Coastal plume regions represent a small fraction of Earth's surface and are an active component in global cycling of carbon and nutrients (Bourgeois et al., 2016; Carroll et al., 2020; Fennel et al., 2019; Lacroix et al., 2020; Landschützer et al., 2020; Roobaert et al., 2019). Recent satellite-based observations with quasi-global coverage have been greatly improved to monitor sea surface salinity (SSS), a key tracer for tracking the river plumes. The European Space Agency (ESA) Soil Measure and Ocean Salinity (SMOS; Mecklenburg et al., 2012) with 33 km–10 d space–time gridding and National Aeronautics and Space Administration (NASA) Soil Moisture Active Passive (SMAP) missions with 40 km–8 d space–time gridding are acquiring SSS observations with sufficient resolution to track the plume pathways and evaluate coastal plume dynamics (Fournier et al., 2016a, b, 2017a, b, 2019; Gierach et al., 2013; Liao et al., 2020). To date, however, the coastal plume regions have not been explicitly resolved in most global ocean general circulation models (OGCMs), Earth system models (ESMs), and Global Ocean Data Assimilation System (GODAS) products (Ward et al., 2020). As a result, the plume region produced by OGCMs, ESMs, and GODAS are not consistent with satellite observations. For example, Fournier et al. (2016a) found that the 1/12∘ global circulation Hybrid Coordinate Ocean Model (HYCOM) did not accurately capture SSS during extreme flood events in the northern Gulf of Mexico. Denamiel et al. (2013) found that the Congo River nearshore SSS in global HYCOM was underestimated compared to other regional simulations, even though the models had comparable horizontal grid resolution. Santini and Caporaso (2018) suggested that most CMIP5 models might lack skill in representing the Congo River Basin runoff and SSS in the vicinity of river mouths. Most OGCMs, ESMs, and GODAS products usually had large grid cells; a few cells may encompass the entire plume. As a result, water delivered to the cells are fully mixed and diluted and therefore cannot accommodate the complex dynamics. Additionally, riverine freshwater input to the ocean is forced in the top model layer over a pre-determined surface area in the vicinity of river mouths with climatological signal; thus the system disturbance by extreme weather events, e.g., floods and droughts, cannot been explicitly resolved (Griffies et al., 2005; Tseng et al., 2016). Finally, virtual salt fluxes (VSFs) have been widely employed, where freshwater affects salinity without a change in mass or volume flux (Bentsen et al., 2013; Halliwell, 2004; Timmermann et al., 2009; Volodin et al., 2010). The above model configurations may limit the representation of coastal plume regions in global-scale models.

Estimating the Circulation and Climate of the Ocean (ECCO) is a data-assimilating model that uses observational data to make the best possible estimates of ocean circulation and its role in climate. The model takes the cube–sphere (ECCO2) to latitude–longitude–polar-cap (ECCOv4) grids for global application. Like most OGCMs, ESMs, and GODAS products, the current ECCO routes riverine freshwater from land directly to the ocean by taking observed river runoff as seasonal climatology mass flux over the top of several surface grid cells near the river mouths (Fekete et al., 2002; Stammer et al., 2004). Recent ECCO efforts have been extended to address the global-ocean estimates of pCO2 and air–sea carbon exchange (Carroll et al., 2020), and model resolution as fine as 1 km has been promoted globally to investigate mesoscale-to-submesoscale dynamics in the open ocean (Su et al., 2018). However, current ECCO lacks representation of coastal interfaces and related feedbacks limiting their predictability to global climate change, and this may further impede our ability to make informed resource management decisions. In this study, we improve the representation of river runoff in the ECCO and systematically evaluate model performance in reproducing SSS within the vicinity of large tropical and temperate river mouths. We also investigate the impact of runoff forcing, model grid resolution, and grid type on coastal dynamics and critical physical properties near the plume regions. The goal of this work is to provide a comprehensive sensitivity analysis of runoff forcing in multiple simulations, which will aid in the development of global ECCO that more robustly reflecting the land–ocean aquatic continuum (LOAC).

The paper is organized as follows. Section 2 briefly introduces the ECCO model and the various runoff forcing methods used in this study. Section 3 provides a comprehensive evaluation of model sensitivity to horizontal grid resolution and river forcing. Section 4 discusses the sensitivity of plume properties and coastal stratification. Results are summarized in Sect. 5.

