Empirical model to estimate permeability of surface sediments in the German Bight (North Sea)

SEARES-01491; No of Pages 10 Journal of Sea Research xxx (2016) xxx–xxx

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Empirical model to estimate permeability of surface sediments in the German Bight (North Sea) Andreas Neumann a,⁎, Jürgen Möbius b, H. Christian Hass c, Walter Puls a, Jana Friedrich a a b c

Helmholtz-Zentrum Geesthacht, Institut für Küstenforschung, Max-Planck-Straße 1, D-21502 Geesthacht, Germany Universität Hamburg, Institut für Geologie, Bundesstraße 55, D-20146 Hamburg, Germany Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung, Wattenmeerstation, Hafenstraße 43, D-25992 List, Germany

a r t i c l e

i n f o

Article history: Received 6 April 2016 Received in revised form 23 November 2016 Accepted 14 December 2016 Available online xxxx Keywords: North Sea Surface sediment Permeability Sediment structure RGPZ model

a b s t r a c t As the determinant of solute and particle fluxes through sediments, quantifying sediment permeability is vital step in understanding of the exchange phenomena between the water column and sediment as permeability determines the mode and intensity of solute and particle fluxes. Reliable estimates of sediment permeability are therefore a constraint on the accurate implementation of benthic biogeochemical models. This is particularly true for the North Sea, as field data are scarce and available grain-size-based models fail to represent the full range of sediment types. In this study, we combine measurements of sediment permeability and grain size analysis with a generic permeability model to establish a high-resolution permeability map of the sediment in the German Bight (North Sea). Our results show a good agreement between model-based prediction and measurements of permeability, even for a wide range of permeability values. © 2016 Published by Elsevier B.V.

1. Introduction Sediment permeability describes the resistance to flow of water through the sediment (Bear, 1972). Permeability is thereby a key characteristic of surface sediment as it governs the exchange of solutes (e.g. Elliott and Brooks, 1997, Precht et al., 2004) and particles (e.g. Huettel et al., 1996, Huettel and Rusch, 2000). Sediment permeability also governs early diagenetic pathways and the spatial distribution of permeability is of great importance when answering many biogeochemical questions. For example, flushing of permeable surface sediment with oxygenated bottom water favors oxygen consuming microbial and chemical reactions such as aerobic decomposition of organic matter, nitrification and sulphide oxidation. By contrast, stagnant pore water in impermeable sediment promotes reducing reactions such as denitrification, sulphate reduction and methanogenesis, as well as anaerobic decomposition pathways. Unfortunately, direct measurements of sediment permeability are still scarce in the southern North Sea. The distribution of pervious and impervious sediment, a constraint for the implementation of biogeochemical models, is not known in detail yet. A sound representation of sediment physical properties in coupled pelagic-benthic biogeochemical models is a prerequisite to translate point benthic flux measurements into spatial/regional flux estimates, for example, in ecosystem service assessment. ⁎ Corresponding author. E-mail address: [email protected] (A. Neumann).

Obtaining direct measurements of sediment permeability at a spatial resolution equivalent to current ecosystem models is usually not feasible, so permeability has to be deduced from other, known parameters. Fortunately, the grain size distribution in the German Bight is already mapped with very high spatial resolution (Figge, 1981) and estimating permeability on measured grain size is a common practice. However, the grain size map (Fig. 1A) reveals that the German Bight sediments comprise a wide variety of sediment types; including cohesive mud with high silt content in deeper areas such as the submerged valley of the Palaeo Elbe (Fig. 1B) as well as coarse sand and gravel along the coast. This variety of sediment types present in the study area implies that existing simple permeability models such as Krumbein and Monk (1943) or Soulsby (1997) are insufficient here as they are only valid for specific sediment types. More complex permeability models such as the Carman-Kozeny model (CK, Glover et al., 2006), the JKS-model (Johnson et al., 1986; Glover and Walker, 2009), or the RGPZ-model (Glover et al., 2006) use specific sediment parameters (e.g. pore dimension, connectedness or topology), which are not available for all sediment types. Moreover, the Cozeny-Karman model was recently discredited by e.g. Walker and Glover (2010) as it takes not account for the porosity component that is not contributing to the flow. But although the complex permeability models (CK, JKS, RGPZ) are not applicable in this study due to a lack of data for the specific sediment parameters, they may help to explain why the simple models fail to predict the permeability for a wide range of sediment types. Permeability of a sediment or rock (K) is generally controlled by the characteristics of the pore space network such as pore dimensions, topology, or

http://dx.doi.org/10.1016/j.seares.2016.12.002 1385-1101/© 2016 Published by Elsevier B.V.

