The fate of Lagrangian tracers in oceanic convective conditions: on the influence of oceanic convection in primary production

Nonlinear Analysis: Real World Applications 1 (2000) 3 – 21

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The fate of Lagrangian tracers in oceanic convective conditions: on the in uence of oceanic convection in primary production Henning Wehde ∗ , Jan O. Backhaus Institute of Oceanography, University of Hamburg, Troplowitzstr.7, D-22529 Hamburg,Germany Received 11 October 1999

Keywords: Oceanic convection; Primary production; Dispersion of phytoplankton

1. Introduction The onset of the phytoplankton spring bloom takes place in March–April in northern Norwegian fjords and arctic areas of the northern hemisphere [17,12]. Phytoplankton spring blooms normally require a stable surface mixed layer to develop [37]. In northern areas, where increasing insolation and sea temperature is decoupled, such spring blooms have for a long time been known to take place in apparently unstrati ed or weakly strati ed water masses since strong pycnoclines are not established until May=June when water temperature and fresh water input increase [17,11,16]. New investigations have demonstrated the probability of diatom resting spores functioning as the bloom inoculum [10,16] and thereby playing an essential role in phytoplankton population dynamics. In northern Norway the winter situation is characterised by very small cell numbers within the water column and an availability of spores within the bottom layer [10,34]. Typical sinking rates of marine phytoplankton cover a wide range from a few meters (for vegetative cells) up to several hundred meters (for phytoplankton spores) per day [35,7,6,33,31,22]. The physical mechanism accounting for an initialisation of a plankton bloom is generally not considered in detail in models of marine primary production [25,1]. Several mechanisms have been suggested to bring spores from the bottom layers to the euphotic zone turbulent mixing [10] or upwelling ∗

Corresponding author. E-mail address: [email protected] (H. Wehde).

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[21,32], being the most common. Oceanic Convection as a mechanism was introduced by Backhaus et al. [5]. An overview of the present knowledge about oceanic convection, comprising observations and model simulations, is given by Marshall and Schott [23]. Convection, in contrast to predominantly horizontal ocean dynamics, is characterised by substantial vertical, both down (caused by negative buoyancy of waters at the sea surface which results from a cooling of the surface waters) and upward (required by conservation of mass) motions with vertical velocities up to 20 cm=s. The aspect ratio of convection [18] which is the relation between the horizontal separation of plumes and their vertical extent, has been found to be of the order of 1 : 2:5 (vertical versus horizontal scale). The upward motion is generally less energetic and occurs on larger spatial scales. In terms of primary production the upward motion appears to play the most important role. 2. The coupled phytoplankton convection model ( PCM ) A coupled phytoplankton convection model (PCM) [5] was applied to investigate the relationship between oceanic convection and Primary Production. A nonhydrostatic, rotational convection model [2,4] was coupled to a Lagrangian phytoplankton model [38,5]. The convection model has previously been applied to investigate convection, resulting water mass formation and ice–ocean interactions in the Greenland Sea [2,18,19,3]. The model ignores large-scale advective transports and works on sub-meso spatial scales, i.e. on scales well below the internal Rossby radius of deformation. 3. The ocean model The nonhydrostatic, 2.5-D ocean model which is based on the non-linear, primitive Boussinesq equations for an incompressible uid and further details about its numerical scheme are described in detail in [18]. The model utilises an equidistant numerical grid (Arakawa C) with grid sizes of 5 m. In contrast to previous convection studies, which considered the rotational phase of convection [23], our grid is isotropic to avoid any distortions of convective dynamics. The model domain is a vertical ocean slice assuming vanishing normal gradients of all variables. The time step depends on the courant number of the applied explicit numerical advection scheme for both momentum and water mass properties and lies in the range 5 – 45 s for the experiments discussed below. Cyclic boundary conditions at the open lateral boundaries of the model domain are applied, thereby excluding lateral advection by the large-scale ow. Independent conservation equations for heat and salt are linked to the momentum equations via a non-linear equation of state (UNESCO). The model predicts the spatial and temporal evolution of T; S (density), nonhydrostatic pressure and ow elds from an initial horizontally homogeneous temperature and salinity pro le. The turbulent eddy viscosity, and

