, RMSE values are also calculated by hydrological year spanning from 1 October to the next 30 September (Frame et al., 2023). These annual RMSE values are subsequently used for regression analysis. The annual RMSE values of streamflow (eQi,t), precipitation (ePi,t) and temperature (eTi,t) are calculated: 2eQi,t=1ni,t∑d=1ni,tQi,t,d-Q^i,t,d2ePi,t=1ni,t∑d=1ni,tPi,t,d-P^i,t,d2eTi,t=1ni,t∑d=1ni,tTi,t,d-T^i,t,d2 where Q^i,t,d, P^i,t,d and T^i,t,d respectively denote the streamflow, precipitation and temperature reanalysis for catchment i on day d of hydrological year t; Qi,t,d, Pi,t,d and Ti,t,d represent the corresponding observations, respectively; ni,t is the number of data pairs in hydrological year t for catchment i.

The linear regression is used to identify the responses of streamflow reanalysis errors to precipitation reanalysis errors (Over et al., 2025; Anderson et al., 2022; Steinschneider et al., 2013). The catchment-specific linear regression avoids the assumptions regarding the homogeneity of the responses across all catchments that are needed for panel regression models (Over et al., 2025; Anderson et al., 2022). For each catchment, it is fitted using the ordinary least squares estimator: 3eQi,t=β1iePi,t+β2ieTi,t+β0i+ϵi,t where β1i and β2i represent the regression coefficients for precipitation and temperature errors in catchment i, respectively; β0i and ϵi,t denote the regression intercept and residuals, respectively. The β1i quantifies how much streamflow reanalysis error responds to every 1 mm increase in precipitation reanalysis error. The coefficient of determination (R2) is used to quantify the goodness-of-fit for regression models (Wang et al., 2026; Over et al., 2025; Steinschneider et al., 2013). For linear regression of catchment i, the R2 is calculated: 4R2=1-∑eQi,t-eQ^i,t2∑eQi,t-eQ‾i2 where eQ^i,t and eQ‾i denote the fitted value and mean value of eQi,t, respectively.

Panel regression can be used to quantify the average response using both the spatial and temporal dimensions of the errors (Steinschneider et al., 2013). It is intended to identify cross-catchment average relationships rather than to provide precise predictions for individual catchments (Wang et al., 2026; Over et al., 2025). The pooled panel regression assumes no heterogeneity across catchments: 5eQi,t=β1ePi,t+β2eTi,t+β0+ϵi,t where β1 and β2 are the average effects of precipitation errors and temperature errors on streamflow errors across all catchments, respectively; β0 and ϵi,t denote the regression intercept and residuals, respectively. The random-effects panel regression accounts for unobserved time-invariant variations across catchments. It assumes that these individual effects are uncorrelated with the included independent variables: 6eQi,t=β1ePi,t+β2eTi,t+β0+αi+ϵi,t where αi is a random independent variable that represents the individual effects of catchment i. The fixed-effects panel regression assumes that omitted factors controlling the dependent variable are correlated with the included independent variables. The entity fixed-effects model is utilized: 7eQi,t=β1ePi,t+β2eTi,t+μi+ϵi,t where μi is the intercept representing individual effect for catchment i that is constant in time and characterizes the time-averaged heterogeneity. The two-way fixed-effects model is used to further consider synchronous region-wide temporal shocks: 8eQi,t=β1ePi,t+β2eTi,t+μi+λt+ϵi,t where λt is the intercept representing the time fixed effect for hydrological year t.

To evaluate how catchment attributes influence the responses of streamflow reanalysis, the random-effects panel regression is extended by incorporating interaction terms between climate reanalysis errors and catchment attributes: 9eQi,t=β1ePi,t+β2eTi,t+β3PSiePi,t+β4SFieTi,t+β0+αi+ϵi,t where PSi and SFi respectively represent the seasonality and timing of precipitation (hereafter precipitation seasonality) and the fraction of precipitation falling as snow (hereafter snow fraction) for catchment i that are included in the CAMELS dataset. The precipitation seasonality is estimated by fitting sinusoidal functions to the mean annual cycles of temperature and precipitation. Positive (negative) values indicate that precipitation peaks in summer (winter), whereas values near zero represent relatively uniform distributions of precipitation throughout the year (Addor et al., 2017). The marginal effects of the precipitation reanalysis error (β1′) and temperature reanalysis error (β2′) are the first derivatives of Eq. (9) with respect to the corresponding independent variables: 10β1′=β1+β3PSiβ2′=β2+β4SFi where β3 and β4 are the regression coefficients of the two interaction terms, respectively. They capture how catchment attributes linearly modulate the baseline average effects of precipitation error and temperature error (β1 and β2).

