Climate Change Influences Carrying Capacity in a Coastal Embayment Dedicated to Shellfish Aquaculture

Abstract

A spatially explicit coupled hydrodynamic-biogeochemical model was developed to study a coastal ecosystem under the combined effects of mussel aquaculture, nutrient loading and climate change. The model was applied to St Peter’s Bay (SPB), Prince Edward Island, Eastern Canada. Approximately 40 % of the SPB area is dedicated to mussel (Mytilus edulis) longline culture. Results indicate that the two main food sources for mussels, phytoplankton and organic detritus, are most depleted in the central part of the embayment. Results also suggest that the system is near its ultimate capacity, a state where the energy cycle is restricted to nitrogen-phytoplankton-detritus-mussels with few resources left to be transferred to higher trophic levels. Annually, mussel meat harvesting extracts nitrogen (N) resources equivalent to 42 % of river inputs or 46.5 % of the net phytoplankton primary production. Under such extractive pressure, the phytoplankton biomass is being curtailed to 1980’s levels when aquaculture was not yet developed and N loading was half the present level. Current mussel stocks also decrease bay-scale sedimentation rates by 14 %. Finally, a climate change scenario (year 2050) predicted a 30 % increase in mussel production, largely driven by more efficient utilization of the phytoplankton spring bloom. However, the predicted elevated summer temperatures (>25 °C) may also have deleterious physiological effects on mussels and possibly increase summer mortality levels. In conclusion, cultivated bivalves may play an important role in remediating the negative impacts of land-derived nutrient loading. Climate change may lead to increases in production and ecological carrying capacity as long as the cultivated species can tolerate warmer summer conditions.

Appendices

Appendix 1

All dissolved and particulate pelagic variables are transported by water movements. This transport is represented using the following 2D depth-averaged advection–dispersion equation:

$$ h\left(\frac{\partial C}{\partial t}+u\frac{\partial C}{\partial x}+v\frac{\partial C}{\partial y}\right)-\frac{\partial }{\partial x}\left({D}_xh\frac{\partial C}{\partial x}+{D}_{xy}h\frac{\partial C}{\partial y}\right)-\frac{\partial }{\partial y}\left({D}_{xy}h\frac{\partial C}{\partial x}+{D}_yh\frac{\partial C}{\partial y}\right)-h{\theta}_{\mathrm{C}}=0 $$

where t represents the time; (x, y) the cartesian coordinates; (u, v) the velocities in the cartesian directions obtained from the hydrodynamic model simulation; h the water depth from the hydrodynamic model; C the concentration of any transported constituent; D _x , D _y , D _xy the eddy diffusion coefficients; and θ _C the source/sink for the transported constituent. These source/sink terms as well as the equations for the mussel and benthic variables are detailed below.

Phytoplankton (P; mg C m⁻³)

$$ {\theta}_{\mathrm{P}}={P}_{\mathrm{P}\mathrm{ROD}}-{P}_{\mathrm{RESP}}-{P}_{\mathrm{MORT}}-{\mathrm{MUS}}_{\mathrm{GRAZ}}^{\mathrm{P}}-{Z}_{\mathrm{GRAZ}}^{\mathrm{P}} $$

• P _PROD: P gross primary production. ${P}_{\mathrm{P}\mathrm{ROD}}={\mu}_0^{\mathrm{P}}{e}^{k_{\mathrm{P}}^{\mathrm{P}}T}{X}_{\mathrm{N}}^{\mathrm{P}}{X}_{\mathrm{L}}^{\mathrm{P}}\cdot P$

  with ${X}_{\mathrm{N}}^{\mathrm{P}}={X}_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}+{X}_{{\mathrm{N}\mathrm{O}}_3}^{\mathrm{P}}\ \mathrm{where}\ {X}_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}=\frac{{\mathrm{N}\mathrm{H}}_4}{{\mathrm{N}\mathrm{H}}_4+{K}_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}};{X}_{{\mathrm{N}\mathrm{O}}_3}^{\mathrm{P}}=\frac{{\mathrm{N}\mathrm{O}}_3}{{\mathrm{N}\mathrm{O}}_3+{K}_{{\mathrm{N}\mathrm{O}}_3}^{\mathrm{P}}}\frac{K_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}}{{\mathrm{N}\mathrm{H}}_4+{K}_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}}$; the uptake of NO₃ is inhibited by NH₄ (second term of ${X}_{{\mathrm{NO}}_3}^{\mathrm{P}}$) as proposed by Parker (1993)