We first estimate how the various ECCOv4 LLC simulations (Table 1) compare to observations in the vicinity of 10 large river mouths. The synchronized SMAP SSS (1 April 2015 to 31 December 2017, 33-month) is used as the main verification dataset (Yueh et al., 2013, 2014). SMAP SSS has been documented to exhibit bias compared to observed SSS in shallow waters near river mouths (Fournier et al., 2017a). Therefore, as an indication of absolute SSS, we also compare the model simulations to the World Ocean Atlas 2018 (WOA18). We note that there may be relatively few observations incorporated into the objectively analyzed WOA18 product near the coast, which may over-smooth salinity fronts. Additionally, WOA18 is a 55-year climatology from 1955–2010; therefore, we can only compare model climatology from 2015–2017. Overall, we use SMAP and WOA18 as “observational references”, where our model–observation comparisons provide useful information on how SSS changes between experiments rather than determine which experiment is closer to the real world.

The upper 10 m SSS biases relative to SMAP, averaged over the 33-month period, for CS510C (standard ECCO2) as well as the LLC540R (highest resolution) are shown in Fig. S2. Both SMAP and WOA18 have 1/4∘ horizontal grid resolution; therefore, we interpolated all model fields to this grid. For both simulations, negative biases are found from low latitudes to mid-latitudes, while positive biases occur at high latitudes. When focusing on large river mouth regions (e.g., AZ, PA, and CJ), the SSS bias is reduced in LLC540R. This demonstrates that the choice of runoff forcing impacts SSS at predominantly local scales; however, background currents can transport the signal downstream or offshore to the open ocean (Liu et al., 2009; Molleri et al., 2010).

Next, we compute mean model SSS near all selected river mouth regions, along with SMAP and WOA18 (Table 2). The corresponding Willmott skill (WS) numbers are listed in Table 3. We use the first empirical orthogonal function (EOF) derived from WOA18 to determine river mouth regions, since WOA18 represents persistent low-salinity zones over the 30-year period. We remove the mean SSS field before the EOF analysis. The first mode explains ∼ 47 %–67 % of the total variance. We then reconstruct the dominant SSS anomaly field by multiplying the first PC with the spatial pattern. Locations with salinity that is 1–2 PSU lower in the reconstructed SSS field are taken as the river mouth region, and all eight regions are shown in Fig. S3. We first found that SMAP SSS is lower than WOA18 for large rivers. The underestimation is high over 5 PSU for the Amazon region. The deviation between satellite products and in situ observations is consistent with Fournier et al. (2016b, 2017a). Near the selected large river mouths, experiments with daily, point-source runoff forcing generally have lower SSS than experiments forced by climatological diffusive runoff (LLC90R vs. LLC90C; LLC270R vs. LLC270C; CS510R vs. CS510C). Increasing model resolution generally results in regions becoming fresher (Table 2; LLC90C to LLC270C; LLC90R to LLC270R to LLC540R). With the intermediate resolution, the diffusive daily JRA55DO runoff forcing LLC270R_spread had lower salinity than the climatological Fekete-driven forcing run (LLC270C). This is not surprise, since the Fekete river discharge file is more spatially spread than JRA55DO before the model automatic interpolation (Fig. S1), which means less freshwater has been input to the top of the river mouth region, resulting a relatively high salinity. Meanwhile, with the daily JRA55DO forcing, the sea surface salinity with the point-source forcing (LLC270R) was lower than that with the diffusive forcing (LLC270R_spread). It is possible that decreasing the number of cells adding the freshwater was equivalent to decreasing the river mouth inlet width, which results in the inflow velocity increasing and thus spreads the riverine water more widely. In contrast, we found the point-source river forcing run using year-by-year JRA55DO and climatological JRA55DO shows a lack of consistency in SSS change compared to the above two cases.

A comparison with SMAP shows that Wskill scores become higher when model resolution increases from 1 to 1/3∘ (LLC90C vs. LLC270C, LLC90R vs. LLC270R), but lower when it increases further to 1/6∘ (e.g., LLC270R vs. LLC540R for Amazon, Ganges/Brahmaputra, Parana). The higher or lower Wskill score is consistent with the SSS decrease. At the AZ region, SSS from LLC270R is less than 1 PSU lower than the SMAP average, while that from LLC540R is roughly 3 PSU lower. Therefore, LLC270R receives a skill score of 0.92, higher than LLC540R (0.74). Although the SSS reduction lowers the model score overall, we should note that SMAP only has 1/4∘ resolution. This means it may not have the capability to resolve those fine-scale dynamic feathers of the plume compared to high-resolution model simulation. In addition, SMAP may underestimate SSS near the river mouth. Therefore, a larger discrepancy with SMAP in the high-resolution run does not indicate that the simulation deviates from the truth.