The statistical and spatial distributions of reanalysis errors quantified by RMSE are shown in Fig. 1. As the GloFAS-ERA5 is upgraded from v2.1 to v4.0, the median RMSE across 671 catchments decreases from 2.16 to 1.81 mm. Due to the improvement of performance, the subsequent analyses focus on the GloFAS-ERA5 v4.0. Both streamflow and precipitation reanalysis errors are influenced by regional aridity. The higher RMSE values are predominantly found in the humid Eastern and Western coastal regions, while lower errors are observed in the arid Midwest region (Zhao et al., 2025). The correlation coefficient between streamflow and precipitation reanalysis errors increases from 0.27 for GloFAS-ERA5 v2.1 to 0.45 for v4.0, highlighting the critical role of precipitation accuracy in streamflow reanalysis. By contrast, temperature reanalysis errors peak primarily in the complex topography of the western mountainous region. The overall correlation between streamflow and temperature reanalysis errors remains near zero for both GloFAS-ERA5 versions, suggesting that temperature errors do not exert a consistent direct influence on streamflow errors across all catchments.

The relationships among annual RMSE of streamflow, precipitation and temperature reanalysis are illustrated in Fig. 2. Significant positive correlations between streamflow and precipitation errors are observed in 567 (85 % of 671) catchments. The coefficients for individual catchments range from 0 to 0.88 with the median value of 0.56, while the correlation for pooled data across all catchments is 0.44. By contrast, the correlation between streamflow and temperature errors is unstable and statistically insignificant in 603 (90 % of 671) catchments. The local coefficients fluctuate widely between -0.68 and 0.65 with the median value of -0.04, while the correlation for pooled data across all catchments is -0.01. In addition, the correlation between precipitation and temperature errors is insignificant in 535 (80 % of 671) catchments, with the median value of 0.13 compared to -0.22 for pooled data. Their Variance Inflation Factor (VIF) values are consistently below 5 across all catchments, indicating that precipitation and temperature errors by hydrological year do not exhibit severe collinearity. Consequently, both variables can be utilized as predictors in the subsequent regression models.

The streamflow reanalysis errors and their corresponding estimations from panel regression models are shown in Fig. 3. While the R2 ranges from 0.15 to 0.20, the p-values of all regression coefficients are below 0.01, indicating that precipitation and temperature reanalysis errors significantly affect the streamflow reanalysis errors. Except for the pooled panel regression, the regression coefficients of the other three panel regression models are close. The Breusch-Pagan Lagrange multiplier test rejects the null hypothesis that residuals of the pooled panel regression are homogeneous (p<0.01), indicating significant unobserved heterogeneity across catchments. Since the pooled panel regression cannot account for the unobserved heterogeneity, it is inadequate for capturing the average effects here (Steinschneider et al., 2013). Furthermore, the Hausman test cannot reject the null hypothesis that the unobserved catchment-specific effects are uncorrelated with the explanatory variables at the 1 % significance level (p=0.03 and p=0.90), indicating that the random-effects panel regression is appropriate. The random-effects model not only requires fewer parameters but also can accommodate time invariant predictors, such as catchment attributes, whereas these effects are absorbed and cannot be estimated in fixed-effects models (Steinschneider et al., 2013; Bassiouni et al., 2016). Consequently, the random-effects panel regression is selected for subsequent analyses. The coefficient of precipitation error for the random-effects panel regression is 0.51, indicating that a 1 mm increase in precipitation RMSE is associated with an average increase of 0.51 mm in streamflow RMSE. It is noted that the value 0.51 is the average statistical response estimated from the panel regression for 671 catchments, rather than a direct quantitative estimate of any single hydrological process.

The local responses of streamflow reanalysis errors for individual catchments are compared with the average responses across all catchments, as shown in Fig. 4. Compared with the Southeastern U.S. and the West Coast, the R2 is lower in the central and the western mountainous regions, likely due to the high nonlinearity of runoff processes in these arid and complex terrains. The median R2 of linear regression across the 671 catchments is 0.36. The local effects of precipitation reanalysis errors are positive and statistically significant in 564 (84 % of 671) catchments, where the corresponding regression coefficients are relatively high (from nearly 0 to 2.5) in humid catchments (aridity index < 2) but low (from nearly 0 to 0.7) in arid catchments (aridity index ≥ 2). The aridity index is calculated as the ratio of mean potential evapotranspiration to mean precipitation. The panel regression coefficients roughly correspond to the central distribution of catchment-specific linear regression coefficients. Across the 671 catchments, the median coefficients of precipitation errors and temperature errors are respectively 0.43 and -0.17, while the coefficients are respectively 0.51 and -0.23 for the panel regression. While the panel regression provides a stable estimate of the average responses across all catchments, it inherently masks the divergent local responses (Anderson et al., 2022).

