On the calculation of carbon and nutrient transport to the oceans

The observed water velocity exhibited a clear diurnal tidal oscillation in the 24-h survey period, with a flood tide in the initial (~ hour 0 to hour 5) and final phases (~ hour 17 to hour 24), and an ebb tide occurring in the middle of the survey (~ hour 5 to hour 17). The concentrations of the measured parameters varied significantly both temporally and spatially. Variability was observed across the channel at the western, central, and eastern stations, and in the vertical profiles at different depths (sub-surface, mid-depth, and near-bottom stations).

Intra-tidal and spatial variations of TSS and TVS

The total suspended solid (TSS) concentration (Fig. 2a–c) was consistently higher at the bottom than at the surface, with concentrations decreasing over time at the eastern station. In contrast, the central and western stations exhibited more fluctuating concentrations, particularly between hours 8 and 10, when the tide was ebbing, suggesting an outward flux of water with a higher suspended sediment concentration. The TSS concentration variations ranged from 10 to 470 mg L^− 1, underscoring the importance of considering multiple horizontal and vertical sampling locations to minimize uncertainty in total flux measurements.

The organic fraction of TSS accounted for up to 67% of the total TSS, with an average of 28%±17%. The variations in total volatile solids (TVS) mirrored those of TSS (thin lines in Fig. 2a–c), with a clear increase in TVS at greater depths. During ebb, TVS concentrations were similar along the transect at corresponding depths.

Intra-tidal and spatial variations of nitrate

Nitrate concentrations decreased monotonically from 0.08 to 0.09 mg N L^− 1 to undetectable level at all depths after the 10th hour (Fig. 2d–f). The dramatic drop in nitrate suggested different water masses were present before and after hour 10. The maximum flux of nitrate occurred early in the survey, coinciding with the first flood tide and a strong southwest wind (Fig. 4). In contrast, nitrate remained low during the second flood period, when wind were weaker.

These observations suggest that the southwesterly wind reversed the normally westward coastal currents toward the northeast and the Mississippi River plume was pushed into Barataria Pass during the first flood period. This reversal of the coastal current is well-documented^{22,23,24,25,26,27} in the region and further supports the hypothesis that the Mississippi River plume introduced nitrate into the bay. In addition, exchange flows through estuarine mouths also responds to wind significantly^28,29,30,31. This phenomenon challenges typical expectations for most estuaries, where nitrate is usually exported during periods of freshwater influx, but highlights the unique dynamics of coastal river plumes in the region.

Intra-tidal and spatial variations of dissolved silica

The concentration of silica (Fig. 2g–i) showed a different pattern of variation. Spatially the concentration was relatively uniform, with the curves mostly overlapping, except the latter period. However, temporal variation was high. During the first half of the survey, the concentration decreased from ~ 0.6-1 to 0.4–0.6 mg Si L^− 1 and swung upward rapidly between hours 5 and 15 before decreasing slightly toward the end of the survey. The maximum concentration was during the ebb which demonstrates the estuary was a source of this critical nutrient for diatoms³². At all stations, variations were similar at all depth, with surface values being slightly higher (~ 1.3 mg Si L^− 1). The overall spatial-temporal variability in silica was about 300% (between 0.4 and 1.3 mg Si L^− 1).

Intra-tidal and spatial variations of total P

The total phosphorus (Fig. 3a–c) was higher in deeper water than the surface by more than 10 times, e.g., at the central station during ebb (0.4:0.04) and decreased over time in the surface. The surface concentration peaked at hour 10 close to the maximum ebb at the eastern and central stations, after which the eastern station decreased sharply, while the central station decreased first but increased again slightly before levelling out at a value of ~ 0.02 mg P L^− 1, about 1/3 of the value at the beginning of the survey. The mid-depth and bottom waters were more heterogeneous. The maxima occurred during the ebb. The overall temporal-spatial variability was more than two orders of magnitude (the maximum concentration ~ 0.4 mg P L^− 1 at western bottom and minimum concentration ~ 0.003 mg P L^− 1 at eastern surface). Again, the flux of total P was mostly dominated by the water mass during ebb except on the surface, where the flood water during the beginning of the survey had the maximum concentration (Fig. 3a). The water mass during the second flood had a much lower concentration in total P, similar to what was seen with NO₃⁻. This pattern further supports the contention that the coastal current brought the coastal river plume proximal to the inlet during the first flood but during the second flood period, the flux may have less influence from the river plume due to the much-reduced southwesterly wind (Fig. 4). For the Mississippi River, the vast majority of total P is in the particulate fraction³³.

Intra-tidal and spatial variations of DOC

The DOC concentration (Fig. 3d-f) had a decreasing trend over time. Overall, all stations showed similar trends. At the start of the survey, the maximum concentration (~ 13 mg C L^− 1) was observed at the eastern stations, while the western station near the bottom recorded the minimum DOC concentration (~ 5 mg C L^− 1). During the first flood period, the DOC flux was primarily influenced by the water mass. However, the water mass during the second flood period had a lower DOC concentration, which supports the idea that the coastal plume may have been pushed by the southwesterly winds, bringing in water with relatively higher nutrient concentrations during the first flood period. While surface variability can be assessed using a proxy like CDOM, vertical variability in dissolved C cannot be captured through remote sensing.

