[42] 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 (O_{2}) and two nutrients, nitrate (NO_{3}) and phosphate (PO_{4}) which are linked through exchanges with the biological variables by constant (∼Redfield) stoichiometry (Table A1). The biological variables include two classes of phytoplankton, nitrogenfixing diazotrophs (P_{D}), and other phytoplankton (P_{O}), as well as zooplankton (Z) and particulate detritus (D); all biological variables are expressed in units of mmol nitrogen per m^{3}. Although very simple, this ecological structure captures the essential dynamic of competition for phosphorus highlighted by Tyrell [1999], in which phytoplankton capable of rapid growth using available nutrients (P_{O}) are pitted against slow growers capable of fixing their own supply of nitrogen (P_{D}). Additional information on the nitrogen cycle is given by Schmittner et al. [2007a].
Table A1. Ocean Ecosystem and Carbon Cycle Model ParametersParameter  Symbol  Value  Units 

Phytoplankton (P_{O}, P_{D}) Coefficients 
Initial slope of PI curve  α  0.1  (W m^{−2})^{−1} d^{−1} 
Photosynthetically active radiation  PAR  0.43  
Light attenuation in water  k_{w}  0.04  m^{−1} 
Light attenuation through phytoplankton  k_{c}  0.03  m^{−1}(mmol m^{−3})^{−1} 
Light attenuation through sea ice  k_{I}  5  m^{−1} 
Maximum growth rate  a  0.11  d^{−1} 
Halfsaturation constant for N uptake  k_{N}  0.7  mmol m^{−3} 
Specific mortality rate  μ_{P}  0.025  d^{−1} 
Fast recycling term (microbial loop)  μ_{P0}  0.02  d^{−1} 
Diazotrophs' handicap  c_{D}  0.5  

Zooplankton (Z) Coefficients 
Assimilation efficiency  γ_{1}  0.925  
Maximum grazing rate  g  1.575  d^{−1} 
Prey capture rate  ɛ  1.6  (mmol m^{−3})^{−2} d^{−1} 
Mortality  μ_{Z}  0.34  (mmol m^{−3})^{−2} d^{−1} 
Excretion  γ_{2}  0.01  d^{−1} 

Detritus (D) Coefficients 
Remineralization rate  μ_{D0}  0.048  d^{−1} 
Sinking speed at surface  w_{D0}  7  M d^{−1} 
Increase of sinking speed with depth  m_{w}  0.04  d^{−1} 
Efolding temperature of biological rates  T_{b}  15.65  °C 

Other Coefficients 
Molar elemental ratios  R_{C:N}  7  
R_{O:N}  13  
R_{N:P}  16  
R_{C:P}  112  
CaCO_{3} over nonphotosynthetical POC production ratio  R_{CaCO3/POC}  0.035  
CaCO_{3} remineralization efolding depth  D_{CaCO3}  3500  m 
[43] 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 J_{O} = J(I, NO_{3}, PO_{4}) provides the growth rate of nondiazotrophic phytoplankton, determined from irradiance (I), NO_{3} and PO_{4},
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 nutrientreplete conditions, the lightlimited growth rate J_{OI} is calculated according to
where α is the initial slope of the photosynthesis versus irradiance (PI) 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 J_{Omax} and the nutrient uptake rates, u_{N} = NO_{3}/(k_{N} + NO_{3}) and u_{P} = PO_{4}/(k_{P} + PO_{4}), with k_{P} = k_{N}R_{P:N} providing the respective nutrient uptake rates.
[44] Diazotrophs grow according to the same principles as the other phytoplankton, but are disadvantaged in nitratebearing waters by a lower maximum growth rate, J_{Dmax}, which is zero below 15°C:
The coefficient c_{D} handicaps diazotrophs by dampening the increase of their maximal growth rate versus that of other phytoplankton with rising temperature. We use c_{D} = 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 NO_{3} concentrations:
although they do take up NO_{3} if it is available (see term 5 in the righthand side of equation (A3)). The N:P of model diazotrophs is equal to other phytoplankton (16:1). Although there is evidence that the beststudied diazotrophs of the genus Trichodesmium can have much higher N:P [e.g., SanudoWilhelmy 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.
[45] The firstorder mortality rate of phytoplankton is linearly dependent on their concentration, P_{O}. DOM and the microbial loop are folded into a single fast remineralization process, which is the product of P_{O} and the temperaturedependent term
Diazotrophs do not undergo this fast remineralization, but die at a linear rate.
[46] 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 w_{D0} = 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 O_{2} decreases from 5 μM to 0 μM:
Remineralization returns the N and P content of detritus to NO_{3} and PO_{4}. Photosynthesis produces oxygen, while respiration consumes oxygen, at rates equal to the consumption and remineralization rates of PO_{4}, respectively, multiplied by the constant ratio R_{O:P}. Dissolved oxygen exchanges with the atmosphere in the surface layer (F_{sfc}) according to the OCMIP protocol.
[47] Oxygen consumption in suboxic waters (<5 μM) is inhibited, according to
but is replaced by the oxygenequivalent oxidation of nitrate,
Denitrification consumes nitrate at a rate of 80% of the oxygen equivalent rate, as NO_{3} is a more efficient oxidant on a mol per mol basis (i.e., 1 mol of NO_{3} can accept 5e^{−} while 1 mol of O_{2} can accept only 4 e^{−}). Note that the model does not include sedimentary denitrification, which would provide a large and less timevariant 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.