Predicted Effects of Climate Change on Northern Gulf of Mexico Hypoxia

Abstract

We describe the application of a coastal ocean ecosystem model to assess the effect of a future climate scenario of plus (+) 3 °C air temperature and + 10% river discharge on hypoxia (O₂ < 63 mmol m⁻³) in the northern Gulf of Mexico. We applied the model to the Louisiana shelf as influenced by the runoff from the Mississippi River basin. The net effect of the future climate scenario was a mean increase in water temperature of 1.1 °C and a decrease in salinity of 0.09 for the region of the shelf where hypoxia typically occurs (<50 m depth). These changes increased the strength of water column stratification at the pycnocline and increased phytoplankton biomass. In the future scenario, the hypoxic area was only 1% larger than the present. A more significant effect was in the duration and extent of severe hypoxic areas. Severe hypoxic areas, defined as model cells having hypoxia for more than 60 days in the year, had a mean increase in hypoxia duration of 9.5 days (a 10% increase). The severely hypoxic area also increased by 1,130 km² (an 8% increase) in the future scenario. The results confirm that a warmer and wetter future climate will, on average, worsen the extent and duration of hypoxia in this system. Thus, it is probable that long-term Mississippi River nutrient management for hypoxia will need to be adapted for climate change.

Appendices A–F

8.1.1 A. State Variables

CGEM state variables (Table A.1) are represented by time-dependent differential equations. Horizontal and vertical currents, vertical mixing, and sinking are implicit, and these terms are not shown in state variable equations. Currents, mixing, and temperature are hydrodynamic model outputs that are provided to CGEM by NCOM-LCS at each model time-step and point in the grid. State variables are presented below in the order that they appear in Table A.1.

Table A.1 State variables in CGEM code

8.1.1.1 A.1 Phytoplankton

For simplicity, in this implementation of CGEM, one phytoplankton functional type is modeled based on the dominant diatom on the Louisiana shelf, Skeletonema costatum. S. costatum accounted for 58% of the total phytoplankton abundance observed on the Louisiana shelf from 2002 to 2007 (data reported in Murrell et al. 2014). CGEM, however, is flexible in being able to represent up to 99 phytoplankton groups. Phytoplankton abundance (A, cells m⁻³) per group (i = 1:99) is calculated as

$$ \frac{d}{dt}A_{i} = Agrow_{i} - Aresp_{i} - ZgrazA\_tot_{i} - Amort_{i} . $$

(A1)

where Agrow is production (cells m⁻³ s⁻¹), Aresp (cells m⁻³ s⁻¹) is the sum of somatic and basal respiration, ZgrazA_tot (cells m⁻³ s⁻¹) is the total zooplankton grazing on A _i by the two zooplankton represented in the model, and Amort (cells m⁻³ s⁻¹) is the non-grazing mortality rate. Agrow, Aresp, Amort, and ZgrazA_tot are described in Appendix C, Eqs. (C1), (C7), (C11), and (C12), respectively.

Phytoplankton internal cell quotas (Q, mmol cell⁻¹) for nitrogen and phosphorus are calculated as

$$ \frac{d}{dt}Qn_{i} = vN_{i} - Qn_{i} \cdot uA_{i} - \frac{{AexudN_{i} }}{{A_{i} }} $$

(A2)

$$ \frac{d}{dt}Qp_{i} = vP_{i} - Qp_{i} \cdot uA_{i} - \frac{{AexudP_{i} }}{{A_{i} }} $$

(A3)

where vN and vP (mmol cell⁻¹ d⁻¹) are phytoplankton uptake of nitrogen and phosphorus, respectively (Eqs. C15–C17), Q·uA (mmol cell⁻¹ d⁻¹) is the utilization of Q to support the growth rate (uA, Eq. C2), and AexudN and AexudP are exudation (mmol cell⁻¹ d⁻¹) of nitrogen and phosphorus, respectively, associated with Aresp (Eqs. C9 and C10).

8.1.1.2 A.2 Zooplankton

Zooplankton (Z, individuals m⁻³) dynamics for two types (j = 1:2) are represented as

$$ \frac{d}{dt}Z_{j} = Zgrow_{j} - Zresp_{j} - Zmort_{j} $$

(A4)

where zooplankton growth (Zgrow), respiration (Zresp), and mortality (Zmort) are described in Eqs. (D1), (D6), and (D9), respectively.

8.1.1.3 A.3 Organic Matter

Particulate organic matter (OM1, mmol C m⁻³) from phytoplankton (OM1_A), zooplankton (OM1_Z), rivers (OM1_R), and boundary conditions (OM1_BC) are calculated as

$$ \frac{d}{dt}OM1\_A = ROM1\_A + \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \frac{{Q\,min\,N_{i} }}{{Qn_{i} }} \cdot Qc_{i} } \right)} , $$

(A5)

$$ \begin{aligned} \frac{d}{dt}OM1\_Z & = ROM1\_Z + ZegC_{1} + ZunC_{1} + ZmortC_{1} + ZmortC_{2} \\ & \quad + \left( {OM1\_Ratio \cdot ZslopC\_tot} \right) \\ \end{aligned} $$

