OSOcean ScienceOSOcean Sci.1812-0792Copernicus GmbHGöttingen, Germany10.5194/os-10-993-2014Sensitivity of phytoplankton distributions to vertical mixing along a North
Atlantic transectHahn-WoernleL.l.hahn-woernle@uu.nlDijkstraH. A.Van der WoerdH. J.https://orcid.org/0000-0002-8901-7567Institute for Marine and Atmospheric Research Utrecht (IMAU), Dept.
of Physics and Astronomy, Utrecht University, P.O. Box 80.005, 3508 TA
Utrecht, the NetherlandsInstitute for Environmental Studies (IVM),
Free University of Amsterdam, the NetherlandsL. Hahn-Woernle (l.hahn-woernle@uu.nl)11December2014106993101131January201414March201423October201411November2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.ocean-sci.net/10/993/2014/os-10-993-2014.htmlThe full text article is available as a PDF file from https://www.ocean-sci.net/10/993/2014/os-10-993-2014.pdf
Using in situ data of upper ocean vertical mixing along a transect in the
North Atlantic and a one-dimensional phytoplankton growth model, we study
the sensitivity of the surface phytoplankton concentration to vertical mixing
distributions. The study is divided into two parts. In the first part, the
model is calibrated to the observations. The optical model parameters are
determined from measurements of the light attenuation. The biological
parameters are calibrated to three different reference stations with observed
vertical profiles of the chlorophyll a (Chl a)
concentration and the nutrient concentration. In the second part, the
sensitivity of the three model calibrations to the vertical mixing is
studied. Therefore measured vertical mixing profiles are applied to the
model. These mixing profiles are based on the measurements along the transect
and are treated as a set of possible mixing situations of the North Atlantic.
Results show that shifts in vertical mixing are able to induce a transition
from an upper chlorophyll maximum to a deep one and vice versa. Furthermore,
a clear correlation between the surface phytoplankton concentration and the
mixing induced nutrient flux is found for nutrient-limited cases. This may
open up the possibility to extract characteristics of vertical mixing from
satellite ocean colour data using data-assimilation methods.
Introduction
Thanks to long-term in situ and satellite observations of ocean surface
chlorophyll a (Chl a) concentrations, the plankton
variability can be studied on timescales longer than seasonal. On
interannual-to-decadal timescales, Chl a concentrations show
changes that correlate well to variations in climate indices such as the
North Atlantic Oscillation . Long-term trends in
Chl a were presented in based on a century long
database of in situ Chl a and ocean transparency measurements.
Although the results are under debate, it is clear that long-term trends in
Chl a are non-uniform over the globe and well correlated to the
increase in sea surface temperature (SST). For the North Atlantic (north of
20∘ N), found an average rate of increase of
about 0.0071 mg m-3 yr-1 over
the last century. On a shorter timescale (decades), however, much larger
local variations are observed .
The most significant feature of the local Chl a variations is a
phytoplankton bloom. Although the actual cause for the bloom is still not
clarified, most of the theories consider vertical mixing as a key factor in
its onset . The growth progression is
described as follows: during winter, the deep mixing brings nutrients into
the euphotic layer. Simultaneously, the deep mixing distributes the
phytoplankton over the euphotic layer and below, reducing the total exposure
to photosynthetically active radiation (PAR). During spring, the shallowing
of the mixed layer (ML) exposes the phytoplankton to more PAR. This enhances
growth at the surface and leads to an upper chlorophyll maximum (UCM) given
that enough nutrients are available .
Since PAR is absorbed by the phytoplankton, less of it reaches below the UCM
where growth becomes light limited. The shallowing of the mixed layer also
reduces the nutrient entrainment into the euphotic layer. As the warm season
proceeds the necessary nutrients (e.g. phosphorus and nitrogen) become
depleted in the ML, resulting in less phytoplankton growth at the surface.
Consequently, PAR can again penetrate below the ML to the nutrient richer
water. The dominant phytoplankton growth is shifted below the ML. A so-called
deep chlorophyll maximum (DCM) is formed. The DCM is the most dominant
appearance of phytoplankton in strongly stratified regions such as the
subtropical North Atlantic.
Since stratification is strongly connected to the SST, climate warming could
have a strong influence on the Chl a concentration. Qualitative
mechanisms aiming to explain the consequences for Chl a
concentrations due to climate warming have, for example, been suggested by
. In areas where phytoplankton is nutrient limited, e.g. in
the mid-latitude Atlantic, an increase in SST will inhibit vertical mixing
and lead to stratification. In a warming ocean the transport of nutrients
into the upper ocean is hence expected to decrease. In areas where the
phytoplankton is light limited, such as in the northern North Atlantic, a SST
increase will reduce the depth of the ML (MLD) and hence one would expect an
increase in phytoplankton. The fact that this trend is not observed in
high-latitude regions according to data in indicates that
vertical mixing processes are not solely controlled by stratification.
Indeed, it is known from basic upper-ocean turbulence measurements and theory
that, apart from the surface buoyancy forcing, vertical mixing is also
strongly dependent on the surface wind-stress forcing. In addition, the
background stratification can also be substantially affected by advection of
heat and salt due to ocean currents, and in particular by the presence of
meso-scale eddies .
In order to understand the Chl a patterns at the surface, the
turbulent processes controlling the upper ocean need to be understood. The
mixing coefficient KT [m2 s-1] is a measure for the vertical mixing of heat and salt. At any
particular location in the open ocean, the vertical profile of KT is
determined by the background stratification (or buoyancy frequency N), the
turbulent kinetic energy dissipation rate ε and a mixing
efficiency . Over the last decade, microstructure
turbulence measurements of the upper ocean have been carried out along a few
sections in the Atlantic Ocean, see for an overview. Using
a microstructure profiler, the distribution of KT along a south–north
transect in the eastern North Atlantic during the STRATIPHYT-I cruise in
July–August 2009 and the STRATIPHYT-II cruise in April–May 2011 was
determined . The averaged station profiles
of KT along this section clearly indicate high values in the upper ML and
a decrease near its base. At some locations the profiles of KT slightly
increase below the ML before background values of
10-5–10-4 m2 s-1 are approached at about 100 m depth.
Satellite ocean colour observations (MODIS-AQUA) of August 2009 indicate a
meridional gradient in Chl a with values increasing northward. The
combined observations support the correlation between stratification and
growth: while the stratification leads to a nutrient limitation in the ML in
the south, it enhances growth in the ML due to higher PAR availability in the
north. In spring 2011, satellite ocean colour observations are characterised
by a high concentration around 45∘ N and decreasing Chl a
concentrations north and south of this. In situ vertical mixing profiles of
KT indicate that the water column is stratified up to about 45∘ N.
Further north the water column is almost homogeneously mixed down to 100 m
depth . The low Chl a
concentrations in the north follow thus from light limitation.
The effect of vertical mixing on phytoplankton distributions is difficult to
monitor in the ocean and it is common to do laboratory experiments and use
ocean–phytoplankton models . The results in show that the state of the
phytoplankton profile is strongly dependent on the strength of the vertical
mixing. studied the effect of stratification on the model
state and forced the system into DCM and UCM states by changing the strength
of the vertical mixing. These models, however, contain a number of uncertain
parameters both in the turbulence model and in the plankton model.
