414 J. L. Tiwari et al. 



A diagrammatic representation of the system structure involving 

 state variables and their interactions can be illustrated in the form of a 

 block diagram (Figures 10-1 and 10-2). The square boxes in the diagrams 

 represent the state variables and the arrows joining these boxes depict the 

 processes of the system. The incoming arrows express the positive 

 processes, which are increasing the rate of change of the biomass, and the 

 outgoing arrows describe the negative processes, which are contributing 

 towards the loss of carbon from a state variable. The RB and RP numbers 

 associated with each of the arrows are the equation numbers describing the 

 mathematical form of the processes. Thus, the net rate of change of a 

 particular state variable at time / can easily be obtained by taking the 

 difference between the magnitudes of the positive and negative processes. 



The dynamics of the system can be visualized in terms of loss and gain 

 of carbon ascribable to its component biological processes. The effects of 

 these processes are to either increase or decrease the magnitude of carbon 

 from a state variable. Thus the time-dependent net rate of change of a 

 particular state variable at any instant of time / is equal to the difference 

 between the sum of all the processes adding to the amount of carbon and 

 the sum of all the processes subtracting from the amount of carbon. 



Let the loss of variable z, toz^ and that ofz; to z, (i.e. the gain of z, due to 



Zj) attributable to some process be denoted by z,^ and Zj^ , respectively. 

 The quantity z, at any time / can be computed by summing all z,^ and all 

 Zj and taking the difference. Thus 



J J 



The values of z, can easily be obtained by integrating z, using any one 

 of the standard numerical methods of integration. 



To illustrate this let us consider the dynamics of the benthic algal 

 biomass. Photosynthesis is the only process contributing towards the 

 growth of this population. On the other hand, there are several negative 

 processes (respiration, excretion of usable DOC (U-DOC), death and 

 burial) whose net effect is to reduce the algal biomass. Therefore, the net 

 rate of change in algal biomass (Table 10-1) is given by 



X 1 — X 602 — X 1 — X 1 — ^X 1 — X 1 — X 1 X 1 



Xl Xo X2OI X202 A401 A501 X602 



(7) 



X 1 ^ — X 1 ^ X 1 ^ — A 1 



XSOI X802 X803 X804 



where 