(A6)

$$ \frac{d}{dt}OM1\_R = ROM1\_R $$

(A7)

$$ \frac{d}{dt}OM1\_BC = ROM1\_BC. $$

(A8)

In Eq. (A5), ROM1 is the OM1 remineralization rate and is a loss term for OM1 (e.g., Eq. E39), QminN and Qc are parameters for the minimum cellular N quota and the fixed C quota per phytoplankton cell (Table A.2), respectively. In Eq. (A6), ZegC ₁ is the Z ₁ carbon in excess of growth requirements that is egested in fecal pellets (Eq. E18), ZunC ₁ is the Z ₁ ingested carbon that is unassimilated in the gut and also released in fecal pellets (Eq. D4), ZslopC_tot is the organic matter released during sloppy feeding by both Z ₁ and Z ₂ (Eq. D4), and OM1_Ratio (Eq. E19) is the fraction of organic matter derived from sloppy feeding that becomes OM1_Z.

Table A.2 Phytoplankton parameters

Dissolved organic matter (OM2, mmol C m⁻³) dynamics are represented by

$$ \frac{d}{dt}OM2\_A = - ROM2\_A + \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \frac{{Qn_{i} - Q\hbox{min} N_{i} }}{{Qn_{i} }} \cdot Qc_{i} } \right)} , $$

(A9)

$$ \frac{d}{dt}OM2\_Z = - ROM2\_Z + ZegC_{2} + ZunC_{2} + \left( {OM2\_Ratio \cdot ZslopC} \right) $$

(A10)

$$ \frac{d}{dt}OM2\_R = - ROM2\_R $$

(A11)

$$ \frac{d}{dt}OM2\_BC = - ROM2\_BC. $$

(A12)

In (A9), ROM2 is the OM2 remineralization rate (e.g., Eq. E40). In (A10), ZegC ₂ is the Z ₂ carbon in excess of growth requirements that is egested (Eq. E18), ZunC ₂ is the Z ₂ ingested carbon that is not assimilated (Eq. D5), and OM2_Ratio (Eq. E20) is the fraction of organic matter derived from sloppy feeding that becomes OM2_Z.

CDOM in concentration units (QSE ppb) is input to the model from riverine loading, and once in the model, the only biogeochemical fate is to decay. Thus, the time rate of change for CDOM is

$$ \frac{d}{dt}CDOM = - Kcdom\_decay \cdot CDOM $$

(A13)

where Kcdom_decay is the decay rate (Table A.5).

Table A.3 Optical parameters

8.1.1.4 A.4 Nutrients

NH ₄ (mmol m⁻³) sources and sinks are described by

$$ \frac{d}{dt}NH_{4} = RNH_{4} - R\_11 - AupN\frac{NH_{4}}{NH_{4} + NO_{3}} + AexudN + ZexN. $$

(A14)

where RNH ₄ (Eq. E51) is the production of NH ₄ due to remineralization of organic matter (Eq. E28), R_11 is the nitrification rate (Eq. E43), AupN (Eq. C17) is the phytoplankton uptake of dissolved inorganic nitrogen (NH ₄ + NO ₃ ), AexudN is the phytoplankton exudation of nitrogen driven by respiration (Eq. C9), and ZexN is the zooplankton excretion of nitrogen driven by respiration (Eq. D7).

Change in NO ₃ (mmol m⁻³) is represented as

$$ \frac{d}{dt}NO_{3} = RNO_{3} + R\_11 - AupN\frac{NO_{3}}{NO_{3} + NH_{4}} $$

(A15)

where RNO ₃ (Eq. E48) is negative and represents NO ₃ lost to denitrification (Eq. E30) and AupN is modified by the fraction of NO ₃ in the pool of NO ₃ +NH ₄ to represent phytoplankton NO ₃ uptake.

PO ₄ (mmol m⁻³) is calculated as

$$ \frac{d}{dt}PO_{4} = RPO_{4} - AupP + AexudP + ZexP $$

(A16)

where RPO ₄ (Eq. E49) is the production of PO ₄ from remineralization of organic matter, AupP is phytoplankton uptake of PO ₄ (Eq. C17), AexudP is phytoplankton exudation of PO ₄ driven by respiration (Eq. C10), and ZexP is zooplankton excretion of PO ₄ (Eq. D8).

Change in Si (mmol m⁻³) is represented by

$$ \frac{d}{dt}Si = RSi - AupSi + ZegSi + ZunSi. $$

(A17)

where RSi (Eq. E53) is Si produced by remineralization of organic matter, where the organic matter stoichiometry is assumed to have an Si:N = 1. AupSi is the phytoplankton uptake of Si (Eq. C17). ZegSi and ZunSi are the zooplankton egestion of Si and zooplankton unassimilated Si, respectively, and are set equal to ZegN (Eq. E18) and ZunN (Eq. D5), respectively.

8.1.1.5 A.5 Oxygen

O ₂ (mmol m⁻³) is represented by

$$ \begin{aligned} \frac{d}{dt}O_{2} & = RO_{2} - 2 \cdot R\_11 + Agrow \cdot Qc - Aresp \cdot Qc - Zresp \cdot Zc \\ & \quad \pm Air{ - }Sea \, Exchange \\ \end{aligned} $$

(A18)

where RO ₂ is the aerobic oxygen consumption associated with organic matter remineralization (Eqs. E41 and E42) and air-sea exchanges are described in Appendix F.