  $$ {X}_{\mathrm{L}}^{\mathrm{P}}=\frac{1}{h}{\displaystyle {\int}_0^h\frac{I(z)}{I_0^{\mathrm{P}}}} \exp \left(1-\frac{I(z)}{I_0^{\mathrm{P}}}\right)\mathrm{d}z\ \mathrm{f}\mathrm{o}\mathrm{r}\ I<{I}_0^{\mathrm{P}}\ \left(\mathrm{Steele}\ 1962\right)\ \mathrm{and}\ {X}_{\mathrm{L}}^{\mathrm{P}}=1\ \mathrm{f}\mathrm{o}\mathrm{r}\ I\ge {I}_0^{\mathrm{P}} $$

  where I(z) = I _S e ^− λz with I _S: water surface light intensity

  λ: light attenuation coefficient $\lambda ={\lambda}_0+{\lambda}_1P*+{\lambda}_2P{*}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

  P ^* is P expressed in mg Chl a m⁻³ (P ^* = Chl a/C ^P ⋅ P)

  T: water temperature

• P _RESP: P respiration. ${P}_{\mathrm{RESP}}={\beta}_0^{\mathrm{P}}{e}^{k_{\mathrm{r}}^{\mathrm{P}}T}\cdot P$

• P _MORT: P mortality. ${P}_{\mathrm{MORT}}={\lambda}^{\mathrm{P}}{e}^{k_{\mathrm{r}}^{\mathrm{P}}T}\cdot P$

• MUS ^P_GRAZ : Mussel grazing on P. MUS ^P_GRAZ  = FC ^M_P  ⋅ MUS_GRAZ

  with ${\mathrm{M}\mathrm{US}}_{\mathrm{GRAZ}}=\mathrm{J}\;\mathrm{mg}\;{\mathrm{C}}^{-1}{n}^{\mathrm{M}}\frac{{\dot{p}}_{\mathrm{A}}}{{\mathrm{A}\mathrm{E}}^{\mathrm{M}}};\ {\mathrm{FC}}_{\mathrm{P}}^{\mathrm{M}}=\frac{\varepsilon_{\mathrm{P}}^{\mathrm{M}}\cdot P}{{\mathrm{food}}^{\mathrm{M}}}$

  $$ {\mathrm{food}}^{\mathrm{M}}=\left({\varepsilon}_{\mathrm{D}}^{\mathrm{M}}\cdot D*+{\varepsilon}_{\mathrm{P}}^{\mathrm{M}}\cdot P+{\varepsilon}_{\mathrm{Z}}^{\mathrm{M}}\cdot Z\right);\ D*=\frac{D}{N/{C}^{\mathrm{D}}};\ {\dot{p}}_{\mathrm{A}}\ \mathrm{see}\ \mathrm{Mussel} $$

• Z ^P_GRAZ : Mesozooplankton grazing on P. Z ^P_GRAZ  = FC ^Z_P Z _GRAZ

  with ${Z}_{\mathrm{GRAZ}}={c}_{\mathrm{I}}^{\mathrm{Z}}{X}_{\mathrm{F}}^{\mathrm{Z}}{I}^{\mathrm{Z}}{e}^{k_{\mathrm{P}}^{\mathrm{Z}}T}\cdot Z;\ {\mathrm{F}\mathrm{C}}_{\mathrm{P}}^{\mathrm{Z}}=\frac{\varepsilon_{\mathrm{P}}^{\mathrm{Z}}\cdot P}{{\mathrm{food}}^{\mathrm{Z}}};\ {X}_{\mathrm{F}}^{\mathrm{Z}}=\frac{{\mathrm{food}}^{\mathrm{Z}}}{{\mathrm{food}}^{\mathrm{Z}}+{K}_{\mathrm{F}}^{\mathrm{Z}}};\ {\mathrm{food}}^{\mathrm{Z}}=\left({\varepsilon}_{\mathrm{D}}^{\mathrm{Z}}\cdot D*+{\varepsilon}_{\mathrm{P}}^{\mathrm{Z}}\cdot P\right)$

