Large-scale groundwater flow and sedimentary diagenesis in continental shelves influence marine chemical budgets

Domain: earth_science
Published: 2024-02-07
Editorial outcome: minor_revision

Abstract
The major ion chemistry of the ocean has been assumed to be controlled by river input, hydrothermal circulation at mid-ocean ridges, carbonate production, and low-temperature alteration of seafloor basalt, but marine chemical budgets remain difficult to balance. Here we propose that large-scale groundwater flow and diagenetic reactions in continental shelf sediments have been overlooked as an important contributor to major ion budgets in the ocean. Based on data synthesized from 17 passive margin basins, continental shelves contribute fluid exchanges comparable to hydrothermal circulation at mid-ocean ridges. Chemical exchange is similarly significant, indicating removal of Mg2+ from the oceans at rates similar to mid-ocean ridge convection. Continental shelves likely contribute Ca2+ and K+ to the oceans at rates that, in combination with low-temperature basalt alteration, can close current budget deficits. Flow and reaction in continental shelf sediments should be included in a new generation of studies addressing marine isotope budgets.

Introduction
The major ion budgets of the ocean influence marine ecosystems1, global carbon cycling2, and the evolution of seawater chemistry over geologic time3,4. In current conceptual models, the major ion chemical budgets of the ocean are controlled by river discharge, MOR hydrothermal convection, low-temperature alteration of oceanic crust on MOR flanks, and accumulation of calcium carbonate in marine environments2,5–9 (Fig. 1). However, significant imbalances persist in these models that suggest a missing budget component. Global riverine contributions are reasonably well constrained and contribute cations (Ca2+, Mg2+, Na+, and K+) from weathered continental material. Carbonate accumulation removes ~3 Gt of carbonate per year2,10, strongly influencing Ca2+ and carbon budgets and also removing a small amount of Mg2+. High-temperature MOR circulation removes Mg2+ and contributes Ca2+ and K+ to the oceans, and a general consensus has been reached concerning the volumetric flux and fluid compositions that support this exchange8. Low-temperature alteration of oceanic crust removes Mg2+ and K+ and releases Ca2+ to seawater, but the degree of alteration is highly temperature-dependent, and consequently, the rates of mass exchange are highly uncertain11.

Current budget discrepancies include an insufficient supply of Ca2+ to balance removal by carbonate precipitation2, and insufficient sinks of K+ and Mg2+ to balance inputs from rivers11,12. A new generation of studies based on stable isotopes of Ca, K, and Mg promise significant advances in quantifying these budgets9,13–17 and have already begun to identify new discrepancies, including the need for a major sink of Mg2+ in the form of dolomite15. This rules out low-temperature basalt alteration as a way to close Mg budgets and suggests that other major chemical exchanges are required.

Suggestions that marine chemical budgets can be influenced by groundwater flow and sedimentary diagenesis in continental shelves date back decades2,18,19 but are not included in current marine chemical budget models. Groundwater migration is widespread throughout deep sedimentary basins in continental margins19–26, and water compositions in such settings are pervasively altered by sedimentary diagenetic reactions27,28. The net effect of common sedimentary diagenetic reactions like dolomitization, albitization, and illitization is to sequester Mg2+ and K+ while releasing Ca2+ (Table 1). Note that the groundwater that participates in sedimentary diagenesis in continental shelves is overwhelmingly saline (near seawater salinity or higher, including brines), originating as seawater rather than rainwater. Although fresh submarine groundwater discharge (SGD) may influence marine isotope budgets29, relatively short fluid residence times and low temperatures mean that neither fresh SGD nor tidally-driven saline SGD are likely to participate in significant sedimentary diagenetic reactions. Overall, continental margin basins have the potential to generate significant saline discharge with ion concentrations that differ markedly from seawater.

Here, we show that regional groundwater flow through continental shelves is likely a major contributor to the major ion chemistry of the ocean. We focus on flow through passive continental margins for this first-order assessment of fluid and chemical mass fluxes through continental shelves, because broad passive margins host the majority of continental shelf sediments in the world by area and volume, and the global length of passive margins is roughly twice that of convergent margins30. Our calculations confirm that fluxes from passive margins greatly exceed reported fluxes from compaction-driven dewatering of accretionary prisms in active continental margins31–33. We find that fluid and geochemical fluxes from passive margin basins are comparable to fluxes from high-temperature fluid circulation at MORs. Including chemical fluxes from passive margins and low-temperature basalt alteration allows us to close deficits in existing chemical budgets for modern seawater.

Results
Volumetric fluxes
In passive continental margins, flow of saline groundwater is driven by sediment compaction and fluid density gradients34. Global compaction-driven discharge was estimated based on the decompacted thickness and age of six representative overpressured basins (Fig. 2, Table 2). These shale-rich basins (Supplementary Fig. 1) represent ~20% of global overpressured basins, so we multiplied our result by five to obtain a global estimate. The resulting global volumetric groundwater flux from compacting sedimentary basins was 6.8 × 108 m3 yr−1, with a range of 2.7 × 108 m3 yr−1 to 1.7 × 109 m3 yr−1, accounting for uncertainty in shale content (Supplementary Fig. 2). The fluxes for individual basins (Fig. 3) varied according to their offshore area, age, and the percent shale component of the sedimentary prism. For example, the area of the GoM is slightly smaller than that of the North Sea (Table 2) yet has a much higher estimated volumetric flux due to its higher shale content. The Nam Con Son Basin has a relatively low shale component but has been actively compacting throughout its short (Table 2) history.

With respect to flow driven by density gradients in passive margins, we focused on thermal gradients rather than salinity gradients, because thermal gradients exist as a reasonably stable and predictable driver in all continental shelves19. Global discharge from geothermal convection was estimated based on numerical models19 and the dominant sediment type in 11 representative basins (Fig. 2, Table 3), again representing ~20% of continental shelves globally that are likely to host geothermal convection. The resulting global volumetric groundwater flux from geothermal convection was 1.4 × 1010 m3 yr−1, with a range of 2.8 × 109 to 6.9 × 1010 m3 yr−1 when a factor of five uncertainty related to sediment composition was considered. Estimates for volumetric discharge due to geothermal convection in individual basins ranged from 3.6 × 107 m3 yr−1 to 7.2 × 108 m3 yr−1 (Fig. 4).

Summing the global compaction-driven and geothermal fluxes yields a global volumetric flux (Qs) of 1.5 × 1010 m3 yr−1, with a range of uncertainty from 3.0 × 109 to 7.1 × 1010 m3 yr−1. This estimate is dominated by geothermal convection. Although the fluxes per kilometer of coastline (or of basin length, for most overpressured basins) are of the same order of magnitude for geothermal convection and sediment compaction, compaction-driven flow comprises just 5% of the global flow. This is largely because compaction-driven flow is relatively uncommon in continental shelves. Note that our lower-bound estimate of global discharge from continental shelves is very comparable to the estimated volumetric flux from high-temperature MOR convection, 6.54 × 109 m3 yr−1, which we note is also subject to uncertainty of roughly a factor of four35. Thus, our best estimate of passive margin flux is similar to the upper-bound estimate for high-temperature MOR fluxes, and our upper-bound estimate exceeds the best estimate for high-temperature MOR convection by a factor of 25.

Chemical mass fluxes
We considered four example fluid compositions to estimate possible chemical mass fluxes, as a proof of concept and to inform later mass balance calculations. The four examples, hereafter referred to as archetypes, are not endmembers but rather representative of the continuum of groundwater/brine compositions encountered in deep sedimentary basin settings36 (Supplementary Fig. 3), including representative compositions from (1) observed saline cold seeps, (2) clastic-dominated basins, (3) deep CaCl2 brines28, and (4) carbonate-dominated basins (Table 4). The cold seep archetype comes from observed brine seeps in the Gulf of Mexico. These relatively highly-reacted fluids differ somewhat from cold seep fluids in other settings, including gas hydrate systems37,38 and convergent margins33, but a key feature of all of these seeps is that they are depleted in Ca2+ relative to seawater. Deep CaCl2 brines represent highly evolved fluids characterized by high temperatures (>100 °C), high salinities, and long reaction times (millions of years). The clastic- and carbonate-dominated archetypes represent specific sediment compositions, in which dolomitization is excluded (clastic) or is the dominant form of diagenesis (carbonate). The sources and justifications for these archetypes are discussed in more detail in the methods.