The relationships between local responses quantified by linear regression and catchment attributes are shown in Fig. 5. The R2 is negatively correlated with the latitude and the snow fraction, with the correlation coefficients of -0.43 and -0.29, respectively. This result suggests that the linear regression tends to capture more error variance in warmer, lower-latitude catchments than in snow-dominated regions. The effects of precipitation reanalysis errors are negatively correlated with precipitation seasonality and aridity index but positively related to mean precipitation. The correlation coefficients are respectively -0.36, -0.25 and 0.31. This result suggests that streamflow errors may be more directly associated with precipitation errors under the saturation-excess conditions while soil moisture deficits can dampen their effects. In the meantime, the effects of temperature reanalysis errors are positively correlated with latitude, snow fraction and elevation. This indicates that temperature errors become important drivers of streamflow reanalysis errors in high-latitude or mountainous catchments where snowmelt processes are critical. These correlations indicate that the responses of streamflow errors are influenced by the specific physical and climatic characteristics of the catchments.

The modulating influences of precipitation seasonality and snow fraction on the effects of precipitation and temperature reanalysis errors are illustrated in Fig. 6. For catchments with statistically significant linear regression coefficients, the effects of precipitation reanalysis errors are negatively correlated with precipitation seasonality. The correlation coefficient is -0.38. The effects of temperature reanalysis errors are positively related to snow fraction, with the correlation coefficient of 0.52. By incorporating these hydroclimatic attributes into the panel regression via two interaction terms as specified in Eq. (9), the model's explanatory power improves substantially, with the R2 increasing from 0.16 to 0.36. The derived marginal effects reveal a systematic shift in error propagation. Specifically, as the value of precipitation seasonality increases, the precipitation regimes transition from winter-concentrated to summer-concentrated patterns and the marginal effects of precipitation errors decrease. In the meantime, the marginal effects of temperature errors amplify as the snow fraction increases, indicating that the effects of temperature errors are enhanced in snow-dominated catchments. These trends are consistent with the local responses derived from catchment-specific linear regression.

The reanalysis data and observations of precipitation, temperature and streamflow for the rain-dominated catchment 14166500 are showcased in Fig. 7. The three years are selected for visualization because they represent contrasting levels of precipitation errors, allowing the responses of streamflow errors to be compared clearly. The responses of streamflow reanalysis errors are almost synchronous with the precipitation errors. Specifically, the periods where GloFAS-ERA5 underestimates streamflow peaks are consistent with instances where ERA5 underestimates precipitation. The effect of precipitation errors is statistically significant with the regression coefficient of 0.69, indicating that the streamflow errors increase with precipitation errors. By contrast, the effect of temperature errors is statistically insignificant, demonstrating that temperature fluctuations play a negligible role in the streamflow RMSE of this rain-dominated catchment. Among hydrological years spanning from 2009 to 2011, the highest precipitation error occurred in 2011 with the RMSE of 5.15 mm, leading to the largest streamflow RMSE of 1.41 mm. This case study indicates that in humid rain-dominated catchments, the performance of streamflow reanalysis is predominantly associated with the accuracy of precipitation reanalysis rather than temperature.

The reanalysis data and observations of precipitation, temperature and streamflow for the snow-dominated catchment 13310700 are showcased in Fig. 8. This catchment is characterized by substantial snow accumulation from November to next March, followed by a seasonal surge in runoff starting in April as the rising temperature triggers snowmelt. The displayed years are selected to include years with comparable precipitation RMSE but contrasting temperature RMSE, thereby showing the potential role of snowmelt errors related to temperature. The streamflow errors are driven jointly by precipitation and temperature errors. Both effects are statistically significant with regression coefficients of 0.43 and 0.37, respectively. Among hydrological years spanning from 1998 to 2000, the precipitation error and streamflow error in 1999 are simultaneously the highest with the RMSEs of 3.81 and 1.57 mm, respectively. Although the precipitation error in 1998 is equal to that in 2000, the streamflow error in 1998 is higher due to the larger temperature error. The underestimation of precipitation from November to next March leads to the deficit in simulated snow storage, while the underestimation of temperature from April to June delays and reduces simulated snowmelt. Consequently, these combined errors result in the underestimation of GloFAS-ERA5 streamflow from April to June. These results indicate that in snow-dominated catchments, temperature reanalysis errors directly interfere with the simulated timing and magnitude of snowmelt, thereby amplifying streamflow reanalysis errors.