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diusivity, in the ocean model are parameterised by a simple diagnostic one-equation turbulence closure scheme [2,20]. Coecients for turbulent exchange of momentum and diusion of water mass properties are assumed to be equal. The validity of this concept is con rmed by our previous convection studies [18,3]. The high spatial and temporal resolution of the model allows to resolve a good deal of the turbulent spectrum which is usually parameterised in larger-scale models. The ocean model is forced with uxes of momentum and heat computed from bulk formulae [14]. For the computation of the heat ux the sea surface temperature (SST), predicted by the model, and prescribed atmospheric data (air temperature, humidity, wind speed, and cloudiness) are used. The thermodynamic forcing comprises sensible and latent heat uxes and short- and long-wave radiation [13].

4. The Lagrangian transport model The simulation of the motion of phytoplankton in the vertical ocean slice of the coupled PCM is accomplished by Lagrangian tracers which follow the convective dynamics. We preferred to use a Lagrangian approach, as opposed to an Eulerian, because it allows to follow single tracers in time (and space). With each newly predicted ow eld the actual positions of the Lagrangian tracers are updated. Convective dynamics may change rapidly on small spatial and temporal scales. Any temporal interpolation in a strongly variable ow might result in erroneous trajectories of tracers. Therefore, a temporal interpolation of ow elds, sampled from the model output with a time step larger than the (dynamical) model time step, was avoided.

5. The phytoplankton model The equations and further details of the phytoplankton model are described in detail in [5,38]. Therefore, only a brief description is given here. The phytoplankton model applied in this study is based on the phytoplankton model developed by Moll [25,26]. The model predicts changes in the phytoplankton stock due to gross primary production, respiration, mortality and grazing. We created a process-study void of any second-order eects by reducing our model to essential mechanisms only. In our simple model respiration, mortality and grazing are assumed proportional to the phytoplankton stock. Following Liebig’s law the gross primary production is calculated from the minimum of the limitation functions for light with an optimal light intensity of 46 W=m2 and nutrients. We used Steele’s [36] formulation for underwater light intensity including photoinhibition as limitation function for light. The self-shading eect of phytoplankton is ignored in the model because our interest is con ned to the onset of a phytoplankton bloom (which coincides with the decaying of convective activity). The amount of incoming short-wave solar radiation depending on time, latitude, and observed local cloudiness, is calculated after Dobson and Smith [9]. The Michaelis–Menton relationship is applied to describe nutrient limitation.

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Fig. 1. Observed T; S pro le from Balsfjord used for initialisation of experiments.

The sinking of tracers representing spores was set to a constant rate of 120 m=d, in order to simulate observed sinking rates of diatom spores [15,8]. With the onset of plankton growth a self-induced buoyancy of growing diatoms, i.e. vegetative cells, was simulated by reducing the sinking velocity of tracers to 1 m=d [25]. 6. Experimental set-up Experiments with the PCM were conducted to study the in uence of convection on primary production. The experiments concerned Balsfjord near TromsH northern Norway with 160 m water depth. Considering the expected aspect ratio of convection we de ned a horizontal dimension of 1.25 km for our model domain. With this choice we made sure that at least three convection cells are always included within our model domain. The model domain was resolved by an isotropic grid size of 5 m. Two records of 6-hourly meteorological forcing (wind speed, air temperature, humidity, and cloudiness), provided by the Norwegian Meteorological Institute (NMI) and the (European Centre for Medium Range Weather Forecast) (ECMWF) from the years 1990 and 1994 were available for experiments. Two model runs were conducted. Both runs were initialised with the same observed T; S-pro le from Balsfjord (Fig. 1) obtained during winter. This pro le is prescribed for the entire model domain as an initial condition

