ROMS is configured as part of the Coupled-Ocean-Atmosphere-Wave-Sediment Transport Model COAWST v3.8, implementation. Several versions of this model have been used to study processes on the TXLA shelf . The domain covers the TXLA shelf and outer continental slopes (Fig. c). The curvilinear mesh has 1.28×105 horizontal cells with a mean resolution of 1.7 km; a finer horizontal resolution of 650 m at the M–A River mouths, expanding out to 3.7 km on the outer continental slopes. The model uses 30 terrain-following vertical layers refined at the surface (Fig. ). The vertical resolution ranges from O (20 cm) close to the coast to O (100 m) near the seafloor on the continental slope. Mean vertical resolutions for the entire domain, inshore of 10 m depth, and inshore of 50 m depth are shown in Fig. a to better compare with the MPAS–O simulations. The minimum water depth is 5 m. The model uses a 75 s baroclinic timestep and a 1.5 s barotropic timestep.

The vertical mixing scheme deserves special consideration. To be consistent with the last version of the model used for validation , we use the k–ω scheme for our “base case” (hereinafter ROMS: k–ω), which solves prognostic equations for turbulent kinetic energy k and specific dissipation rate ω. We also perform a simulation using the ROMS specific implementation of the K-Profile Parameterization (KPP, hereinafter ROMS: KPP), which is closest to the KPP formulation included in the MPAS–O configuration of the Community Vertical Mixing (CVMix) library . See Part 1 for a more detailed discussion on the differences between ROMS' native KPP scheme and the CVMix implementation. Background viscosity and diffusivity values for the simulations can be found in Table . Other aspects of this simulation are the same as ROMS: k–ω. Lateral mixing is parameterized with harmonic viscosity (ν2u=5.0 m² s⁻¹) and diffusivity coefficients (κ2=1.0 m² s⁻¹) scaled to the grid size. Lateral viscosity is rotated along terrain-following layers and lateral diffusion is rotated along geopotential surfaces.

The simulations use repeat year forcing from 2003–2004 . This is advantageous because it makes it easier to identify model differences that could be obscured by interannual variability. A downside is that it prevents us from validating the simulations with regional climatologies because the forcing from two calendar years is combined. Japanese Reanalysis (JRA) v1.3 is used to provide the following atmospheric forcings every three hours on a 55 km grid : 10 m air temperature, pressure, and winds; specific humidity; downward longwave and shortwave radiation; and precipitation. Outgoing longwave is parameterized using the model sea surface temperature. The model applies a Jerlov water type that transitions from Type III near the river mouths to Type IA near the open boundaries . Outgoing shortwave is parameterized using a constant albedo of 0.06 to be consistent with MPAS–O. ROMS uses a virtual salt flux surface boundary condition. Open boundary and climatology forcing is provided by daily output from Global HYCOM Reanalysis, which uses a horizontal resolution of 1/12° (see Code and Data Availability). The model is initialized on 1 January from the HYCOM climatology file. Tides are neglected because they are weak in the GoM .

As is common practice in regional models (e.g. GETM, ), rivers are configured as point sources (Fig. c), using United States Geological Survey (USGS) and United States Army Corps of Engineers  USACE) streamflow data from nine regional rivers (see Code and Data Availability): Mississippi, Atchafalaya, Sabine, Calcaseiu, Trinity, Brazos, San Antonio, Lavaca, and Nueces. The overwhelming majority of the transport comes from the M–A rivers . To represent the complex geometry of river outflow, individual rivers may be represented by multiple localized source cells. The Mississippi River is distributed across 43 grid cells and the Atchafalaya across 8 grid cells to better represent observations, while each of the remaining rivers is represented by a single grid cell. For each river, the runoff flux, runoff direction, vertical distribution, temperature, and salinity are prescribed at a land-sea boundary. Horizontal momentum associated with river inflows is represented by prescribing volume fluxes along with their vertical distribution across river cell faces; ROMS then computes horizontal velocities and accounts for the resulting momentum through flux divergence. Volume fluxes for the M–A rivers are distributed as piecewise functions to resemble observations, with the majority of the discharge in the upper 13 layers. For the other rivers, volume fluxes linearly decrease over all 30 layers starting from 6.5 % in the top vertical layer. The river salinity is set to zero. Daily river temperatures are prescribed using the approach of , where river temperature is estimated from air temperature using the empirical relationship Triver=5.0+0.75Ta, where Ta is the air temperature, often collocated with the streamflow gauge.