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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A. Neumann et al. / Journal of Sea Research xxx (2016) xxx–xxx

Notation a sediment packing constant, unitless effective grain diameter, m deff D15, D50 grain size of the 15th/50th percentile, m EEZ Exclusive Economic Zone F formation resistivity factor, unitless G geometric mean grain size, m K permeability, m2 m cementation exponent, unitless reff effective pore radius, m ϕ porosity, unitless s(deff) empirical structure function, represents am2F3, unitless

connectedness (Eq. (1)) as shown by Schwartz et al. (1989), Avellaneda and Torquato (1991), Kostek et al. (1992), Bernabé and Revil (1995), and Glover et al. (2006). K¼

r 2eff 8F

¼

r 2eff χφ 8

ð1Þ

The effective pore radius (reff) cannot be regarded as an actual geometric measure but as a characteristic length scale. The formation resistivity factor (F) represents the effective electric resistivity and combines information about porosity (ϕ), connectedness (χ) and electric tortuosity (τ) via F = ϕ−m = τ ϕ−1 = (χ ϕ)−1 (Glover and Walker, 2009). The exponent m is often called the cementation exponent for historical reasons and describes the sensitivity of connectedness to variations of porosity (Glover, 2009). The characterisation of the pore network, from

Fig. 1. A: Spatial distribution of sediment samples and D15 grain size values used for calculation of permeability map. Each dot represents an individual sediment sample. The solid, black, polygonal outline indicates the German Exclusive Economic Zone. B: Schematic map of bathymetric structures. Features in shallow water such as Dogger Bank, Borkum Reef, and Sylt Outer Reef consist of coarser sediment (blue and green hue in panel A; features in greater water depth such as Oyster Ground, Helgoland Mud Area (HMA) or the Paleo Elbe consist of finer sediment (yellow and orange hue in A). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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which the permeability is derived, can also be obtained through a thorough characterisation of the sediment particles and how they pack together. This is expressed by Glover and Walker (2009) as the Theta transformation to describe the relationship between effective grain diameter (deff) and the effective pore radius (reff) (Eq. (2))

deff

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi am2 F 2 r eff ¼2 8

ð2Þ

The packing constant (a) describes the topology of the pore space and is discussed in detail by Walker and Glover (2010). The sediment permeability is then estimated with the RGPZ-model of Glover et al. (2006) as KRGPZ with Eq. (3) K RGPZ ¼

1 4am2 F 3

2

deff

ð3Þ

This model separates the effects of sediment structure (expressed by the variables a, m, and F) on permeability from the effects of the characteristic grain size (deff). Many existing empirical relationships between permeability and grain size replace these structural variables (a, m, F) with an empirically defined coefficient that represents only those sediments for which it was created (e.g. Krumbein and Monk, 1943, Soulsby, 1997). The shortcoming of such simple models (Krumbein-Monk, Eq. (4), or Soulsby, Eq. (5)) can be demonstrated by assuming a well sorted medium sand, which can be approximated by an unconsolidated pack of spheres with equal diameter with porosity of 0.4, a cementation exponent m of 1.5, and a packing constant a of 8/3 (Glover and Walker, 2009). For this special case the RGPZ model can be written as 2

K RGPZ ≈ 0:00067deff

ð4Þ

3

which essentially employs different sets of structure variables (a, m, F). By contrast with the simple Krumbein-Monk and Soulsby models, permeability is estimated by the popular Karman-Cozeny equation on the basis of specific surface area and porosity (Revil and Cathles, 1999; Glover et al., 2006). However, to calculate the specific surface area using grain sizes requires knowledge of the actual shape of the grains. For the North Sea, typical grain shapes are not available. Therefore, to apply the Karman-Cozeny equation, we would have to assume a certain shape (e.g. sphere, ellipsoid) to convert grain size to specific surface area, which would only be valid for a certain sediment type. As a result, these models are only able to predict permeability of sandy sediment if grain size is the only available measurement and all other parameters have to be assumed (Revil and Cathles, 1999; Forster et al., 2003, this study). In summary, we cannot apply any of the established permeability models to the German Bight sediment: Simple models such as Krumbein-Monk or Soulsby are valid only for certain sediments while the German Bight comprises diverse sediment types; and there is insufficient information about the sediment structure (parameters a, m, F) to apply detailed models such as KC, JKS or RGPZ. 1.1. Scope of the present study In an attempt to overcome the lack of sediment structure data in the German Bight, we assume that the different types of surface sediment in the southern North Sea may be regarded as a continuum, and that it is possible to empirically establish the function s(deff) to estimate the sediment structure from grain size analyses alone. The function s(deff) can then be fitted with empirical data on grain size and permeability (Eq. (7)). 2

