Multimodality of a particle size distribution of cohesive suspended particulate matters in a coastal zone

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jc007552, 2012 Multimodality of a particle size distribution of cohesive suspended particulate matters in a coastal zone Byung Joon Lee, 1 Michael Fettweis, 2 Erik Toorman, 1 and Fred J. Molz 3 Received 27 August 2011; revised 20 December 2011; accepted 10 January 2012; published 9 March [1] Particle size distributions (PSDs) of suspended particulate matters in a coastal zone are lognormal and multimodal in general. The multimodal PSD, which is caused by the mixing of multiple particle and aggregate size groups under flocculation and erosion/resuspension, is a record of the particle and aggregate dynamics in a coastal zone. Curve-fitting software was used to decompose the multimodal PSD into subordinate lognormal PSDs of primary particles, flocculi, microflocs, and macroflocs. The curve-fitting analysis for a time series of multimodal PSDs in the Belgian coastal zone showed the dependency of the multimodality on (1) shear-dependent flocculation in a flood and ebb tide, (2) breakage-resistant flocculation in the spring season, and (3) silt-sized particle erosion and advection in a storm surge. Also, for modeling and simulation purposes, the curve-fitting analysis and the settling flux estimation for the multimodal PSDs showed the possibility of using discrete groups of primary particles, flocculi, microflocs, and macroflocs as an approximation of a continuous multimodal PSD. Citation: Lee, B. J., M. Fettweis, E. Toorman, and F. J. Molz (2012), Multimodality of a particle size distribution of cohesive suspended particulate matters in a coastal zone, J. Geophys. Res., 117,, doi: /2011jc Introduction [2] Particle size distributions (PSDs) of suspended particulate matters in a coastal zone are often multimodal with superposition of the subordinate lognormal PSDs [Christiansen et al., 2006; Mikkelsen et al., 2006]. The log normality describes a more or less skewed distribution toward small size and the multimodality describes a distribution consisting of multiple modal peaks. The multimodal PSD is common in coastal water because of mixing of multiple particle and aggregate size groups. Suspended particulate matter in coastal water is composed of various constituents including clay minerals, organic matter, salts, trace metals and so on [Berlamont et al., 1993; Maggi, 2009]. When such various constituents are subject to flocculation (i.e., aggregation and breakage) and transport (i.e., in and out flux) in highly dynamic tidal currents of a coastal zone, they will never reach an equilibrium state but rather undergo a transient state while alternating the rise and sink of the modal peaks [Gibbs et al., 1989; Li et al., 1993; Yuan et al., 2009]. [3] Erosion of large sand particles and/or sand-sized clay aggregates from the seabed often causes the mixing of different particle and aggregate size groups and develops the 1 Hydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven, Heverlee, Belgium. 2 Management Unit of the North Sea Mathematical Models, Royal Belgian Institute of Natural Sciences, Brussels, Belgium. 3 Department of Environmental Engineering and Earth Sciences, Clemson University, Anderson, South Carolina, USA. Copyright 2012 by the American Geophysical Union /12/2011JC multimodal PSDs in a coastal zone [Christiansen et al., 2006; Yuan et al., 2009]. For example, Yuan et al. [2009] reported that the mixing of advected clays/silts from the upstream and eroded sands from the local seabed causes a bimodal PSD of suspended sediments. Individual clay/silt particles, which are presumably noncohesive considering no reported flocculation at the measuring site, become predominant in a mild tide without erosion and resuspension of local sands and compose a unimodal PSD. However, sands start eroding and resuspending from the seabed at the critical shear stress for erosion (t c ), and the mixture of background clays/silts and eroded/resuspended sands develop a bimodal PSD. When the tidal current becomes mild again, slow-settling clays/silts remain in suspension but fast-settling sands deposit back to the seabed. The mixture of clays/silts and sands will continuously change their relative mass fractions and alternately develop a unimodal, bimodal or multimodal PSD in the flowvarying tidal cycle of a coastal zone. Often sediments in coastal areas, such as the Belgian nearshore zone, consist of fine mud and coarse sand. The mud sand ratio influences the transition between cohesive and noncohesive behavior, and therefore affects erosion, SPM concentration and composition as well as on the PSD of the suspended material [Fettweis et al., 2012; van Ledden et al., 2004; Manning et al., 2010]. If the ratio of cohesive mud to noncohesive sand is high enough to prevent the seabed from erosion and resuspension in a flood and ebb tide, a multimodal PSD could be caused by processes other than erosion and resuspension. [4] Flocculation of fine-grained cohesive sediments may also develop a multimodal PSD in a coastal zone. Flocculation is a dynamic process combining the counteracting processes of aggregation and breakage in a fluid shear field [Eisma, 1986; van Leussen, 1994; Maggi, 2005; Mietta, 1of17