The spinup time is two years, consistent with previous studies , after which the M–A freshwater volume on the shelf remains relatively constant with respect to the day of year. This is quantified by tagging the M–A rivers with passive dyes similar to , who used an earlier version of the ROMS model to study freshwater transport on the shelf. This is discussed more in Sect. . The simulations were run for five years on 120 CPU cores (one node has 128 cores) at the National Energy Research Scientific Computing Center. ROMS: k–ω achieved approximately 1.9 simulated years per wall-clock day, ROMS: KPP achieved 2.1 simulated years per day. Snapshots and averages of all variables were saved every 12 h. Analysis of model output was done from years three through five.

The simulations use the E3SMv3.0.0 version of MPAS–O , only differing in the mesh and a few notable additions to rivers and analysis members described below. The simulations employ MPAS–O coupled to MPAS Sea Ice , forced by data-driven atmosphere and river runoff forcings. The simulations also use the same atmospheric forcing as the ROMS model. MPAS–O uses a kinematic surface boundary condition for volume conservation. The model uses a 30 s baroclinic timestep and a 1.5 s barotropic timestep (Table ).

The unstructured horizontal mesh is generated using the JIGSAW library . The mesh has 1.26×106 horizontal cells consisting of hexagons and pentagons (Fig. d). The target resolution in the GoM is 1.5 km to match the mean resolution of the ROMS model on the inner shelf (Fig. e), but the actual resolution is 0.95–1.4 km, with the majority of cells near 1.4 km. The target resolution in the entire GoM is uniform to minimize any potential impacts of flow impedance on Loop Current dynamics. The remainder of the mesh transitions to a target resolution of 60 km in the Atlantic and 100 km in the Pacific and Indian Oceans (not shown) using hyperbolic tangent functions similar to . Actual resolutions are closer to 55 and 95 km, respectively. The resolution is sub-10 km across part of the North Atlantic and Caribbean Sea (Fig. a). We note that high resolution cells in the GoM “leaked” across the Pacific coast of Mexico due to the need to maintain a continuous global ocean and land mesh, as the resolution was unable to discontinuously taper. To prevent numerical instabilities, and because there is sufficient geographical separation from the area of interest, these cells were culled from the ocean mesh.

The simulations use a z* vertical coordinate with partial bottom cells . The layer thickness Δz is calculated as: 1Δz(k)=Δzmax-Δzmintanh⁡πk-k0Δ+Δzmin, where k is the layer index, Δzmax=250 m and Δzmin (defined below) are the prescribed maximum and minimum layer thicknesses, respectively, k0 is the origin in vertical index space of the transition, and Δ=28 is the number of transition layers over which the tanh⁡ function transitions from Δzmin to Δzmax. The minimum water depth is 5.0 m.

We show results from two simulations that vary in vertical grid, river forcing, and their horizontal mixing coefficients. The first (MPAS–O: JRA) uses 80 vertical layers with Δzmin=1.0 m and the second (MPAS–O: USGS) uses 64 layers with Δzmin=0.5 m (Fig. ). MPAS–O: JRA is intended to be more representative of the model run with parameters and forcing used in fully-coupled climate simulations, whereas MPAS–O: USGS was tuned over a number of six month trial simulations to produce the highest-fidelity result with new river forcing. For example, different vertical grids were used because a trial simulation with MPAS–O: USGS that used the same vertical grid as MPAS–O: JRA did not produce submesoscale eddies on the shelf (not shown). Trial simulations of six months were used because the plume, although not spun up, develops sufficient eddies during the first summer for preliminary tuning evaluation. Example cross-sections for MPAS–O: USGS and ROMS near Atchafalaya Bay are shown in Fig. c and d. We refer the reader to Table  for a summary of differences between the MPAS–O simulations.