The mass flux calculations revealed groundwater chemical fluxes that rival MOR contributions for most archetypes (Fig. 5a), indicating that groundwater contributions have the potential to influence the major ion chemistry of seawater. The pattern of inputs and outputs varies for the different archetypes and ions, with the exception of Mg2+, which shows net removal of Mg2+ from the ocean for every archetype. Trends are difficult to assign for Na+ and K+, but all archetypes except the cold seep archetype indicated the export of Ca2+ to the ocean. The clastic- and CaCl2 brines show similar trends in inputs and outputs for all ions except for K+, but to better interpret the pattern of inputs and outputs for the archetypes it is helpful to place our calculated fluxes in the context of the global budget deficits.

We calculated the theoretical composition of groundwater needed to balance marine chemical budgets using our calculated volumetric fluxes (Qs) and assuming no contribution from low-temperature basalt alteration. To do this, we rewrote the mass balance model of Spencer and Hardie6 to incorporate more recent estimates of volumetric fluxes from high-temperature MOR convection35 and mass flux estimates of CaCO3 accumulation2,10. We solved the theoretical composition of groundwater, Cth, according to

Cth = (QmorCmor + QrCr + MC) / Qs (1)

where Qmor is the volumetric flux of hydrothermal fluid through MORs, 6.54 × 109 m3 yr−135, Cmor is the adjusted concentration of hydrothermal fluids6 (Table 4), Qr is the global volumetric river discharge, 3.75 × 1013 m3 yr−1 (ref. 6), Cr is the adjusted concentration of river water6 (Table 4), MC is ion removal by carbonate precipitation, −1.06 × 1012 kg yr−1 Ca2+ and −7.15 × 1010 kg yr−1 Mg2+2, and Qs is the volumetric flux of groundwater from passive margins. This allowed us to quickly assess (1) the compositional trends needed to balance the budget and (2) whether any of the archetypes could balance the budget in the absence of low-temperature basalt alteration.

The pattern of modifications in the theoretical fluid composition needed to balance marine chemical budgets in the absence of low-temperature basalt alteration showed sinks of K+, Mg2+, and Na+ and a source of Ca2+. This is consistent with the clastic-derived archetype, but this theoretical fluid showed unrealistic levels of alteration compared to seawater. Less alteration was required when we used our upper-bound estimate for the groundwater flux, but the degree of enrichment in Ca2+ still significantly exceeded that of any of the archetypes (Fig. 5b). These discrepancies strongly suggest that balancing marine chemical budgets requires contributions from low-temperature basalt alteration as well as groundwater discharge from passive margins.

Global mass balance
We then calculated the average modified composition of low-temperature hydrothermal fluids (Clt) that would be needed to balance the major ion budget of the ocean when our estimated passive margin fluxes are included, using an expanded mass balance equation:

QmorCmor + QrCr + QsCs + QltClt + MC = 0 (2)

where Qlt is the volumetric flux of water through low-temperature hydrothermal systems, 0.6 × 1013 to 2.0 × 1013 m3 yr−1 (ref. 11), and Cs is the adjusted composition of groundwater discharging from passive margins. We created a range of compositions for Cs using the clastic-derived and CaCl2 brine archetypes, and we tested the range of volumetric fluxes for low-temperature hydrothermal fluids (Qlt) suggested by Coogan and Gillis11. Using a range of compositions for Cs resulted in relatively small differences in Clt for Ca2+, Mg2+, and K+, whereas the differences in Na+ contributions between the clastic and CaCl2 archetypes created larger variations in Na+ (Fig. 6a, b). Our calculations showed that varying Qlt altered the degree of chemical alteration of Clt without changing the ratios of the ions with respect to one another (Fig. 6c, d). The resulting compositions for low-temperature basalt alteration are similar to observed fluid compositions at low-temperature basalt alteration sites (e.g., Dorado39, 10–20 °C) for all elements except Ca2+ (Supplementary Table 2), and the higher Ca2+ concentrations can be achieved easily with a <3% contribution by fluids from higher temperature basalt alteration (e.g., Baby Bare39, 60–65 °C).

Variations in seawater chemistry over geologic time
The ratio of Ca2+ to Mg2+, Na+, and SO42- in seawater has varied significantly over the Phanerozoic3, with changes attributed mainly to variations in high-temperature MOR hydrothermal circulation and continental weathering. We suggest that changes in fluid and chemical fluxes through continental shelves contributed strongly to these variations. We specifically suggest a causal link between the significant flow in continental shelf area 300–200 Ma40 and a major trough in the Ca/Mg ratio of seawater circa 250 Ma41. Consider also the large increase in the Ca/Mg ratio during the Cretaceous, when rising sea levels and temperatures drove an increase in carbonate platforms and shelves. Large fluxes through abundant, permeable carbonate platforms and associated dolomitization during this period would have sequestered significant Mg2+ and while releasing equal moles of Ca2+. This would have created a positive feedback loop, in which relatively high Ca2+ concentrations supported increased carbonate deposition. Rapid growth of carbonate platforms in turn would support increased dolomitization and further release of Ca2+. This feedback loop would only have been disrupted by falling sea levels, as the continents moved apart and the increasing average age of ocean crust allowed the depth of ocean basins to increase3. The rapid decrease in Ca/Mg ratios in seawater since the end of the Cretaceous is consistent with lower rates of geothermal convection during sea level lows19 and a transition to lower-permeability clastic margins.

These findings also place the observed correlation between sea level and variations in seawater chemistry3,42 in a new perspective. This link has so far appeared to be coincidental, in the sense that increases in MOR spreading lead to increases in the Ca/Mg ratio of seawater while also causing sea level to rise. We suggest a causal link instead, in which high sea levels increase fluid and chemical fluxes through passive margins, and these fluxes directly raise the Ca/Mg ratio in seawater.

Other types of groundwater flow in continental shelves
Although we ignored submarine groundwater discharge (SGD) in our analysis, SGD may ultimately influence major ion chemistry and isotope systematics in the ocean. Studies have increasingly acknowledged the role of fresh SGD in Sr isotope ratios29, but the volumetric flux of fresh SGD is <2% of river discharge globally43,44. In contrast, the volumetric flux of tide- and wind driven45,46 saline (commonly 35 ppt) SGD rivals river discharge in the Atlantic basin47. We suggest that tide- and wind-driven saline SGD may be a candidate for future investigations of ocean chemistry. This type of SGD has much less time to react with sediments than geothermal convection or compaction-driven flow, but the sheer volume of flow in these systems has the potential to compensate for the relatively short residence time.

Passive margins and marine isotope budgets
Continental shelves in passive margins act as huge flow-through reactors for saline water that affect the major ion chemistry of the ocean to a degree similar to that of high-temperature fluid circulation through MORs. Thus groundwater flow and reaction in continental shelves almost certainly affect marine isotope budgets as well. For example, recent mass balance calculations suggest that large volumes of dolomite must precipitate to balance Mg isotope budgets for the ocean15. Estimates of the contribution of fresh SGD to marine Mg isotope budgets29 further increase the need for this sink. Although dolomite formation is extremely limited at low temperatures in shallow seafloor environments, dolomitization is a major sink for Mg2+ in deep continental shelf settings. Thus, our model for flow and reaction in passive continental margin sediments solves the recent mystery of a “hidden” dolomite sink for Mg15 and provides a mechanism to resolve decades of speculation about additional sources and sinks for other ions2,18,19. Particularly as a new generation of isotope studies are emerging, it is critical that studies of the major ion chemistry and isotope budgets of the ocean consider chemical fluxes from continental shelves in addition to rivers, mid-ocean ridges, and low-temperature basalt alteration.

Methods
In this work, we estimated groundwater fluxes based on large-scale flow of groundwater with salinities similar to or exceeding seawater. Although fresh groundwater discharge has the potential to influence marine isotope budgets29, we neglected fresh groundwater in the context of major ion budgets because its composition is similar to river water, and direct discharge of fresh groundwater to the ocean is less than 2% of global river discharge44,48. In contrast, fluids circulating through passive continental margins are significantly altered compared to the original seawater composition owing to sedimentary diagenetic reactions that occur over millions of years27,28,49.

