The marine ecosystem model (Figure A1) is an improved version of Schmittner et al. [2005a] and includes interactive cycling of nitrogen, phosphorus and oxygen. It is based on seven prognostic variables and embedded within the ocean circulation model. The inorganic variables include dissolved oxygen (O2) and two nutrients, nitrate (NO3) and phosphate (PO4) which are linked through exchanges with the biological variables by constant (∼Redfield) stoichiometry (Table A1). The biological variables include two classes of phytoplankton, nitrogen-fixing diazotrophs (PD), and other phytoplankton (PO), as well as zooplankton (Z) and particulate detritus (D); all biological variables are expressed in units of mmol nitrogen per m3. Although very simple, this ecological structure captures the essential dynamic of competition for phosphorus highlighted by Tyrell , in which phytoplankton capable of rapid growth using available nutrients (PO) are pitted against slow growers capable of fixing their own supply of nitrogen (PD). Additional information on the nitrogen cycle is given by Schmittner et al. [2007a].
Figure A1. Ocean ecosystem model schematic. Different compartments (squares) are connected through the fluxes (arrows) as explained in detail in the text.
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Table A1. Ocean Ecosystem and Carbon Cycle Model Parameters
|Phytoplankton (PO, PD) Coefficients|
|Initial slope of P-I curve||α||0.1||(W m−2)−1 d−1|
|Photosynthetically active radiation||PAR||0.43|| |
|Light attenuation in water||kw||0.04||m−1|
|Light attenuation through phytoplankton||kc||0.03||m−1(mmol m−3)−1|
|Light attenuation through sea ice||kI||5||m−1|
|Maximum growth rate||a||0.11||d−1|
|Half-saturation constant for N uptake||kN||0.7||mmol m−3|
|Specific mortality rate||μP||0.025||d−1|
|Fast recycling term (microbial loop)||μP0||0.02||d−1|
|Diazotrophs' handicap||cD||0.5|| |
|Zooplankton (Z) Coefficients|
|Assimilation efficiency||γ1||0.925|| |
|Maximum grazing rate||g||1.575||d−1|
|Prey capture rate||ɛ||1.6||(mmol m−3)−2 d−1|
|Mortality||μZ||0.34||(mmol m−3)−2 d−1|
|Detritus (D) Coefficients|
|Sinking speed at surface||wD0||7||M d−1|
|Increase of sinking speed with depth||mw||0.04||d−1|
|E-folding temperature of biological rates||Tb||15.65||°C|
|Molar elemental ratios||RC:N||7|| |
|CaCO3 over nonphotosynthetical POC production ratio||RCaCO3/POC||0.035|| |
|CaCO3 remineralization e-folding depth||DCaCO3||3500||m|
 Each variable changes its concentration C according to the following equation
where T represents all transport terms including advection, isopycnal and diapycnal diffusion, and convection. S denotes the source minus sink terms, which describe the biogeochemical interactions as follows:
The function JO = J(I, NO3, PO4) provides the growth rate of nondiazotrophic phytoplankton, determined from irradiance (I), NO3 and PO4,
The maximum growth rate is dependent only on temperature (T):
such that growth rates increase by a factor of ten over the temperature range of −2 to 34°C. We use a = 0.11 d−1 for the maximum growth rate at 0°C which was determined to optimize surface nutrient concentrations. Under nutrient-replete conditions, the light-limited growth rate JOI is calculated according to
where α is the initial slope of the photosynthesis versus irradiance (P-I) curve. The calculation of the photosynthetically active shortwave radiation I and the method of averaging equation (13) over 1 day is outlined by Schmittner et al. [2005a]. Nutrient limitation is represented by the product of JOmax and the nutrient uptake rates, uN = NO3/(kN + NO3) and uP = PO4/(kP + PO4), with kP = kNRP:N providing the respective nutrient uptake rates.
 Diazotrophs grow according to the same principles as the other phytoplankton, but are disadvantaged in nitrate-bearing waters by a lower maximum growth rate, JDmax, which is zero below 15°C:
The coefficient cD handicaps diazotrophs by dampening the increase of their maximal growth rate versus that of other phytoplankton with rising temperature. We use cD = 0.5, such that the increase per °C warming of diazotrophs is 50% that of other phytoplankton. However, diazotrophs have an advantage in that their growth rate is not limited by NO3 concentrations:
although they do take up NO3 if it is available (see term 5 in the right-hand side of equation (A3)). The N:P of model diazotrophs is equal to other phytoplankton (16:1). Although there is evidence that the best-studied diazotrophs of the genus Trichodesmium can have much higher N:P [e.g., Sanudo-Wilhelmy et al., 2004], the more abundant unicellular diazotrophs are uncharacterized [Montoya et al., 2002] and for simplicity of interpretation we opted to keep the N:P of both phytoplankton groups identical.
 The first-order mortality rate of phytoplankton is linearly dependent on their concentration, PO. DOM and the microbial loop are folded into a single fast remineralization process, which is the product of PO and the temperature-dependent term
Diazotrophs do not undergo this fast remineralization, but die at a linear rate.
 Grazing of phytoplankton by zooplankton is unchanged from Schmittner et al. [2005a]. Detritus is generated from sloppy zooplankton feeding and mortality among the three classes of plankton, and is the only component of the ecosystem model to sink. It does so at a speed of
increasing linearly with depth z from wD0 = 7 m d−1 at the surface to 40 m d−1 at 1 km depth and constant below that, consistent with observations [Berelson, 2002]. The remineralization rate of detritus is temperature dependent and decreases by a factor of 5 in suboxic waters, as O2 decreases from 5 μM to 0 μM:
Remineralization returns the N and P content of detritus to NO3 and PO4. Photosynthesis produces oxygen, while respiration consumes oxygen, at rates equal to the consumption and remineralization rates of PO4, respectively, multiplied by the constant ratio RO:P. Dissolved oxygen exchanges with the atmosphere in the surface layer (Fsfc) according to the OCMIP protocol.
 Oxygen consumption in suboxic waters (<5 μM) is inhibited, according to
but is replaced by the oxygen-equivalent oxidation of nitrate,
Denitrification consumes nitrate at a rate of 80% of the oxygen equivalent rate, as NO3 is a more efficient oxidant on a mol per mol basis (i.e., 1 mol of NO3 can accept 5e− while 1 mol of O2 can accept only 4 e−). Note that the model does not include sedimentary denitrification, which would provide a large and less time-variant sink for fixed nitrogen. Because sedimentary denitrification would not change the qualitative dynamics of the model's behavior, but would slow the integration time, it is not included in the version presented here.