Many experiments and measurements are made to determine for example the
growth rate of individual phytoplankton species under certain environmental
conditions . Results show that growth rates do not only
vary between species but also due to environmental changes. Alternatively,
parameter values can be “tuned” to observations at one particular
well-observed location and the response of the model at other locations to a
different surface forcing is studied under the assumption that the tuned
parameters do not change . Only in very special
circumstances is a vertical profile of the mixing coefficient KT
available for verification of the quality of the turbulence model used
.
This work is motivated by the availability of an observed integral picture
(forcing, mixing, nutrients, phytoplankton, optical properties) over the
eastern North Atlantic during summer 2009 and spring 2011 from the STRATIPHYT
cruises. Using ocean–plankton models and data-assimilation methods we
eventually aim to tackle an ambitious inverse problem: given the
meteorological surface forcing, can we estimate the vertical mixing
coefficient KT of the upper ocean based on satellite-derived ocean colour
data? The sensitivity of the phytoplankton growth to changes in vertical
mixing plays a key role in this problem, even more so when trying to
reproduce it in a model. As a first step, we study here the effect of
different vertical mixing profiles on the modelled surface phytoplankton
concentration. Thereto we use the advection–reaction–diffusion phytoplankton
model by , which we calibrate to the in situ measurements
of three STRATIPHYT stations. To study the effect of the vertical mixing on
the phytoplankton growth, the three model calibrations are run under
different mixing conditions. These conditions are based on the KT
measurements of the STRATIPHYT cruises and are treated as a representative
set of vertical mixing situations common for the North Atlantic. The
calibration of model parameters to a specific location in the North Atlantic
and the subsequent use of measured vertical mixing profiles for the
calibrated model distinguishes this work from previous sensitivity studies.
The aim is to improve the understanding of the effect of small-scale
variances in the vertical mixing on the phytoplankton growth.
The paper is structured as follows. In Sect. , the relevant
satellite data and the measurements of the STRATIPHYT cruises are presented.
Next, in Sect. , the phytoplankton model is presented and its
calibration (e.g. parameter tuning) is discussed in Sect. . The
main analysis of the sensitivity of the equilibrium phytoplankton
distributions to the vertical mixing profiles is presented in
Sect. . Finally, in Sect. the results are
discussed and conclusions are formulated.
Data
For the analysis presented in this paper, we use both satellite colour data
as well as in situ data measured during the STRATIPHYT cruises. Additional
information on the data can be obtained from
http://oceancolor.gsfc.nasa.gov and
http://projects.nioz.nl/stratiphyt, respectively.
Satellite data
During the past decades the range of applications for satellite data and
their reliability has improved significantly. An important application is the
measurement of Chl a surface concentration which can be used as a
measure for the phytoplankton concentration close to the ocean surface. The
data are based on the reflectance of blue and green wavelengths and can
therefore only be obtained for the first metres of the water column.
Figure b shows 1∘×1∘ box averaged and
monthly mean values of the Chl a surface concentration recorded by
the MODIS on the Aqua satellite. To retrieve the Chl a
concentrations from MODIS Aqua ocean colour data, the OC3M algorithm
is used. The data are plotted along the ship track in
the North Atlantic during the STRATIPHYT cruises (shown in
Fig. a) over the years 2009 to 2011. Black data points
correspond to gaps in the data, e.g. due to high cloud coverage or the lack
of sunlight.
(a) Bathymetry of the North Atlantic with the track of the
STRATIPHYT cruises. The colours show the water depth in metres. (b)
MODIS Aqua chlorophyll a surface concentration plotted along the
track in (a). The black crosses and pluses indicate measurement
stations during the STRATIPHYT cruises in summer 2009 and spring 2011,
respectively.
The daily mean Aqua MODIS PAR data is used in the model to determine the
intensity of the incoming PAR at each station. In situ data would have been
also available, but would have been too sparse and variable to determine the mean
incoming PAR over an entire day. In order to facilitate the reading, the term
light is used instead of PAR when dealing with the model.
In situ data
During the two STRATIPHYT cruises in summer 2009 and spring 2011 the ship
stopped at one latitudinal station per day to measure several depth profiles.
Though these measurements give only snapshots into the vertical structure of
the North Atlantic, there is evidence that they are a
good representation of the seasonal characteristics. We refer
to the data sets of the 2009 and 2011 cruises as summer data and spring data,
respectively.
The obtained temperature microstructure measurements were used to derive
depth profiles for the vertical mixing coefficient KT according to the
Osborn and Cox model . KT was computed from the
temperature variance dissipation rate, χT, according to
KT=χT2∂T‾∂z-2;χT=6DT∂T′∂z2‾,
where DT is the molecular diffusivity of heat (≈1.4×10-7 m2 s-1). The overbar indicates a
trimmed-smoothed-sharpened-filtered and depth-binned quantity and T′ is the
temperature fluctuation part (for details see ).
In Fig. the station-mean, smoothed and interpolated
profiles for KT are shown for both cruises
. Here, the profiles are smoothed over
windows of 5 m depth to guarantee the compatibility with the numerical
scheme used in the phytoplankton model, as will be explained below. The MLD
is defined as the depth at which the temperature difference with respect to
the surface is 0.5 ∘C . In spring, the MLD
ranges between 20 and 60 m for stratified stations up to 46∘ N.
Further north, the water column is nearly homogeneously mixed. In summer, the
profiles of the mixing coefficient show stratified characteristics for all
stations with maximum values of the MLD around 45 m. The strength of the
vertical mixing and its vertical properties change both seasonally as well as
latitudinally.
Interpolated and smoothed vertical mixing coefficient in spring
(top) and summer (bottom) along the transect in Fig. a. The
dashed curve indicates the MLD.
For the model implementation, missing data points within the vertical profile
were linearly interpolated and profiles were smoothed over windows of 10 m
depth. This is done to guarantee the compatibility with the diffusion scheme
used in the phytoplankton model.
Figure shows the phytoplankton concentration measured
during the spring and the summer cruise, respectively. The profiles were
derived from CTD fluorescence measurements in units of the Chelsea Aqua 3
Chl a concentration [g L-1]
. For the model the data needed to be converted from
Chl a to cells. The ratio of Chl a per cell can vary
significantly depending on species and environmental conditions. Up to now
there is no universal equation explaining this complex relation
. Therefore a general ratio of 0.2×109 cells (µg Chl a)-1 is chosen for simplicity. This ratio is based on the
cell : nutrient content ratio and the nutrient content : Chl a
ratio given by and , respectively.
Phytoplankton cell concentration converted from the interpolated and
smoothed Chl a concentrations measured during the spring (top) and
summer (bottom) cruise. The dashed curve indicates the MLD.
During spring, well-mixed stations at the northern part of the transect show
a homogeneous distribution of phytoplankton over the first 100 m. Further
south and especially during summer, stratification forces the phytoplankton
to grow either within the mixed layer in a UCM, or to grow below the mixed
layer in a DCM.
