Sediments play an important role in organic matter mineralisation and nutrient recycling, especially in shallow marine systems. Marine ecosystem models, however, often only include a coarse representation of processes beneath the sea floor. While these parameterisations may give a reasonable description of the present ecosystem state, they lack predictive capacity for possible future changes, which can only be obtained from mechanistic modelling.
This paper describes an integrated benthic–pelagic ecosystem model developed for the German Exclusive Economic Zone (EEZ) in the western Baltic Sea. The model is a hybrid of two existing models: the pelagic part of the marine ecosystem model ERGOM and an early diagenetic model by Reed et al. (2011). The latter one was extended to include the carbon cycle, a determination of precipitation and dissolution reactions which accounts for salinity differences, an explicit description of the adsorption of clay minerals, and an alternative pyrite formation pathway. We present a one-dimensional application of the model to seven sites with different sediment types. The model was calibrated with observed pore water profiles and validated with results of sediment composition, bioturbation rates and bentho-pelagic fluxes gathered by in situ incubations of sediments (benthic chambers). The model results generally give a reasonable fit to the observations, even if some deviations are observed, e.g. an overestimation of sulfide concentrations in the sandy sediments. We therefore consider it a good first step towards a three-dimensional representation of sedimentary processes in coupled pelagic–benthic ecosystem models of the Baltic Sea.
Shallow coastal waters are the most dynamic part of the ocean due to the
various effects of natural forcing and anthropogenic activities; they are
characterised by the processing and accumulation of land-derived discharges
(nutrients, pollutants, etc.), which influence not only the coastal ecosystem
but also the adjacent deeper sea areas. Shallow marine ecosystems often
differ significantly from those in the deeper parts of the sea
Remineralisation of organic matter produced in the water column fuels the subsequent release of nutrients and enhances the productivity of these regions At the same time, nutrients can be buried in the sediment in a particulate form Sulfate reduction in the sediments may lead to a release of toxic hydrogen sulfide Benthic biomass and the primary production of benthic microalgae exceeds that of the phytoplankton in the overlying waters Sediments serve as habitats for the zoobenthos, thereby affecting the overlying waters mainly via bioturbation or filtration Other benthic organisms are food for opportunistic benthic–pelagic predator species, whose presence influences the pelagic system as well Organisms typically inhabiting the pelagic may have benthic life stages and therefore rely on sediment properties for reproduction
This list, which could be continued, illustrates the importance of
bentho-pelagic coupling for the functioning of shallow marine ecosystems.
In spite of this importance, the representation of sediments in marine ecosystem models is often strongly oversimplified. This is understandable, since these models are constructed to answer specific research questions, and if these focus on pelagic processes, it can be desirable to represent sediment functions by the simplest possible parameterisations. The drawback of using simple parameterisations is that they are mostly obtained from the present-day state. An example for such a parameterisation could be a percentage of organic matter which is remineralised in the sediments after its deposition and returned to the water column as nutrients. When ecosystem models are used not only to understand the present, but also to estimate future ecosystem changes in response to external drivers, this causes a problem: the use of such simple parameterisations means an implicit no-change assumption. In other words, the quantitative relationships described by the parameterisation will remain unchanged in future conditions, e.g. after the construction of a fish farm or in a changing climate. It is not straightforward to estimate the error introduced into the model system if this assumption is not valid.
An alternative to empirical parameterisations is the use of mechanistic models which try to derive the functionality of the subsystem from process understanding. For nutrient recycling in the sediments, this could be an early diagenetic model which estimates the final nutrient fluxes from a set of individual diagenetic processes.
Our aim is to construct a three-dimensional fully coupled model of pelagic
and sediment biogeochemistry which does not make the no-change assumption.
Specifically, we want to understand the following.
How do changes in early diagenetic processes affect the reaction of a shallow marine ecosystem to climate change? Can pelagic ecosystem modelling provide realistic deposition of particulate organic matter to reproduce the local variability in early diagenetic processes?
In this paper, we report the first successful approaches of this goal: the
construction of a combined benthic–pelagic biogeochemical model formulated in
a one-dimensional, vertically resolved domain. The model is calibrated and
applied to a specific area of interest, the south-western Baltic Sea. It
provides the basis for the development of a three-dimensional framework.
Marine biogeochemical models and process-resolving sediment models are very
similar to each other in terms of their approach. They both try to describe a
complex biogeochemical system with a limited set of state variables.
Transformation processes are formulated as a parallel set of differential
equations
In the simplest case, this coupling is only one-way: water column
biogeochemistry is calculated first and then used as input for a sediment
model. This type of model has been applied, for example, to the North Sea
To the best of our knowledge, the first fully coupled benthic–pelagic model
system with vertically resolved benthic processes was published by
A number of fully coupled benthic–pelagic models have been published for
different regions, each differing in the way the compartments are vertically
resolved. In our study, we use several fixed-depth vertical layers both in
the water column and in the sediment
There are a few successful regional applications of three-dimensional set-ups
with coupled water column and sediment biogeochemistry.
Our region of interest is the Baltic Sea, particularly its
south-western part where coastal marine sediments play an important role in
the transformation and removal of nutrients from the water column. We combine
two existing models which have already been successfully applied in the
Baltic Sea, namely the pelagic ecosystem model ERGOM
The Baltic Sea is a marginal sea with only narrow and shallow connections to
the adjacent North Sea. The small cross sections of these channels, the
Danish Straits, and the correspondingly constrained water exchange have
several implications for the Baltic Sea system.
It is essentially a non-tidal sea. It is brackish due to mixing between episodically inflowing North Sea water with Baltic river waters, which causes an overall positive freshwater balance. It shows a pronounced haline stratification. It is prone to eutrophication due to the accumulation of mostly river-derived nutrients.
The German Exclusive Economic Zone (EEZ) in the Baltic Sea is situated to the
south of the Danish Straits. It consists of different bights, islands and
peninsulas and exhibits a strong zonal gradient and a strong temporal
variability in salinity. This varies from 12 to over 20 g kg
Understanding and quantifying the scope and scale of such sedimentary
services in the German Baltic Sea has been the aim of the SECOS project (The
Service of Sediments in German Coastal Seas, 2013–2019). The project
contained a strong empirical part, including several interdisciplinary
research cruises focused on sediment characterisation. Seven study sites
were selected based on different granulometric parameters, each of them
representative of a larger area. These were sampled several times in order to
capture the effect of seasonality on biogeochemical functioning (see
Fig.