This is very similar to the empirically derived models of Krumbein and Monk (1943) and Soulsby (1997). The effective grain size is assumed to be represented by the geometric mean grain size G (in m) in the former (Eq. (5)), and the 15th percentile grain size D15 (in m) in the latter (Eq. (6)). K Krumbein−Monk ¼ 0:00076eð−1:31σ Þ G2

ð5Þ

K Soulsby ¼ 0:0011D215

ð6Þ

These models are essentially meant for sand, for which they provide good estimates. However, they fail to correctly predict the permeability for fine-grained, muddy sediment, and this effect is very pronounced if the grain size is determined by sieving (Fig. 2). Both models may be adopted for other sediment types by applying different constants,

deff   s deff ¼ am2 F 3 ¼ 4K

ð7Þ

As the product am2F3 comprises all variables that describe the fine structure of the sediment, we will refer to this product as the structure term. This structure term enables to derive an empirical permeability model that covers all sediment types in the form K≈

1   d2 4s deff eff

ð8Þ

With the present study we test our assumption that (a) the different sediment types in the southern North Sea may be regarded as a continuum, and (b) that it is possible to empirically establish the structure function s(deff) for each sediment type to estimate the permeability from grain size analyses alone. We further assume that the

Fig. 2. Crossplots of calculated permeability using the Soulsby equation (Eq. (7)) and D15 grain sizes from laser diffraction measurement (A) and sieving (B) vs. measured permeability.

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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A. Neumann et al. / Journal of Sea Research xxx (2016) xxx–xxx

unconsolidated North Sea surface sediments can be described with the RGPZ model. In the following we present our method to establish the function s(deff) and its application in Eq.s (8) to 25,421 sediment samples collected in the German Bight. The resulting high-resolution map of the distribution of permeability will help to identify typical sedimentological regions and improve our understanding of the distribution of distinct benthic communities. The permeability map may therefore support the setting of suitable targets for environmental monitoring. Moreover, the permeability model can provide realistic permeability values to existing North Sea benthic- pelagic models such as ECOHAM (IfM, University of Hamburg). 2. Material and methods 2.1. Sampling The surface sediment of the southern North Sea was sampled during the RV Heincke cruises 394, 411, 412, 432, 433, and 447 between 2013 and 2015. The majority of samples were retrieved by a Van-Veen type HELCOM grab, and a few samples were retrieved by means of a Multicorer, Box corer, and Shipek grab. Once on-board, sediment cores with lengths of 4 to 6 cm and a diameter of 3.3 cm were immediately taken with acrylic liners from the coring devices. These sediment cores were visually inspected and cores with holes, bubbles, burrows and other perturbations were discarded. Sediment cores were also discarded when all overlying water percolated through the sediment, because re-wetting of such cores might entrap bubbles and thereby alter the permeability. 2.2. Permeability measurement Permeability measurements were calibrated using randomly packed glass beads with high sphericity and known permeability as described in Glover and Walker (2009). The glass beads had median diameters of 25 / 150 / 500 / 850 / 3100 μm. The hydraulic conductivity (in m s−1) of sediment cores was measured within a few hours after sampling by falling head permeametry (Head, 1982). The measurement was repeated three times for each core, and the results were averaged. The intrinsic permeability (in m2) was calculated from the hydraulic conductivity and values of bottom water density and viscosity estimated according to Millero and Poisson (1981) and Millero (1974), respectively.

We therefore decided to include the Heincke 411 results in our analysis to broaden our data basis. The cumulative distribution curves of weight or volume per grain size class of all three sample sets were then used to fit a sigmoid function originally proposed by Tauber (1995) and modified by Bobertz (2000) and Forster et al. (2003) in order to calculate the grain size of the 15th and 50th percentile (D15 and D50). 2.4. Data analysis The regression equations of the empirical structure term were fitted with a numerical approach to minimize the median of squared relative errors (SRE) since (a) this method is robust with respect to outliers (Rousseeuw, 1984), (b) the relation of characteristic grain size and permeability is non-linear, and (c) we assume that the measurement error is dependent on the magnitude of the measured value. The squared relative error was calculated with Eq. (9) as  SRE ¼

ypred −yobs

2

ðyobs Þ2

ð9Þ

2.5. Grain size map We collected the grain size data with full grain size distributions of 25,421 surficial sediment samples in the German Bight (maximum sub-bottom depth: 20 cm). The data sources were the Geological Survey of the Netherlands (TNO), the German Maritime and Hydrographic Agency (BSH) and the German research project “Geopotenzial Deutsche Nordsee”. Grain sizes were obtained by means of dry sieving (Laurer et al., 2014). Again, we used the Tauber-Bobertz fit function to calculate D15 and D50 for each individual sample. Through the interpolation of the resulting values of D15 and D50 full-coverage maps of the entire German Bight were generated. These grain size maps provided the basis to map the distribution of permeability in the German Bight. The collection and treatment of grain size data is described in-depth in Puls et al. (manuscript in preparation). Measured and calculated permeability were mapped with Ocean Data View software (Schlitzer, 2011), gridding and interpolation was performed with the DIVA gridding method (Troupin et al., 2012). 3. Results and discussion

