Introduction
Biogeochemical cycling and functioning of marine coastal and shelf sea
systems crucially relies on particle transport. Vertical fluxes of suspended
particulate matter (SPM) are determined by sinking velocity ws and
indirectly affect the horizontal transport. In coastal systems, SPM is
composed of living and nonliving particulate organic matter (POM) and fine
cohesive and non-cohesive resuspended minerals. Fine-grained minerals of
sizes typically up to 8 µm and POM can undergo
aggregation and fragmentation processes that change sinking velocity and thus
transport properties. As a consequence of flocculation, SPM aggregates
ubiquitously possess a broad spectrum of size and composition
. This heterogeneity between flocs increases the
methodological effort required to analyze ws in situ
. On larger scales, SPM concentration (SPMC) and
composition additionally exhibit strong spatiotemporal variability that is the result of manifold interplaying processes. Tidal and wind-induced
currents are the major driver for resuspension and subsequent horizontal
transport, while biological processes, such as algae growth and bio-induced
sediment stabilization , interfere and thus
shape the complex distribution of SPM in coastal and estuarine systems.
Typically, SPMC and composition show cross-shore gradients
. In shallow waters near the coast,
where turbulence and thus resuspension are high, SPMC consists of flocs that
are mainly composed of mineral particles with high densities. By contrast, in
deeper offshore regions, SPMC is lower and the flocs are looser and more
organic. This general pattern of changing SPMC and composition from coast to
open waters is typical for our research area, the German Bight
, and is observed worldwide in estuaries
e.g., and across coastal seas
e.g.,. Since both SPMC and turbulence control the ws of cohesive material , it is likely that these
cross-shore SPM gradients induce considerable spatial variability in ws
and thus affect the transport and fate of SPM in coastal marine systems. However,
to date and to the authors' knowledge, no comprehensive analysis has
addressed system-wide cross-shore gradients in sinking velocity, especially
in relation to possible drivers.
The sinking velocity of SPM is determined by floc size and density, both
resulting from a complex interplay of processes. Particle size distribution
is locally governed by restructuring , aggregation and
processes mainly driven by turbulence-induced shear,
G‾=(ϵ/ν)1/2 . This turbulence is
generated by energy dissipation ϵ with
kinematic viscosity ν. Under a given shear regime, aggregation is
controlled by floc volume concentration and the adhesion properties of the
primary particles of mineral and organic origin that form the floc. The
higher the volume concentration of flocs, the higher is the encounter rate.
Subsequently, adhesion forces of the particles involved eventually determine
the probability of the particles sticking together. In addition, adhesive
forces limit the intrusion of particles during clustering and loosen the floc
structure . This leads to a floc morphology that shows
self-similar fractal scaling . As a result, aggregates
possess decreased density compared to the aggregates comprising primary
particles. In addition, adhesion forces between the particles within a
floc strengthen the resistance of aggregates to fragmentation
, while the smallest eddies, with sizes on the
Kolmogorov microscale , potentially limit the maximum
particle size . In sum, ws is locally
governed by turbulence-driven processes whose rates depend on the
physicochemical properties and volume concentration of particles.
To date, there is still a lack of understanding of how environmental
conditions and especially biological processes affect physicochemical
properties and thus ws of cohesive SPM. Typically, a power law
relation between median ws and SPMC is postulated and found at
local measurements . However, these relations vary
considerably in their power factor among different systems as summarized by
for various estuaries. This variation can be attributed to
different shear stresses and physicochemical properties of the particles
involved. They are particularly subjected to algae and microbial
extracellular polymeric substance (EPS) excretions such as
transparent exopolymer particles (TEPs) that are known to mediate aggregation
processes. TEPs bridge and glue mineral particles together
and potentially increase resistance to particle fragmentation
. By these mechanisms, TEPs are hypothesized to enable
phytoplankton to clear the water column of suspended sediments
. Such clearing ability may contribute to spatial
variability of ws, which would affect biogeochemical cycles. So
far, knowledge on spatial variations of ws on a system scale is
rare. A study on a transect in San Francisco Bay has been carried out
, but generally, there is no systematic understanding of
the relevance of sedimentation variability for biogeochemical cycles in
coastal ecosystems. Such knowledge, though, is needed to understand and model
coastal shelf biogeochemistry and sedimentology. For example, it is still an
ongoing scientific discussion which processes are involved and to what extent they sustain the net sediment
transport towards the Dutch, German and Danish coast into the Wadden Sea
. We therefore aim at a reconstruction and analysis of the
ws of SPM for the German Bight, North Sea. We develop a new
approach to retrieve ws from high-resolution turbidity profiles
in combination with vertical mixing rates estimated by a hydrodynamical
model. Our findings are discussed particularly in light of their relevance
for biogeochemical cycling of matter in coastal waters.
Methods
In the following section, the study area, sampling and preprocessing of
observational data are described. We further explain the procedure for
extracting sinking velocities from observations with the aid of
hydrodynamical model results.
