Evaluation of river discharges derived from remote sensing and land surface models

doi:10.21203/rs.3.rs-4725805/v1

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Evaluation of river discharges derived from remote sensing and land surface models

https://doi.org/10.21203/rs.3.rs-4725805/v1

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This study assesses river discharges derived using remote sensing and hydrologic modeling approaches throughout the CONUS. The remote sensing methods rely on total water storage anomalies (TWSA) from the GRACE satellite mission and water surface elevations from altimetry satellites (JASON-2/3, Sentinel-3). Surface and subsurface runoff from two Land Surface Models (NOAH, CLSM) are routed using the Hillslope River Routing model to determine discharge. The LSMs are part of NASA’s Global Land Data Assimilation System (GLDAS). Differences in key physical processes represented in each model, model forcings, and use of data assimilation provide an intriguing basis for comparison. Evaluation is performed using the Kling Gupta Efficiency and USGS stream gauges. Results highlight the effectiveness of both satellite-derived discharge methods, with altimetry generally performing well over a range of discharges and TWSA capturing mean flows. LSM-derived discharge performance varies based on hydroclimatic conditions and drainage areas, with NOAH generally outperforming CLSM. CLSM-derived discharges may be impacted by the use of data assimilation (GLDAS v2.2). Low correlation and high variability contribute to lower KGE values. GLDAS models tend to perform poorly in snow dominated, semi-arid and water-regulated systems where both the timing and magnitude of the simulated results are early and overestimated.

Earth and environmental sciences/Hydrology

Earth and environmental sciences/Planetary science/Hydrology

Earth and environmental sciences/Climate sciences/Hydrology

GLDAS

CLSM

NOAH

KGE

GRACE-FO

saturation-excess

River discharge, associated with an individual river cross-section or reach segment, integrates all upstream hydrologic stores and fluxes and is largely influenced by spatial-temporal variability in precipitation. While understanding the behavior these relevant stores (e.g., soil moisture) and fluxes (e.g., surface and subsurface runoff) is critical for many applications, especially in terms of assessing impacts of landcover and/or climate change, their spatial-temporal patterns are highly variable and in-situ measurements capturing these quantities are typically obtained from sensors capturing dynamics at a limited number of point locations within a given system. Thus, river discharge is commonly used to capture the variability or hydrologic state of a catchment. Understanding river discharge characteristics is also vital in the design and management of critical infrastructures (e.g., water supply, flood control).

Given that discharge is associated with individual river cross-sections or reaches, in-situ measurements are typically limited in terms of availability ^1,2. Thus, discharge is commonly estimated from models intended to capture the relevant hydrologic and hydraulic processes but can vary widely in their approach: physical ³, statistical ⁴, conceptual⁵, and, mostly recently, machine ^6,7. In these models, key inputs typically include static landscape characteristics and time varying estimates of precipitation, temperature and vegetation characteristics.

For large scale systems (CONUS to global scales), many physics-based models operate on rectangular computational grids such as those within NASA’s National Land Data Assimilation Systems (LDAS) and Global LDAS (GLDAS) ⁸ Thus, hydrologic conditions such as soil moisture or snow cover within a grid cell are relatively straightforward to assess with corresponding in-situ data. The evaluation of river discharge derived from LSMs is more challenging. For example, gridded runoff estimates from LSMs generally integrate only vertical stores and fluxes; a river routing step is required to integrate the lateral fluxes (e.g., surface and subsurface runoff) to derive discharge. Only a limited number of studies have evaluated river discharges at the global ^9–13Additionally, these studies usually only focus on a single model, a limited number of similar types of models (Bai et al., 2016), or a small number of catchments.

In addition to hydrologic models, data from Earth Observing Satellites (EOS) are used for estimating river discharges: passive-sensor (optical/near-infrared/microwave) reflectance ^14–16, active-sensors (radar backscatter/altimetry) ^17–23, and quasi-active (GRACE) ^24–29. These methods have also been combined, such as ^30,31, using estimates river widths (i.e., reflectance) and water surface elevation (i.e., altimetry) to enable discharge estimates. The use of satellite altimetry to measure the water level of rivers, lakes, and floodplains begin in the early 1990s ^23,32,33. While altimetry satellites such as TOPEX/Poseidon, JASON series and Sentinel-3A/B monitor water surface elevations, they do not provide a paired observation of river width or slope, which are generally a key component to estimating river discharge. Gehring et al., 2022 developed an approach to specifically address how to use unpaired altimetry measurements and Landsay derived river widths to estimate river discharges. The Surface Water and Ocean Topography (SWOT) satellite, which launched in December 2022, provides paired measurements of river WSE, slope, and width which can be used to provide improved estimates of discharge ^19,34. GRACE/GRACE-FO Total Water Storage Anomalies (TWSA) signals, while not directly observing individual rivers as sensors for reflectance/altimetry, have been used in conceptual models to estimate river discharge (Q) ^29,35,36. Thus, there are numerous Remote Sensing (RS) methods that provide estimates of river discharges offering new opportunities for assessing large scale hydrologic models, which is currently lacking in the existing literature ^10,13 .

In this study, we provide an evaluation of river discharges derived using remote sensing and models, specifically, surface and subsurface runoff from NASA’s GLDAS ⁸ and routing from the Hillslope River Routing (HRR) model ³⁷. In this process, gridded GLDAS runoff values from the NOAH and CLSM models, are remapped to topographic-based catchments and routed along the river network providing discharge estimates for all rivers draining at least 1,000 km² throughout the CONUS (Fig. 1), where the quantity and quality of available gauged discharge data is high. Model derived discharges are compared to values from 2,858 in-situ U.S. Geological Survey (USGS) discharge gauges, 387 virtual altimetry stations ²³, and 2,858 river reaches with TWSA-Q relationships ²⁹ for the period 2002–2021. Monthly and annual discharges derived from these estimation methods are evaluated using Kling Gupta Efficiency (KGE), relative bias and interannual variability. Investigating the differences between these methods and gauge observations provides valuable insights on the strengths/weaknesses of each method and where/when these models should be used individually or as ensembles for ungauged locations.