Areas of Study
We considered 17 sedimentary basins in passive continental margins for this study (Fig. 2). We chose six basins with literature-verified overpressures (Table 2) to estimate compaction-driven flow. The overpressured basins were almost entirely composed of clastics (Supplementary Fig. 1), some with shale constituents greater than 90% (Supplementary Fig. 2). We assumed that basins that were dominated by coarse clastics and carbonates, and whose seafloor geometries resembled those in previous investigations of geothermal convection19, were subject to geothermal convection (Table 3). Based on estimates by Mouchet et al.50 and our own measurements using Google Earth, there are 7.0 × 106 km2 of overpressured submarine sediments along passive margins, which account for 24,000 km of coastline worldwide. We assumed that the remaining 81,000 km of passive margins had the potential to host geothermal convection. The six basins chosen to estimate compaction-driven flow in this study account for 23% of the earth’s overpressured passive margin area. The 10 margins chosen to estimate geothermal convection in this study represent 17% of the 81,000 km. Given that both sets encompass roughly one fifth of the respective total lengths, the calculated groundwater fluxes were multiplied by a factor of 5 to provide an estimate for global groundwater flux.

Groundwater discharge from compacting basins
Total pore-volume loss from the compacting basins was estimated by decompacting the layers in the stratigraphic columns (Supplementary Figs. 1 and 2) of the six continental shelf complexes in Table 2. The current porosity of each layer at depth was estimated based on generalized compaction curves from Baldwin and Butler51 for sand and shale. For sand/sandstone,

ϕ = 0.49e−3.7d (3)

where ϕ is the porosity, d is the depth in km, and e is Euler’s number. For normally compacted mud/shale,

ϕ = 1 − 8d/15 (4)

For overpressured shale,

ϕ = 1 − 6.35d/6.02 (5)

To obtain a conservative estimate of compaction-driven flow, all sediments at depths below 200 m were assumed to be overpressured. Assuming all sediments were normally compacted throughout the basins increased compaction by ~10%.

The sediments were decompacted to obtain the original thickness according to:

bo = Xsh(b / (1 − ϕsh)) + Xsand(b / (1 − ϕsand)) (6)

where bo is the original thickness of the layer, b is the current thickness of the layer, Xsh is the percent shale composition of the layer, Xsand is the percent sand composition of the layer, ϕsh is the porosity of shale at the depth of the layer, ϕo is the original porosity of shale at deposition (60%), ϕsand is the porosity of sand at the depth of the layer, and ϕo is the original porosity of sand (35%). This process was repeated for every layer in the stratigraphic column and summed to obtain the total original thickness. Fracturing in the sediment column was not mathematically considered because it does not affect the volume of the sediment. Cases of basin inversion and unconformities in the sedimentary record were also not considered in the calculations. Neglecting basin inversion and unconformities could lead to under-estimates of the total fluxes from the basin.

The change in thickness from decompaction was then multiplied by the basin’s area to calculate the total volume of fluid lost during compaction. The offshore area of each basin was estimated based on measurements from previous studies (Table 2) and confirmed by estimates using Google Earth (Supplementary Fig. 4). The resulting volume of compaction was divided by the age of the basin, yielding an average annual flux of groundwater (Qt) since initial deposition:

Qt = (bo − b) / dt * A (7)

where A is the basin’s area and dt is the basin’s age. Calculating the discharge this way results in an average flux over time, whereas the rate of compaction in real sedimentary basins is unlikely to remain constant. For this reason we included basins of a variety of ages, and we consider these “average annual” fluxes to be very long-term (10s of My) averages.

The estimated fluxes are subject to uncertainty from several sources, including uncertainty in basin area, porosity at depth, and sediment composition. We considered uncertainty in shale fractions by calculating fluid discharges for each continental shelf complex using upper and lower bound values for the shale fraction in each layer (Supplementary Fig. 2). The uncertainty in the initial porosity is unlikely to be more than a factor of two, and the estimated basin areas are probably accurate to within 10%. We applied these uncertainties to the upper and lower bounds from the shale fraction uncertainty to generate estimated maximum and minimum fluxes. As will be shown, the annual flux from geothermal convection proved to be much larger, reducing the impact of uncertainty in compaction-driven fluxes on our results.

Groundwater discharge from geothermal convection
Geothermal fluxes were estimated based on Wilson19, who used numerical models to estimate a range of possible groundwater fluxes due to geothermal convection using the bathymetry of continental shelves from the east coast of North America. Wilson used realistic seafloor geometries for seven cross-sections and reported a range of fluxes representative of five composite rock types. We calculated an average flux for each composite rock type by taking a geometric mean of the fluxes from the cross-sections. The dominant lithology of each shelf complex considered in this study was estimated from published cross-sections (Table 3), and the averaged representative flux from Wilson19 was assigned to each basin and multiplied by the length of the coastline. The length of the coastline was estimated from the publications in Table 3 and confirmed using Google Earth. We estimated that the uncertainty associated with applying a single lithology to an entire shelf complex was plus or minus a factor of five. This gives minimum and maximum flux values that differ by a factor of 25 for each basin.

Groundwater archetypes and net chemical exchange
As previously indicated, the groundwater archetypes represent example fluid compositions across the spectrum of compositions observed in sedimentary basin settings. The first fluid archetype represents cold seeps, a global phenomenon of seepage of volatile elements and fluids from the seafloor. We chose example fluids based on observed discharge to the ocean in the form of seafloor brine pools in the Gulf of Mexico (GoM)24,26,52. They are enriched in K+ and Na+ and depleted in Ca2+ and Mg2+, and they have a high chlorinity (103,000 mg/l) relative to seawater. These fluids differ from cold seeps observed in convergent margins, which are typically depleted in K+ via such reactions as the smectite-illite transition33, and in gas hydrate settings, which also show depletion in K+ refs. 37,38. Discharge of such high-salinity fluids can only be driven by overpressures at depth, which are well-documented in the Gulf of Mexico. Depletion of Ca2+ relative to seawater is a common feature of cold seep fluids in all of these settings and likely reflects precipitation of calcite during CO2 degassing as the fluid emerged from high pressures at depth.

The second archetype represents fluids in basins dominated by clastic sediments. We compiled eight groundwater samples from depths of 350–400 m below the seafloor on the New Jersey continental shelf53, an interval where high salinities (averaging ~75% of seawater salinity) indicate mild dilution of seawater by fresh groundwater during sea level lowstands. We also compiled 17 samples from depths of 1500–4100 m below the land surface from the San Joaquin Basin54, a well-studied basin that lacks carbonate sediment layers36. Salinities from San Joaquin samples averaged roughly 80% of seawater salinity, reflecting dilution by release of water during illitization55. Despite very different geological histories, these fluids show remarkably similar chemical trends. They are enriched in Ca2+ and depleted in K+, Mg2+, and Na+ relative to seawater.

The third fluid archetype was modeled after deep basinal CaCl2 brine fluids28, also known as oil-field brines. These fluids are representative of high salinity (five to 10 times the salinity of seawater), high density fluids with long residence times at elevated temperatures (>100 °C). The composition of the archetype is an arithmetic average of eight samples from the GoM, the Illinois Basin, the Michigan Basin, and the Dead Sea presented by Hardie28 as representative CaCl2 brines. As is common for this kind of deep basin brine, these fluids are enriched in Ca2+ and K+ and depleted in Mg2+ and Na+.

The final fluid archetype represents fluids in carbonate-dominated basins. This archetype was created by averaging ion concentrations of 26 samples (depths 2 to 409 mbsf) from the Great Australian Bight56, which represents a spectrum from barely altered seawater at shallow depths to concentrated (three times seawater salinity) brines at depth, suggesting evaporation or interaction with evaporite sequences. These brines are enriched in Ca2+ and Na+ and depleted in Mg2+ and K+, clearly reflecting dolomitization. These trends are also consistent with trends from warm spring samples from the Floridan platform57 for Ca2+, Mg2+, and K+. The Floridan samples are slightly depleted in Na+ and have a salinity roughly equal to seawater. We did not include the Floridan samples in the archetype calculations because they are significantly diluted by mixing with modern seawater.