Vertical mixing is parameterized using KPP as part of the CVMix library . The model uses harmonic and biharmonic viscosity coefficients scaled to the grid size as: 2ν2u=ν20ΔxΔxref,3ν4u=ν40ΔxΔxref3, where Δx is the cell width, Δxref is the reference cell width equal to 30 km, and ν20 and ν40 are the background harmonic and biharmonic viscosities, respectively. These coefficients were tuned to be as small as possible without noise appearing at the grid scale such that ν20 is 66.6 m² s⁻¹ for MPAS–O: JRA and 33.3 m² s⁻¹ for MPAS–O: USGS. ν40 is 3.33×1011 m⁴ s⁻¹ for MPAS–O: JRA and 2.22×1011 m⁴ s⁻¹ for MPAS–O: USGS. No lateral diffusion is applied to the tracers. Mesoscale eddy effects are parameterized at non-eddying resolutions (>20 km) using isoneutral diffusion with a constant, slope-limited diffusivity of 300 m² s⁻¹ and a Gent–McWilliams scheme with the same constant diffusivity. Both coefficients are linearly tapered to zero between horizontal resolutions of 30 and 20 km. The scheme, which restratifies the upper ocean through submesoscale mixed layer instabilities, is disabled throughout the domain.

In global models, river runoff fluxes derived from river routing models or observational datasets are often remapped from the terrestrial grid to the ocean grid and spread across many coastal grid cells . This provides a practical representation of river plume spreading that is otherwise unresolved at coarse resolutions (O (10–100 km)). As resolution approaches the kilometer scale, the prescribed spatial scale of the discharge can substantially exceed the characteristic width of observed plumes and modify the localized buoyancy forcing that drives their resolved dynamics. In response, several global ocean models (e.g., ICON-Coast, ECCO-Darwin) use point source formulations that localize runoff fluxes to one or more model cells . However, the common application of a single configuration globally across rivers of widely varying discharge and coastal geometry can still result in point source schemes that are typically less flexible than those used in regional models, which can assign specific characteristics (e.g., salinity, vertical runoff distribution) for individual rivers.

In E3SM v3.0, river runoff fluxes are prescribed daily from the 0.25° JRA river discharge dataset . Runoff is initially assigned to the ocean grid cell nearest to the location specified by the data and then horizontally distributed over several surrounding cells using external mapping files . The magnitude of the horizontal spreading, which is applied in the same way for each river (i.e., over the same number of grid cells), was originally dictated by Amazon River outflow stability requirements. This resulted in river fluxes being spread hundreds of kilometers offshore (Fig. a) and was not tested here. In future E3SM versions, spreading distance will instead scale with each river's inflowing runoff flux (Fig. b), using a Gaussian distribution whose length scale depends on both the maximum runoff flux in the JRA forcing and the local grid resolution – allowing the number of grid cells over which runoff is distributed to vary by river according to discharge. For all simulations, the vertical distribution of river runoff follows an exponential decay with depth of the form exp⁡(z/0.75). The Jerlov water type is set to three everywhere.

In this study, we used this newer spreading in the MPAS–O: JRA simulation to evaluate the model's strengths and limitations when configured in a manner typical of global ocean studies. For example: (1) much of the river water remains spread over the 100 m isobath, where it often exits the shelf permanently , (2) the spreading distributes Mississippi River water primarily along the western edge of Bird's foot, whereas the ROMS model and observations suggests the rates are closer to 64 % , with the remainder distributed around several other passes to the northeast (Fig. c), (3) many river discharge points are spuriously placed in the open ocean by the mapping file, and (4) JRA forcing does not account for the USACE's Old River Control structure that diverts roughly 30 % of the Mississippi River water to the Atchafalaya (Fig. ). As a result, the Atchafalaya River volume fluxes are severely underestimated, which contributes to major salinity biases on the shelf (see Sect. ).