Zooplankton (Z; mg C m⁻³)

$$ {\theta}_{\mathrm{Z}}={Z}_{\mathrm{ASML}}-{Z}_{\mathrm{RESP}}-{Z}_{\mathrm{MORT}}-{\mathrm{MUS}}_{\mathrm{GRAZ}}^{\mathrm{Z}} $$

• Z _ASML: Z food assimilation. Z _ASML = AE^Z ⋅ Z _GRAZ

  with ${\mathrm{AE}}^{\mathrm{Z}}=\frac{{\mathrm{AE}}_{\mathrm{D}}^{\mathrm{Z}}{\varepsilon}_{\mathrm{D}}^{\mathrm{Z}}\cdot D*+{\mathrm{AE}}_{\mathrm{P}}^{\mathrm{Z}}{\varepsilon}_{\mathrm{P}}^{\mathrm{Z}}\cdot P}{{\mathrm{food}}^{\mathrm{Z}}}$

• Z _RESP: Z respiration. ${Z}_{\mathrm{R}\mathrm{ESP}}={c}_{\mathrm{R}}^{\mathrm{Z}}{\beta}_{\mathrm{R}}^{\mathrm{Z}}{e}^{k_{\mathrm{r}}^{\mathrm{Z}}T}\cdot Z$

• Z _MORT: Z mortality. ${Z}_{\mathrm{MORT}}={\lambda}^{\mathrm{Z}}{e}^{k_{\mathrm{r}}^{\mathrm{Z}}T}\cdot Z$

• MUS ^Z_GRAZ : Mussel grazing on Z. MUS ^Z_GRAZ  = FC ^M_Z  ⋅ MUS_GRAZ with ${\mathrm{FC}}_{\mathrm{Z}}^{\mathrm{M}}=\frac{\varepsilon_{\mathrm{Z}}^{\mathrm{M}}\cdot Z}{{\mathrm{food}}^{\mathrm{M}}}$

Organic Detritus (D; mg N m⁻³)

$$ {\theta}_{\mathrm{D}}=N/{C}^{\mathrm{P}}\left({P}_{\mathrm{RESP}}+{P}_{\mathrm{MORT}}\right)+N/{C}^{\mathrm{Z}}\left({Z}_{\mathrm{MORT}}+{Z}_{\mathrm{FCS}}\right)-{\mathrm{MUS}}_{\mathrm{GRAZ}}^{\mathrm{D}}-{Z}_{\mathrm{GRAZ}}^{\mathrm{D}}-{D}_{\mathrm{MIN}}-{D}_{\mathrm{SETL}} $$

• Z _FCS: Z faeces production. Z _FCS = (1 − AE ^Z_P ) ⋅ Z ^P_GRAZ  + (1 − AE ^Z_D ) ⋅ Z ^D_GRAZ

• MUS ^D_GRAZ : Mussel grazing on D. MUS ^D_GRAZ  = FC ^M_D  ⋅ MUS_GRAZ with ${\mathrm{FC}}_{\mathrm{D}}^{\mathrm{M}}=\frac{\varepsilon_{\mathrm{D}}^{\mathrm{M}}\cdot D*}{{\mathrm{food}}^{\mathrm{M}}}$

• Z ^D_GRAZ : Zooplankton grazing on D. Z ^D_GRAZ  = FC ^Z_D  ⋅ Z _GRAZ with ${\mathrm{FC}}_{\mathrm{D}}^{\mathrm{Z}}=\frac{\varepsilon_{\mathrm{D}}^{\mathrm{Z}}\cdot D*}{{\mathrm{food}}^{\mathrm{Z}}}$

• D _MIN: D mineralization. ${D}_{\mathrm{MIN}}= \min {}_0^{\mathrm{D}}{X}_{{\mathrm{O}}_2}^{\mathrm{D}}{e}^{k_{\min}^{\mathrm{D}}T}\cdot D$with ${X}_{{\mathrm{O}}_2}^{\mathrm{D}}=\frac{{\mathrm{O}}_2}{{\mathrm{O}}_2+{K}_{{\mathrm{O}}_2}^{\mathrm{D}}}$

• D _SETL: D settling. ${D}_{\mathrm{S}\mathrm{ETL}}=\frac{w_{\mathrm{S}}^{\mathrm{D}}}{h}\cdot D$