Study area
The surveyed area of the German Bight (Fig. )
is located in the southeast of the North Sea and features a typical depth of
about 30 m to a maximum of 50 m. The North Sea is a shallow
shelf sea with an average depth of 80 m and
is connected to the North Atlantic via the English Channel in the southwest
and opens towards the north, spanning the European continental shelf. The
North Sea is exposed to tides whose tidal range is between approximately 1.8
and 3.4 m in the southeastern German Bight. The main North Sea tidal
wave turns counterclockwise and drives the large-scale current system
. SPM originating from the British coast is
transported eastwards by the East Anglian Plume and occasionally reaches the
surveyed area . In the southern North
Sea, SPM and dissolved nutrients that enter through the River Rhine are
transported eastward along the Dutch and German East Frisian shore by this
large-scale current system. In addition, the German rivers Ems, Weser and
Elbe discharge into the German Bight. As a result of the riverine nutrient
input, the German Bight features a generally high primary productivity
while it possesses pronounced heterogeneity with strong
cross-shore gradients in (i) nutrients
and (ii) SPMC and composition . The near-coastal waters of
the German Bight are characterized by relatively high SPMC of few to several
hundred grams per cubic meter in near-bottom regions. SPMC possesses a
pronounced seasonality, showing higher values in winter than in summer. In
the shallow parts of the tidal back barriers of the Wadden Sea, this seasonal
pattern is reflected by the bottom fraction of fine, cohesive sediments
accumulating during spring and summer due to aggregation and subsequent
increased sedimentation . The sediment catchment area for
the Dutch and East Frisian Wadden Sea system, an area sheltered from the
North Sea by a chain of islands, is hypothesized to be defined by a
line of no return located alongshore off the coast
. The line of no return is conceptually described as an
imaginary line beyond which particles escape coastal trapping mechanisms such
as density gradient-driven undercurrents .
Map of water depth in the German Bight. Gray lines indicate the
ScanFish sampling transects. The inset shows the North Sea and in red the
region in the larger drawing. For East and North Frisian subregions, see
Fig. .
Sampling and processing of observational data
Measurements were carried out as part of the “Coastal Observing System for
Northern and Arctic Seas” project COSYNA: www.cosyna.de; see
also. Sensors were mounted on board a towed vehicle
(ScanFish, Mark II, EIVA a/s, Denmark). The ScanFish was remotely operated
behind a vessel sailing with a speed of 6 to 8 knots. Cruises were carried
out during May, July–August and September 2009; March,
May, July and September 2010; and April, June and September 2011 during
moderate weather conditions. No winter measurements were carried out. The
transect grid covered the German Exclusive Economic Zone
(Fig. ). The ScanFish was forced to operate
in nearly V-curved undulating path mode between approximately 3 m
below the water surface and the sea bottom, with a vertical speed of
0.4 ms-1 and a sampling rate of 11 Hz, yielding a
vertical data spacing of about 0.04 m. Our analysis considered
measurements of specific conductance (Conductivity Sensor, ADM Elektronik,
Germany), water temperature T (PT100, ADM Elektronik, Germany), pressure
p (PA-7, Keller AG, Switzerland), optical turbidity (Seapoint Turbidity
Meter 880 nm, Seapoint Sensors inc., USA) and chlorophyll a
fluorescence F (TriOS MicroFlu-chl, TRIOS Inc., Germany). Specific
conductivity and T were calibrated against reference standards directly
before and after the ship surveys. Potential water density ρθ,
expressed as σT=ρθ-1000 kgm-3, was
calculated according to the EOS-80 equations of state .
Thermal lag effects were visible in σT near the
thermoclines, but this effect was neglected since the selection criteria for
profiles diminished their relevance for this analysis, as described below.
During post-processing, data generally underwent tests for any stuck values
and spikes and were finally visually inspected to remove remaining faults.
Turbidity, measured in formazine turbidity units (FTU), was converted to SPMC
using a factor of 1.08 g (dry weight) m-3FTU-1 that
was determined by linear regression r2=0.967;.
Laboratory investigations revealed a sensitivity of the fluorescence signal
to turbidity. Therefore, a correction factor was applied to measured
fluorescence. A factor of
(0.32+(1-0.32)exp(-0.025turbidity))-1 was experimentally
determined with commercially available chlorophyll a dissolved in
varying formazine concentrations. As a final step, data sets were split into
up- and down casts between consecutive vertical extrema of the undulating
flight path. Casts with deficient pressure data were discarded.
Data processing and sinking velocity extraction
Sinking velocities were obtained by fitting an analytical solution of the
vertical distribution of SPMC to observations. Assuming steady state and
neglecting horizontal advection, the SPM transport equation in time t for
concentration C reduces to
∂∂tC=∂∂zkv∂∂zC-∂∂z(wsC)=0.
This describes the balance between fluxes in the positively downward pointing
vertical direction z due to sinking and turbulent eddy diffusivity
kv. If we assume that the sinking timescale is larger than the
tidal period, we can simplify Eq. () by
using the vertically averaged kv of a profile. This assumes a
rather homogeneous turbulence intensity which we account for in the data
processing described below. If we further allow fluxes across profiles
borders, which cancel out under steady state, we can derive an analytical
model (Cm(z)) for depth-dependent SPMC:
Cm(z)=λexp(λz*/Hp)exp(λ)-1〈C〉whereλ=wsHp〈kv〉.