The data used in this study include river networks, associated catchment boundaries and hydrologic characteristics (i.e., GRACE/GRACE-FO TWSA, GPM IMERG precipitation, and GLDAS runoff). Catchment boundaries and river reaches were obtained from MERIT Basins database ^10,38. There are 8 hydrobasins in CONUS numbered 71–78; here, hydrobasin 76 has no USGS gauges and was excluded. The observed discharges at gauges were obtained from USGS’s National Water Information System⁷³. The TWSA-Q ²⁹ and satellite altimetry ²³ derived river discharges use the above data plus altimetry from Hydroweb Theia⁷⁴ and river reach characteristics from the SWOT A priori River Database (SWORD) database ³⁹.

3.1 Study Area

The study area (Fig. 1) covers the CONUS. Hydrobasin 74 is the largest and includes the Mississippi River Basin draining into the Gulf of Mexico. This hydrobasin has a mostly humid, subtropical climate with varied levels of precipitation and isolated semi-arid regions. The Mississippi River Basin represents the larger drainage area in the study (3M km²). Within the Mississippi, its largest tributary, the Missouri River, is impacted by snow processes and highly regulated. Hydrobasin 73 covers the east coast, which has a somewhat north–south gradient in temperature and precipitation with snow effects in the Appalachian Mountains and New England regions, which receive 100–250 cm of snow annually. Hydrobasin 75 includes New Mexico and Texas and generally has a semi-arid climate with some subtropical regions, especially in Texas. This region includes the Rio Grande, which drains into the Gulf of Mexico. Snowfall throughout this region is less than 10 cm per year on average, but in select catchments, it can be up to 50 cm. As is typical for semi-arid regions, many of its rivers are highly regulated. The watersheds in Hydrobasin 77 generally have arid to semi-arid climates toward the east side of the region and a Mediterranean climate in the California portion. The watersheds include major rivers, such as the Colorado and Sacramento Rivers draining into the Pacific Ocean. The mountainous areas within this region tend to be snow dominated. Hydrobasin 78 consists of the Columbia River draining into the Pacific Ocean. Hydrobasin 72 includes the Great Lakes, with rivers draining to lakes Huron, Michigan, Erie, Superior and Ontario. In the Results and Discussion sections, select USGS gauges are used to highlight the findings related to climate (e.g., snow impacts), water regulation and proximity to the Great Lakes, which are common to many gauges within their respective hydrobasins.

3.2 Land Surface Models

NASA GLDAS utilizes satellite and ground-based observational data, as well as data assimilation techniques, to provide accurate information about land surface conditions such as soil moisture, temperature, and various fluxes like evapotranspiration and runoff ^8,40. GLDAS incorporates four LSMs: NOAH, Catchment Land Surface Model (CLSM), Community Land Model (CLM), and Variable Infiltration Capacity (VIC). GLDAS-2.1 is forced with a combination of observation and model data from the NOAA/GDAS (Global Data Assimilation System), GPCP (Global Precipitation Climatology Project), and the AGRMET (Air Force Weather Agency’s AGRicultural Meteorological modeling system) starting in 2000. GLDAS-2.2 includes data assimilation from the Gravity Recovery and Climate Experiment (GRACE)^41–44 and has data starting in 2002 and meteorological analysis fields from ECMWF. In this study, GLDAS-2.1 (NOAH) and − 2.2 (CLSM) model outputs are used; temporal resolutions of 3-hourly (NOAH) to daily (CLSM) and a spatial resolution of 0.25 degrees. The outputs encompass three main categories: water balance (e.g., rainfall rate, snowfall rate, surface and subsurface runoff, evapotranspiration, and soil moisture), energy balance, and forcing parameters ⁸. Here, we use the water balance outputs from the NOAH⁷¹ and CLSM⁷² models. The two models were selected to highlight runoff (surface and subsurface) from fundamentally different formulations (i.e., NOAH - infiltration excess, and CLSM – saturation excess) ⁴⁵. In general, previous research tends to focus on GLDAS NOAH more often than CLSM, especially in the context of version GLDAS-2.2. For more detailed information on the GLDAS-2 products, refer to the work of Rodell et al., 2004.

3.3 River Routing of LSM’s Runoff

Hydraulic routing is performed for hydrobasins regions 71 to 78 in CONUS. Surface, baseflow and snowmelt runoff from the LSM’s are routed using a 1hr time step; runoff is assumed constant for each 3hr interval for NOAH and daily for CLSM. The hourly river discharges are averaged to monthly values at the USGS gauge locations. Routing was performed using HRR which is based on diffusion wave methodologies via Muskingum–Cunge methods. In this application, the hourly runoff averaged over a given catchment is directly integrated along the catchment’s river reach. HRR requires inputs of channel width, length and slope. For more information on the model setup see Beighley et al., 2009.

The routing model requires input variables: channel roughness, width, length and slope; and a reference discharge (Q_r). Slope and length are extracted from the MERIT Basins river network. The reference discharge (m³/s) and channel width (m) are estimated using relationships with upstream drainage area (A, km²) (Fig. 2). This approach has been used in numerous applications ^37,46–49). The relationships are determined using data from the USGS gauge locations, where USGS reported gauge drainage area and MERIT Basins upstream drainage area are within ± 5%. At the gauge locations, the channel width is based on the width from the nearest SWORD node within a distance of roughly 100 meters. For reference discharge, the mean daily discharge at each gauge was used. The number of gauges in Fig. 2b are different as only gauges with river discharge estimates available after 2002 were considered. The channel roughness (n) varies between 0.02–0.05 vbased on the drainage area of the catchment.

3.4 Remote Sensing Based Discharge Estimates

3.4.1 Estimation using GRACE Total Water Storage Anomalies (TWSA)

Exponential models for discharge and GRACE TWSA were proposed and proof-of-concept was demonstrated at 2,870 gauges by Duvvuri et al. (2023). The exponential model is:

$$\:Q=a{\:e}^{\beta\:\:TWSA}$$

where Q is mean monthly discharge (cm/month), ⍺ and 𝛽 are coefficients, and TWSA (cm) is spatially averaged over the land area upstream of the gauge location. This study optimized the months of Q-TWSA data pairs to include and lag between Q-TWSA data pairs to estimate discharge. For additional details, refer to ²⁹. The study showed that this relation has potential for regionalization as the ⍺ parameter is correlated to mean monthly precipitation and 𝛽 is correlated to the mean annual range in TWSA. Here, we are comparing the results at gauged locations to understand the variability from the different models available for discharge estimation. In the future, the regionalized parameters could be used to compare model results at ungauged locations.