2.3. Grain size analysis 3.1. Grain size analysis by sieving or laser diffraction? One set of 104 sediment samples (Heincke 394, 433, 447) was freeze-dried and passed through a series of sieves (Retsch) with 20 / 63 / 125 / 500 / 1000 / 2000 μm openings. A second set of 51 samples (Heincke 412, 432, 447) was stored at 4 °C and analysed without further preparation by laser diffraction using a CILAS 1180 L laser particle sizer (range: 0.04–2500 μm). Particles larger than 2 mm were removed before the measurement. All CILAS results refer to volume percentages. A third set of 41 samples (Heincke 411) was chemically treated to remove carbonates and organics prior to the grain size analysis, because the analyses were primarily meant for a different study. The samples were stored at 4 °C and samples were treated with acetic acid (c. 25%) and hydrogen peroxide (c. 8%) to remove organic materials and carbonates prior to grain size analysis. Both chemicals were allowed to react over night and washed twice with water after each treatment. This treatment might have led to biased results in grain size analysis in the case that the sediment substantially consists of carbonate (e.g. bivalve shells) and/or organic particles (e.g. peat). However, virtually all Heincke 411 samples were sand with very low carbonate and organics content. As a result, the grain sizes and permeability of these Heincke 411 samples are not distinguishable from the untreated sediment (Heincke 394, 412, 432, 447) and did not add uncertainty to the results.

Employing the grain size as the characteristic length scale calls for the selection of an appropriate grain sizing method. In the past, sieving was the method of choice, whereas today, a tendency to apply the laser diffraction method can be observed. However, it is known that the results of sieving and the laser diffraction method are not equivalent as discussed e.g. in Konert and Vandenberghe (1997), Eshel et al. (2004), and Blott and Pye (2006). The differences between the two methods start with the sample preparation, where samples for the sieving method are freeze-dried while samples for the laser diffraction are diluted in water. Hence, the sediment properties are affected by the type of treatment. We observe that fines tend to form larger aggregates in freezedried samples, which cannot always be fragmented completely during sieving. Additionally, a few large grains in the sample from coarser size classes (e.g. pebbles, shells) may be enough to shift the calculated D15 / D50 value toward higher grain size, even if their impact on bulk sediment permeability might be negligible. Since the sieving method uses the weight of each size class, D15 / D50 estimates from sieving might overestimate the actual grain size as a result. On the other Hand, laser diffraction is also not free of artefacts. This method measures the volume-dependent diffraction of the particles.

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

A. Neumann et al. / Journal of Sea Research xxx (2016) xxx–xxx

The laser particle sizer used to measure particle size has an upper threshold diameter of 2 mm, and larger particles had to be excluded. Additionally, Kaye et al. (1997) discuss that sharp edges, as they may occur on angular silt and sand grains (Fig. 3), cause high angle diffractions, which is then interpreted as small objects. Hence, the exclusion of large grains and artificial counts in the fines range may bias the calculated D15 / D50 toward smaller grain sizes. Additionally, the results of the laser diffraction method are apparently shape-dependent, which means that grains of similar volume but different shape are measured differently (e.g. Gabas et al., 1994). Since the results of both routine methods are potentially biased, we do not exclusively recommend one method and reject the other. For our purpose, we apply both methods in parallel, for two reasons: Firstly, we report our results of the sieving method because grain size analyses of North Sea sediment using this technique are already available with high spatial resolution (see methods section, Fig. 1A), which is not the case for grain size analyses using laser diffraction. Secondly, as the laser diffraction method is becoming increasingly popular, we also present our results based on the laser diffraction method for the sake of future application. We will re-address this subject below, following the discussion of our data. 3.2. Sediment description The sampled sediments were mostly composed of well- sorted sands that originate from reworked Pleistocene glacial and alluvial deposits (Houbolt, 1976). Spatial patterns in grain size distribution show that