Soil moisture deficits, evapotranspiration and subsurface water storage can limit runoff generation from precipitation in arid catchments (Farmani et al., 2025; Assouline et al., 2024; Cui and Tian, 2026). As shown by Fig. S1 in the Supplement, the correlation between streamflow reanalysis error and soil wetness index (SWI) is statistically significant across 473 catchments, with the median correlation coefficient being 0.52. This result is consistent with the relatively weaker responses of streamflow reanalysis errors to precipitation errors observed in arid catchments and stronger responses in some humid catchments. Dry antecedent soil conditions generally allow a large proportion of precipitation to infiltrate and replenish soil water storage before reaching the thresholds to generate runoff (Liu et al., 2025; Tian and Xu, 2024). As antecedent soil moisture increases, the remaining storage deficit decreases, thereby enhancing the sensitivity of runoff generation to precipitation inputs (Ye et al., 2023; Ran et al., 2022). Evapotranspiration and groundwater recharge may further modulate the contemporaneous relationship between precipitation and streamflow errors (Berghuijs et al., 2025). Since evapotranspiration and groundwater data are not provided in GloFAS-ERA5 or Daymet datasets (Grimaldi et al., 2023; Thornton et al., 2016), their contributions and the specific distribution of precipitation errors among them cannot be determined.

In high-latitude or mountainous catchments, the seasonal snow storage and subsequent melt can alter the timing and magnitude of the streamflow responses to precipitation (Zhu et al., 2023; Wang et al., 2021; Nan et al., 2026). Precipitation errors in snow season may be retained in snow storage and appear months later as streamflow errors (Wang et al., 2021; Hale et al., 2023). As shown in Fig. S2 in the Supplement, the correlation between precipitation RMSE and temperature RMSE over cold days (Daymet temperature ≤ 0 °C) for each hydrological year is statistically significant in 56 catchments but not significant in 275 catchments. Temperature influences precipitation phase, snow accumulation and melt timing, but these physical linkages do not necessarily imply a strong statistical coupling between precipitation errors and temperature errors. The errors calculated over hydrological year partly integrate intra-annual effects of storage and lag (Berghuijs et al., 2025; de Lavenne et al., 2022), but they obscure seasonal contrasts, snow accumulation–melt transitions and intra-seasonal phase errors (Hale et al., 2023; de Lavenne et al., 2022). The annual errors therefore cannot resolve seasonal or event-scale errors, particularly for extreme precipitation and flood events. In addition, as the Daymet dataset is generated by interpolating observations (Thornton et al., 2016), uncertainties associated with station density and interpolation methods may affect the precipitation errors (Zhao et al., 2025).

The performance of streamflow reanalysis is primarily constrained by climate forcings, initial conditions, representation of physical processes and model parameterization (Liu et al., 2023; Nourani et al., 2026; Nanding et al., 2021b). Due to the improvements in hydrological model and calibration method, the performance of GloFAS-ERA5 improves when upgraded from v2.1 to v4.0 (Prudhomme et al., 2024; Alfieri et al., 2020). The panel regression shows that precipitation reanalysis errors have a statistically significant average effect on streamflow reanalysis errors, which aligns with previous findings of the positive linear relationships between precipitation and streamflow errors (Nanding et al., 2021a; Wu et al., 2017). To assess whether the positive relationships are primarily driven by the shared dependence on hydroclimatic magnitude, the sensitivity analysis is performed using normalized RMSE (Sect. S2 in the Supplement). The regression coefficients remain positive and statistically significant in the panel regressions and in linear regressions for 435 (65 % of 671) catchments, as shown in Figs. S3 and S4 in the Supplement, indicating that these relationships persist after reducing the influence of hydroclimatic magnitude. The panel regression is robust in capturing average effects from large-sample datasets (Anderson et al., 2022; Over et al., 2025). The precipitation errors can explain only a limited proportion of the variance in GloFAS-ERA5 streamflow errors, with the R2 of the panel regression not exceeding 0.36. The remaining variance may be related to catchment heterogeneity, hydrological models and uncertainties in the reference datasets.

Due to inherent catchment heterogeneity, each catchment has unique and often unmeasured characteristics that may affect hydrological processes (Chen et al., 2026; Zhu et al., 2023; Ma et al., 2026). While the linear regression is effective for uncovering local relationships within individual catchments, it often lacks the generalizability required to characterize hydrological responses across a larger number of catchments (Anderson et al., 2022; Steinschneider et al., 2013). By contrast, the standard panel regression assumes that the responses of streamflow reanalysis errors to precipitation errors are homogeneous across all catchments, thereby ignoring the influence of catchment heterogeneity (Over et al., 2025; Anderson et al., 2025). The panel regression is designed to estimate the average relationship across catchments, but it can obscure catchment-specific responses or the behavior of extreme events (Wang et al., 2026; Steinschneider et al., 2013). This paper incorporates two interaction terms into the panel regression to account for the influence of precipitation seasonality and snow fraction. These two moderators effectively account for the fact that the responses of streamflow errors to climate forcing errors are associated with the specific catchment conditions (Nanding et al., 2021a; Miao et al., 2024). These findings indicate that catchment heterogeneity modulates the responses of streamflow errors to precipitation errors.