Atlantis operating model equations

The production of waste products by invertebrate and vertebrate consumers are handled in the same way, but in the case of vertebrates the mortality term has to be converted from a density to a biomass before being used in the following equations. The production of labile detritus (DL) by consumer group XX is given by:

with _XX the proportion of mortality losses assigned to detritus, _XX the proportion of the growth inefficiency of XX when feeding on live prey that is sent to detritus, _XX,DL the proportion of the growth inefficiency of XX when feeding on DL that is sent to detritus, _XX,DR the proportion of the growth inefficiency of XX when feeding on refractory detritus (DR) that is sent to detritus and f_XX,DL is the proportion of the total detritus produced that is of the type DL. The same equation is used for the production of DR (W_DR), except that the final multiplication of the brackets by f_XX,DL is replaced by multiplication by (1-f_XX,DL).

The only physical processes in Atlanits that differ from those in the Port Phillip Bay Integrated Model (PPBIM, detailed in Murray and Parslow 1997, Walker 1997) are bioturbation, bioirrigation and the calculation of the light attenuation coefficient.

with n_w the background extinction coefficient, n_DON the contribution due to DON, n_D the contribution due to detritus, n_P the contribution due to phytoplankton (PX) and n_susp the contribution due to suspended sediments (SUSP).

The equations for bioirrigation are as detailed in Walker (1997) for PPBIM, but it is tied to the dynamical sediment fauna via an “enhancement” term similar to that of ERSEM I (Ebenhöh et al. 1995).

As Atlantis uses explicit sediment layers it can approximate particulate diffusion, expulsion (whereby material at depth is moved to the surface) and exchange with the surface by transferring sediment between the appropriate layers of the model. Only those particulate components (tracers) that are allowed in the sediments and are not macrobenthos (sediment grains, settled phytoplankton, microphytobenthos, meiobenthos, detritus and sediment bacteria) can be acted upon by bioturbation. The formulation implemented expresses the tracer concentration in the ith sediment layer (BX_i(t)) at the end of a time step as:

Where k_i represents the thickness transferred from i due to particulate diffusion, c_i is the thickness moved to the surface from layer i by expulsion and w_i is the thickness moved from layer i due to exchange with surface layers and z_i is the thickness of layer i. The thicknesses f_i, c_i and w_i only differ in a single parameter. For the parameters they share,  represents the base density of biological activity;  represents the modification to the baseline to reflect dynamic sediment fauna activity in the ecological sub-model (calculated in much the same way as that of ERSEM (see Ebenhöh et al. 1995)); and _i is the depth dependence of the mixing process (this is a simple functional form, as of PPBIM, and though usually constant it is also possible to implement linear, parabolic and half-Gaussian forms (Walker 1997)). The parameter which does differ in the calculation of f_i, c_i and w_i is the base rate of each process -  is the rate of particle diffusion (m² per t per unit biomass of bioturbative benthos per m²),  is the rate of expulsion (m per t per unit biomass of bioturbative benthos per m²) and  is the rate of exchange between the surface and deeper layers (m per t per unit biomass of bioturbative benthos per m²). A small amount of burial of sediments and associated detrital particles is also enabled using a similar formulation.