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grains become finer with bottom depth (Fig. 1A), reflecting gradients of wave energy and bottom shear stress as a function of water depth. Sediment in shallow water (b 30 m) cover the remnants of glacial moraines present as shoals, e.g. Borkum Reefground, Horns Reef, Sylt Outer Reef, Dogger Bank (see Fig. 1B), and contains coarser fractions from medium sand up to pebbles and boulders. By contrast, sediment in deeper water (30 to 50 m) consists of finer particles in the silt to fine-sand range. Significant exceptions form this general pattern are (a) sedimentary rocks of the Mesozoic basement around Helgoland, and (b) muddy sediment with high porosity present in the Helgoland Mud Area (HMA). Sandy sediments are almost exclusively composed of quartz, with only minor ferrous oxide and feldspar constituents. Coarser fractions still contain fragments of glacial rubble from Scandinavia such as granite, gneiss and flint stone. Only a few shallow stations reveal elevated amounts of shell fragments in combination with coarse sand and gravel. An example is station He-447/82 at Borkum Reefground where one third of the sediment consisted of bivalve shell debris, in a matrix of coarse sand. Overall, the total carbon content rarely exceeds 0.3%, and organic carbon is mostly below 0.15%. Individual samples may have higher concentrations with the highest values found in the HMA sediment with up to 2.1% total carbon and 0.8% organic carbon (Wiesner et al., 1990). Recent surveys from Boeckel (2016) and Ahmerkamp et al. (2016) report values for the organic carbon content in the range of 0.03 to 0.78%. Intense bioturbation by worms, echinoderms or molluscs is evident at all stations. Since sediment structure and thus permeability is dependent on grain shape, we examined the grain shape visually by comparison with a classification chart (Powers, 1953). We conclude that grains in the fine-sand range are rounded (Fig. 3A). Grains larger than fine sand are more irregular and sub-rounded to rounded, and grains in the silt range are sub-angular to angular (Fig. 3B). The measured sediment permeability ranged from 10−15 to −10 10 m2, corresponding on the low end to impervious mud with high porosity (ϕ max = 0.87), and on the high end to pervious medium sand (K N 10−11 m2) with low porosity (ϕ min = 0.35). The accepted threshold between pervious and impervious sediment is 10− 12 m2 (e.g. Huettel et al., 1996, Precht et al., 2004). Effective grain sizes of the corresponding sediment were D15 = 4 to 350 μm and for D50 = 50 to 500 μm (Fig. 4). The measured permeability values are available in the Pangaea database (Neumann, 2015a, 2015b, 2015c). 3.3. Permeability as a function of grain size, shape, and packing

Fig. 3. Microphotographs of A) fine and medium sand from station HE-394/22, and B) silty fine sand from station HE-432/31, German Bight (North Sea).

Using the measurements on grain size and permeability, we further established empirical values of the sediment structure term am2F3 with Eq. (7) for both grain sizing methods and two grain size percentiles. Fig. 5 displays values of the sediment structure term plotted against effective grain size (D15, D50) to establish the empirical function s(deff) for different granulometric methods (Table 1) and for a wide range of grain sizes. Our results indicate that the sediment structure term am2F3 generally decreases with increasing grain size, reaching an approximately constant value at high grain sizes with D15 N 200 μm and D50 N 300 μm, respectively. This constant is in the range of an unconsolidated sediment composed of equally sized spheres for which a = 8/3, m = 1.5, and F = 4 (Glover and Walker, 2009). Therefore we conclude that well-sorted sand with a D15 N 200 μm or a D50 N 300 μm can be considered as loosely packed spheres. This assumption does not however hold for finer particles and implies that the lower permeability of finer sediment cannot only be accounted for by the reduction of grain size. Our results confirm findings by Revil and Cathles (1999) and Forster et al. (2003) that this non-linear effect explains why simple models with a constant structure term fail to predict the permeability of fine-grained sediments. An additional factor, along with change in grain size is the difference in grain shape. Sand grains in the fine and medium sand

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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Fig. 4. Measured permeability plotted against effective grain sizes D15 and D50 as established by laser diffraction method (A & B, n = 92), and sieving of freeze-dried samples (C & D, n = 104), respectively. Full circles represent untreated sediment, open circles represent chemically treated sediment (see methods for details).