In the study area, different types of sediments dominated by varying grain
size fractions are found ranging from sand to mud. This implies differences
in the biogeochemical processes associated with organic matter mineralisation
and physical processes that are responsible for pore water and elemental
transport in the sediment and across the sediment–water interface. Due to
its relatively larger grain sizes, sand acts as a permeable substrate,
which means that lateral pressure variations may induce the advection of
interstitial water. These pressure variations may be caused by waves or by
the interaction between horizontal near-bottom currents and ripple formation.
In muddy sediments, in contrast, molecular diffusion often controls the
transport of dissolved species, which may be superimposed by the
bioirrigating activity of macrozoobenthos
These substantial differences cause differences in the biogeochemical
properties of the substrate types. Pore water advection in permeable sediments
not only transports solutes but also particulate material. Fresh and
labile organic matter (POC and DOC) from the fluff layer can be quickly
transported into permeable sediments, the latter in this way acting as a kind
of bioreactor. The typically low contents of reactive organics in sand led
for a long time to the consideration of sands as “geochemical deserts”
As mentioned earlier, the transport of fluffy layer material from coast to
basin areas is an important process in our region of interest. Previous
studies with a pelagic ecosystem model
This article is structured as follows. In Sect.
In this section, we give a description of the combined benthic–pelagic model.
We start in Sect.
The core of the model is obviously the biogeochemical processes represented
within it. Their description therefore forms the major part of this
paper. Biogeochemical processes in the water column are described in
Sect.
The model description is completed by details on numerical aspects given in
Sect.
The combined benthic–pelagic model is based on two ancestors.
The water column part is based on ERGOM, an ecological model developed
originally for the Baltic Sea ERGOM is typically used in a three-dimensional context as a part of marine
ecosystem models. With some modifications, it has been applied for different
ecosystems such as the North Sea The sediment part is based on a model developed for a study on the effect of
seasonal hypoxia on sedimentary phosphorus accumulation in the Arkona Sea
Like the present one, the model by
Since our model is a purely biogeochemical model, it requires a physical
environment in which it is embedded. In a final, three-dimensional
application, this will be a hydrodynamic host model, and the biogeochemical
model described in this communication will be coupled into it. Since we do an
intermediate step first and run the model in one-dimensional set-ups, we need
to provide physical quantities as model input. The variables which influence
the biogeochemical processes in the water column are
temperature, salinity, light intensity, bottom shear stress and vertical turbulent diffusivity.
These are prescribed by forcing files
The one-dimensional model consists of four compartments as shown
schematically in Fig. the water column, a fluff layer deposited on the sediment surface, the sedimented solids and the pore water between them.
The water column and sediment are vertically resolved, with the former in
layers of 2 m depth such that their number depends on the water depth of the
specific site and the latter in 22 layers increasing in depth from 1 mm at the
sediment surface to 2 cm at the bottom of the modelled sediment at 22 cm
of depth. These specific numbers are not intrinsic to the model but can be
changed in the input files
Tracers used in the ERGOM SED v1.0 model.
W: water column, F: fluff layer, S: solid sediment, P: pore
water,
The chosen vertical resolution must be seen as a compromise between speed and
accuracy. Especially for the 3-D application, we want to keep the numerical
effort of the calculations as small as possible. A comparison to a run with
double resolution is shown in Appendix
Sediment porosity is prescribed
Schematic view of the compartments and vertical exchange processes in the model. Compartments: (I) water column, (II) fluff layer, (III) pore water, (IV) solid sediment. Both the water column and sediment consist of several vertically stacked grid cells. Vertical transport processes: a – turbulent mixing, b – particle sinking, c – sedimentation, d – resuspension, e – bioirrigation combined with molecular diffusion, f – bioturbation, g – sediment growth, h – burial. Bioactive solid material is shown in orange, bioinert solid material in grey and water in blue.
The tracers (model state variables) present in each of the compartments are
listed in Table
Total alkalinity is a parameter describing the buffering capacity of a
solution against adding acids; it describes the amount of a strong acid that
needs to be added to titrate it to a pH of 4.3. In our model, it is
represented as a “combined tracer”, which means that its rate of change
depends on its constituents (
The state variables will not be discussed one by one here, but rather in the
section about the biogeochemical processes
(Sect.
The processes which transport the tracers vertically are schematically shown
in Fig.
Horizontal exchange (transport) is neglected in our one-dimensional model.
This is obviously an inadequate approximation for the water column processes,
as we do not consider basins, but rather single stations, some of which are
situated in proximity to river mouths where lateral transport processes have
a major impact
In this model, we are not specifically interested in the water column as such but rather see it as being responsible for delivering the right amount of sedimenting detritus at the right time. To obtain this, we relax the wintertime nutrients in the surface layer to a realistic value. This may be seen as a parameterisation of a lateral exchange process. In addition, transport of fluff layer material away from or towards the modelled location is a lateral process included in the model. The physical processes which are explicitly included in our model are described here.
Vertical exchange due to turbulent mixing in the water column is
prescribed externally
In our model, suspended particulate matter sinks at a constant rate through
the water column. We choose 4.5 m day
Shear stress at the bottom determines whether erosion or sedimentation takes
place. We apply the combined shear stress of currents and waves calculated by
the same MOM5 model as the turbulent mixing. If this shear stress
In our model, no material will ever be resuspended from the sediment itself,
which starts below the fluff layer. This means that our model is incapable of
realistically capturing extreme events like storms or bottom trawling which
winnow the upper layers of the sediment, removing organic material, which has
a lower sinking velocity, by separating it from the heavier mineral
components
In environments with oxic bottom waters, we assume that in addition to waves
and currents, macrofaunal animals or demersal fish can resuspend organic
material from the fluff layer by active movements
Bioturbation describes the movement and mixing of particles inside the
sediment caused by the zoobenthos. While bioturbation in reality
causes both a transport of solids and solutes, we use the term
“bioturbation” in the model to describe the transport of solids only, while
the transport of solutes is done by the “bioirrigation” process.
We consider bioturbation to act as a vertical diffusivity
The diffusivity
The value 3 mm describes a volume estimate of SPM (suspended particulate
matter) taken from this region: typical SPM concentrations in the lowermost
40 cm of the water column are about 8 mg L
The vertical structure of bioturbation intensity,
In the uppermost part of the sediment, we assume a constant bioturbation
rate. Below that, it decays exponentially with depth until it reaches a
maximum depth, which may be below the bottom of our model. So, we externally
prescribe (a) the maximum mixing
intensity
The present formulation of the model has no explicit dependence of bioturbation depth on the availability of oxidants, i.e. bioturbation will take place in oxic as well as in sulfidic environments; adding this dependence should be essential if the model is applied to sulfidic areas.
