# Numerical Modeling of Long-Term Biogeochemical Processes and Its Application to Sedimentary Bed Formation in Tokyo Bay

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Description

#### 2.1. Integrated Model Framework

#### 2.2. Hydrodynamic Model

#### 2.3. Wave Hindcasting Model

#### 2.4. Bed Shear Stress (BSS) Model

#### 2.5. Pelagic Model

#### 2.6. Pelagic Model Boundary Conditions and Numerical Procedure

#### 2.7. Benthic Model

^{3}; ${C}_{\mathrm{DO}\_\mathrm{C}}$ is the critical concentration in water, which is considered as 2 g/m

^{3}at the bottom water; and ${\pi}_{\mathrm{A}}$ represents the anaerobic value of $\pi $ while $(\Delta \pi )$ represents the enhancement of sorption in the aerobic layer in (m

^{3}/g). Both ${\pi}_{\mathrm{A}}$ and $(\Delta \pi )$ depend on the type of nutrient.

#### 2.8. Benthic Model Boundary Conditions and Numerical Procedure

#### 2.9. Benthic and Pelagic Model Coupling

#### 2.9.1. Diffusion Flux at Sediment–Water Interface

^{3}[53].

#### 2.9.2. Particulate Matter Settling or Resuspension

## 3. Model Application to Tokyo Bay

^{2}. The upwelling of the anoxic bottom water, which creates blue tides resulting in substantial economic losses to coastal fisheries, is still unsolved. Given the availability of data, Tokyo Bay was selected for the calibration and validation of the model.

#### 3.1. Model Grid System

#### 3.2. Initial Conditions

#### 3.3. Boundary Conditions

#### 3.4. Model Calibration and Validation

## 4. Results

#### 4.1. Water Quality

^{3}[53], especially appears during summer in Tokyo Bay. Seasonal hypoxia at the three locations in Tokyo Bay has been well reproduced qualitatively, though it was underestimated to some extent (Figure 17). Measured and simulated values of surface and bottom DO at three locations (Figure 18) show considerable discrepancies in both surface and bottom layers [43]. As the reproducibility of seasonal hypoxia in the water column has a strong correlation with the reproducibility of chlorophyll a, accurate modeling of chlorophyll a will improve the DO model. Moreover, it has been noticed that the surface DO concentration is highly affected by both primary production and the saturated concentration of DO.

#### 4.2. Sediment Quality

## 5. Discussion

#### 5.1. Environmental Controls of Water Quality

#### 5.2. Bed Formation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Symbol | Unit | Description | |
---|---|---|---|

[Water] | [Sediment] | ||

$S$ | $[\mathrm{psu}]$ | Salinity | |

$T$ | [°C] | Temperature | |

${C}_{\mathrm{phy}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Phytoplankton concentration | |

${C}_{\mathrm{zoo}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Zooplankton concentration | |

${C}_{\mathrm{chl}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Chlorophyll a concentration | |

${C}_{\mathrm{POC}}$ | ${B}_{\mathrm{POC}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Particulate organic carbon concentration |

${C}_{{\mathrm{NH}}_{4}}$ | ${B}_{{\mathrm{NH}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Ammonium nitrogen concentration |

${C}_{{\mathrm{PO}}_{4}}$ | ${B}_{{\mathrm{PO}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Phosphate phosphorous concentration |

${C}_{{\mathrm{NO}}_{3}}$ | ${B}_{{\mathrm{NO}}_{3}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Nitrate nitrogen concentration |

${C}_{\mathrm{Si}}$ | ${B}_{\mathrm{Si}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Dissolved silica concentration |

${C}_{\mathrm{PSi}}$ | ${B}_{\mathrm{PSi}}$ | ${[\mathrm{mg}/\mathrm{m}}^{3}]$ | Particulate biogenic silica concentration |

${C}_{\mathrm{DO}}$ | ${B}_{\mathrm{DO}}$ | ${[\mathrm{g}/\mathrm{m}}^{3}]$ | Dissolved oxygen concentration |

${C}_{{\mathrm{S}}^{2-}}$ | ${B}_{{\mathrm{S}}^{2-}}$ | ${[\mathrm{g}/\mathrm{m}}^{3}]$ | Sulfide concentration |

${C}_{\mathrm{Silt}}$ | ${B}_{\mathrm{Silt}}$ | ${[\mathrm{g}/\mathrm{m}}^{3}]$ | Silt concentration |

Pelagic model | |||

[Phytoplankton model] | |||

${R}_{\mathrm{phy}\_\mathrm{PP}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of primary production | |

${R}_{\mathrm{phy}\_\mathrm{Met}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of metabolism | |

${R}_{\mathrm{phy}\_\mathrm{Mor}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of mortality | |

${R}_{\mathrm{zoo}\_\mathrm{GE}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton grazing on each food | |

${G}_{\mathrm{phy}}$ | [1/s] | Maximum rate of phytoplankton growth at 20 °C | |

${M}_{\mathrm{phy}}$ | [1/s] | Maximum rate of phytoplankton metabolism at 20 °C | |

${D}_{\mathrm{phy}}$ | [1/s] | Maximum rate of phytoplankton mortality at 20 °C | |

${f}_{\mathrm{TLphy}}$ | - | Temperature limit for phytoplankton growth | |

${f}_{\mathrm{LLphy}}$ | - | Light limit for phytoplankton growth | |

${f}_{\mathrm{NLphy}}$ | - | Nutrient limit for phytoplankton growth | |

${\mathrm{PO}}_{4\mathrm{NLphy}}$ | - | Phosphate nutrient limit for phytoplankton growth | |

${\mathrm{nit}}_{\mathrm{NLphy}}$ | - | Nitrogen nutrient limit for phytoplankton growth | |

${\mathrm{Si}}_{\mathrm{NLphy}}$ | - | Silica nutrient limit for phytoplankton growth | |

${T}_{\mathrm{LO}}$ | [°C] | Lower end of optimal temperature | |

${T}_{\mathrm{UO}}$ | [°C] | Upper end of optimal temperature | |

${K}_{{\mathrm{PO}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant of phosphorous limitation | |

${K}_{\mathrm{nit}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant of nitrogen limitation | |

${K}_{\mathrm{Si}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant of silica limitation | |

$\mathrm{PAR}$ | ${[\mathrm{J}/\mathrm{m}}^{2}/\mathrm{s}]$ | Photosynthetically active radiation | |

${\mathrm{PAR}}_{\mathrm{sur}}$ | ${[\mathrm{J}/\mathrm{m}}^{2}/\mathrm{s}]$ | Photosynthetically active radiation at surface | |

${\mathrm{PAR}}_{\mathrm{opt}}$ | ${[\mathrm{J}/\mathrm{m}}^{2}/\mathrm{s}]$ | Optimum of photosynthetically active radiation | |

${\mathrm{PAR}}_{\mathrm{min}}$ | ${[\mathrm{J}/\mathrm{m}}^{2}/\mathrm{s}]$ | Minimum of photosynthetically active radiation | |

${k}_{e}$ | - | Light extinction coefficient | |

[Zooplankton model] | |||

${R}_{\mathrm{zoo}\_\mathrm{Gro}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton growth | |

${R}_{\mathrm{zoo}\_\mathrm{Mor}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton mortality | |

${R}_{\mathrm{zoo}\_\mathrm{A}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton absorption | |

${R}_{\mathrm{zoo}\_\mathrm{MF}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of availability of minimum food for zooplankton | |

${R}_{\mathrm{MAX}\_\mathrm{MF}}$ | [1/s] | Maximum rate of minimum food for zooplankton at 20 °C | |

${C}_{\mathrm{zoo}\_\mathrm{AP}}$ | - | Maximum absorb portion of food by zooplankton at 20 °C | |

${K}_{\mathrm{DO}\_\mathrm{zoo}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for zooplankton metabolism | |

${R}_{\mathrm{zoo}\_\mathrm{G}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton grazing at 20 °C | |

${R}_{\mathrm{zoo}\_\mathrm{GE}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton grazing for each food at 20 °C | |

${R}_{\mathrm{zoo}\_\mathrm{GP}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Grazing primitive of zooplankton | |