Ammonium (NH₄; mg N m⁻³)

$$ {\theta}_{{\mathrm{NH}}_4}={D}_{\mathrm{MIN}}+{\mathrm{MUS}}_{\mathrm{EXCR}}+{Z}_{\mathrm{EXCR}}-{{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}-{P}_{\mathrm{UPTK}}^{{\mathrm{NH}}_4}+{{\mathrm{NH}}_4}_{\mathrm{DIFF}} $$

• MUS_EXCR: Mussel excretion. (see Mussel below for ${\dot{p}}_{\mathrm{M}},\ {\dot{p}}_{\mathrm{C}},\ {\dot{p}}_{\mathrm{J}}$)

  $$ {\mathrm{M}\mathrm{US}}_{\mathrm{EXCR}}=\mathrm{J}\;\mathrm{mg}\;{\mathrm{C}}^{-1}{n}^{\mathrm{M}}N/{C}^{\mathrm{M}}\left({\dot{p}}_{\mathrm{M}}+\left(1-{\kappa}_{\mathrm{R}}\right)\left[\left(1-\kappa \right){\dot{p}}_{\mathrm{C}}-{\dot{p}}_{\mathrm{J}}\right]+{\dot{p}}_{\mathrm{J}}+\frac{\left[{E}_{\mathrm{G}}\right]-\left[{E}_0\right]}{\left[{E}_{\mathrm{G}}\right]}\left(\kappa {\dot{p}}_{\mathrm{C}}-{\dot{p}}_{\mathrm{M}}\right)\right) $$

• Z _EXCR: Z excretion. Z _EXCR = N/C ^Z ⋅ Z _RESP

• NH_4 NITR: NH4 nitrification. ${{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}={\mathrm{nitr}}_0^{{\mathrm{NH}}_4}{X}_{{\mathrm{O}}_2}^{{\mathrm{NH}}_4}{e}^{k_{\mathrm{nitr}}^{{\mathrm{NH}}_4}T}\cdot {\mathrm{NH}}_4$ with ${X}_{{\mathrm{O}}_2}^{{\mathrm{NH}}_4}=\frac{{\mathrm{O}}_2}{{\mathrm{O}}_2+{K}_{{\mathrm{O}}_2}^{{\mathrm{NH}}_4}}$

• ${P}_{\mathrm{UPTK}}^{{\mathrm{NH}}_4}$: NH₄ uptake by P. ${P}_{\mathrm{UPTK}}^{{\mathrm{N}\mathrm{H}}_4}=N/{C}^{\mathrm{P}}\frac{X_{{\mathrm{N}\mathrm{H}}_4}^{\mathrm{P}}}{X_{\mathrm{N}}^{\mathrm{P}}}{P}_{\mathrm{P}\mathrm{ROD}}$

• NH_4 DIFF: NH₄ diffusion from sediment. ${{\mathrm{NH}}_{4\;}}_{\mathrm{DIFF}}={\mathrm{Diff}}_0^{{\mathrm{NH}}_4}\left(1+\frac{T}{20}\right)\frac{\alpha }{\frac{\left(\mathrm{B}\mathrm{L}\mathrm{T}+h\right)}{2}}\frac{\left({\mathrm{BNH}}_4-{\mathrm{NH}}_4\right)}{h}$

Nitrate (NO₃; mg N^.m⁻³)

$$ {\theta}_{{\mathrm{NO}}_3}={{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}-{P}_{\mathrm{UPTK}}^{{\mathrm{NO}}_3}+{{\mathrm{NO}}_{3\;}}_{\mathrm{DIFF}} $$

• ${P}_{\mathrm{UPTK}}^{{\mathrm{NO}}_3}$: NO₃ uptake by P. ${P}_{\mathrm{UPTK}}^{{\mathrm{N}\mathrm{O}}_3}=N/{C}^{\mathrm{P}}\frac{X_{{\mathrm{N}\mathrm{O}}_3}^{\mathrm{P}}}{X_{\mathrm{N}}^{\mathrm{P}}}{P}_{\mathrm{P}\mathrm{ROD}}$

• NO_3 DIFF: NO₃ diffusion from sediment. ${{\mathrm{NO}}_{3\;}}_{\mathrm{DIFF}}={\mathrm{Diff}}_0^{{\mathrm{NO}}_3}\left(1+\frac{T}{20}\right)\frac{\alpha }{\frac{\left(\mathrm{B}\mathrm{L}\mathrm{T}+h\right)}{2}}\frac{\left({\mathrm{BNO}}_3-{\mathrm{NO}}_3\right)}{h}$