Figure as well as the MODIS Aqua data in
Fig. b show that the further north one observes the surface
Chl a concentration, the later the transition from the UCM to the
DCM happens, if at all. At latitudes north of 45∘ N surface
concentrations remain relatively high throughout the entire light season,
while regions south of 45∘ N exhibit very low Chl a
concentrations during summer. Irrespective of the latitude, locally and
temporally restricted surface Chl a maxima are also seen independent
of the stratification cycle. These maxima have been suggested to be connected
to ocean eddies .
In situ measurements of PAR at the water surface and over the water column
were measured with optical sensors attached to a CTD profiler. The profiles
are used to determine the optical parameters (see Appendix A).
In situ measurements of phosphate (PO4), nitrogen dioxide (NO2) and
nitrate (NO3) show that there is a gradient in the nutricline between
south and north . According to the measured data, the water
column provides sufficient nutrients for the phytoplankton to grow close to
the surface in the northern stations, a so-called mesotrophic state. At
stations further south the surface layer is practically depleted of nutrients
and therefore oligotrophic. The transition between the oligotrophic and the
mesotrophic stations lies at about 40∘ N during the spring cruise
and at about 45∘ N during the summer cruise. The comparison with the
Chl a profiles in Fig. shows that these are also
the latitudes of transition from an deep chlorophyll maximum (DCM) to an
upper chlorophyll maximum (UCM).
In the model only one generalised nutrient concentration is used and the
measurements of PO4, NO2 and NO3 are in the following summed up and
generalised as nutrient concentration.
The phytoplankton model
The phytoplankton model is a simple one-dimensional model based on the
advection–reaction–diffusion models of and
. Figure provides a sketch of the basic
model setup and the processes controlling growth and phytoplankton
distribution in the model. Phytoplankton cells need nutrients and light to
grow and their number is reduced at a constant rate representing
sedimentation and grazing. Sunlight penetrates the water at the surface and
its intensity decreases exponentially with depth due to the background
attenuation of sea water and the absorption by phytoplankton cells. Vertical
mixing is represented as a depth-dependent diffusion coefficient and it
distributes nutrients and phytoplankton cells over the one-dimensional water
column.
Governing equations
In a water column of depth Zb the concentration of phytoplankton
cells at time t>0 and vertical position z∈[0,Zb], where
z=0 indicates the surface and z is positive downwards, is denoted by
P(z,t) (Fig. ). The two controlling factors for
phytoplankton growth are the concentration of nutrients N(z,t) and the
intensity of light I(z,t). The coupling of nutrient and phytoplankton
dynamics is described by the following two equations :
∂P∂t=growth-loss-sinking+vertical mixing=μ(N,I)P-mP-v∂P∂z+∂∂zKT(z)∂P∂z,
∂N∂t=-uptake+recycling+vertical mixing=-αμ(N,I)P+εαmP+∂∂zKT(z)∂N∂z,
where μ(N,I) describes the local growth. Furthermore, m is the
mortality, v is the sinking velocity, KT(z) is the depth-dependent
vertical mixing coefficient, α is the nutrient content of a
phytoplankton cell and ε is the nutrient recycling coefficient.
Schematic representation of the processes and the setup of the
model.
Standard values used in the model.
SymbolDescriptionUnitsValueSystem parametersZbDepth of the systemm150IinIncident light intensityµmol photons m-2 s-1390–625NbNutrient concentration at Zbmmol nutrients m-35.7–12.7KTVertical mixing coefficient (depth dependent)m2 s-11.0 × 10-5–0.85Optical parametersKbgBackground attenuation of sea waterm-10.032kAbsorption coefficient of phytoplanktonm2 cell-11.0×10-9Biological parametersμmaxMaximum specific growth rateh-10.04HIHalf saturation constant of light limited growthµmol photons m-2 s-185–186HNHalf saturation constant of nutrient limited growthmmol nutrients m-30.0425–0.1001mSpecific loss rateh-10.01αNutrient content of phytoplanktonmmol nutrients cell-11.0 ×10-9εNutrient recycling coefficient–0.034–0.5vSinking velocitym h-10.042Numerical parametersΔzSpatial stepm0.25ΔtTemporal steph240
No-flux conditions are assumed at the surface z=0 for both the
phytoplankton concentration and the nutrient concentration. At the bottom
boundary, z=Zb, the nutrient concentration is prescribed as
constant value Nb, which represents an infinite source of
nutrients in the deep ocean. The magnitude of this source is latitude
dependent and based on measurements as discussed below and shown in
Table . The initial phytoplankton concentration P is
based on the measured profiles. At the bottom boundary the no-flux condition
is applied. Since the boundary lies well below the euphotic layer, this is
only important for cases of very strong mixing. Generally, the cells die
before they reach the bottom boundary, which is in agreement with the
measurements. Further description as well as standard values of the
parameters can be found in Table .
Growth and loss couple P to N via the uptake of nutrients and the partial
recycling of dead phytoplankton cells. The growth rate μ(N,I) has a
strong local dependence on the available resources and is written as
μ(N,I)=μmaxminNHN+N,IHI+I,
where μmax is the maximum growth rate of phytoplankton and HN
and HI are the half-saturation constants of nutrient-limited growth and
of light-limited growth, respectively. For example, the value of HN is
relatively low for species which are well adapted to nutrient-limited
regimes.
The intensity of light as a function of vertical position z and time t is
given by the Beer–Lambert equation
I(z,t)=Iinexp-Kbgz-k∫0zP(ξ,t)dξ,
where Iin denotes the intensity of the incoming light at the
surface of the water column. The intensity of light within the water column
decreases with depth due to a constant background attenuation represented by
Kbg. Additionally, each phytoplankton cell absorbs light which
leads to a shading effect on the whole water column below the cell. This
effect is represented by the integral over P times k in
Eq. ().
The total nutrient budget consists of all nutrients stored as nutrients and
as phytoplankton cells. In a steady state it is constant and from
Eqs. () and () (including the boundary conditions) it
follows that
KT(Zb)∂N∂zZb=(1-ε)mα∫0ZbP(z)dz.
This means that in the steady state the nutrient flux coming into the system
at the bottom boundary is balanced by the nutrient loss due to the
inefficient recycling.
Numerical implementation
All model parameters are given in Table . Parameters for
which a range of values is given change with latitude and season of the
observation. All parameters remain constant during one model run. The depth
of the system is chosen to be well below the euphotic layer and the other
system parameters can be directly defined from measurements. Initial profiles
of the phytoplankton concentration and the nutrient concentration are read in
from the observations. To fulfil the boundary conditions, the nutrient
concentration at Zb is fixed to the 10 m mean of the deepest
values per station. The vertical mixing is defined by the measured,
vertically varying mixing profiles of KT(z) shown in
Fig. .
The optical parameters and some of the biological parameters will be
determined from the observations in the following section. All other
biological parameters are based on .