2 Figure 1. A multimodal PSD and schematic diagrams of the discrete aggregate groups of primary particles, flocculi, microflocs, and macroflocs. 2010; Winterwerp, 1998]. Whereas aggregation assembles aggregates with building blocks (i.e., fine-grained cohesive sediments), breakage disassembles aggregates down to building blocks. Flocculation continuously changes the relative volume fractions of building blocks and aggregates and develops distinct peaks in a PSD, while balancing aggregation and breakage in a flow-varying tidal cycle [Verney et al., 2011]. Furthermore, flocculation of marine or coastal clay minerals has been reported to develop a four-level ordered conceptual structure, namely, primary particles, flocculi, microflocs and macroflocs (Figure 1) [van Leussen, 1994]. Primary particles consist mostly of fine particles with a wide size range of mm, including fragmented clay minerals, organic and calcareous particles, picophytoplankton and heterotrophic bacteria [Andrews et al., 2010]. Flocculi, a compound word of floc and nuclei, consist of strongly bound clay minerals with a size range of mm. Flocculi are the smallest clay-based aggregates which are seldom broken down to the lowest-level primary particles (e.g., clay minerals) even at the highest turbulent shear of a coastal zone, and therefore they may be regarded as the basic and major building blocks of aggregates besides primary particles [van Leussen, 1994]. Microflocs consist of flocculi and primary particles with a size range of mm. Macroflocs are built from microflocs, primary particles and flocculi, and have a size range of hundreds to thousands of micrometers. Macroflocs are sometimes referred to as marine snow because of their large and fluffy structure [Alldredge and Silver, 1988]. In the flow-varying tidal cycle of a coastal zone, primary particles, flocculi, microflocs, and macroflocs are highly interactive, resulting in a transient, multimodal PSD [Manning and Bass, 2006; Mikkelsen et al., 2006]. [5] A time-varying multimodal PSD constitutes a scientific record of flocculation and transport of the constituent particles and aggregates. One can use a time series of such PSDs to understand the possible causes of a multimodal PSD and investigate the particle and aggregate dynamics. For example, the occurrence of an additional peak at sand size besides an existing peak at clay/silt size can be evidence of erosion of sands or aggregation of fine-grained cohesive sediments. However, most current researchers have used observed multimodal PSDs in a qualitative and descriptive manner for investigating the particle and aggregate dynamics in a coastal zones or estuaries [Chen et al., 2005; Manning and Bass, 2006; Mikkelsen et al., 2006]. Thus, a quantitative and systematic statistical approach may provide new information for interpreting the particle and aggregate dynamics underlying multimodal PSDs. [6] A quantitative statistical method is also required for practical purposes in modeling and simulation. The recent mathematical models with multiple and discrete aggregate size groups are more accurate for simulating flocculation and transport of multimodal PSDs than models with a single size group under unimodal approximation [Lee et al., 2011; Maerz et al., 2011]. Therefore, characterization of each modal peak of a multimodal PSD and logical simplification of such a modal peak as a discrete aggregate group are required for better modeling and simulation. A statistical method, which had been developed and applied to investigate aerosol dynamics [Banerjee et al., 2009; Hussein et al., 2005; Whitey, 2007], is adopted herein to analyze and interpret a coastal zone multimodal PSD in a quantitative and systematic way. The statistical method with automated curve-fitting software (DistFit, Chimera Technologies Inc., USA) helped us to decompose a multimodal PSD to the subordinate lognormal PSDs of primary particles, flocculi, microflocs and macroflocs, to quantify the mean diameter, standard deviation and volume fraction of the subordinate PSDs, and to investigate the statistics of a large and complicated PSD time series in a quantitative and systematic way. For modeling and simulation purposes, this paper will apply the selected statistical method to analyze the time series of the multimodal PSDs in terms of the characteristics of the subordinate lognormal PSDs. 2. Materials and Methods 2.1. Regional Settings [7] The study area is situated in the Belgian coastal zone facing the southern North Sea. The coastal zone is characterized by a mean tidal range between 4.3 and 2.8 m at spring and neap tide, respectively, and by maximum current velocities of more than 1 m/s. The wind from the southwest dominates for 33% of the year, followed by the wind from the northeast. The maximum wind speed coincides with the wind from the southwest, but the highest wave action occurs under the wind from the northeast [Fettweis et al., 2012]. The area is of interest due to the occurrence of a highly turbid coastal zone. The SPM concentration ranges between a minimum of mg/l and a maximum of mg/l. SPM concentrations decrease during periods of southwest wind due to the advection of less turbid English Channel water, but increase during northeast winds due to an increased SPM outflow from the Westerschelde estuary [Baeye et al., 2011]. The nearshore area is characterized by bottom sediments varying from pure sand to pure mud [Verfaillie et al., 2006]. The sediment underneath fine-grained cohesive sediment suspension at the measuring site consists of silts and fine 2of17