Bioirrigation describes the mixing of solutes within the pore water and the
exchange with the bottom water. We describe it as a mixing intensity
Molecular diffusion in the sediment can be described by the equation
A diffusive exchange between the pore water and the overlying bottom water is
controlled by the thickness of a diffusive boundary layer. While in reality
this relates to the viscous sublayer thickness and is therefore inversely
related to the velocity of the bottom water
In reality, the diffusive boundary layer thickness is on the order of 1 mm at
low-bottom-shear situations and becomes even shallower if the bottom shear
increases
Molecular diffusivities for the different solute species are calculated from
water viscosity following
In nature, sediments grow upwards as new particulate matter is deposited onto
them. In our model, this process is taken into account, but represented as
the
downward advection of material in the sediment. So, our coordinate system
moves upward with the sediment surface. We assume that the sediment growth is
supplied by terrigenous, bioinert material and
prescribe
We use a simple Euler-forward advection to move the material from each grid
cell into the cell below. Material leaving the model through the lower
boundary is lost. Except for organic carbon, we assume that a part of it is
mineralised, as will be explained in
Sect.
The Baltic Sea sediments can be classified as accumulation, transport and
erosion bottoms
For the sandy and silty sediments, we assume transport away from the site.
This is described by a constant removal rate for all material deposited in
the fluff layer. For the mud stations, we assume transport of organic
material towards the site. This is described by a constant input of detritus.
Our model contains six detritus classes which degrade at different rates, as
will be explained later in Sect.
In the 3-D version of the model, these processes are no longer required, as the material is dynamically removed from the shallow sites and transported to deeper ones by advection.
In this subsection, we will describe the equations of motion solved by the
model. The equations in the water column can be derived from the assumption
that the vertical (upward) flux of a tracer can be described by an advective
and a diffusive flux, which follows Fick's law:
The equations in the sediment are different because we need to take porosity
into account and treat dissolved tracers (in the pore water) and solid
tracers differently. For the pore water tracers, the upward flux is given by
For particulate tracers, we also consider storage in the fluff layer,
Boundary conditions are required for the partial differential equations given
above. We give two boundary conditions for the water column concentrations:
one at the sea surface,
The pore water tracers have a zero-flux boundary condition at the bottom of
the model:
At the sediment–water interface, we assume that the dissolved tracers are
exchanged between pore water and the water column via a diffusive boundary layer
of a depth
To satisfy mass conservation, the vertical flux applied as the lower boundary
condition for the dissolved species concentrations in the water column
depends on the upward flux from the sediment:
Now the boundary conditions for the particulate state variables are different. The reason is that the water column and the sediment do not directly interact, but we consider the fluff layer as an intermediate layer between the two. Particulate material which sinks to the bottom is deposited in the fluff layer, from which it is incorporated into the sediments.
At the bottom of the water column, there can be two possible situations.
If the bottom shear stress is lower than the critical shear stress, we assume a deposition of particulate material.
This sinking material If the bottom shear stress exceeds the critical shear stress, particulate material from the fluff layer is eroded and enters the water column.
In both cases, we additionally consider the bioresuspension process which was
described above in Sect.
The fluff interacts with the surface sediment layer in two ways. Firstly,
sediment growth means an incorporation of fluff layer material into the
surface sediments. Secondly, bioturbation, which is considered
diffusion–analogue mixing, leads to an exchange of particulate material between
the fluff layer and surface sediment. So, the boundary condition for solids at
the sediment surface is given by
The concentration change in the fluff layer is then defined by mass
conservation and is simply given by
Reaction network table for the processes in the water column. See
Table
Finally, the burial of particulate material at the lower model boundary can
be described by the following boundary condition:
In this section, we describe the biogeochemical processes acting in the water
column. These are mostly identical to previously published ERGOM versions
A reaction network table giving the reaction equations, including their
stoichiometric coefficients, is given in Table
There are three classes of phytoplankton in the model, representing
large-cell and small-cell microalgae as well as diazotroph cyanobacteria.
Their growth is determined by a class-specific maximum growth rate, but
contains two limiting factors for nutrients and light. The light limitation
is a saturation function with optimal growth at a class-specific optimum
level or at 50 % of the surface radiation. The shortwave light flux at the
surface is taken from a dynamically downscaled ERA40 atmospheric forcing
However, according to
We assume a constant respiration of phytoplankton which is proportional to its biomass. As the model maintains the Redfield ratio, the degradation of biomass (catabolism) goes along with the excretion of ammonium and phosphate. This simplified description of phytoplankton growth does not describe day–night metabolism or temperature dependence. A small fraction of the nitrogen is released as dissolved organic nitrogen (DON). In the model, this represents the DON fraction which is less utilisable by phytoplankton, while the fraction with high bioavailability is considered to be part of the ammonium state variable.
Due to simplification, in our model phytoplankton experiences a constant background mortality, although we know this is far away from reality in which it is species specific and depends on abiotic (e.g. nutrient, light, etc.) and biotic conditions. An additional mortality is generated by the grazing of zooplankton as described next.
Zooplankton is only represented as one bulk state variable. It grows by assimilating any type of phytoplankton; however, it has a smaller food preference for the cyanobacteria class compared to the other classes. The uptake becomes limited by a Michaelis–Menten function if the zooplankton's food approaches a saturation concentration. Feeding can only take place in oxic waters and is temperature dependent. It shows a maximum at an optimum temperature and a double-exponential decrease when this temperature is exceeded.
Both zooplankton respiration and mortality represent a closure term for the model. They are meant to include the respiration and mortality of the higher trophic levels (fish) which feed on zooplankton, and therefore we use a quadratic closure. Mortality is additionally enhanced under anoxic conditions, which do not occur in our study area.
The description of detritus Throughout the paper, we use the
term “detritus” in its biological meaning; here, it describes dead
particulate organic material only, as opposed to its use in geology, where
the term includes deposited mineral particles.
Details on the specific choice of the classes are given in
Appendix
The mineralisation is, however, temperature dependent by a
When organic detritus is created by plankton mortality, it is partitioned
into the different classes in a constant ratio. This ratio was determined
from a fit of the multi-G model to an empirical relation between detritus age
and its relative decay rate, which was proposed by
The chemical composition of detritus is, in contrast to phytoplankton and
zooplankton, not determined by the Redfield ratio. It is enriched in carbon
and phosphorus by 50 % such that it has a C : N : P ratio of 159 : 16 : 1.5. This
resembles detritus compositions as they were determined in sediment traps and
by investigating fluffy layer material in the Baltic Sea
In the water column, detritus can be mineralised by three different oxidants: oxygen, nitrate and sulfate. They are utilised in this order; if the preferential oxidant's concentration declines, the specific pathway is reduced by a Michaelis–Menten limiter and the next pathway takes over such that the total mineralisation is held constant. In all pathways, DIC, ammonium and phosphate are released. Nitrate reduction also produces molecular nitrogen (heterotrophic denitrification), while sulfate reduction generates hydrogen sulfide.