Dissolved Oxygen (O₂; mg O₂ L⁻¹)

$$ {\theta}_{{\mathrm{O}}_2}={{\mathrm{O}}_{2\;}}_{\mathrm{ATMR}}+\frac{1}{1000}\left[{P}_{\mathrm{PROD}}^{*}-{P}_{\mathrm{RESP}}^{*}-{Z}_{\mathrm{RESP}}^{*}-{\mathrm{MUSS}}_{\mathrm{RESP}}-{D}_{\mathrm{MIN}}^{*}-{{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}^{*}-\frac{\mathrm{wfract}}{h}{\mathrm{SOD}}_{\mathrm{RWAT}}+{{\mathrm{O}}_{2\;}}_{\mathrm{DIFF}}\right] $$

• O_2 ATMR: water reaeration from the atmosphere. ${{\mathrm{O}}_{2\;}}_{\mathrm{ATMR}}={K}_{\mathrm{a}}^{{\mathrm{O}}_2}\left({{\mathrm{O}}_{2\;}}_{\mathrm{sat}}-{\mathrm{O}}_2\right)$

  with O_2 sat: O₂ saturation concentration at the local temperature, salinity and pressure;

  ${K}_{\mathrm{a}}^{{\mathrm{O}}_2}$: atmospheric reaeration rate (day⁻¹) based on wind speed (u _w in m s⁻¹) and given by:

  ${K}_{\mathrm{a}}^{{\mathrm{O}}_2}=0.048\cdot {u}_{\mathrm{w}}$ for u _w < 3.6 m s⁻¹;

  ${K}_{\mathrm{a}}^{{\mathrm{O}}_2}=0.773\cdot {u}_{\mathrm{w}}-2.61$ for 3.6 < u _w < 13 m s⁻¹;

  ${K}_{\mathrm{a}}^{{\mathrm{O}}_2}=1.6\cdot {u}_{\mathrm{w}}-13.3$ for u _w > 3 m s⁻¹ (Liss and Merlivat 1986)

• P ^*_PROD : O₂ produced by P photosynthesis. ${P}_{\mathrm{P}\mathrm{ROD}}^{*}={p}_{{\mathrm{O}}_2}^{\mathrm{P}}\cdot {P}_{\mathrm{P}\mathrm{ROD}}$

• P ^*_RESP : O₂ consumed by P respiration. ${P}_{\mathrm{RESP}}^{*}={r}_{{\mathrm{O}}_2}^{\mathrm{P}}\cdot {P}_{\mathrm{RESP}}$

• Z ^*_RESP : O₂ consumed by Z respiration. ${Z}_{\mathrm{RESP}}^{*}={r}_{{\mathrm{O}}_2}^{\mathrm{Z}}\cdot {Z}_{\mathrm{RESP}}$

• MUSS_RESP: O₂ consumed by Mussel respiration. ${\mathrm{M}\mathrm{USS}}_{\mathrm{RESP}}={r}_{{\mathrm{O}}_2}^{\mathrm{M}}\cdot {n}^{\mathrm{M}}\cdot {\dot{p}}_{\mathrm{C}}$

• D ^*_MIN : O₂consumed by D mineralization. ${D}_{\mathrm{MIN}}^{*}={r}_{{\mathrm{O}}_2}^{\mathrm{D}}\cdot {D}_{\mathrm{MIN}}$

• NH₄  ^*_NITR : O₂ consumed by NH₄ nitrification. ${{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}^{*}={r}_{{\mathrm{O}}_2}^{{\mathrm{NH}}_4}\cdot {{\mathrm{NH}}_{4\;}}_{\mathrm{NITR}}$

• SOD_RWAT: O₂ consumed by sediment oxygen demand (SOD) released to the water column.

  SOD_RWAT = rel^SOD ⋅ SOD and wfract = α ⋅ BLT, the sediment interstitial water fraction.