Here, Hp represents the profile height and z*=z-z1, where
z1 is the depth at which the profile starts. The application of the
analytical solution to observed SPMC profiles requires information on
corresponding kv values. These and energy dissipation rate
ϵ and water density σT were obtained from
hydrodynamical simulations of , based on a 1 nmi
numerical model of the North Sea and the Baltic Sea. In the vertical, 42
terrain-following levels were used. Vertical mixing was parametrized by means
of a two-equation k-ϵ turbulence model coupled to an algebraic
second-moment closure . The implementation of the
turbulence module was done via the General Ocean Turbulence Model
GOTM; . The hydrodynamic parameters were stored as
2-hourly snapshots.
Hydrodynamic model results for kv, ϵ and
σT were linearly interpolated in space and time to extract a
corresponding value for every measured data point. Even though
state-of-the-art hydrodynamical models generally perform very well, they may
locally exhibit discrepancies with observations. To
discriminate between profile congruency or the lack thereof, both observed and
modeled σT were interpolated on a common vertical grid of
Δz=0.05 m and filtered by applying a least-square straight
line fit to the data and a “natural” cubic spline interpolant. The latter
had a weight of 80 % to produce a smooth interpolation curve
σT′(z′). Subtracting the respective vertical mean resulted
in profiles σT̃ for both observed and modeled
data. We further constrained our analysis to casts that satisfy two criteria.
First, after the subtraction of modeled σT̃ from
observed data, the standard deviation should not exceed
std(ΔσT̃)≤0.015 kgm-3.
Second, the density gradients defined as
δzσT=(〈σT′(lastmeter)〉-〈σT′(firstmeter)〉)/H, where 〈x〉 represents the mean of a variable x and specifically, in this
case, the vertical mean, should not exceed a difference of
ΔδzσT≤0.015 kgm-3m-1 between
observed and modeled data. Both limits for
std(ΔσT̃) and
ΔδzσT were applied to select similar vertically
structured observed and modeled density profiles. The chosen values, however,
were somewhat arbitrary and therefore considered in a Monte Carlo-type
sensitivity simulation (see below).
ScanFish cruises covered well-mixed coastal but partly also stratified waters
in the inner German Bight. A consistent approach to retrieve ws was
required to meet both conditions. When needed, we chose to split casts into
subprofiles and to fit the single analytical solution,
Eq. (), to (sub-) profiles. If observed
δzσT<5×10-4 kgm-3m-1, the whole
profile was used for fitting, otherwise the cast was split. Since the
critical value was set by visual inspection, sensitivity of this critical
value was also considered in the Monte Carlo-type simulation described below.
Strong gradients in σT are typically considered to indicate dampening
of turbulent mixing. The squared buoyancy frequency (N2)
N2=gρ∂ρ∂z,
where g denotes the gravitational acceleration constant, is related to the
vertical eddy diffusivity kv by :
kv=cϵN2,
with the current standard value for c=0.2 . A strong
vertical sea water density gradient thus reflects low turbulent diffusion,
which would imply spliting profiles in stratified
waters at the maximum density gradient(s). However, as recently discussed by
, mixed layer depths defined by density gradients are a
rather inadequate proxy for turbulence intensity. Since particle properties
such as size and density are a function of shear rate and SPM components, it
is reasonable to expect them to differ with vertical turbulence intensity,
thus leading to different sinking velocities. For example,
reported vertically varying mean aggregate sizes for the Baltic Sea. While we
generally expect vertical gradients in SPMC, strong vertical gradients in
SPMC potentially reflect weak mixing and are thus a possible indication for
changes in turbulence intensities. The co-occurrence of strong gradients in
σT and SPMC can thus signal changes in turbulence intensity
and particle property. Splitting at these points allowed us to apply the
analytical SPMC model (Eq. ), where we assumed a
rather homogeneous turbulent diffusion by using the vertically averaged
kv. Thus, end points of subprofiles were set, where regions in
the profile with
1C′∂C′∂z′⋅1σT′∂σT′∂z>1C′∂C′∂z′1σT′∂σT′∂z
occur and reach their maximum. Here, 〈x〉 denotes the vertical
average and C′ is the SPMC smoothing spline-interpolated analogously to
σT. Start points of the subprofiles were either the first data point
from the surface or where regions defined by
Eq. () end with increasing depth. Only
subprofiles longer than 4 m were considered for further analysis.
Example for the (a) spline-fitted profiles, (b) comparison between
observed and modeled spline-fitted σT′, (c–g) the splitting
and subsequent fitting of the analytical model to vertical SPMC subprofiles;
derived ws and analytical model errors (Eq. )
are given by the corresponding numbers. (h) Turbulence model-calculated ϵ
(green) and kv (magenta) profile. For (a–g) lines in black: raw
observations; red: spline fits; magenta: hydrodynamical spline fits; blue
dashed line in (f) critical depth-averaged value (right-hand side of
Eq. ); green: analytical model fit; red dots:
derived split points from Eq. ().
