Modeling Tools for Environmental Engineers and Scientists

order process with respect to algae concentration, where the rate constant isa function of zooplankton concentration, with a temperature correction factor:aGrazing loss = –k gz za = – C gz Ks,a + a gz(T–20) zawhere K s,a is the half saturation constant for the zooplankton grazing on algae(ML –3 ). In order to use the above, an MB equation for zooplankton isrequired, assuming growth of zooplankton due to assimilation of algae andloss due to respiration and death. Thus, the MB equation based on zooplanktonconcentration, z, can be formulated as follows: d za = a ca εdtC gz Ks,a + a gz(T–20) za – k dzzwhere a ca is the ratio of carbon to chlorophyll a in algae (–), is the grazingefficiency factor, and k dz is the first-order rate constant for respiration anddeath (T –1 ).A more complete representation of the system is now possible with theabove equations. With some practice, a comprehensive model could be generatedwith simulation packages such as ithink ® , Extend , or Simulink ® . Amodel that incorporates algae, herbivorous zooplankton, carnivorous zooplankton,particulate organic carbon, dissolved organic carbon, ammoniumnitrogen,nitrate-nitrogen, and soluble phosphorous has been developed basedon the research by Chapra (1997). This model is based on a total of eight coupleddifferential equations derived from MB on the above species in a lake,interacting as shown in Figure 9.14, and driven by seasonal variations in temperatureand sunlight.The graphical interface of this model developed with the ithink ® packageis illustrated in Figure 9.15. Results from a typical run (included in Figure9.15) follow the general trend reported by Chapra (1997). The model requiresseveral simplifying assumptions and over 30 input parameters (Chapra,Figure 9.14 Interactions between model compartments.© 2002 by CRC Press LLC