3.4.2 Estimation using Satellite Altimetry

Gehring et al., 2022 estimated river discharge using satellite-derived, time-varying altimetry measurements, Landsat-derived river widths⁵⁰ and static mean river-reach characteristics for sites within the Mississippi River Basin (USA) using Manning’s equation:

$$\:Q=\frac{1}{n}\:A\:{R}^{\frac{2}{3}}{S}^{\frac{1}{2}}$$

where n is the channel roughness coefficient (unitless), A is the cross-sectional flow area of the channel (m²), R is the hydraulic radius (m) measured as cross-sectional flow area divided by the wetter perimeter of the cross-section, and S is the water surface slope along the channel (m/m). The cross-sectional area and hydraulic radius parameters require information regarding the channel width, depth, and form. For ease of application, mean reach characteristics derived from remote sensing were used. However, there is a portion of the channel that is not observed by satellite altimetry—that is, the depth below the minimum altimetry measurement (i.e., Water Surface Elevation, WSE). The study is built around approximating the depth of the missing cross-section (h_o) which generally represents low flow conditions, to determine the effective channel flow depth (h_e) at a given time:

$$\:{h}_{e}\left(t\right)\:=\:{h}_{m}\left(t\right)\:+\:{h}_{o}\:$$

where h_m is WSE at time t from the altimetry observation minus the minimum WSE from the observation period (i.e., min WSE from the multi-year time series). They optimized the roughness coefficient (n), missing depth (h_o), and channel shape for the portion not observed by the altimetry satellite. The river reach data for observed channel location are obtained from the Surface Water and Ocean Topography River Database (SWORD) ³⁹. Satellite altimetry data from JASON-2/3 (2008–Present) and Sentinel-3A/B (2015–Present) are obtained from Hydroweb Theia database ^51,52. Please refer toGehring et al., 2022 for additional details.

3.5 Model Performance Section

The discharge time series, monthly and annual, are evaluated with Kling Gupta Efficiency (KGE) and its components such as mean bias, variance bias and correlation. The variations in these components leading to high or low KGE for the different estimation methods used in the study are discussed. Additional performance metrics evaluated for annual estimates include: Normalized Root Mean Squared Error (NRSME) and relative bias (rbias). The key equations are shown below:

$$\:NRSME=\frac{RSME}{{\mu\:}_{obs}};\:KGE\:=\sqrt{{(1-\frac{{\mu\:}_{sim}}{{\mu\:}_{obs}})}^{2}+{(1-\frac{{\sigma\:}_{sim}}{{\sigma\:}_{obs}})}^{2}+{(1-R)}^{2}};\:\:rbias\:\left(\%\right)=\frac{{Q}_{m}-\:{Q}_{o}}{{Q}_{o}}*100$$

where $\:{\mu\:}_{obs}$, $\:{\mu\:}_{sim}$ are mean of observed and simulated monthly discharges; $\:{\sigma\:}_{obs}$, $\:{\sigma\:}_{sim}$, are standard deviations of observed and simulated monthly discharges, respectively; R is correlation; and $\:{Q}_{m}$, $\:{Q}_{o}$ are estimated and observed monthly discharges, respectively.

Four discharge estimation methods are compared in this study to assess variability relative to gauge discharges. To evaluate impacts of scale (drainage area) and hydrologic conditions (regions) within the CONUS, discharge results from four watersheds are highlighted in this study. The rivers include the Mississippi, Columbia, Colorado, Rio Grande and Susquehanna; highlighted in Fig. 1. The Mississippi River Basin is the largest in the CONUS, with a drainage area of roughly 3M km² from major tributaries: Ohio, Arkansas, Red, and Missouri rivers. While the Missouri River (1.26 M km²) contributes the largest land area, the Ohio River (0.53M km²) contributes the most water⁵³. The mean monthly precipitation and discharge for the Mississippi River at Baton Rouge are roughly 3.5 cm and 1.7 cm (50 km³). An increase in the annual streamflow has been observed due to land cover change and increasing temperatures over the period 2000 to 2020⁵³. One of the largest east coast rivers, the Susquehanna River (71K km²), is fed by snowmelt, including potentially large rain-on-snow events, and rainfall-induced runoff ⁵⁴. It has a mean monthly precipitation of 10.5 cm and mean monthly discharge of 4.7 cm (3.32 km³). The largest west coast river, the Columbia River (0.6M km²), is governed by atmospheric rivers and baseflow recharge from melting snowpacks ⁵⁵. The Columbia River has a mean monthly discharge of 2.6 cm (17.3 km³) resulting from an average monthly precipitation of 5.1 cm. The Colorado River (0.64M km²) discharges less than 0.3 cm (1.69 km³) annually into the Gulf of Mexico but receives a monthly precipitation of 4.5 cm.

Results for monthly and annual discharges are presented in the following sections. A total of 2,848 gauges are used to assess TWSA-, NOAH-HRR and CLSM-HRR derived discharges for the period 2002–2022. For the altimetry-based estimates, 276 gauges are used. For all cases, only gauges with at least 2 years of complete data records are used.

4.1 Monthly Discharge

4.1.1 CONUS

Mean monthly discharge estimated from the four methods generally show spatial distributions similar to observed values (Fig. 3). While it is not clearly visible due to the limited number of locations, Altimetry-derived discharges are most similar, with a few notable areas with degraded performance (e.g., Great Lakes Region and the Northeast). In general, mean monthly TWSA-derived discharges are most like the observed values throughout the western half of CONUS; noticeable differences are visible in the upper Mississippi and portions of the Great Lakes and East Coast regions, which tend to be overestimated. NOAH-HRR discharges tend to be overestimated in Northern California and portions of Florida and underestimated in upper Missouri and Columbia River Basins, portions of the Great Lakes and Tennessee River Basin. CLSM-HRR discharges are underestimated in upper Missouri, Columbia, and Mississippi River Basins, and most of the Great Lakes Region, and overestimated in watershed draining to the Gulf Coast east of the Mississippi River.