${G}_{\mathrm{zoo}}$ | [1/s] | Maximum rate of zooplankton growth at 20 °C | |

${f}_{\mathrm{TLzoo}}$ | - | Temperature limit for zooplankton | |

${f}_{\mathrm{FLzoo}}$ | - | Food limit for zooplankton | |

$\mathrm{Food}\_\mathrm{Thr}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Threshold food concentration | |

${K}_{\mathrm{Ivlev}}$ | $[{\mathrm{m}}^{3}/\mathrm{mgC}]$ | Total food proportionality constant for Ivlev formulation | |

${R}_{\mathrm{zoo}\_\mathrm{Fecal}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of zooplankton fecal at 20 °C | |

${C}_{\mathrm{zoo}\_\mathrm{MAX}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | Maximum concentration of zooplankton at 20 °C | |

${D}_{\mathrm{zoo}}$ | [1/s] | Maximum rate of zooplankton mortality at 20 °C | |

[Particulate organic carbon model] | |||

${R}_{{C}_{\mathrm{POC}}\_\mathrm{O}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of aerobic decomposition | |

${k}_{{C}_{\mathrm{POC}}\_\mathrm{O}}$ | [1/s] | Maximum rate of aerobic decomposition at 20 °C | |

${\theta}_{{C}_{\mathrm{POC}}}$ | - | Temperature coefficient for aerobic decomposition | |

${K}_{\mathrm{DO},{C}_{\mathrm{POC}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for aerobic decomposition | |

${R}_{{C}_{\mathrm{POC}}\_{\mathrm{NO}}_{3}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of denitrification as a fraction of POC | |

${R}_{{C}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of denitrification | |

${k}_{{C}_{{\mathrm{NO}}_{3}}\_D}$ | [1/s] | Maximum rate of denitrification at 20 °C | |

${\theta}_{{C}_{{\mathrm{NO}}_{3}}}$ | - | Temperature coefficient for denitrification | |

${K}_{\mathrm{dec},{C}_{\mathrm{POC}}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}]$ | Half saturation constant for POC in denitrification | |

${R}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of anaerobic decomposition | |

${k}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | [1/s] | Maximum rate of anaerobic decomposition at 20 °C | |

${\theta}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | - | Temperature coefficient for anaerobic decomposition | |

${K}_{{C}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant for denitrification | |

$F$ | - | Fraction of particulate organic carbon | |

[Ammonia model] | |||

${R}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of nitrification | |

${k}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | [1/s] | Maximum rate of nitrification at 20 °C | |

${\theta}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | - | Temperature coefficient for nitrification | |

${K}_{\mathrm{DO},{C}_{{\mathrm{NH}}_{4}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for nitrification | |

[Silica model] | |||

${R}_{{C}_{\mathrm{Si}}\_\mathrm{Pro}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of silica production | |

${k}_{{C}_{\mathrm{Si}}}$ | [1/s] | Maximum rate of silica production at 20 °C | |

${\theta}_{{C}_{\mathrm{Si}}}$ | - | Temperature coefficient for particulate silica dissolution | |

${K}_{{C}_{\mathrm{PSi}}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant for particulate silica dissolution | |

${C}_{\mathrm{Si},\mathrm{sat}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Saturated concentration of silica | |

[Sulfide model] | |||

${R}_{{C}_{{S}^{2-}}\_\mathrm{O}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of sulfide oxidization | |

${k}_{{C}_{{S}^{2-}}\_\mathrm{O}}$ | [1/s] | Maximum rate of sulfide oxidization at 20 °C | |

${\theta}_{{C}_{{S}^{2-}}}$ | - | Temperature coefficient for sulfide oxidization | |

${K}_{\mathrm{DO},{C}_{{S}^{2-}}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for sulfide oxidation | |

Benthic model | |||

[Particulate organic carbon model] | |||

${R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of aerobic decomposition | |

${k}_{{B}_{\mathrm{POC}}\_\mathrm{O}}$ | [1/s] | Maximum rate of aerobic decomposition at 20 °C | |

${\theta}_{{B}_{\mathrm{POC}}}$ | - | Temperature coefficient for aerobic decomposition | |

${K}_{\mathrm{DO},{B}_{\mathrm{POC}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for aerobic decomposition | |

${R}_{{B}_{\mathrm{POC}}\_{\mathrm{NO}}_{3}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of denitrification as a fraction of POC | |

${R}_{{B}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of denitrification | |

${k}_{{B}_{{\mathrm{NO}}_{3}}\_D}$ | [1/s] | Maximum rate of denitrification at 20 °C | |

${\theta}_{{B}_{{\mathrm{NO}}_{3}}}$ | - | Temperature coefficient for denitrification | |

${K}_{\mathrm{dec},{B}_{\mathrm{POC}}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}]$ | Half saturation constant for POC in denitrification | |

${R}_{{B}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of anaerobic decomposition | |

${k}_{{B}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | [1/s] | Maximum rate of anaerobic decomposition at 20 °C | |

${\theta}_{{B}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | - | Temperature coefficient for anaerobic decomposition | |

${K}_{{B}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant for denitrification | |

[Ammonia model] | |||

${R}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of nitrification | |

${k}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | [1/s] | Maximum rate of nitrification at 20 °C | |

${\theta}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | - | Temperature coefficient for nitrification | |

${K}_{\mathrm{DO},{B}_{{\mathrm{NH}}_{4}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | Oxygen half saturation constant for nitrification | |

[Silica model] | |||

${R}_{{B}_{\mathrm{Si}}\_\mathrm{Pro}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of silica production | |

${k}_{{B}_{\mathrm{Si}}}$ | [1/s] | Maximum rate of silica production at 20 °C | |

${\theta}_{{B}_{\mathrm{Si}}}$ | - | Temperature coefficient for particulate silica dissolution | |

${K}_{{B}_{\mathrm{PSi}}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Half saturation constant for particulate silica dissolution | |

${B}_{\mathrm{Si},\mathrm{sat}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | Saturated concentration of silica | |

[Sulfide model] | |||

${R}_{{B}_{{S}^{2-}}\_\mathrm{O}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}/\mathrm{s}]$ | Rate of sulfide oxidization | |

${k}_{{B}_{{S}^{2-}}\_\mathrm{O}}$ | [1/s] | Maximum rate of sulfide oxidization at 20 °C | |

${\theta}_{{B}_{{S}^{2-}}}$ | - | Temperature coefficient for sulfide oxidization | |

${K}_{\mathrm{DO},{B}_{{S}^{2-}}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}]$ | Half saturation constant of oxygen for sulfide oxidization | |

[Transfer ratios] | |||

${r}_{\mathrm{PC}\_\mathrm{dec}}$ | $[\mathrm{mmolP}/\mathrm{mgC}]$ | Ratio of phosphorous to carbon for particulate organic carbon decomposition | |

${r}_{\mathrm{NC}\_\mathrm{dec}}$ | $[\mathrm{mmolN}/\mathrm{mgC}]$ | Ratio of nitrogen to carbon for particulate organic carbon decomposition | |

${r}_{\mathrm{CN}\_\mathrm{D}}$ | $[\mathrm{mgC}/\mathrm{mmolN}]$ | Ratio of carbon to nitrogen for denitrification | |

${r}_{\mathrm{SiC}\_\mathrm{phy}}$ | $[\mathrm{mmolSi}/\mathrm{mgC}]$ | Ratio of silica to carbon for particulate organic carbon decomposition | |

${r}_{\mathrm{Si}\_\mathrm{PSi}}$ | $[\mathrm{mgSi}/\mathrm{mmolSi}]$ | Ratio of dissolved silica to particulate silica | |

${r}_{\mathrm{CS}\_\mathrm{dec}}$ | $[\mathrm{gS}/\mathrm{mgC}]$ | Ratio of carbon to sulfur for particulate organic carbon anoxic decomposition | |

${r}_{\mathrm{OC}\_\mathrm{dec}}$ | ${[\mathrm{gO}}_{2}/\mathrm{mgC}]$ | Ratio of oxygen to carbon for particulate organic carbon decomposition | |

${r}_{\mathrm{ON}\_\mathrm{nit}}$ | ${[\mathrm{gO}}_{2}/\mathrm{mmolN}]$ | Ratio of oxygen to nitrogen for nitrification | |

${r}_{\mathrm{OS}\_\mathrm{oxi}}$ | ${[\mathrm{gO}}_{2}/\mathrm{gS}]$ | Ratio of oxygen to sulfur for sulfide oxidization | |