• O_2 DIFF: O₂ diffusion from sediment. ${{\mathrm{O}}_{2\;}}_{\mathrm{DIFF}}={\mathrm{Diff}}_0^{{\mathrm{O}}_2}\left(1+\frac{T}{20}\right)\frac{\alpha }{\frac{\left(\mathrm{B}\mathrm{L}\mathrm{T}+h\right)}{2}}\frac{\left({\mathrm{BO}}_2-{\mathrm{O}}_2\times 1000\right)}{h}$

Mussel Biodeposits (BDP; mg N m⁻³)

$$ {\theta}_{\mathrm{BDP}}=N/{C}^{\mathrm{M}}\cdot {\mathrm{M}\mathrm{USS}}_{\mathrm{FCS}}-{\mathrm{BDP}}_{\mathrm{M}\mathrm{IN}}-{\mathrm{BDP}}_{\mathrm{SETL}} $$

• MUSS_FCS: Mussel faeces production. MUSS_FCS = (1 − AE^M)MUSS_GRAZ

• BDP_MIN: BDP mineralization. ${\mathrm{BDP}}_{\mathrm{MIN}}= \min {}_0^{\mathrm{D}}{X}_{{\mathrm{O}}_2}^{\mathrm{D}}{e}^{k_{\min}^{\mathrm{D}}T}\cdot \mathrm{B}\mathrm{D}\mathrm{P}$

• BDP_SETL: BDP settling. ${\mathrm{BDP}}_{\mathrm{S}\mathrm{ETL}}=\frac{w_{\mathrm{S}}^{\mathrm{BDP}}}{h}\cdot \mathrm{B}\mathrm{D}\mathrm{P}$

Mussel Energy Pools (E _S, E _V, E _R; J)

• Storage: $\frac{\mathrm{d}{E}_{\mathrm{S}}}{\mathrm{d}t}={\dot{p}}_{\mathrm{A}}-{\dot{p}}_{\mathrm{C}}$

  where $\begin{array}{l}{\dot{p}}_{\mathrm{A}}={\mathrm{A}\mathrm{E}}^{\mathrm{M}}\dot{k}(T)\left\{{p}_{\mathrm{Xm}}\right\}{X}_{\mathrm{F}}^{\mathrm{M}}{V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\hfill \\ {}{\dot{p}}_{\mathrm{C}}=\frac{\left[{E}_{\mathrm{S}}\right]}{\left[{E}_{\mathrm{G}}\right]+\kappa \left[{E}_{\mathrm{S}}\right]}\dot{k}(T)\left[\frac{\left[{E}_{\mathrm{G}}\right]{\mathrm{A}\mathrm{E}}^{\mathrm{M}}\left\{{p}_{\mathrm{Xm}}\right\}{V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{\left[{E}_{\mathrm{m}}\right]}+\left[{p}_{\mathrm{M}}\right]V\right]\hfill \end{array}$

  with $\begin{array}{l}V=\frac{E_{\mathrm{V}}}{\left[{E}_{\mathrm{G}}\right]};\ {X}_{\mathrm{F}}^{\mathrm{M}}=\frac{{\mathrm{food}}^{\mathrm{M}}}{{\mathrm{food}}^{\mathrm{M}}+{K}_{\mathrm{F}}^{\mathrm{M}}};\ \left[{E}_{\mathrm{S}}\right]=\frac{E_{\mathrm{S}}}{V}\hfill \\ {}\dot{k}(T)= \exp \left\{\frac{T_{\mathrm{A}}}{T_1}-\frac{T_{\mathrm{A}}}{T}\right\}\frac{s(T)}{s\left({T}_1\right)};\kern0.5em s(T)={\left(1+ \exp \left\{\frac{T_{\mathrm{A}\mathrm{L}}}{T}-\frac{T_{\mathrm{A}\mathrm{L}}}{T_{\mathrm{L}}}\right\}+ \exp \left\{\frac{T_{\mathrm{A}\mathrm{H}}}{T_{\mathrm{H}}}-\frac{T_{\mathrm{A}\mathrm{H}}}{T}\right\}\right)}^{-1}\hfill \end{array}$

• Structure: $\frac{\mathrm{d}{E}_{\mathrm{V}}}{\mathrm{d}t}=\kappa \cdot {\dot{p}}_{\mathrm{C}}-{\dot{p}}_{\mathrm{M}}$ where ${\dot{p}}_{\mathrm{M}}=\dot{k}(T)\cdot \left[{p}_{\mathrm{M}}\right]\cdot V$