To solve the differential Eqs. () and () the NAG
D02EJF routine is used (see for more details http://www.nag.co.uk). The
temporal step size for the integration is determined by the routine itself to
guarantee that the integration is stable and efficient at the same time. The
model state is saved to a file every 10 days. The inhomogeneous profiles of
vertical mixing can vary by three orders of magnitude. To guarantee a
sufficient spatial resolution a grid spacing of Δz=0.25 m is
applied. In all simulations, the model is run a minimum of 1000 days and
until it reaches an equilibrium. To determine the equilibrium the relative
change per time step is defined as
R=maxP(t)-P(t+Δt)P(t),N(t)-N(t+Δt)N(t),
where |⋅| defines the absolute value. The equilibrium is reached for R≤1×10-4.
Before applying realistic vertical mixing profiles, results in
and are successfully reproduced to test
the model. These computations have been done with homogeneous vertical mixing
in the non-stratified case and an artificial vertical mixing profile in the
stratified case (based on a generalised Fermi function, see
, for more details).
Calibration of the model
The biological data of the STRATIPHYT project show that the Chl a
profiles originate from compositions of different phytoplankton species
. Simulating the phytoplankton growth at STRATIPHYT with
the simple model presented here (one generalised phytoplankton community)
requires the calibration of the biological parameters to the measured data.
The optical parameters are determined by combining Eq. () with
the measured light profiles. Details of the method are described in the
Appendix and the results are given in Sect. .
In Sect. , two of the biological parameters are calibrated in
order to reproduce the observations at three different stations. The three
sets of parameters obtained are assumed to characterise the phytoplankton
community at a given location and during the given season. The results of the
optical and biological parameter calibration are discussed in
Sect. .
Optical parameters Kbg and k
The transmittance of light in water can be affected by waves and a high
concentration of small air bubbles at the surface as well as phytoplankton,
sediments and dissolved organic material in the water column. Since surface
effects are very localised and sediment concentrations are very low in open
water they are both not taken into account in the analysis. Our aim is rather
to identify the characteristics of the light attenuation due to the two major
contributions: the background attenuation of sea water Kbg and
the absorption coefficient of phytoplankton k.
Figure in the Appendix shows an example of CTD data of
fluorescence, surface irradiance and corrected irradiance (percentage of
surface irradiance measured at depth, see Appendix A for definitions and
calculations). For the calibration the fluorescence and corrected irradiance
profiles are divided into two sections: a Chl a free section at the
bottom of the euphotic layer to determine Kbg and a section with
a high Chl a concentration in the euphotic layer to determine k.
Figure shows that values of Kbg derived from DCM
states are homogeneously spread around their mean of 0.032 m-1 and more
scattered in spring. Stations with a UCM tend to show higher values.
Homogeneously mixed stations were not qualified for the analysis since they
do not have Chl a free sections. Since the UCM states can be
effected by e.g. backscattering (see Sect. for detailed
discussion), the value of Kbg is set to 0.032 m-1.
Based on the determined Kbg value, results for k are shown in
Fig. . For the summer data, values have a mean of
5.9 ± 1.9 ×10-10 m2 cell-1 and the state of
the station does not seem to influence this result. The mean k derived from
the spring data is more than twice as high. To take both seasons into
account, k=10-9 m2 cell-1 is chosen.
Biological parameters HI, HN and ε
When calibrating the biological model parameters with the help of the
observations, the model is run with a certain parameter set until it reaches
an equilibrium and the result is compared to the observations. In order to
efficiently compare the model result with the observations the least
squares method (LSM) as implemented in the NAG E04FCF (an unconstrained
optimisation solver) is used. The routine changes the biological parameters
with the aim of minimising the sum of squares S defined as
S=∑i1-CmodiCmeasi2,
where Cmodi and Cmeasi are characteristics of the
model results and the observations, respectively. The definition of these
characteristics depends on the state of the observations. In the case of a DCM,
the main characteristics are the depth and the value of the DCM. In the case of a
UCM, the main characteristics are the mean phytoplankton concentration and
the mean nutrient concentration within the ML. This categorisation into
states and characteristics needs to be done because the model cannot
reproduce the small-scale vertical variations in the observations. The
normalisation by Cmeasi allows to compare values of different
orders equally (e.g. the depth with the concentration of O(P)=8).
The phytoplankton growth is controlled by several environmental factors, such
as light and nutrient availability. The limitation of one factor can lead to
dramatic changes in concentration and vertical location. A DCM is known to
establish due to nutrient limitation in the upper layer, while a UCM
establishes when sufficient nutrients are available at the surface and it
limits the growth at depth due to a low light availability below the ML. For
the model it follows that the controlling growth parameter in the case of the
DCM should be the half-saturation constant of nutrient-limited growth HN
and in case of the UCM, it should be the half-saturation constant of light-limited growth HI.
Additionally the recycling coefficient ε, which connects the
nutrient budget to the phytoplankton budget (see Eq. ), is
calibrated. This coefficient incorporates two important mechanisms, the
sedimentation and the remineralisation of dead phytoplankton cells. Choosing
a constant value is a crude simplification of the model, which is improved by
the calibration to the biochemical environment. In contrast to m and
α, which also play a central role in Eq. (),
ε does not directly impact the phytoplankton concentration but
only indirectly due to the change in the local nutrient concentration.
The measured profiles are assumed to be in a steady state. Since the model is
incapable of reproducing the fine-scale variations of the vertical profiles,
the calibration focuses on two main features of the measured profile. These
features depend on the state of the system (DCM, UCM or homogeneously mixed)
and have to be reproduced by the model which makes it possible to calibrate the
parameters ε and HI, respectively HN. In the case of a DCM
dominant features are the depth of the DCM and its associated maximum
phytoplankton concentration. In the case of a UCM state, the mean phytoplankton
concentration and the mean nutrient concentration within the ML are defining
the dominant features.
The model parameters are calibrated to two stations of the summer cruise that
have different steady states, a DCM and a UCM. The DCM is measured at the
southern part of the track (40.5∘ N) and the UCM at the northern
part (60.7∘ N). These stations are in the following referred to as
the southern and northern station, respectively. Additionally, a station of
the spring cruise at 44.3∘ N is used. The observations show a clear
UCM in spring and a deep DCM in summer (see Fig. ). This
station is referred to as the transition station, because of the change of
states with the seasons.
In Table the value ranges for the calibration and the
final results as well as the station-specific boundary conditions are given.
The fixed biological parameters are based on values of previous work by
and a number of runs to test the sensitivity and behaviour
of the model (Table ).
The southern station
At the southern station, the measured vertical mixing profile is generally
about four times stronger in the upper 25 m than in the lower 75 m
(Fig. , right panel). Two peaks between 60 and 70 m as
well as around 90 m depth stand out from the relatively low mixing at depth.
In the left panel, the measured phytoplankton concentration has a maximum of
1.72 × 108 cells m-3 at 58.25 m depth, clearly showing a DCM. The respective model
result has a negligible smaller maximum concentration (-0.0019 %) at
52.25 m depth. The spread of the measured phytoplankton concentration is
remarkably wider than the modelled concentration. The nutrient concentration
shows for both data sets a similar distribution from the surface down to the
DCM, where concentrations are first very low and then start to increase at
the DCM. Below the DCM, the in situ data increase faster than the model
data. The model data show a linear slope below 100 m depth due to the
fixed nutrient concentration at the bottom and the uniform mixing.