Mineralisation of particulate organic carbon in transparent exopolymers takes place via the same pathways, but only releases DIC. DON is also mineralised after some time and decays to ammonium (which may represent the transformation to bioavailable DON compounds).
In the presence of oxygen, ammonium is nitrified to nitrate
In the sediments, we additionally assume that
Dissolved phosphate can be adsorbed to iron oxyhydroxide particles suspended
in the water column. In the same way, phosphate adsorbed to iron oxyhydroxide
particles can be released if the ambient concentration of phosphate is low.
The process is identical to the one in the sediments and is discussed in
Sect.
In this section, we qualitatively describe the sedimentary biogeochemical
processes contained in the model. For a quantitative description including
the model constants, we refer to the Supplement.
Figure
Reaction network table for the primary redox reactions in the
sediment and the fluff layer. See Table
Reaction network table for the secondary redox reactions in the sediment and in the fluff layer.
Reaction network table for adsorption–desorption and precipitation–dissolution processes in the sediment and in the fluff layer.
The stoichiometry of the processes included in the model is shown in three
reaction network tables.
Primary redox reactions are given in Table Secondary redox reactions are given in Table Adsorption–desorption and precipitation–dissolution reactions are given in Table
Simplified sketch of state variables and processes in the sediment model. Boxes to the left and right indicate sediment and pore water state variables, respectively. pH is not a state variable but calculated from DIC and total alkalinity. Red arrows show primary redox processes driven by the oxidation of organic carbon. The red numbers indicate the order in which the oxidants are utilised. Black arrows show secondary redox reactions, which means reoxidation of reduced substances. Blue arrows show adsorption–desorption or precipitation–dissolution reactions, which may depend on pH. Abbreviations: det – detritus, Rhodoc. – rhodochrosite, tot.Alk. – total alkalinity, DIC – dissolved inorganic carbon.
The mineralisation of detritus is the dominant biogeochemical process in the sediments, as the oxidation of the carbon therein is the major supply of chemical energy for microbes.
As in the water column, oxidants are utilised in a specific order, and a
smooth transition to the next mineralisation pathway occurs when the
preferred one gets exhausted. However, the number of possible oxidants is
increased in the sediment, as here solid components may also act as electron
acceptors. The order in which they are utilised is oxygen, nitrate, manganese oxide, iron oxyhydroxide, Fe (III) contained in clay minerals and sulfate.
After sulfate is exhausted, typically the formation of methane would start.
This process is omitted in the current model, as we designed our model for
the top 22 cm of the south-western part of the Baltic Sea, where we do not
expect sulfate to be limiting. This depth restriction is based on the
limited length of the sediment cores taken in the empirical part of our
research project. We do, however, describe the process implicitly, since we
assume that a part of the organic carbon which leaves the model domain
through the lower boundary will be transformed to methane, which as it
diffuses upward will be oxidised by sulfate and generate
As in the water column, we distinguish six different classes of detritus with different basic mineralisation rates.
Details on the specific choice of the classes are given in
Appendix
These rates are only controlled by temperature, not by the specific oxidant
which is available. There is an ongoing controversy as to what determines the
rate of sedimentary carbon decay and whether it is the oxidant (and therefore
the accessible energy per mole of carbon) or the degradability of the
detrital carbon itself Middelburg's
equation states that material which is decomposed later will be decomposed
slower. This may be because the material itself is different or because the
oxidant is different. The Middelburg model includes both effects, and
splitting them in a mechanistic model would mean preferring one theory or the
other. So what we do assume if we just apply the Middelburg model is that the
time which a particle spends in the oxic zone, the anoxic zone and the
sulfidic zone is similar in our setting to Middelburg's experiments. In this
case, the Middelburg model will include the correct slowing-down of
degradation caused by the less efficient oxidant.
Sedimentary organic phosphorus (OP) may degrade faster than the corresponding
nitrate and carbon, an effect known as preferential P mineralisation
Here, we describe the implementation of the primary redox reactions, indicated
by the red numbers in Fig.
Oxic mineralisation and heterotrophic denitrification are formulated in the
same way as in the water column; see Sect.
The next pathway is the reduction of Mn (IV) to Mn (II), which produces dissolved manganese.
The reduction of iron oxyhydroxides should produce dissolved Fe (II). This,
however, may precipitate very quickly, especially where hydrogen sulfide is
present. So for numerical reasons, we combine these reactions, and the
reduced Fe (III) is directly converted into iron monosulfide or considered as
adsorbed by clay minerals, as we describe below in Sect.
Some clay minerals, especially sheet silicates which are abundant in the
German part of the Baltic Sea
The primary redox reaction follows process 32 in
Table oxygen concentration is low, nitrate concentration is low, manganese oxides in the sediment are depleted and iron oxyhydroxides in the sediment are depleted, but reducible structural Fe (III) in the clay minerals is still abundant.
Sulfate reduction produces hydrogen sulfide. As discussed above, it
represents the terminal mineralisation process in our model. This process,
described by processes 33 and 34 in Table
Solids can precipitate from a solution when it becomes supersaturated. This
happens in an aqueous solution when the actual ion activity product exceeds
the respective solubility product and a critical degree of supersaturation is
reached
Diagenetic models often simplify the calculation by multiplying the
concentrations rather than the activities
Ca–rhodochrosite precipitates at elevated concentrations of manganese and
carbonate. Its solubility product is composition dependent, as the Ca : Mn
ratio varies
If the solution becomes undersaturated, rhodochrosite will be dissolved
again. Then, process 53 is reversed, and a fixed amount of
Iron monosulfide precipitates on contact with dissolved Fe (II) and sulfide,
depending on pH, with a solubility product taken from
We then assume a precipitation or dissolution of iron monosulfide, which
relaxes the present concentration of Fe (II) against this equilibrium. This is
in agreement with a pore water chemistry model for the central Baltic Sea
As a simplification, we neglect the change in porosity which would be caused by precipitation (or dissolution) of any solids.
