🌊 Coastal Ocean Oxygen Distribution Calculator

$$\frac{\partial O_2}{\partial t} = -w\frac{\partial O_2}{\partial z} + \frac{\partial}{\partial z}\left(K_z\frac{\partial O_2}{\partial z}\right) + P - R$$

Where: O₂ = oxygen concentration, w = vertical velocity, K_z = vertical diffusivity, P = production, R = respiration

$$P(z) = P_{max} \cdot \frac{I(z)}{I(z) + K_I} \cdot e^{-k \cdot z}$$

Where: P_max = maximum production rate, I(z) = light intensity at depth z, k = light attenuation coefficient

$$K_z = K_{z0} + K_{wind} \cdot U_{10}^2 + K_{tidal} \cdot \sin\left(\frac{2\pi t}{T_{tidal}}\right)$$

Where: K_z0 = background diffusivity, U_10 = wind speed at 10m, T_tidal = tidal period

$$w_{up} = \frac{\tau_x}{\rho f L} \cdot \left(1 - e^{-\frac{t}{T_{relax}}}\right)$$

Where: τ_x = wind stress, ρ = density, f = Coriolis parameter, L = coastal length scale, T_relax = relaxation time

$$O_{2sat} = \exp\left(A_0 + A_1\frac{100}{T} + A_2\ln\frac{T}{100} + S\left(B_0 + B_1\frac{T}{100}\right)\right)$$

Where: T = temperature (K), S = salinity, A_i and B_i are empirical constants

$$R(z) = R_0 \cdot e^{0.069(T-20)} \cdot \frac{O_2(z)}{O_2(z) + K_{O2}}$$

Where: R_0 = reference respiration rate, T = temperature, K_O2 = half-saturation constant

$$K_{eddy} = K_{z0} \cdot \left(1 + A_{eddy} \cdot \sin\left(\frac{2\pi x}{L_{eddy}}\right) \cdot e^{-\omega_{eddy} t}\right)$$

Where: A_eddy = eddy amplitude, L_eddy = eddy length scale, ω_eddy = eddy frequency

$$K_{fresh} = K_{z0} \cdot \left(1 + \frac{Q_{river}}{Q_{ref}} \cdot e^{-\frac{z}{H_{fresh}}}\right)$$

Where: Q_river = river discharge, Q_ref = reference discharge, H_fresh = freshwater influence depth

$$R_{nitrif} = k_{nitrif} \cdot [NH_4^+] \cdot \frac{O_2}{O_2 + K_{O2,nitrif}}$$

Where: k_nitrif = nitrification rate constant, [NH₄⁺] = ammonium concentration

$$N^2 = -\frac{g}{\rho_0}\frac{\partial \rho}{\partial z} = -\frac{g}{\rho_0}\left(\alpha\frac{\partial T}{\partial z} - \beta\frac{\partial S}{\partial z}\right)$$

Where: N² = buoyancy frequency, g = gravity, α = thermal expansion, β = haline contraction

$$F_{O2} = k_{gas} \cdot (O_{2sat} - O_{2surf}) \cdot \sqrt{\frac{Sc}{660}}$$

Where: k_gas = gas transfer velocity, Sc = Schmidt number, depends on wind speed and temperature

$$I(z) = I_0 \cdot e^{-(k_w + k_{turb} \cdot Turb) \cdot z}$$

Where: I_0 = surface irradiance, k_w = water attenuation, k_turb = turbidity coefficient, Turb = turbidity