Benthic–pelagic interaction parameters | |||

${\mathrm{F}}_{{\mathrm{PO}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of phosphate between sediment and water | |

${\mathrm{F}}_{{\mathrm{NH}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of ammonia between sediment and water | |

${\mathrm{F}}_{{\mathrm{NO}}_{3}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of nitrate between sediment and water | |

${\mathrm{F}}_{\mathrm{Si}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of Silica between sediment and water | |

${\mathrm{F}}_{{\mathrm{S}}^{2-}}$ | ${[\mathrm{gS}/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of sulfide between sediment and water | |

${\mathrm{F}}_{\mathrm{DO}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{2}/\mathrm{s}]$ | Diffusion flux of oxygen between sediment and water |

Parameter | Units | Value | Main Source |
---|---|---|---|

Pelagic model | |||

Phytoplankton model | |||

${G}_{\mathrm{phy}}$ | [1/d] | (2.772, 2.772, 2.772) ^{a} | [6,75,76] |

${M}_{\mathrm{phy}}$ | [1/d] | (0.083, 0.083, 0.083) ^{a} | [6,56,76] |

${D}_{\mathrm{phy}}$ | [1/d] | (0.1386, 0.1386, 0.1386) ^{a} | [6,56,76] |

${k}_{\mathrm{GKL}}$ | - | (0.8, 0.8, 0.8) ^{a} | [20] |

${k}_{\mathrm{GKU}}$ | - | (0.8, 0.8, 0.8) ^{a} | [20] |

${K}_{{\mathrm{PO}}_{4}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | (1 × 10^{−8}, 0.01, 1 × 10^{−3}) ^{a} | [6,56,76] |

${K}_{\mathrm{nit}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | (0.5, 0.25, 1 × 10^{-3}) ^{a} | [6,56,76] |

${K}_{\mathrm{Si}}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | (1 × 10^{−3}, 0.02, 1 × 10^{−3}) ^{a} | [77] |

${\mathrm{PAR}}_{\mathrm{min}}$ | ${[\mathrm{J}/\mathrm{m}}^{2}/\mathrm{s}]$ | (2, 25, 25) ^{a} | Tu^{c} |

Zooplankton model | |||

${R}_{\mathrm{MAX}\_\mathrm{MF}}$ | [1/d] | 0.04 | [78] |

${C}_{\mathrm{zoo}\_\mathrm{AP}}$ | - | 0.6 | [76,78,79] |

${K}_{\mathrm{DO}\_\mathrm{zoo}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | 1.0 | [78] |

${G}_{\mathrm{zoo}}$ | [1/d] | 0.2 | [6,56,78] |

$\mathrm{Food}\_\mathrm{Thr}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | 0.01 | [76,78,79] |

${K}_{\mathrm{Ivlev}}$ | $[{\mathrm{m}}^{3}/\mathrm{mgC}]$ | 50.0 | [78] |

${C}_{\mathrm{zoo}\_\mathrm{MAX}}$ | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | 100.0 | Tu^{c} |

${D}_{\mathrm{zoo}}$ | [1/d] | 0.05 | [78] |

Particulate organic carbon model | |||

${k}_{{C}_{\mathrm{POC}}\_\mathrm{O}}$ | [1/d] | (0.35, 0.018, 0.0) ^{b} | [19] |

${\theta}_{{C}_{\mathrm{POC}}}$ | - | (1.08, 1.08, -) ^{b} | [19] |

${K}_{\mathrm{DO},{C}_{\mathrm{POC}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | 0.1 | [6] |

${k}_{{C}_{{\mathrm{NO}}_{3}}\_D}$ | [1/d] | (2.0, 0.1, 0.0) ^{b} | Tu^{c} |

${\theta}_{{C}_{{\mathrm{NO}}_{3}}}$ | - | 1.086 | [19] |

${K}_{\mathrm{dec},{C}_{\mathrm{POC}}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}]$ | 10.0 | Tu^{c} |

${k}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | [1/d] | (0.035, 0.0018, 0.0) ^{b} | [19] |

${\theta}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | - | (1.08, 1.15, -) ^{b} | [19] |

${K}_{{C}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | 0.5 | [19] |

$F$ | - | (0.65, 0.25, 0.1) ^{b} | [19] |

Ammonium model | |||

${k}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | [1/d] | 0.06 | Tu^{c} |

${\theta}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | - | 1.123 | [19] |

${K}_{\mathrm{DO},{C}_{{\mathrm{NH}}_{4}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | 0.37 | [19] |

Silica model | |||

${k}_{{C}_{\mathrm{Si}}}$ | [1/d] | 1.925 × 10^{−3} | [19] |

${\theta}_{{C}_{\mathrm{Si}}}$ | - | 1.059 | [19] |

${K}_{{C}_{\mathrm{PSi}}}$ | $[\mathrm{mgSi}/\mathrm{l}]$ | 19.8 | [19] |

${C}_{\mathrm{Si},\mathrm{sat}}$ | $[\mathrm{mgSi}/\mathrm{l}]$ | 26.5 | [19] |

Sulfide model | |||

${k}_{{C}_{{S}^{2-}}\_\mathrm{O}}$ | [1/d] | 6.0 | Tu^{c} |

${\theta}_{{C}_{{S}^{2-}}}$ | - | 1.123 | [19] |

${K}_{\mathrm{DO},{C}_{{S}^{2-}}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}]$ | 2.0 | [19] |

Benthic model | |||

Particulate organic carbon model | |||

${k}_{{B}_{\mathrm{POC}}\_\mathrm{O}}$ | [1/d] | (0.35, 0.018, 0.0) ^{b} | [19] |

${\theta}_{{B}_{\mathrm{POC}}}$ | - | (1.08, 1.08, -) ^{b} | [19] |

${K}_{\mathrm{DO},{B}_{\mathrm{POC}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | 0.1 | [6] |

${k}_{{B}_{{\mathrm{NO}}_{3}}\_D}$ | [1/d] | (2.0, 0.1, 0.0) ^{b} | Tu^{c} |

${\theta}_{{B}_{{\mathrm{NO}}_{3}}}$ | - | 1.086 | [19] |

${K}_{\mathrm{dec},{B}_{\mathrm{POC}}}$ | ${[\mathrm{mgC}/\mathrm{m}}^{3}]$ | 5000.0 | Tu^{c} |

${k}_{{B}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | [1/d] | (0.035, 0.0018, 0.0) ^{b} | [19] |

${\theta}_{{B}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}$ | - | (1.08, 1.15, -) ^{b} | [19] |

${K}_{{B}_{{\mathrm{NO}}_{3}}\_D}$ | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ | 0.5 | [19] |

Ammonium model | |||

${k}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | [1/d] | 140.63 | Tu^{c} |

${\theta}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}$ | - | 1.123 | [19] |

${K}_{\mathrm{DO},{B}_{{\mathrm{NH}}_{4}}}$ | ${[\mathrm{gO}}_{2}{/\mathrm{m}}^{3}]$ | 0.37 | [19] |

Silica model | |||

${k}_{{B}_{\mathrm{Si}}}$ | [1/d] | 1.925 × 10^{−3} | [19] |

${\theta}_{{B}_{\mathrm{Si}}}$ | - | 1.059 | [19] |

${K}_{{B}_{\mathrm{PSi}}}$ | $[\mathrm{mgSi}/\mathrm{l}]$ | 19.8 | [19] |

${B}_{\mathrm{Si},\mathrm{sat}}$ | $[\mathrm{mgSi}/\mathrm{l}]$ | 26.5 | [19] |

Sulfide model | |||

${k}_{{B}_{{S}^{2-}}\_\mathrm{O}}$ | [1/d] | 6.0 | Tu^{c} |

${\theta}_{{B}_{{S}^{2-}}}$ | - | 1.123 | [19] |

${K}_{\mathrm{DO},{B}_{{S}^{2-}}}$ | ${[\mathrm{gS}/\mathrm{m}}^{3}]$ | 0.0001 | [19] |

Transfer ratios | |||

${r}_{\mathrm{PC}\_\mathrm{dec}}$ | $[\mathrm{mmolP}/\mathrm{mgC}]$ | 1.0/(12.0 × 106.0) | [19] |

