Coastal Ocean Biogeochemical Model

🦠 Primary Production

PP = Pmax × (I/Ik) × exp(1 - I/Ik) × f(T) × f(N)

Where:
• Pmax = Maximum photosynthetic rate
• I = Light intensity at depth
• Ik = Light saturation parameter
• f(T) = Temperature function
• f(N) = Nutrient limitation

Pmax (mg C m⁻³ h⁻¹)

Ik (μmol photons m⁻² s⁻¹)

Surface Light (μmol m⁻² s⁻¹)

Nitrate (μM)

🍃 Respiration & Decomposition

R = R₀ × Q₁₀^((T-T₀)/10) × [DOC]

Decomposition:
dDOC/dt = -k × [DOC] × f(T) × f(O₂)

Where:
• R₀ = Base respiration rate
• Q₁₀ = Temperature coefficient
• k = Decomposition rate constant

R₀ (mg C m⁻³ h⁻¹)

Q₁₀

DOC (mg C L⁻¹)

k (day⁻¹)

🔄 Nitrogen Cycling

Nitrification: NH₄⁺ + O₂ → NO₂⁻ + H₂O + H⁺
Rate = k_nit × [NH₄⁺] × [O₂] × f(T)

Denitrification: NO₃⁻ → N₂O → N₂
Rate = k_denit × [NO₃⁻] × f(O₂) × f(T)

N₂ Fixation: N₂ + 8H⁺ + 8e⁻ → 2NH₃ + H₂
Rate = k_fix × f(T) × f(Fe)

NH₄⁺ (μM)

NO₃⁻ (μM)

O₂ (μM)

k_nit (day⁻¹)

🫧 Carbon System

CO₂ + H₂O ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺ ⇌ CO₃²⁻ + 2H⁺

DIC = [CO₂] + [HCO₃⁻] + [CO₃²⁻]
Alk = [HCO₃⁻] + 2[CO₃²⁻] + [OH⁻] - [H⁺]

Air-Sea CO₂ flux:
F = k × K₀ × (pCO₂_air - pCO₂_sea)

DIC (μmol kg⁻¹)

Alkalinity (μmol kg⁻¹)

pCO₂ air (μatm)

Wind Speed (m/s)

⚡ Redox Processes

Sulfate Reduction:
SO₄²⁻ + 2CH₂O → H₂S + 2HCO₃⁻

Iron Cycling:
Fe³⁺ + e⁻ → Fe²⁺ (reduction)
Fe²⁺ + ¼O₂ + H⁺ → Fe³⁺ + ½H₂O (oxidation)

Rate = k_redox × [Substrate] × f(O₂) × f(T)

SO₄²⁻ (mM)

Fe²⁺ (μM)

H₂S (μM)

k_redox (day⁻¹)

🌊 Physical Transport

Advection: ∂C/∂t = -u∂C/∂x - v∂C/∂y - w∂C/∂z

Diffusion: ∂C/∂t = Kₓ∂²C/∂x² + Kᵧ∂²C/∂y² + Kᵤ∂²C/∂z²

Vertical mixing:
K_vertical = K₀ × (1 + Ri)⁻ⁿ

Where Ri = Richardson number

u velocity (m/s)

v velocity (m/s)

K₀ (m²/s)

Richardson No.

🌊 Coastal Ocean Biogeochemical Model