The analytical model, Eq. (), was fitted to the
original observation of each (sub-) profile with Np data points, and the
cost function
err=1Np∑i=1Nc(C(zi)-Cm(zi))20.5(δRC2+δPC2)
was calculated accordingly. δPC2 and δRC2 represent the
variance in concentration of a profile and in a region, respectively. The
latter was defined as the variance for measurements around the profile within
±5 min to account for higher variability in coastal than in open-water
regions found in a pre-analysis of the data. Only profiles below a cost
function value of 0.05, chosen by visual inspection, were considered for the
analysis. The splitting and subsequent fitting of the analytical model is
visualized in Fig. . The variables SPMC and
fluorescence-to-SPMC ratio (F / SPMC) were vertically averaged for the
respective (sub-) profiles. Afterward, variables were binned with respect to
modeled ϵ and eventually averaged bin-wise, resulting in respective
bin-wise ensemble means 〈SPMC〉, 〈F/SPMC〉, 〈ws〉 and 〈ϵ〉.
To test for significant changes in binned 〈ws〉 with 〈ϵ〉, we applied a Mann–Whitney U test with a significance level
of p<0.05 for each binned 〈ws〉 against each other. In
summary, approximately 67 % of the ≈68 000 profiles initially measured passed the congruency check with modeled ones. After the application of the cost
function threshold, this resulted in about 12 260 ws values.
All applied threshold values were carefully selected by visual inspection
during each filtering step. To quantify their influence on the result, we
performed a Monte Carlo-type simulation with a variation of ±50 % for
the following parameters:
std(ΔσT̃),
ΔδzσT, δzσT and the cost function
error. The analysis was repeated for variations of all parameters against
each other. For each parameter variation, binned mean values for 〈ws〉 vs. ϵ were calculated and are then averaged and
their standard deviation σ quantified (see
Fig. c).
Conceptual cross-coastal sinking velocity model
We introduce and apply a conceptual model for the cross-shore variation of ws as a tool to interpret our results.
According to , ws of a
particle of diameter D can be described by
ws=118μ(ρf-ρ)gD2,
where μ is the dynamic viscosity, ρ is the water density and g the
gravitational acceleration constant. The floc density ρf is
strongly related to the particles' composition and structure. The latter can be
described as fractal dimension df according to
, who derived the excess
floc density Δρf=ρf-ρ for a particle
composed of primary particles of diameter Dp and density
ρp:
Δρf=(ρp-ρ)DpD3-df.
Following the approach of and assuming equally sized primary particles of diameter
Dp, derived
the excess floc density for an aggregate composed of mineral and organic
particles with density ρs and ρo, respectively:
Δρf=(ωΔρs+(1-ω)Δρo)⋅DpD3-df.
For ws of an aggregate, it follows
ws=118μ(ωΔρs+(1-ω)Δρo)gDp3-dfDdf-1,
where ω=ns/(ns+no) and ns
and no are the number of mineral and organic primary particles,
respectively.
This simple ws model, Eq. (), allows the
calculation of trends in ws on a cross-shore transect. Based on
observations, we presume the general following parameter changes from coastal
to open waters: (i) average primary particle size and aggregate size
increase, (ii) particles become more organic, and (iii) particles become more
porous; thus, df decreases. Based on a first-order approach, we
assume a linear decrease or increase in parameters with distance from coast.
For boundary conditions in coastal waters, we therefore assume an average
〈Dp〉=4 µm due to the dominance of
cohesive sediment , 〈D〉=100 µm , ω=0.9 to account for a loss on ignition
(LoI) of ≈0.04 and df=2.0 as an
average coastal fractal dimension . By contrast, for
open waters we presume the following: 〈Dp〉=10 µm for algae-dominated particles; 〈D〉=500 µm since we assume similar trends as in
for the Irish Sea; ω=0.05, to parallel a
LoI≈0.89 ; and df=1.6 as a typical
value for fluffy aggregates . The densities of
primary particles are set to ρp=2650 kgm-3
and ρo=1100 kgm-3, which is
computed as an average of the range given in . The water
density and the dynamic viscosity are set to ρ=1000 kgm-3
and μ=0.001 kgm-1s-1, respectively. The sensitivity of
ws to changes in each parameter is assessed by varying each
parameter separately while keeping the other parameters at their typical
values for coastal waters; e.g., for an organic-rich aggregate with an
assumed diameter of D=100 µm and ω=0.5,
Dp=4 µm and df=2.
Map of hydrodynamic model-calculated time- and depth-averaged energy dissipation rate ϵ for the times of the cruises.
Results
Cross-coastal gradients
Energy dissipation rates ϵ generally possess spatiotemporal
variability. Most relevant for this study, vertically and temporally averaged
model-derived ϵ exhibits a cross-shore gradient from the inner German
Bight towards the coast. The temporal averaging is carried out for the time
of the cruises while accounting for the length of the tidal cycle. Values
range between ϵ≈10-9 m2s-3 and
ϵ≈10-4m2s-3 (Fig. ).