${r}_{\mathrm{NC}\_\mathrm{dec}}$ | $[\mathrm{mmolN}/\mathrm{mgC}]$ | 16.0/(12.0 × 106.0) | [19] |

${r}_{\mathrm{CN}\_\mathrm{D}}$ | $[\mathrm{mgC}/\mathrm{mmolN}]$ | (106.0 × 12.0 × 5.0)/424.0 | [18,19] |

${r}_{\mathrm{SiC}\_\mathrm{phy}}$ | $[\mathrm{mmolSi}/\mathrm{mgC}]$ | 1.0/(12.0 × 8.0) | [19] |

${r}_{\mathrm{Si}\_\mathrm{PSi}}$ | $[\mathrm{mgSi}/\mathrm{mmolSi}]$ | 28.0 | [19] |

${r}_{\mathrm{CS}\_\mathrm{dec}}$ | $[\mathrm{gS}/\mathrm{mgC}]$ | (53.0 × 32.0 × 10^{−3})/(106.0 × 12.0) | [18,19] |

${r}_{\mathrm{OC}\_\mathrm{dec}}$ | ${[\mathrm{gO}}_{2}/\mathrm{mgC}]$ | (32.0 × 10^{−3})/12.0 | [19] |

${r}_{\mathrm{ON}\_\mathrm{nit}}$ | ${[\mathrm{gO}}_{2}/\mathrm{mmolN}]$ | 4.33 × 14.0 × 10^{−3} | [18,19] |

${r}_{\mathrm{OS}\_\mathrm{oxi}}$ | ${[\mathrm{gO}}_{2}/\mathrm{gS}]$ | 2.0 | [19] |

^{a}—values for three groups of phytoplankton,

^{b}—values for three groups of POC (POC-L, POC-R, and POC-I). Tu

^{c}—tuning parameter.

**Table A3.**Kinetic equations for source terms in pelagic model (see Appendix A (Table A1) for symbols).

Biochemical Process | Formulation |
---|---|

Phytoplankton | $\frac{d{C}_{\mathrm{phy}}}{dt}=\left[\begin{array}{l}\mathrm{Primary}\_\mathrm{Production}-{\mathrm{Metabolism}}_{\mathrm{phy}}-{\mathrm{Mortality}}_{\mathrm{phy}}\\ -\mathrm{Zoo}\_\mathrm{Grazing}\end{array}\right]$ $\frac{d{C}_{\mathrm{phy}}}{dt}=\left[{R}_{\mathrm{phy}\_\mathrm{PP}}-{R}_{\mathrm{phy}\_\mathrm{Met}}-{R}_{\mathrm{phy}\_\mathrm{Mor}}-{R}_{\mathrm{zoo}\_\mathrm{GE}}\right]$ |

Primary production: | ${R}_{\mathrm{phy}\_\mathrm{PP}}={G}_{\mathrm{phy}}{f}_{\mathrm{TLphy}}{f}_{\mathrm{LLphy}}{f}_{\mathrm{NLphy}}{C}_{\mathrm{phy}}$ |

${f}_{\mathrm{TLphy}}=\left\{\begin{array}{cc}\mathrm{exp}\{-{k}_{\mathrm{GKL}}{(T-{T}_{\mathrm{LO}})}^{2}\}\hfill & (T<{T}_{\mathrm{LO}})\\ 1\hfill & ({T}_{\mathrm{LO}}\text{}T\text{}{T}_{\mathrm{UO}})\\ \mathrm{exp}\{-{k}_{\mathrm{GKU}}{(T-{T}_{\mathrm{UO}})}^{2}\}\hfill & (T{T}_{\mathrm{UO}})\end{array}\right\}$ | |

${f}_{\mathrm{LLphy}}=\frac{\mathrm{PAR}}{{\mathrm{PAR}}_{\mathrm{opt}}}\mathrm{exp}\left\{1-\frac{\mathrm{PAR}}{{\mathrm{PAR}}_{\mathrm{opt}}}\right\}$ | |

$\mathrm{PAR}={\mathrm{PAR}}_{\mathrm{sur}}\mathrm{exp}\{-{k}_{\mathrm{e}}\mathrm{D}\}$ | |

${k}_{\mathrm{e}}=0.32+0.016{C}_{\mathrm{chl}}+0.094{C}_{\mathrm{Silt}}$ | |

${\mathrm{PAR}}_{\mathrm{opt}}=\mathrm{MAX}\left(\frac{\mathrm{PAR}}{\mathrm{PI}},{\mathrm{PAR}}_{\mathrm{min}}\right)$ | |

${f}_{\mathrm{NLphy}}=\mathrm{MIN}\left({\mathrm{PO}}_{4\mathrm{NLphy}},{\mathrm{nit}}_{\mathrm{NLphy}},{\mathrm{Si}}_{\mathrm{NLphy}}\right)$ | |

${\mathrm{PO}}_{4\mathrm{NLphy}}={f}_{\mathrm{Monod}}({C}_{{\mathrm{PO}}_{4}},\text{}{K}_{{\mathrm{PO}}_{4}})$ | |

${\mathrm{nit}}_{\mathrm{NLphy}}={f}_{\mathrm{Monod}}({C}_{{\mathrm{NH}}_{4}}+{C}_{{\mathrm{NO}}_{3}},\text{}{K}_{\mathrm{nit}})$ | |

${\mathrm{Si}}_{\mathrm{NLphy}}={f}_{\mathrm{Monod}}({C}_{\mathrm{Si}},\text{}{K}_{\mathrm{Si}})$ | |

${f}_{\mathrm{Monod}}(\mathrm{Nut},\text{}\mathrm{Hf}\_\mathrm{Nut})=\frac{\mathrm{Nut}}{\mathrm{Hf}\_\mathrm{Nut}+\mathrm{Nut}}$ | |

Metabolism: | ${R}_{\mathrm{phy}\_\mathrm{Met}}={M}_{\mathrm{phy}}\mathrm{exp}(0.04(T-20)){C}_{\mathrm{phy}}$ |

Mortality: | ${R}_{\mathrm{phy}\_\mathrm{Mor}}={D}_{\mathrm{phy}}{C}_{\mathrm{phy}}$ |

Zooplankton Grazing: | ${R}_{zoo\_\mathrm{GE}}=\mathrm{From}\text{}\mathrm{zooplankton}\text{}\mathrm{model}$ |

Zooplankton | $\frac{d{C}_{\mathrm{zoo}}}{dt}=\left[\mathrm{Growth}-{\mathrm{Mortality}}_{zoo}\right]$ $\frac{d{C}_{\mathrm{zoo}}}{dt}=\left[{R}_{\mathrm{zoo}\_\mathrm{Gro}}-{R}_{\mathrm{zoo}\_\mathrm{Mor}}\right]$ |

Growth: | ${R}_{\mathrm{zoo}\_\mathrm{Gro}}={R}_{\mathrm{zoo}\_\mathrm{A}}-{R}_{\mathrm{zoo}\_\mathrm{MF}}$ |

${R}_{\mathrm{zoo}\_\mathrm{A}}={C}_{\mathrm{zoo}\_\mathrm{AP}}{R}_{\mathrm{zoo}\_\mathrm{G}}{f}_{\mathrm{Monod}}({C}_{\mathrm{DO}},\text{}{K}_{\mathrm{DO}\_\mathrm{zoo}})$ | |

${R}_{\mathrm{zoo}\_\mathrm{G}}={\displaystyle \sum _{\mathrm{F}\_\mathrm{iter}=1}^{\mathrm{p}}{R}_{\mathrm{zoo}\_\mathrm{GE}}(\mathrm{F}\_\mathrm{iter})}$ | |

${R}_{\mathrm{zoo}\_\mathrm{GE}}(\mathrm{F}\_\mathrm{iter})={R}_{\mathrm{zoo}\_\mathrm{GP}}\frac{\mathrm{F}\_\mathrm{each}(\mathrm{F}\_\mathrm{iter})}{\mathrm{Total}\_\mathrm{F}}$ | |

${R}_{\mathrm{zoo}\_\mathrm{GP}}={G}_{\mathrm{zoo}}{f}_{\mathrm{TLzoo}}{f}_{\mathrm{FLzoo}}{C}_{\mathrm{zoo}}$ | |