8.1.2 B. Optical Equations

Irradiance is modeled using inherent optical properties (IOPs) to calculate light attenuation (k). The main advantage of this approach is that the absorption (a) and backscattering (b _b ) of light are calculated, which could facilitate comparison of modeled and observed IOPs as these observations become more common. This approach could also be extended to a multi-spectral treatment. k is calculated (Penta et al. 2008; 2009) as

$$ \begin{aligned} & E_{z} = E_{0} e^{ - k(z)z} \\ & k(z) = k_{1} + \frac{{k_{2} }}{{\left( {1 + z} \right)^{0.5} }} \\ & k_{1} = \left[ {\chi_{0} + \chi_{1} \left( {a_{490} } \right)^{0.5} + \chi_{2} b_{{b_{490} }} } \right]\left( {1 + \alpha_{0} sin\,\theta_{a} } \right) \\ & k_{2} = \left[ {\zeta_{0} + \zeta_{1} \left( {a_{490} } \right)^{0.5} + \zeta_{2} b_{{b_{490} }} } \right]\left( {\alpha_{1} + \alpha_{2} cos\,\theta_{a} } \right) \\ \end{aligned} $$

(B1)

where E _z is irradiance at depth z, E ₀ is the irradiance at the surface layer above z, model coefficients include χ, ζ, and α (Table A.3), and θ _a is the solar zenith angle calculated as a function of latitude and time. Absorption at wavelength 490 nm (a _490, m⁻¹) is calculated as

$$ a_{490} \, = a_{{Chl_{490} }} + a_{{CDOM_{490} }} + a_{{SPM_{490} }} + a_{{w_{490} }} $$

(B2)

where a _Chl is the absorption by chlorophyll (Chl), a _CDOM is the absorption by colored dissolved organic matter (CDOM), a _SPM is the absorption by suspended particulate matter (SPM), and a _w is the absorption by seawater and is a model parameter (Table A.3). a _Chl is calculated as

$$ a_{{Chl_{490} }} = astar490 \cdot Chl $$

(B3)

where astar490 (Table A.3) is Chl-specific absorption and total Chl (mg m⁻³) is calculated as

$$ Chl = \sum\limits_{i = 1}^{6} {\left( {Chl:cell} \right)} \cdot A_{i} $$

(B4)

where Chl:cell is the chlorophyll per cell (mg cell⁻¹) (see Eq. B5) and A _i is the phytoplankton cell abundance (cells m⁻³ d⁻¹). Chl:cell is calculated for the Louisiana shelf using an empirical equation based on observations of cell abundance and Chla (Murrell et al. 2014). A regression relating these variables (R² = 0.81), with intercept set equal to zero, has the form $Chl = 3.0 \times 10^{ - 9} \cdot CellAbundance$, where 3.0 × 10⁻⁹ is the slope of the observed relationship between chlorophyll a and phytoplankton abundance (i.e., Chl:cell).

a _CDOM is based on CDOM (Eq. A13) loaded to the model domain from terrestrial sources. In the case of the Louisiana shelf, CDOM loaded from the rivers is derived from regression equations relating observed riverine CDOM and DOC concentrations. The Mississippi River monthly time-series of observed DOC (mg l⁻¹) (USGS data) was converted to a _CDOM at wavelength 440 (m⁻¹) by the regression equation (Spencer et al. 2012)

$$ a_{{CDOM_{440} }} \, = \, 1.10 \cdot DOC - 2.76. $$

(B5)

Next, $a_{{CDOM_{440} }}$ was converted to $a_{{CDOM_{312} }}$ with the general a _λ = a _λref ∙e ^-S(λ-λref), i.e.,

$$ a_{{CDOM_{312} }} = a_{{CDOM_{440} }} \cdot e^{{ - S\left( {312 - 440} \right)}} $$

(B6)

where S is the spectral slope of CDOM (S = 0.016) (Spencer et al. 2012; D’Sa and Dimarco 2009). Then, $a_{{CDOM_{312} }}$ was converted to CDOM concentration using the regression equation (Conmy et al. 2004)

$$ {\text{CDOM}} = \, 2.933 \cdot a_{{CDOM_{312} }} + 0.538 $$

(B7)

Thus, in the model for the Louisiana shelf, Eqs. (B5–B7) are applied to riverine DOC observations. CDOM concentration is then input by the rivers to the shelf model domain where it is decayed by Eq. (A13) and advected and mixed. $a_{{CDOM_{490} }}$ is required in Eq. (B2). Thus, CDOM is first back-transformed to $a_{{CDOM_{312} }}$ using the Conmy et al. (2004) equation, and then $a_{{CDOM_{312} }}$ is converted to $a_{{CDOM_{490} }}$ by

$$ a_{{CDOM_{490} }} = a_{{CDOM_{312} }} \cdot e^{{ - S\left( {490 - 312} \right)}} . $$

(B8)

a _SPM (m⁻¹) at 490 nm is calculated as the sum of absorption by the different types of OM1 as

$$ a_{{SPM_{490} }} \, = \left( \begin{aligned} astarOMA \cdot OM1\_A + astarOMZ \cdot OM1\_Z + \hfill \\ astarOMR \cdot \frac{OM1\_R}{CF\_SPM} + astarOMBC \cdot OM1\_BC \hfill \\ \end{aligned} \right) \cdot \frac{12}{1000} $$

(B9)

where astarOM terms are parameters (Table A.3), CF_SPM is a conversion factor for adjusting OM1_R to river SPM. For the application of CGEM to the Louisiana shelf, CF_SPM = 1.8% (Table A.3) was based on the average observed POC/SPM = 1.8% in the Mississippi and Atchafalaya Rivers (USGS data). The factor 12/1000 converts from mmol m⁻³ to g m⁻³.