3 sands with a median grain size of about 150 mm. Ephemeral fluffy layers of fine-grained cohesive sediment have been frequently observed on the top of the silty and sandy bed [Baeye et al., 2011]. The suspended matters in the same area consist mostly of clay (41%) and silt (57%) sized particles with a small amount of sand (2%); the mean primary particle size is mm Instrumentation [8] A tripod was deployed at about 1 km from the shore line in a water depth of 5.5 m below MLLWS (mean lowest low water at spring tide), and current velocity, turbulent shear, salinity, and suspended sediment data were collected for the two field campaigns from 28 January 2008 to 11 February 2008 and from 15 April 2008 to 30 April The measuring instruments on the tripod were a 5 MHz SonTek R Acoustic Doppler Velocimeter (ADV Ocean), a 3 MHz SonTek R Acoustic Doppler Profiler (ADP), two D&A R optical backscatter sensors (OBS), a Sea-Bird R SBE37 CT system, a Sequoia Scientific R Laser In Situ Scattering and Transmissometer 100C (LISST-100C), and two SonTek R Hydra systems for data storage and batteries. The measured values from OBS, LISST, and ADV were averaged over each 10 min period and recorded. Two OBSs measured SPM concentrations at 0.2 and 2 m above the bed (mab) and the LISST was attached at 2 mab. The ADV measured a time series of flow velocity and turbulent intensity at 0.2 mab. The high-frequency ADV (25 Hz) measurements permitted to decompose the velocity in terms of a mean and a fluctuating part and to calculate the turbulent kinetic energy (TKE). TKE is proportional to bottom shear stress [Pope et al., 2006; Thompson et al., 2003; Verney et al., 2007]. However, in the presence of waves the bottom shear stress was estimated with the inertial dissipation method adopting the spectrum of the vertical velocity component and a correction for the advection by waves [Fettweis et al., 2010; Sherwood et al., 2006; Trowbridge and Elgar, 2001]. The LISST-100C measured particle size distributions (PSDs) in 32 logarithmically spaced size groups over the range of mm [Agrawal and Pottsmith, 2000]. The volume concentration of each size group was estimated with an empirical volume calibration constant, which was obtained under a presumed sphericity of particles. It is important to note that uncertainties using LISST-100C detectors may arise due to nonspherical flocs, floc sizes exceeding the instrument range, a too high SPM concentration, or stratification of the water column [Agrawal and Pottsmith, 2000; Andrews et al., 2010; Fettweis, 2008; Mikkelsen et al., 2007]. Air bubbles can make errors of the LISST measurements, especially due to breaking waves during the storm period. However, the water depth was high enough to prevent breaking waves and trapping air bubbles during the measuring campaign [U.S. Army Corps of Engineers, 2003; Fettweis et al., 2012] Curve Fitting and Decomposition of a Multimodal PSD [9] The observed multimodal (4-peaked) PSD was assumed to be formed by overlapping four unimodal lognormal PSDs of primary particles, flocculi, microflocs, and macroflocs (Figure 1), and these data served as input to the selected software which performed the curve fitting analysis and the decomposition of the observed PSD into the subordinate lognormal PSDs (equation (1)) [Hussein et al., 2005; Mäkelä et al., 2000; Whitey, 2007]. dv dd ¼ X4 i¼1 " V i pffiffiffiffiffi 2p ln ð si Þ exp 1 2 # lnðd=d i Þ 2 lnðs i Þ [10] In equation (1), V and D are the volumetric concentration and diameter of each size interval of the LISST-100C measured PSD. dv/dd is the normalized volumetric fraction by the width of the size interval and used for curve fitting to a lognormal distribution [Hinds, 1999]. D i is the geometric mean diameter (D g;i ), which is equivalent to the median diameter (D 50,i ) for a lognormal distribution (E. W. Weisstein, Log normal distribution, from MathWorld A Wolfram Web Resources, 2006, available at s i is the geometrical standard deviation, and V i is the volumetric concentration of an ith unimodal PSD. Equation (1) has twelve fitting parameters for D i, s i and V i of primary particles, flocculi, microflocs and macroflocs. Based on observation, the mean diameters of microflocs and macroflocs were set to change as curve-fitting parameters in the ranges of and mm, respectively. However, the mean diameters of primary particles and flocculi were fixed at 3 and 15 mm because the bands of those mean diameters were found to be narrow within about 1 and 5 mm, respectively. These approximations reduce the number of curve-fitting parameters and the complexity of the curve-fitting procedure. The standard deviation of a subordinate PSD (s i ) was limited under 3 to prevent unrealistically wide PSDs comprising the best quality PSD. [11] DistFit (Chimera Technologies, USA), which has been widely used in analyzing aerosol particles, was used to find the best quality fit to a measured PSD. The best quality PSD was defined by the minimum error between the simulated and measured PSDs [Hussein et al., 2005; Whitey, 2007]. Noteworthy is that the recent version of DistFit has an automated fitting algorithm to handle a large number of PSDs. Therefore, DistFit can free users from the laborious task for finding the best quality PSD curves for a large number of measured PSDs. (In the present application, data were collected at 10 min intervals for two to three weeks.) The best quality PSD provided parameter values (D i, s i and V i ) for the subordinate lognormal PSDs of primary particles, flocculi, microflocs and macroflocs. The quality of the curve fitting analysis was monitored with the sum of errors between simulations and experimental data (c) (e.g., Table 1). The resulting parameter values were then used as indicators of the particle and aggregate dynamics Estimation of the Settling Flux of a Multimodal PSD [12] The reference sediment settling flux of a PSD (SF ref ) was calculated by summing the settling fluxes of all the 32 aggregate size intervals of the LISST instrument. Each settling flux was calculated by multiplying the settling velocity and volume concentration of an aggregate size interval of the LISST instrument. The settling velocity was calculated by the modified Stokes equation with floc fractal dimensions (equation (2)) [Winterwerp, 1998]. The reference settling flux was then compared to the estimated settling fluxes, ð1þ 3of17