Measurements (solid lines) and model results (dashed lines) at the
southern station. Left panel: phytoplankton concentration (green), nutrient
concentration (red) and light intensity (blue). The LSM is based on the
depth and the value of the DCM. Right panel: vertical mixing coefficient
KT.
The light intensity decays exponentially and has very low values at depths of
the DCM and further below. Both profiles have a similar shape, but the
modelled profile has in general higher values and is shifted slightly upwards
as is the modelled DCM. The effect of the DCM on the light intensity due to
the shading is clearly seen in the step of the modelled light intensity
profile, while the effect on the measured profile is less strong.
The northern station
At the northern station, the vertical is very inhomogeneous with moderate
mixing in the upper 25 m, very weak mixing around 25 m depth, the strongest
peak around 40 m depth and weaker mixing below 50 m depth
(Fig. , right panel). In the left panel, the measured
phytoplankton concentration shows a significant UCM with a mean of
1.55 ×108 cells m-3 in the ML. The cell concentration
increases from the surface to the bottom of the ML and decreases
exponentially below. The modelled result shows a high surface concentration
with a mean of 1.56×108 cells m-3 that decreases slightly
towards the bottom of the ML and then drops rapidly below. The nutrient
concentration is low in the ML with a mean of
2.24 mmol nutrients m-3
and increases rapidly below. In contrast to the southern station, the ML is
not depleted of nutrients. Since the model parameters are calibrated to the
mean nutrient concentration in the ML, the model result (mean of
2.26 mmol nutrients m-3) fits well to the measured results in the ML.
Below the ML the concentration increases first in several small steps and
then linearly. The steps are located at depths where the vertical mixing is
very low. The light intensity profile decreases quickly over depth due to the
high phytoplankton cell concentration within the ML, which is especially
apparent in the modelled profile.
Measurements (solid lines) and model results (dashed lines) at the
northern station. Left panel: phytoplankton concentration (green), nutrient
concentration (red) and light intensity (blue). The LSM is based on the mean
phytoplankton concentration and the mean nutrient concentration in the ML
(grey area). Right panel: vertical mixing coefficient KT.
The transition station
At the transition station, strong mixing in a well-defined ML with 35.6 m
depth and low mixing below the ML is measured (Fig. , right
panel). In the left panel, the phytoplankton concentration shows an UCM with
lower concentrations (mean of 7.21×107 cells m-3) than at
the northern station, which is also differently distributed: the highest
concentration is close to the surface and it decreases exponentially between
30 and 50 m depth. The modelled phytoplankton concentration behaves similar
as at the northern station, where the concentration is maximal at the
surface, decreases slightly towards the bottom of the ML and then decreases
exponentially below. The mean phytoplankton concentration in the ML is 7.19×107 cells m-3. The measured nutrient concentration is very
homogeneously distributed over the ML with a mean value of
1.54 mmol nutrients m-3. The concentration increases just below the
ML where it soon reaches its bottom boundary value. The mean value of the
modelled nutrient concentration is also 1.54 mmol nutrients m-3. The
almost homogeneous vertical mixing below the ML leads to a smooth increase of
modelled nutrients towards the bottom. The measured irradiance intensity has a
comparatively low surface irradiance and decreases strongly with depth. The
modelled irradiance profile is based on a higher irradiance and is not capable
to capture the strong gradient.
Measurements (solid lines) and model results (dashed lines) at the
transition station. See caption of Fig. for details.
a Units were converted from [m mol N]-1 to
[cell]-1 using conversion factor 1×10-9 mmol
nutrients cell-1 by . b In unit
[mmol phosphorus m-3].
Discussion on the model calibration
As comparing the results of highly idealised models, such as the one used
here, to in situ measurements and using them for the calibration of model
parameters may raise concerns (see e.g. ), we provide in
this section a rather extensive discussion of the model calibration results.
Kbg and k
In general all values for Kbg as well as for k, shown in
Figs. and , lie in the range of values used in
other models (see Table ). The relatively high standard
deviation at some stations can be partially explained by the varying fraction
of light which is reflected at the surface due to the zenith angle. When the
sun stands low, a higher fraction of the incoming light will be reflected
already at the water surface . This effect
leads to a lower ratio of the intensity of light in the water column to the
intensity of the incoming light and is primarily independent of the optical
properties of the water column. To avoid extreme influence of the solar
angle, data measured early in the morning and late in the afternoon are not
taken into account.
The values of Kbg during the summer cruise (Fig. b)
are characterised by two different domains. Data of stations with a
well-defined DCM lead to values of Kbg that are close to their
mean of 0.032 m-1. For stations with phytoplankton distributions
dominated by a UCM, Kbg increases with increasing latitude. A
possible explanation of this difference is the effect of particulate
backscatter which increases the absorption and becomes more important at
higher latitudes .
The analysis of the optical properties during the spring cruise is mainly
limited to the DCM stations. For homogeneously mixed stations our method
cannot be used since it is not possible to distinguish between the effect of
phytoplankton absorption and Kbg in such systems. The results in
Fig. show that Kbg values are more widely spread for the
spring cruise and the standard deviation can be up to 100 %. Still most of
the values are close to the mean of the summer data, 0.032 m-1. This
value is also consistent with those determined from the detailed (spectrally
resolved) measurements in the clearest oceanographic waters
and hence it is used for the model parameterisation.
Figure shows that k derived from the spring data shows higher
values as well as a wider spread compared to the results derived from the
summer data. The origin of these high variations can be manifold (e.g. the
biological composition and species-dependent properties) and an explanation
is outside the scope of this paper. The strong consistency of the summer
results and the comparison with the literature (see Table )
would suggest choosing k=6.0×10-10 m2 cell-1.
Instead the mean of the spring and summer result, k=10-9 m2 cell-1 is chosen to represent the whole phytoplankton
community.
HI, HN and ε
Before applying the LSM method a series of sensitivity tests were performed
to study the behaviour and the robustness of the model. The tests were based
on two standard model setups with biological parameters values calibrated to
lead to a DCM and a UCM state, respectively. Biological parameters, like the
growth rate and the recycling rate, as well as Nb and
Iin have been varied (one at the time) over a range of realistic
values as measured or used in the literature. The most important outcome of
this study is that none of these parameter variations shows unexpected growth
dynamics. The phytoplankton concentration for the DCM parameterisation
responds generally quicker to changes in the biological or environmental
parameters than the phytoplankton concentration for the UCM parameterisation.
Generally the growth function is controlled by one limited resource, light or
nutrients, which also determines the equilibrium state. Changes of the half-saturation constant based on the other resource have less effect on the
growth. The tests also show a high sensitivity to parameters which connect to
the total nutrient budget, like the nutrient concentration at the bottom of
the system Nb and the recycling coefficient ε. While
the first is determined by measurements, the latter involves more complex
processes like grazing, remineralisation and sedimentation.
Generally, the results of the LSM for HN and ε are in the
range of commonly used values (see Tables and
) and their observed properties are similar to previous
studies of ecological model parameters (e.g. ). Both
HI values are an order higher than the common values. Possible reasons
and explanations are discussed per station in the following.