The Wskill scores when taking SMAP as the reference show that LLC270R_spread is better than LLC270C for AZ, GB, MR, PA, and CO. This is not surprising since the JRA55DO runoff had better temporal resolution than Fekete runoff. Meanwhile, Wskill scores of LLC270R_spread is worse than LLC270R, mainly because of diffusive surface runoff bringing higher SSS than point-source surface runoff (Fig. S8).

When taking the climatological WOA18 as the observational reference, experiments forced with the climatological river forcing had a better Wskill score than with real-time forcing for the Amazon River, but no such pattern for other rivers. The lack of consistency is possibly because the simulations and data are not synchronized in years. A comparison with the SMAP score shows that most ECCO SSS products had comparable skill with SMAP, indicating that they are reliable to use at the climatological mean level.

The higher or lower Wskill score is consistent with how much the model deviates from the observational reference. At the AZ region, SSS from LLC270R is less than 1 PSU lower than the SMAP average, while LLC540R is roughly 3 PSU lower. Therefore, LLC270R receives a skill score 0.92, higher than LLC540R (0.74). This also occurs with LLC270C and LLC270R when using WOA18 as the reference.

For rivers in tropical and temperate zones, the CS510 grid has a resolution comparable with the LLC540 grid; therefore, the SSS and skill scores are comparable between CS510R and LLC540R. Since the model grid type has a negligible impact on SSS for low-latitude to mid-latitude rivers, we next focus on discussing model sensitivity to runoff forcing and model grid resolutions only.

To better compare the sensitivity of SSS to river forcing, we provide zoomed-in plots of the same comparison shown in Fig. 1 for AZ, MR, and CO Rivers for all LLC simulations, representing large, medium, and small rivers (Figs. 2 and S8). The positive bias is greatly reduced when applying daily, point-source river forcing, as well as increasing the horizontal grid resolution.

Time series for all LLC simulations and SMAP, at these three river mouths, are shown in Fig. 3. As in Fig. 2, the bias decreases when daily, point-source river forcing is used and as the horizontal grid resolution increases. Additionally, We found the 2017 spring Amazon flood can be clearly seen when forced by diffusive daily JRA55DO (LLC270R_spread), but not in the diffusive climatological Fekete case (LLC270C). The Mississippi River mouth region is different from the Amazon in that the annual cycle of LLC270_spread is stronger than LLC270C. This is because the seasonality of the Mississippi–Atchafalaya river has been oversmoothed in the climatological Fekete. The Columbia river region is consistent with the Amazon in that there is an abnormal low salinity in 2017 in LLC270R_spread and LLC270R, which is because the peak discharge is successfully resolved by JRA55DO.

It is interesting to see the intermediate LLC270 resolution run is better than the high CS510 resolution run at the Amazon region. This is because the Stammer et al. (2004) runoff is smoother spatially and lacks seasonal variability compared to the Fekete et al. (2002) runoff in this region (Fig. S7). When using DPR forcing, the SSS differences associated with the river discharge interannual variability can be resolved as well. For example, the 2017 abnormally low SSS near the Amazon river mouth is associated with an extreme flooding event (Barichivich et al., 2018).

Next, we quantify the difference in mean and variance between the SSS time series of LLC simulations and that of SMAP under daily JRA55DO runoff but using diffusive and point source methods for each (Fig. 4). We found the normalized bias with point source is lower than experiments with diffusive source. The normalized unbiased RMSD decrease is ignorable compared to the normalized bias decrease. This means the total normalized RMSD improvements are primarily due to the normalized bias decrease. We find that most unbiased RMSD remains negative when varying the runoff forcing from climatological to daily. This implies that the variance of LLC simulations remains lower than SMAP observations as the runoff forcing changes. The only exception is the Congo river, which is a near-Equator eastern boundary plume that freshwater transport may distinguish from others (Palma and Matano, 2017).

We also examine the bias and variance on the target diagram for experiments with varying grid resolution but similar daily runoff forcing (Fig. 5). Our results show that the normalized bias decreases as the model resolution increases, which is consistent with the SSS reduction in Table 2 and relatively low Wskill in Table 3. The unbiased RMSD decreases slightly with the sign remaining negative as the model resolution increases. This occurs everywhere, except for the two largest rivers (AZ and CG) where the sign becomes positive for LLC540R, indicating that the model variance exceeds the SMAP variance when using the high-resolution grid. In summary, the comparison with synchronized SMAP shows that using daily runoff and finer horizontal grid resolution improves the representation of SSS variability but at a cost of increased SSS bias.

