Pockmark morphology and turbulent buoyant plumes at a submarine spring

Continental Shelf Research 148 (2017) 19–36

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Pockmark morphology and turbulent buoyant plumes at a submarine spring a,b,⁎,1

a,1

c,1

B. Buongiorno Nardelli , F. Budillon , R. Watteaux , F. Ciccone G. De Falcoa, G. Di Martinoa, S. Innangia, R. Toniellia, D. Iudiconec

a,d

MARK

a

, A. Conforti ,

a

Consiglio Nazionale delle Ricerche–Istituto per l’Ambiente Marino Costiero, Napoli, Italy Consiglio Nazionale delle Ricerche–Istituto di Scienze dell’Atmosfera e del Clima, Roma, Italy Stazione Zoologica Anton Dohrn, Napoli, Italy d Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Trieste, Italy b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Submarine groundwater discharge Inner shelf topography Turbulent plume dynamics In situ observations Analytical modelling Gulf of Policastro Southern Tyrrhenian Sea

The input flow of groundwater from the seabed to the coastal ocean, known as Submarine Groundwater Discharge (SGD), has been only recently recognized as an important component of continental margin systems. It potentially impacts physical, chemical and biological marine dynamics. Independently of its specific nature (seepage, submarine springs, etc.) or fluid chemical composition, a SGD is generally characterized by low flow rates, hence making its detection and quantification very difficult, and explaining why it has been somewhat neglected by the scientific community for a long time. Along with the growing interest for SGDs emerged the need for in-situ observations in order to characterize in details how these SGDs behave. In this work, we describe the morphology of a pockmark field, detected in the Southern Tyrrhenian Sea (Mediterranean Sea), and provide observational evidences of the presence of active submarine springs over the coastal shelf area. We describe the effect of the fluid seeps on the water column stratification close to the main plumes and in the neighbouring areas, providing quantitative estimates of the intensity of the turbulent mixing and discussing their potential impact on the seabed morphology and pockmark formation in the context of turbulent buoyant plumes analytical modelling.

1. Introduction The existence of submarine sources of groundwater has been documented for centuries, recognizing their potential relevance for freshwater management issues (e.g. Moore, 2010). However, information on submarine springs were never collected and organized consistently and, for a long time, the scientific community has almost neglected their eventual effects on the coastal environment and potential impacts on coastal dynamics. While this was mainly due to the difficulty in identifying and measuring submarine sources of water of terrestrial origins, a number of studies have highlighted their importance in coastal hydrology, based on modern technologies and/or modelling (e.g. Taniguchi et al., 2003; Lambert and Burnett, 2003; Moore, 1996, 2003; Oberdorfer, 2003; Smith and Zawadzki, 2003; Destouni and Prieto, 2003). Despite the fact that Submarine Groundwater Discharge (SGD) is estimated to account only for a few percent of the total freshwater flux in the global oceans, mainly occurring through river input and precipitations, springs and diffuse seepage through the sea floor can still represent

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important contributions to the coastal ecosystem (Zhang and Mandal, 2012). Indeed, SGD not only brings fresh (or less saline) waters through usually undetected pathways, but it can also affect chemical composition of sea water, due to both anthropogenic land use and natural interactions with aquifer and sediments. Coastal SGD can also be contaminated by fertilizers, pesticides or industrial wastes, as well as by sewage and other pathogen substances, potentially diffusing pollution to the ocean, with potentially devastating effects on local ecosystems and related economies (e.g. Laroche et al., 1997; Gobler and Sanudo-Wilhelmy, 2001). SGD can also modify the nutrient availability along the water column (e.g. Slomp and Van Cappellen, 2004) as well as benthic habitats, and low-salinity input may create particular habitats on the sea floor, especially for fishery stock. Besides, Rodellas et al. (2015) have highlighted the importance of SGD as a source of nutrients to the Mediterranean Sea, demonstrating that SGD involve a large volume of freshwater, actually larger in magnitude than riverine discharge. They indicate that SGD represents a major source of dissolved inorganic nitrogen, phosphorous, and silica to the oligotrophic Mediterranean Sea, with relevant impact on the Mediterranean primary productivity.

Corresponding author at: Consiglio Nazionale delle Ricerche–Istituto per l’Ambiente Marino Costiero, Napoli, Italy. E-mail address: [email protected] (B. Buongiorno Nardelli). Equally contributing.

http://dx.doi.org/10.1016/j.csr.2017.09.008 Received 11 February 2017; Received in revised form 5 September 2017; Accepted 18 September 2017 Available online 21 September 2017 0278-4343/ © 2017 Elsevier Ltd. All rights reserved.

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Loher et al. (2016) assert that sediment remobilization and spill over the rims of the pockmarks is accounted for by the switch from ‘quiescent’ to ‘eruptive’ activity mode of rising fluids. In any case, a fine-grained sediments medium (clayey silt or silty clays) is needed to support their structure and long-time existence (Papatheodorou et al., 1993). Pockmarks are often clustered around two main dimensional classes within the same field (Hustoft et al., 2010; Wessels et al., 2010; Moss et al., 2012), possibly reflecting different hydrodynamic regimes and mechanisms behind the initial stage of pockmark development (Riboulot et al., 2016). The smaller elements are generally composed by unit pockmarks whose diameters average around 18–20 m, normally not exceeding 40 m, and depths attains around 3.5–5 m, with flanking slopes 3° to > 6° steep; their geometry is near circular and aspect ratio of 1:1.5. The wider elements cluster around 350 m in diameter within a dimensional range of 100–700 m and 10–50 m deep, with planform geometries ranging between circular to highly-elliptical and average aspect ratio up to 1:3.7 (Moss et al., 2012). The pockmarks density and spatial distribution appears to be attributable to differences in shallow fluids availability and deeper geology controlling fluid migration pathways (Gafeira et al., 2012). In this work, we investigated the presence and effect of submarine springs in a coastal shelf area initially surveyed during CARG CMS03 (CARtografia Geologica, GeoMare Sud −2003) campaign and successively monitored during the ARCOSE (Age and Recurrence of Campania Offshore Slide Events) cruise, both carried out by the Istituto per l’Ambiente Marino Costiero (IAMC) of the Research National Council of Italy (CNR). ARCOSE survey was carried out in September 2010 in the Southern Tyrrhenian Sea (Mediterranean Sea) and was mainly devoted to the acquisition of geophysical data and hydrographic profiles. The observations revealed the presence of characteristic pockmarks in the Gulf of Policastro (Figs. 1–3). Conductivity Temperature Depth (CTD) profiles were collected in correspondence of each of these pockmarks and in the area close to Punta Infreschi (Fig. 1). Unfortunately, a more regular and wider mapping of the hydrographic parameters in the area was not possible due to a combination of adverse weather conditions and time constraints. Available data allowed to identify which submarine springs were effectively active and made it possible to characterize the dynamics governing the mixing of groundwater with surrounding marine waters. Satellite data showed that the area considered is characterized by very low mean surface currents with low variance (Rinaldi et al., 2010), so that preferential erosion due to strong currents along the shelf can be reasonably excluded. As a consequence, a consistent scenario for the mechanisms creating and maintaining the pockmarks has been proposed by comparing the observations with the results of an analytical model describing the evolution of turbulent buoyant plumes in a stably stratified environment with a distinct vertical structure in the background salinity and temperature field.