4 Table 1. A Summary of Median and Mean Diameters, Best Fit Parameters From Curve Fitting Analysis With One to Four Particle and Aggregate Groups, and Estimated Settling Fluxes for the PSDs in Figures 4, 6, 8, and 10 a Measurement Curve Fitting: One Mode Curve Fitting: Two Modes Group Day VT SFref D50 SFD50 ErD50 Dwt SFDwt ErDwt V1 Dg,1 sg,1 c1m SF1M Er1M V1 Dg,1 sg,1 V2 Dg,2 sg,2 c2m SF2M Er2M Spring tide Neap tide Shear-resistant flocculation Storm surge a VT and V i represent the volumetric concentration of a multimodal PSD and a decomposed PSD, respectively. SF represents the settling flux of a PSD. Er represents the error between the reference and estimated fluxes for a PSD. Here c is the sum of errors between measurement and simulation for a PSD, representing the quality of simulation. 4of17

5 Table 1. (continued) Curve Fitting: Three Modes Curve Fitting: Four Modes Group V 1 D g,1 s g,1 V 2 D g,2 s g,2 V 3 D g,3 s g,3 c 3M SF 3M Er 3M V 1 D g,1 s g,1 V 2 D g,2 s g,2 V 3 D g,3 s g,3 c 3M SF 3M Er 3M V 1 D g,1 s g,1 Spring tide Neap tide Shear-resistant flocculation Storm surge of17

6 which were calculated with the median diameter (D 50 ), the volume-weighted mean diameter (D wt ) and the mean diameters of the discrete aggregate groups (D i ) obtained from the curve-fitting analysis. The purpose of the comparison between the reference and estimated settling fluxes was to check if the discrete aggregate groups of primary particles, flocculi, microflocs and macroflocs could approximate a continuous multimodal PSD in the settling flux calculation. SF ¼ X i V i w s;i ¼ X i 1 ðr Vi s r w Þg 18 m D 3 ni P D ni 1 i 1 þ 0:15Re 0:687 i [13] In equation (2), the volumetric concentration of an aggregate size interval (V i ) was obtained from the LISST instrument or the curve fitting analysis. The densities of primary particle and seawater (r s and r w ) were fixed at 2600 and 1030 kg/m 3. The diameter of primary particles (D P ) was approximated at 2 mm from the previous research [Fettweis, 2008]. The gravitational acceleration and the fluid viscosity (g and m) were 9.81 m/s 2 and kg/m/s. Re i represents the Reynolds number of an aggregate. The two stepwise fractal dimensions (n i ) of 2.5 and 2.0 were used to represent the two distinct structures of less porous and hard building blocks (primary particles and flocculi; D i <20mm) and highly porous and fluffy flocs (microflocs and macroflocs; 20 mm <D i < 500 mm) [Winterwerp and van Kesteren, 2004]. 3. Results and Discussion [14] Each particle size distribution (PSD) alternately developed one to four modal peaks in a flood/ebb tidal cycle. The first and second modal peaks of the PSD appeared consistently at about 3 mm and 15 mm for primary particles and flocculi, whereas the third and fourth modal peaks varied in the size ranges of mm and > 200 mm for microflocs and macroflocs (Figure 1). In the entire measuring period, the median diameters (D 50 ) of the PSDs seemed dependent on turbulent shear and temperature (Figure 2). High turbulent shear decreased the median diameter down to about 50 mm. Low turbulent shear and/or temperature rise concurred with increasing the median diameters up to about 100 mm. [15] The hydrodynamic condition (i.e., flow velocity and turbulent intensity) of the measuring site varied with storm, neap, and spring tidal periods (Figure 2). A storm period was characterized by more disordered flow vectors and five to ten times higher wave height and turbulent shear than the other regular neap and spring tidal periods (Figure 2a). Both the neap and spring tidal periods were found to have ordered flow vectors, which direct toward or away from the shore line for the flood and ebb currents, respectively (Figures 2a and 2b). However, the neap tide had two to three times lower flow velocity and turbulent shear than the spring tide, and it had a more asymmetric flood and ebb tidal current (i.e., high flow velocity for a flood current but low flow velocity for an ebb current) (Figure 2a). [16] The following paragraphs will explain in more detail the unique behaviors of the PSDs under flocculation and transport for the periods of (1) a spring tide with a symmetric ð2þ tidal current, (2) a neap tide with a flood-dominant asymmetric tidal current, (3) breakage-resistant flocculation in the spring season and (4) a storm surge Spring Tide With a Symmetric Tidal Current [17] The spring tide in Figure 2b had a symmetric pattern of flow velocity and turbulent shear for the flood and ebb currents. The highest turbulent shear coincided with the flood and ebb peak flow, and the lowest shear coincided with the flood-to-ebb and ebb-to-flood slack waters (i.e., zero flow velocity) (Figure 3a). The spring tide with a symmetric tidal current also caused a symmetric behavior of a multimodal PSD for the flood and ebb currents. The highest turbulent shear at both the flood and ebb peak flows increased the volume fractions of building blocks of primary particles and flocculi (i.e., the section between the bottom and the line of PP + Flocculi in Figure 3b) but decreased the volume fractions of aggregates of microflocs and macroflocs (i.e., the section between the line of PP + Flocculi and the top in Figure 3b) and skewed the PSD toward small size with a rising tail at the smallest size group (Figures 4a and 4c). In contrast, the lowest shear at both the slack waters increased the volumetric fractions of aggregates but decreased the volumetric fractions of building blocks (Figure 3b), and skewed the PSD toward large size with a distinct peak or hump of macroflocs (Figures 4b and 4d). [18] The multimodality of a PSD appears influenced by shear-dependent flocculation, in which aggregation and breakage counteract each other in a flow- and shear-varying tidal cycle [Fettweis et al., 2006; Winterwerp and van Kesteren, 2004; Winterwerp et al., 2006]. The highest shear of the