Backscattering in Eq. (B1) was calculated (Penta et al. 2008; 2009) as a function of Chl as

$$ b_{b,490} \, = 0.015 \cdot \left( {0.3 \cdot Chl^{0.62} \cdot \left( {\frac{550}{490}} \right)} \right). $$

(B10)

8.1.3 C. Phytoplankton Equations

8.1.3.1 C.1 Phytoplankton Growth

Growth (Agrow, cells m⁻³ d⁻¹) for each phytoplankton group is calculated as

$$ Agrow_{i} = \mu_{{A_{i} }} A_{i} $$

(C1)

where µ _A is the specific growth rate (d⁻¹) and A is the phytoplankton abundance (cells m⁻³). Agrow is converted to units of carbon (mmol C m⁻³ d⁻¹) by the product $Agrow_{i} \cdot Q_{{C_{i} }}$, where Q _C is a parameter specifying the carbon per cell (mmol C cell⁻¹) (Table A.2).

The specific growth is calculated based on Liebig’s law of the minimum

$$ \mu_{{A_{i} }} = u_{{\hbox{max} A_{i} }} \cdot func\_T_{i} \cdot MIN\left[ {func\_E_{i} ,func\_N_{i} ,func\_P_{i} ,func\_Si_{i} } \right] $$

(C2)

where func_T, func_E, func_N, func_P, and func_Si are limiting factors due to temperature (Eldridge and Roelke 2010), PAR, nitrogen, phosphorus, and silica, respectively. PAR- and nutrient-dependent growth equations are shown below.

8.1.3.2 C.2 Phytoplankton Light–Growth Dependence

Light dependence func_E is represented by

$$ func\_E = \left( {1 - e^{{\frac{{ - alpha_{i} E}}{{u\max_{i} }}}} } \right). $$

(C3)

8.1.3.3 C.3 Phytoplankton Nutrient–Growth Dependence

Nitrogen and phosphorus dependence are modeled (Droop 1973) as

$$ func\_N = \frac{{Qn_{i} - Q\,min\,N_{i} }}{{Qn_{i} }} $$

(C4)

$$ func\_P = \frac{{Qp_{i} - Q\,min\,P_{i} }}{{Qp_{i} }} $$

(C5)

where Q _min is the minimum nutrient cell quota (mmol cell⁻¹) per phytoplankton group required for survival and Q is the cell quota (mmol cell⁻¹).

Silica dependence is modeled as a function of seawater silicate concentration

$$ func\_Si = \frac{Si}{Si + Ksi} $$

(C6)

where Si is the modeled silicate concentration (mmol m⁻³) and Ksi is the half-saturation concentration (mmol m⁻³) of silica uptake.

8.1.3.4 C.4 Phytoplankton Losses

Phytoplankton respiration (cells m⁻³ d⁻¹) is represented as a function of growth, cell abundance, and temperature

$$ Aresp_{i} = respg_{i} \cdot Agrow_{i} + respb_{i} \cdot A_{i} \cdot func\_T $$

(C7)

where respg is a respiration coefficient that scales to growth rate and respb represents basal maintenance activities that scale to abundance. Phytoplankton respiration results in a loss of carbon from the cell (ArespC) and nutrient exudation (Aexud _i , mmol m⁻³ d⁻¹) as

$$ Aresp\,{\text{C}} = \sum\limits_{i = 1}^{6} {Aresp_{i} \cdot Qc_{i} } $$

(C8)

$$ AexudN = \sum\limits_{i = 1}^{6} {Aresp_{i} \cdot Qn_{i} } $$

(C9)

$$ AexudP = \sum\limits_{i = 1}^{6} {Aresp_{i} \cdot Qp_{i} } . $$

(C10)

Phytoplankton mortality (Amort, cells m⁻³ d⁻¹) is calculated by

$$ Amort_{i} = A_{i} \cdot mA_{i} $$

(C11)

where mA _i is the mortality rate (d⁻¹).

Phytoplankton sinking losses (cells m⁻³ d⁻¹) are applied implicitly in the advection and mixing routines with sinking velocities prescribed by the parameter sink (Table A.2).