In this range, mean SPMC first increases from values below
1 gm-3 to approximately 10 gm-3. Above
log10(ϵ)=-5.5, mean SPMC moderately decreases to approximately
6 gm-3 and increases again to 10 gm-3 with a further increase in ϵ (Fig. a)
towards the coast.
Under the assumption that fluorescence can be applied as a proxy for POM, the
potential significance of algae and their products for particle composition
is depicted by the mean ratio between measured fluorescence and SPMC. High
F / SPMC ratios indicate rather organic-rich particles, while low F / SPMC ratios
indicate rather mineral particle-dominated flocs. The F / SPMC ratio shows
rather high variability for log10(ϵ)<-6 (Fig. b). With a further increase in ϵ, the
ratio drops and levels at approximately a fourth of the open German Bight
value for log10(ϵ)>-5.
Average sinking velocities 〈ws〉 show very low values
of the order of 10-6 to 10-5 ms-1 in
regions of log10(ϵ)<-7.5 (Fig. c).
At higher ϵ, 〈ws〉 increases significantly reaching a
maximum of about 7×10-4 ms-1 around
log10(ϵ)≈-5.5. This maximum 〈ws〉 around
log10(ϵ)≈-5.5 coincides with an increase in SPMC and a
drop in fluorescence to SPMC ratio. By further increasing ϵ,
〈ws〉 decreases again to values of 〈ws〉≈3×10-4 ms-1. The
Monte Carlo-type simulation to estimate parameter uncertainties exhibits the
same pattern, expressed as σ and 2σ confidence levels (68 %
and 95 %, respectively; Fig. c) around their
ensemble mean and thus underpins the results of 〈ws〉 along
ϵ.
(a) 〈SPMC〉, (b)
〈F/SPMC〉 ratio and (c) 〈ws〉 vs. 〈log10(ϵ(m2s-3))〉. Gray error bars represent the standard
deviation and red error bars represent the confidence intervals
(α-quantile=0.05) for the averages in each bin. Average values for the
bins were used for the color coding. In (c) σ and 2σ represent
the confidence levels of 68 and 95 %, respectively, for the
Monte Carlo-type parameter variation.
Conceptual model
The sinking velocity of an average particle (as parametrized in
Sect. ) changes almost linearly with variations of single
parameters from open to coastal waters (Fig. ,
upper four panels). Flocs would sink less rapidly because of the decreasing
diameter of the aggregate or primary particles in the coastal region. By
contrast, increasing amounts of mineral particles and fractal dimension would
both lead to increased ws. As an overall effect, when considering all
parameters, ws reaches a maximum in between the nearshore and open waters
(lowest panel of Fig. ).
Schematic view of potential influences on sinking velocity (red
lines) from open waters (left) to coastal waters (right) and the changing
parameters' total impact on the resulting sinking velocity (lowest panel)
calculated according to Eq. (). The sinking velocities
shown in the upper four panels are based on a particle of D=100 µm, ω=0.5, Dp=4 µm and df=2, while
the respective parameter shown in the panel is varied (blue lines) (constant
parameters are μ=0.001 kgm-1s-1,
ρ=1000 kgm-3, ρo=1100 kgm-3 and
ρs=2650 kgm-3).
Discussion
Sinking velocity on a gradient of prevailing energy dissipation rate
Sinking velocities were determined along a cross-shore transect in the German
Bight defined by the prevailing ϵ. For the reconstruction of
〈ws〉, we had to assume congruency between in situ
measurements and hydrodynamic model results within a range defined by the
applied filters. The estimated 〈ws〉 of the order of
10-6 to 5×10-4 ms-1 in low- and
high-energy dissipation regions, respectively (Fig. ), compare very well with previous in situ
studies in the German Bight and adjacent areas. found
ws≈10-6 ms-1 to 2×10-5 ms-1
for the open German Bight, a low-ϵ region, and
reported median ws of 1×10-4 to
11×10-4 ms-1 for the Rømø and Højer Dyb, Danish
Wadden Sea, where ϵ is comparably high. Our estimated 〈ws〉 is also well within the range found in other regions, e.g., in
Chesapeake Bay or at the Belgian coast
. In agreement with previous studies e.g.,
compiled in, 〈ws〉 increases with increasing
〈SPMC〉 (Fig. ), which gives further
confidence in the methodological approach. However, the correlation is rather
poor compared to previous local studies and can be explained by the
heterogeneity of the German Bight system, seasonal effects and the
intrinsically high variability of sinking velocities
and of turbulence . The significant maximum of 〈ws〉 at 〈ϵ〉≈10-5.5 m2s-3
can be explained by the balance between aggregation and fragmentation. Both
processes are controlled by turbulent shear that is generated by energy
dissipation, SPM volume concentration and adhesion properties of the particles
involved. Previous flocculation modeling studies point to a formation of
ws maximum along ϵ . Our
findings of a maximum 〈ws〉 between
ϵ≈10-6 and
10-5m2s-3, which translates to shear rates of about
1–3.2 s-1 for ν=10-6 m2s-1,
should thus be comparable to previous theoretical studies. For example, in a
field-work-based modeling approach, found the maximum of
sinking velocity to occur under higher shear rates of about
8.5 s-1. By contrast, calculated highest mean
sinking velocities of about 5×10-4 ms-1, similar to our
findings, for a jar test device-based laboratory experiment with natural SPM
at shear rates of about 1 s-1. Given the underlying
uncertainties in calculating the shear rate in both cases, our study agrees
well with previous theoretical studies. Hence, as suggested by
and , in addition to SPMC, turbulent
shear can be regarded as the major determinant for ws.