In the MPAS–O: USGS simulation, we used the same JRA river spreading and forcing as in the MPAS–O: JRA simulation outside of the ROMS model domain. Inside the ROMS domain, the JRA river flux is set to zero and replaced by what we are calling “pseudo point sources” that result in a substantially more realistic river configuration in the nGoM (Fig. c). These are the fluxes and locations specified by the USGS streamflow data used in the ROMS simulations interpolated to the nearest MPAS–O grid cell. We refer to them as pseudo point sources because E3SM/MPAS–O has no generic capability to override the mapping file's placement and prescribe river runoff fluxes into specific grid cells. In addition, the horizontal momentum fluxes associated with the river runoff is still zero and the vertical structure is the same as MPAS–O: JRA, which may significantly alter dynamics in the M–A plume's near-field. There are some small mismatches in the locations of the ROMS point sources and the MPAS–O: USGS pseudo point sources (Atchafalaya, Calcasieu, San Antonio) due to differences in model bathymetry and interpolation discrepancies.

In E3SM v3.0, river runoff temperatures are set equal to the sea surface temperature of the nearest ocean cell. As explicit river temperatures are not yet available from the river model (MOSART), this approach was chosen in the interim in E3SM to preserve energy conservation in fully-coupled simulations. While this nearest-neighbor approach has little impact in coarse-resolution, fully coupled climate simulations, it is problematic in the northern Gulf of Mexico (nGoM), where river temperatures during summer are often cooler than the surrounding ocean. In MPAS–O: JRA trial simulations, this treatment produced spurious temperature spikes at the Mississippi River mouth that could not be corrected by adjusting runtime parameters. To address this, and because energy conservation is not a constraint in the ocean and sea ice only simulations used here, we implemented an option to set river temperatures equal to the 10 m JRA air temperature, with an upper limit of 30 °C, keeping river temperatures consistent with observations and ROMS model inputs. This feature is applied to all rivers in both MPAS–O: JRA and USGS simulations. While it substantially improved temperature fidelity in the nGoM relative to the original E3SM v3.0 approach, it likely reduced accuracy in polar regions but is neglected due to the short simulation length. A geographically based hybrid approach will be explored in future work.

The simulations were run on 5120 cores (one node has 128 cores) at Los Alamos National Laboratory Institutional Computing, with 4864 cores used for MPAS–O and 256 cores used for MPAS Sea Ice. MPAS–O: JRA achieved approximately 0.4 simulated years per day and MPAS–O: USGS achieved roughly 0.5 simulated years per day. Snapshots and averages of two dimensional variables were saved every 12 h, whereas three dimensional variables were saved weekly. MPAS–O: JRA was run for four years to conserve computational resources because it did not produce summer shelf eddies comparable to ROMS throughout the entire simulation (discussed in Sect. ). Analysis of model output was conducted over years three through four. MPAS–O: USGS was run for five years and analysis of model output was conducted over years three through five.

We first assess whether MPAS–O qualitatively reproduces the well-established seasonal cycle of open ocean submesoscale activity. At 1.4 km resolution, the open ocean GoM resolution can be considered submesoscale-permitting, as work by showed that the mixed layer deformation radius varies from 1 km in summer to 2.2 km in winter. Figure  shows winter and summer snapshots of relative vorticity normalized by the Coriolis parameter (i.e., the Rossby number), ζf-1=(∂xv-∂yu)/f, from the MPAS–O: JRA simulation. Numerous small-scale frontal and filamentary structures with O(1) Rossby numbers are evident throughout the GoM during winter, including within and around Loop Current eddies, over the continental shelves, and near river outflow regions. These features are less prevalent during summer, consistent with previous studies showing stronger open ocean submesoscale activity in the GoM during winter . The seasonal contrast is consistent with the expected enhancement of mixed layer instabilities under deeper winter mixed layer conditions , which increase the amount of available potential energy that can be extracted from lateral density gradients.