Grazing losses (ZgrazA_tot, cells m⁻³ d⁻¹) are calculated as

$$ ZgrazA\_tot_{i} = \sum\limits_{j = 1}^{2} {\frac{{Zgrazvol_{ji} }}{{volcell_{i} }}} . $$

(C12)

The term Zgrazvol _ji is the grazing rate by each zooplankton (j = 1:2) on each phytoplankton (i) in units of biovolume (µm3 m⁻³ d⁻¹) and is calculated by

$$ Zgrazvol_{ji} = Z_{j} \cdot Zu\,max_{j} \cdot monod\,Z_{ji} $$

(C13)

where Zumax _j is the maximum growth rate of the zooplankton in terms of volume of prey (Table A.4) and monodZ _ij is a hyperbolic function represented by

$$ monodZ_{ij} = \frac{{\left( {Abiovol_{i} - \, Athresh_{i} \cdot volcell_{i} } \right) \cdot ediblevector_{i} }}{{ZKa_{j} + \sum\limits_{i = 1}^{6} {\left( {Abiovol_{i} \cdot ediblevector_{i} } \right)} }}, $$

(C14)

where Abiovol (= A _i ·volcell _i ) is the biovolume, Athresh is the threshold abundance (cells m⁻³) below which grazing of A _i does not occur, ediblevector is a vector expressing prey edibility (unitless, range = 0–1), and ZKa is the grazing half-saturation (Table A.4).

Table A.4 Phytoplankton parameters

8.1.3.5 C.5 Phytoplankton Uptake and Utilization of N, P, and Si

Nutrient uptake by the modeled phytoplankton only occurs during the day. For the rate-limiting nutrient substrate (S), which is determined as the min[f_N, f_P, f_Si], the nutrient uptake rate (vS, mmol cell⁻¹ d⁻¹) for each phytoplankton group is calculated as

$$ vS_{i} = vmaxS_{i} \cdot \frac{S}{{\left( {S + K_{{S_{i} }} } \right)}} \cdot Q10 $$

(C15)

where v _max S is the maximum uptake rate (mmol cell ⁻¹ d⁻¹), K _S is the half-saturation concentration (mmol m⁻³) (Table A.2), and Q10 is the temperature adjustment factor such that a doubling of the rate occurred for a 10 °C change in temperature.

If S is not the rate-limiting nutrient, the uptake is modified by an additional limitation term as

$$ vS_{i} = vmaxS_{i} \cdot \frac{S}{{\left( {S + K_{{S_{i} }} } \right)}} \cdot Q10 \cdot func\_Qs_{i} \cdot \frac{RLN}{{RLN + a_{S} \cdot K_{{RLN_{i} }} }} $$

(C16)

where RLN is the substrate concentration of the rate-limiting nutrient (RLN), K _RLN is the half-saturation concentration of the RLN, and a _S is a scaling factor (Roelke et al. 1999).

The total phytoplankton uptake of nutrient (shown here for nitrogen, i.e., AupN) is then

$$ AupN = \sum\limits_{i = 1}^{6} {\left( {vN_{i} \cdot A} \right)_{i} } . $$

(C17)

8.1.4 D. Zooplankton Equations

Zooplankton growth rates (individuals m⁻³ d⁻¹) are modeled as

$$ Zgrow_{j} = func\_T \cdot MIN\left( {\frac{{ZinN_{j} }}{{ZQn_{j} }},\frac{{ZinP_{j} }}{{ZQp_{j} }}} \right). $$

(D1)

where ZinN and ZinP are zooplankton ingestion rates of nitrogen and phosphorus (mmol m⁻³ d⁻¹), and ZQn and ZQp are zooplankton N and P quota parameters, respectively (mmol per individual, Table A.4). ZinN, ZinP, and zooplankton ingestion of carbon (ZinC) are calculated similarly. For brevity, only the nitrogen equations are shown. Carbon and phosphorus equations are analogous. Thus, for ZinN,

$$ ZinN_{j} = ZgrazN_{j} - ZslopN_{j} - ZunN_{j} $$

(D2)

$$ ZgrazN_{j} = \sum\limits_{i = 1}^{6} {ZgrazA_{ij} \cdot Qn_{i} } $$

(D3)

$$ ZslopN_{j} = Zslop_{j} \cdot ZgrazN_{j} $$

(D4)

$$ ZunN_{j} = \left( {1 - Zeffic_{j} } \right) \cdot \left( {ZgrazN_{j} - ZslopN_{j} } \right) $$

(D5)

where ZgrazN (mmol N m⁻³ d⁻¹) is the grazing in units of nitrogen, ZgrazA is described in Eq. (C12), ZslopN is sloppy feeding (mmol N m⁻³ d⁻¹), Zslop is a sloppy feeding parameter (range = 0–1, Table A.4), and ZunN (mmol N m⁻³ d⁻¹) is the amount of zooplankton unassimilated nitrogen, which is a function of the assimilation efficiency (Zeffic, range = 0–1, Table A.4) of each zooplankton.