• Reproduction: $\frac{\mathrm{d}{E}_{\mathrm{R}}}{\mathrm{d}t}=\left(1-\kappa \right){\dot{p}}_{\mathrm{C}}-{\dot{p}}_{\mathrm{J}}$ where ${\dot{p}}_{\mathrm{J}}=\left(\frac{1-\kappa }{\kappa}\right)\cdot \min \left(V,{V}_{\mathrm{p}}\right)\cdot \dot{k}(T)\cdot \left[{p}_{\mathrm{M}}\right]$

Bed Organic Detritus (BD; mg N m⁻³)

$$ \frac{\mathrm{d}\mathrm{BD}}{\mathrm{d}t}=\frac{h}{\mathrm{pfract}}\left({D}_{\mathrm{SETL}}+{\mathrm{BD}\mathrm{P}}_{\mathrm{SETL}}\right)-{\mathrm{BD}}_{\mathrm{MIN}}-{\mathrm{BD}}_{\mathrm{BUR}}-{\mathrm{BD}}_{\mathrm{EROS}} $$

• BD_MIN: BD mineralization. ${\mathrm{BD}}_{\mathrm{MIN}}= \min {}_0^{\mathrm{BD}}{e}^{k_{\min}^{\mathrm{BD}}T}\cdot \mathrm{B}\mathrm{D}$

• BD_BUR: BD burial in inactive sediment layers. BD_BUR = burial^BD ⋅ BD

• BD_EROS: BD erosion. BD_EROS = M ^BD ⋅ δ ^BD_r  ⋅ BD

  with ${\delta}_{\mathrm{r}}^{\mathrm{BD}}=0\kern0.5em \mathrm{f}\mathrm{o}\mathrm{r}\kern0.5em {\tau}_{\mathrm{b}}<{\tau}_{\mathrm{crit}}^{\mathrm{BD}}\kern0.5em \mathrm{and}\kern0.5em {\delta}_{\mathrm{r}}^{\mathrm{BD}}=\frac{\tau_{\mathrm{b}}-{\tau}_{\mathrm{crit}}^{\mathrm{BD}}}{\tau_{\mathrm{crit}}^{\mathrm{BD}}}\mathrm{f}\mathrm{o}\mathrm{r}\kern0.5em {\tau}_{\mathrm{b}}\ge {\tau}_{\mathrm{crit}}^{\mathrm{BD}}\kern0.5em \mathrm{where}\kern0.5em {\tau}_{\mathrm{b}}:\kern0.5em \mathrm{bottom}\ \mathrm{shear}\ \mathrm{stress}$

• pfract = (1 − α) ⋅ BLT, the sediment solid fraction.

Bed Ammonium (BNH₄; mg N m⁻³)

$$ \frac{{\mathrm{d}\mathrm{BNH}}_4}{\mathrm{d}t}=\frac{\mathrm{pfract}}{\mathrm{wfract}}\cdot {\mathrm{BD}}_{\mathrm{MIN}}-{{\mathrm{BNH}}_4}_{\;\mathrm{B}\mathrm{U}\mathrm{R}}-{{\mathrm{BNH}}_4}_{\;\mathrm{NITR}}+{{\mathrm{BNO}}_3}_{\;\mathrm{R}\mathrm{ED}}-\frac{h}{\mathrm{wfract}}\cdot {{\mathrm{NH}}_{4\;}}_{\mathrm{DIFF}} $$

• BNH_4BUR: BNH₄ burial in inactive sediment layers. ${{\mathrm{BNH}}_{4\;}}_{\mathrm{BUR}}={\mathrm{burial}}^{{\mathrm{BNH}}_4}\cdot {\mathrm{BNH}}_4$

• BNH_4NITR: BNH₄ nitrification. ${{\mathrm{BNH}}_4}_{\;\mathrm{NITR}}={\mathrm{nitr}}_0^{{\mathrm{BNH}}_4}{X}_{{\mathrm{BO}}_2}^{{\mathrm{BNH}}_4}{e}^{k_{\mathrm{nitr}}^{{\mathrm{BNH}}_4}T}\cdot {\mathrm{BNH}}_4$

  with ${X}_{{\mathrm{BO}}_2}^{{\mathrm{BNH}}_4}=\frac{{\mathrm{BO}}_2}{{\mathrm{BO}}_2+{K}_{{\mathrm{BO}}_2}^{{\mathrm{BNH}}_4}}$