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implying homogeneity in the horizontal. The applied cyclic boundary conditions account for a closed system; it excludes lateral advection and allows to investigate convective modi cation of the water column in isolation. Making use of one and the same initial strati cation allows a judgement of the in uence of the meteorological forcing on convection without considering the dependence on dierent initial conditions. In the model initially the ocean is at rest and we started with small random disturbances for temperature at the sea surface. Lagrangian tracers were randomly distributed in a thin (15 m) bottom layer. The existence of such a layer can be inferred from observed bottom nepheloid layers which are created with the bottom Ekman layer, for instance, by tidal stirring, or mixing due to internal waves [24]. 45,000 tracers were chosen to ensure a high resolution in our dispersion study. Based on our pervious experience in convection modelling [2,18] we expected a high temporal and spatial variability of tracer distributions as a consequence of the randomness of convective dynamics. 7. Results Backhaus et al. [5] presented the oceanic convection as a mechanism to maintain phytoplankton spores near the surface to initiate a phytoplankton bloom in spring. In this paper we concentrate on the relationship between light and convective motion. The coupled phytoplankton convection model was applied for two dierent January–April periods (1990 and 1994) in which the model was forced by 6-hourly atmospheric data obtained from the Norwegian Meteorological Institute and the ECMWF. Each of the two separate model runs covers 120 d. The data (Fig. 2) were chosen because they represent the forcing for a comparatively mild (1994) and a colder winter (1990), respectively. The atmospheric forcing leads to a mean heat loss of the water column of 136.3 W=m2 for winter 1990 and 99.47 W=m2 for 1994. These heat loss rates causes a cooling of surface waters which is followed by destabilisation of strati cation. The convective activity erodes the initial strati cation and accounts for a total homogenisation of the water column in both winters. With ongoing cooling of the ◦ ◦ system the predicted water temperature goes down to 2:7 C in winter 1990 and 3:0 C for winter 1994. This is caused by the milder meteorological forcing in winter 1994. After decaying of convective activity the onset of a seasonal thermocline is predicted around simulation day 100 for both winters. The evolution of the thermal strati cation in the winter 1994 experiment is given by a series of temperature pro les (cf. Fig. 3). Predicted temperatures agree very well with the observed temperatures [27–30]. The internal mixing induced by nonhydrostatic pressure uctuations which are caused by convection originating from the sea surface and which act across isopycnals [2,4], leads to a wavy structure in the shape of the bottom layer well before convection reached the bottom (Fig. 4a). After erosion of the warm intermediate layer convective dynamics penetrating towards the seabed and the tracers leave the thin bottom layer within the ocean slice due to the upward convective motion. At rst the instantaneous tracer positions remain close together (Fig. 4b). However, with time, tracers

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Fig. 2. Atmospheric forcing for experiments. Wind speed ((m=s1 ); thin line) and air temperature ( C); bold line) for winter obtained from ECMWF. Data for winter 1990 (top) for 1994 (bottom).

increasingly cover the entire water column. Up until ca. 40 d of simulation, a thin region near the sea surface remained remarkably free of tracers (Fig. 4c). During later stages of the simulation, with the onset of solar radiation, tracers were also found close to the sea surface, and a nearly homogeneous distribution within the entire water column

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◦

Fig. 3. Predicted Evolution of temperature [ C] for experiment winter 1994. (a) simulation time: 0 to 30 d; (b) simulation time: 100 to 110 d and (c) simulation time: 110 to 120 d. Note dierences in scaling of the x-axis.

was obtained. Fig. 5a illustrates the increasing incoming solar radiation which becomes available at simulation day 21.5. The mean amount of light available for growth of plankton cell increases during the simulation and at the end of a simulation each plankton cell received a quota of about 270 W=m2 (cf. Fig. 5b). The increasing

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Fig. 4. Temperature contours ( C) and tracer distribution in ocean slice for experiment winter period 1990 after (a) 15.5, (b) 16.5 and (c) 21 d of simulation (only tracer distribution).

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Fig. 5. Incoming solar radiation (W=m2 ) which becomes available at simulation day 21.5 (top). The mean amount of light (W=m2 ) available for each plankton cells.

available light leads to a signi cant change in the plankton distribution. Tracers initially de ned as spores under light the tracers changes buoyancy while they become vegetative cells. The total number of vegetative cells (initially=0) increased rapidly after solar radiation becomes available. The start of this increase was predicted at simulation day 40 for winter 1990 and at simulation day 34 for winter 1994. After

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Fig. 6. Evolution of total number of spores (thin line) resp. vegetative cells (bold line). Simulation: (a) winter period 1990 and (b) winter period 1994.

about 70 simulation days almost all tracers becomes vegetative cells for both simulation periods (Figs. 6a and b). The in uence of convection is demonstrated by orbital motions of a selected tracer during 100 h of simulation from day 16.5 (Fig. 7a) which is the erosion phase of the simulation. Starting at the thin bottom layer the tracer leaves the bottom after penetration of convection down to the seabed and carries out trajectories which are

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Fig. 7. Orbital motions of selected Lagrangian tracers. Tracerpositions sub-sampled every minute during 100 hours of simulation starting at (a) day 16.5 (erosion phase), (b) day 60 (fully penetrating convection phase) and (c) day 98 (decaying convective activity phase) in experiment winter 1990.