Pyrite (
An additional pathway which does not rely on elemental sulfur, but instead
reduces hydrogen sulfide to hydrogen gas, has been proposed by
In our model, the reaction therefore follows process 39 in
Table
Adsorption in our model takes place on the surfaces of two particle types:
iron oxyhydroxides and clay minerals. Adsorption on silicate particles is not
explicitly represented in the model, but parameterised by a reduction of the
effective diffusivity of phosphate and ammonium, following
Iron oxyhydroxides adsorb dissolved phosphate. This is a well-known process
responsible for the sedimentary retention of phosphate derived from
mineralisation processes
Following
Clay minerals, due to their large surface area, can also adsorb pore water
species. We allow for an adsorption of phosphate, ammonium and Fe (II). For
simplicity, we assume that the ratio of adsorbed species to clay mass is
proportional to the pore water concentration until a saturation threshold is
exceeded. For Fe (II), this proportionality constant is derived from
To calculate
For numerical reasons, we allow for an immediate precipitation of the desorbed Fe (II) as iron monosulfide in the case of oversaturation, leaving out the intermediate transformation to dissolved Fe (II). The inverse is also true: if iron monosulfide is dissolved, the released Fe (II) may directly be adsorbed by the clay minerals instead of being released to the pore water first.
This is described by process 52 in Table
For the adsorption isotherm of phosphate on clay minerals, we follow the
study by
For ammonium adsorption to clay minerals, the processes are in principle
identical to those of phosphate. Since the adsorption is weak compared to
that of phosphorus
Reduced substances can be reoxidised if the appropriate oxidant is present in
a sufficient concentration. Table
Ammonium is oxidised to nitrate in the presence of oxygen. The rate of this process is proportional to both the ammonium and the oxygen concentration and, as in the water column, increases exponentially with temperature.
Dissolved manganese (II) will be oxidised in the presence of oxygen and precipitates as manganese oxide. This is also assumed to be a second-order process proportional to both precursor concentrations.
Dissolved Fe (II) is oxidised by oxygen in a pH-dependent way. The rate of this
process is proportional to the Fe (II) and oxygen concentration, as well as to
the square of the hydronium ion concentration. It is also influenced by
temperature and ionic strength, as described by
Structural iron in clay minerals can be reoxidised as well. We only allow this process in the presence of oxygen, when it transforms back to Fe (III), which is kept bound in the clay minerals.
This reaction follows process 43 in Table
Reaction network of secondary redox reactions in the sediment, giving the possible reoxidation processes in the presence of the oxidants listed in the first row.
Hydrogen sulfide can reduce any of the previously mentioned oxidants being
converted to sulfate. The reaction with oxygen or nitrate is carried out as
a two-step reaction. The intermediate species formed in these reactions is
elemental sulfur, which can be further oxidised to sulfate. These processes
follow the same kinetics as in the water column; see
Sect.
This reaction follows process 47 in Table
Iron monosulfide is typically not directly oxidised but dissolves at low sulfide concentrations. However, if it is exposed to oxygen, we assume complete oxidation to Fe (III) and sulfate.
Finally, pyrite can be oxidised in the presence of oxygen or manganese (IV),
but in marine environments not by Fe (III)
The carbon cycle in this model is included, following pH, total alkalinity (TA), dissolved inorganic carbon concentration (DIC) and
Knowledge of any two of them allows for the determination of the other two
parameters. We use TA and DIC as state variables. The reason for this is that
both pH and
The DIC concentration can increase by the mineralisation of organic carbon and
decrease when DIC is assimilated by phytoplankton. Also, it can be modified
by
The tracer value changes by 1 unit if (see Table
As the pH (for adsorption and precipitation reactions) and
The sum of all their alkalinities should then match the total known
alkalinity, but a difference occurs because the approximated pH was
incorrect.
So, we do a Newton iteration to find an improved pH estimate.
This is done by calculating the derivative
Finally, we can calculate
The equations which determine the temporal evolution of the state variables
are solved by a mode-splitting method; i.e. concentration changes due to
physical and biogeochemical processes are applied alternately in separate
sub-time steps. For a discussion of this method and alternatives we refer to
Vertical diffusion is done explicitly by multiplying each vertical tracer
vector by a diffusion matrix. This includes turbulent mixing in the water
column as well as pore water diffusion, bioturbation (faunal solid transport)
and bioirrigation (faunal solute transport). This diffusion matrix is
tridiagonal, and for a small time step, which is in our case limited by the
thin layers at the top of the sediment, a Euler-forward method can be
applied. Larger time steps could be split into smaller Euler-forward steps,
which means a repeated multiplication by the tridiagonal matrix. We instead
use an efficient algorithm to calculate powers of the tridiagonal matrix
The sources and sinks for the different tracers are calculated from the process rates. These include not only biogeochemistry, but also parameterisations for lateral transport processes as well as sedimentation and resuspension.
To calculate the changes in a tracer concentration with time, we form the sum
of the processes consuming or producing it
The model code is not handwritten. Instead, the model is described in a
formal way in terms of its tracers, constants and processes in a set of text
files. The model code is then generated by a code generation tool (CGT)
which fills this information into a code template file. The advantage is
that the same biogeochemical equations can in this way be integrated into
different models. While the current version is written in Pascal, the
three-dimensional version in MOM5 has been created as a Fortran code. The CGT
is open-source software and can be downloaded at
We use four different observational datasets for model calibration and validation. The data used are (a) pore water profiles for different dissolved species, (b) sediment elemental composition, (c) estimates of bioturbation intensity and (d) bentho-pelagic fluxes measured in benthic chamber lander incubations.
All data were collected at seven different stations in the southern Baltic
Sea (see Fig.
All the stations were sampled during 12 cruises which took place between
July 2013 and January 2016 to cover different seasons
Short sediment cores with intact sediment–water interfaces were taken by a
multicorer, a device which simultaneously extracts eight sediment cores from the
sea floor. Pore water was extracted at different depths by rhizones. For a
detailed description of the analytical methods used, we refer to
Instead of directly comparing sulfate concentrations between model and
reality, which change over time with salinity, we use the sulfate deficit
defined as
Parallel sediment cores from the same multicorer casts as used for the pore
water analysis were subsampled in 1 cm steps, freeze-dried under vacuum and
homogenised for geochemical analyses. Total carbon (TC) as well as nitrogen
(TN) and sulfur (TS) contents were measured by combustion, chromatographical
separation of the released gases and their determination with a thermal
conductivity detector. The total inorganic carbon (TIC) content was measured
by acidic removal of carbonates and analysis of the released
In order to analyse bioturbation intensities (
Total oxygen uptake (TOU) and bentho-pelagic nutrient fluxes (
Porosity and sediment accumulation rate data used as model input and clay volume content estimated by the model based on an initial guess.
There are three ways in which observations feed into our model:
model constants which were derived in earlier studies and which our model
adopted from previous models; initial and boundary conditions determining tracer concentrations at the
beginning and throughout the model run; and calibration data which help to confine uncertain model parameters during a
repeated model calibration process.
Most of the observations which help constrain our model processes enter our
model indirectly, since model constants are inherited from ancestor models.