peak flow would be expected to enhance breakage of aggregates to building blocks, while the lowest shear at slack water would enhance aggregation of building blocks to aggregates [Lee et al., 2011; Verney et al., 2009, 2011]. In addition to shear-dependent flocculation, one may suspect that turbulence-mediated erosion and resuspension would increase the influx of large particles and aggregates from the seabed into the water column [Orange et al., 2005; Yuan et al., 2009]. However, the peak flows, which are the best condition for erosion and resuspension of larger particles, instead decreased the volume fraction of large particles and aggregates, pointing thus to mainly floc breakup. Only a small amount of sands, less than 2% of the total suspended matters (see also section 2.1) was responsible for the tiny peaks of the macrofloc-sized class at the peak flows (Figures 4a and 4c). Therefore, erosion and resuspension might neither cause the influx of large particles and aggregates nor affect the multimodality in the nonstormy regular tidal cycle of the measuring site at 2 mab or higher in the water column Neap Tide With a Flood-Dominant Asymmetric Current [19] A neap tide at the measuring site had a flood-dominant asymmetric current, which consists of a shorter flood cycle with a higher flow velocity but a longer ebb cycle with a lower flow velocity. A sharp peak of flow velocity and turbulent shear was found in a flood cycle, whereas a stretched mound was found in an ebb cycle (Figure 5a). The geographical characteristics of a coastal zone and/or the periodic 6of17

7 Figure 2. A time series of the flow velocity vector with x and y direction components (U and V), median diameter (D 50 ), turbulent shear (t), and temperature ( C) in the measuring periods of (a) 28 January 2008 to 11 February 2008 and (b) 15 April 2008 to 5 June The dotted lines show the smoothed curves with the moving averages of 70 data points. The shaded area represents a tidal cycle which has a specific flow condition and flocculation behavior. 7of17

8 Figure 3. (a) A time series of time-averaged flow velocities in x and y direction (U and V) and turbulent shear (t) and (b) a time series of the cumulative volumetric fractions of primary particles (PP), flocculi, microflocs (Micro), and macroflocs (Macro), for the spring tide with a symmetric tidal current. The symbols represent the measured data, and the lines show the smoothed curves with the moving averages of three data points. In Figure 3b, each section between two lines represents the individual volume fraction of primary particles, flocculi, microflocs, and macroflocs. The four vertical lines, from the left to right, indicate the flood peak flow, the flood-to-ebb slack water, the ebb peak flow, and the ebb-to-flood slack water, of which PSDs are plotted in Figure 4 for comparison. change of oceanic currents have been reported to cause such an asymmetric tidal current [Brown and Davies, 2010; Latteux, 1995; van der Molen et al., 2004]. The flooddominant asymmetric current caused asymmetric behavior of the resulting multimodal PSD for the flood and ebb currents. For example, macroflocs appeared in the entire ebb cycle even at the ebb peak flow but disappeared in the flood cycle. Building blocks (i.e., primary particles and flocculi) developed a sharp rise of the volumetric fraction at the flood peak flow but did not at the ebb peak flow (Figure 5b). The PSDs in the ebb cycle and the slack water skewed toward large size with a peak or hump of macroflocs (Figures 6b, 6c, and 6d), but the PSDs in the flood cycle skewed toward small size (Figure 6a). [20] The neap tide with a flood-dominant asymmetric current generally enhanced the overall flocculation rate (i.e., increased aggregation and decreased breakage) more than the spring tide with a symmetric current, considering that the neap tide had a smaller volume of building blocks but a larger volume of aggregates especially during the ebb cycle. Why did the neap tide enhance the flocculation rate? First, the lower turbulent shear in the neap tide, which was about one third of the shear in the spring tide, necessarily enhanced the flocculation rate (Figures 3a and 5a). Flood/ebb flow imbalance further decreased turbulent shear and enhanced the flocculation rate during the ebb cycle by keeping the turbulent shear under a threshold of floc breakage. Second, stratification of sediment concentration in the water column might also enhance the flocculation rate, especially in the mild flow and shear condition of the ebb current. Winterwerp [2011] reported that the lower turbulent shear of the ebb current could reduce vertical dispersion and stratify sediment concentration (i.e., the deeper water depth, the higher sediment concentration) in the cohesive sediment suspension in the Ems-Dollard estuary, Germany/Netherlands. Similarly, the low-turbulence ebb current at the measuring site might enhance vertical stratification of the cohesive sediment suspension. The highly concentrated sediments near the bottom could enhance the flocculation rate by increasing the frequency of aggregate collision and attachment. In contrast, the higher turbulent shear of the flood current could increase vertical dispersion and homogenize sediment concentration in the water column in a breakage-dominant condition. In flocculation theory, turbulent shear (G) and sediment concentration (C) control the flocculation rate [van Leussen, 1994; Winterwerp and van Kesteren, 2004], we therefore conclude that substantial turbulent shear reduction and possible sediment stratification during the ebb cycle are the major causes of the enhanced flocculation rate in the neap tide, compared to the spring tide Breakage-Resistant Flocculation [21] The pattern of flow velocity during the observed