Despite a growing recognition of the importance of SGD (UNESCO, 2004; Moore, 2010), only a partial quantification and chemical characterization of known SGD has been carried out (e.g. Burnett et al., 2006), and a complete identification of SGD areas along with an evaluation of their impacts on local ecosystems, water stratification and coastal dynamics, as well as on seabed morphology, are still lacking. Several indirect potential indicators of SGD have been suggested, based on water colour, temperature, salinity or some other geochemical fingerprint, but not yet routinely applied (see also Bokuniewicz et al., 2003 and references therein). Salinity anomalies, in particular, have been used to detect submarine freshwater seeps looking either at regional water budgets or vertical profiles at specific locations (e.g., Johannes and Hearn, 1985; Valiela et al., 1990). Pockmarks are among the most common manifestations of fluid flow from the subsurface to the seafloor and may occur also in the subsurface as buried and stacked features, in presence of persisting fluid migration through preferential pathways (Andresen and Huuse, 2010). They consist of concave, crater-like depressions in the seabed, almost ubiquitous along continental margins and in lakes (Judd and Hovland, 2007; Moss et al., 2012; Loher et al., 2016). Generally, pockmarks are associated with fast buoyant fluid flows (fresh-water submarine springs or fluid seeps) typically found in submerged areas constrained by karst topography or by a fractured limestones bedrock (Roxburgh, 1985; Fleury et al., 2007), along continental margins in presence of gas-hydrates decomposition, hydrocarbons (Solheim and Elverhøi, 1985; Pau et al., 2014) or pore-fluid expulsion (Harrington, 1985; Lafuerza et al., 2009;), and in volcanic areas with residual hydrothermal activity (Passaro et al., 2014; Tudino et al., 2014; Ingrassia et al., 2015). Understanding their formation and morphodynamical behaviour has been a major challenge since their first discovery (King and MacLean, 1970), in particular for the hazard-related concerns, for their relevant role in hydrocarbons exploitation issues, and for being indicators of methane release to the oceans (e.g. Judd and Hovland, 2007). A variety of mechanisms have been proposed, which involve either continuous processes (seeps) or rapid and sudden events of episodic releases and blowout (vents) of fluids (e.g. Marcon et al., 2014; Loher et al., 2016). These include:

• suspension of fine-grained sediment with low sediment/water ratio, • • • •

by ascending fluid drags and formation of a coarse-grained lag deposits, ensuing removal of fines from the pockmark rims through bottom water currents (Cartwright et al., 2007; Cathles et al., 2010); localized collapse after emptying of a fluid reservoir in the subsurface, even by discrete blowout events (Cartwright et al., 2007), with a volume loss (Leon et al., 2010; Wessels et al., 2010, Cartwright and Santamarina, 2015), sediment fluidization (liquefaction) and ensuing volume compaction of particles, induced by fluid seeps or vents (Draganits and Janda, 2003); development of a syn-sedimentary, self-regulated process, growing vertically during prolonged fluid seeps, between particles settlement and fluid pressure drag, that promote the coarser grains to deposit in the space above the plume site; decrease of the shear strength of the matrix by ascending fluid flow through sediments and preferential erosion caused by strong bottom currents, including episodic storm surges (Schlüter et al., 2004).

2. Geographical and geological setting The study area is located off the Cilento coast (Southern Italy), a mountainous region belonging to the fold and thrust belt of the Southern Apennines (Mostardini and Merlini, 1986), with a mean elevation of 450 m asl and mean annual precipitations exceeding 1800 mm, in 1951–1980 time span (Desiato et al., 2014). The wide outcrops of carbonate deposits, part of the BulgheriaVerbicaro and Albuno-Cervati Units, and clayey-marly flysch succession belonging to the Liguride Unit (Bonardi et al., 2009; Ciarcia et al., 2009), constitute the ideal ground for the development of large karst aquifers along the coast (Cotecchia et al., 1990). Indeed, the peculiar geology of the subsurface (high permeability due to karstic cavities and tectonic fracturation) and the position of watershed seem to favour the dispersion at sea of large amount of underground water towards two preferential coastal sectors (Fig. 1). Besides, the hydrogeological balances of the phreatic aquifers document the loss at sea (Allocca et al., 2007).

Pockmark maintenance is thus generally accompanied by significant sediment redistribution in the surrounding seabed. Observations (Draganits and Janda, 2003; Schlüter et al., 2004) and numerical models (Hammer et al., 2009; Brothers et al., 2011) suggest that pockmarks can be maintained and reshaped through vertical flow and seabed currents, in stormy- or tidally-controlled conditions (Fandel et al., 2017). Simulations in scaled laboratory tests, indeed, have proved that seabed currents are deflected by pockmarks depression and have a role in modifying pockmarks’ original shape through time (Pau et al., 2014). 20

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Fig. 1. Hydrogeological scheme (modified from Carta Idrogeologica dell’Italia meridionale, Ispra 2012) and sites of submarine freshwater discharge off Sapri; (1) Paleogene carbonatic complex; (2) Miocene turbidite complex; (3) calcareous complex of Bulgheria-Verbicaro Unit; (4) clayey-limestone complex of Nord-Calabrese Unit; (5) dolomitic complex of BulgheriaVerbicaro and Monti della Maddalena Units; (6) calcareous complex of Alburno Cervati Unit; (7) continental epiclastic complex; (8) coastal-alluvial complex; (9) main path of underground fresh-water flow; (10) main fault; (11) Ruotolo submarine spring; (12) Vuddù submarine spring, this paper; (13) submarine springs. Mainland elevation is depicted by isohypse every 250 m.

Fig. 2. a) Sparker Seismic section across the shelf and P2 pockmark; U0 Middle Pleistocene Stratigraphic inconformity, U1 Late Pleistocene stratigraphic unconformity; (AS) acoustic substratum, (A1) wedge-shaped seismic unit (middle Pleistocene); (B), (B1), (C), seismic units (late Pleistocene) with evidences of active fluid migration; (D) post-glacial fine-grained seismic unit; (1) sub-vertical zones of disrupted reflections; (2) acoustic turbidity front in fluid-charged deposits; (3) relict and buried pockmark; (4) normal fault. (b) Sidescan sonar image of SGD area with pockmarks marking the freshwater seeps. P2 pockmark is characterized by higher backscatter intensity (light gray) due to high bulk density of sediments and roughness of the sediment–water interface, if compared with the surrounding seabed (dark gray). Acoustic shadows are projected by steep slopes within the hole. Three distinct sites of emissions are observed in P2. (c) navigation track of Sparker section and location (square) of sidescan sonar image.

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Fig. 3. (a) Multi-beam mapping of the bottom topography in the shelf area off Sapri. The black box highlights the pockmark field analysed here. (b) Temperature (red) and salinity (black) profiles collected in correspondence of each of the P1-P9 pockmarks. Temperature (orange) and salinity (green) reference profile collected at Punta Infreschi. Temperature is expressed in (°C) and salinity in (g/ kg). The horizontal lines in (b) panels identify the upper mixed layer base as estimated from density (continuous line) or temperature (dashed line) threshold criteria (0.03 kg/m3 and 0.1 °C, respectively) for each profile.

mouth and are covered by coarse sand and talus blanketing the cliff foot (Celico et al., 1994). Stratigraphic information on the marine sectors in the Gulf of Policastro are provided by previous studies (Pennetta, 1996; Ortolani et al., 1997; De Pippo and Pennetta, 2000). Bathymetric and seismic survey off Punta Infreschi (Budillon et al., 2011a) and Maratea (Colantoni et al., 1997) and a geomorphological survey by scuba diving (Toccaceli, 1992) evidenced that:

Two main hydrogeological karst reservoirs have been identified in the area (Celico et al., 1994; Piscopo et al., 1993) (Fig. 1): a) the Mt. Coccovello aquifer, made of carbonate and marls (Lias-Lower Eocene) and b) the Mt. Bulgheria aquifer consisting of dolomitic carbonates with marls and cherty intercalations (Upper Triassic–Lower Miocene). The Mt. Salice - Mt. Coccovello aquifer is a fresh-water reservoir 140 km2 wide, with a potential yield of 0.029 m3/s km2 (Celico et al., 1994). It feeds the Ruotolo (5 m bsl, Allocca et al., 2007) and Vuddù (12 m/50 m bsl, this paper) submarine springs (Fig. 1) by an estimated production rate around 2.5 m3/s (Allocca et al., 2007). The Mt. Bulgheria aquifer is a fresh-water reservoir 112 km2 wide, with a potential yield of 0.013 m3/s km2 (Piscopo et al., 1993). The underground water-flow toward the southern coast has been estimated in about 1.1 − 1.5 m3/s, ∼50% of which is thought to flow out in the surrounding of Infreschi Cape, according to indirect evaluations by infrared surveys (Celico, 1983; Allocca et al., 2007). The Ruotolo submarine spring is fed through karst canalizations which end along the submerged coastal cliffs in the first 5 m bsl. Secondary outlets have been reported in the surroundings of the main

– the acoustic substratum (AS), consisting of lithified rocks has been correlated to the carbonate units, widely outcropping onland (mainly limestones and dolostones, secondarily arenites, claystones and cemented breccias) and in shallow waters to 25 m/30 m depth; it is overlaid by high-amplitude, irregular clino-stratified reflectors (A1 Unit), of undefined lithology; – the AS and A1 are both dissected by sub-vertical fault planes, primarily NE-SW oriented and parallel to the coast, that originate subangular, in echelon relieved outcrops and are bounded at the top by an angular unconformity (U0), generally stated as due to a 22

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(1957), estimating the measure of average sediment size through a graphic mean (Mz), the uniformity of grain size (sorting) of sediments (s), through a so-called inclusive graphic standard deviation, the skewness (Sk), i.e. the degree of asymmetry of the grain size distribution, and the kurtosis (K), i.e. the peakedness of a grain-size distribution, here derived from the weight percentage of discrete diameter classes (Fig. 2(a–b).

prolonged subaerial exposure. – a thick detrital cover overlies the AS and A1 with different internal geometries (B, B1, C, D units), where the uppermost, lying above the U1 unconformity, is the fine-grained sedimentary wedge, deposited in postglacial times (< 20 ky); the B unit is made of high-angle clinoform reflections in lateral aggradation on the acoustic substratum, and accounts for the enlargement of the shelf during the sea level regression of the Late Pleistocene; the B1 is a wedge-shaped deposit with downlapping reflectors above B unit which develops at the rear of the subvertical cliffs of AS; – a marked unconformity U1 cuts at the top both the AS and the detrital cover and is genetically related to the subaerial and submarine erosive surface of the last sea level lowstand; – the shelf extends for about 8 km off Sapri, while is less wide to the southeast and northwest, due to slope sediment mass failure.

3.2. CTD data and processing Hydrographic measurements have been carried out in the Gulf of Policastro (Figs. 1 and 3), offshore the town of Sapri, in the area reported as a potential SGD source (Carta Idrogeologica dell’Italia meridionale, Ispra 2012). Vertical profiles have been acquired by means of a SeaBird electronics (SBE) 911 plus Conductivity Temperature Depth probe, including dissolved oxygen (SBE 43), light transmittance (Chelsea/Seatech) and fluorescence sensors (Chelsea Aqua 3). CTD casts were carried out during ARCOSE survey in correspondence of each of the pockmarks identified in multi-beam mapping, as well as at the western edge of the Gulf of Policastro (Punta Infreschi, see Figs. 1 and 3). The CTD data went through Seabird recommended processing steps before further computations were carried out with Ocean Data View (ODV) software (Schlitzer, R., http://odv.awi.de, 2015). ODV was used, in particular, to characterize the stability of the water column by estimating the Turner angle (Ruddick, 1983).

Sedimentological analysis and backscatter images of the seabed, performed for geological mapping issues (ISPRA, Servizio Geologico d’Italia, 2014), report a shoreface down to −10 m made by well-sorted sand, an inner shelf down to −40 m where a fine –grained deposition (muddy sand or sandy-mud) occurs and a truly muddy sedimentation beyond this depth. 3. Data and methods 3.1. Geological and geophysical data Swath bathymetric data have been acquired by using a Reson Seabat 8111R (100 kHz), hull mounted on R/V Thetis, and a Reson Seabat 8160 (50 kHz), hull-mounted on R/V Urania, in water deeper than 50 m. Navigation was tracked by a 12-channel DGPS, a motion sensor and a gyrocompass, in order to perform a real-time correction. Processing was performed by the Reson PDS 2000 software obtaining a digital elevation model (DEM) with a grid cell of 5×5 m. Seismic lines have been acquired in 2010 by means of a Geotech multi-tip spark array (M.T.S.A.), sparking at 0.6–1 kJ; data were processed with bias correction, filtering and gain corrections by using Geosuite® software. Seismic signal enters the shelf record by about 50 ms (two-way travel time, about 43 m beneath the sea floor, bsf) with a maximum vertical resolution not exceeding 40–60 cm. The conversion of two-way travel time to real depth was obtained assuming an average velocity of about 1550 ms−1 below the sea floor (Carlson et al., 1986). Seismic lines were interpreted considering reflections geometries and relative lateral terminations among reflectors, to define the overall stratigraphy of the area. Side Scan Sonar images of the seabed were recorded in 2003 (CARG CMS03 survey) by a deep tow Klein 2000 system and ISIS® platform in the frame of a geological mapping project of marine areas (ISPRA, Servizio Geologico d’Italia, 2014; Budillon et al., 2011b). The acoustic images measure the acoustic energy scattered back towards the receivers after interaction with the seafloor, which depends mainly on sediments inhomogeneity and bottom roughness (Briggs et al., 2002). Fine sediments generally exhibit low backscatter intensity due to low sediment bulk density and low acoustic impedance contrast at the water–sediment interface, whereas coarse sediments generally result in higher backscatter intensity due to higher bulk density, high acoustic impedance contrast and greater roughness of the sediment–water interface; acoustic shadows are projected when obstacles interpose to the propagation of acoustic wave front (Stewart et al., 1994; Collier and Brown, 2005; Tonielli et al., 2016). One seabed sample, recovered from the bottom of P1 pockmark (depth −43 m, Fig. 3), was measured for grain-size by conventional procedures and dry-sieved at the sedimentological lab of the IAMC-CNR in Naples (Molisso et. al, 2000) to compare the lateral variation of sediment texture in- (this paper) and out- (ISPRA, 2014) pockmarks. Grain-size analysis was then carried out following Folk and Ward