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Fig. 8. Predicted convectve activity demonstrated by (a) temperature contours ( C), (b) contours of velocity (cm=s1 ) and (c) contours streamfunction.

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better described by a drunkard’s walk than by a well-de ned orbital cell. The motion of a tracer during the phase of fully penetrating convection is shown in Fig. 7b. The motions of the tracer are caused by ambient turbulence which is induced by convection itself (cf. Figs. 8a–c). During the phase of decaying convection activity vertical displacements of tracers become smaller and the trajectories are characterised by horizontal motions (Fig. 7c). Note that the tracer ending up at surface is more in uenced by the horizontal ow than the one ending up at bottom, far away from euphotic zone. The evolution of the phytoplankton stock for both winter=spring periods is characterised by a slow production after light becomes available. The high initial concentration of plankton spores within the bottom layer is rapidly reduced after convection penetrates down to the seabed (between days 14 and 18 for winter 1990 (Fig. 9a) and between days 20 and 25 for winter 1994 (Fig. 9b)). Thereafter predicted concentrations increased very slowly throughout the water column. A rapid increase of plankton concentrations in the upper 40 m of the water column with a peak at a depths of 20 m coincides with the onset of a weak seasonal thermocline (Fig. 9c, resp. d). In the experiment winter=spring 1994 a new onset of convection was predicted by the model which is followed by another homogenisation of the water column. As a result vegetative plankton cells which had previously grown in the young thermocline were dispersed again over the entire water column (Fig. 9d). At the end of the simulation predicted concentrations arrive at a value of about 0.9 Chl a (mg=m3 ) for winter 1990 and about 0.3 Chl a (mg=m3 ) for winter 1994. 8. Conclusions This paper attempts to describe the in uence of oceanic convection on primary production. With an application of the coupled phytoplankton convection model to hydrographic conditions in a northern Norwegian fjord it was shown that convection plays an important role in the development of a phytoplankton spring bloom. The coupled model was able to predict the dispersion of diatom spores from a thin bottom layer to surface waters. Typical predicted magnitudes of velocities in the developed convective regime are of the order of 1–10 cm=s (cf. Fig. 8). With the large dierence between convective dynamics and sinking rates (120 m=d = 0:138 cm=s) it is very likely that the vertical motions induced by convection will always override the eect of a sinking. After solar radiation becomes available the existence of both stages (spores and vegetative cells) at the same time is a result of the randomness of convective dispersion. Next the model predicted that vegetative cells dispersed throughout the water column. In later spring all the cells within the water column became vegetative. After becoming vegetative the sinking rate of plankton cells in our model was reduced to 1 m=d. This simulated growing vegetative cells with a largely reduced negative buoyancy. In any case, the predicted growth until the onset of a seasonal thermocline was very small (cf. Fig. 9) because growing cells were always removed from the euphotic layer by convective action. After the onset of a seasonal thermocline the plankton cells which were in the euphotic layer initiated a phytoplankton spring bloom. This increased

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Fig. 9. Predicted evolution of chlorophyll a concentration (mg=m3 ) for beginning phase of both winters. (a) simulation winter 1990; (b) simulation winter 1994. Predicted Evolution of chlorophyll a concentration (mg=m3 ) for later phase of experiments. (c) simulation winter 1990; (d) simulation winter 1994. Note dierences in scaling of the x-axis.

growth can be interrupted in the case of a new cooling event when another onset of convective activity caused a homogenisation of the entire water column with the dispersion of plankton cells over the entire water column. Thereafter, the strati cation stabilised again and, when light and nutrients were available a new bloom occurred.

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Fig. 9. Continued.