Intra-tidal and spatial variations of ammonium

Ammonium concentration also exhibited significant intra-tidal and spatial variability (Fig. 3g–i). Generally, the surface concentrations were higher (0.4 mg N L^− 1) at the eastern station, where the bottom concentrations remained near zero throughout the entire survey period. In contrast, at the western and central stations, the maximum ammonium concentration (~ 0.5 mg N L^− 1) was found in the bottom water, suggesting different influences from the water masses across the transect. By the end of the survey, ammonium concentrations were generally lower at all stations. The overall concentration variability exceeded tenfold, ranging from ~ 0.03 to 0.45 mg N L^− 1 at the surface of the eastern station, excluding the near-zero values at the bottom of the eastern station (Fig. 3i).

Intra-tidal variations in fluxes

The intra-tidal variations of the mass fluxes (Fig. 5) through the eastern, central, and western segments of the transect were computed by Eqs. (2), (3), and (4), respectively as given in the Methods. The intra-tidal variations of the fluxes through the entire transect were computed by Eq. (5) in Methods.

The fluxes of water mass (Fig. 5a) are quite regular and symmetric. The maximum total inward flux was a little over 6000 tons s^− 1 across the entire transect during both the first and second flood periods. The maximum outward flux during ebb was close to 8000 tons s^− 1.

The flux of TSS (Fig. 5b) was similar but with a slight asymmetry. The inward flux of TSS had its maximum in the beginning of the survey with a magnitude of ~ 700 kg s^− 1. Near the end of the survey, the maximum flux of TSS was ~ 400 kg s^− 1. The outward flux of TSS reached its maximum after hour 10 with a magnitude of ~ 1000 kg s^− 1. The inorganic component of TSS comparable with the inorganic/total ratio ranging between 33% and 100% with an average of 73% ± 17% (Fig. 5c). The TVS had a larger inward flux in the beginning of the survey during the first flood with a maximum of ~ 220 ton s^− 1, about three times that during the second flood (Fig. 5d). The larger inward flux of organic particles is likely related to primary production which is supported by the nutrient concentrations of the Mississippi River plume³⁴. A similar pattern emerges when the Mississippi flood discharges in the Lake Pontchartrain estuary³². The fluxes of TSS, inorganic TSS, and TVS between the eastern / central segments and western segments had slightly different phases during the ebb – the maximum outward flux of them was reached later on the central segment with a 2–3 h delay.

The peak inward flux of DOC (Fig. 5e) was ~ 70 kg s^− 1 at the start of the survey, with a secondary peak of ~ 40 kg s^− 1 at the end, a 43% reduction. Both the eastern and western segments showed similar trends with no clear phase differences. The total outward flux reached a maximum of ~ 50 kg s^− 1.

Nutrient fluxes were smaller than carbon fluxes. Total P had maximum inward and outward fluxes of ~ 0.6 and 0.5 kg P s^− 1, respectively (Fig. 5f). The first flood showed a greater inward flux of total P (~ 0.6) than the second flood (~ 0.3), while the outward flux remained constant at ~ 0.5 kg P s^− 1 during the ebb. The western segment peaked in outward flux about 5 h earlier, while the central segment had a more sustained flux during ebb.

Nitrate flux was measurable only during the first ~ 12 h, peaking at just over 0.1 kg N s^− 1 around hour 7 of the ebb (Fig. 5g). It remained below detection for the second half of the survey. Silica flux differed from other nutrients, with maximum inward flux occurring during the second flood tide at the end of the survey (Fig. 5h). In the first flood, inward flux peaked at ~ 5 kg Si s^− 1, rising to ~ 7 kg Si s^− 1 during the second flood. Outward flux peaked at ~ 8.5 kg Si s^− 1 around hour 13, just after the maximum ebb tide. There were no obvious phase differences across the eastern, central, and western segments or the total flux.

Unlike other nutrients, the first inward flux peak of ammonium (Fig. 5i) occurred after hour 2, at ~ 1.8 kg N s^− 1, for both the central segment and the entire section. The western segment, however, saw maximum flux at the beginning and end of the survey, similar to other nutrients. The difference in maximum inward flux between the two flood periods was negligible. The peak outward flux occurred around hour 11 at ~ 2.3 kg N s^− 1, with a phase difference of about an hour between the central and western segments.

Net transport

Table 1 presents the total accumulated positive (inward) and negative (outward) fluxes, along with net mass transports over the 24-hour period for each constituent, computed using Eq. (6) in the Method section and hourly interpolated concentration values from shape-preserved cubic interpolation.

Over the 24-h survey period, the total mass transport of all constituents was out of bay (as indicated by the negative sign) except nitrate, which had a net inward mass transport. This pattern is unusual for most coastal bays, where surface water discharges from runoff, wastewater and rivers in the watershed lead to an export of nitrate to the coastal ocean. However, Barataria Bay is essentially isolated from the Mississippi River by a continuous network of levees. Consequently, the coastal river plume became a source of nitrate, previously not measured. Since the upper part of Barataria Basin is dominated by emergent wetlands, any river discharge associated nitrate from the Davis Pond diversion is removed through denitrification³⁵.

The mass transport of water through the 600 m cross channel transect with an area of 6450 m² amounted to more than 27 million tons in 24 h (Table 1). This yields a flushing time of the system of about 19 days if we only consider transport through Barataria Pass. The total mass transport of the TSS was 9.21 thousand tons, whereas the inorganic component was 7.45 thousand tons, which makes up about 81% of the total load, consistent with the intra-tidal concentration time series as discussed above. The source of this large component of TSS is deltaic silts and clays that dominate the basin. The inward mass transport of nitrate was about 4 tons over the 24-h period. Silica on the other hand had an outward mass transport of 42 tons. The total P mass transport, 3.92 tons, was comparable to that of nitrate except that it was transported to the coastal ocean and linked to inorganic TSS. The DOC mass transport was 57 tons, while that for ammonium was 11.5 tons, all outward.