We calculated net chemical fluxes for each input fluid based on the assumption that the net chloride flux is zero6. We first adjusted the compositions of all input fluids to zero chloride by subtracting ions in proportion to the composition of modern seawater. This approach assumes that seawater-derived salt aerosols dissolved in rainwater are the source of chloride in river waters6 and that seawater was the original source of water for seafloor hydrothermal convection and for our groundwater archetypes. Details of this process are shown in Supplementary Table 1.

Net chemical fluxes were calculated by multiplying the adjusted concentration of each archetype by the volumetric fluxes estimated above to generate a mass flux (Tmol yr−1) for each ion. The resulting mass fluxes represent individual points in a range of possible groundwater compositions, as they each assume total discharge is representative of only one archetype.

Mass balance model for the major ion chemistry of the ocean
The mass balances are represented in Eqs. (1) and (2) required fluxes from several sources other than our calculations. River chemical mass fluxes were gathered from Spencer and Hardie6. Chemical mass fluxes from high-temperature MOR hydrothermal flow were synthesized using the MOR brine composition chosen by Spencer and Hardie6, from Reykjanes, Iceland, and the MOR axial fluid flux presented by Nielsen et al.35, given the agreement between their upper bound estimates and the heat flow estimates of Mottl and Wheat12. Removal of ions due to precipitation of carbonates assumed a formula for high-Mg calcite of (Ca0.9, Mg0.1)CO3 58. A recent review of estimated carbonate accumulation10 suggests differences of no more than 20% from Milliman2, so we used Milliman’s estimate for the total carbonate accumulation rate, 3.2 billion tons per year. Fluid fluxes in low-temperature hydrothermal systems have been estimated based on energy balances11, but the average composition of those fluids is highly uncertain. We first tested our model to ensure that it could replicate the results of Spencer and Hardie6 before we updated it to use the volumetric hydrothermal fluid flux through MORs of Nielsen et al.35 and added terms for passive margin and low-temperature hydrothermal fluxes. We note that the estimates of low-temperature hydrothermal volumetric fluxes include only off-axis flow, which excludes low-temperature axial flows11.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper by Wilson et al. Esfimated the flux of ions to the ocean through groundwater circulafion from confinental shelves of passive margins that is driven by both sediment compacfion and geothermal convecfion. The authors claim that, such a flux, together with low-temperature basalt alterafion, has the potenfial to close the budget for several major cafions in the ocean. While it is excifing to see studies like this put diagenefic fluxes into the discussion of marine cafion budget, I found the study not convincing enough given the loose constraints for the fluid composifion. The authors have gone through a comprehensive effort to derive volumetric fluxes for 17 different basin and show that the overall flux is at least compafible to that from high temperature MOR convecfion and could very likely be higher. I think this finding is significant and well constrained. However, the authors didn’t seem to dedicate the same amount of effort to constrain fluid composifion. For example, why four archetype? Why the fluid composifion from those few locafions? Are they representafive enough for a global scale esfimafion? I happen to have done quite a bit of work from the cold seeps along passive margins (northern Norwegian margin, Barents Sea, and Fram Straight. See later for selected papers. It is not my intenfion to press for citafion but simply showing what has been done) and we have documented very different fluid composifion from the that of GoM. For example, we see that these cold seep fluids contain less potassium than seawater (ie K sink). In addifion, these cold seeps are not such a strong Mg sink as the authors claimed (ie sfill a Mg sink but of very different magnitude). Arguably GoM is a very unique fluid system when comparing to any cold seeps around the world and it needs further jusfificafion why this site was thought to be representafive by the authors. I don’t have enough experiences to crifique the authors’ choices on the end-member of fluid composifion for the other archetypes. Nonetheless, I nofice the choice is only based on a handful of locafions (2 locafions for type 2, 4 locafions from type 3 and 1 locafion for type 4). This makes me wonder how representafive are these end-member composifions overall. I wonder if the authors can compile pore fluid data from ocean drilling programs (eg ODP and IODP) which should have a much befter coverage of fluid composifion data. Similar kind of applicafions can be found from the list included at the end.\nI have another minor comment. It will be very nice if the authors can be more specific about the kind of “groundwater” they are talking about in the introducfion. To me, the authors were dealing with circulafion of seawater that is further modified by diagenefic processes. The term “groundwater” they used is a bit confusing to me, though I understand that, mechanisfically speaking, the fluid focus here falls into the category of saline groundwater. However, later in the discussion, the authors also tried to disfinguish the fluid they discussed in the paper with the saline SGD that transports Ra, which makes the actual definifion of “groundwater” in this paper more confusing.\nDr. Wei-Li Hong\nStockholm University\nRelevant papers for cold seep fluid composifion from passive margins:\nHong, W.-L. et al. Seepage from an arcfic shallow marine gas hydrate reservoir is insensifive to momentary ocean warming. Nat. Commun. 8, 15745 doi: 10.1038/ncomms15745 (2017).\nHong, W.-L., Lepland, A., Himmler, T., Kim, J.-H., Chand, S., Sahy, D., et al. (2019). Discharge of meteoric water in the eastern Norwegian Sea Since the last glacial period. Geophysical Research Lefters, 46, 8194–8204. hftps://doi.org/10.1029/2019GL084237\nHong, W-L., Thomas Pape, Christopher Schmidt, Haoyi Yao, K. Wallmann, Andreia Plaza-Faverola, J. W. B. Rae, Aivo Lepland, Stefan Bünz, and Gerhard Bohrmann. \"Interacfions between deep formafion fluid and gas hydrate dynamics inferred from pore fluid geochemistry at acfive pockmarks of the Vestnesa Ridge, west Svalbard margin.\" Marine and Petroleum Geology 127 (2021): 104957.\nExamples for the use IODP data:\nSun, Xiaole, and Alexandra V. Turchyn. \"Significant contribufion of authigenic carbonate to marine carbon burial.\" Nature Geoscience 7, no. 3 (2014): 201-204.\nBerg, Richard D., Evan A. Solomon, and Fang-Zhen Teng. \"The role of marine sediment diagenesis in the modern oceanic magnesium cycle.\" Nature communicafions 10, no. 1 (2019): 4371.", "reviewer_2": "In their manuscript, Wilson et al. propose and demonstrate that offshore submarine groundwater discharge from confinental shelf sediments in passive margins can account for missing sources and sinks in global marine chemical budgets for calcium (Ca), magnesium (Mg) and potassium (K). They integrate a combinafion of calculafions, observafions, and models from past studies, focusing their efforts around quanfifying chemical sources/sinks for two hydrologic processes: compacfion-driven dewatering in areas of rapid sedimentafion and geothermal convecfion. This paper could be an important contribufion to marine geochemistry and geophysics communifies. It is novel in that it offers a fresh take on longstanding geochemical budgets. It also may open the door to interpretafing new processes from old paleochemistry measurements in seafloor sediments. The analysis appears technically sound, but the methods are rather thin or vague in places, and the results are difficult to digest in tabular form. I offer the following suggesfions for clarifying methods and results.\nEquafion 4 is a key equafion, and the tables and figures in the main text all lead towards populafing unknowns in the equafion, but it is hard to put together the pieces unfil the reader finishes the methods. I’d suggest presenfing the equafion sooner with a graphical illustrafion of the terms. This can be done by expanding Figure 1 to show rivers and MOR’s (the full cycle and fluxes for the elements of interest). A more detailed conceptual figure with all the processes that go into the geochemical budgets in Equafion 4 would also help clarify some of the ideas in L181-194. This figure and the overall paper would also be clearer for non-geochemists if reacfion equafions were shown for dolomifizafion, illifizafion, and albifizafion. For example, this would clarify the statement in L 66.\nThe calculafion of fluxes for compacfion-driven flow left much to be accepted on faith. I see that this process contributes less to Qs than geothermal convecfion and therefore would not change the results much, even if the numbers changed. That said, the inputs to Table 1 should be described in more detail in a supplement. For example, all of the Gulf of Mexico is not undergoing similar sedimentafion rates and is not subject to the same degree of compacfion-driven dewatering. How does the area esfimate, which appears to be approximated as a rectangle, account for this? It would help to include a supplement with a couple of paragraphs and a basin-scale map for each basin, along with a more detailed explanafion of the datasets used in the parameter esfimates. One example of a supplement that has more detailed paragraphs on different regions of analysis can be found in Befus et al. (2017). The same suggesfion could also be made for the basins subject to geothermal fluxes. For example, “length of coastline” in L 337 may not be the same as basin length, especially if coastline length includes all its inlets and peninsulas. These are relafively small uncertainfies either way that should not substanfially modify the results, but it is sfill important to understand what the authors have measured and reported.