range are subrounded to rounded, whereas silt is more angular (Fig. 3). Angular grains support looser packing with higher porosity and lower permeability (Fraser, 1935; Selley, 2000). One reason for the lower permeability of sediment composed of angular grains is the higher surfaceto-volume ratio of angular grains compared to rounded grains. According to the Karman-Cozeny model, a higher specific surface area results in a lower permeability (Revil and Cathles, 1999; Glover et al., 2006). The observed variability of the structure term is more pronounced in the sieving dataset than in the laser diffraction dataset. Using a constant value for the structure term would result in an up to 100-fold overestimated permeability. This overestimation is illustrated in Fig. 2(B) where we compare permeabilities calculated with D15 grain sizes and the Soulsby model (Eq. (6)). Similarly, Revil and Cathles (1999) and Forster et al. (2003) found that the Karman-Cozeny Equation and Krumbein-Monk Equation, respectively, overestimated permeability by several orders of magnitude for permeability b 10−14 m2. In both studies, permeability estimates are close to measured values in sediments with permeability N 10−12 m2, for which the implicitly assumed spherical sediment structure is realistic. In contrast to sieving results, permeability estimates based on D15 from laser diffraction analysis (Fig. 5A) agree far better with measurements. The difference becomes evident when comparing the trends of the structure term for both methods. The slope of the structure term is steep for the sieving method (Fig. 5C), while the structure term for the laser diffraction method may be approximated by a constant value of 103 (Fig. 5A), although some values are one order of magnitude higher and over two orders of magnitude lower than this, especially in sediments with small grain size. In the light of the differences between structure estimates based on sieving and laser diffraction, we now re-address the question of choosing an appropriate grain sizing method. The curve of the structure function increases substantially toward very fine sediment and probably reflects overestimated grain sizes by the sieving method (Fig. 5). A direct comparison of sieving and laser diffraction grain sizes reveals that

both methods give equal results for grain sizes N100 μm (Fig. 7). At smaller grain sizes, sieving results appear increasingly overestimated compared to laser diffraction results (Fig. 7B) and explains why the values of the sieving-based structure term are in the fines range approximately one order of magnitude higher than the laser-based structure term vales. Still, permeability estimates based on grain sizes established with laser diffraction are considerably less scattered than the estimates based on sieving, which may be attributed to the fact that the laser diffraction method has a much finer size resolution. One could assume that the laser diffraction method is less prone to false fitting of the TauberBobertz-Equation. However, we noticed that some size distributions from laser diffraction measurement tended to have a heavy tail in the fines range, which is not always fitted well with the Tauber-Bobertz Equation. The laser diffraction-based structure functions also have considerably less variation and might even be approximated by a constant value. But this habit might be coincidental, as the increasing trend of the structure function might be balanced by the tendency of laser diffraction to underestimate grain sizes. However, since laser-diffraction results are shape-dependent and grain shape also affects permeability, it might be interesting in future studies to examine whether or not laser diffraction results contain sufficient information of the grains' specific surface area, which might then be used as a parameter for permeability prediction (e.g. with Cozeny-Karman). The fact that the relative fitting residuals of the laser diffraction data have a substantially narrower distribution than the sieving data (Table 1) indicates that the laser diffraction is at least more precise than sieving. The uncertainties in the applied granulometric methods cannot account for all of the observed variability of the structure term. If the sediment structure was similar in all sediment types, the observed permeability would only be a function of grain size. In turn, the bulk porosity would be the same for all samples, since porosity is dependent on the structure variables m and F (ϕ = F1̄/m). Our measurements show that permeable sand with K N 10−11 m2 has a porosity of approximately

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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Fig. 5. Sediment structure term am2F3 plotted against effective grain sizes D15 and D50 as established by laser diffraction method (A & B), and sieving of freeze-dried samples (C & D), respectively. The horizontal, dashed lines represent the value of the structure term for spherical particles (a = 8/3, m = 1.5, F = 4). The solid, curved lines represent the best fit (least median of squared residuals) for each dataset, see also Table 1.

0.4, which agrees with the theoretical value of ≈ 0.4 of well-sorted spheres with m = 1.5 and F = 4. Sediment with lower permeability generally had a higher porosity, which indicates that either F or m, or both vary with permeability, and that the sediment structure is not similar in all sampled sediment. A further determination of the parameters a, m, and F of the structure term would require measurements of at least one more parameter to solve for the unknowns in Eq. (3). This could be addressed by measurement of the electrical impedance to obtain the formation factor F, which in combination with the porosity enables to calculate the cementation exponent m and even the packing constant a. Unfortunately, this was not feasible during this study. However, it is at least possible to deduce the trends of the individual variables. By definition, F becomes unity if sediment porosity is 1 (Glover, 2009; Glover and Walker, 2009). For this case, electrical resistivity measurements on marine surface sediment suggest that m ≈ 1.8 (Manheim and Waterman, 1974; Ullman and Aller, 1982; Revil and