To assess estimated discharges, KGE, which considers correlation, mean bias, and standard deviation variability, is used. Figure 4 shows KGE at each gauge location. Here, a threshold of 0.32 is set as acceptable or good performance for KGE, which is based on our previous findings ²⁹. For sites with KGE greater than 0.32, correlation is between 0.32-1, bias ratio is between 0.4–1.6 and variability is between 0.4–1.7. TWSA-derived discharges have a larger fraction of gauges (75%) with KGE greater than 0.32, followed by 48% and 29% for NOAH-HRR and CLSM-HRR, respectively. For the altimetry-derived discharges, only 276 of the total 2,400 locations are used, and the fraction of sites with KGE greater than 0.32 is 70%. In general, the range in correlation, bias, and variability for sites with KGE > 0.32 was similar between all four methods. One clear difference is variability, where the range was 0.53–1.18 for TWSA-derived compared to 0.38–1.61, 0.45–1.61, 0.41–1.64 for Altimetry, NOAH-HRR, CLSM-HRR, respectively. Overall, the median KGE for all gauges in this study are 0.43, 0.39, 0.1 and − 0.05 for TWSA-derived, altimetry-derived, NOAH-HRR, and CLSM-HRR, respectively.

4.1.2 Major Watersheds

Results for major rivers and their tributaries are shown in Fig. 5 and Table 1. The KGE and magnitude of its individual components for all sites are provided in supplemental material.

Table 1: Monthly summary statistics for selected gauges highlighted in Figure 1; were column labels 1-4 correspond to TWSA (1), Altimetry (2), NOAH-HRR (3), and CLSM-HRR (4) results; KGE ≥ 0.32 are highlighted in gray.

ID	River Name, Location	Area (km²)	Mean Monthly Q (cm/month)					KGE
ID	River Name, Location	Area (km²)	Obs.	1	2	3	4	1	2	3	4
01578310	Susquehanna, PA	0.07M	4.57	5.92	4.69	4.96	2.66	0.46	-0.29	0.49	0.32
03294500	Ohio, KY	0.2M	4.44	5.00	2.86	3.76	2.61	0.72	0.06	0.76	0.37
06610000	Missouri, NE	0.8M	0.35	0.36	0.45	0.53	0.71	0.49	0.97	-1.7	-1.3
07022000	Mississippi, IL	1.8M	1.10	1.15	1.07	1.18	0.93	0.66	0.33	0.01	0.19
09522000	Colorado, AZ	0.6M	0.02	0.02	0.02	0.38	0.38	0.37	-0.13	-58	-51
14105700	Colombia, WA	0.6M	2.13	2.13	2.00	2.36	1.78	0.73	0.87	-0.78	0.08

Mississippi

The four methods were evaluated in the Mississippi watershed at gauges on the upper Mississippi, Ohio, and Missouri Rivers (see Fig. 1). The timeseries of the discharge for Mississippi tributaries and upper mainstem are shown in the 1st row of Fig. 5. Observed discharge for the Missouri peaks in summer, but the peaks in the GLDAS discharges tend to occur early in the year, which is likely due to timing of snow accumulation and melt and not including reservoir routing. The seasonality and peaks in the upper Mississippi at Illinois are captured by TWSA- and altimetry-derived discharges but the GLDAS models result in peaks appearing earlier. However, these impacts are muted when comparing discharges on the lower Mississippi at Baton Rouge, where the seasonality and peaks mimic the observed values (Fig. S1). Note that, altimetry-derived discharges are not available at Baton Rouge, and this gauges is not included in this detailed analysis. For the Ohio, altimetry-derived and CLSM-HRR discharges underpredict observed peaks but tend to capture seasonality reasonably well.

The TWSA-derived discharges have KGE greater than 0.32 at all three gauges. Only NOAH-HRR and CLSM-HRR for the Ohio had KGE greater than 0.32. The altimetry-derived discharges resulted in KGEs of 0.33 (Mississippi River at Illinois) and 0.97 (Missouri River at Nebraska) but only 0.06 for the Ohio. For TWSA-derived discharges, all three KGE components had reasonable values at all the gauges. However, GLDAS-derived values had lower KGE mainly due to low correlation and high variability. Similarly, for the altimetry-derived discharges, all three KGE components had reasonable values for the Missouri but poor bias and variability in the Ohio and upper Mississippi.

Columbia

A gauge on the mainstream of Columbia River in Oregon upstream of the outlet was selected to avoid tidal effects (Fig. 1). Figure 5 shows streamflow peaks in the winter with the lowest flows in summer. The KGE of the estimated monthly discharges was highest (0.87) for Altimetry-derived followed by TWSA-derived (0.73). The impacts of snow processes and not accounting for water regulation likely results in the GLDAS-derived methods consistently overestimating high flows, especially for NOAH-HRR, and underestimating low flows (Fig. 5). The peak timings tend to be early in the case of GLDAS derived discharges. The GLDAS models performed poorly (KGE = 0.08 and − 0.78).

Colorado

The methods were evaluated on the Colorado River (Fig. 1), which is characterized as semi-arid. A gauge in Arizona above Morelos Dam was selected for evaluating the Colorado. The TWSA-derived discharges had KGE greater than 0.32 backed by good correlation and mean bias ratio. The NOAH-HRR and CLSM-HRR discharges had very poor KGE (-58 and − 51, respectively) but good correlation as they predicted the seasonal variation but not the magnitudes or the recession timing (Fig. 5). The altimetry-derived discharges had KGE of -0.13. The GLDAS models significantly overestimate discharge, which is likely due to challenges associated with simulating runoff generation in semi-arid environments, where runoff response to rainfall is highly non-linear.

Susquehanna

For the Susquehanna River in Pennsylvania, Fig. 5 shows that the hydrographs capture the peak timings and seasonality reasonably well, but the magnitude of the peaks is different than observed for all methods except altimetry-derived. The TWSA-, NOAH-HRR and CLSM-HRR discharges had KGE greater than 0.32 at this gauge, but the TWSA-derived discharges tended to significantly overestimate discharge. The altimetry-derived discharges failed to approximate discharge at this gauge (KGE = -0.29), which could be related to uncertainty in derived WSE as the width tends not to vary much.

4.2 Annual Discharges

The annual discharges were calculated by summing the estimated monthly discharges in a given calendar year (i.e., not water year Oct-Sept). Only gauges with at least 2 years of complete data records, observed annual discharge greater than 10 cm/year and at least 11 months data are used in the evaluation. The annual discharges were evaluated with NRSME and relative bias.