breakage-resistant period was similar to that in the spring tide with a symmetric tidal current. Turbulent shear remained two to three times lower than the shear in the spring tide, but was still higher than the shear in the neap tide (Figures 3a and 7a). However, the flocculation rate in this period was higher than in any other periods, i.e., less building blocks of primary particles and flocculi but more aggregates of microfloc and macroflocs due to increasing aggregation but decreasing breakage. For example, the volume fraction of macroflocs (i.e., the section between the line of PP + Flocculi + Micro and the top in Figure 7b) reached up to 40% at slack water and still remained high at 10% even at the peak flow. It is more important to note that the volume fraction of building blocks (i.e., the section between the line of PP + Flocculi and the bottom in Figure 7b) remained low (under 20%) without substantial floc breakage in the entire flood and ebb cycle. Therefore, all the PSDs skewed toward large size with a large volume fraction of aggregates, even at the highest turbulent shear of the peak flow (Figure 8). [22] This period had calm weather and low tidal amplitude without storms, which could increase the flocculation rate due to an aggregation-dominant condition with low turbulent shear. However, flocculation in this period did not follow 8of17

9 Figure 4. (a) A PSD in the flood peak flow, (b) a PSD in the flood-to-ebb slack water, (c) a PSD in the ebb peak flow, and (d) a PSD in the ebb-to-flood slack water for the spring tide with a symmetric tidal current. Meas represents a PSD measured with the LISST instrument. PP, Flocculi, Micro, Macro, and Sum represent the decomposed PSDs of primary particles, flocculi, microflocs and macroflocs, and the superposition of the decomposed PSDs. 9of17

10 Figure 5. (a) A time series of time-averaged flow velocities in x and y direction (U and V) and turbulent shear (t) and (b) a time series of the cumulative volumetric fractions of primary particles (PP), flocculi, microflocs (Micro), and macroflocs (Macro), for the neap tide with a flood-dominant asymmetric tidal current. The symbols represent the measured data, and the lines show the smoothed curves with the moving averages of three data points. In Figure 5b, each section between two lines represents the individual volume fraction of primary particles, flocculi, microflocs, and macroflocs. The four vertical lines, from the left to right, indicate the flood peak flow, the flood-to-ebb slack water, the ebb peak flow, and the ebb-to-flood slack water, of which PSDs are plotted in Figure 6 for comparison. the typical pattern of shear-dependent flocculation (see sections 3.1 and 3.2). For example, the volume fractions of building blocks remained low without developing a significant peak even at the highest turbulent shear of the flood or ebb peak flow (Figure 7b). Aggregates seemed armored against breakage. This might indicate the involvement of other breakage-resistant flocculation mechanisms besides the shear-dependent mechanism. Biologically mediated flocculation could be one of the most probable causes of breakageresistant flocculation [Maggi, 2009]. [23] An algae bloom was observed in the vicinity of the measuring site, concurring with temperature rise and high nutrient influx in the manuring season (Figure 2b). This would be expected to stimulate growth of biological species (e.g., phytoplankton, bacterioplankton and benthic fauna) in the coastal zone [Droppo et al., 2005]. Simultaneously, the algae bloom and associated biological activity might enhance biologically mediated flocculation by increasing the production of particle-binding microbial exudates such as Extracellular Polymeric Substances (EPS) or Transparent Exopolymeric Particles (TEP) [Chen et al., 2005; Droppo, 2001; Droppo and Amos, 2001]. Such biologically mediated flocculation might increase not only floc size and but also breakageresistance at the measuring site, and therefore prevented floc breakage into building blocks. This may explain the fact that the volume fractions of building blocks remained low under 20% irrespective of turbulent shear (Figure 7b) Storm Period [24] Turbulent shear in the storm period was about ten times higher than in the other nonstorm periods, and so did not favor flocculation (Figure 9a). Under such strong turbulent shear, each volumetric fraction of primary particles, flocculi, microflocs and macroflocs was rather consistent. The volumetric fractions of primary particles and flocculi were consistent at about 0 and 20%, respectively. The volumetric fraction of macroflocs remained low, mostly under 10% (i.e., the section between the line of PP + Flocculi + Micro and the top in Figure 9b). Therefore, all the PSDs in the storm period developed a similar structure, having a dominant modal peak at about 50 mm with a small tail of building blocks (Figure 10). [25] The unique PSD during the storm period might be caused by influx of sand- and silt-sized particles but not by flocculation of suspended cohesive sediments. Advection of oceanic water masses by wind-induced currents with lower SPM concentration resulted in disappearance of high concentrated mud suspension near the bed and consequently in erosion of the previously covered local sand- and silt-sized particles at the measuring site. Changes in PSD distribution and median diameter during these events have been reported [Fettweis et al., 2012]. Results from the PSD analysis in this research also support this finding. A PSD is composed of breakage-resistant primary sediments, when it is subject to the highest turbulent shear in a storm surge or a peak flood/ ebb flow, and therefore the PSD gives information about the origin and characteristics of the lowest-level sediment