3.3. Turbulent buoyant plume model A turbulent buoyant plume of horizontal area A = πr 2 , with characteristic radius r , can be characterized at any height z by its density ρ , itself determined by temperature T and salinity S, its volume flux πQ = Aw , momentum flux M = Aw 2 (where w is the mean vertical velocity of the plume) and buoyancy flux, B = Awg (ρa −ρ)/ρa (where ρ and ρa are the densities inside the plume and in the ambient fluid outside the plume) (Fig. 4). In a steady-state, and assuming that the entrainment velocity at the edges of the plume is proportional to the vertical velocity, ue = αw , with α the entrainment coefficient (α =0.12; Morton et al., 1956; Fischer et al., 1979;Kaminski et al., 2005), the vertical variations of these various fluxes are governed by the generic steady-state transport equation (with the Boussinesq approximation ρa −ρ < <ρa ):

d (ϕ) = Jϕ dz

(1)

with the flux ϕ and spatial variation of the flux Jϕ being (ϕ = Q , JA = 2rαw ), (ϕ = QT , JT = 2rTa αw ), (ϕ = QS , JS = 2rSa αw ), (ϕ = M , g dρ JM = Ag (ρa − ρ)/ρa ), and (ϕ = B , JB = −AN 2w ), where Na2 = − ρ dza is a

the buoyancy frequency of the ambient fluid (Morton et al., 1956; Speer, 1989). Although various analytical solutions exist for Eq. (1) in simplified geometries (Morton et al., 1956; Speer, 1989; Scase et al., 2006; Kaye, 2008; Woods, 2010), the typical non-linear vertical structure of temperature and salinity observed in the Mediterranean sea during the stratified summer season makes their use impossible and a numerical solution is thus computed here. The plume source can be classified, using the conditions at the source of the plume, by means of two non-dimensional numbers:

Γ0 =

Δ=

8Q02 B0 5

5αM02

(2a)

Na2 M02 B02

(2b)

where Q0, M0 and B0 are the volume, momentum and buoyancy fluxes at the source of the plume and Na the buoyancy frequency (or 23

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Fig. 4. (A) grain size analysis of sample B1332, retrieved at 19 m bsl, is representative of present-day deposition in offshore (mainly sandy silt); (B) grain size analysis of sample B17, retrieved from the bottom of P1 pockmark (43 m bsl), shows the occurrence of a lag deposit lacking in fine fractions (< 31 µm). The position of the sampling is displayed in Fig. 3a.

stability at source and maximum stratification levels, respectively. To classify the observed plume, we thus need to compute the numbers Γ0 , Δ0 and Δmax . This requires to infer the optimal source parameters for which the model reproduces more accurately the observed data. Further details on the physics of plumes can be found in Morton and Middelton (1973), Hunt and Kaye (2005), Kaye (2008), and Woods (2010).

4. Observations and modelling 4.1. Geomorphological and stratigraphic features A pockmark field of eleven circular depressions has been localized 0.8 km off the coast, between 12 and 45 m of depth, over an area of 0.3 km2 (Fig. 2 and Fig. 3); it should represent the morphological appearance of the Vuddù submarine spring (Celico et al., 1994), despite Allocca et al. (2007) report the seep at 10 m bsl. Dimensionally, pockmarks are clustered in two groups, hereafter indicated as A-type (100–200 m large and about 20–25 m deep) and Btype ( 20–40 m large and 3–5 m deep) (Fig. 3). All pockmarks exhibit a negative conic shape, except the largest, which is flat based; besides, none of them has relieved rims, thus suggesting a complete removal of fine grained particles from the system and a negative budget of the depositional rate in the holes. P1 pockmark in particular, is characterized by a very regular conic shape with smoothed edges and slopes as steep as 28°−30°. The SSS image (Fig. 2b) of the seepage area returns single highbackscatter spots in correspondence of B-type pockmarks; a nonhomogeneous backscatter, acoustic shadows due to the steepness of lateral flanks and possible acoustic artefacts bounce back from A-type pockmarks. P2 pockmark is marked by three distinct emission points occurring in the deepest portion of the seabed. The Sparker section (Fig. 2) goes from −75 m to −40 m and crosses the P2 pockmark. The seismic facies analysis reveals a number of vertically-stacked amplitude anomalies, acoustic turbidity horizons, concave-upward erosive features, columnar zones of disrupted reflections, which are generally seen as the most common seismic expressions of cross-stratal fluid migration, fluid escape features and seepages at the seabed (Cartwright et al., 2007).

Fig. 5. Modelling the turbulent buoyant plume observed in P2. We consider the plume as axisymmetric, and we only consider values averaged over cross-depth sections, hence modelling the plume as a 1d feature with, at each depth z, a characteristic radius r, vertical velocity w, entrainment velocity ue, density ρ and corresponding density ρa in the ambient fluid outside the plume. The plume's dynamics is modelled by defining source volume Q0, momentum M0, and buoyancy fluxes, B0. The simulation of Eq. (1) gives the neutral height hN. In situ observations give hR.

normalized stratification) at a reference height. The number Γ0 quantifies the forcing at the source (Hunt and Kaye, 2001) while Δ quantifies the environmental stability (Morton et al., 1959; Morton and Middleton, 1973; Kaye, 2008). A small Γ0 < 1 implies the case of a forced plume, while a large Γ0 > 1 is a lazy plume. A small Δ characterizes a plume which will evolve easily across depth while a large Δ is a plume strongly damped by stratification or mixing. Note that Γ0 is equivalent to the inverse of the square of a Froude number. The parameter Δ is usually considered for cases of constant or uniformly stable stratified environment. Here, as we expect a nonuniform stratification in the surrounding of the plume, we consider two different parameters, Δ0 and Δmax , quantifying the environmental 24

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Fig. 6. (A) Temperature-Salinity diagram of the CTD profiles collected during ARCOSE survey; (B) Location of CTD profiles.

the un-removable heavy particles, stacked originally in the stratigraphic section, or occasionally trapped down-hole or either in-situ concreted, thus forming a coarse lag deposit (Buffington and Montgomery, 1999). The lack of fines at the base of pockmarks, the coarse skewed (sensu Blott and Pye, 2001) lag deposit with a tail of coarse particles, the perfect conical shape, the smoothed edges and the absence of rims point to a very efficient system in removing fine particles, by an unremitting and strong vertical flux, possibly with sudden pulses of increased velocity (e.g. at seasonal and/or annual scales).

Seismic geometries are consistent with those recognized by Colantoni et al. (2007), comprising (downward from seabed): – a wedge-shaped, vertically aggraded post-glacial unit (D), made of fine-grained sediment which act as a moderate seal for underground waters; P2 pockmark is incised through the D unit; – a wedge-shaped, laterally aggrading unit (C), made of oblique-tangential reflections and topped by U1 unconformity; zones of ongoing rising fluids are marked by sub-vertical columns of disrupted reflections; – a wedge-shaped unit (B1), depicting several enhanced high-amplitude reflection anomalies, typical of fluid-charged porous sediments; it includes a number of pockmark-like relic features and a front of acoustic turbidity; – a vertical aggrading unit (B), lying directly on the hangingwall block of AS and onto the U0 unconformity; the unit is almost 10–12 m thick and shows paleo-pockmarks, amplitude anomalies and columnar zones of disrupted reflections, in analogy with B1 unit; – a normal fault, almost sub-vertical, cuttings As and A1 units, with an apparent downthrown of about 25 m; the fault plane is in correspondence of P2 pockmark and few meters distant with respect to the buried pockmarks; – an acoustic-impeding unit (A1), representing the acoustic substratum in the area.