Submesoscale variability in the open GoM is also shown with probability density functions (PDFs) of surface normalized relative vorticity (Fig. a and c) and divergence δf-1=(∂xu+∂yv)f-1 (Fig. b and d). The skewness of these PDFs are hallmarks of abundant submesoscale activity . The relative vorticity PDFs are positively skewed (towards cyclonic vorticity) in both seasons (Fig. a), with qualitatively similar distributions among the MPAS–O simulations. The winter distribution exhibits broader tails than the summer distribution. The divergence PDFs are negatively skewed (towards convergence) in both seasons, and likewise exhibit broader tails in winter than in summer. These diagnostics demonstrate the seasonal modulation of submesoscale variability but do not, by themselves, establish the instability mechanisms responsible for generating these features. A detailed analysis of submesoscale generation in the open GoM is beyond the scope of this study, which focuses on the representation of the M–A plume and its associated submesoscale activity.

We begin with an analysis of the ROMS simulations because previous studies have shown that the model reproduces the seasonal evolution of the horizontal salinity gradient magnitude and the observed variability in eddy kinetic energy on the TXLA shelf . As discussed in Sect. , the M–A plume undergoes a dynamical transition between summer conditions, when regional wind patterns cause freshwater to pool on the shelf and broaden the plume, supporting a field of O (20–50 km) eddies due to the strong lateral salinity gradients that form. During non-summer conditions, mean downcoast winds confine the plume and associated stratification along the shelf, and frequent storms suppress eddies of the same scale from forming . Instabilities on the shelf are distinct from mixed layer eddies, as eddies extend throughout the water column rather than remaining confined to the mixed layer . The type of submesoscale processes prominent on the shelf during winter is less understood. We therefore use surface normalized relative vorticity to qualitatively demonstrate the seasonal transition, illustrated by plan view snapshots during winter (Fig. a and b) and summer (Fig. a and b).

This seasonal variability is further reflected in the normalized relative vorticity and divergence PDFs on the inner shelf. We focus on the inner shelf (0–50 m depth; Fig. b and c) because circulation there is primarily wind-driven, whereas outer-shelf variability is more strongly influenced by interaction with Loop Current eddies . Differences between MPAS–O and ROMS on the inner shelf therefore primarily reflect each model's ability to represent the M–A plume, rather than differences in how MPAS–O and HYCOM (used for the ROMS open boundary forcing) represent Loop Current eddies. The normalized relative vorticity distributions narrow slightly during winter (Fig. c) – in contrast to the broadening seen in the open-GoM distributions (Sect. ) – while the divergence PDFs (Fig. d) show the opposite seasonal response, broadening during winter. To our knowledge, this behavior has not been previously reported. We hypothesize that the broader winter divergence distributions may result from increased wind forcing , which could enhance frontogenesis and produce more intermittent, spatially localized convergence and divergence; this mechanism warrants further investigation but is beyond the scope of this study. ROMS: k–ω has the broadest distribution of the four simulations for both variables. ROMS: KPP has narrower distributions than ROMS: k–ω. We attribute this to ROMS: KPP being more diffusive. An example of this elevated diffusion is shown in Fig.  and discussed below.

A key result is that the MPAS–O simulations (Fig. c and d) do not produce a submesoscale eddy field with the same complexity or qualitative characteristics as the ROMS simulations during summer (Fig. a and b). We refer to this reduction in submesoscale activity as eddy suppression, meaning a reduction in the growth and persistence of the frontal instabilities. The MPAS–O simulations produce some eddies and organized meanders on the Texas shelf (e.g., west of 93.5° W) but they have weaker relative vorticity than the ROMS model. This is especially true on the Louisiana Shelf for MPAS–O: USGS. Surprisingly, MPAS–O: USGS features less submesoscale activity than MPAS–O: JRA near the M–A river mouths and on the Louisiana shelf despite improved river forcing, increased minimum layer thickness, and reduced horizontal mixing. In contrast, the MPAS–O simulations show substantially better qualitative agreement with ROMS during winter (Fig. c and d). Both MPAS–O simulations exhibit numerous small-scale fronts, filaments, and vortices, although these features generally have weaker relative vorticity than those in the ROMS simulations.

