be affected significantly (at least not within the variability usually inherent 

 in field verification data). The following example demonstrates one way in 

 which compensating errors at the process level can lead to erroneous conclusions 

 regarding system controls. 



After initial calibration to measurements of state variables for the model 

 described above (fig. 1), simulated process rates were compared to measurements. 

 For this comparison, a summer-averaged (July-Sept.) phosphorus flow diagram was 

 constructed as described above from aggregated model output. Flow (or transfer) 

 rates were then compared to measurements and calculations from Lake Ontario and 

 to other, more theoretical estimates. Many of the simulated process rates 

 (fig. 14a) were very low (as much as 3-7 times lower) compared to measured 

 values. Most serious discrepancies in transfers were among available phosphorus, 

 phytoplankton, and zooplankton. I recalibrated the model keeping process rates 

 in mind and most coefficient values still within acceptable ranges. The new 

 calibration, shown in figure 14b, is the same as that discussed above (fig. 8). 

 Here, state variables are close to the originally calibrated values and can 

 still be considered calibrated; however, process rates are much higher and, in 

 fact, much closer to observed values (Scavia 1979). 



This example demonstrates that if the model were calibrated only against 

 state variables and then used to examine control of phosphorus cycling, then 

 the relative importance of certain processes would be overestimated by almost 

 an order of magnitude. For example, regeneration of available phosphorus from 

 detritus P is relatively more important in figure 14a than in figure 14b and 

 the relative importance of external loads and of transport into and out of the 

 epilimnion is exaggerated in figure 14b. 



Because of increased degrees of freedom and the usual lack of long-term 

 verification data, mechanistic models need verification tests beyond the 

 standard tests used for state variable simulation. Two general types of 

 verification can be useful additions to the usual tests (Scavia 1980b): 1) 

 comparison of aggregated output from the mechanistic model with output from 

 simpler models and empirical correlations that have been verified or proven to 

 be generally applicable and 2) a comparison of simulated process rates with 

 rates measured in the field or in the laboratory to determine if the model's 

 internal dynamics are consistent with measured and theoretical dynamics. 



Effects of uncertain inputs : Numerical models have become relatively 

 common tools in lake management. In many cases, they have also become useful 

 for suggesting research needs, synthesizing extant information, and analyzing 

 aquatic ecosystems in ways that are not tractable through field and laboratory 

 studies alone. Models used most often in both contexts have similar attributes; 

 they are generally time-dependent, often nonlinear, ordinary differential 

 equation models based on parameterized physiological processes and mass 

 conservation. 



These models, whether from the management or the research milieu, have 

 another common thread: they are generally deterministic. That is, although it 

 is often recognized that model initial conditions, parameters, and forcing 

 functions have stochastic components, they are seldom accounted for. Moving 

 beyond acknowledgment of variances of these elements to assessment of their 

 effect is important because these stochastic properties affect the confidence 



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