\nI am sfill fuzzy on the porosity or lithology sequences that were decompacted. The authors cite Baldwin and Butler’s compacfion curves—are they just using the idealized curves? What strafigraphic columns did they use (L 272, LL 299)? The authors menfion shale fracfions for each layer, but I’m not sure what layers or datasets they refer to without a strafigraphic column or similar figure. This is an example where it would help to have more graphical informafion in a supplement.\nCompacfion-driven flow also exists in tectonic basins, but this is not shown to be small unfil L 248. Consider stafing sooner.\nEquafion 4 and the geochemical analyses are difficult to envision, especially using tables. This informafion would be befter presented graphically, perhaps through ternary diagrams showing the 4 end-members. This could also help graphically explain statements like L 127. The authors would also do well to present (using smaller symbols or at least boxes) the scafter in samples from the cited papers for each water type (Table 3) to show how well the chosen archetypes represent the natural variability in each water type.\nFigures 3 and 4: I would also be keen to see this informafion in m/y, to account for differences in the map view area of each basin. In general, this would help clarify the relafive punch that compacfing basins provide—maybe they are small but mighty for their size when it comes to the total fluid they expel?\nL 57: By volume or map area? The lafter seems more relevant to this statement.\nL 95: I think the authors are suggesfing that the flux in the GoM is higher because shales can compact more, but as menfioned earlier, it would also depend on deposifion rates and ages. Please add something like “…shale content and deposifion rate.”\nTable 5 is difficult to follow, as units for most columns are in the capfion, but units for the left column are in the column header. Also, the term off-axis isn’t really introduced unfil Table 5, adding some uncertainty in terminology.\nL 216: This conclusion can be driven home with an improved conceptual figure (Figure 1).\nL 242: Rather than cifing a regional study from Befus et al. for a global esfimate, consider cifing Zhou et al.\nBefus, K. M., Kroeger, K. D., Smith, C. G., & Swarzenski, P. W. (2017). The magnitude and origin of groundwater discharge to eastern U.S. and Gulf of Mexico coastal waters. Geophysical Research Lefters, 44, 10,396–10,406. hftps://doi.org/10.1002/ 2017GL075238\nZhou, Y. Q., Sawyer, A. H., David, C. H., & Famigliefti, J. S. (2019). Fresh submarine groundwater discharge to the near-global coast. Geophysical Research Lefters, 46. hftps://doi.org/ 10.1029/2019GL082749"}, "author_response": "Response to Reviewer’s Comments\nThese reviewer comments were very helpful, particularly in realizing that the audience for offshore groundwater flow has evolved significantly over the years to now include many researchers who are not familiar with regional-scale groundwater flow in sedimentary basins. We made a serious effort to clarify our terminology for an audience with a broader range of perspectives. We also included the Source Data file with this submission, which was accidentally omitted last time. At the excellent suggestion of Reviewer 2 we also completely redrafted Figure 1, converted tables 4&5 to a single figure (now Figs 5a and b), and made quite a number of other new supplemental figures.\nIn addition to changed suggested by the reviewers, we edited the paper to fit Nature Communications guidelines. This primarily involved moving material from the last paragraph of the introduction to the methods, to avoid having figures other than the conceptual model in the Introduction.\nLine numbers refer to the clean copy rather than the track-changes version, which was messy.\nReviewer #1 (Remarks to the Author):\n1. The paper by Wilson et al. Estimated the flux of ions to the ocean through groundwater circulation from continental shelves of passive margins that is driven by both sediment compaction and geothermal convection. The authors claim that, such a flux, together with low-temperature basalt alteration, has the potential to close the budget for several major cations in the ocean. While it is exciting to see studies like this put diagenetic fluxes into the discussion of marine cation budget, I found the study not convincing enough given the loose constraints for the fluid composition. The authors have gone through a comprehensive effort to derive volumetric fluxes for 17 different basin and show that the overall flux is at least compatible to that from high temperature MOR convection and could very likely be higher. I think this finding is significant and well constrained. However, the authors didn’t seem to dedicate the same amount of effort to constrain fluid composition. For example, why four archetype? Why the fluid composition from those few locations? Are they representative enough for a global scale estimation?\n> We should have done a better job explaining the choice of four archetypes in the original draft. We have now clarified this starting line 148, and we added Supplementary Figure 3 to the supplement to show how the archetypes compare with other groundwaters in sedimentary basins. New wording at line 87 is:\n“We considered four example fluid compositions to estimate possible chemical mass fluxes, as a proof of concept and to inform later mass balance calculations. The four examples, hereafter referred to as archetypes, are not endmembers but rather representative of the continuum of groundwater/brine compositions30 encountered in deep sedimentary basin settings 30 (Supplementary Figure 3), including representative compositions from (1) observed saline cold seeps, (2) clastic-dominated basins, (3) deep CaCl brines 23, and (4) carbonate-dominated basins (Table 4). The cold seep archetype comes from observed brine seeps in the Gulf of Mexico. Deep CaCl brines represent highly evolved fluids characterized by high-temperatures (>100ºC), high salinities, and long reaction times (millions of years). The clastic- and carbonate-dominated archetypes represent specific sediment compositions, in which dolomitization is excluded (clastic) or is the dominant form of diagenesis (carbonate).\n2. I happen to have done quite a bit of work from the cold seeps along passive margins (northern Norwegian margin, Barents Sea, and Fram Straight. See later for selected papers. It is not my intention to press for citation but simply showing what has been done) and we have documented very different fluid composition from the that of GoM. For example, we see that these cold seep fluids contain less potassium than seawater (ie K sink). In addition, these cold seeps are not such a strong Mg sink as the authors claimed (ie still a Mg sink but of very different magnitude). Arguably GoM is a very unique fluid system when comparing to any cold seeps around the world and it needs further justification why this site was thought to be representative by the authors. I don’t have enough experiences to critique the authors’ choices on the end-member of fluid composition for the other archetypes.\n> Dr. Hong is correct that our cold seeps are very different from (and more highly reacted than) the cold seeps he has documented in other settings. In addition to clarifying our intentions for the archetypes (see comment #1), we also added this clarification in the 4th paragraph (line 46), to let readers know much earlier that we are considering saline groundwater rather than fresh groundwater:\nNote that the groundwater that participates in sedimentary diagenesis in continental shelves is overwhelmingly saline (of seawater salinity or higher, including brines), originating as seawater rather than rainwater.\nI appreciate learning of Dr. Hong’s papers about fresh and brackish seeps. I know of another researcher who will be very interested to have these references, and I will certainly share them with my students.\n3. Nonetheless, I notice the choice is only based on a handful of locations (2 locations for type 2, 4 locations from type 3 and 1 location for type 4). This makes me wonder how representative are these end-member compositions overall. I wonder if the authors can compile pore fluid data from ocean drilling programs (eg ODP and IODP) which should have a much better coverage of fluid composition data. Similar kind of applications can be found from the list included at the end.\nThis is now addressed in the revised discussion of the groundwater archetypes and Supplementary Figure 3 (see #1). The new figures make it clear, for example, that the single citation for type 4 actually represents a compilation from 8 well-studied sites. The new figures also show the archetypes in the context of broader compilations.\nRegarding IODP datasets: We used IODP data for our clastic and carbonate archetypes, but these data are rare. Continental shelves are not well sampled by IODP because most of the relevant areas are in waters too shallow for their dedicated ships. (The Resolution was not equipped to handle overpressures and other dangerous drilling conditions in the Gulf of Mexico, either.) (This is beside the point of the paper, so we do not go into this in the text, but this gap in IODP data makes it very difficult to know how to interpret Sun and Turchyn 2014 or Berg et al. 2019.)