Especially in
The initial conditions for most biogeochemical state variables in the water
column are taken from the previous run of a three-dimensional ERGOM model as
described in Sect.
In contrast, fluff and sediment were initialised empty. We allowed them to fill up with material derived from the water column during the simulated period of 100 years. While this period of 100 years is not sufficient to fill the considered 22 cm of sediment by accumulation, it is sufficient to almost reach a steady state in the pore water concentrations. While the sixth class of detritus, which is considered non-biodegradable, continues accumulating in the sediments after 100 years, those classes which affect the pore water concentrations decay on smaller timescales.
Since the model conserves nitrogen and phosphorus, the filling of the sediments would have led to a depletion in the water column. To overcome this, we relax the winter concentrations of dissolved inorganic nitrogen and phosphorus (DIN and DIP) against values obtained from the previous 3-D model run. This relaxation is applied every winter, so the nutrients required to fill the model domain are provided from an artificial external source. Their input is large at the beginning of the model run and decreases over time as the sediment reaches a state which is almost in equilibrium with the organic matter supply from the water column above.
Pore water profiles from
Please note that the physical input data and initial conditions used during
the model optimisation phase were taken from a preliminary, unpublished 3-D
model run. It differs from the cited model version
The first step in such an optimisation is to define a metric or a penalty function quantifying the misfit between model and observations. Our aim is then to minimise this function.
We chose to penalise the relative deviation between model and measurement and define the penalty function by
This term differs per variable, but is the same
at each station and sampling depth.
The pore water species fitted are ammonium, phosphate, silicate,
sulfide, iron, manganese, the total alkalinity and the relative sulfate
deficit Defined as
After we defined a penalty function, the second step is to choose an
algorithm to minimise it. Several such algorithms exist; however, our choice
of methods was restricted by the relatively long runtime of a single model
iteration. Since it took about 8 min to run a single station for 100 years, we had to choose methods which
needed a relatively small number of iteration steps and therefore allowed for a high degree of parallelism in the individual optimisation step in order to effectively search the 115-dimensional parameter space.
Our first choice was the Adaptive Hierarchical Recombination–Evolutionary
Strategies (AHR-ES) algorithm implemented in the R package calibraR
Therefore, our second choice was a simple alternative algorithm: our own
extension of the generalised pattern search (GPS) algorithm
The optimisation converged after 30 iteration steps and reduced the error function from 6363 (the value obtained by previous manual tuning) to 4797.
The algorithm obviously does not guarantee that we reach a global optimum, which can be seen as a drawback. The automatic method was started after manual calibration of the model. Since the optimisation method is deterministic, the local optimum is defined by this initial condition. However, in a vector space with a dimension as high as ours, it is anyway difficult to find a non-local point with a better score, no matter if it is by manual optimisation or a different search algorithm.
For the sand stations and the single silt station, the automatic optimisation resulted in an unrealistic set of parameters. The bioturbation rates were estimated as low as those of the mud stations. However, at these low bioturbation rates, the sediments failed to accumulate realistic amounts of organic matter. The pore water profiles we obtained, however, seemed to match the observations relatively well. This was due to the fact that the realistically low concentrations of solute species were obtained by an unrealistically low incorporation of degradable particulate material into the sediments. The model assumed relatively high rates of lateral removal of fluff such that only a small fraction of the locally produced detritus was actually processed in the sediments.
This illustrates the problem that if the diffusivity is unknown, very
different transports can be caused by the same pore water gradient. We
therefore decided to manually modify the solution. This modification meant
raising bioturbation and bioirrigation intensity by a factor of 10 at each
station. Afterwards we reduced the parameter
This led to similar pore water profiles, but higher turnover rates and organic content in the sediments.
In this section, we compare and discuss the observed and simulated pore water profiles of several chemical species relevant for early diagenetic processes. Model results are taken from the last year of the 100-year simulation, which was driven by a repeated forcing every year. After this simulated period, the model almost reached a quasi-steady state, which means the annual cycle of pore water concentrations was nearly repeated year after year at each of the stations. The sixth class of detritus, in contrast, which we defined as non-degradable, did not reach a stable concentration, but continued to accumulate in the sediment during the period of 100 years, but this continued accumulation did not influence the pore water profiles due to the fact that it was assumed to be bioinert.
Figure
Pore water concentrations of several dissolved species at the three
mud stations Lübeck Bight
In the left panels, we see that the rise of alkalinity with depth is captured well by the model, except for the AB site where observations show a higher alkalinity below 10 cm of depth. The decline in sulfate follows the lower range of the observations.
The panels in the second column show that the vertical profiles of ammonium and silicate are also represented relatively well by the model. However, especially at the Arkona Basin station, the observed range of both ammonium and sulfide shows strong variation (by an order of magnitude). The model does not capture that but rather sticks to the lower range of the observations. Most probably, the variability in the observations is not due to seasonality, but a consequence of spatial variability between sampling sites, since the samples were taken from two sites 23 km apart.
Surprisingly, the model is able to reflect the differently steep sulfide
profiles between the stations LB and MB. While
The right panels show that the modelled manganese concentrations match the observations quite well. The dissolved iron profiles show their maxima at the correct depths and a relatively large seasonal spread. The measurements show an even larger spread than the model. For the phosphate profiles, the model results mostly resemble the lowest of the measured values, except for station AB where we see a clear underestimation. This can be seen as an artefact of our fitting method, more precisely of the choice of our penalty function. Giving a penalty for the relative error means that the same absolute error is punished more heavily if the observation is smaller, making the model try harder to fit low values compared to high ones.
The model results for the mud stations fit quite well, considering the fact that the real pore water profiles may be shaped by very different temporal variations. These include, for example, mixing events, changing loads of organic matter, or temperature and salinity variations. Our model, not knowing the sediments' past, can only try to estimate the average conditions that might produce similar pore water concentrations.
Figure
Pore water concentrations of several dissolved species at the three
sand stations Stoltera
All of the sandy stations have one major error in common: sulfide concentrations are strongly overestimated at depths below 5 cm. We suppose that the precipitation or reoxidation of sulfide is underestimated. For all other pore water species, the agreement between measured and modelled ranges is reasonable. The rise of alkalinity with depth is especially well captured by the model. The sulfate deficit in the empirical data has a large uncertainty, as it is calculated as a small difference of similarly large quantities.
In our model, the sandy sites show a more pronounced seasonal cycle in the pore water profiles compared to the muddy stations. Especially iron and manganese concentrations vary considerably due to the seasonally different supply of quickly degradable organic matter and corresponding differences in mixing intensity. While the variability in the supply of fresh organic matter is captured by the model, the variation in mixing is not. Still, the simulated ranges are supported by the variability in the observed pore water concentrations.