4.3. Hydrographic data CTD profiles were collected in correspondence of each of the pockmarks identified in the multi-beam data, and show distinct characteristics depending on the pockmark size (Fig. 3). In correspondence of A-type pockmarks, a significant reduction of salinity close to the bottom is detected with respect to all other stations. At station P2, carried out in the centre of the largest pockmark, the temperature displays a rather constant value of ~18 °C, while salinity stays below 37.2 from a few meters above the bottom, up to a depth of about 20 m. Bottom salinity itself does not exceed 37.5, well below the open Tyrrhenian Sea seasonal background values (Brasseur et al., 1996), and also well below the values recorded during ARCOSE at Punta Infreschi (we have taken here as reference the CTD profile collected at 15.43°E, 39.97°N, approximately 16 km away from the pockmark field). Quite regular small-scale oscillations of both temperature and salinity are found all along this salinity minimum. Similar profiles are observed at station P1, even if both temperature and salinity lowest values are higher with respect to P2 (~20.5 °C and 37.4, respectively). Again, the salinity minima are observed in a thick layer beneath the upper surface mixed layer extending down to 10–15 m above the bottom of the pockmark. Conversely, in the profiles collected over the B-type pockmarks, the fresher (37.4–37.5) layer found below the surface does not extend to the bottom, and remains constrained between 15 m and 25 m, below the upper mixed layer base, with salinity rising again to > 37.7 in the lower layer. P5 station represents the only exception, with fresh and cold waters also in the first 3–5 m close to the bottom. The slightly different depths at which the B-type salinity minima are observed in the

4.2. Seabed sediment textures in- and out-pockmarks The relative weight percentages of seabed sediment diameter classes vary significantly in- and out-pockmark, resulting in distinct sediment textures. Out of the pockmarks, at 18 m of water depth, a sandy silt deposit is found (Mz = 5.26), poorly sorted (s = 2.02) and with clasts not exceeding the 500 µm – size, with a positive skewness, i.e. a tail towards the fine diameter classes. Within the pockmark P1, whose rim lies between −18 and −28 m, a very poorly-sorted (s = 4.57) coarse grained deposit is found (Mz = 1.2), with a marked negative skewness (−0.47) (Fig. 4). Coarse grains and granules at this site include a very heterogenic and hetero-metric compound made of large bioclasts, pumices, lithics, algal concretions and organic material; this association appears as the result of the selective concentration through the time of 25

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Fig. 7. Characterization of water mass stratification and mixing in the main pockmarks (P1, P2, P5). (a) Density (red) profiles, expressed in kg/m3 and Turner angle (squares). (b) Turbulent mixing coefficient estimated from Thorpe scale (blue), expressed in m2/s, and light attenuation coefficient, given in m-1 (black). (c) Schematic interpretation of the observations. The horizontal lines in (A,B) identify the upper mixed layer base as estimated from density (continuous line) or temperature (dashed line) threshold criteria (0.03 kg/m3 and 0.1 °C, respectively). Red and yellow dots identify the levels selected to optimize the analytical model, identifying the neutral level depth and the largest depth for which the CTD sensor was still in the plume, respectively.

resident waters. Observed depth differences of the salinity minimum simply reflect the local variations in the mixed freshwater neutral buoyancy level (Fig. 6). The same θ-S analysis also evidences that the water found inside P2 and P1 has mixed with relatively warm waters, at 18 °C and 20.5 °C, respectively, that correspond to the temperatures observed in the unperturbed profile at the depth of the pockmarks’ rim and not with the ones found at the same depth (see Fig. 3). A more complete picture is obtained by analysing light attenuation coefficient, density and Turner angle profiles (describing the local stability of the water column to double diffusive or convective processes, e.g. Ruddick, 1983), and by estimating the vertical diffusion coefficient, k, through the Thorpe scale, defined as the RMS vertical length scale of observed density overturns (Fig. 7a and b). Through a simple algorithm,

pycnocline reflect the presence of a gradual cross-shelf density gradient, associated with relatively fresher waters close to the coasts, which might originally come from nearby Lao and Noce rivers or other diffuse terrestrial discharges. Analysis of river plumes in MODIS ocean colour images for the period of the survey (not shown) and relatively high surface salinity values (> 37.7) found in all casts, however, indicate that riverine waters have no direct impact on the Vuddù spring area and observed minimum salinity layer (which has no surface signature) must originate from the active submarine groundwater springs P1-P2. Indeed, the low salinity anomaly in B-type profiles appears perfectly aligned with that found in A-type profiles in θ/S space (Fig. 6). This is a clear indication that these waters come from a common source (identified as an edge in θ-S diagrams) that has been gradually mixed with 26

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decrease in density when reaching the pycnocline (Fig. 7a). An optimization study was conducted for both P1 and P2 in order to find the source parameters (Q0M , M0M , S0M , T0M ) that allow Eq. (1) to reproduce as accurately as possible the measured plume neutral height, salinity and temperature at the neutral level, and at the largest depth for which the CTD sensor was still in the plume (Fig. 7c). Details of the analyses are given in Appendix A and B. Results showed that observed values could be reproduced by the model only by making two additional hypotheses. On one hand, given the topography of the pockmark, the lateral convective recirculation generated by the plume (Moore, 2010) could induce a potential active role of suction of shallower waters from outside the pockmark (Fig. 7c) and, in turn, enhance mixing within the pockmark. This would favour the homogenization of salinity and temperature conditions already suggested by the θ/S analysis in Section 4.3, therefore largely reducing the stratification. On the other hand, porewater/seawater mixing zones might be present in the bedrock (i.e. regions in which freshwater is premixed with seawater, see also Moore, 2010), with the result that water rising from the plume source may be saltier and warmer than that of the aquifer. Note however that the improvement of our numerical results was mainly due to considering homogeneous background temperature and salinity inside the pockmarks. Conversely, porewater/seawater mixing was crucial to recover observed range of volume fluxes. The observed properties of the plume were best recovered when considering the ideal source temperature, T0M , equal to the homogeneous value found inside the pockmark (i.e. 20.4 °C for P1 and 17.6 °C for P2) and an ideal momentum flux ,M0M , of about 25 m4/s for P2 and 0.1 m4/s for P1. However, due to the nonlinearities present in the system (whether due to stratification or to the dynamics of the plume), various combinations of source volume and salinity (Q0M , S0M ) were possible (see Appendix A for details). Using the ideal volume flux, Q0M , closest to the expected source volume flux of about Q0 = 1.1–1.5 m3s−1 (see Section 2), we obtained that the pre-mixed water would correspond to a source salinity of about S0M = 35.5–36 for P1 and S0M = 15–20 for P2(Fig. 8(b–c). Injecting these aforementioned values of source conditions in Eqs. 2a and 2b, we could characterize the two pockmarks P1 and P2. The plume in P2 is associated with a small value of Γ0 (less than 0.1), and large values of Δ0 and Δmax (larger than 10) (Fig. 8(c–d). While it was expected for Δmax to be large, as the pycnocline exhibits a strong stratification, it is interesting to see that even Δ0 is large, therefore characterizing the ambient stratification as a strong damping for the plume. Hence, results suggest that the plume in P2 can be defined as forced but strongly damped by the stratified environment. On the contrary, the plume in P1 was found to be lazy (Γ0 > > 1), but it could easily evolve across the water column (Δ0 and Δmax«1). Note that values of Γ0, Δ0 and Δmax were of the same order of magnitude regardless the value of Q0M and S0M (Fig. 8(c-d), hence suggesting that this result is robust despite the substantial range of uncertainty introduced at various steps of the computation. However, only additional in-situ measurements could allow to describe in more details the plume's characteristics. As stated in the introduction, currents can greatly alter the dynamics of SGDs. Given the range of volume and momentum flux studied here, one can derive the corresponding radius and water velocity at the source. With typical surface currents rarely exceeding a few cm/s (Rinaldi et al., 2010) and an estimated source velocity always larger than few m/s (see Appendix A), even if plume velocities will decrease to zero at the neutral zone, a weak influence of currents on the dynamics of the plume, especially for P2, is expected in the context studied here. Finally, note that regular small-scale anomalies of both temperature and salinity observed in P1 and P2 profile (both inside the core of the plume and close to the bottom) could not be reproduced by the turbulent model, suggesting that these anomalies emerge from physical processes not taken into account by the model itself, possibly related to interleaving.