4.2.1 CONUS

Normalized root mean squared (NRSME) represents the error in annual prediction relative to the mean observed discharge. At roughly 60% of the gauges, TWSA- and NOAH-HRR discharges have NRMSE < 35%. Further, at roughly 80% of study gauges these estimation techniques had NRSME < 50% (Fig. 6). Altimetry-derived discharges have NRSME < 35% at 80% of the sites (275). CLSM-HRR discharges have noticeably larger NRMSE values.

Because of the variability of annual runoff throughout the CONUS, we separated the gauges with relatively low runoff (< 10 cm/yr) and more typical runoff (> 10 cm/yr) values. At the gauges where annual discharge is > 10 cm/yr, all methods had bias less than roughly ± 25% (Fig. 7). The goodness of fit (R²) is best (0.98) for TWSA. Given the sensitivity of R² to outliers, the altimetry-derived discharges had the lowest R² but reasonable bias. Noticeable differences for gauges with < 10 cm/yr include larger bias and somewhat lower R² values.

Considering only gauges with annual runoff > 10 cm/yr (Fig. 8), the average relative bias in mean annual discharge estimates is 9% (TWSA-), 5% (Altimetry-), -9% (NOAH-HRR), and − 35% (CLSM-HRR). The TWSA-derived method overestimates annually at most gauges in eastern half of the CONUS, except for the Ohio and Tennessee River Basins (Fig. 8a). NOAH-HRR discharges tend to have relative bias within ± 30%; underestimates in Western half of CONUS (Fig. 8c). For CLSM-HRR, there are fewer gauges within ± 30% rbias and more defined clusters of high or low rbias (Fig. 8d). The altimetry-derived discharges have relative bias within ± 30% at most gauges, but where rbias is high or low, the pattern is generally consistent for several nearby gauges. Overall, the median NRMSE is 0.4, 0.28, 0.46 and 0.6 and median relative bias is 9.17, 10.93, 3.94 and − 8.63 for TWSA-derived, altimetry-derived, NOAH-HRR, and CLSM-HRR, respectively.

4.2.2 Major Watersheds

Results for major rivers and their tributaries are shown in Fig. 9 and Table 2. The error metrics for all sites are provided in supplemental material.

Table 2: Annual summary statistics for selected gauges highlighted in Figure 1; were column labels 1-4 correspond to TWSA (1), Altimetry (2), NOAH-HRR (3), and CLSM-HRR (4) results; note USGS Gauge ID and drainage area are listed in Table 1; NRMSE <30% highlighted in gray.

Name	Mean Annual Q (cm/month)					NRMSE (%)				Relative Bias (%)
Name	Obs.	TWSA	ALT	NOAH	CLSM	TWSA	ALT	NOAH	CLSM	TWSA	ALT	NOAH	CLSM
Susquehanna, PA	54.82	71.09	56.30	59.47	31.91	54.6	23.3	14.6	45.8	30	2.7	8.5	-42
Ohio, KY	53.32	60.03	35.35	45.12	31.32	30.3	74.1	17.7	42.4	13	-36	-15	-41
Missouri, NE	4.18	4.35	5.46	6.37	8.53	26.0	3.4	78.3	110.2	4.0	31	52	104
Mississippi, IL	13.19	13.86	12.82	14.13	11.15	24.5	63.5	24.7	23.4	5.1	-2.8	7.1	-16
Colorado, AZ	0.27	0.29	0.22	4.54	4.52	15.3	17.7	1753	1615	8.1	-18	1580	1570
Colombia, WA	25.62	25.55	24.05	28.31	21.31	6.0	1.5	18.3	22.2	-0.3	-6.1	11	-17

Mississippi

The NOAH-HRR and TWSA-derived discharges capture annual discharge in the Mississippi reasonably well. At the gauges in the Mississippi, TWSA- annual discharges had lowest relative bias (4 to 13%), while NOAH-HRR, altimetry-derived, CLSM-HRR estimates had relative bias of -15 to 52%, -36 to 31%, and − 41 to 104%, respectively. Results for the Ohio showed the highest bias ± 40% for all methods except for NOAH-HRR (-15%). For the upper Mississippi, the relative bias in annual discharge was lowest (-2.8%) for NOAH-HRR followed by TWSA-derived (22%) and CLSM-HRR (-3.9%). Annual discharges are significantly underestimated for the Ohio River by CLSM-HRR (Fig. 9), which is also evident for the broader region (Figure. 8d, blue points). However, NOAH-HRR performs well. For the Missouri River, NOAH-HRR overestimates annual discharge more noticeably for years prior to 2012 and then matches the annual patterns much better during the following 10 years, while CLSM-HRR consistently overestimates discharge. In case of Mississippi river at Baton Rouge, the NOAH-HRR overestimates annual discharge more noticeably for years prior to 2012 and then matches the annual patterns much better during the following 10 years, while CLSM-HRR consistently matches the annual patterns.

Columbia

The annual discharge for the Columbia River was underestimated by all methods except NOAH-HRR, which consistently overestimated discharge. The relative bias is 11% for NOAH-HRR, -0.3% for TWSA-derived, -6.1% for altimetry-derived, and − 17% for CLSM-HRR. The GLDAS models tended to consistently overestimate (NOAH-HRR) or underestimated (CLSM-HRR) annual discharges. However, the temporal correlation is generally good for all methods; especially the GLDAS models.

Colorado

Given the small discharges in the Colorado River, TWSA-derived and observed discharges are on the right y-axis and GLDAS models are on the left y-axis. The annual discharges are significantly overestimated by both GLDAS models by: 1570% (NOAH-HRR) and 1580% (CLSM-HRR). However, the TWSA- and altimetry-derived discharges are much more reasonable: 8.1 and − 18%, respectively. Note, the large relative bias values for the GLDAS models are a result overestimating discharge and normalizing by extremely small observed values (observed mean is only 0.27 cm/month).

Susquehanna

The NOAH-HRR and altimetry-derived discharges successfully captured mean annual discharge with 8.5% and 2.7% relative bias at the gauge on the Susquehanna River. However, the mean relative bias of CLSM-HRR and TWSA-derived discharges are − 42% and 30%, respectively. The annual discharges are consistently underestimated by the CLSM-HRR (Fig. 9, Table 2) and overestimated by TWSA; especially during the GRACE-FO period (after 2018).