Pore water concentrations of several dissolved species at the silt station Tromper Wiek. Points and horizontal lines indicate the range of measurements. Curves and shading present the model results and indicate year-average concentrations and the seasonal range.
For the station Tromper Wiek, we used data from two different cruises in April and June 2014. Even if the idea in the SECOS project was to repeatedly sample the same station, the locations were approximately 6 km apart for this station, and the substrate type at the station sampled in April was sand rather than silt. The amount of sulfide in the pore waters showed a large difference between the April and the June cruise, with the latter concentrations exceeding the former by a factor of 20. This reflects spatial rather than temporal variations. Some of the depth intervals were only sampled during the June cruise, which explains the different observed ranges at the different depths.
The good agreement in the profiles of ammonium and phosphate (middle and
right panel in Fig.
Mass fractions of nitrogen (blue), sulfur (yellow) and organic carbon (black) in the dry sediment: model results (curves and shading for seasonal range) versus measurements (vertical segments). Please note that the scales on the horizontal axes differ by a factor of 40.
In Fig.
For the mud stations LB and MB, the modelled element concentrations show a quantitative agreement with the measurements. The main difference is that the measured values show strong vertical fluctuations, which may be the result of the deposition history. Another difference is that the vertical gradients of sulfur are considerably steeper in the model than in reality. In the mud station AB (Arkona Basin), however, the actual concentrations of all three elements are heavily underestimated. Nonetheless, the depth gradients of the concentrations match quite well, so there is perhaps just a constant offset. This might be caused by the accumulation of bioinert organic material, possibly of terrigenous origin from the Oder River.
In all sand stations (ST, DS, OB), the amount of sulfur in the sediments is underestimated. The observed sulfur in the sediments varies with depth and shows a maximum at around 10 cm of depth. The fact that sulfide, in contrast, was overestimated in the pore waters, suggests that the precipitation of sulfur may be underestimated in the sandy cores. Particulate N and TOC are present in realistic quantities at the OB station. At the other two sand stations, the N and TOC observations show maxima at the top (station DS) or bottom (station ST) of the profile, which are not captured by the model. These are most likely the traces of past sedimentation or bioturbation events.
Reproducing subsurface TOC maxima, as they occur in permeable sediments,
represents a challenge for early diagenetic models. They can be caused by
different processes, such as
non-local, fauna-driven ingestion of fluff material into a specific depth, washout of organic material from the surface sediment e.g. during storm events or lateral relocation of sediments.
The empirically estimated bioturbation intensities span a large range at each
station. A reason for this may be that while our model assumes a temporally
constant bioturbation, in reality it is highly variable. Mixing events by
animals or shear stress alternate with periods without mixing
In Fig.
Fluxes between the sediment and bottom water of selected pore water species at mud stations. Positive values denote fluxes out of the sediment. Solid line: modelled fluxes between sediment and bottom water only. Dashed line: fluxes including mineralisation of the fluff layer material. Dots: measured fluxes by two benthic chambers (BC1 in red and BC2 in green). Vertical ranges: uncertainties of these fluxes estimated by a bootstrapping method. For phosphate: full circles are estimates based on phosphate determination by photometric methods, and open circles are estimates based on P quantification by the ICP-OES method.
The automatic model calibration yielded diffusivities at the sand and silt
stations which were as low as those at the mud stations. Such weak mixing,
however, could not supply enough organic matter to the sediments to reach
measured element compositions. Therefore, they were corrected upwards,
resulting in higher mixing at the sandy than at the muddy sites. This agrees
with recent estimates of the bioturbation potential
The net fluxes of selected pore water species (
Fluxes between the sediment and bottom water of selected pore water species at sand stations. Positive values denote fluxes out of the sediment. Solid line: modelled fluxes between sediment and bottom water only. Dashed line: fluxes including mineralisation of the fluff layer material. Dots: measured fluxes by two benthic chambers (BC1 in red and BC2 in green). Vertical ranges: uncertainties of these fluxes estimated by a bootstrapping method. For phosphate: full circles are estimates based on phosphate determination by photometric methods, and open circles are estimates based on P quantification by the ICP-OES method.
The comparison of annual average oxygen fluxes between the model and measurements
shows a reasonable quantitative agreement. Taking the rather high
fluctuations in the measurements into account, we cannot assume a perfect
fit. The model correctly reproduces the fact that similar oxygen consumption
occurs at sand and mud stations in spite of their order-of-magnitude
differences in organic content and pore water concentrations
In this paper, we applied our model in a one-dimensional context. The aim was to reproduce early diagenetic processes taking place in the sediments at seven exemplary sites thought to be representative for the south-western Baltic Sea by a mechanistic model. In our fully coupled model, the pelagic biogeochemistry and an assumed lateral transport supplied the organic material which drove the early diagenetic processes in the sediments. A comparison to a variety of different observations showed that the model gives a reasonable reconstruction of sediment biogeochemistry. Still, we found differences in the details. For example, a strong overestimation of sulfide concentrations in sandy sediment pore waters most likely points to the underestimation of sulfide precipitation–reoxidation.
The analysis we show suggests that the processes most relevant for these observations are adequately represented in the model. This does not include all parts of the model. For example, the nitrogen cycle was not compared to observations, which is due to the fact that the project SECOS, in which this work was done, did not focus on it and so the required observations of nitrification or denitrification rates are missing.
The ultimate aim of the model is its application in a fully coupled
three-dimensional framework. A fully coupled pelagic and benthic model could
answer a wide range of questions such as the following.
Are the strongly simplifying sediment parameterisations which we use in marine
ecosystem models today consistent with our understanding of sediment biogeochemistry, or
is there a mismatch between our assumptions in the pelagic models and the sediment–water fluxes in early diagenetic models, which are directly constrained by observational data? How might sedimentary services such as nutrient removal change under different
conditions, and what feedbacks into pelagic biogeochemistry can be expected? On which timescales can organic material stored in the sediments affect the eutrophication status
of the pelagic ecosystem, e.g. for how long will sedimentary nutrient release counteract nutrient abatement
measures aimed at reducing the winter nutrient concentrations in the water column?
The applicability of the one-dimensional model is limited. There is little added value in using this coupled benthic–pelagic model compared to a classical early diagenetic model, since in most cases a one-dimensional description of a pelagic ecosystem will be strongly oversimplified. One could, however, imagine that it can be useful for enclosed marine areas where the horizontal exchange is limited or well known. An application to an area other than the south-western Baltic Sea will, however, require a new model calibration, since critical parameters like bioturbation intensity might differ. We strongly discourage the use of the model as it is by just applying it to derive estimates of benthic biogeochemical process rates from pelagic biogeochemistry unless there is a large set of benthic data available against which the model can be validated.