composition. The PSD in the storm period consisted mostly of silt-sized particles (80% volume fraction; mm diameter) (e.g., Figure 10a), whereas the PSD at the peak flow in the regular tidal period consisted of primary particles (5 10% volume fraction; 2.5 mm diameter), flocculi (40 50% volume fraction; 15 mm diameter) and small-size microflocs (30 40% volume fraction; mm diameter) (e.g., Figure 4a). The observed difference of the sediment composition proves an influx of eroded and advected silt-sized particles replacing suspended cohesive sediments during the storm period. [26] Generally, high flow velocity and turbulent shear made particles/flocs small because of decreasing the flocculation rate (i.e., decreasing aggregation but increasing breakage). However, the shear-dependent flocculation was not the only factor affecting the PSD. Other physicochemical and biological factors also changed the particle/floc size and the multimodality of a PSD. For example, flocculation 10 of 17

11 Figure 6. (a) A PSD in the flood peak flow, (b) a PSD in the flood-to-ebb slack water, (c) a PSD in the ebb peak flow, and (d) a PSD in the ebb-to-flood slack water for the neap tide with a flood-dominant asymmetric tidal current. Meas represents a PSD measured with the LISST instrument. PP, Flocculi, Micro, Macro, and Sum represent the decomposed PSDs of primary particles, flocculi, microflocs and macroflocs, and the superposition of the decomposed PSDs. 11 of 17

12 Figure 7. (a) A time series of time-averaged flow velocities in x and y direction (U and V) and turbulent shear (t) and (b) a time series of the cumulative volumetric fractions of primary particles (PP), flocculi, microflocs (Micro), and macroflocs (Macro), for the period of breakage-resistant flocculation. The symbols represent the measured data, and the lines show the smoothed curves with the moving averages of three data points. In Figure 7b, each section between two lines represents the individual volume fraction of primary particles, flocculi, microflocs, and macroflocs. The four vertical lines, from the left to right, indicate the flood peak flow, the flood-to-ebb slack water, the ebb peak flow, and the ebb-to-flood slack water, of which PSDs are plotted in Figure 8 for comparison. became more breakage resistant in the spring season with decreasing floc breakage against turbulent shear and increasing particle aggregation. Besides flocculation, the previously covered silts and find sands might be eroded and advected to the measuring site by a strong wind-driven oceanic current and developed a unique PSD consisting mostly of silt-sized particles in the storm period [Baeye et al., 2011; Fettweis et al., 2012] Characterization and Discretization of the Multimodal PSD [27] Particle size distributions (PSDs) developed a multimodality in a flow-varying tidal cycle at the measuring site. Based on the decomposition of the measured PSDs into a superposition of lognormal PSDs, it was concluded that the multimodal PSDs consisted of the four unimodal PSDs of primary particles, flocculi, microflocs and macroflocs that varied their dynamic behavior in a flow-varying tidal cycle. This led us to the idea that the continuous curve of a multimodal PSD might be discretized and simplified to the multiple particle/aggregate groups for practical purposes in modeling and simulation [Lee et al., 2011]. Therefore, it is necessary to review the characteristics of each discrete particle/aggregate group for reasonable discretization and simplification in modeling and simulation. The following paragraphs will review the characteristics and approximate nature of the discrete particle/aggregate groups as a replacement for a continuous multimodal PSD. [28] Primary particles have been reported to consist of various organic and inorganic particles (e.g., fragmented clay minerals, organic and calcareous particles, picophytoplankton and heterotrophic bacteria). A substantial amount of such primary particles are out-of-range fine particles with a wide size range of mm, although they appear as a single peak at the smallest measurable size bin of the LISST instrument [Andrews et al., 2010; Fettweis et al., 2012]. Andrews et al. [2010] reported that such out-of-range particles sharply increased the volume concentration of the smallest and second smallest size bins, and irrationally outof-range particles decreased the volume concentrations of the nearby size bins up to 7 mm but increased the volume concentration of the largest size bin. This bias might further enhance the separation between the two peaks of primary particles and flocculi and develop a small peak of macroflocs in the breakage-dominant condition during the peak flows (e.g., Figures 4a and 4c). Considering the analytical error of the LISST instrument and the reported composition of out-ofrange fine particles, the actual volume concentration peak of primary particles, including out-of-range fine particles with a wide size range of mm, might be a long extended tail of the peak of flocculi. [29] Clay minerals have been reported to aggregate into breakage-resistant flocculi and sequentially into microflocs due to the physicochemical binding mechanisms of (1) Coulombic attraction and (2) charge dilution [Mietta, 2010; Mpofu et al., 2003; Tombacz and Szekeres, 2004]. In spite of the net negative surface charge, the sporadic positive sites available on the edges of clay minerals can induce strong Coulombic attraction between clay minerals (e.g., face-to-edge attachment). Otherwise, the charge dilution by abundant salt ions in brackish and marine water, which, in aquatic chemistry, is called electric double layer compression [Stumm and Morgan, 1996], can reduce the net negative surface charge and electrostatic repulsion of clay minerals and enhance aggregation. Based on the observed difference between flocculi and microflocs with respect to structure and shear resistance, we conclude that the Coulombic attraction is likely to make strongly bound flocculi but the charge dilution favors loosely bound microflocs (Figure 1). [30] Macroflocs developed an additional peak in the PSD beyond the major peak of microflocs (e.g., Figure 8). The gluing capability of microbial exudates (EPS or TEP) is known to enhance the building of organic-rich macroflocs [Chen et al., 2005; Droppo, 2001; Droppo and Amos, 2001]. Floc sizes of marine sediments have been reported to range 12 of 17