Results for both monthly and annual discharges are discussed together. In general, TWSA- and altimetry-derived discharges provide reasonable monthly and annual estimates due to their being calibrated to the observed data (Fig. 3). In contrast, the GLDAS models are largely uncalibrated in the context of matching observed river discharges and do not account for water regulation. In this study, NOAH generally provided better estimates of discharge as compared to CLSM. While this study used NOAH (GLDAS 2.1) and CLSM (GLDAS 2.2), these findings are consistent with Hou et al. (2017)⁹ that shows NOAH (GLDAS 2.0) exhibited stronger correlations with observed monthly streamflow globally compared to CLSM (GLDAS 2.0). For both GLDAS models, results tended to be better in the eastern US as compared to western US. This finding is consistent with other studies⁵⁶ and likely associated with non-linearly rainfall-runoff behavior in arid and semi-arid watersheds (e.g., western US) which runoff generation is highly variable.

A major difference between the GLDAS models used in this study, CLSM (GLDAS 2.2) and NOAH (GLDAS 2.1), is that the CLSM model assimilates GRACE TWSA. This difference is a likely reason for performance in the Great Lakes region. While NOAH discharges are reasonable in this region, both CLSM and TWSA-derived discharges perform poorly likely due to ‘leakage effects’ in the GRACE-derived TWSA estimates in this region ⁵⁷. This was also highlighted in Duvvuri & Beighley, 2023²⁹ which shows strong temporal correlation between TWSA and Great Lake levels for watersheds near the Great Lakes. While not linked to GRACE leakage, the altimetry-derived discharges also tended to perform poorly in this region. One potential reason for this finding is the magnitude of uncertainty in altimetry derived WSE relative to the range in monthly river WSE. For example, the Great Lakes region receives less precipitation and generally has lower landscape gradients as compared to the Eastern US^58,59which generally leads to lower variability in river WSE. However, additional research is needed to better understand what is causing the lower performance in altimetry-derived discharges in this region.

In addition to potential leakage impacts, GRACE data assimilation appears to not compensate for the lack of a groundwater withdrawal scheme in CLSM for regions with intensive groundwater abstraction ⁴². Girotto et al., 2016⁶⁰ also suggests the use of GRACE data can sometimes introduce negative trends in shallow groundwater. Thus, in irrigated areas, GRACE data assimilation might not properly attribute mass change to the different soil layers (i.e., surface soil moisture, root-zone soil moisture and groundwater). This could be a possible cause for the poor performance of CLSM model, particularly where the ground water depletion is caused by anthropogenic impacts ⁶¹ such as in Great plains and the Colorado. This is true in cases where ground water impacts river discharge. For example, Nie et al. (2018)⁶² has shown that accounting for groundwater pumping in the Great Plains improved the representation of TWS variability by LSMs and agreement with GRACE.

As noted above, the performance for the GLDAS models is lower in the western US as compared to eastern US. Challenges associated with runoff generation and its sensitivity to soil moisture are likely contributing factors. In the western US, simulated ET estimates tend to exhibit high relative uncertainty due to the limited availability of water, sparse vegetation cover, and high evaporative demand in the⁶³. Additionally, human interventions and intricate terrain and topography, such as mountain ranges and deep valleys, exert localized influences on weather patterns, atmospheric stability, and wind dynamics, creating microclimates and local meteorological conditions that affect ET model performance ⁶⁴. Yu et al., 2023 ⁶³identified CLSM as one of the models with high uncertainties in ET estimates among nine models in their study. Though not explicitly discussed in their study, annual average ET for CLSM showed a cluster of grid cells in the southeast US with anomalously small ET values. In this study, CLSM-HRR derived discharges are overestimated for a cluster of gauges in the southeast US (red points in Fig. 8) that correspond with these low ET estimates.

Performance of the GLDAS models did not appear to vary with drainage area while the remote sensing methods’ performance tended to improve for larger areas. The mean KGE and correlation at the gauges with KGE greater than 0.32 increased slightly with drainage area for TWSA- and altimetry-derived discharges. In the case of altimetry-derived, the mean correlation and KGE increased by nearly 0.2 for gauges draining less than 10,000 km² to gauges greater than 25,000 km². This finding was expected as both remote sensing methods are best suited for larger rivers. Fig S1 in the supplementary material highlights these findings.

Overall, all methods tend to perform better as watershed precipitation increases. This result is somewhat expected. For the GLDAS models, this is likely due to runoff generation being less impacted by dry initial conditions (i.e., highly non-linear infiltration behavior). For the TWSA-derived discharges, the TWSA-Q relationship tends to be strong as regulation is somewhat limited in these regions and large increases in monthly precipitation tends to show corresponding increases in TWSA and discharge. For the altimetry-derived discharges, large increases in monthly precipitation tends to result in large increases in discharge (i.e., WSE), which limits the impacts of altimetry derived WSE uncertainties on derived discharge.

To investigate contributions (i.e., correlation, bias and variability) to low KGE values (i.e., poor discharge estimates), the KGE component causing the largest reduction in KGE from its optimal value of 1 was determined at each gauge. In general, low correlation and high variability were the primary causes of the low KGE values. Here, we highlight results at the gauges with KGE less than 0.32 (i.e., locations where performance is less than our targeted value). Table 3 shows the fraction of sites most impacted by the three KGE components. Several key points are taken from Table 3. First, contributions from poor bias are lowest for TWSA- and altimetry-derived discharges, which is likely due to these methods being trained on gauge observations (i.e., training results in predication trending towards the mean). In addition, variability in TWSA-derived discharges is muted due the nature of the TWSA signal (i.e., large variability is not likely). These contributions are also consistent for monthly and annual estimates. In contrast, contributions from poor correlation are highest for these two methods at the monthly scale, which is likely due to TWSA signals impacted by regulation or GRACE leakage or uncertainty in altimetry measurements exceeding variations in water surface elevations. At the annual scale, there is a noticeable increase in sites where variability is the leading cause of low KGE suggesting that the overall uncertainty in the effective relationships is significant.