Scatterplot of 〈SPMC〉 and 〈ws〉. Error bars represent the confidence intervals
(α-quantile=0.05) for the averages in each bin. The rather poor
correlation can be attributed to the heterogeneity of the German Bight
system. See text for discussion.
Sinking velocity as a result of SPMC, composition and a turbulence gradient
Our study additionally suggests a change in particle composition, with
ϵ as proxied by the fluorescence-to-SPMC ratio. With ϵ,
SPMC increases towards the coast and the mineral fraction becomes dominant
compared to organic particles at low ϵ . Hence,
density and other physicochemical properties of primary particles such as
size and adhesion can change accordingly and thus influence ws
along a cross-shore transect. Our conceptual model illustrates the effect of
varying particle properties on ws independent of the observations
used in our data analysis. However, the course of the parameters implicitly
presumes certain environmental conditions, such as particle size being, among
other factors, a function of SPMC and shear. Single-parameter changes in the
conceptual model result in mostly linear responses in ws, while
considering all parameters leads to a maximum in ws on the
conceptual cross-shore transect, in agreement with our findings in the data
analysis. The assumption of linearly changing parameters is a first-order
approximation. Different and nonlinear changes in parameters would lead to a
transformation of the maximum sinking velocity zone such as a shifting and/or
stretching (not shown). Previous model studies show that for a given shear
regime, varying particle properties such as particle adhesion can lead to a
change in particle size and thus sinking velocity
e.g.,. Hence, higher particle adhesion would translate
to larger particles and stronger fragmentation resistance, which would allow
particles to sink out of the water column closer to the coast under higher
turbulence intensity. This implies that spatial changes in SPMC and
composition, and accordingly physicochemical properties of particles,
potentially affect the location of the transition zone. As discussed below,
this probably happens on a seasonal timescale due to the modulation of the
transition zone by phytoplankton exudations, which requires further
investigations. While the cross-shore distribution of ws is
predominantly controlled by prevailing shear, the conceptual model indicates
a potential additional relevance of physicochemical properties for the
formation of the high-sinking velocity zone.
Implications of a cross-coastal maximum of sinking velocity for biogeochemical cycling in the coastal zone
The region of log10(ϵ)≈-5.5 with highest 〈ws〉 coincides with a zone located off the coast at a depth
of about 15 to 20 m. It is accompanied by a strong gradient in SPMC
and SPM composition that is depicted by the F / SPMC ratio. This suggests
that the region can be considered a transition zone, hindering mineral
particles from escaping further offshore. To simplify this, consider the
course from the coast to open waters. Once formed, relatively dense
fast-sinking flocs, whose properties are adapted to the transition zone
turbulence level, would easily settle out of the water column when
transported offshore. This is because turbulence becomes too weak to break
those aggregates apart and to retain them in suspension. Thus, only loose,
organic-rich particles are kept suspended in the water column while
mineral-rich particles tend to settle out of the water column. Such trapping
is previously described conceptually for other regions, e.g., by
and for river plumes. High 〈ws〉 in the transition zone thus implies an enhanced link
between pelagic and near-bottom processes. Among them, different transport
mechanisms are discussed in the literature that potentially lead, on average,
to a net transport of fine sediments shorewards into the tidal back barriers.
Settling lag is caused by the different time durations for particles
to sediment in different water depths after the bottom shear stress for
erosion falls below the critical stress . Another process
is scour lag, which potentially arises from needing lower bottom
shear stresses to keep particles in suspension than for their erosion in
combination with an asymmetry in the flow . These
effects are investigated under different topographical settings
, and the authors concluded that ws in the
range of 0.5 and 1 mms-1 leads to the highest deposition rates
and underlined the necessity of fine mineral particle flocculation for the
buildup of tidal flat systems. Recently, another potential major driver, the
estuarine circulation, has been suggested for sediment accumulation in the
Wadden Sea. Residual currents of the estuarine circulation are driven by
density gradients that can be caused by (i) horizontal temperature gradients,
(ii) differential precipitation, (iii) river discharges and (iv) all possible
superpositions. Residual currents of the estuarine circulation flow
shorewards in near-bottom waters and offshore in surface waters
. This probably causes a net SPM flux into
the Wadden Sea . The Wadden Sea is
hypothesized to act as bioreactor, where organic components of SPM become
remineralized and are exported in dissolved form
by the offshore-directed
component of the estuarine circulation. Along this pathway, dissolved
nutrients are assimilated by phytoplankton and thus transferred to bio
particulates. This is likely to happen particularly within the region of
prevailing ϵ≈10-5.5 m2s-3, where
phytoplankton experience favorable growth conditions as found by
for different places on the northern European
continental shelf. Algae exude EPSs like TEPs that can undergo and mediate
flocculation by bridging and embedding minerals. The mineral particles
ballast the organic matrix and lead to enhanced sinking velocities, as
previously described for the deep ocean ,
which again links pelagic processes to the residual near-bottom currents of
the estuarine circulation. In summary, this would imply that the transition
zone characterized by its high 〈ws〉 accompanied with
strong SPMC gradients acts as an important off-coastal feature for closing
the nearshore nutrient and mineral cycle. Such a biologically mediated
trapping mechanism would retain nutrients and minerals in the coastal zone
and inside the Wadden Sea back barriers.