These trends are also shown in PDFs of relative vorticity (Fig. c), where both MPAS–O simulations have narrower distributions than the ROMS simulations, with MPAS–O: USGS having the smallest distribution for both seasons. Because the characteristic summer eddy field does not form in these simulations, the interpretation of seasonal differences in MPAS–O's PDFs is complicated. For example, MPAS–O: JRA has a broader relative vorticity distribution in winter rather than summer that is nearly identical to ROMS: KPP. On the other hand, MPAS–O: USGS has a larger anticyclonic tail in winter, but is narrower in summer. However, the divergence PDF for MPAS–O: USGS is similar to ROMS: KPP during winter but is substantially weaker in summer than the other simulations.

Figure  shows cross-sections of salinity (Fig. a, c and e) and vertical eddy viscosity νv (Fig. b, d and f) west of Atchafalaya Bay averaged over June of year four, for MPAS–O: USGS and the ROMS simulations. The cross-sections are located in the plume's far-field, defined as the region where the plume has lost all memory of inflowing momentum fluxes . The surface boundary layer depth is shown for MPAS–O: USGS (Fig. a and b) and ROMS: KPP (Fig. c and d) because it is the fundamental diagnostic that controls the extent of nonlocal turbulent mixing. In MPAS–O: USGS, a brackish lens forms in the top several meters of the water column that is absent in the ROMS simulations. The mean boundary layer depth for MPAS–O: USGS is 3.3 and 3.4 m for ROMS: KPP, but the two may differ by over a meter locally. Values of νv are generally smaller in MPAS–O: USGS, except in the ocean interior where the default to prescribed background levels (10⁻⁵ for ROMS: KPP, 10⁻⁴ for MPAS–O: USGS). Within the boundary layers, νv in ROMS: KPP can exceed MPAS–O: USGS by over an order of magnitude. We note that MPAS–O: USGS demonstrates weaker mixing close to the seafloor relative to ROMS: KPP because CVMix lacks an explicit bottom boundary layer parameterization. In ROMS: KPP, we use a bottom boundary layer parameterization that is analogous to the surface boundary layer parameterization. The salinity and νv sections for ROMS: k–ω (Fig. e and f) are similar to ROMS: KPP, but ROMS: KPP is generally more diffusive. These trends are also confirmed in PDFs of νv computed over the same region as in Fig.  (not shown). It remains unclear to what extent the reduced vertical viscosity – and therefore weaker vertical mixing (i.e., destruction of scalar variance) – is a cause of eddy suppression, a consequence of eddy suppression, or how different configuration choices contribute to these behaviors. For example, the CVMix implementation of KPP has not been tuned for coastal buoyancy-driven flows and differs in several respects from ROMS’ native KPP scheme . We discuss how various configuration choices could contribute to eddy suppression in MPAS–O in Sect. .

The objective of this section is to understand how summer eddy suppression affects MPAS–O's ability to represent the larger-scale circulation and seasonal evolution of the M–A plume. We are also interested in comparing the bulk transport and fate of M–A plume water between models. One tool that accomplishes both simultaneously is an analysis of freshwater dyes following , who used an earlier version of the ROMS model to investigate freshwater transport on the TXLA shelf. For all simulations except MPAS–O: JRA, the M–A rivers are tagged using passive dyes ϕ with an initial concentration of one at the point sources and zero elsewhere. A concentration of one means a parcel consists of purely river water, whereas a parcel with a concentration of zero has no river water. We omitted this feature when running MPAS–O: JRA for two reasons: (i) the Atchafalaya River fluxes dramatically differ from streamflow observations (Fig. ), and (ii) the river spreading scheme for the Mississippi instantaneously deposits freshwater offshore of how the shelf freshwater volume is defined. Thus, we did not expect an analysis of MPAS–O: JRA to be meaningful relative to the other simulations, even if by coincidence the freshwater volume ended up being similar.

We define the freshwater volume Vf for each river as: 4Vf=∬Ωb∫H>-100ηϕ(x,y,z,t)dzdxdy, where Ωb denotes the lateral boundaries of the ROMS model domain, η is the sea surface height, and ϕ is the dye concentration in each grid cell. We note that the domain volume inshore of the 100 m isobath is approximately 4.4 % smaller in ROMS than MPAS–O due to differences in bathymetry and the culling of land cells during the MPAS mesh generation process. Time series of Vf with the river volume fluxes overlaid for the simulations are shown in Fig. . After two years, the freshwater volume for both rivers in the ROMS simulations show a clear seasonal cycle with little day of year variability (for the ROMS simulations), confirming the two year spinup time discussed in Sect. .