In cases in which these data are available, we think that the model system has high potential to serve as a starting point for detailed studies because it can be easily modified. Adding, removing or adapting processes is very easy because of the automatic code generation principle. Only a formal mathematical formulation of the process is required, and no coding skills are needed to e.g. add additional state variables to the model system. Reuse of parts of the model, e.g. the explicit representation of the fluff layer, is also possible.
In this paper, we describe an integrated model for ocean biogeochemistry. It simulates ocean biogeochemistry both in the water column and in the sediments.
The model was obtained by combining two ancestor models: the water column
model ERGOM closing the carbon cycle in the sediments, which allows for the determination of pH, adding a specific numerical scheme for the diffusion of the tracer “total alkalinity”, using ion activities rather than concentrations to determine precipitation and dissolution potentials, allowing us to account for salinity differences, the explicit description of adsorption to clay minerals considering their mineralogy, and an alternative pyrite formation pathway via
An automated model calibration approach was used to fit the model to pore water observations at seven sites in the study area. It was successful for the mud stations, but underestimated bioturbation rates and consequently the organic content of the sediment at the sand and silt sites. Therefore, these model parameters were adjusted manually at the sand and silt sites. This issue illustrates a general problem related to models of this complexity. The large quantity of unknown model parameters results in many degrees of freedom, and different types of observations are needed to constrain them. Even so, a good fit to a constrained set of observations does not guarantee that the model dynamics are captured realistically.
Applying the model in a three-dimensional framework
Apart from these constraints, the implementation of the model in a 3-D framework is straightforward. Physically, the coupling between different locations would be controlled by the fluff layer and its erosion and redeposition. Technically, the coupling is simplified due to the use of automatic code generation. Describing the model processes and constants in a formal way, keeping them separate from code for specific models, means it is easy to switch between different “host models”. The major difficulty in going 3-D is the limited amount of validation data, such as pore water profiles and sediment–water fluxes, compared to the strong spatial and temporal variability. A first step is the application of the model to the limited area of the German EEZ for which the model is calibrated.
In the long term, biogeochemical ocean models should aim at a process-resolving description of surface sediments. This is especially true for shallow ocean areas where the efflux of nutrients from the sediment strongly influences water column biogeochemistry, like in our study area. The magnitudes of denitrification and phosphate retention, or the spatial and seasonal patterns in which oxygen consumption occurs, may strongly influence marine ecosystems.
Very often, model studies discussing “what if” scenarios use a relatively simple sediment representation. This includes studies on nutrient abatement, human-induced stresses on ecosystems (e.g. by fish farming) and climate sensitivity analyses. But the use of a present-day parameterisation for future scenarios means a neglect of possible changes. In the context of limited data and process understanding, this implicit “no-change” assumption may be the best we can presently do. But we should be aware of the uncertainty introduced by this pragmatic choice. Studying the sensitivity of sediment functions to external drivers in a process-resolving sediment model can be a way to quantify these uncertainties and possibly derive an ensemble of alternative future parameterisations.
A source code version of the model can be obtained from
The code is not handwritten, but can be generated automatically from a set of text files describing the model biogeochemistry and a code template containing the physical and numerical aspects of the model code. All three ingredients required to obtain the model source code (the text files, the code template and the code generator program) are also included.
These components in their current and previous versions are GPLv3 licenced
and can also be downloaded from our website at
For the calibration and validation data used in this study, we refer to the
following publications: the pore water data can be found in
The stoichiometric composition of the model tracers is shown in
Table
Stoichiometric composition of tracers.
Tracer
The study by
Decay rates of different classes of detritus.
We assume a faster detritus mineralisation at higher temperatures. This is
controlled by a factor
Decay rates of organic carbon in detritus depending on its time of creation. Comparison of the reactivity predicted by our model at different temperatures to the Middelburg decay rate prediction; see text.
Here, we use a set of sensitivity experiments to illustrate how the model
refinements introduced by us influence the results. In each of these, we
switch off one of our model improvements. This means that we use three
simplified model versions, in which
total alkalinity always diffuses with the bicarbonate diffusivity
no matter how many hydroxide ions contribute to it, which in reality diffuse faster, the saturation indices for precipitation–dissolution reactions are calculated neglecting the (salinity-dependent) activity coefficients, and the adsorption of ammonium, phosphate and iron onto clay minerals, as well as their reducible Fe (III) content, is neglected.
As an example, we apply these reduced models to the silt station TW. (Please
note that the calibration procedure was not repeated after the model
modifications, but the model parameters were left unchanged.)
The results are shown in Fig.
Pore water concentrations of several dissolved species at the silt
station Tromper Wiek. Points and horizontal lines indicate the range of
measurements. Solid curves and shading present the model results and indicate
year-average concentrations and the seasonal range. Dashed curves show the
same, but for a model version which neglects one of our improvements:
We used vertically constant porosity in our application of the model. Here, we
illustrate the effect of this simplification by comparison to a model with a
realistic porosity profile; see Fig.
In Fig.
Pore water concentrations of several dissolved species at the silt station Tromper Wiek. Points and horizontal lines indicate the range of measurements. Solid curves and shading present the model results and indicate year-average concentrations and the seasonal range. Dashed curves show the same, but for a model version with double vertical resolution.
For solutes, we assume that the flux (positive upward) between two
neighbouring cells takes the form
This allows us to construct a matrix
We approximate the limit by choosing
An identical approach is used for the solids.
The supplement related to this article is available online at:
HR developed the model and performed the simulations. ML, DB, CM and JW carried out the experimental work and obtained the data which went into model calibration and validation. MEB, SF, TL, GR and BC contributed to the interpretation of the results and the structuring and formulation of the article. TN was the work package supervisor and developer of the pelagic ecosystem model.
The authors declare that they have no conflict of interest.
This study is embedded in the KÜNO project SECOS (03F0666A) funded by the German Federal Ministry for Education and Research (BMBF). The model optimisation runs were performed on the HLRN supercomputing facilities. Free software which supported this work includes R, R Studio and Free Pascal Lazarus. Marko Lipka and Michael E. Böttcher wish to thank Iris Schmiedinger, Anne Köhler and Iris Scherff for their invaluable help in the laboratory. They also wish to express their gratitude to Bo Liu for helpful discussions on transport processes. Jana Woelfel and Gregor Rehder thank Peter Linke and Stefan Sommer for the long-lasting loan and technical support (Sergiy Cherednichenko) of the two mini benthic chamber landers (GEOMAR, Kiel, Germany). Edited by: Sandra Arndt Reviewed by: three anonymous referees