4.2
Model Setup
4.2.1 The PhysicsThe setup of the physical part of the model is essentially identical to Chapter 3 with the exception that density variations are taken into account in this case and are able to alter the turbulent mixing. The turbulence is forced through tidal currents and the particle displacement is calculated using Eq. (2.15). The diffusivities obtained from the turbulence closure scheme
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 20 40 60 80 0.02 0.04 0.06 0.08 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 20 40 60 80 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 m s−1 m2s−1 (a) (b) Time [d] H ei gh t ab ov e b ed [m ] H ei gh t ab ov e b ed [m ] 8 10 12 14 0 10 20 30 40 50 60 70 80 ° C
Height above bed [m]
Figure 4.4: (a) Springs-neaps variation of tidal current strength. (b) Associated model eddy diffusivities for the constant temperature stratification shown on the right. In the surface mixed layer the values forK are about 3·10−3m2s−1, in the centre of the thermoclineK≈10−5m2s−1.
are smoothed using the method from Section 2.2.2and K′
= 0 is forced at the boundaries as described in Section 2.2.3.
The tides are driven with a simple M2/S2 combination, such that the current strength at
spring tide is slightly above the values observed bySharples et al. (2001) which were obtained partway between neap and spring. The ratio of S2:M2was set to the equilibrium tide ratio of
0.465 (Emery and Thomson, 1998). The modelled spring neap cycle of currents [Fig. 4.4(a)] drives a cycle in the mixing [Fig. 4.4(b)], limited to the bottom layer by the imposed form of the temperature profile (Fig.4.4inset). No wind mixing was applied, so that the results could be interpreted in terms of the tidal forcing variability only. The stratified experiments use the constant temperature gradient shown here, i.e. there is no heat exchange with the atmosphere and no diffusion of the temperature gradient by the turbulent mixing. The turbulent mixing will therefore be able to intrude into the base of the thermocline and the depth of the intrusion will vary with the tidal current strength (see below), but it cannot erode the stability of the temperature stratification. Tests where the temperature diffusion was enabled showed negli- gible differences in the results over a springs-neaps cycle and diffusion was therefore discarded as a means to speed up the simulations.
4.2.2 Light and Nutrient Dynamics
In Chapter 3 we could assume that the estuary was only light but not nutrient limited. The growth model could therefore be formulated based solely on the light availability to the cells. In shelf seas, and in particular in stratified shelf seas, this is no longer a valid assumption and we need to include the possibility of nutrient limitation. The simple light-based growth model from Section 2.3 is therefore extended by a nutrient model in which the cells are able to take up a nutrient from the water, store it up to a maximum nutrient-to-carbon ratio, and consume it when they produce carbon during photosynthesis. The model is very simple in that it neglects temperature effects on the growth and respiration rates and that it uses nitrogen as the only nutrient, thereby neglecting other important nutrients such as phosphate or silicate. The latter can become limiting in particular for diatoms. While the main model remains in a Lagrangian formulation, the nutrient is modelled on a Eulerian grid (Broekhuizen,1999) (see below).
Fig. 4.5 gives a summary of the programme flow. Each model particle represents initially 100 000 ‘real’ cells, each of which is given a carbon content of 2·10−6
mg C. The model contains a lower carbon threshold, Wstarve, at which some of the cells die (i.e. the number of
take up as much nutrient as possible from the water column, based on ambient concentraion and cellular nutrient levels (nutrient-to-carbon ratio) and add to cellular nutrient pool
calculate particle displacement obtain diffusivities from TCS
calculate the max. possible production based on cellular nutrient levels (using the Redfield ratio C:N=6.6): PN acclimatise cells to new light levels,
calculate production based on light availability: P
I
Use the lesser of P or P for the amount of new production and deduct the cost from the cellular nitrogen pool
N I
the cellular nutrient levels are well above the subsistence quota: swim up at next time step to minimise light limitation
the cellular nutrient levels are only slightly above the subsistence quota: swim down at next time step to replenish cellular nutrients
Deduct repiratory costs and increase/de- crease number of live cells represented by each model particle, depending on total carbon per model particle
advance one time step
Figure 4.5: Flow diagram for the shelf sea experiments showing one of the swimming strategies used.