At the southern station the best result of the LSM was found for HN=0.10014 mmol nutrients m-3 and ε=0.61703. The profiles
in Fig. show that the main characteristics of all three
environmental variables are well reproduced. The recycling rate at the
southern station is higher than the standard value, underlining that the
supply of nutrients is an essential driver for the DCM state. Sensitivity
studies have shown (results not presented here) that the equilibrium state is
sensitive to changes of the half-saturation constant HI. Considering
that a DCM is by default a very sensitive state that establishes as a
compromise between light and nutrient limitation, it is not surprising that
the growth is affected by changes of the biological parameters. Nevertheless,
since nutrient limitation is the driving force behind the DCM, the
calibration of HN and ε with a fixed HI appears to be a
reasonable choice and results show a good representation of the measured
profiles.
At the northern station the best result of the LSM was found for HI=148.81µ mol photons m-2 s-1 and ε=0.4018. The high value of HI
indicates that the light availability at the surface is very high, even
though the incoming light intensity is almost half the strength of the
incoming irradiance at the southern station. The strong attenuation due to
the phytoplankton concentration leads to a rapid decay over depth. The light
intensity goes below 10 µ mol photons m-2 s-1 at not even
20 m depth, while at the southern station this value is crossed at 72 m
depth. It is therefore not only the strength of the light availability, but
also the effective time a cell spends in the light. Due to the strong mixing
in the ML the cells are moved more actively towards the surface and down
again. To achieve an effective limitation of growth due to the light
intensity, the half-saturation constant HI needs to be high in order to
control the growth. Remineralisation is less effective at the northern
station than at the southern station. In terms of the nutrient budget, this
means that nutrients are more effectively resupplied from the bottom boundary
at the northern station even though vertical mixing close to the boundary is
weaker at the northern station. This is possible due to the large
Nb which is more than double the bottom concentration of the
southern station.
At the transition station the parameter set HI=186.7µ mol photons m-2 s-1 and ε=0.034 was
found. The value of HI is even higher here than at the northern station.
The possible explanations are similar to the ones given for the northern
station and the intensification of the effect can be explained by the higher
incoming radiation at the transition station. The recycling rate is very low,
but compares to the one given by . The main source of
nutrients is therefore the resupply from the bottom boundary and over 95 %
of the nutrients taken up by phytoplankton are lost.
Remineralisation rates depend on a number of factors like grazing, nutrient
composition and temperature (e.g. ), which can all lead to
the differences shown for the three reference stations.
Description of the reference stations with the boundary conditions
for the bottom nutrient concentration Nb and the incoming light
intensity Iin as well as the biological parameters calibrated
with the LSM. Numbers in parentheses give the range of values tested during the
calibration.
DescriptionCruiseNbIinHNHIεS& Latitude & Datemmolnutrientsm-3µmolphotonsm-2s-1mmol nutrientsm-3µmolphotonsm-2s-1––SouthernSummer5.36250.10014850.617030.004340.5∘ N, 13.2∘ W23 July 2009(1×10-3–1.5)(fix)(0.302–0.802)NorthernSummer12.43904.25 × 10-2148.80.40181.66 × 10-560.7∘ N, 19.3∘ W8 August 2009(fix)(85–190)(0.3–0.8)TransitionSpring8.85504.25 × 10-2186.70.0341.67 × 10-544.3∘ N, 13.2∘ W20 April 2011(fix)(85–250)(0.007–0.5)
In Fig. a the relative change per time step as given in
Eq. () is shown. To reach the equilibrium the model takes 7820
days for the southern station, 5980 days for the transition station, and
12 150 days for the northern station. The time is normalised such that the
three graphs can be shown in one figure. All stations undergo rapid changes
during the first quarter of the run and then approach their final state
with an exponentially decreasing rate of change. The small wiggles are
numerical artefacts. The temporal evolution of the sum of squares S as
given in Eq. () is shown in Fig. b. The southern
station deviates only a little from its initial state and remains close to
its final value after 50 % of the time to reach the equilibrium. Results of
the northern and the transition station undergo a greater change in the
beginning of the run and approach their equilibrium state exponentially.
Their result is closer to the measurements and undergoes changes until the
whole system is in equilibrium. This stands in contrast to the result of the
southern station where the value of S remains constant even though the
model does not reached its equilibrium for a further 3000 days.
Temporal evolution of (a) the relative change of the system
per time step R and (b) the sum of squares S for the three
reference stations. On the x axis the time is given as the percentage of
the total duration until the equilibrium is reached. The y axis is in
logarithmic scaling.
Sensitivity to turbulent vertical mixing
Based on the model calibrations of Sect. the vertical mixing
profiles of the STRATIPHYT cruise are applied to the three reference states
to study the sensitivity of the phytoplankton growth to changes in the
vertical mixing. In Sect. the observed vertical mixing
coefficients along the zonal transect from 29 to 63∘ N for the
STRATIPHYT cruises in summer 2009 and spring 2011 were presented. In this
section these vertical mixing profiles (for both spring and summer cruises)
are applied to the three calibrations of the model, while the other model
parameters remain fixed. The idea is to simulate different mixing scenarios
at one location. For this purpose the mixing profiles are treated as
realistic mixing states of the northern Atlantic which can occur at these
stations. To facilitate the discussion of the result the profiles are
rearranged according to their mean strength in mixing (Fig. ).
The strong variability within one mixing profiles makes the categorisation of
the profiles difficult. Instead of the mean mixing strength other
characteristics, e.g. MLD, could have been chosen. Eventually, the actual
sensitivity analysis will be independent of the order of the profiles.
Phytoplankton profiles
The distribution of states in Fig. shows that the three
calibrations respond differently to the vertical mixing. As could be seen
already for the parameter calibration, the southern station is more
responsive to changes than the other two stations. Even though the biological
parameters of the southern and the transition station are very different,
their results show more similarity than the results of the northern station.
This indicates that the boundary conditions for the nutrients and the light
have a very strong impact on the growth.
Measured vertical mixing profiles aligned according to the mean
mixing strength with increasing strength along the x axis as shown in the
lower graph (logarithmic y axis).The red boxes indicate the vertical mixing
used for the model calibration at the southern, northern and transition
station (left to right).
Overall, the phytoplankton concentration varies between very deep DCM states,
DCM states close to the MLD, UCM states of different concentrations, and
homogeneously mixed states. For the DCM states an increase of the mean mixing
leads, with some exceptions, to a shift of the phytoplankton towards the
surface. Results for the southern station show that the depth of the DCM is
less controlled by the mean vertical mixing than by the strength of the
mixing below the DCM. As a consequence the resupply of nutrients is limited
and the nutrient concentrations of the deep DCM states are almost completely
depleted (Fig. ). Additionally, DCM states establish in depth
sections of the water column in which the vertical mixing is low. Profile 16
has for example a high nutrient concentration below the DCM, which is even
higher than at most of the UCM states. Still growth is restricted to a DCM
and a possible explanation could be the very low vertical mixing between 40
and 70 m depth that leads to a bottleneck for the nutrient supply. At the
southern station Nb is relatively low which intensifies this
effect even more.