Vf is strongly correlated with river discharge, with higher discharge corresponding to higher Vf . Previous studies have shown that eddies are the dominant mechanism for transporting material off the shelf , since strong bathymetric gradients at the shelf break otherwise constrain cross-isobath flow and largely isolate shelf and open ocean dynamics. Given that both simulations use the same river discharge within the ROMS domain, we primarily attribute the larger Vf in MPAS–O to reduced submesoscale activity. Differences in Loop Current dynamics may also contribute to differences in freshwater content, since Loop Current eddy interactions influence circulation between the 50–100 m isobaths ; in ROMS, the Loop Current position is held fixed with respect to day of year through the open boundary forcing, unlike in MPAS–O.

Mississippi River discharge (Fig. a) peaks in late March and early June and generally decreases until late November. For the ROMS simulations, Vf is higher in late spring and early summer, peaking in July. Trends are similar for the Atchafalaya (Fig. b). For ROMS: k–ω, the maximum correlation between the Mississippi discharge and the freshwater volume is 0.84, which occurs with a 39 d lag (discharge leads volume). The maximum correlation for the Atchafalaya is 0.75, also with a 39 d lag. Results are similar for ROMS: KPP, however the freshwater volume associated with each river are slightly higher than ROMS: k–ω (4 % for the Mississippi, 10 % for the Atchafalaya). Thus, it takes over a month for freshwater discharge to interact with the continental shelf before it is possibly exported to open water. We note that performed a similar analysis from 2005–2011 and found similar values for the correlation coefficients, but with lags of 21 d for the Mississippi and 33 d for the Atchafalaya. We attribute this to reduced summer eddy activity for 2003–2004 relative to other years, which can be confirmed by comparing PDFs of surface vorticity (compare Fig.  to Fig. 3 of ).

MPAS–O: USGS qualitatively captures the seasonal evolution of the freshwater volume for both rivers. However, the time-averaged freshwater volume is 42 % higher than ROMS: k–ω for the Mississippi and 58 % higher for the Atchafalaya. In summer, the freshwater volume for MPAS–O: USGS may occasionally be over twice that of the ROMS simulations. The freshwater volume is also more variable year over year in MPAS–O: USGS than the ROMS simulations. This could be due to internal variability in Loop Current dynamics within MPAS–O, whereas Loop Current effects are implicitly represented and held constant from year to year in the open boundary forcing of the ROMS simulations. As a result, correlations between discharge and freshwater volume are lower in MPAS–O: USGS, with a maximum correlation of 0.32 between Mississippi discharge and volume with a 41 d lag. For the Atchafalaya, the maximum correlation is 0.53 with a 56 d lag. This analysis indicates that MPAS–O has much more freshwater on the shelf than ROMS. It also takes longer for freshwater to leave the shelf in MPAS–O, especially for the Atchafalaya.

In addition, there are peaks in MPAS–O: USGS freshwater volume in late summer and early fall that are absent in the ROMS simulations. These peaks occur several weeks after increases in M–A river discharge and intense downcoast winds (not shown). There is a strong northward return flow on the western Texas shelf not present in the ROMS simulations (e.g., 96° W, 23–27° N) and several mesoscale features that appear to be the cause of this excessive freshwater accumulation. This can be interpreted with the help of a supplementary plan view animation of seasonally-averaged M–A freshwater thickness h and transport Q for MPAS–O: USGS and ROMS: k–ω (see Code and Data Availability), which we define as: 5h=∫-Hηϕdz,6Q=∫-Hηuhϕdz, where uh is the horizontal velocity vector.