${f}_{\mathrm{TLzoo}}=\mathrm{exp}(0.035(T-20))$ | |

${f}_{\mathrm{FLzoo}}=1-\mathrm{exp}({K}_{\mathrm{Ivlev}}\mathrm{MIN}((\mathrm{F}\_\mathrm{Thr}-\mathrm{Total}\_\mathrm{F}),\text{}0.0)$ | |

$\mathrm{Total}\_\mathrm{F}={\displaystyle \sum _{\mathrm{F}\_\mathrm{iter}=1}^{\mathrm{p}}\mathrm{F}\_\mathrm{each}(\mathrm{F}\_\mathrm{iter})}$ | |

$\mathrm{F}\_\mathrm{each}(\mathrm{F}\_\mathrm{iter})={C}_{\mathrm{F}\_\mathrm{iter}}$ | |

${R}_{\mathrm{zoo}\_\mathrm{MF}}={R}_{\mathrm{MAX}\_\mathrm{MF}}{C}_{zoo}$ | |

Mortality: | ${R}_{\mathrm{zoo}\_\mathrm{Mor}}={D}_{\mathrm{zoo}}{C}_{\mathrm{zoo}}{f}_{\mathrm{TLzoo}}\frac{{C}_{\mathrm{zoo}}}{{C}_{\mathrm{zoo}\_\mathrm{MAX}}}$ |

Fecal: | ${R}_{\mathrm{zoo}\_\mathrm{Fecal}}={R}_{\mathrm{zoo}\_\mathrm{G}}-{R}_{\mathrm{zoo}\_\mathrm{A}}$ |

Metabolism: | ${R}_{\mathrm{zoo}\_\mathrm{Met}}=\mathrm{MIN}({R}_{\mathrm{zoo}\_\mathrm{A}},\text{}{R}_{\mathrm{zoo}\_\mathrm{MF}})$ |

Particulate organic carbon | $\frac{d{C}_{\mathrm{POC}}}{dt}=\left[\begin{array}{l}\left({\mathrm{Mortality}}_{\mathrm{phy}}+{\mathrm{Fecal}}_{\mathrm{zoo}}+{\mathrm{Mortality}}_{\mathrm{zoo}}\right)\mathrm{Fraction}-\mathrm{Zoo}\_\mathrm{grazing}\\ -\mathrm{Oxic}\_\mathrm{dec}-\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}-\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{SO}}_{4}\end{array}\right]$ |

$\frac{d{C}_{\mathrm{POC}}}{dt}=\left[\begin{array}{l}\left({R}_{\mathrm{phy}\_\mathrm{Mor}}+{R}_{\mathrm{zoo}\_\mathrm{Fecal}}+{R}_{\mathrm{zoo}\_\mathrm{Mor}}\right)F-{R}_{\mathrm{zoo}\_\mathrm{GE}}\\ -{R}_{{C}_{\mathrm{POC}}\_\mathrm{O}}-{R}_{{C}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}-{R}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}\end{array}\right]$ | |

Aerobic carbon diagenesis: | ${R}_{{C}_{\mathrm{POC}}\_\mathrm{O}}={k}_{{C}_{\mathrm{POC}}\_\mathrm{O}}{\theta}_{{C}_{\mathrm{POC}}}^{(T-20)}\left[\frac{{C}_{\mathrm{DO}}}{{K}_{\mathrm{DO},{C}_{\mathrm{POC}}}+{C}_{\mathrm{DO}}}\right]{C}_{\mathrm{POC}}$ |

Anaerobic carbon diagenesis with nitrate as electron accepter or denitrification: | ${R}_{{C}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}={R}_{{C}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}\mathrm{rCN}\_\mathrm{D}$ ${R}_{{C}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}={k}_{{\mathrm{C}}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}{\theta}_{{C}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}^{(T-20)}\mathrm{MIN}\left[\frac{{K}_{\mathrm{DO},{C}_{\mathrm{POC}}}}{{K}_{\mathrm{DO},{C}_{\mathrm{POC}}}+{C}_{\mathrm{DO}}},\frac{{C}_{\mathrm{POC}}}{{K}_{\mathrm{dec},{C}_{\mathrm{POC}}}+{C}_{\mathrm{POC}}}\right]{C}_{{\mathrm{NO}}_{3}}$ |

Anaerobic carbon diagenesis with sulfate as electron accepter or sulfide production: | ${R}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}={k}_{{C}_{\mathrm{POC}}\_{\mathrm{SO}}_{4}}{\theta}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}^{(T-20)}\mathrm{MIN}\left[\frac{{K}_{\mathrm{DO},{C}_{\mathrm{POC}}}}{{\mathrm{K}}_{\mathrm{DO},{C}_{\mathrm{POC}}}+{C}_{\mathrm{DO}}},\frac{{K}_{{C}_{{\mathrm{NO}}_{3}},\mathrm{D}}}{{K}_{{C}_{{\mathrm{NO}}_{3}},\mathrm{D}}+{C}_{{\mathrm{NO}}_{3}}}\right]{C}_{\mathrm{POC}}$ |

Phosphorous | $\frac{d{C}_{{\mathrm{PO}}_{4}}}{dt}=\left[\begin{array}{l}({\mathrm{Metabolism}}_{\mathrm{phy}}+{\mathrm{Metabolism}}_{\mathrm{zoo}}-\mathrm{Primary}\_\mathrm{Production}\\ +\mathrm{Oxic}\_\mathrm{dec}+\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}+\mathrm{Anoxic}\_\mathrm{deco}\_{\mathrm{SO}}_{4})\mathrm{P}2\mathrm{C}\_\mathrm{ratio}\\ +\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}\end{array}\right]$ |

$\frac{d{C}_{{\mathrm{PO}}_{4}}}{dt}=\left[\begin{array}{l}({R}_{\mathrm{phy}\_\mathrm{Met}}+{R}_{\mathrm{zoo}\_\mathrm{Met}}-{R}_{\mathrm{phy}\_\mathrm{PP}}+{R}_{{C}_{\mathrm{POC}}\_\mathrm{O}}+{R}_{{C}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}\\ +{R}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}){r}_{\mathrm{PC}\_\mathrm{dec}}+{{(\mathrm{F}}_{{\mathrm{PO}}_{4}}/\Delta \mathsf{\sigma})|}_{k=1}\end{array}\right]$ | |

Ammonia | $\frac{d{C}_{{\mathrm{NH}}_{4}}}{dt}=\left[\begin{array}{l}({\mathrm{Metabolism}}_{\mathrm{phy}}+{\mathrm{Metabolism}}_{\mathrm{zoo}}-\mathrm{Primary}\_\mathrm{Production}\\ +\mathrm{Oxic}\_\mathrm{dec}+\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}+\mathrm{Anoxic}\_\mathrm{deco}\_{\mathrm{SO}}_{4})\mathrm{N}2\mathrm{C}\_\mathrm{ratio}\\ +\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}-\mathrm{Nitrification}\end{array}\right]$ |

$\frac{d{C}_{{\mathrm{NH}}_{4}}}{dt}=\left[\begin{array}{l}({R}_{\mathrm{phy}\_\mathrm{Met}}+{R}_{\mathrm{zoo}\_\mathrm{Met}}-{R}_{\mathrm{phy}\_\mathrm{PP}}\cdot \mathrm{r}\_\mathrm{f}+{R}_{{C}_{\mathrm{POC}}\_\mathrm{O}}+{R}_{{C}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}\\ +{R}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}){r}_{\mathrm{NC}\_\mathrm{dec}}+{{(\mathrm{F}}_{{\mathrm{NH}}_{4}}/\Delta \mathsf{\sigma})|}_{k=1}-{R}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}\end{array}\right]$ | |

Nitrification: | ${R}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}={k}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}{\theta}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}^{(T-20)}\left[\frac{{C}_{\mathrm{DO}}}{{K}_{\mathrm{DO},{C}_{{\mathrm{NH}}_{4}}}+{C}_{\mathrm{DO}}}\right]{C}_{{\mathrm{NH}}_{4}}$ |

Nitrate | $\frac{d{C}_{{\mathrm{NO}}_{3}}}{dt}=\left[\begin{array}{l}\mathrm{Nitrification}-\mathrm{Primary}\_\mathrm{Production}\cdot \mathrm{C}2\mathrm{N}\_\mathrm{ratio}\\ -\mathrm{Denitrification}+\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}\end{array}\right]$ |