Comparing the DCM states of the southern station to those of the transition
station, Fig. shows that even though the DCMs of the
transition station are closer to the surface and have more nutrients
available, their concentration is lower than the one at the southern station
under the same mixing conditions.
Phytoplankton concentration results of the sensitivity study based
on the vertical mixing shown in Fig. and the three reference
stations: southern, transition and northern (top to bottom). The red boxes
show the respective reference state.
For the UCM states an increase of the mean mixing leads first to more
nutrients in the ML and therefore a higher phytoplankton concentration. The
change in the nutrient distribution can be seen in Fig. . The
stronger the mixing gets the faster nutrients are resupplied and distributed
over the water column. Another effect of the stronger mixing is the deepening
of the ML. This leads to a lower phytoplankton concentration due to two
reasons: the cells are diluted over a wider depth range and they are moved
into deeper water, where the growth is limited by the lower light conditions.
The latter has an especially strong impact when the vertical mixing becomes
homogeneous and concentration decreases even more. Since growth rates are
reduced by the lack of light, less nutrients are consumed and the nutrient
concentration increases. In particular, the homogeneously mixed stations are
characterised by surface nutrient concentrations close to the bottom value
Nb.
In general the vertical mixing below the ML is about one order higher for the
UCM states than for the DCM states. The turning point from an enhancing to a
reducing effect of the mixing is different for each reference state. At the
northern station it appears already for low mixing leading to only one DCM
state. At the transition station the window between the first UCM state and
the highest surface concentration is rather small and concentrations decrease
quickly as the mean vertical mixing increases further. Even though the
calibration of the southern station makes it less likely to reach a UCM
state, as soon as it is reached, growth is very strong leading to high
surface concentrations.
Mixing profile 11 appears to have an ideal combination of nutrient supply and
light availability for all reference stations. Other profiles with a similar
MLD show a lower concentration while profiles with a deeper MLD spread the
cells deeper. The latter is most significant for the phytoplankton
concentrations based on homogeneous mixing. In particular, the last profile shows
very little phytoplankton for all three calibrations.
Bulk and surface sensitivity
The results from the previous section indicate that the phytoplankton
concentration at each of the reference stations is sensitive to the vertical
mixing profile. The inhomogeneity of the vertical mixing profiles complicates
the identification of the main controlling processes. Therefore different
characteristics of the mixing are analysed for their correlation to the
phytoplankton growth.
Nutrient concentration results of the sensitivity study based on the
vertical mixing shown in Fig. and the three reference stations:
southern, transition and northern (top to bottom). The red boxes show the
respective reference state.
As mentioned above, the DCM states appear to be more sensitive to the mixing
below the DCM. In Fig. a the depth of the DCM is therefore
given as function of the mean vertical mixing below the DCM (and not over the
whole profile as above). The data of the southern station and the transition
station show an exponential decrease of the depth of the DCM with the
increasing mixing, while the DCMs at the transition station are generally
shallower. The data point for the northern station fits into this behaviour,
but is not sufficient for further analysis. The outlier of the southern
station at the high end of the mean mixing corresponds to profile 16, whose
special behaviour was discussed in the previous section.
To compare the phytoplankton distributions of the UCM or homogeneous states,
the mean surface phytoplankton concentration over the upper 20 m is
calculated, here indicated by Ps. Values of Ps
computed from the results in Fig. lie in the range of
0.5–23.2×108cellsm-3 for the stratified vertical
mixing profiles and between 0.3 and 5.8×108cellsm-3 for
the homogeneously mixed profiles (Fig. b). The strong
vertical mixing at profile 30 leads to the extinction of phytoplankton at the
transition station and the northern station. Overall, the behaviour of
Ps as a function of the mean vertical mixing is very similar at
these two reference stations.
The sensitivity of the southern station can also be seen in the high values
of Ps. Phytoplankton profiles based on profiles with strong
vertical mixing (e.g. the homogeneously mixed profiles) lead to larger
Ps values at the southern station than those at the other two
reference stations. The reason for the enhanced growth is the combination of
the high Iin and the low HI at the southern station.
Comparison of the model results for the three reference stations.
(a) Depth of the DCM as a function of the mean vertical mixing below
the DCM. (b) Mean surface phytoplankton concentration for all UCM
and homogeneously mixed states.
The growth function in Eq. () divides the water column into a
light-limited and a nutrient-limited growth regime. The transition between
the two coincides with the position of the nutricline, which is defined as
the depth of the largest gradient in the vertical nutrient concentration. In
Fig. a, the total biomass is plotted as a function of the
depth of the nutricline. Model states which are not limited by nutrients have
no nutricline and are found along the y axis. Though data points are fairly
spread, their distribution indicates that a shallower nutricline leads to an
increase of the total biomass.
These results suggest that the vertical mixing in combination with the
boundary condition Nb play a very important role in the supply of
nutrients to the euphotic layer. Still, their result does not show a
clear trend nor does the method take the vertical characteristics of the
mixing into account. To obtain a more quantitative measure of the effect of
the vertical mixing on the vertical distribution of the nutrient
concentration, a (dimensionless) relative nutrient flux ρNi is
defined as
ρNi=-Ki(z)∂Ni∂z-K(z)∂N∂zref‾‾≈∑j=0J-1KTi(zj)Ni(zj+1)-Ni(zj)∑j=0J-1KT(zj)(N(zj+1)-N(zj))ref,
where i is the profile number, J is the number of grid points in the
vertical and the bar indicates vertical averaging. The denominator normalises
the flux with the nutrient flux of the correspondent reference station (e.g.
at the reference stations ρNref is 1). It follows that
values of ρNi measure the influence of the change in the vertical
mixing compared to the reference state.
In Fig. b the normalised values of Ps are
plotted against ρNi. Every Ps is normalised by the
maximum value of each reference station to facilitate the comparison between
reference stations. (The reference nutrient flux at the southern station is
very low, which leads to high values of ρNi and hence a different
scale is used.) In all three cases Ps increases with the
increasing nutrient flux. The relative nutrient flux shows a strong
correlation for all reference stations. The STRATIPHYT data (taking the
measured nutrient at the transition station as reference) shows a wider
spread but generally a similar correlation. In contrast to the other measures
above, ρNi incorporates the vertical characteristics of the mixing
as well as the nutrient concentration and is therefore capable of giving a more
integrated picture of the growth environment.
(a) The total biomass integrated over the water column as
a function of the depth of the nutricline. (b) Normalised surface
phytoplankton concentration vs. the relative nutrient flux for the three
reference stations and the measured STRATIPHYT data. For the modelled data
only the nutrient-limited states are taken into account.
Summary and discussion
In this work, we used in situ measurements of the STRATIPHYT project to
calibrate three sets of model parameters for a one-dimensional phytoplankton
model. Subsequently, the three model calibrations were used to study the
sensitivity of the phytoplankton distribution to measured vertical mixing.
A discussion of the calibration of the parameters in the model was
given in Sect. 4.3. We are confident that the three parameters are a good
choice to represent characteristic phytoplankton growth with the model.
When compared to in situ as well as to the ocean colour data, the
phytoplankton concentration at the surface for the deep DCM states is up to
two orders of magnitude too low. However, the model results for shallow DCM
states and for UCM states are of the same order as the measurements.