Zooplankton respiration loss (individuals m⁻³ d⁻¹) is represented with two terms

$$ Zresp_{j} = Zrespg_{j} \cdot Zgrow_{j} + Zrespb_{j} \cdot Z_{i} \cdot func\_T $$

(D6)

where Zrespg and Zrespb are respiration coefficients (Table A.4) on zooplankton growth and basal metabolism. Zooplankton excretion of nutrients (Zex, mmol m⁻³ d⁻¹) is used to mass balance zooplankton respiratory loss of CO₂ by

$$ ZexN = \sum\limits_{j = 1}^{2} {ZrespTot_{j} \cdot ZQn_{j} } $$

(D7)

$$ ZexP = \sum\limits_{j = 1}^{2} {ZrespTot_{j} \cdot ZQp_{j} } . $$

(D8)

Zooplankton mortality (individuals m⁻³ d⁻¹) is treated as a quadratic function of zooplankton abundance (Cerco and Noel 2004) and is assumed to mainly occur by predation from other trophic levels

$$ Zmort_{j} = Zm_{j} Z_{j}^{2} $$

(D9)

where Zm is the zooplankton mortality coefficient (Table A.4)

8.1.5 E. Organic Matter Equations

8.1.5.1 E.1 Organic Matter Types and Stoichiometry

Eight classes of organic matter representing phytoplankton, zooplankton, river, and boundary condition OM are tracked in the model in both particulate (OM1) and dissolved (OM2) forms and with variable stoichiometry C _x N _y P _z . OM1 and OM2 are created (mmol m⁻³ d⁻¹) in the model by phytoplankton and zooplankton mortality, zooplankton sloppy feeding, zooplankton egestion, and unassimilated OM that passes through the zooplankton. We simply represent partitioning of Amort to OM1_A and OM2_A based on cell quotas, which assumes that Qmin may be used as a proxy for separating particulate and dissolved fractions

$$ OM1\_CA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \frac{{Qn_{i} - Q\,min\,N_{i} }}{{Qn_{i} }} \cdot Qc_{i} } \right)} $$

(E1)

$$ OM1\_NA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot Q\,min\,N_{i} } \right)} $$

(E2)

$$ OM1\_PA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot Q\,min\,P_{i} } \right)} $$

(E3)

$$ OM2\_CA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \frac{{Q\,min\,N_{i} }}{{Qn_{i} }} \cdot Qc_{i} } \right)} $$

(E4)

$$ OM2\_NA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \left( {Qn_{i} - Q\,min\,N_{i} } \right)} \right)} $$

(E5)

$$ OM2\_PA = \sum\limits_{i = 1}^{6} {\left( {Amort_{i} \cdot \left( {Qp_{i} - Q\,min\,P_{i} } \right)} \right)} . $$

(E6)

Dynamic stoichiometric ratios (C _x N _y P _z ) of OM1_A and OM2_A are tracked as

$$ stoich\_x1A = \frac{{\left( {OM1\_CA + OM1\_A} \right)}}{{OM1\_PA + \frac{1}{stoich\_x1A} \cdot OM1\_A}} $$

(E7)

$$ stoich\_y1A = \frac{{\left( {OM1\_NA + \frac{stoich\_y1A}{stoich\_x1A} \cdot OM1\_A} \right)}}{{OM1\_PA + \frac{1}{stoich\_x1A} \cdot OM1\_A}} $$

(E8)

$$ stoich\_x2A = \frac{{\left( {OM2\_CA + OM2\_A} \right)}}{{OM2\_PA + \frac{1}{stoich\_x2A} \cdot OM2\_A}} $$

(E9)

$$ stoich\_y2A = \frac{{\left( {OM2\_NA + \frac{stoich\_y2A}{stoich\_x2A} \cdot OM2\_A} \right)}}{{OM2\_PA + \frac{1}{stoich\_x2A} \cdot OM2\_A}} $$

(E10)

$$ stoich\_z1A = stoich\_z2A = 1. $$

(E11)

Organic matter C, N, and P derived from zooplankton are calculated as

$$ OM1\_CZ = ZegC_{1} + ZunC_{1} + ZmortC_{1} + ZmortC_{2} + \left( {OM1\_Ratio \cdot ZslopC} \right) $$

(E12)

$$ OM1\_NZ = ZegN_{1} + ZunN_{1} + ZmortN_{1} + ZmortN_{2} + \left( {OM1\_Ratio \cdot ZslopN} \right) $$

(E13)

$$ OM1\_PZ = ZegP_{1} + ZunP_{1} + ZmortP_{1} + ZmortP_{2} + \left( {OM1\_Ratio \cdot ZslopP} \right) $$

(E14)

$$ OM2\_CZ = ZegC_{2} + ZunC_{2} + \left( {OM2\_Ratio \cdot ZslopC} \right) $$

(E15)

$$ OM2\_NZ = ZegN_{2} + ZunN_{2} + \left( {OM2\_Ratio \cdot ZslopN} \right) $$

(E16)

$$ OM2\_PZ = ZegP_{2} + ZunP_{2} + \left( {OM2\_Ratio \cdot ZslopP} \right) $$

(E17)

where Zun and Zslop equations are presented in Appendix D and zooplankton egestion (Zeg) is calculated as follows. Zeg in the model is governed by an optimal nutrient ratio of the zooplankton, i.e., ZQn/ZQp, such that

$$ \begin{aligned} & if\,ZinN_{j} \, > \, \frac{{ZQn_{j} }}{{ZQp_{j} }} \cdot ZinP_{j} \\ & ZegN_{j} = ZinN_{j} - ZinP_{j} \cdot \frac{{ZQn_{j} }}{{ZQp_{j} }} \\ & ZegC_{j} = ZinC_{j} - \frac{{ZinP_{j} }}{{ZQp_{j} }} \cdot ZQc_{j} \\ & ZegP_{j} = 0 \\ \\ & else \\ & ZegP_{j} = ZinP_{j} - ZinN_{j} \cdot \frac{{ZQp_{j} }}{{ZQn_{j} }} \\ & ZegC_{j} = ZinC_{j} - \frac{{ZinN_{j} }}{{ZQn_{j} }} \cdot ZQc_{j} \\ & ZegN_{j} = 0. \\ \end{aligned} $$

