which parameters were most important in terms of both model sensitivity and 

 model errors. Identification of those parameters and associated processes 

 suggest areas requiring further research. 



One final aspect of model uncertainty becomes apparent when viewing the 

 distributional properties of model output generated from Monte Carlo simulations 

 (Scavia et al. 1981b). In this analysis the following procedure was used. The 

 model equations were solved repeatedly. Each model execution was performed with 

 initial conditions and parameter values selected randomly from their individual 

 distributions. From these repeated model executions, state variable means, 

 variances, and other statistics were calculated at 4-week intervals throughout 

 the period of simulation. The analysis was terminated after 1000 simulations, 

 at which time state variable means and variances were converging. 



Histograms generated from the 1000 simulations for selected state variables 

 at different points in time during the annual cycle are shown in figure 16. It 

 is interesting to note that even though the initial conditions and parameter 

 values are drawn from relatively smooth, symmetric distributions, the resulting 

 model output distributions can be dramatically asymmetric and polymodal. 



Several implications are suggested by these distributions. Those that are 

 spread out suggest that variability in control parameters (initial conditions 

 and coefficients) has a dramatic effect. That is, a fairly uniform output 

 distribution suggests many possible model outcomes are equally likely as control 

 parameters vary within their confidence ranges. Distributions that are dramati- 

 cally narrow indicate relative insensitivity of that state variable to the 

 uncertainty in control parameters. Bimodal or polymodal distributions suggest 

 that even though control parameter values have probabilities of occurring that 

 vary smoothly through their distributions, the model produces state-variable 

 values that jump from one category of high probability to another with very few 

 outcomes occurring in between. Controls of such threshold behavior both in 

 models and in nature are not well understood, but careful attention must be paid 

 to the possibility of it occurring. 



SUMMARY AND CONCLUSIONS 



I have outlined how a particular ecosystem model has been used to better 

 understand the structure and dynamics of Lake Ontario. This is but one example 

 of how integrated modeling and experimental science has advanced our ability to 

 understand and perhaps simulate and predict dynamics of the Great Lakes. This 

 and similar models generally represent collections of process relationships 

 developed through independent empirical studies and as such they merely test 

 those relationships in the context of the whole system. That is, the models 

 test our ability to simulate algal dynamics, for example, by balancing rates of 

 gain and loss calculated from expressions developed independent of the whole 

 system. While certain relationships among processes may be testable, it usually 

 becomes intractable to study such relationships in nature. This is particularly 

 true in systems like the Great Lakes and marine waters where physical processes 

 can be important. In those cases, a model that is firmly based on independent, 

 empirically tested constructs and exercised within the framework of carefully 

 designed field observations may be the only means to improve our understanding 

 of, and thus our ability to predict, responses of the aquatic ecosystem to 

 altering stresses. 



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