Plan view plots of seasonally-averaged freshwater thickness and transport (Fig. ) show that MPAS–O: USGS qualitatively reproduces the extent of the plume and the direction of freshwater transport. Consistent with the freshwater volume, both freshwater thickness and transport may be several times larger in MPAS–O than ROMS: k–ω locally. For both models, the plume is confined closer to the coast and extends southward toward the Mexico border in winter (Fig. a and b). In summer (Fig. c and d), the plume shifts northward and spreads over the shelf. Both models contain several similar features on the inner shelf, including (i) a recirculating bulge west of Bird's Foot, which has been extensively documented , (ii) a persistent gyre near 94° W in summer, which is also visible in surface snapshots of relative vorticity (Fig. b), and (iii) the largest freshwater transport generally occurs near the M–A river mouths, consistent with . The freshwater thickness is larger in MPAS–O: USGS than the ROMS simulations on most of the shelf.

On the continental slopes (see red lines in Fig. ), model differences are more dramatic and highlight a limitation of using a limited-domain model. In ROMS, the freshwater thickness and transport is smaller year round. This is likely due to the radiation boundary conditions and the climatological nudging layer, which relaxes the passive dyes to zero over the first 10 interior grid points. Thus, we do not expect the behavior of the ROMS model to be realistic close to the open boundaries. Despite the lack of shelf eddies, a major advantage of MPAS–O is that it can be used to study the fate and transport of M–A river water into the open GoM. For example, the imprint of M–A river water is apparent as far south as 22° N and on the Florida shelf, interacting with the Loop Current and numerous mesoscale features. It can also be seen in the Gulf Stream (not shown). An interesting result is that the freshwater transport in the Loop Current eddies can exceed the transport on much of the shelf, likely due to the energetic surface currents.

Finally, we compare the surface tracer fields between the simulations using summer (Fig. ) and winter (Fig. ) averages of sea surface salinity (SSS) and temperature (SST). The 33 g kg⁻¹ isohaline, which is the operational plume boundary , and the 100 m isobath, are shown in the SSS panels (Figs. –a–d). These complement the freshwater analysis by highlighting the seasonal variability of the plume extent in a different way. Differences between ROMS: k–ω SSS and the MPAS–O simulations (ΔSSS) are shown in Figs. - e and f with MPAS–O fields interpolated onto the ROMS grid using Delaunay triangulation. On the Louisiana shelf, ROMS: k–ω is significantly fresher than MPAS–O: JRA (ΔSSS < -9 g kg⁻¹; Fig. e) due to the underestimation of Atchafalaya River discharge. The imprint of MPAS–O: JRA's river spreading is visible in both the SSS (Fig. a) and the ΔSSS fields (Fig. e). ROMS is saltier north of the Mississippi delta because brackish water from Lake Pontchartrain and the Mobile River is excluded. Qualitatively, ROMS: k–ω more closely resembles MPAS–O: USGS than JRA on the Louisiana shelf but is saltier almost everywhere. SST is relatively uniform on the shelf in summer (Fig. g–j). As a result, the differences between ROMS: k–ω and both MPAS–O simulations (ΔSST) are approximately ±1.5 °C despite the lack of eddies in MPAS–O (Fig. k and l). ROMS: k–ω is slightly warmer (ΔSST < 0.5 °C) than both MPAS simulations, except close to the river discharge points, likely due to differences in how river temperatures are prescribed (see Sect. ).

In winter, the salinity fields and plume boundary between MPAS–O and ROMS are more similar. The shelf becomes saltier as the plume is confined closer to the coast (Fig. a–d). As a result, ΔSSS shrinks (Fig. e and f), with ROMS: k–ω remaining fresher than MPAS–O: JRA near Atchafalaya Bay (ΔSSS < 6 g kg⁻¹). The opposite is true for MPAS–O: USGS, with it being fresher than ROMS: k–ω (ΔSSS < -6 g kg⁻¹) near Atchafalaya Bay. As the SST distribution broadens (Fig. g–l), ΔSST increases to over 2 °C southwest of Bird's Foot for both MPAS–O simulations, but is smaller almost everywhere else. These results suggest MPAS–O demonstrates increased performance in winter when larger eddies are naturally suppressed despite elevated freshwater content from the previous summer influencing the results.