Table 3

Leading cause of low KGE for monthly (1st value) and annual (2nd value) discharges at gauges with KGE less than 0.32; values represent percent of sites with a given KGE component providing the largest impact on KGE.
KGE Component	TWSA-derived	NOAH-HRR	CLSM-HRR	Altimetry-derived
Correlation	88 to 57	34 to 20	40 to 9	52 to 28
Bias	0 to 1	19 to 42	25 to 27	13 to 13
Variability	12 to 42	47 to 38	35 to 64	35 to 59

The GLDAS models tend to show a somewhat more uniform distribution of contribution to low KGE but also suggest low correlation controls at the monthly scale and poor variability controls at the annual scale. As noted above and in other studies (e.g., Lv et al., 2018; Xia et al., 2017 ^65,67), peaks from GLDAS derived runoff/discharges tend to occur early. This could be the possible reason for poor correlation at the monthly scale. For example, Lv et al., 2018 observed that the snowmelt start time of GLDAS2.1-NOAH tends to be early, causing early peaks in discharges as compared to in-situ gauges in the northern hemisphere. At the annual scale, the impacts of poor peak timing is muted as the number of sites impacted by low correlation decreases, especially for CLSM-HRR (40% for monthly to only 9% for annual). The number of sites with low correlation also reflects the GLDAS models’ ability to provide reasonable water balance behavior (e.g., more precipitation – more runoff) at the annual scale where impacts due to water regulation and snow accumulation and melt are muted.

In all four methods, bias is least likely to be the dominate cause of low KGE at the monthly scale and three of the four methods at the annual scale (i.e., bias is the major contributor a 42% of sites for NOAH-HRR). As noted previously, the remote sensing methods are calibrated to the gauges, which explains why bias a not a significant contributor. For the GLDAS models, the general water balance framework appears to be suited for average discharges.

In this discussion, results from the major watersheds are grouped together with a focus on differences between discharge estimation methods. First, the TWSA- and Altimetry-derived discharges tend to track the monthly patterns in observed discharges reasonably well. However, at the annual scale, altimetry-derived discharges are limited due to gaps in the data. The most noticeable exception is the Susquehanna, especially for the Altimetry-derived discharges, which are almost temporally opposite to the gauge (e.g., for most of 2020 in Fig. 5). For this river, the TWSA-derived discharges are also generally much larger than the gauge. Additional research is needed to better understand these results as the river is not heavily regulated and sufficiently wide for extracting water surface elevations from the altimetry observations. While there is a seasonal snowpack in the mountains, snowmelt is not a significant fraction of streamflow. One possible issue for TWSA-derived discharges could be the watershed’s proximity to the Great Lakes to the North/Northwest and the Atlantic Ocean to the East/Southeast both of which could have leakage impacts on the TWSA signal. Difference in GRACE and GRACE-FO may also be an issue. For example, in Fig. 9e (2019–2022; GRACE-FO), TWSA-discharges are consistently overestimated in the Susquehanna. However, in Fig. 9e (2004–2016), TWSA-discharges track much closer to the observations, suggesting a difference in TWSA between the GRACE and GRACE-FO periods. In general, TWSA-derived annual discharge in the eastern US were often overestimated (Fig. 8a), which is similar to the findings in Mohanasundaram et al., 2021³⁶, where the GRACE-PY model was shown to overestimate annual discharges in some eastern US watersheds, especially the Ohio, Susquehanna and some New England rivers.

For the Mississippi River, the results for are mixed. For example, CLSM-HRR consistently overestimated discharges for Missouri and underestimated discharges for the Ohio, with varied for the upper Mississippi. This represents a shift in model performance from west to east across the watershed which is consistent with results presented in Tijerina et al., 2021. The underestimation pattern for the Ohio River was also documented byZaitchik et al., 2008 for runoff from CLSM after data assimilation with GRACE in Ohio Basin compared to CLSM open loop, which is similar to the application for CLSM (GLDAS 2.2) used in this study. The study pointed out that the data assimilation possibly degraded hydrologic fluxes despite improving the simulation of hydrologic states. Additional research is needed to better understand differences in model forcings and impacts resulting from assimilating GRACE TWSA into CLSM, especially given the differences between NOAH-HRR and CLSM-HRR are significant in all the Mississippi Basin gauges (20–40 cm/yr). Here, NOAH provides generally favorable results with one clear exception is 2019, where the model significantly overestimate discharges in the beginning of the year (Fig. 5). This appears in the Missouri and upper Mississippi Rivers suggesting a large faction of winter precipitation may have been simulated as rainfall and associated rapid runoff. The gauge data suggests a several month delay and a slower release of runoff. Results for the Ohio were generally consistent with the gauge, and the resulting impacts of overestimating discharges in the Missouri and upper Mississippi were muted at the lower Mississippi gauge. For the Ohio River, as with the Susquehanna, TWSA-derived discharges tend to be overestimated to a larger degree in 2019–2022 but tend to agree better with observations for the GRACE period.

The GLDAS derived discharges failed to accurately predict discharge in the upper Missouri and Columbia River Basins. This is a consistent finding in that the GLDAS models tend to perform poorly in cold regions, which may be related to challenges in capturing cryosphere hydrologic processes (e.g., snow, glacier and/or permafrost) ⁹. For gauges in South, Midwest and Southwest, all methods appear to agree with the observed mean monthly discharges (Fig. 3), however, the KGEs are less than 0.32 for all the estimation methods. This could be due to the failure to predict the irregularities in the time series caused by regulation from the large number of dams in the region ⁶⁹ and the semi-arid environment (e.g., < 60 cm/yr), which is especially challenging for estimating runoff (i.e., runoff generation highly sensitive to soil moisture). The presence of reservoirs/dams in the region likely influence the relationship between discharge and TWSA, which has been previously shown by Duvvuri & Beighley, 2023b.

For the Columbia River, the differences in CLSM-HRR and NOAH-HRR are the most noticeable as compared to the other selected major rivers. CLSM-HRR captures the observed temporal pattern reasonably well while NOAH-HRR peaks higher and earlier than the gauge; followed by a rapid recession much faster than the gauge. NOAH-HRR shows a similar pattern to the TWSA-derived discharges suggesting that NOAH-HRR is mimicking a large influx of water (i.e., increase of TWSA) and loss of water (i.e., decrease of TWSA) differently than CLSM-HRR and the gauge. This could be related to not capturing snow accumulation and melt correctly. For the other major rivers, CLSM-HRR and NOAH-HRR tend to track temporally with each other suggesting their forcings and runoff processes are generally capturing similar behavior. However, their magnitudes of discharge tend to be different suggesting that their magnitudes of precipitation and/or fractions of precipitation converted to runoff are different. This could be attributed to the different sources of metrological fields used to force the GLDAS LSM models. However, in most of the major rivers, the differences in discharge magnitude are consistent with the exception of the Columbia River.