$\frac{d{C}_{{\mathrm{NO}}_{3}}}{dt}=\left[{R}_{{C}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}-{R}_{\mathrm{phy}\_\mathrm{PP}}(1-\mathrm{r}\_\mathrm{f}){r}_{\mathrm{NC}\_\mathrm{dec}}-{R}_{{C}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}+{({\mathrm{F}}_{{\mathrm{NO}}_{3}}/\Delta \mathsf{\sigma})|}_{k=1}\right]$ | |

Particulate silica | $\frac{d{C}_{\mathrm{PSi}}}{dt}=\left[({\mathrm{Mortality}}_{\mathrm{phy}}\cdot \mathrm{Si}2\mathrm{C}\_\mathrm{ratio}-\mathrm{Silica}\_\mathrm{production})\mathrm{Si}2\mathrm{PSi}\_\mathrm{ratio}\right]$ |

$\frac{d{C}_{\mathrm{PSi}}}{dt}=\left[({R}_{\mathrm{phy}\_\mathrm{Mor}}{r}_{\mathrm{Si}2\mathrm{C}\_\mathrm{phy}}-{R}_{{\mathrm{C}}_{Si}\_\mathrm{pro}}){r}_{\mathrm{Si}\_\mathrm{PSi}}\right]$ | |

Dissolved silica production or particulate silica dissolution: | ${R}_{{C}_{\mathrm{Si}}\_\mathrm{pro}}={k}_{{C}_{\mathrm{Si}}}{\theta}_{{C}_{\mathrm{Si}}}^{(T-20)}\left[\frac{{C}_{\mathrm{PSi}}}{{C}_{\mathrm{PSi}}+{K}_{{C}_{\mathrm{PSi}}}}\right]\left[{C}_{\mathrm{Si},\mathrm{sat}}-{C}_{\mathrm{Si}}\right]$ |

Dissolved silica | $\frac{d{C}_{\mathrm{Si}}}{dt}=\left[\mathrm{Silica}\_\mathrm{production}-\mathrm{Primary}\_\mathrm{Production}\cdot \mathrm{Si}2\mathrm{C}\_\mathrm{ratio}+\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}\right]$ |

$\frac{d{C}_{\mathrm{Si}}}{dt}=\left[{R}_{{C}_{\mathrm{Si}}\_\mathrm{pro}}-{R}_{\mathrm{phy}\_\mathrm{PP}}{r}_{\mathrm{SiC}\_\mathrm{phy}}+{({\mathrm{F}}_{\mathrm{Si}}/\Delta \sigma )|}_{k=1}\right]$ | |

Sulfide | $\frac{d{C}_{{\mathrm{S}}^{2-}}}{dt}=\left[\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{SO}}_{4}\cdot \mathrm{C}2\mathrm{S}\_\mathrm{ratio}-\mathrm{Sulfide}\_\mathrm{Oxidation}+\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}\right]$ |

$\frac{d{C}_{{\mathrm{S}}^{2-}}}{dt}=\left[{R}_{{C}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}{r}_{\mathrm{CS}\_\mathrm{dec}}-{R}_{{C}_{{\mathrm{S}}^{2-}}\_\mathrm{O}}+{({\mathrm{F}}_{{\mathrm{S}}^{2-}}/\Delta \sigma )|}_{k=1}\right]$ | |

Sulfide oxidation: | ${R}_{{C}_{{\mathrm{S}}^{2-}}\_\mathrm{O}}={k}_{{C}_{{\mathrm{S}}^{2-}}\_\mathrm{O}}{\theta}_{{C}_{{\mathrm{S}}^{2-}}}^{(T-20)}\left[\frac{{C}_{\mathrm{DO}}}{{K}_{{C}_{{\mathrm{S}}^{2-}},\mathrm{DO}}+{C}_{\mathrm{DO}}}\right]\frac{1}{{r}_{\mathrm{OS}\_\mathrm{oxi}}}$ |

Dissolved oxygen | $\frac{d{C}_{\mathrm{DO}}}{dt}=\left[\begin{array}{l}(\mathrm{Primary}\_\mathrm{Production}-{\mathrm{Metabolism}}_{\mathrm{phy}}-{\mathrm{Metabolism}}_{\mathrm{zoo}}\\ -\mathrm{Oxic}\_\mathrm{dec})\mathrm{OC}\_\mathrm{ratio}-\mathrm{Nitrification}\cdot \mathrm{ON}\_\mathrm{ratio}\\ -\mathrm{Sulfide}\_\mathrm{oxidation}\cdot \mathrm{OS}\_\mathrm{ratio}+\mathrm{Aeration}+\mathrm{Flux}\_\mathrm{sed}2\mathrm{water}\end{array}\right]$ |

$\frac{d{C}_{\mathrm{DO}}}{dt}=\left[\begin{array}{l}({R}_{\mathrm{phy}\_\mathrm{PP}}-{R}_{\mathrm{phy}\_\mathrm{Met}}-{R}_{\mathrm{zoo}\_\mathrm{Met}}-{R}_{{\mathrm{C}}_{\mathrm{poc}}\_\mathrm{O}}){r}_{\mathrm{OC}\_\mathrm{dec}}\\ -{R}_{{C}_{{\mathrm{NH}}_{4}\_\mathrm{nit}}}{r}_{\mathrm{ON}\_\mathrm{nit}}-{R}_{{C}_{{\mathrm{S}}^{2-}}\_\mathrm{O}}{r}_{\mathrm{OS}\_\mathrm{oxi}}\\ +{({k}_{\mathrm{re}}({C}_{\mathrm{DO}}\_\mathrm{sat}-{C}_{\mathrm{DO}})/\Delta \sigma )|}_{k=\mathrm{ke}}+{({\mathrm{F}}_{\mathrm{DO}}/\Delta \sigma )|}_{k=1}\end{array}\right]$ |

**Table A4.**Kinetic equations for source terms in benthic model (see Appendix A (Table A1) for symbols).

Biochemical Process | Formulation |
---|---|

Particulate organic carbon | $\frac{d{B}_{\mathrm{POC}}}{dt}=\left[-\mathrm{Oxic}\_\mathrm{dec}-\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}-\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{SO}}_{4}\right]$ |

$\frac{d{B}_{\mathrm{POC}}}{dt}=\left[-{R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}-{R}_{{B}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}-{R}_{{B}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}\right]$ | |

Aerobic carbon diagenesis: | ${R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}={k}_{{B}_{\mathrm{POC}}\_\mathrm{O}}{\theta}_{{B}_{\mathrm{POC}}}^{(T-20)}\left[\frac{{B}_{\mathrm{DO}}}{{\mathrm{K}}_{\mathrm{DO},{B}_{\mathrm{POC}}}+{B}_{\mathrm{DO}}}\right]{B}_{\mathrm{POC}}$ |

Anaerobic carbon diagenesis with nitrate as electron accepter or denitrification: | ${R}_{{B}_{{\mathrm{POC}\_\mathrm{NO}}_{3}}}={R}_{{B}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}{r}_{\mathrm{CN}\_\mathrm{D}}$ ${R}_{{B}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}={k}_{{B}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}{\theta}_{{B}_{{\mathrm{NO}}_{3}}}^{(T-20)}\mathrm{MIN}\left[\frac{{K}_{\mathrm{DO},{B}_{\mathrm{POC}}}}{{K}_{\mathrm{DO},{B}_{\mathrm{POC}}}+{B}_{\mathrm{DO}}},\frac{{B}_{\mathrm{POC}}}{{K}_{\mathrm{dec},{B}_{\mathrm{POC}}}+{B}_{\mathrm{POC}}}\right]{B}_{{\mathrm{NO}}_{3}}$ |

Anaerobic carbon diagenesis with sulfate as electron accepter or sulfide production: | ${R}_{{B}_{{\mathrm{POC}\_\mathrm{SO}}_{4}}}={k}_{{B}_{{\mathrm{POC}\_\mathrm{SO}}_{4}}}{\theta}_{{B}_{{\mathrm{POC}\_\mathrm{SO}}_{4}}}^{(T-20)}\mathrm{MIN}\left[\frac{{K}_{\mathrm{DO},{B}_{\mathrm{POC}}}}{{K}_{\mathrm{DO},{B}_{\mathrm{POC}}}+{B}_{\mathrm{DO}}},\text{}\frac{{K}_{{B}_{{\mathrm{NO}}_{3}},\mathrm{D}}}{{K}_{{B}_{{\mathrm{NO}}_{3}},\mathrm{D}}+{B}_{{\mathrm{NO}}_{3}}}\right]{B}_{\mathrm{POC}}$ |