\n4. I have another minor comment. It will be very nice if the authors can be more specific about the kind of “groundwater” they are talking about in the introduction. To me, the authors were dealing with circulation of seawater that is further modified by diagenetic processes. The term “groundwater” they used is a bit confusing to me, though I understand that, mechanistically speaking, the fluid focus here falls into the category of saline groundwater. However, later in the discussion, the authors also tried to distinguish the fluid they discussed in the paper with the saline SGD that transports Ra, which makes the actual definition of “groundwater” in this paper more confusing.\nAs indicated in comments #1 and #2, we revised the wording early on to clarify the kind of groundwater were are interested in in this paper. As for the discussion, we simplified this paragraph by simply referring to the driving force for flow (tide- and wind-driven vs. compaction-driven or geothermal flow). It makes the point without getting tangled up in what is or is not “SGD”:\n“In contrast, the volumetric flux of tide- and wind-driven39,40 saline (commonly 35 ppt) SGD rivals river discharge in the Atlantic basin 41. We suggest that tide- and wind-driven saline SGD may be a candidate for future investigations of ocean chemistry. This type of SGD has much less time to react with sediments than geothermal convection or compaction-driven flow, but the sheer volume of flow in these systems has the potential to compensate for the relatively short residence time.”\nDr. Wei-Li Hong\nStockholm University\nRelevant papers for cold seep fluid composition from passive margins:\nHong, W.-L. et al. Seepage from an arctic shallow marine gas hydrate reservoir is insensitive to momentary ocean warming. Nat. Commun. 8, 15745 doi: 10.1038/ncomms15745 (2017).\nHong, W.-L., Lepland, A., Himmler, T., Kim, J.-H., Chand, S., Sahy, D., et al. (2019). Discharge of meteoric water in the eastern Norwegian Sea Since the last glacial period. Geophysical Research Letters, 46, 8194–8204. https://doi.org/10.1029/2019GL084237\nHong, W-L., Thomas Pape, Christopher Schmidt, Haoyi Yao, K. Wallmann, Andreia Plaza-Faverola, J. W. B. Rae, Aivo Lepland, Stefan Bünz, and Gerhard Bohrmann. \"Interactions between deep formation fluid and gas hydrate dynamics inferred from pore fluid geochemistry at active pockmarks of the Vestnesa Ridge, west Svalbard margin.\" Marine and Petroleum Geology 127 (2021): 104957.\nExamples for the use IODP data:\nSun, Xiaole, and Alexandra V. Turchyn. \"Significant contribution of authigenic carbonate to marine carbon burial.\" Nature Geoscience 7, no. 3 (2014): 201-204.\nBerg, Richard D., Evan A. Solomon, and Fang-Zhen Teng. \"The role of marine sediment diagenesis in the modern oceanic magnesium cycle.\" Nature communications 10, no. 1 (2019): 4371.\nReviewer #2 (Remarks to the Author):\n1. In their manuscript, Wilson et al. propose and demonstrate that offshore submarine groundwater discharge from continental shelf sediments in passive margins can account for missing sources and sinks in global marine chemical budgets for calcium (Ca), magnesium (Mg) and potassium (K). They integrate a combination of calculations, observations, and models from past studies, focusing their efforts around quantifying chemical sources/sinks for two hydrologic processes: compaction-driven dewatering in areas of rapid sedimentation and geothermal convection. This paper could be an important contribution to marine geochemistry and geophysics communities. It is novel in that it offers a fresh take on longstanding geochemical budgets. It also may open the door to interpretating new processes from old paleochemistry measurements in seafloor sediments. The analysis appears technically sound, but the methods are rather thin or vague in places, and the results are difficult to digest in tabular form. I offer the following suggestions for clarifying methods and results.\n> Let me apologize here: I accidentally left the “Source Data” spreadsheet out of the original submission. It is now included. Meanwhile, the suggestion to turn more of the tables into figures is an excellent one. We definitely followed this suggestion, as detailed below.\n2. Equation 4 is a key equation, and the tables and figures in the main text all lead towards populating unknowns in the equation, but it is hard to put together the pieces until the reader finishes the methods. I’d suggest presenting the equation sooner with a graphical illustration of the terms. This can be done by expanding Figure 1 to show rivers and MOR’s (the full cycle and fluxes for the elements of interest). A more detailed conceptual figure with all the processes that go into the geochemical budgets in Equation 4 would also help clarify some of the ideas in L181-194. This figure and the overall paper would also be clearer for non-geochemists if reaction equations were shown for dolomitization, illitization, and albitization. For example, this would clarify the statement in L 66.\n> This was a great suggestion. We redrafted Figure 1. None of the prominent papers on marine major ion chemistry that I have seen show conceptual diagrams (including all the recent ones published in this journal), but now that we have one I like it quite a lot. We put Table 1 (stoichiometric equations for sedimentary diagenetic reactions) back in the paper. We moved the mass balance equations up (now lines 179 and 209). Thanks to the reviewer here.\n3. The calculation of fluxes for compaction-driven flow left much to be accepted on faith. I see that this process contributes less to Qs than geothermal convection and therefore would not change the results much, even if the numbers changed. That said, the inputs to Table 1 should be described in more detail in a supplement. For example, all of the Gulf of Mexico is not undergoing similar sedimentation rates and is not subject to the same degree of compaction-driven dewatering. How does the area estimate, which appears to be approximated as a rectangle, account for this? It would help to include a supplement with a couple of paragraphs and a basin-scale map for each basin, along with a more detailed explanation of the datasets used in the parameter estimates. One example of a supplement that has more detailed paragraphs on different regions of analysis can be found in Befus et al. (2017). The same suggestion could also be made for the basins subject to geothermal fluxes. For example, “length of coastline” in L 337 may not be the same as basin length, especially if coastline length includes all its inlets and peninsulas. These are relatively small uncertainties either way that should not substantially modify the results, but it is still important to understand what the authors have measured and reported.\n> We digitized these using Google Earth, as now explained in more detail (line 367 and Supplementary Figure 4). We resisted showing diagrams of each basin, given the simplicity of this operation and the fact that a quick look at any of the references in Table 2 gives a good idea of the extent of any given basin, but we showed an example from the Gulf of Mexico in the Supplement, to illustrate the degree of detail (not very high, given that we were only going for two significant figures).\n4. I am still fuzzy on the porosity or lithology sequences that were decompacted. The authors cite Baldwin and Butler’s compaction curves—are they just using the idealized curves? What stratigraphic columns did they use (L 272, LL 299)? The authors mention shale fractions for each layer, but I’m not sure what layers or datasets they refer to without a stratigraphic column or similar figure. This is an example where it would help to have more graphical information in a supplement.\n> The stratigraphic datasets are in the Source Data, and we plotted strat columns and shale content in the Supplement (new Supplementary Figures 1 and 2).\n5. Compaction-driven flow also exists in tectonic basins, but this is not shown to be small until L 248. Consider stating sooner.\n> We moved this statement (L248) from the methods to the introduction (line 64).\n6. Equation 4 and the geochemical analyses are difficult to envision, especially using tables. This information would be better presented graphically, perhaps through ternary diagrams showing the 4 end-members. This could also help graphically explain statements like L 127. The authors would also do well to present (using smaller symbols or at least boxes) the scatter in samples from the cited papers for each water type (Table 3) to show how well the chosen archetypes represent the natural variability in each water type.\n> Good suggestions. We moved Table 4 to the supplement and replaced it with a graph (Figure 5a) showing the archetype fluxes relative to MOR fluxes, to demonstrate the likely importance of the groundwater contribution. We also removed Table 5, replacing it with a graph showing the theoretical groundwater composition needed to close the budgets in the absence of low-temperature basalt alteration, to identify important trends (Figure 5b). This allowed us to rewrite the Chemical Mass Fluxes section to be much simpler (including the former L 127, which needed simplifying), and this section now incorporates what was previously the first paragraph or so of the Global Mass Balance section. The archetypes are now shown in the context of earlier (1994) compilations of basin fluids in Supplementary Figure 3.