Comparisons to in situ measurements have shown that the OCM3 algorithm (used
for the satellite data) underestimates Chl a concentrations below
1 mgm-3, and overestimates them at larger values. In the latter
case this would mean that the model might perform even better at high
concentrations than the comparison would suggest. On the other hand the
performance at low concentration might be even poorer (see
, and http://oceancolor.gsfc.nasa.gov/ for more
details).
In contrast to previous sensitivity studies, the model is forced by measured
profiles of vertical mixing as shown in Fig. . To compare the
results to previous work, correlations with general measures such as the mean
vertical mixing strength are analysed. For mixing profiles with a weak mean
mixing, the low value of Nb combined with the relative high
HN leads mainly to DCM states at the southern station. At the northern
station, the high Nb leads predominantly to UCM states.
Independent of the distinctive values of HN and ε at the
transition station, the model results lie in between those of the other
two stations. Mixing profiles which lead to a DCM at the southern station
result either in a shallower DCM for the transition station (see
Fig. a) or even a UCM as for the northern station. Also the
nutrient concentration in Fig. underlines the intermediate
character of the transition station. This suggests that the boundary
conditions for the light and the nutrients have a stronger impact on the
model results than the calibration of the model parameters. It also shows
that changes of the mean mixing lead to changes in the equilibrium state, as
can be seen in Fig. and was shown for example by
.
Results also show that the phytoplankton distribution based on strong mean
mixing are less diverse among the three reference stations and almost all show
a UCM state. The difference lies in the concentration of the UCM: at the
southern station the low HI paired with a high Iin and the
effective resupply of nutrients to the ML makes the plankton grow stronger
than at the other two stations. This result is also obtained from
Fig. b where a clear offset between the southern data and
the more northern data can be seen, especially for high vertical mixing.
find similar conclusions and discuss the underlying
processes in more detail.
For weaker mean mixing the model results show the importance of the nutrient
supply to the euphotic layer. Nutrient-limited states show an increase in
total biomass with the shallowing of the nutricline
(Fig. a). Based on this result, the relative nutrient flux
was defined as a new measure that incorporates both the vertical structure of
the mixing and the distribution of nutrients. With this measure changes of
surface phytoplankton concentration can be directly correlated to the
strength of the vertical mixing and its impact on the nutrient supply.
Results in Fig. b show a stronger correlation than
previous results, which were based on the mean vertical mixing. This implies
that information gets lost when the vertical structure of the mixing is
generalised to a mean value and most importantly that the growth is sensible
to small-scale variations of the vertical mixing.
In summary, the usage of measured vertical mixing profiles instead of
idealised mixing schemes leads generally to similar results as previous
studies. Including the characteristics of the vertical structure in the
analysis showed that small-scale variations in the vertical mixing and the
nutrient distribution have a strong impact on the surface phytoplankton
concentration. This strong correlation of ρN to the surface
phytoplankton concentration suggests that data-assimilation techniques may be
useful to constrain properties of turbulent vertical mixing with the help of
surface Chl a concentrations. However, the results also indicate that this
will be challenging as the surface concentration in the case of the modelled
DCM is in most cases underestimated and has also a strong variability.
Further research on the impact of the temporal change in the vertical mixing
and the boundary conditions will show to what extent the surface Chl a
concentration can be used to remotely determine properties of the small-scale
structure of the upper ocean.
Calculation of k and Kbg
Figure shows the vertical profiles of fluorescence, corrected
irradiance and the surface irradiance as one example of the total of 100 CTD
measurements used for the analysis. The corrected irradiance is the
percentage of the instantaneous surface light intensity measured at depth.
Variations of the surface irradiance on short timescales (e.g. change in
cloud coverage) as well as long timescales (e.g. diurnal changes) do
therefore not affect the analysis of the transmittance of the water. The
x axis goes from 0 (surface) to 250 m depth. At depths below 140 m the
fluorescence signal shows slightly varying values above zero. These appear
due to measurement artefacts, the so-called dark current, and Chl a
concentrations can be assumed to be very low or even zero here.
In Fig. the blue interval limited by z1 and z2 defines
the phytoplankton-free depth section. The integral over P(z) in the
exponent of Eq. () remains constant over this interval since
there is no additional phytoplankton found below z1. This constant term is
used to eliminate the k dependency by combining Eq. () at
depth z2 with the same equation at depth z1. Rearranging leads to
Kbg=logI(z1)Iin(z1)-logI(z2)Iin(z2)z2-z1
from which Kbg is determined for the given irradiance profiles.
As soon as a value for Kbg is found, the effect of the
phytoplankton distribution within the water column can be determined. To do
so, another section [z3,z4], which contains a high concentration of
phytoplankton cells, is defined. Here we choose the depths in which the
phytoplankton concentration reaches half of its maximum value, above and
below the depth of the maximum phytoplankton concentration. In
Fig. this section is marked by the green shaded area. We first
write Eq. () for both depths z3 and z4 and take the
logarithm of both equations (which linearises the dependency on k).
Substituting the two resulting equations leads to
logI(z3)Iin(z3)-logI(z4)Iin(z4)=-Kbg(z3-z4)-∫0z3kP(ζ)dζ-∫0z4kP(ζ)dζ.
The term in parentheses in the right-hand side of Eq. () can be
combined into one integral. To calculate the integral numerically, we use the
trapezoidal rule given by
PPEAK=∫z3z4P(ζ)dζ≈0.5P(z3)+2∑n=z3+1z4-1P(n)+P(z4)
which gives the total amount of phytoplankton PPEAK within the
section [z3,z4]. Rearranging Eq. () gives an expression
for the absorption coefficient of phytoplankton k as
k=1PPEAKKbg(z3-z4)+logI(z3)Iin(z3)-logI(z4)Iin(z4).
CTD data at Station 7 (36.3∘ N
13.5∘ W)
21 July 2009, 11 a.m. Depth profile of the Chl a concentration
(green line), depth profile of the corrected irradiance (blue line), and
surface irradiance at the time of the measurement at depth (red line). The
light blue lines indicate the depth section used to extract Kbg.
The green-shaded area symbolises the phytoplankton concentration which is
used to determine k.
Mean Kbg per station based on irradiance profiles
measured in spring (left) and summer (right). Error bars give the standard
deviation per station. The vertical dashed lines define the latitude at which
the system changes its state: red is the transition from a DCM to a UCM state
and green from a UCM to a homogeneously mixed state (from south to north).
Mean k per station based on irradiance profiles and Chl a
concentration profiles measured in spring (left) and summer (right). See
caption of Fig. for further description.
Acknowledgements
Special thanks go to Elena Jurado for her help with the
STRATIPHYT data, to Corina Brussaard, the chief scientist of
the two STRATIPHYT cruises, and the crew of the R/V
Pelagia. We also thank Roeland van de Vijsel for his work on the satellite data. This work was funded by the NSO User Support
Programme under Grant ALW-GO-AO/11-08 through the COLOURMIX project
with financial support of the Netherlands Organization for
Scientific Research (NWO). Edited by: O. Zielinski
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