Table 1 Model process equations. Equations used to describe the processes included in the ecological model CAEDYM

∂Z_i/∂t = [G_iA_if(Z)_if₁(T)(1-f_ex-f_eg) - (R_i+M_i)f₂(T) - Pred_i]Z_i

   = (assimilation - excretion - egestion) - (respiration + mortality) - predation

∂P/∂t = [P_max,jf₁(T)min(f(I),f(P),f(N)) - (R_j)f₂(T) - Pred_j]P_j ± S_j

   = photosynthetic uptake - (respiration + excretion + mortality) - predation ± settling

∂POC/∂t = Σ[G_if(Z)_if₁(T)_i((1-A_i) + A_if_eg) + M_if₂(T)_i]Z_i + Σ[R_j(1-f_res)(1-f_DOM)f₂(T)]P_j - Pred_POCPOC - R_POCf(DO)f₁(T)POC ± S_POM

   = (unassimilated zooplankton food + zooplankton egestion + zooplankton mortality) + phytoplankton mortality - zooplankton predation - POC decomposition ± settling

∂DOC/∂t = Σ[R_j(1-f_res)f_DOMf₂(T)]P_j + R_POCf_POC(POC)f (DO)f₂(T)POC - R_DOCf (DO)f₂(T)DOC

   = phytoplankton excretion + POC decomposition - DOC mineralisation

∂POP/∂t = Σ[G_if(Z)_if₁(T)_i((1-A_i) + A_if_eg) + M_if₂(T)_i]IP_ZiZ_i + Σ[R_j(1-f_res)(1-f_DOM)f₂(T)]IP_j - Pred_POCPOP - R_POPf(DO)f₁(T)POP ± S_POM

   = (unassimilated zooplankton food + zooplankton egestion + zooplankton mortality) + phytoplankton mortality - zooplankton predation - POP decomposition ± settling

∂DOP/∂t = Σ[R_j(1-f_res)f_DOMf₂(T)]IP_j + Σ[A_if_exG_if(Z)_if₁(T)_i]IP_ZiZ_i + R_POPf (DO)f₁(T)POP - R_DOPf (DO)f₁(T)DOP

   = phytoplankton release + zooplankton excretion + POP decomposition - DOP mineralisation

∂PO4/∂t = R_DOPf (DO)f₂(T)DOP - Σ[UN_max,jf₁(T)_jf(IP)_jf(P)_j]P_j + S_dPO4f(DO)f₂(T)LA/LV

   = DOP mineralisation - phytoplankton uptake + PO4 sediment flux

∂PON/∂t = Σ[G_if(Z)_if₁(T)_i((1-A_i) + A_if_eg) + M_if₂(T)_i]IN_ZiZ_i + Σ[R_j(1-f_res)(1-f_DOM)f₂(T)]IN_j - Pred_PONPON - R_PONf(DO)f₁(T)PON ± S_POM

   = (unassimilated zooplankton food + zooplankton egestion + zooplankton mortality) + phytoplankton mortality - zooplankton predation - PON decomposition ± settling

∂DON/∂t = Σ[R_j(1-f_res)f_DOMf₂(T)]IN_j + Σ[A_if_exG_if(Z)_if₁(T)_i]IN_ZiZ_i + R_PONf(DO)f₂(T)PON - R_DONf(DO)f₂(T)DON

   = phytoplankton release + zooplankton excretion + PON decomposition - DON mineralisation

∂NH4/∂t = R_DONf(DO)f₁(T)DON - Σ[UN_max,jP_Nf₁(T)_jf(IN)_jf(N)_j]P_j - R_NOf(DO)f₂(T)NH4 + S_dNH4f(DO)f₂(T)LA/LV

   = PON mineralisation - phytoplankton uptake - nitrification + NH4 sediment flux

∂NO3/∂t = R_NOf(DO)f₂(T)NH4 - R_N2f(DO)f₂(T)NO3 - Σ[UN_max,j(1-P_N)f₁(T)_jf(IN)_jf(N)_j]P_j

   = nitrification - denitrification - phytoplankton uptake

∂DO/∂t = k_O2(DO_atm - DO) + Σ[P_max,jf₁(T)_jmin(f(I),f(P),f(N)) - R_jf₂(T)_j]P_jY_O2:C Σ[R_if₂(T)_i]Z_iY_O2:C - R_DOCf (DO)f₁(T)DOCY_O2:C - R_NOf (DO)f₂(T)NH4 - S_dO2f(DO)f₂(T)LA/LV

   = atmospheric flux + (phytoplankton oxygen production - phytoplankton respiratory consumption) - zooplankton respiratory consumption - utilisation of oxygen in mineralisation of DOM - utilisation of oxygen in nitrification - sediment oxygen demand.

Temperature functions

f₁(T) = θ^T-20 - θ^k(T-a) + b

where k, a and b are constants solved numerically to satisfy the following conditions:

f₁(T) = 1; at T = Tsta

∂f₁(T)/∂T = 0; at T = Topt

f₁(T) = 0; at T = Tmax

f₂(T) = θ^T-20

Limitation equations

f(Z)_i=(ΣP_j+ΣZ_k+POC)/(K_i+ΣP_j+ΣZ_k+POC)

f(I)_j = I/I_s exp(1-I/I_s)

f(IP)_j = [IP_max/(IP_max-IP_min)] [1-IP_min/IP]

f(IN)_j = [IN_max/(IN_max-IN_min)] [1-IN_min/IN]

f(DO) = DO/(K_DO+DO)

f(P) = PO4/(K_PO4+PO4)

f(N) = (NH4+NO3)/(K_N2+NH4+NO3)

P_N = (NH4 NO3)/[(NH4+K_N)(NO3+K_N)] + (NH4 K_N)/[(NH4+K_N)(NO3+K_N)]

Settling

S_j = (ws/Δz)P_j

S_POM = (g(ρ_POM - ρ_w)(D_POM)²/18μ)/Δz)POM

Predation

Pred_i = Σ(G_kf(Z)_kf₁(T)_kZ_kPzZOO_k,i)

Pred_j = Σ(G_if(Z)_if₁(T)_iZ_iPzPHY_i,j)

Abbreviations: Z, zooplankton; P, phytoplankton; POC, particulate organic carbon; DOC, dissolved organic carbon; POP, particulate organic phosphorus; PO₄, phosphate; PON, particulate organic nitrogen; NH₄, ammonium; NO₃, nitrate; POM, particulate organic matter (C, N or P); IP_zi, zooplankton internal phosphorus; IN_zi, zooplankton internal nitrogen; IP_j, phytoplankton internal phosphorus; IN_j, phytoplankton internal nitrogen; DO, dissolved oxygen; DOatm, concentration of oxygen in the atmosphere; LA, layer area; LV, layer volume; Δz, layer thickness; ρ_w, density of water; μ, viscosity of water; k_O2, oxygen transfer coefficient. Subscripts: i, zooplankton group; j, phytoplankton group; k, zooplankton predator group.