In this study, we investigate the model sensitivity of runoff forcing and grid resolution and type under the ECCO framework. We find that DPR greatly improves model representation of global rivers, with horizontal model resolution having a substantial control on SSS in the vicinity of river mouths. We observe no major changes in tropical and temperate river mouth SSS when using cube–sphere or LLC grid types when using the same river forcing. A comparison with synchronized SMAP observations shows that the use of DPR forcing and intermediate grid resolution can increase the model performance in simulating SSS in the vicinity of river mouths. However, further increasing model grid resolution from intermediate to high may result in an additional SSS bias towards fresher values.

Previous theoretical modeling studies have demonstrated that, in the absence of external forcing, large river plumes influenced by rotational effects tend to veer anticyclonically and form a bulge region near the river mouth as well as an along-shore downstream coastal current as Kelvin waves (Kourafalou et al., 1996; Yankovsky and Chapman, 1997). Additionally, idealized numerical simulations have revealed that river plume behavior is greatly impacted by external forcing. Chao (1988a, b) demonstrated that vertical mixing, bottom drag, and bottom slope greatly impact the spin-up, maintenance, and dissipation of river plumes. Fong and Geyer (2001) revealed that a surface-trapped river plume would thin and be advected offshore by cross-shore Ekman transport. Fong and Geyer (2002) suggested that the ambient current, which is in the same direction as the geostrophic coastal current, can augment plume transport. Our ECCO experiments are examining the above river plume dynamic theory globally with realistic topography and external atmospheric forcing. Our EOF analysis of SSS at the AZ, MR, and CO shelves show that the general spatial and temporal patterns plume related to river discharge, wind, and currents are independent of the grid resolutions and forcing formulations examined in this study, which are quite consistent with those previous studies. However, higher resolution and DPR forcing may be particularly important for resolving the fine-scale plume dynamics for small rivers. Using DPR forcing and increasing the model grid resolution from coarse to intermediate increases the river plume area and volume, while further increasing the model resolution from intermediate to high has mostly regional effects. Shallow and wide shelf regions, such as the Mississippi Delta, are more sensitive compared to AZ and CO. Nowadays, the increased computational power allows GODAS products such as ECCO to provide data at different resolutions, which supports regional scientific studies using a data analytical approach or offline method (e.g., the Lagrangian method; Meng et al., 2020; Liang et al., 2019). Our results suggest that how high-resolution products should be used depending on the spatiotemporal dynamics as well as geomorphology characteristic of the studied region itself.

We also found that using DPR forcing and increasing the model grid resolution can stabilize the water column at the subsurface and shoal the MLD. This may have significant implications for biogeochemical cycles and air–sea exchange in coastal zones. From the biogeochemistry perspective, freshwater introduced by the river increase shelf stratification, preventing the reoxygenation of bottom waters and thus may generate large hypoxic regions (Fennel et al., 2013; Feng et al., 2019). From the air–sea interaction perspective, on one hand, SST can trigger deep atmospheric convection and strong rainfall. On the other hand, strong near-surface stratification may inhibit cooling and intensify tropical cyclones (Cione and Uhlhorn, 2003; Neetu et al., 2012; Rao and Sivakumar, 2003; Sengupta et al., 2008; Vialard and Delecluse, 1998; Vinaychandran et al., 2002). We envision that future work investigating river impacts on ocean–atmosphere and Earth system dynamics could be accomplished by coupling our improved ECCO simulations with an atmospheric general circulation model (AGCM).

In the state-of-the-art OGCMs, ESMs, and most GODAS products, river runoff is incorporated into coarse-resolution grids as augmented precipitation. Climatological runoff forcing is often used in conjunction with artificial spreading, along with a virtual salt flux scheme. Tseng et al. (2016) examined model sensitivity to the spreading radius, turbulent mixing parameterization, reference salinity, and vertical distribution of riverine freshwater on 1∘ resolution in the Community Earth System Model (CESM). For all factors examined, they found that the model results are most sensitive to the spreading radius, which substantiates the importance of our finding that the associated plume properties, including the area and hence the SSS near river mouths, exhibit strong responses when switching the runoff flux from diffusive climatological to daily point source.