overturns (i.e. positions where dense water is found above light water) are identified, and Thorpe-Scale is estimated by comparing the original depth of the dense water parcel with its position along the virtual profile obtained by sorting the density values to reach statical stability. The diffusion coefficient is then estimated as in Iudicone et al. (2003). At P2 station (Fig. 7), Turner angle values reflect a markedly statically unstable density stratification, related to a number of convective overturning at various depths. Indeed, potential density profile displays numerous inversions all the way up to the base of the surface mixed layer, never exceeding 27.2 kg/m3. These observations thus describe a well-developed plume of freshwater coming up from a deep source of groundwater, driving intense mixing with background resident waters (with a vertical diffusion coefficient k > 0.03). The slightly higher salinity found at the bottom of this profile points to a small mismatch between the effective position of the spring mouth within the pockmark and the CTD profile location (as suggested also by the SideScanSonar data, Fig. 2b). High light attenuation values mainly in this lower part of the profile suggest a strong transport of sediments from the edges of the pockmark to the spring mouth. A similar situation is observed at station P1, though only few density inversions are present in that case, with density values never exceeding 1026.5 kg/m3 and with the minimum of the light attenuation recorded between 20 m and 30 m, not at the bottom. Conversely, the salinity minimum found at the bottom of P5 (Fig. 3) is associated with low temperatures that lead to a quite stable density profile (though clearly favourable to salt-fingering), possibly due to a very weak local freshwater source (Fig. 7a). A schematic description of the regime observed during ARCOSE survey can thus be proposed (Fig. 7c). Two main fresh plumes were sampled by P1 and P2 profiles, though not perfectly aligned with the spring mouth. The freshwater is mixed with the saltier and warmer resident waters, characterized by the values observed at the pockmark's edge, until it gets to a neutral buoyancy level, in this case identified just below the upper mixed layer base (about 15 m deep). Once at this level, this cold and fresh water spreads horizontally, finding favourable conditions for further vertical and/or horizontal mixing. In particular, in absence of other stronger mixing mechanisms (e.g. turbulence driven by air-sea interactions), the presence of a cold and fresh water mass on top of a warmer and saltier water mass can favour double diffusive mixing due to the more efficient and rapid diffusion of heat with respect to salt, as clearly indicated also by the values of the Turner angle at the base and top of this cold intrusion. 4.4. Plume analytical modelling We investigate here the dynamics of the turbulent buoyant plume observed in P1 and P2 using the model of Eq. (1). As described in section 2.3, the plume regimes are characterized by numbers Γ0 , Δ0 and Δm (from Eqs. 2a and 2b respectively) which are defined by the source parameters (Q0 , M0 , S0 , T0 ). The depth corresponding to the maximum ambient stratification is here 23.5 m. The ambient fluid stratification close to the turbulent plume was not measured in the immediate vicinity of the SGD. However, as discussed in Section 4.3, the CTD data measured offshore Punta Infreschi (Figs. 6,7,8a) provide a background stratification reasonably close to that expected in the immediate vicinity of P1 and P2, hence they will be used for simulating the turbulent plumes. Note that a weighted-average filter has been applied to the reference CTD profile in order to avoid numerical instabilities due to noise in the experimental measurements (Fig. 8a) The presence of a non-linear ambient fluid stratification precludes the use of classic theory on turbulent buoyant plumes in a linearly stratified environment states. Indeed, such theory predicts that the ratio between height of rise and neutral level is hR / hN = 1.28 (Turner, 1979; Moore, 2010). Here, the observed ratio is hR / hN = 1.05, reflecting the known (Walsh and Ruddick, 2000) large influence of the sudden 27

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Fig. 8. Results obtained computing Eq. (1). (a) In dotted line: measured in-situ profiles of ambient temperature Ta, salinity Sa and stratification Na. In solid line: filtered version of (a) used in simulations. (b–c) Ideal source volume fluxes Q0I according to ideal source salinity S0I when source momentum flux and source temperature are (b) M0 = 0.1 m4/s and T0 = 20.4 °C for pockmark P1 and (c) M0 = 25 m4/s and T0 = 17.6 °C for pockmark P2. d-e) Plumes’characteristic numbers Γ0, Δ0 and Δmax with respect to Q0I . Pockmark P1 is characterized as lazy (Γ0 > > 1) but easily evolving across the water column (Δ0 and Δmax «1) while pockmark P2 is forced (Γ0 < < 1) but strongly damped by stratification (Δ0 and Δmax > > 1).

associated with focused flow through a fractured carbonate bedrock, while B-type pockmarks may be considered as individual elements medium and diffuse flow through a porous medium (see also Marcon et al., 2014). Specifically, the highest body corresponds to a Late Pleistocene-Holocene infralittoral lithosome that overlapped on the

5. Discussion In general, sediment lifting by ascending buoyant fluids is expected to depend on the freshwater flux regime and on the characteristics of the medium crossed by the fluid. In our case, A-type pockmarks are 28

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horizontal gravity currents which eventually stabilizes far from the turbulent plume at the neutrally buoyant height (Schmidt and Angew, 1941). This condition is compatible with the CTD observations in the areas away from the main pockmarks (see Figs. 3 and 7), where conditions favourable to double diffusive mixing are found. In fact, cold fingers and downward unsalted fingers could potentially contribute to SGD freshwater mixing. Finally, our analysis could not explain the oscillations present in the profiles of salinity and temperature collected at the major pockmark (P2). We speculate that these oscillations can be explained by the presence of lateral interleaving double diffusive fingers. Indeed, it has been demonstrated that double diffusive fingers can co-exist with turbulence as long as effects on mixing of turbulent fluxes do not exceed that of the ratio of temperature to salinity fluxes which governs the fingers (Walsh and Ruddick, 2000). At the edges of the plume, turbulent mixing is attenuated by its interaction with ambient laminar fluid, hence potentially allowing for the formation of cold and fresh fingers.

acoustic substratum originating a continuous porous substratum. Atype pockmarks have migrated upwards, in step with aggradation of sedimentary units. A sequence of stacked buried pockmarks, with comparable dimension and deepness, is in fact observed above the main bedrock fractures (Fig. 2a) in the sedimentary coastal wedge. This feature configuration provides evidence for the longevity of fluid migration. When freshwater streams through the bedrock and sediments, and finally outflows in the denser seawater, difference in density between the two fluids creates an ascending flux which, combined with the initial momentum flux, leads to the formation of a turbulent plume. As the fluid moves upward, the buoyancy flux turns into momentum flux. At the edges of the plume, turbulence generates lateral mass exchange with the ambient fluid, therefore creating a horizontal velocity which entrains fluid and increases the width of the plume. Here we showed that the presence of an uneven topography (as in the case of the largest pockmarks in our study area, Fig. 3) can be expected to induce a larger scale recirculation (see schematics in Fig. 7), and related small-scale turbulence can thus homogenize the environmental conditions within the pockmark. Such interaction between the plume and sediments could indeed explain the mechanism by which the pockmarks are formed and maintained: at the source, turbulence entrains sediments from the bottom, leaving behind a void which is filled by the neighbouring sediments, thus gradually creating the pit, until an equilibrium slope is reached (over geological times). This scenario is suggested by a number of factors:

6. Conclusions Laboratory experiments carried out in the past mainly looked at the interaction of fluid flow regimes and pockmark growth and dimensions, since the understanding of such relation is crucial to quantify seabed discharges from the subsurface. However, the processes by which pockmark are maintained in the presence of fluid seepages have not yet been investigated and this work represents a first attempt to relate geological and hydrographic observations through analytical modelling of plume dynamics. In this specific case, the pockmark field is located in an area characterized by low currents in the surface layers. It is fed by a perennial, but seasonal varying, freshwater spring (even if a certain degree of salt water intrusion and mixing might not be ruled out according to Müller et al., 2011), whose flow depends on the hydraulic head gradient between the aquifer and the top of permeable rocks at sea. Our observations thus provide a first description of the complexity of mixing processes driven by SGD plumes in shelf areas during the stratified season, and represent an initial step toward more extensive investigations including the bio-chemical characterization of the SGD sources in the Southern Tyrrhenian Sea and their effect on pockmark morphology and potential impact on local ecosystem. In particular, on one hand, a full understanding and description of the interaction between turbulent buoyant plumes and bottom morphology would require going beyond standard analytical plume models, e.g. by including the effects of both 2D/3D complex topography, and sediment transport. On the other hand, different scenarios and dynamical regimes can then be expected in other seasons, and in particular when the background water column stratification is eroded by surface cooling and mixing driven by air-sea interactions, thus requiring specific investigations at sea and targeted analytical modelling.

1) Beam attenuation profiles reflect enhanced sediment concentration close to the turbulent plume (Section 4.2). Hence, fine-grained sediments are likely re-suspended by the secondary circulation, transported toward the plume and successively redistributed by the turbulent plume. 2) Only by assuming an active role of suction of shallower waters from outside the pockmark, leading to well-mixed θ/S conditions inside the pockmark (but outside the core of the plume) was it possible to get close to the conditions observed within the plumes in our analytical plume model (Section 4.3), specifically reducing the difference between both observed and modelled θ/S values and plume height. More specifically, the plume in P1 has been characterized as lazy but traveling easily along the water column, while the plume in P2 was found to be forced but strongly damped. Note that parameters characterizing the source forcing and environmental stability were in both cases of the same order of magnitude regardless the value of the volume flux and salinity at the source chosen (Fig. 8.c-d), hence suggesting that these results are robust despite the substantial range of uncertainty introduced at various steps of the computation. Going up along the water column, the buoyancy flux associated with the plume is then zeroed at the neutral buoyant level, and remaining momentum flux carries the plume higher to the rising level where velocity falls to zero. At the rising level, the fluid inside the plume is now denser than its environment and therefore falls. Horizontal density gradients then initialize lateral movements, inducing an intruding

Acknowledgements R.W. thanks Henry Burridge for insightful discussion on theory of turbulent plumes.

Appendix A We describe here the optimization analysis conducted to set the source parameters that allow Eq. (1) to best reproduce observed properties of the turbulent plumes in pockmarks P1 and P2. Distance between numerical and in-situ observations (model misfit) was measured as a standardized Euclidean distance N

D=

∑ i=1

PiM

(PiM − PiO )2 σ P2O

(3)

i

PiO

where and are values from the model and observations, respectively, and quantifies the variation of the observed values at neutral level and is usually considered as the variance. We consider N=5 parameters, namely, the plume neutral height, and temperature and salinity at both

σ PO i

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Fig. 9. Standard plume model results for P2 as a function of the source volume flux Q0, taking S0 = 0 and T0 = 16 °C and different M0 fluxes: (a) model misfit estimated through the Euclidean distance defined by Eq. (2), (b) neutral height, (c) salinity at neutral height, (d) temperature at neutral height, (e) salinity at 40 m and (f) temperature at 40 m. Solid black lines represents values observed in P2 pockmark. None of the conditions explored here could reproduce the observed conditions, essentially due to a bad capture of temperature at neutral height and 40 m. Properties in the legend are combined in the plots. Namely, a curve display different marker sizes depending on momentum flux.

neutral level and largest depth for which observations in the plume was accessible (−30 m for P1 and −40 m for P2), i.e. Pi=(hn,Sn,Tn,Sc and Tc). In the following, it is useful to keep in mind that the uncertainties in the observations lead to an Euclidean distance equal to N ≈2.2 (namely, if values from the model are distant σ P O from the observed value). As we could only measure one vertical profile of salinity and temperature along P1 and P2, i here, instead of the variance, we consider σ P O as the uncertainty on the neutral level measurements, that we infer from oscillations of profiles of i measurements. Looking at neighbouring CTD profiles, we observe that the vertical profile of salinity (e.g. at P5) exhibits a sudden decrease of salinity 30

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Fig. 10. Modified plume model results for P2 as a function of the source volume flux Q0, considering different S0 and T0 pairs and M0 fluxes: (a) model misfit estimated through the Euclidean distance defined by Eq. (2), (b) neutral height, (c) salinity at neutral height, (d) temperature at neutral height, (e) salinity at 40 m and (f) temperature at 40 m. Solid black lines represents values observed in P2 pockmark. Properties in the legend are assembled in the plots. When considering the case of homogeneous pockmark with porewater/seawater premixing, the existence of multiple minimum Euclidean distances shows that various set of conditions (S0, Q0, M0) can reproduce the observed data in P2. Properties in the legend are combined in the plots. Namely, a curve will be dark or light (temperature), coloured (salinity), with different marker sizes (momentum flux).

at depth of 17 m (Fig. 3). This corresponds to the entrance of the sensor in the layer originating from the turbulent plume of P2, that has spread laterally once reaching the neutral level. From this depth, and assuming that the level of maximum rise is the same in P5 and P2, one can derive the height of the plume in P2, hR = 43 m (with a bottom depth of 60 m; see Figs. 3, 5a, 6). Instead, the neutral level corresponds to that of maximum input of freshwater in the intrusion layer i.e. the depth of minimum salinity, which is here 19 m, therefore giving hN = 41 m (Fig. 3). Looking at the 31

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Fig. 11. Ideal source's radius and velocity inferred from ideal volume and momentum fluxes for (a) P2 and (b) P1. For P2, the large source velocity (at least 7 m/s) shows that the plume is not influenced by surface currents (of few cm/s). On the contrary, the small source velocity for P1 suggests that an interaction between the plume and currents occur.