13 Figure 8. (a) A PSD in the flood peak flow, (b) a PSD in the flood-to-ebb slack water, (c) a PSD in the ebb peak flow, and (d) a PSD in the ebb-to-flood slack water for the period of biologically mediated flocculation. Meas represents a PSD measured with the LISST instrument. PP, Flocculi, Micro, Macro, and Sum represent the decomposed PSDs of primary particles, flocculi, microflocs and macroflocs, and the superposition of the decomposed PSDs. 13 of 17

14 Figure 9. (a) A time series of time-averaged flow velocities in x and y direction (U and V) and turbulent shear (t) and (b) a time series of the cumulative volumetric fractions of primary particles (PP), flocculi, microflocs (Micro), and macroflocs (Macro), for the storm period. The symbols represent the measured data, and the lines show the smoothed curves with the moving averages of three data points. In Figure 9b, each section between two lines represents the individual volume fraction of primary particles, flocculi, microflocs, and macroflocs. The four vertical lines, from the left to right, indicate the flood peak flow, the flood-to-ebb slack water, the ebb peak flow, and the ebb-to-flood slack water, of which PSDs are plotted in Figure 10 for comparison. from hundreds to thousands of micrometers in organic-rich conditions, but only from tens to a few hundred micrometers in organic-scarce conditions [Fettweis et al., 2006]. The reported size ranges of the two floc groups in organic-scarce and organic-rich conditions agrees with the measured size ranges of microflocs and macroflocs in this research ( mm and > 200 mm). This suggests that our observed microflocs and macroflocs were built by the respective physicochemical and biological flocculation mechanisms in the organic-rich seawater. In fact, the subordinate aggregate groups of primary particles, flocculi, microflocs and macroflocs have their unique assemblage mechanisms and physicochemical and biological characteristics. However, the interactions between the particle and aggregate groups and their kinetics remain unknown and need further investigation, because they involve the complexity and heterogeneity of floc binding mechanism, composition, morphology, etc. [e.g., Maggi, 2009]. [31] We further investigated if the discrete groups of primary particles, flocculi, microflocs and macroflocs could approximate a continuous multimodal PSD in the settling flux calculation. The estimated settling fluxes of the discrete aggregate groups approached the reference settling flux of a multimodal PSD, as the number of the discrete aggregate groups increased (Figure 11 and Table 1). For example, the estimated settling fluxes with a single median diameter (D 50 ) had the largest error of 25 50% against the reference settling flux, but the estimated settling fluxes with a volumeweighted mean diameter (D wt ) had smaller errors up to 4.5%, because the volume-weighted mean diameter takes into account the volumes of all 32 aggregate size groups of the LISST instrument. Although one could accurately estimate the sediment settling flux with a volume-weighted mean diameter, it would be very difficult to track all the 32 groups in large-scale multidimensional simulation. Therefore, decomposing a continuous multimodal PSD to the discrete aggregate groups of primary particles, flocculi, microflocs and macroflocs appears to be a practical strategy for simulating flocculation and transport in a coastal zone. [32] When calculating the estimated settling flux with the discrete aggregate groups of primary particles, flocculi, microflocs and macroflocs, we used the expected mean diameter (D mean;i ) that is statistically the most probable value, instead of the geometric mean diameters (D g;i ) obtained from the curve fitting analysis (equation (3)). The latter is equivalent to the median diameters (D 50,i ) and thus subject to erroneous estimation of the settling flux, as discussed in the earlier paragraph. The geometric mean diameters (D g;i ) were converted to the expected mean diameter (D mean;i ) with equation (3) (Weisstein, online reference, 2006). 1 D mean;i ¼ exp ln D g;i þ ð 2 lns iþ 2 ð3þ [33] The estimated settling fluxes with a single discrete aggregate group had up to 45% errors against the reference settling flux of a continuous multimodal PSD. However, as the number of discrete aggregate groups increased, the estimated settling fluxes approached the reference values. The settling fluxes with two discrete groups of building blocks (i.e., primary particles and flocculi) and aggregates (i.e., microflocs and macroflocs) produced up to 9.5% errors. The settling flux with three discrete groups of building blocks, microflocs and macroflocs has up to 3.5% errors. The settling flux with four discrete groups of primary particles, flocculi, microflocs and macroflocs had up to 3.2% errors. The smallest error between the estimated and reference settling fluxes indicates that the multiple discrete aggregate groups could be a reasonable approximation of a continuous multimodal PSD. 4. Conclusion [34] The new curve fitting analysis allowed us to decompose multimodal PSDs to the subordinate unimodal lognormal 14 of 17