(E18)

Similar to the OM derived from mortality of phytoplankton cells being split into OM1_A and OM2_A, OM from sloppy feeding on phytoplankton cells is split into particulate and dissolved OM fractions based on the calculated OM1_Ratio and OM2_Ratio as

$$ OM1\_Ratio = \frac{{\sum\nolimits_{i = 1}^{6} {A_{i} \cdot \frac{{Qn_{i} - Q\,min\,N_{i} }}{{Qn_{i} }}} }}{{\sum\nolimits_{i = 1}^{6} {A_{i} } }} $$

(E19)

$$ OM2\_Ratio = \frac{{\sum\nolimits_{i = 1}^{6} {A_{i} \cdot \frac{{Q\,min\,N_{i} }}{{Qn_{i} }}} }}{{\sum\nolimits_{i = 1}^{6} {A_{i} } }}. $$

(E20)

C, N, and P stoichiometry of OM1_Z and OM2_Z are tracked as

$$ stoich\_x1Z = \frac{{\left( {OM1\_CZ + OM1\_Z} \right)}}{{OM1\_PZ + \frac{1}{stoich\_x1Z} \cdot OM1\_Z}} $$

(E21)

$$ stoich\_y1Z = \frac{{\left( {OM1\_NZ + \frac{stoich\_y1Z}{stoich\_x1Z} \cdot OM1\_Z} \right)}}{{OM1\_PZ + \frac{1}{stoich\_x1Z} \cdot OM1\_Z}} $$

(E22)

$$ stoich\_x2Z = \frac{{\left( {OM2\_CZ + OM2\_Z} \right)}}{{OM2\_PZ + \frac{1}{stoich\_x2Z} \cdot OM2\_Z}} $$

(E23)

$$ stoich\_y2Z = \frac{{\left( {OM2\_NZ + \frac{stoich\_y2Z}{stoich\_x2Z} \cdot OM2\_Z} \right)}}{{OM2\_PZ + \frac{1}{stoich\_x2Z} \cdot OM2\_Z}} $$

(E24)

$$ stoich\_z1Z = stoich\_z2Z = 1. $$

(E25)

8.1.5.2 E.2 Reaction Equations

Primary production (PrimProd) of organic matter by phytoplankton is

$$ Prim\,Prod = \sum\limits_{i = 1}^{6} {Agrow_{i} \cdot Qc_{i} } $$

(E26)

and proceeds according to the photosynthesis reaction

$$ xCO_{2} + yDIN + zDIP {\mathop{\longrightarrow }^{uptake}} C_{x} N_{y} P_{z} + xO_{2} $$

(E27)

where dissolved inorganic nitrogen (DIN) and dissolved inorganic phosphorus (DIP) are taken up to produce organic matter with C:N:P stoichiometry of Qc:Qn:Qp.

Organic matter oxidation by aerobic respiration is represented by

$$ C_{x} N_{y} P_{z} + xO_{2} {\mathop{\longrightarrow }^{RI}}xCO_{2} + yNH_{4} + zPO_{4} $$

(E28)

where R1 is

$$ R1 = \frac{O_{2}}{KO_{2} + O_{2}} $$

(E29)

and KO ₂ is the Monod half-saturation constant (Table A.5).

Table A.5 Organic matter parameters

The organic matter reaction during denitrification uses the reaction equation of Van Cappellen and Wang (1996)

$$ \begin{aligned} & C_{x} N_{y} P_{z} + \left( {\frac{4x + 3y}{5}} \right)NO_{3}\mathop{\longrightarrow}\limits{R2} \\ & \left( {\frac{2x + 4y}{5}} \right)N_{2} + \left( {\frac{x - 3y + 10z}{5}} \right)CO_{2} + \left( {\frac{4x + 3y - 10z}{5}} \right)HCO3 + zPO_{4} \\ \end{aligned} $$

(E30)

where R2 is

$$ R2 = \frac{NO_{3}}{KNO_{3} + NO_{3}}\frac{KstarO_{2}}{KstarO_{2} + O_{2}} $$

(E31)

and KNO ₃ is a Monod half-saturation constant (Table A.5), and KstarO ₂ is an O ₂ -based inhibition constant (Table A.5) that limits denitrification when O ₂ concentrations approach and exceed KstarO ₂ .

Reaction rates (R) are determined for organic matter remineralization (ROM, mmol C m⁻³ d⁻¹), O ₂ utilization (RO ₂ , mmol O₂ m⁻³ d⁻¹), nitrification (R_11, mmol N m⁻³ d⁻¹) and denitrification (RNO ₃ , mmol N m⁻³ d⁻¹), and remineralization of PO ₄ (RPO ₄ , mmol P m⁻³ d⁻¹), NH ₄ (RNH4, mmol C m⁻³ d⁻¹), and Si (RSi, mmol C m⁻³ d⁻¹). The remineralization equations are identical for the four sources of OM and, for brevity, are only shown for OM_A.