salinity profiles one can fix σ SO = σ S O = 0.1 and an uncertainty of about a meter for hN , i.e. σ h O = 1 m, being comprised between 41 m and 42 m. N 40 N Variations of temperature in this range of neutral heights correspond to σ T O = 0.1 °C. At 40 m depth, the temperature variability is quite low and we N take σ T O = 0.05 °C. For consistency, we take the same uncertainties for P1. 40 We now focus on the case P2. Hence, from now on everything described below is related to pockmark P2 unless stated otherwise. The freshwater emerging at the Ruotolo spring was measured with zero salinity and a temperature of approximately 16 °C. Thus, we conducted a set of simulations by computing Eqs. (1) and (3) using S0 = 0,T0 = 16°C, and varying volume and momentum fluxes in the range πQ0 = [0.01 − 5] m3/s and πM0 = [0.01 − 30] m4/s2 (the source radius b0 and velocity w0 are then determined by Q0 and M0 ). Results show that none of the configurations of volume and momentum fluxes could reproduce the observed values, with model misfits always larger than D = 17 (Fig. 9a). It can be noticed that the lowest distance is found for values of the volume flux Q0 below 1 m3s−1. However, several relative minima are also present, highlighting the fact that various source settings (Q0, M0) can lead to similar final conditions. This is explained by the balance between forces in play inside the plume and how this balance emerges from various conditions, as detailed in Appendix B. Overall, the inability of the model to reproduce accurately the observed values (Fig. 9c–f) comes from the impossibility for any pair (Q0, M0) to recover the relatively high and homogeneous temperature values observed at depth (Fig. 9f), as the modelled temperature at 40 m is 1.5 °C below the in-situ measure (Fig. 9f). As described in the main text in Section 4.3, two processes could explain this discrepancy: (1) lateral convective recirculation forces mixing and hence makes temperature and salinity homogeneous along depth in the interior of the pockmark, and (2) porewater/ seawater pre-mixing in the bedrock with the consequence that temperature and salinity at the source of the plume are not that of the freshwater of the aquifer. We tested these two hypotheses by adjusting the boundary conditions in our simulations. The first hypothesis, i.e. the effect of potential homogenization from lateral suction in the pockmark, was tested by using the same source conditions S0 = 0 and T0 = 16°C but keeping constant the ambient salinity and temperature within the pockmark using the conditions at the top of the pockmark (i.e. Sa= 37.7 and Ta = 17.6°C between depth 60 m and 40 m). Considering these homogenized values significantly reduced the Euclidean distance (with a minimum of about D = 4.25), with minimum model misfit found at volume fluxes of approximately Q0 = 0.7–0.8 m3s−1 (Fig. 8a). Indeed, by removing the ambient stratification inside the pockmark, the plume can travel more easily to higher levels, and to recover the correct neutral level one needs to decrease the volume flux hence increasing the lateral turbulent mixing and decreasing the neutral height (see Appendix A). Note, however, that in this case the minimum Euclidean distances were reached for values of momentum flux in a range where the effects of buoyancy, lateral mixing and kinetic energy are substantially balanced (Appendix B). The effect of potential porewater/seawater mixing was tested by conducting various simulations of the plume varying both source's salinity and temperature in the range S0 = [0−30] and T0 = [16–17.6]°C. Increasing the source salinity induced a shift of the minimum model misfit toward larger volume fluxes (Fig. 10a). Indeed, as one increases the salinity, the differential with the ambient condition decreases and the buoyancy force with it, therefore decreasing the neutral level. Hence, to compensate for this loss of buoyancy one has to increase the volume flux to decrease turbulent mixing and increase the neutral level (see Appendix B). If one increases S0 keeping T0 = 16 °C, the minimum distance gets larger. However, these results are very sensitive to variations in the source temperature, and increasing source temperature up to that of the pockmark T0 = 17.6 °C largely reduced the model misfit, mainly due to improvement at 40 m (Fig. 10e), and showed almost equal minimum distances, below D = 4, for all S0 values (Fig. 10a). A momentum flux of about M0 = 25 m4/s appeared to be ideal for all cases. Hence, the combination of a homogeneous stratification inside the pockmark and porewater/seawater pre-mixing allows for Eq. (1) to reasonably recover values of observations for P2 with source temperature of T0 = 17.6 and momentum flux of M0 = 25 m4/s but with several equivalent scenarios of volume flux and salinity (Q0,S0). Fig. 11a shows the ideal volume fluxes and salinities, Q0 and S0 for all minima of the Euclidean distance. Note however that the expected volume flux of the source of about 1 m3/s lies within the range of acceptable values. Using these values, one can get Γ0, Δ0 and Δmax, and characterize the plume for all possible ideal source conditions. Results show that all ideal source conditions give a plume with small Γ0 (less than 0.01), and large Δ0 and Δmax (larger than 10) (Fig. 8.b). While it was expected for Δmax to be large, as the pycnocline exhibits a strong stratification, it is interesting to see that even Δ0 is large, therefore characterizing the ambient stratification as strongly stable overall. Hence the plume can be characterized as lazy and

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Fig. 12. Standard plume model results for P1 as a function of the source volume flux Q0, taking S0 = 0 and T0 = 16 °C and different M0 fluxes: (a) model misfit estimated through the Euclidean distance defined by Eq. (2), (b) neutral height, (c) salinity at neutral height, (d) temperature at neutral height, (e) salinity at 30 m and (f) temperature at 30 m. Solid black lines represents values observed in P1 pockmark. None of the conditions explored here could reproduce the observed conditions, essentially due to a bad capture of temperature at neutral height and 30 m. Namely, a curve will display different marker sizes depending on momentum flux.

evolving in a highly stable stratified environment. Finally, Fig. 11.b shows the various source radius and flow velocity corresponding to the possible ideal volume fluxes Q0. As can be seen, due to a reasonable radius (about half a meter), the output velocity does not go below 7 m/s. We conducted the same optimization study in the case of pockmark P1. Here too, only by considering a homogeneous pockmark and a source temperature equal to that of the pockmark could we recover observed values (Figs. 12 and 13). 33

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Fig. 13. Modified plume model results for P1 as a function of the source volume flux Q0, considering different S0 and T0 pairs and M0 fluxes: (a) model misfit estimated through the Euclidean distance defined by Eq. (2), (b) neutral height, c) salinity at neutral height, (d) temperature at neutral height, (e) salinity at 30 m and (f) temperature at 30 m. Solid black lines represents values observed in P1 pockmark. Properties in the legend are assembled in the plots. When considering the case of homogeneous pockmark with porewater/seawater premixing, the existence of multiple minimum Euclidean distances shows that various set of conditions (S0, Q0, M0) can reproduce the observed data in P1. Properties in the legend are combined in the plots. Namely, a curve will be dark or light (temperature), coloured (salinity), with different marker sizes (momentum flux).

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Appendix B In the first analytical model of the plume (described in Section 4.3), for a given momentum M0, increasing the volume Q0 results on one hand in an increase of the buoyancy B0 and in a decrease of the entrainment velocity ue = αw0 (i.e. of the turbulent lateral mixing), both contributing to increase the neutral height, but on the other hand in a decrease of the kinetic energy w02 , hence potentially inducing a lower neutral level. The influence of w0 can be seen when looking at the variations of the neutral height when increasing M0 and keeping Q0 (and hence B0) constant (Fig. 10b and Fig. 14). At small Q0, about 0.5 m3s−1, an increase of M0 first induces a decrease of hN highlighting the effect of lateral mixing. Continuing to increase M0, a minimum height appears, highlighting values of momentum flux above which the influence of kinetic energy takes upon that of lateral mixing, where an increase of hN can be seen. The value associated to the minimum neutral height then depends on volume flux. At larger volume fluxes, the minimum is less discernible and there appears an interval of weak sensitivity of the neutral height with respect to momentum flux, which gets larger as Q0 increases (Fig. 8b and Fig. 10a). For values of Q0 associated to the minimum Euclidean distances, the range M0 = [20−30]m4/s3 gave somewhat the same neutral height, making it difficult to choose a momentum flux over another. However, the absolute minimum was located at M0 = 25. Thus, the multiple local minima of Euclidean distances arise from the fact that, when increasing volume flux, the increase of neutral height due to larger buoyancy flux can be compensated by an increase of lateral mixing (from an increase of momentum) which will fasten the decrease of buoyancy by more rapidly entrains fluid from outside the plume and decrease neutral level. Note however that as one increases Q0 the minimum gets larger mainly because of the temperature at 40 m depth (Fig. 9f).

Fig. 14. Neutral height hn as a function a source momentum flux M0. The minimum for each volume flux Q0 is witness of the balance between effects of buoyancy and mixing.

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