real cells per model particle is reduced) and an upper level,Wf ission, at which the cells di-
vide (and the number of real cells per model particle doubles). Table4.1gives a summary of the main parameters used. For the nutri- ent uptake a Michaelis-Menten type function of the ambient nutrient concentration N is used U =Um 1− Q Qmax N κN +N (4.1) Q is the cellular nitrogen-to-carbon ratio which needs to remain above a subsistence quota Qmin and below a maximum storage
quotaQmax. Umis the maximum uptake rate
and κN the half-saturation constant. Once
the uptake is added to the cellular nutrient pool, the maximum possible carbon produc- tion based on the light availability using the
Denman and Marra (1986) formulation from Section 2.3 is calculated. If the cell has sufficient nitrogen to produce the calculated amount of carbon (light limitation), the cellular carbon content increases and the cost is deducted from the nutrient pool using the Redfield ratio of C:N = 6.6 (Sharples,1999). If the cell does not have sufficient nitrogen (nutrient limitation), the entire amount of cellular nitrogen that is above the subsistence level is used for carbon production leaving the cell at the subsistence quota. After each time step the cell also respires at the rates given in Table4.1.
4.2 Model Setup 107
The ambient nutrient concentration in each model bin thus changes according to ∂N ∂t = ∂ ∂z K∂N ∂z − n X i=1 Ui (4.2)
where Ui is the uptake of nitrogen in [mg N] by the i-th particle in the bin containing a total
of n particles. Nutrient is added to the bottom mixed layer at a constant rate RN through
resuspension at the seabed with a boundary condition applied to the bottom depth cell of the model (Sharples,1999)
∆N1 =RN(Nb−N1)∆t (4.3)
where N1 is the nutrient concentration in the bottom depth cell and Nb the maximum value
for near bed dissolved organic nitrogen (DIN) (Table 4.1). This simulates the resupply of nitrate to the overlying water through bacterial regeneration of organic to inorganic nitrogen in the bottom sediments. This is often the dominant source of inorganic nitrogen to water in stratified shelf seas away from sources of freshwater or the shelf edge. Another important source to the bottom layer can be regenerated nitrogen by grazers. Although the effect of grazing on the biomass is included in the loss terms of the growth equation, recycled nitrogen as such is neglected as a possible nutrient source in the model.
For the fully dynamic experiment (Section4.4) two different swimming strategies will be tested. The diagram in Fig. 4.5 shows the program flow for one of the swimming strategies which is based on the physiological state of the cell. If the cell is approaching the subsistence nutrient quota, it will swim down towards higher nutrient concentrations. If it has sufficient nitrogen
Table 4.1: Physiological parameters for the motile and non-motile cells in the experiments. The sources are: 1 =Sharples(1999), 2 =Broekhuizen(1999), 3 =Sharples et al.(2001) and 4 = assumed.
SYMBOL MEANING UNITS VALUES REF.
Physical
H total water depth m 80 4
I0 irradiance at midday µE m−2s−1 2300 4
kbg background absorption coefficient m−1 0.09 3
Nb max. value for near bed DIN mg N m−3 70.0 3
RN input rate of DIN by resuspension s−1 1.8·10−5 1
Biological motile non-motile
Ib lower inhibition threshold µE m−2s−1 150 150 4
Id/l saturation onset light intensity µE m−2s−1 50 50 3
κN DIN half saturation concentration mg N m−3 3.0 3.0 1
km cell spec. absorption coef. m2 (mg cell. C)−1 0.004 0.004 2
Pd
m max. dark acclimatised production mg C (mg cell. C d)−1 1.5 2.5 3,2
Pl
m max. light acclimatised production mg C (mg cell. C d)−1 0.08 0.12 4
Qmin subsistence nutrient quota mg N (mg cell. C)−1 0.056 0.056 1
Qmax max. cellular nutrient quota mg N (mg cell. C)−1 0.28 0.28 1
r cellular metabolic rate mg C (mg cell. C d)−1 0.1 0.1 4
Um max. nitrogen uptake rate mg N (mg cell. C d)−1 0.5 0.5 2
w vertical sinking/swimming velocity mm s−1 0.1 0.0 4
Wstarve min. cellular carbon mg C (cell)−1 1·10−6 1·10−6 2
then it could potentially produce more if it was at higher light intensities and hence it swims up towards the light. During night time, if the cellular nitrogen levels are sufficiently above the subsistence quota, the cell will swim upwards to be as high as possible in the water column once the sun rises again. In the second tested swimming strategy, the cells follow a certain nutrient isoline which coincides with the half saturation concentration (HSC),κN, for nutrient
uptake.
Before examining the results of this fully dynamic biological-physical model, the next section will focus on the issue of motility and examine its use in a stratified and tidally energetic shelf sea.