• BNO_3 RED: BNO₃ dissimilatory reduction. ${{\mathrm{BNO}}_3}_{\;\mathrm{RED}}=\%{\mathrm{red}}^{{\mathrm{BNO}}_3}\cdot {{\mathrm{BNO}}_{3\;}}_{\mathrm{DNITR}}$

  with ${{\mathrm{BNO}}_{3\;}}_{\mathrm{DNITR}}={\mathrm{denitr}}_0^{{\mathrm{BNO}}_3}{X}_{{\mathrm{BO}}_2}^{{\mathrm{BNO}}_3}{e}^{k_{\mathrm{denitr}}^{{\mathrm{BNO}}_3}T}\cdot {\mathrm{BNO}}_3\kern0.5em \mathrm{where}\kern0.5em {X}_{{\mathrm{BO}}_2}^{{\mathrm{BNO}}_3}=1-\frac{{\mathrm{BO}}_2}{{\mathrm{BO}}_2+{K}_{{\mathrm{BO}}_2}^{{\mathrm{BNO}}_3}}$

Bed Nitrate (BNO₃; mg N m⁻³)

$$ \frac{\mathrm{d}\mathrm{BNO}{}_3}{\mathrm{d}t}={{\mathrm{BNH}}_4}_{\;\mathrm{NITR}}-{{\mathrm{BNO}}_3}_{\;\mathrm{DNITR}}-\frac{h}{\mathrm{wfract}}\cdot {{\mathrm{NO}}_3}_{\mathrm{DIFF}} $$

Sediment Oxygen Demand (SOD; mg O₂ m⁻³)

$$ \frac{\mathrm{d}\mathrm{SOD}}{\mathrm{d}t}=\frac{\mathrm{pfract}}{\mathrm{wfract}}\cdot {\mathrm{BD}}_{\mathrm{MIN}}^{*}-{\mathrm{SOD}}_{\mathrm{O}\mathrm{XID}}-{\mathrm{SOD}}_{\mathrm{BUR}}-{\mathrm{SOD}}_{\mathrm{RWAT}}-\frac{r_{{\mathrm{O}}_2}^{\mathrm{BD}}}{r_{\mathrm{BD}}^{{\mathrm{BNO}}_3}}\cdot {{\mathrm{BNO}}_3}_{\;\mathrm{DNITR}} $$

• BD ^*_MIN : Oxygen demand produced by BD mineralization. ${\mathrm{BD}}_{\mathrm{MIN}}^{*}={r}_{{\mathrm{O}}_2}^{\mathrm{BD}}\cdot {\mathrm{BD}}_{\mathrm{MIN}}$

• SOD_OXID: SOD oxidation. ${\mathrm{SOD}}_{\mathrm{OXID}}={\mathrm{oxi}}_0^{\mathrm{SOD}}{X}_{{\mathrm{BO}}_2}^{\mathrm{SOD}}{e}^{k_{\mathrm{r}}^{\mathrm{SOD}}T}\cdot \mathrm{SOD}$ with ${X}_{{\mathrm{BO}}_2}^{\mathrm{SOD}}=\frac{{\mathrm{BO}}_2}{{\mathrm{BO}}_2+{K}_{{\mathrm{BO}}_2}^{\mathrm{SOD}}}$

• SOD_BUR: SOD burial in inactive sediment layers. SOD_BUR = burial^SOD ⋅ SOD

Bed Dissolved Oxygen (BO₂; mg O₂ m⁻³)

$$ \frac{{\mathrm{d}\mathrm{BO}}_2}{\mathrm{d}t}=-{{\mathrm{BNH}}_4}_{\;\mathrm{NITR}}^{*}-{\mathrm{SOD}}_{\mathrm{O}\mathrm{XID}}-\frac{h}{\mathrm{wfract}}\cdot {{\mathrm{O}}_2}_{\;\mathrm{DIFF}} $$

• BNH₄  ^*_NITR : BO₂ consumed by BNH₄ nitrification. ${{\mathrm{BNH}}_{4\;}}_{\mathrm{NITR}}^{*}={r}_{{\mathrm{O}}_2}^{{\mathrm{BNH}}_4}\cdot {{\mathrm{BNH}}_4}_{\;\mathrm{NITR}}$

Appendix 2

Table 6 List of parameters forming the biogeochemical model equations, including the value used in the present study, the units, a range of values found in the literature for calibrated parameters and the corresponding references