Peaks in variance estimates occurred at times when state variables were 

 changing fastest. Maximum coefficients of variation (CV=standard deviation 

 divided by state variable value) ranged between 148 and 722 percent, however, 

 the average CV during the summer ranged between 33 and 407 percent. While 

 these values are large, they are in many cases comparable to natural variability 

 within the bay (table 1, fig. 15). However, because we have included only a 

 subset of potentially important error sources and because we expect longer term 

 prediction errors to be larger than those estimated here, it is of interest to 

 determine the most significant sources of variability in this model. From the 

 standpoint of model variance the relative effects can be demonstrated easily. 

 In the simulations discussed below, initial condition, parameter, load, and 

 mixing parameter variances were each used singly or in simple combinations. 



Assuming perfect knowledge of initial conditions (i.e., initial condition 

 errors=0) reduced maximum output variances only slightly. Conversely, assuming 

 uncertain initial conditions and perfect knowledge of parameter values resulted 

 in much lower errors. Thus, parameter variance contributes far more than initial- 

 conditions variance. (See first 3 lines of table 2.) Variance associated with 

 loadings contributed little, even when compared to the low initial-condition 

 contribution (line 4, table 2). None of the CV increased more than 20 percent 

 when loading variances were included. In fact, only ammonia-nitrogen (NH3-N) 

 and nitrate-nitrogen (NO3-N) CV increased more than a few percent. Including 

 uncertainty (CV=10%) in a mixing parameter describing transport between bay and 

 lake also had little effect (line 5, table 2). In fact, even when its assumed 

 variance was doubled, no state-variable maximum CV increased more than 1 percent. 

 These results are consistent with more detailed analyses performed on an 

 ecologically simpler, two-segment model (Scavia 1980c). 



Input loading variance estimates represent time variability only. It is 

 well known that estimating loads from highly variable, episodic inputs is 

 difficult. To examine the potential influence of these inadequacies, two more 

 cases were run, two and ten times the load variance, respectively. These runs 

 assume that loading standard deviations, other than due to temporal variability, 

 are equal to that due to temporal variability and equal to three times that 

 variability, respectively. Dilution effects of the inner bay (volume 10*0 nH) 

 somewhat mitigated even this variability when compared to variance propagated 

 from initial-condition and parameter sources (lines 6 and 7, table 2). The 

 largest effects were seen in the CV for NH3-N and NO3-N; increasing load variances 

 by a factor of ten, an extreme case, resulted in doubling their model-output 

 standard deviations. 



These tests of relative effects of different variance sources on propagated 

 variances for a 1-year simulation indicated that parameters were by far the 

 most significant contributors. The effects of initial-condition variance were 

 quickly surpassed by the effects of parameter variance during the simulation, 

 and only when very large loading measurement errors are assumed do load variances 

 contribute significantly. We did not examine results of errors propagated over 

 longer than the 1-year time frame. If we were examining long-term prediction 

 errors, the effects of uncertain load predictions (not measurements) would have 

 to be considered. This would certainly increase the variance contribution of 

 loading estimates. 



Because the parameter errors had the largest impact on model output errors, 

 we (Scavia et al. 1981a) made use of the propagated covariance matrix to identify 



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