Phosphorous | $\frac{d{B}_{{\mathrm{PO}}_{4}}}{dt}=\left[\left(\mathrm{Oxic}\_\mathrm{dec}+\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}+\mathrm{Anoxic}\_\mathrm{deco}\_{\mathrm{SO}}_{4}\right)\mathrm{P}2\mathrm{C}\_\mathrm{ratio}\right]$ |

$\frac{d{B}_{{\mathrm{PO}}_{4}}}{dt}=\left[\left({R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}+{R}_{{B}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}+{R}_{{B}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}\right){r}_{\mathrm{PC}\_\mathrm{dec}}\right]$ | |

Ammonia | $\frac{d{B}_{{\mathrm{NH}}_{4}}}{dt}=\left[\begin{array}{l}\left(\mathrm{Oxic}\_\mathrm{dec}+\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{NO}}_{3}+\mathrm{Anoxic}\_\mathrm{dec}\_{\mathrm{SO}}_{4}\right)\mathrm{N}2\mathrm{C}\_\mathrm{ratio}\\ -\mathrm{Nitrification}\end{array}\right]$ |

$\frac{d{B}_{{\mathrm{NH}}_{4}}}{dt}=\left[\left({R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}+{R}_{{B}_{\mathrm{POC}}{\_\mathrm{NO}}_{3}}+{R}_{{B}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}\right){r}_{\mathrm{NC}\_\mathrm{dec}}-{R}_{{B}_{{\mathrm{NH}}_{4}}}\_\mathrm{N}\right]$ | |

Nitrification: | ${R}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}={k}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}{\theta}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}^{(T-20)}\left[\frac{{B}_{\mathrm{DO}}}{{K}_{\mathrm{DO},{B}_{{\mathrm{NH}}_{4}}}+{B}_{\mathrm{DO}}}\right]{B}_{{\mathrm{NH}}_{4}}$ |

Nitrate | $\frac{d{B}_{{\mathrm{NO}}_{3}}}{dt}=\left[\mathrm{Nitrification}-\mathrm{Denitrification}\right]$ |

$\frac{d{B}_{{\mathrm{NO}}_{3}}}{dt}=\left[{R}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{N}}-{R}_{{B}_{{\mathrm{NO}}_{3}}\_\mathrm{D}}\right]$ | |

Particulate silica | $\frac{d{B}_{\mathrm{PSi}}}{dt}=\left[-\mathrm{Silica}\_\mathrm{production}\cdot \mathrm{Si}2\mathrm{PSi}\_\mathrm{ratio}\right]$ |

$\frac{d{B}_{\mathrm{PSi}}}{dt}=\left[-{R}_{{\mathrm{B}}_{Si}\_\mathrm{Pro}}{r}_{\mathrm{Si}\_\mathrm{PSi}}\right]$ | |

Dissolved silica production or particulate silica dissolution: | ${R}_{{B}_{\mathrm{Si}}\_\mathrm{Pro}}={k}_{{B}_{\mathrm{Si}}}{\theta}_{{B}_{\mathrm{Si}}}^{(T-20)}\left[\frac{{B}_{\mathrm{PSi}}}{{K}_{{B}_{\mathrm{PSi}}}+{B}_{\mathrm{PSi}}}\right]\left[{B}_{\mathrm{Si},\mathrm{sat}}-{B}_{\mathrm{Si}}\right]$ |

Dissolved silica | $\frac{d{B}_{\mathrm{Si}}}{dt}=\left[\mathrm{Silica}\_\mathrm{production}\right]$ |

$\frac{d{B}_{\mathrm{Si}}}{dt}=\left[{R}_{{B}_{\mathrm{Si}}}\_\mathrm{Pro}\right]$ | |

Sulfide | $\frac{d{B}_{{S}^{2-}}}{dt}=\left[{\mathrm{Anoxic}\_\mathrm{dec}\_\mathrm{SO}}_{4}\cdot \mathrm{C}2\mathrm{S}\_\mathrm{ratio}-\mathrm{Sulfide}\_\mathrm{oxidation}\right]$ |

$\frac{d{B}_{{\mathrm{S}}^{2-}}}{dt}=\left[{R}_{{B}_{\mathrm{POC}}{\_\mathrm{SO}}_{4}}{r}_{\mathrm{CS}\_\mathrm{dec}}-{R}_{{B}_{{\mathrm{S}}^{2-}}\_\mathrm{O}}\right]$ | |

Sulfide oxidation: | ${R}_{{B}_{{\mathrm{S}}^{2-}}}\_\mathrm{oxi}={k}_{{B}_{{\mathrm{S}}^{2-}}}\_\mathrm{oxi}{\theta}_{{B}_{{\mathrm{S}}^{2-}}}^{(T-20)}\left[\frac{{B}_{\mathrm{DO}}}{{K}_{{{B}_{\mathrm{S}}}^{2-},\mathrm{DO}}+{B}_{\mathrm{DO}}}\right]\frac{1}{{r}_{\mathrm{OS}\_\mathrm{oxi}}}$ |

Dissolved oxygen | $\frac{d{B}_{\mathrm{DO}}}{dt}=\left[\begin{array}{l}-\mathrm{oxic}\_\mathrm{dec}\cdot \mathrm{O}2\mathrm{C}\_\mathrm{ratio}-\mathrm{Nitrification}\cdot \mathrm{ON}\_\mathrm{ratio}\\ -\mathrm{Sulfide}\_\mathrm{oxidation}\cdot \mathrm{OS}\_\mathrm{ratio}\end{array}\right]$ |

$\frac{d{B}_{\mathrm{DO}}}{dt}=\left[-{R}_{{B}_{\mathrm{POC}}\_\mathrm{O}}{r}_{\mathrm{OC}\_\mathrm{dec}}-{R}_{{B}_{{\mathrm{NH}}_{4}}\_\mathrm{nit}}{r}_{\mathrm{ON}\_\mathrm{nit}}-{R}_{{\mathrm{B}}_{{\mathrm{H}}_{2}\mathrm{S}}\_\mathrm{O}}{r}_{\mathrm{OS}\_\mathrm{oxi}}\right]$ |

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**Figure 5.**Schematic diagram for the effect of POCC on layer thickness [42].

**Figure 7.**(

**a**) 2D control volume in a vertical section and (

**b**) boundary flux at sediment–water interface.

**Figure 8.**Relationship between observed porosity and POCC in Tokyo Bay [41].

**Figure 10.**Meteorological conditions during a one-year period: (

**a**) Rainfall, (

**b**) air temperature, (

**c**) solar radiation, (

**d**) air pressure, (

**e**) vapor pressure, (

**f**) relative humidity, (

**g**) cloud cover, and (

**h**) wind vector.

**Figure 11.**Measured and simulated salinity [43].

**Figure 12.**Measured and simulated values of surface and bottom salinity at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 13.**Measured and simulated temperature [43].

**Figure 14.**Measured and simulated values of surface and bottom temperature at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 16.**Measured and simulated values of surface and bottom chlorophyll a at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 17.**Measured and simulated DO [43].

**Figure 18.**Measured and simulated values of surface and bottom DO at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 19.**Measured and simulated ammonia [43].

**Figure 20.**Measured and simulated values of surface and bottom ammonia at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 21.**Measured and simulated phosphate [43].

**Figure 22.**Measured and simulated values of surface and bottom phosphate at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 23.**Measured and simulated values of surface and bottom nitrate (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 24.**Measured and simulated nitrate [43].