For the Colorado River, which has the smallest discharges (cm/month), the assessment of CLSM-HRR and NOAH-HRR is difficult as they both significantly overestimate discharge and are nearly identical. Similar results have been observed for NOAH-MP, which incorporates additional physics, multiple soil layers and improved representations of vegetation and snow processes compared as compared to GLDAS NOAH. Ma et al., 2017 found that NOAH-MP overestimated runoff by roughly two times throughout the year in the Rio Grande and Lower Colorado watersheds. They attributed it to the challenges associated with precipitation forcings and simulating ET. In addition to the possible error in the forcings, uncertainties in the model structure and parameters were listed as possible reasons for poor performance in these regions. As noted previously, the GLDAS models tend to have the seasonal peaks occur early and significantly higher followed by a rapid decrease to below observed discharges magnitude (i.e., rapid recession). These discrepancies are potentially due to incorrect snow accumulation and melt (i.e., simulated as rainfall and rapid runoff) and lack of reservoir regulation/routing. While the altimetry-discharges are largely not available for the Colorado River, the TWSA-discharges performed reasonably well (KGE 0.37 for monthly discharges and 8% relative bias for annual discharges).

Four methods (two physics-based hydrologic models and two remote sensing-based methods) for estimating river discharge are compared to USGS gauges throughout the CONUS for the period 2002–2021. The two models NOAH 2.1 and CLSM 2.2 are part of NASA’s GLDAS and provide differences in data assimilation (e.g., CLSM 2.2 assimilates GRACE TWSA while NOAH 2.1 does not). Here, monthly discharges are evaluated using KGE and its components: mean bias, variability bias and correlation. The annual discharges calculated by aggregating monthly discharges for years with at least 10 months of data are evaluated using NRSME and relative bias.

Overall, the median KGE for all gauges in this study are 0.43, 0.39, 0.1 and − 0.05 for TWSA-derived, altimetry-derived, NOAH-HRR, and CLSM-HRR, respectively; median NRMSE is 0.4, 0.28, 0.46 and 0.6 and median relative bias is 9.17, 10.93, 3.94 and − 8.63.

In general, the TWSA-derived, altimetry-derived and NOAH-HRR methods work well for monthly estimates. Results for CLSM-HRR are mixed. For the remote sensing-based methods, gauge locations where derived discharges result in KGE less than 0.32 (i.e., our targeted minimum KGE value), poor correlation is the primary contributor to low KGE. Given the two methods are calibrated to gauge observations, this finding is consistent with correlation being leading cause of low KGE (i.e., weak TWSA-Q relationship or limited ability of altimetry-derived WSE to accurately observe actual WSEs). In contrast, NOAH and CLSM, correlation was generally good (i.e., not the leading cause of low KGE), which is likely due to these models capturing water cycle processes (i.e., precipitation leads to runoff, capture seasonal discharge patterns). The challenges for the GLDAS models are bias and variability, which highlights the importance of capturing non-linear runoff generation processes (i.e., over/under-estimate runoff for a range of conditions impacting variability or consistently impacting bias).

The primary causes for poor model performance are difficult to determine, but based on previous studies and differences between methods, several likely factors are highlighted: GRACE leakage, water regulations (e.g., reservoir operations), runoff generation in arid/semi-arid climates, and snow accumulation and melt. For example, TWSA-derived and CLSM-HRR both exhibit lower model performance in the Great Lakes Region, where GRACE leakage has been documented in the TWSA. Both the GLDAS models show notably lower model performance in arid/semi-arid watersheds where initial soil moisture is likely impacted by simulated ET rates and runoff generation is highly non-linear. In general, both models tended to significantly overestimate runoff and corresponding river discharges in these regions. In addition, challenges associated with snow accumulation/melt and not accounting for water regulation (reservoir routing, water withdraws) is problematic in both GLDAS models and to some degree the TWSA-derived discharges.

In addition to the above, drainage area does not appear to alter performance in GLDAS models but does affect TWSA- and altimetry-derived discharge performance. The remote sensing methods are limited to larger rivers (e.g., rivers sufficiently wide to obtain WSEs; sufficiently large to better align with GRACE TWSA resolutions). Additional research is needed to further refine optimal watershed scales/conditions for the remote sensing-based methods.

A key finding from this study is that results vary by location and discharge estimation method. Given the number of methods/models available for CONUS wide discharge estimates, an ensemble approach is recommended. This is especially important given the good performance of altimetry-based discharge estimates, which have the benefit of observing the river water surface rise and fall which is directly proportional to the river discharge. Here, the altimetry-derived method captured at least 70% of observed mean annual discharge at 80% of the study gauges. While altimetry-derived discharges are limited to select locations based on altimetry satellite tracks and river width, the launch of the SWOT satellite in 2022, which uses a wide-swath, provides near global coverage with the added benefit of river width and slope estimates. Our results suggest that SWOT-derived river discharges have potential to significantly improve our understanding of river discharge.

Competing interests

7 The author(s) declare no competing interests.

Author Contribution

B.D. – data collection, and processing, analysis, result interpretation and writing original manuscriptJ.G. – data collection, and processing, analysis E.B. – conception of the idea, reviewing and editing manuscript

Data Availability

The datasets analyzed in this study can be found in the Hydroshare repository at Duvvuri, B., E. Beighley (2024). Evaluation of river discharges derived from remote sensing and land surface models, HydroShare, http://www.hydroshare.org/resource/cbafcade27e6418ebe1d45e31cae2426

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Evaluation of river discharges derived from remote sensing and land surface models

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Abstract

Figures

Introduction

Materials and Methods

3.1 Study Area

3.2 Land Surface Models

3.3 River Routing of LSM’s Runoff

3.4 Remote Sensing Based Discharge Estimates

3.4.1 Estimation using GRACE Total Water Storage Anomalies (TWSA)

3.4.2 Estimation using Satellite Altimetry

3.5 Model Performance Section

Results

4.1 Monthly Discharge

4.1.1 CONUS

4.1.2 Major Watersheds

4.2 Annual Discharges

4.2.1 CONUS

4.2.2 Major Watersheds

Discussion

Conclusions

Declarations

Competing interests

Author Contribution

Data Availability

References

Additional Declarations

Supplementary Files

Status:

Version 1