Organic matter decay coefficients are adjusted for temperature by a Q10 relation

$$ KG1\_Q10 = 10^{RQ1} $$

(E32)

$$ KG2\_{\text{Q}}\,10 = 10^{RQ2} . $$

(E33)

where RQ1 and RQ2 are intermediate variables calculated as

$$ RQ1 = LOG10(KG1) - FACTOR $$

(E34)

$$ RQ2 = LOG10(KG2) - FACTOR $$

(E35)

and

$$ FACTOR = LOG10(2) \cdot 0.1 \cdot (TQ1 - TQ2) $$

(E36)

where TQ1 is the reference temperature of 25 °C and TQ2 is the temperature in the model.

The temperature-adjusted reaction (RCT) rates for OM1_A and OM2_A are then calculated as

$$ RCT1\_A = KG1\_Q10 \cdot OM1\_A $$

(E37)

$$ RCT2\_A = KG2\_Q10 \cdot OM2\_A. $$

(E38)

ROM1_A and ROM2_A are calculated as

$$ ROM1\_A = - \left( {RCT1\_A \cdot R1 + RCT1\_A \cdot R2} \right) $$

(E39)

$$ ROM2\_A = - \left( {RCT2\_A \cdot R1 + RCT2\_A \cdot R2} \right). $$

(E40)

O₂ consumption associated with remineralization (RO ₂ , mmol m⁻³ d⁻¹) is

$$ RO_{2}\_A = \left( {RCT1\_A + RCT2\_A} \right) \cdot R1 $$

(E41)

and

$$ RO_{2} = RO_{2}\_A + RO_{2}\_Z + RO_{2}\_R + RO_{2}\_BC. $$

(E42)

Nitrification proceeds as a function of NH ₄ and O ₂ concentration (Van Cappellen and Wang 1996) as

$$ NH_{4}^{ + } + 2O_{2} + 2HCO_{3}^{ - } {\mathop{\longrightarrow}^{R\_11}}NO_{3}^{ - } + 2CO_{2} + 3H_{2} O $$

(E43)

where R_11 is the reaction rate defined as

$$ R\_11 = nit\,max \cdot \frac{O_{2}}{KO_{2} + O_{2}} \cdot \frac{NH_{4}}{KNH_{4} + NH_{4}} \cdot Q10 $$

(E44)

where nitmax is the parameterized maximum nitrification rate and KNH ₄ is the half-saturation constant (Table A.5). For the denitrification reaction (Eq. E30), reaction stoichiometry is taken into account in intermediate variables (GAM14 and GAM24) calculated as

$$ GAM14 = \frac{4 \cdot stoich\_x1A + 3 \cdot stoich\_y1A}{{\frac{5}{stoich\_x1A}}} $$

(E45)

$$ GAM24 = \frac{4 \cdot stoich\_x2A + 3 \cdot stoich\_y2A}{{\frac{5}{stoich\_x2A}}} $$

(E46)

where the coefficients 4, 3, and 5 are the coefficients to NO ₃ in Eq. (E30). Denitrification (RNO ₃ ) using OM1_A and OM2_A as electron donors is represented by

$$ RNO_{3}\_A = - \left( {GAM14 \cdot RCT1\_A + GAM24 \cdot RCT2\_A} \right) \cdot R2. $$

(E47)

Then, RNO ₃ is

$$ RNO_{3} = RNO_{3}\_A + RNO_{3}\_Z + RNO_{3}\_R + RNO_{3}\_BC. $$

(E48)

Remineralization of PO ₄ during the OM oxidation reactions is calculated as

$$ RPO_{4} = RPO_{4}\_A + RPO_{4}\_Z + RPO_{4}\_R + RPO_{4}\_BC $$

(E49)

with

$$ RPO_{4}\_A = ROM1\_A \cdot \frac{stoich\_z1A}{stoich\_x1A} + ROM2\_A \cdot \frac{stoich\_z2A}{stoich\_x2A}. $$

(E50)

Remineralization of NH ₄ is

$$ RNH_{4} = RNH_{4}\_A + RNH_{4}\_Z + RNH_{4}\_R + RNH_{4}\_BC $$

(E51)

with

$$ RNH_{4}\_A = \left( {RCT1\_A \cdot \frac{stoich\_y1A}{stoich\_x1A} + RCT2\_A \cdot \frac{stoich\_y2A}{stoich\_x2A}} \right) \cdot R1 $$

(E52)

The rate of Si remineralization is

$$ RSi = RSi\_A + RSi\_Z + RSi\_R + RSi\_BC $$

(E53)

with Si stoichiometrically linked to remineralization of N as Si:N = 1 such that

$$ RSi\_A = ROM1\_A \cdot \frac{stoich\_y1A}{stoich\_x1A} + ROM2\_A \cdot \frac{stoich\_y2A}{stoich\_x2A}. $$

(E54)

8.1.6 F. Air–Sea Exchange

Air–sea exchanges of O ₂ were modeled based on concentration gradients and wind speed (Eldridge and Roelke 2010).