\n7. Figures 3 and 4: I would also be keen to see this information in m/y, to account for differences in the map view area of each basin. In general, this would help clarify the relative punch that compacting basins provide—maybe they are small but mighty for their size when it comes to the total fluid they expel?\n>This was a good question, which we now address on line 134.\n“Although the fluxes per kilometer of coastline (or of basin length, for most overpressured basins) are of the same order of magnitude for geothermal convection and sediment compaction, compaction-driven flow comprises just 5% of the global flow. This is largely because compaction-driven flow is relatively uncommon in continental shelves”\nL 57: By volume or map area? The latter seems more relevant to this statement.\n> now clarified on line 62 “(by area and volume)”\nL 95: I think the authors are suggesting that the flux in the GoM is higher because shales can compact more, but as mentioned earlier, it would also depend on deposition rates and ages. Please add something like “…shale content and deposition rate.”\n> done\nTable 5 is difficult to follow, as units for most columns are in the caption, but units for the left column are in the column header. Also, the term off-axis isn’t really introduced until Table 5, adding some uncertainty in terminology.\n> Table 5 has been replaced, see #6 above. (Off-axis was supposed to have been changed to low-temperature -- I think we eradicated the rest of them.)\nL 216: This conclusion can be driven home with an improved conceptual figure (Figure 1).\n> done (above)\nL 242: Rather than citing a regional study from Befus et al. for a global estimate, consider citing Zhou et al.\n> done, another great suggestion from this reviewer\nBefus, K. M., Kroeger, K. D., Smith, C. G., & Swarzenski, P. W. (2017). The magnitude and origin of groundwater discharge to eastern U.S. and Gulf of Mexico coastal waters. Geophysical Research Letters, 44, 10,396–10,406. https://doi.org/10.1002/ 2017GL075238\nZhou, Y. Q., Sawyer, A. H., David, C. H., & Famiglietti, J. S. (2019). Fresh submarine groundwater discharge to the near‐global coast. Geophysical Research Letters, 46. https://doi.org/ 10.1029/2019GL082749"}, {"round": 2, "reviewer_comments": {"reviewer_1": "In the previous round of review, I crificised mainly on the choices of representafive fluid composifion for the archetypes that is then used for their mass balance calculafion. While I appreciate the addifional efforts from Wilson et al. to accommodate my comments, such as including supplementary figure 3 to compare the composifion of the four selected archetypes with other saline fluids in sedimentary basin and the addifional paragraphs explaining archetypes, the replies are not enfirely safisfactory to be honest.\nWilson et al. replied that “Note that the groundwater that parficipates in sedimentary diagenesis in confinental shelves is overwhelmingly saline (of seawater salinity or higher, including brines), originafing as seawater rather than rainwater.” They thus maintained their selecfion of using Gulf of Mexico as the case represenfing the “cold seep” archetype. Such a statement is confusing to me as, in their own selecfion of fluid composifion for archetype “clasfic-derived”, the salinity is apparent lower than seawater (448 mM vs. 547 mM of seawater), which apparently contradicts to the statement above. Fresher porewater doesn’t necessarily indicate mixing of meteoric water. Reacfions such as clay dehydrafion, which is common in marine environment, can also result in fresher porewater as compared to seawater. In addifion, the cold seep site I suggested for the northern Atlanfic Ocean margin has a large seawater component with salinity only 10% lower than seawater value, which is comparable to the archetype “clasfic-derived” selected by the authors. Again, I don’t think it is needed for the authors to include the site suggested. I just want to point out the large variafion in fluid composifion and the challenge to generalize.\nDespite my agreement of the author’s point. I need to point out their selecfion of cold seep archetype composifion will have minimum impact on the overall conclusion given that the authors only considered the most extreme composifion for their global mass balance calculafion. Cold seep composifion is well within that range regardless of their choices of representafive sites for cold seep archetype.\nIn my another comment for the fluid composifion for the carbonate archetype, Wilson et al. replied the following: “This is now addressed in the revised discussion of the groundwater archetypes and Supplementary Figure 3 (see #1). The new figures make it clear, for example, that the single citafion for type 4 actually represents a compilafion from 8 well-studied sites. The new figures also show the archetypes in the context of broader compilafions.” I did check back to the reference menfioned (ref 49 in the paper), which is the site report from ODP Leg182 Site 1126 (Great Australian Bight). I’m not sure why Wilson et al. indicated the data were from “8 well-studied site”. To me, this is data from several depths of a single locafion (on a side note, this drilling site has a water depth of 738.8 meters, which is not from confinental shelf). Again, I’m not enfirely convinced this could be representafive for all the carbonate archetype for global sedimentary basins. The authors need to clarify this further. The composifion of this archetype may be crucial to the calculafion in Eqs. 1 and 2 and will deserve a really careful considerafion.\nI also have the following minor comments to help improve the readability of the paper.\nLine 20-24: References should be included to support the statements in this paragraph\nLine 33-35: this statement also needs to be backed up with references.\nLine 36-37: This statement also needs support.\nLine 99: GoM needs to be spelled out\nTable 2: Why not have the full name for GoM?\nFig.4: To avoid confusion, I suggest change the fitle of x-axis to “flux due to geothermal convecfion”, which is also consistent to the fitle of Fig. 3.\nLine 122-124: Can this “predictability” be read from any figure or suppl. Material? Or is it really an important statement that needs to be included?\nTable 4: Though the calculafion for “modified concentrafion” is not included in the main text, a sentence should sfill be included to guide the readers to the calculafion (such as secfion 4.4 of the method).\nSupplementary table 1: Thanks for including detailed calculafion here. Why items 4, 5, 9, 10 were indicated as flux, despite the unit is in concentrafion?Isn’t that you simplify calculate the difference between seawater and the adjusted concentrafion from the brine?\nLine 181, 183, 185: the references 31, 3,1 are easily confused with the exponent. I suggest write “(ref 3)” instead.\nLine 184: the m from “mc” should be capitalized to be consistent with Eq .1. Refer Cmor, Cr, and mc (or Mc) back to table 4 and also include these acronyms in Table 4 to facilitate reading.\nLine 185: is “Qs” the same as Qi in Line 132? If yes, use only one of them for consistency. If not, specify the value.\nLine 197: “but it showed unrealisfic level of seawater modificafions” I don’t understand this sentence. Which “it” was referred to and why seawater modificafion? I thought seawater has been corrected for the archetypes?\nLine 198: Again, not quite sure what does seawater modificafion mean here.\nFigure 5: indicated Eq. 1 in the capfion to help the readers connect.\nEq. 2: is the “mc” in the equafion the same as “Mc” in Eq. 1? Is the Qs the same as Qi in Line 132? Same comment as for Line 184. Refer back to Table 4 when calling the different terms. What is the value of Cit used? I cant see it in Table 4.\nLine 214: reference 32 can be confused with exponent\nFigure 6: Where is Eq. 4 indicated in the capfion?\nLine 218: I’m a bit confused here. So Cit was being calculated from Cs, which you adopted the composifion of the clasfic and CaCl2 types? This could probably be already indicated in Line 211-214.", "reviewer_2": "I have reviewed the revised submission of Wilson et al. and find the revisions to be comprehensive and effecfive. This is an excifing contribufion that fies together a lot of lines of evidence to solve a fundamental quesfion about marine geochemical budgets and hydrogeologic processes. A few very minor remaining suggesfions:\n- In the new conceptual figure (1A), it would help to label the fluxes (i.e. “QrCr next to 1, etc).\n- Figures 3 and 4 could be combined (perhaps with the compacfion-driven fluxes shown in one color above, and the geothermal fluxes in another color below).\n- I could not find a reference to the source of informafion on lithology (Supplementary Figures 1 and 2). Was it the Baldwin and Butler reference? If so, I’d suggest pufting this citafion in the capfions."}, "author_response": "Response to Reviewers\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nIn the previous round of review, I criticised mainly on the choices of representative fluid composition for the archetypes that is then used for their mass balance calculation. While I appreciate the additional efforts from Wilson et al. to accommodate my comments, such as including supplementary figure 3 to compare the composition of the four selected archetypes with other saline fluids in sedimentary basin and the additional paragraphs explaining archetypes, the replies are not entirely satisfactory to be honest.