Spatial biogeochemical implications of a coastal transition zone
Typically, spatial information on biochemical variables are needed to better
understand system-wide cycling and the fate of matter. Unfortunately,
averaging of ws over bins of ϵ means a possible loss of
direct spatial reference. However, our approach made it possible to identify
a general pattern of 〈ws〉 with a defined maximum
along prevailing energy dissipation rates. Even though we neither resolve
tidal cycles nor consider potential seasonal variation of 〈ws〉 along 〈ϵ〉, a map of 〈ws〉 allows insights into the spatial distribution and
variability of 〈ws〉. It is reconstructed by mapping
the bin-wise relationship found between 〈ϵ〉 and
〈ws〉 (Fig. c) onto the
respective spatial 〈ϵ〉 (Fig. ). It must be
highlighted that local, short-term in situ measurements would most likely
deviate from the obtained averaged picture (Fig. ) that would
be challenging to derive by in situ measurements. Nevertheless, strong
spatial variability is visible with a pronounced cross-shore gradient of
〈ws〉 featuring a maximum of sinking velocities along
the coastline as indicated before. However, this maximum varies locally and
is particularly less pronounced at the northern German and southern Danish
coast, where 〈ws〉 declines to values that are in the
range of 〈ws〉 in deeper waters in the southern
German Bight. Applying the aforementioned concept of the transition zone as
an off-coastal closing mechanism for nutrient cycling to the two contrasting
German Wadden sea regions – East Frisian Wadden Sea and North Frisian Wadden
Sea (particularly the Sylt–Rømø Bight) – may help to better
understand regional differences in nutrient concentrations. Lower nutrient
concentrations and thus lower eutrophication levels in the Sylt–Rømø
Bight compared to the East Frisian Wadden Sea are regularly observed
. In this case, the maximal 〈ws〉 calculated in front of the Sylt–Rømø tidal inlet
amounts only to 4×10-4 ms-1, about half the magnitude
found off the other Wadden Sea regions. Hence, the ability to retain
nutrients is diminished and would contribute to the lower nutrient
concentrations compared to other Wadden Sea regions. By contrast, the
potentially pronounced retention capacity of the transition zone, as
predicted for the Dutch coast and German East Frisian islands, may contribute
to the phenomenologically described line of no return ,
expected further off the coast and characterized by low SPMC. The spatial
distribution of 〈ws〉 is probably also reflected in
the SPMC and their cross-coastal gradients (Fig. ).
Flocs with high ws are likely mineral-dominated and would rapidly
sink out of the water column and thus lead to strong cross-coastal
diminishing of SPMC. Generally, dilution of SPMC occurs due to cross-shore
wise increasing water depth and local currents parallel to the coast
potentially confining horizontal SPMC distribution to the near-coast region
. Nevertheless, on average, lower ϵ accompanied
by lower SPMC and smaller horizontal gradients is found along the North
Frisian than along the Dutch and East Frisian coast (Figs. and
). In combination, these conditions, in particular
along the Sylt–Rømø islands, suppress the establishing of a defined
transition zone. Hence, lower ws should be found as implied by
Fig. . As a result, retention efficiency is likely reduced
and potentially contributes to the observed lower nutrient concentrations
compared to the East Frisian Wadden Sea .
Map of spatial distribution of 〈ws〉 in the
German Bight. Results for 〈ws〉 from
Fig. were mapped onto the modeled 〈ϵ〉 shown in Fig. to provide spatial information
on potentially prevailing 〈ws〉. Areas of water depth
smaller than 5m are not considered.
Top: MERIS-derived temporally averaged SPMC in the German Bight.
Averaging of available MERIS scenes was carried out for the times of the
cruises. Regions of water depths smaller than 5 m were whited out.
Bottom: pixel-wise gradients of SPMC calculated by ∂x〈SPMC〉2+∂y〈SPMC〉21/2, where x and y are east–west and
south–north pixel directions, respectively. A Wiener filter of three by three pixels was
subsequently applied. Notice the stronger gradients along the Dutch and
East Frisian coastline compared to the North Frisian coast with the
Sylt–Rømø Bight at 55∘ N. For regions, see also
Fig. .