The present state-of-the-art regional-scale estuarine models can simulate estuarine hydrodynamics and biogeochemical processes in a robust manner. The inlet approach, which defines a rectangular breach in coastal land cells with uniform density and discharge, is widely used (Herzfeld, 2015; Garvine, 2001). An additional barotropic pressure term may be added to account for pressure gradients induced by the freshwater plume (Schiller and Kourafalou, 2011). The inlet approach has also been used in global z-coordinate models by injecting freshwater in multiple vertical grid cells (Griffies et al., 2005). In our simulations, changes in sea level are redistributed over all vertical grid cells by the rescaled height vertical coordinate. This is similar to the inlet approach in the regional models, which add a mass or volume flux of freshwater to a breach in coastal land cells (Garvine, 1999). Herzfeld (2015) investigated the role of model resolution on plume response at the Great Barrier Reef (GBR) using the Regional Ocean Modeling System (ROMS). The study found that the plume veered left and followed a northward trajectory to Cape Bowling Green in a 1 km resolution model but not in a 4 km resolution model. Our findings are consistent with this result; plume properties in our intermediate-resolution simulations are more clearly detected than in the coarse-resolution simulations. In addition, our results expand on their findings by showing that the sensitivity of plume properties in high-resolution models are highly dependent on shelf bathymetry. Schiller and Kourafalou (2010) investigated the dynamics of large-scale river plumes in idealized numerical experiments using HYCOM to address how the development and structure of a buoyant plume is affected by the vertical and horizontal redistribution of river inflow and bottom topography. Their experiments show that a narrow inlet and flat bottom facilitate a larger right-turning plume bulge region compared to a wide inlet and sloped bottom (see their Fig. 8; Riv2c-f, Riv2c-s). This is complementary to our findings that the MR plume, located on the wide and shallow LA shelf, has a larger horizontal plume area compared to the AZ and CO plume when increasing the horizontal resolution from intermediate to high. However, their discussion was limited to an idealized, rectangular model domain without external forcing, while our model simulations provide a realistic application to natural river plume systems. The global application of the regional inlet representation of river forcing was also used by NOAA's Geophysical Fluid Dynamics Laboratory (GFDL) models (Griffies et al., 2005). An internal, pre-computed salinity source term was introduced into multiple vertical layers. However, river representation was done through VSF rather than through real mass or freshwater volume flux. Adding the real volume and mass of freshwater through multiple layers has been widely used in regional models like ROMS; it may be useful to adapt this technology into future ECCO simulations and compare the results with the current surface injection methods.

For the global ocean, river runoff is much smaller than the precipitation and evaporation flux; therefore, for most OGCMs, ESMs, and GODAS products it is parameterized. One of the most significant expected signatures of global warming is an acceleration of the terrestrial hydrological cycle (IPCC, 2021; Piecuch and Wadehra, 2020). Both can significantly affect the magnitude, distribution, and timing of global runoff, leading to extremes in the frequency and magnitude of floods and droughts. When considering issues related to water resource management under climate and land use and land cover change, a key question such as “how will coastal oceans be impacted from flood and drought events?” is challenging to answer (Fournier et al., 2019). In the future, high-resolution global-ocean circulation models with DPR forcing may help identify the primary forcing mechanisms (such as those from climate-driven extreme events) that drive spatiotemporal variability of large river plume systems just as skillfully as regional model setups.

Improved model representation of rivers may not be as important for global- or basin-scale hydrological cycles as precipitation and evaporation (Du and Zhang, 2015) but may be critical for the global carbon cycle (Friedlingstein et al., 2019; Resplandy et al., 2018). River delivers large amounts of anthropogenic nutrients to the coastal zone (Seitzinger et al., 2005, 2010). The autochthonous production will transform inorganic nutrients to organic nutrients while sequestering atmospheric CO2. More importantly, rivers also deliver dissolved organic carbon (DOC) and particulate organic carbon (POC) to the coastal ocean, which can be remineralized and released as CO2 to the atmosphere. Until recently, most global-ocean biogeochemistry models omitted or poorly represented riverine point sources of nutrients and carbon. Lacroix et al. (2020) added yearly-constant riverine loads to the ocean surface layer on coarse-resolution (1.5∘) models and assessed that CO2 outgassing from river loads accounted for ∼ 10 % of the global ocean CO2 sink. We anticipate that the implementation of DPR forcing and higher-resolution grids in ESMs and the ECCO biogeochemical state estimates (ECCO-Darwin, Carroll et al., 2020) will help better resolve the global carbon budget (Friedlingstein et al., 2019).

LOAC development has historically had a low priority in OGCMs, ESMs, and GODAPs and exchange of freshwater between rivers/estuaries and the coastal ocean has been previously neglected. Our results demonstrate that the representation of runoff forcing in ECCO simulations is a major source of bias for coastal SSS. We believed our improvements of river runoff in ECCO will directly contribute to (i) the evaluation, understanding, and improvement of river-dominated coastal margins in global-ocean circulation models; (ii) investigation of mechanisms that drive seasonal and interannual variability in coastal plume processes; and (iii) bridging the gap between land–ocean interactions. These efforts will ultimately help to better resolve land–ocean–atmosphere processes and feedbacks in next-generation Earth system models.