**Figure 25.**Measured and simulated silica [43].

**Figure 26.**Measured and simulated values of surface and bottom silica at (

**a**) CLH, (

**b**) KSB, and (

**c**) TLH [43].

**Figure 27.**Spatial distribution of POCC in sediment: (

**a**) observed (dots are sampling points) [39] and (

**b**) simulated.

**Figure 28.**Spatial distribution of WC in sediment: (

**a**) observed (dots are sampling points) [39] and (

**b**) simulated.

**Figure 29.**Bed formation every 20-year time interval (

**a**) 20-year (

**b**) 40-year (

**c**) 60-year (

**d**) 80-year (

**e**) 100-year (

**f**) 120-year (

**g**) 140-year (

**h**) 160-year (

**i**) 180-year, and (

**j**) 200-year (note that the scales are different in each figure).

**Figure 30.**Schematic diagram showing the movement of POC from the head to the central part of the bay: (

**a**) initial high POCC at the head, (

**b**) erosion due to BSS effect, and (

**c**) effect of WBSS and CBSS to keep the highest POCC at the central area.Initially, the highest accumulation occurs at the head of the bay, as seen in (

**a**), and the accumulated surface sediment is eroded and re-suspended owing to BSS (

**b**). The re-suspended material can be moved to another location owing to physical processes within the bay. The final stable morphology is decided by the effects of WBSS and CBSS, suggesting possible higher accumulation of POCC towards the central part (

**c**).

**Figure 31.**Spatial distribution of (

**a**) current induced, (

**b**) wave induced, and (

**c**) total bed shear stresses.

**Table 1.**Stoichiometric relationships associated with biochemical processes (modified from [6]).

Photosynthesis—ammonia as electron accepter ${106(\mathrm{CO}}_{2}{)+16(\mathrm{NH}}_{3}{)+\mathrm{H}}_{3}{\mathrm{PO}}_{4}{+106(\mathrm{H}}_{2}\mathrm{O})\to {{(\mathrm{CH}}_{2}\mathrm{O})}_{106}{{(\mathrm{NH}}_{3})}_{16}{(\mathrm{H}}_{3}{\mathrm{PO}}_{4}{)+106(\mathrm{O}}_{2})$ |

Photosynthesis—nitrate as electron accepter ${106(\mathrm{CO}}_{2}{)+16(\mathrm{NO}}_{3}^{-}{)+\mathrm{H}}_{3}{\mathrm{PO}}_{4}{+122(\mathrm{H}}_{2}{\mathrm{O})+16\mathrm{H}}^{+}\to {{(\mathrm{CH}}_{2}\mathrm{O})}_{106}{{(\mathrm{NH}}_{3})}_{16}{(\mathrm{H}}_{3}{\mathrm{PO}}_{4}{)+138(\mathrm{O}}_{2})$ |

Oxic mineralization and metabolism ${{(\mathrm{CH}}_{2}\mathrm{O})}_{106}{{(\mathrm{NH}}_{3})}_{16}{(\mathrm{H}}_{3}{\mathrm{PO}}_{4}{)+106(\mathrm{O}}_{2})\to {106(\mathrm{CO}}_{2}{)+16(\mathrm{NH}}_{3}{)+\mathrm{H}}_{3}{\mathrm{PO}}_{4}{+106(\mathrm{H}}_{2}\mathrm{O})$ |

Sub-oxic mineralization or denitrification ${{(\mathrm{CH}}_{2}\mathrm{O})}_{106}{{(\mathrm{NH}}_{3})}_{16}{(\mathrm{H}}_{3}{\mathrm{PO}}_{4})+\raisebox{1ex}{$424$}\!\left/ \!\raisebox{-1ex}{$5$}\right.{(\mathrm{HNO}}_{3})\to {106(\mathrm{CO}}_{2}{)+16(\mathrm{NH}}_{3}{)+\mathrm{H}}_{3}{\mathrm{PO}}_{4}+\raisebox{1ex}{$106$}\!\left/ \!\raisebox{-1ex}{$5$}\right.{(\mathrm{H}}_{2}\mathrm{O})+\raisebox{1ex}{$212$}\!\left/ \!\raisebox{-1ex}{$5$}\right.{(\mathrm{N}}_{2})$ |

Anoxic mineralization or H_{2}S production${{(\mathrm{CH}}_{2}\mathrm{O})}_{106}{{(\mathrm{NH}}_{3})}_{16}{(\mathrm{H}}_{3}{\mathrm{PO}}_{4})+\raisebox{1ex}{$106$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{(\mathrm{H}}_{2}{\mathrm{SO}}_{4})\to {106(\mathrm{CO}}_{2}{)+16(\mathrm{NH}}_{3}{)+\mathrm{H}}_{3}{\mathrm{PO}}_{4}{+106(\mathrm{H}}_{2}\mathrm{O})+\raisebox{1ex}{$106$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{(\mathrm{H}}_{2}\mathrm{S})$ |

Nitrification ${\mathrm{NH}}_{4}^{+}{+2\mathrm{O}}_{2}\to {\mathrm{NO}}_{3}^{-}{+\mathrm{H}}_{2}{\mathrm{O}+2\mathrm{H}}^{+}$ |

H_{2}S oxidization${\mathrm{S}}^{2-}{+2(\mathrm{O}}_{2})\to {{\mathrm{SO}}_{4}}^{2-}$ |

**Table 2.**Initial and boundary conditions for the state variables at bay mouth (see Appendix A (Table A1) for symbols).

Water Variables | Sediment Variables | Unit | |||
---|---|---|---|---|---|

Variable | Initial Value | Boundary Value | Variable | Initial Value | |

$S$ | 33.5 | 33.5 | $\left[\mathrm{psu}\right]$ | ||

$T$ | 13.0 | 13.0 | [°C] | ||

${C}_{\mathrm{phy}}$ | 5.0, 5.0, 5.0 ^{a} | 5.0, 5.0, 5.0 ^{a} | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | ||

${C}_{\mathrm{zoo}}$ | 37.5 | 37.5 | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ | ||

${C}_{\mathrm{POC}}$ | 35.0, 14.0, 5.0 ^{b} | 35.0, 14.0, 5.0 ^{b} | ${B}_{\mathrm{POC}}$ | 0.0, 0.0, 0.0 ^{b} | $[{\mathrm{mgC}/\mathrm{m}}^{3}]$ |

${C}_{{\mathrm{NH}}_{4}}$ | 10.0 | 10.0 | ${B}_{{\mathrm{NH}}_{4}}$ | 0.0 | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ |

${C}_{{\mathrm{PO}}_{4}}$ | 0.5 | 0.5 | ${B}_{{\mathrm{PO}}_{4}}$ | 0.0 | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ |

${C}_{{\mathrm{NO}}_{3}}$ | 14.0 | 14.0 | ${B}_{{\mathrm{NO}}_{3}}$ | 0.0 | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ |

${C}_{\mathrm{Si}}$ | 2.5 | 2.5 | ${B}_{\mathrm{Si}}$ | 0.0 | ${[\mathrm{mmol}/\mathrm{m}}^{3}]$ |

${C}_{\mathrm{PSi}}$ | 16.0 | 16.0 | ${B}_{\mathrm{PSi}}$ | 0.0 | ${[\mathrm{mg}/\mathrm{m}}^{3}]$ |

${C}_{\mathrm{DO}}$ | 7.0 | 7.0 | ${B}_{\mathrm{DO}}$ | 0.0 | ${[\mathrm{g}/\mathrm{m}}^{3}]$ |

${C}_{{\mathrm{S}}^{2-}}$ | 0.0 | 0.0 | ${B}_{{\mathrm{S}}^{2-}}$ | 0.0 | ${[\mathrm{g}/\mathrm{m}}^{3}]$ |

${C}_{\mathrm{Silt}}$ | 1.0 | 1.0 | ${B}_{\mathrm{Silt}}$ | 0.0 | ${[\mathrm{g}/\mathrm{m}}^{3}]$ |

^{a}—values for three groups of phytoplankton,

^{b}—values for three groups of POC (POC-L, POC-R, and POC-I).

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Amunugama, M.; Sasaki, J.
Numerical Modeling of Long-Term Biogeochemical Processes and Its Application to Sedimentary Bed Formation in Tokyo Bay. *Water* **2018**, *10*, 572.
https://doi.org/10.3390/w10050572

**AMA Style**

Amunugama M, Sasaki J.
Numerical Modeling of Long-Term Biogeochemical Processes and Its Application to Sedimentary Bed Formation in Tokyo Bay. *Water*. 2018; 10(5):572.
https://doi.org/10.3390/w10050572

**Chicago/Turabian Style**

Amunugama, Mangala, and Jun Sasaki.
2018. "Numerical Modeling of Long-Term Biogeochemical Processes and Its Application to Sedimentary Bed Formation in Tokyo Bay" *Water* 10, no. 5: 572.
https://doi.org/10.3390/w10050572