Other concepts are presented to explain the observed spatial heterogeneity of
eutrophication levels along the Wadden Sea coast. These explanations are
categorized into two main groups by : either according to (i)
regional differences in organic matter import or (ii) differences in the size
of the tidal basins. Potential differences of the import amount were
attributed to different (i) regional offshore primary production, (ii)
orientation of the coastline with respect to dominant wave and current
directions, and (iii) intensity of shoreward bottom currents. The
eutrophication status can be related to the tidal basin width, where narrow
tidal basins have a higher eutrophication status than wider ones
. While the general buildup of nutrient gradients
towards the coast is attributed to the above discussed processes of settling and scour lag in combination with the estuarine
circulation, no clear mechanistic explanation is given as to why the size of
the tidal basins lead to the relation found.
suggested that POM imported into the tidal basins would be either distributed
over a larger area for wide basins, which would lead to gentle nutrient
gradients compared to steeper nutrient gradients in narrower basins. However,
other explanations cannot be ruled out, e.g., those linked to differences in water
exchange times . It is likely that a multitude of
processes interact, and detailed modeling studies are required to disentangle
their relative contributions to the observed spatial heterogeneity of the
Wadden Sea eutrophication status. Noticeably, the Sylt basin exhibits
exceptionally low eutrophication status in the study of
, which would fit into the picture that the import of
POM is reduced due to the rather weakly established transition zone in this
area.
Since the driving mechanisms behind the transition zone are probably
ubiquitous for coastal marine systems with sufficiently strong cross-shore
water density gradients generated by freshwater runoff,
precipitation–evaporation balance or heat fluxes, local hydrodynamics will
determine its eventual formation. This implies that the concept of the
transition zone with its retention capacity for nutrients may be applicable
to other coastal marine and estuarine systems in general and will help to
better understand different nutrient cycling behavior among those systems.
Biological modulation of the transition zone?
There is increasing evidence that sticky algae excretions such as transparent
exopolymer particles mediate aggregation and increase shear resistance of
particles to fragmentation, potentially enabling algae to clear the water
column from mineral load . As shown in the conceptual
model (Sect. ), high ws occurs due to the
interplay of shear-driven flocculation and primary particle density and size.
Similarly, found a nonlinear effect of the ratio of
mineral–organic weight to weight content on sinking velocity showing first
an increasing ws for increasing mineral load but a stagnation or
even converse effect when exceeding a certain threshold. To hypothesize, a
high concentration of SPM with an optimal ratio between dense mineral and
sticky bio particles might exist in the transition zone under favorable
turbulent conditions to form larger flocs compared to near-coast regions and
denser flocs compared to open waters. In sum, this could lead to the high
〈ws〉 found. This raises the important question as to
what extent algae can affect the transition zone and its seasonal location to
sustain the effective coastal nutrient cycle that is driven by the estuarine
circulation. By sustaining the nutrient cycle, algae potentially support the
development of the pronounced nutrient gradients towards the Wadden Sea. As a
consequence, 3-D biogeochemical models require a representation of the tight
coupling between sediment dynamics and biogeochemical, potentially even
adaptive phytoplankton physiological processes to improve models' capability
to estimate particulate matter fluxes.
Conclusions
The present study provides a strong indication of a maximum of sinking
velocities along a cross-shore transect that is defined by a gradient of
prevailing energy dissipation rates. Towards the offshore areas, the enhanced
sinking velocities are accompanied by a strong decline in SPMC and an
increasing F / SPMC ratio. The interplay of processes leading to the observed
features defines the region as a coastal transition zone. In turn, processes
feed back to SPMC and composition.
The transition zone is probably an important feature on the course from the
coast to the continental shelf. Predominantly driven by turbulent shear
generated by energy dissipation, the transition zone with the highest sinking
velocities potentially acts as a retention zone for dissolved nutrients
leaking from nearshore waters by providing favorable conditions for algae
growth. Phytoplankton take up nutrients and excrete EPSs that mediate flocculation processes. Embedding minerals in the organic matrix leads to enhanced sinking velocities. Algae thus seem to
possess the ability to clear the water column and link
the offshore dissolved nutrient fluxes to residual landward bottom fluxes.
Consequently, these interlinked processes would have the potential to retain
fine sediments and nutrients in coastal areas. The strength of the links
eventually affects the eutrophication state of the coastal region.
It is scarcely understood what relevance individual processes have in forming
the transition zone. Besides favoring energy dissipation rates of about
ϵ≈10-5.5 m2s-3, algae and their extracellular
polymeric excretions are potentially important in forming the transition
zone as EPSs are known to enhance collision efficiency and resistance to fragmentation. Since primary production in the studied area features a
pronounced seasonal cycle, further studies are thus needed to investigate the
temporal and spatial extension of the transition zone. Long-term or repeated
spatial in situ measurements, including SPMC, ϵ profiles
and particle properties such as size, ws and (volume) composition, are
required to underpin the enhanced sinking velocities found indirectly as a
feature of the transition zone. Additionally, modeling approaches are
required to gain a deeper process-based understanding and to disentangle the
closely linked processes among other eutrophication-state-affecting
environmental factors. This also implies the necessity of incorporating biological–mineral interactions in models, especially when system-wide
studies are carried out.