Acknowledgements In this investigation we have made use of model components which were developed with partial support from the Deutsche Forschungsgemeinschaft (DFG-SFB318) and the

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European Union (DG-XII, MAST II and III), within the European Sub-Polar Ocean Project (ESOP-1 and ESOP-2) (MAS2-CT93-0057 and MAS3-CT95-0015). Appendix Set of coupled phytoplankton convection model equations, including parameter values. For more descrition see text. The conservation equation for ocean momentum read:     @U @U @ @ @U @U 1 @P @U ∗ +U +W − fV − f W = − + t + t ; @t @x @z ∞ @x @x @x @z @z     @V @ @ @V @V @V @V +W + fU = t + t ; +U @t @x @z @x @x @z @z     @W @W 0 @ @W @W 1 @P @ @W +U +W + f∗ U = − − t + t g+ @t @x @z ∞ @z ∞ @x @x @z @z with U; V; W the velocities, P the nonhydrostatic part of total pressure,  the reduced density, ∞ the constant reference density, t the eddy viscosity, g the earth gravity, f = 2 sin(’); f∗ = 2 cos(’) the Coriolis forces, and ’ the geographic latitude. The continuity equation: @W @U + = 0: @x @z The conservation equation for heat and salt:     @T @T @ @ ET @T @T @T +U +W = KT KT + + ; @t @x @z @x @z @x @z @t     @ ES @S @S @ @S @S @S KS + KS + +U +W = : @t @x @z @x @x @z @z @t Thermal resp. saline forcing is represented by (ET =t) resp. (ES =t) at the sea surface. The eddy diusivities for heat (Kt ) and salt (KS ) are equal to the eddy viscosity . The thermal forcing changes according to −QNET ET = @t cw where QNET is the net heat ux and cw the speci c heat of seawater, QNET =
QLO + QSH + QLAT + QSENS ; with:
QLO the dierence between long-wave back radiation from the atmosphere and long-wave radiation from sea surface: 4 4
QLO = ∈air Tair; abs − ∈ Tsea; abs

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where Tair; abs and Tsea; abs are the absolute air resp. sea temperature in K,  the Stefan Boltzmann constant, ∈air the atmospheric emissivity depending on cloudiness and ∈ the sea surface emissivity; QSH the amount of incoming short-wave solar radiation: QSH = (1 − a)Q0 S(Ai + Bi S) where a = 0:06 the albedo, the solar constant Q0 , the solar angle S and the cloudiness parameters Ai and Bi ; QLAT the latent heat ux: QLAT = air Lvap ÿlat |W |(qair − q) where air is the density of air, Lvap the latent heat of vaporisation, ÿlat turbulent transfer coecient for latent heat, |W | the wind speed near the sea surface, qair the speci c humidity of ambient air, and q the speci c humidity near sea surface: QSENS the sensible heat ux: QSENS = air ÿsens Cp; air |W |(Tair − T ) where Cp; air is the speci c heat of air, and ÿsens the turbulent transfer coecient for sensible heat. The stock of phytoplankton biomass A (mg C=m3 ) changes according to A = A(rP min(rI ; rN ) − rR − rM − rZ ) t with limitation functions for light rI and nutrients rN , rR , rM , and rZ are respiration, mortality and grazing rates, respectively, and rp is the optimal growth rate for phytoplankton, rI =

I (1−I=I1 ) e I1

with I (W=m2 ) the underwater light intensity and (I1 ) the optimal light intensity. The available underwater light intensity is given by I (z; t) = QSH (t) ∗ e(−k0 ∗z) z with k0 is the extinction coecient which describes a background concentration of suspended matter within the water column, and z (m) is the actual water depth at which the estimate for available underwater light intensity is needed. Nutrients: rN =

P P + kS

with kS the half-saturation constant, and P (mmol=m3 ) the available phosphate. List of constants used in the phytoplankton model are given in Table A.1

(A.1)

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Table A.1 Quantity

Symbol

Value

Unit

Optimum light intensity Extinction coecient Maximum growth rate of phytoplankton Sinking velocity of spores Mortality rate Grazing rate Respiration rate Phosphate half saturation constant

I1 k0 rp ws rM rZ rR kS

46 0,09 1,5 120 0,05 0,5 0,06 0,06

W=m2 m−1 d−1 m=d d−1 d−1 d−1 mmol PO4 -P=m3

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