ABSTRACT
In the previous chapters, a wide range of both physically based and empirical mathematical equations has been presented that may be used to model the transport and fate of substances in soil and water. The equations presented can be used alone, to tackle simple problems, or can be combined to construct complex spatio-temporal environmental models. Figure 15.1 shows an example of a water quality model including many of the transport processes presented in Chapters 12, 13, and 14. The mathematical equations listed in Figure 15.1 were coupled to the general one-dimensional advection-dispersion equation and implemented numerically in computer code. Subsequently, the computer model was used to simulate the short-term dynamics of suspended sediment and dissolved nutrients in the surface water of a rural catchment (Van der Perk, 1998). Note that although models may look impressively
State variables NH4 = ammonium concentration [M.L-3] NO3 = nitrate concentration [M.L-3] O2 = dissolved oxygen concentration [M.L-3] PO4 = phosphate concentration [M.L-3] SS = suspended solids concentration [M.L-3]
Input variables NH4s = ammonium concentration for interstitial water [M.L-3] PO4s = phosphate concentration for interstitial water [M.L-3] SOD = maximum sediment oxygen demand at 20 °C [M.L-2.T-1] T = temperature (in °C) [θ]
Parameters EAC = equilibrium ammonium concentration [M.L-3] EPC = equilibrium phosphate concentration [M.L-3] Fp = oxygen production rate due to photosynthesis [M.L-3.T-1] Fres p = oxygen removal rate due to respiration [M.L-3.T-1] ka = reaeration rate constant at 20 °C [T-1] kd = denitrification rate constant at 20 °C [T-1] kf = ammonium fixation rate constant [T-1] kn = maximum nitrification rate constant at 20 °C [T-1] kp = phosphate fixation rate constant [T-1] ks = maximum suspended solids decomposition rate constant at 20 °C [T-1] Krmin = minimum oxygen mass transfer constant [L.T-1] M = erosion rate parameter [M.L-2.T-1] Mn = Monod half saturation concentration nitrification [M.L-3] MSS = Monod half saturation concentration decomposition SS [M.L-1] Nss = nitrogen content suspended solids [-] p = moisture content stream bed sediment [-] Pss = phosphorus content suspended solids [-] sO2/SS = stoichiometric coefficient oxidation SS [-] Ucrit 1 = critical flow velocity for resuspension [L.T-1] Ucrit 2 = critical flow velocity for settling [L.T-1] Vs = settling velocity suspended solids [L.T-1] γ1 = empirical constant [M.L-3] γ2 = empirical constant [M.L-3.Θ-1] γ3 = empirical constant [M.L-3.Θ-2] θd = temperature coefficient denitrification [-] θn = temperature coefficient nitrification [-] θr = temperature coefficient reaeration [-] θs = temperature coefficient decomposition SS [-] θsod = temperature coefficient SOD [-] ρw = density of water [M.L-3] 18/14 = stoichiometric coefficient NH4:N [-] 62/18 = stoichiometric coefficient NO3:NH4 [-] 64/18 = stoichiometric coefficient oxidation NH4 (2O2:NH4) [-] 95/31 = stoichiometric coefficient PO4:P [-]
complex at first glance, they always remain simplified mathematical representations of the real world.