\nWilson et al. replied that “Note that the groundwater that participates in sedimentary diagenesis in continental shelves is overwhelmingly saline (of seawater salinity or higher, including brines), originating as seawater rather than rainwater.” They thus maintained their selection of using Gulf of Mexico as the case representing the “cold seep” archetype. Such a statement is confusing to me as, in their own selection of fluid composition for archetype “clastic-derived”, the salinity is apparent lower than seawater (448 mM vs. 547 mM of seawater), which apparently contradicts to the statement above. Fresher porewater doesn’t necessarily indicate mixing of meteoric water. Reactions such as clay dehydration, which is common in marine environment, can also result in fresher porewater as compared to seawater. In addition, the cold seep site I suggested for the northern Atlantic Ocean margin has a large seawater component with salinity only 10% lower than seawater value, which is comparable to the archetype “clastic-derived” selected by the authors. Again, I don’t think it is needed for the authors to include the site suggested. I just want to point out the large variation in fluid composition and the challenge to generalize.\nGood point, thank you for being persistent. We got distracted by the meteoric water paper and did not realize that the other papers did indeed describe fluids of seawater origin that have reacted to some degree with sediments. We added a sentence (line 156-159): ”These relatively highly-reacted fluids differ somewhat from cold seep fluids in other settings, including gas hydrate systems 37,38 [refs are Hong et al. 2017; 2021] and convergent margins30, but a key feature of all of these seeps is that they are depleted in Ca2+ relative to seawater.” On line 48 we changed “of seawater salinity” to “near seawater salinity.” We had already noted that San Joaquin fluids were diluted by clay dehydration reactions in the Methods (line 440).\nDespite my agreement of the author’s point. I need to point out their selection of cold seep archetype composition will have minimum impact on the overall conclusion given that the authors only considered the most extreme composition for their global mass balance calculation. Cold seep composition is well within that range regardless of their choices of representative sites for cold seep archetype.\nAnother good point.\nIn my another comment for the fluid composition for the carbonate archetype, Wilson et al. replied the following: “This is now addressed in the revised discussion of the groundwater archetypes and Supplementary Figure 3 (see #1). The new figures make it clear, for example, that the single citation for type 4 actually represents a compilation from 8 well-studied sites. The new figures also show the archetypes in the context of broader compilations.” I did check back to the reference mentioned (ref 49 in the paper), which is the site report from ODP Leg182 Site 1126 (Great Australian Bight). I’m not sure why Wilson et al. indicated the data were from “8 well-studied site”. To me, this is data from several depths of a single location (on a side note, this drilling site has a water depth of 738.8 meters, which is not from continental shelf). Again, I’m not entirely convinced this could be representative for all the carbonate archetype for global sedimentary basins. The authors need to clarify this further. The composition of this archetype may be crucial to the calculation in Eqs. 1 and 2 and will deserve a really careful consideration.\nOur apologies, there was a typo in the letter last time. The single citation with 8 well-studied sites was for the CaCl2 brine archetype, Type 3. Dr. Hong is correct that the Type 4 archetype samples came from multiple depths at a single site in the Great Australian Bight. The justification for the choice of the Great Australian Bight (large range of depths/alteration, consistency with other well-known carbonate locations) is in the Methods, Section 4.4. We considered moving those paragraphs up. But to avoid getting deep into the weeds so early in the paper, we instead added a note on line 163-164: “The sources and justifications for these archetypes are discussed in more detail in Section 4.4.”\nI also have the following minor comments to help improve the readability of the paper.\nDone\nLine 33-35: this statement also needs to be backed up with references.\nDone\nLine 36-37: This statement also needs support.\nDone\nLine 99: GoM needs to be spelled out\nDone\nTable 2: Why not have the full name for GoM?\nGood point, done\nFig.4: To avoid confusion, I suggest change the title of x-axis to “flux due to geothermal convection”, which is also consistent to the title of Fig. 3.\nDone\nLine 122-124: Can this “predictability” be read from any figure or suppl. Material? Or is it really an important statement that needs to be included?\nDeleted\nTable 4: Though the calculation for “modified concentration” is not included in the main text, a sentence should still be included to guide the readers to the calculation (such as section 4.4 of the method).\ndone\nSupplementary table 1: Thanks for including detailed calculation here. Why items 4, 5, 9, 10 were indicated as flux, despite the unit is in concentration?Isn’t that you simplify calculate the difference between seawater and the adjusted concentration from the brine?\nGood point. We had copied Spencer and Hardie, who maybe should have done better. We changed these to “net chemical contribution” instead.\nLine 181, 183, 185: the references 31, 3,1 are easily confused with the exponent. I suggest write “(ref 3)” instead.\ndone\nLine 184: the m from “mc” should be capitalized to be consistent with Eq .1. Refer Cmor, Cr, and mc (or Mc) back to table 4 and also include these acronyms in Table 4 to facilitate reading.\nMc corrected, added “(see Table 4 for adjusted water compositions).”\nLine 185: is “Qs” the same as Qi in Line 132? If yes, use only one of them for consistency. If not, specify the value.\nGood catch, thank you. We now use Qs throughout. (Qi came from some older calculations that did not make it into the paper.)\nLine 197: “but it showed unrealistic level of seawater modifications” I don’t understand this sentence. Which “it” was referred to and why seawater modification? I thought seawater has been corrected for the archetypes?\nWe clarified this by changing this (now line 201-202) and the following lines to “The pattern of modifications in the theoretical fluid composition needed to balance marine chemical budgets in the absence of low-temperature basalt alteration showed sinks of K+, Mg2+, and Na+ and a source of Ca2+. This is consistent with the clastic-derived archetype, but this theoretical fluid showed unrealistic levels of change compared to seawater. Less alteration was required when we used our upper-bound estimate for the groundwater flux, but …”\nLine 198: Again, not quite sure what does seawater modification mean here.\nIncluded in the Line 197 edit\nFigure 5: indicated Eq. 1 in the caption to help the readers connect.\ndone\nEq. 2: is the “mc” in the equation the same as “Mc” in Eq. 1? Is the Qs the same as Qi in Line 132? Same comment as for Line 184. Refer back to Table 4 when calling the different terms. What is the value of Cit used? I cant see it in Table 4.\nMc and Qs/Qi: done, per prior comment about line 184. We deleted this reference to Clt because we realized we had already defined it in the prior sentence (which reads, paraphrased: “We calculated the value of Clt using Eq 2:”). We deleted the definition of Qs from line 216 because it was already defined at Eq. 1. We combined the next paragraph with this one to explain more immediately how we calculated Cs.\nLine 214: reference 32 can be confused with exponent\ndone\nFigure 6: Where is Eq. 4 indicated in the caption?\nGood catch, thanks. It was supposed to be Eq. 2, now corrected.\nLine 218: I’m a bit confused here. So Cit was being calculated from Cs, which you adopted the composition of the clastic and CaCl2 types? This could probably be already indicated in Line 211-214.\nSee our corrections for the comment about Eq. 2. We combined the two paragraphs to make this clearer (see lines 216-225).\nThanks again to Dr. Hong for a really close reading of this paper, which has certainly improved it.\nReviewer #2 (Remarks to the Author):\nI have reviewed the revised submission of Wilson et al. and find the revisions to be comprehensive and effective. This is an exciting contribution that ties together a lot of lines of evidence to solve a fundamental question about marine geochemical budgets and hydrogeologic processes. A few very minor remaining suggestions:\n- In the new conceptual figure (1A), it would help to label the fluxes (i.e. “QrCr next to 1, etc).\nWe removed the equation from Fig 1A for purposes of the paper, because it was complicated (and premature, really) to introduce and define all the variables this early. Better to wait for Eq 1.\n- Figures 3 and 4 could be combined (perhaps with the compaction-driven fluxes shown in one color above, and the geothermal fluxes in another color below).\nThis is a good suggestion, but we are, respectfully, terrified to change figure numbers at this stage. We rationalized our cowardice by noting that the sources of errors and hence graphics differ between the two plots, which makes it somewhat complicated to combine them. We hope that reviewers and editors will overlook our cravenness, given that the paper fits within the word and figure limits.\n- I could not find a reference to the source of information on lithology (Supplementary Figures 1 and 2). Was it the Baldwin and Butler reference? If so, I’d suggest putting this citation in the captions.\nWe added this statement to the captions for Supplementary Figures 1 and 2: “Stratigraphy compiled from the sources listed in Table 2.” And, thanks again for the great suggestions last time."}]

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