Cathles 1999). In impervious mud with high porosity we estimated that the structure term exceeded 103, implying that the packing constant (a) exceeds 100 if we assume F ≈ 1 and m ≈ 1.8. This is a very high value for a compared to accepted values, which are in the range of 2 to 12 (e.g. Glover et al., 2006). Since the employed RGPZ model is not valid for the limit ϕ = 1, future work is necessary to decide whether the high values of the packing constant we estimated here for high porosity mud (ϕ max = 0.87) actually reflect physical properties of the sampled sediment or result e.g. from a failure of the underlying model or from biased grain size estimates as discussed above. 3.4. Application of the empirical permeability model We decided to employ our D15-grain size estimates in combination with our permeability measurements to establish an empirical permeability formula (Eq. (10)) because it has a better fit than the D50 based estimates (Table 1). Additionally, using the D15 enables easier

Table 1 Regression equations of empirically estimated sediment structure term s(deff) for D15 and D50 as effective grain diameter established by laser diffraction or dry sieving, together with distribution of relative errors represented by 17th percentile (P17), median (MRE), and 83rd percentile (P83). The grain diameter in the equations below was divided by 1 m to remove the unit since the term am2F3 is also unitless (Eq. (8)). Laser diffraction D15

D50

sðD15 Þ ¼ 9:3  P83: 2.14 MRE: 0.13 P17: −0.29

Dry sieved

−0:5 15 100 ðD1m Þ

15 sðD15 Þ ¼ 7:0  10−11 ðD1m Þ P83: 3.37 MRE: 0.02 P17: −0.85

−0:5

50 Þ sðD50 Þ ¼ 4:5  10−10 ðD1m P83: 5.28 MRE: 0.00 P17: −0.89

50 sðD50 Þ ¼ 2:9  101 ðD1m Þ P83: 1.36 MRE: −0.02 P17: −0.64

−3:5

−3:5

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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A. Neumann et al. / Journal of Sea Research xxx (2016) xxx–xxx

Fig. 6. Crossplots of calculated permeability using empirical structure terms (Table 1) and D15 and D50 from laser diffraction analysis (A & B), and sieving (C & D) vs. measured permeability. The vertical line indicates 1:1 agreement.

comparison with the results of the Soulsby-equation (Eq. (6)), which employs the same grain size. In Eq. (10), the grain size of the structure term is divided by 1 m (not structure variable m) to obtain consistent units. K ¼ 7:0  10−11

  D15 −3:5 2 D15 ¼ 7:0  10−11 m:3:5 D−1:5 15 1m

ð10Þ

Permeability estimates based on Eq. (10) (compare Figs. 2B and 6D) are noticeably improved for grain size results from sieving when using s(deff) instead of a constant value for the structure term as in the Soulsby or Krumbein-Monk methods (Fig. 2B). Crossplots of calculated vs. measured permeability show, that the empirical structure functions can be used to calculate sediment permeability over a range of several orders of magnitude using either D15 or D50 as effective grain size (Fig. 6).

Fig. 7. Comparison of sieving and laser diffraction results of HE-447 samples (A), and size-dependent ratio of sieving grain size to laser diffraction grain size (B). Full circles represent D15, open circles represent D50 grain sizes (A & B), n = 18.

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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Finally, we calculated the permeability using Eq. (10) and the results of 25,421 grain size analyses from the grain size map. The spatial pattern of observed permeability (Fig. 8A) is in good agreement with the map of calculated permeability (Fig. 8B). Permeable sediment is found at sites with shallow water depth such as Dogger Bank, Amrum Bank, or Borkum Reef (Fig. 1B). Impervious sediment is found in deeper water in the Oyster Ground area and along the submerged valley of the Palaeo Elbe. The Helgoland mud area (HMA) within the Palaeo Elbe valley represents a more recently formed depocenter of fine, muddy material. 3.5. Limitations of permeability prediction We are confident that our permeability model is valid for the southern North Sea and correctly predicts the general pattern of permeability distribution (Fig. 8A & B). Since our permeability model was derived with sediment of the southern North Sea, it may be invalid for sediment of different genesis and origin such as sediment rich in carbonate, clay, mica, organic matter or volcanic ash. Such sediment may have grains with different shape and structure, modifying the sediment packing

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and producing different structure term values. The grain size data we collected from external sources (Methods 2.5) and used to map permeability (Fig. 8B) contains D15 / D50 values, which lie outside the range of our own measurements. The permeability estimates of K N 10−9 m2 for very coarse sediment with D15 N 350 μm or D50 N 500 μm are not supported by our own measurements and are thus uncertain. Generally, permeability predicted with the model we presented here may have a low accuracy for individual samples because it uses trends calculated for the whole dataset. Local sediment features such as bivalve shells or burrows of macrozoobenthos organisms may considerably alter the local permeability. 4. Conclusion Based on measurements of grain size and permeability we conclude that the fine structure of the surface sediment, expressed as the structure term am2F3, varies substantially among different sediment types in the German Bight (North Sea). The measurements were used to derive an empirical function s(deff), which describes differences in the

Fig. 8. A: Measured permeability of North Sea surface sediment. Black dots indicate sampling locations. B: Calculated permeability based on D15 grain size and Eq. (10), including sediment samples beyond German Exclusive Economic Zone (EEZ). The EEZ is indicated in A & B by the solid, black, polygonal outlines.

Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002

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sediment structure as a function of the effective grain size. We combined this empirical function with the RGPZ permeability model (Glover et al., 2006) to successfully map the permeability in the German Bight (southern North Sea) based on 25,000 grain size analyses. Our results indicate that grain sizing by laser diffraction has a higher precision than sieving and a better sensitivity in the fines range (b100 μm), although the accuracy of the laser diffraction method might be debatable as pointed out by Konert and Vandenberghe (1997), Eshel et al. (2004), and Blott and Pye (2006). On the other hand, comparability with historic results should not be an argument in favor for the sieving method. Hence, from the perspective of permeability prediction, laser diffraction particle sizing is superior to sieving. We are now able to estimate sediment permeability in the German Bight, from grain size distributions. The new model-based permeability map for the German Bight suggests that areas with water depths N30 m are impervious, whereas sediment in shallower water, at the Dogger Bank and along the coast, is substantially permeable (Fig. 6A, B). For the application of diagenetic models this implies that benthic fluxes can be estimated with simple diffusion-type models for water depths N30 m (e.g. Fick), whereas coastal sediments require percolation modeling (e.g. Elliott and Brooks, 1997). In our next steps we will apply the grain size-permeability model in a full diagenetic model to estimate benthic fluxes of oxygen and nutrients in the German Bight, thereby translating point measurements into regional estimates. Acknowledgements We wish to thank the crew and scientific parties aboard the RV Heincke for their excellent support during our sampling cruises. We would also like to thank the geology master's students from the University of Hamburg for their enthusiastic and ambitious work during three courses of the Marine Geological Practical Training. Ryan North, Paul Glover and three anonymous reviewers added valuable comments and suggestions to earlier drafts of our manuscript. This study received financial support from the federal state Niedersachsen (VWZN:2869) (Germany) via the WiMo project (Wissenschaftliche Monitoringkonzepte für die Deutsche Bucht). References Ahmerkamp, S., Winter, C., Krämer, K., de Beer, D., Janssen, F., Friedrich, J., Kuypers, M.M.M., Holtappels, M., 2016. Regulation of Benthic Oxygen Fluxes in Permeable Sediments of the Coastal Ocean (Manuscript submitted for publication). Avellaneda, M., Torquato, S., 1991. Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media. Phys. Fluids A 3 (11), 2529–2540. Bear, J., 1972. Dynamics of Fluids in Porous Media. Am. Elsevier, New York. Bernabé, Y., Revil, A., 1995. Pore-scale heterogeneity, energy dissipation and the transport properties of rocks. Geophys. Res. Lett. 22, 1529–1532. Blott, S.J., Pye, K., 2006. Particle size distribution analysis of sand-sized particles by laser fraction: an experimental investigation of instrument sensitivity and the effects of particle shape. Sedimentology 53, 671–685. Bobertz, B., 2000. Facies-Environment-Relationship: an Application in the Western Baltic Sea. IAMG 2001. Boeckel, A., 2016. Bindungsformen von Phosphor in Sedimenten der Deutschen Bucht. Bachelor Thesis. University of Applied Sciences Lübeck, Germany (in German). Elliott, A.H., Brooks, N.H., 1997. Transfer of nonsorbing solutes to a streambed with bed forms: theory. Water Resour. Res. 33 (1), 123–136. Eshel, G., Levy, G.J., Mingelgrin, U., Singer, M.J., 2004. Critical evaluation of the use of laser diffraction for particle-size distribution analysis. Soil Sci. Soc. Am. J. 8, 736–743. Figge, K., 1981. Karte der Sedimentverteilung in der Deutschen Bucht mit Beiheft. Karte Nr. 2900, Deutsches Hydrographisches Institut, Hamburg. Forster, S., Bobertz, B., Bohling, B., 2003. Permeability of sands in the coastal areas of the southern Baltic Sea: mapping a grain-size related sediment property. Aquat. Geochem. 9, 171–190 (2003). Fraser, H.J., 1935. Experimental study of the porosity and permeability of clastic sediments. J. Geol. 43 (8), 910–1010.

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Please cite this article as: Neumann, A., et al., Empirical model to estimate permeability of surface sediments in the German Bight (North Sea), J. Sea Res. (2016), http://dx.doi.org/10.1016/j.seares.2016.12.002