Model uncertainties Clause Samples

Model uncertainties. A calculation model is a physically based or empirical relation between relevant variables, which are in general random variables: Y = f (X1, X2, ... Xn) (3.2) where Y is the model output, f ( )is the model function and Xi are the basic variables. The model f (...) may be complete and exact, so that, if the values of Xi are known in a particular experiment (from measurements), the outcome Y can be predicted without error. This, however, is not normally the situation. In most cases the model will be incomplete and inexact. This may be the result of lack of knowledge, or a deliberate simplification of the model, for the convenience of the modeller. The difference between the model prediction and the real outcome of the experiment can be expressed as: Y = f ′ (X1 ... Xn, θ1 ... θm) (3.3) θi are referred to as parameters which contain the model uncertainties and are treated as random variables. Their statistical properties can in most cases be derived from experiments or observations. The mean of these parameters should be determined in such a way that, on average, the calculation model correctly predicts the test results.
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Model uncertainties. The finite mixture model was built to reflect the City’s conceptual model of stormwater basin discharge concentrations (see Section C4. 1.1). There are many assumptions associated with the development of the conceptual model and the mathematical model used for the analysis of this stormwater dataset. A summary of uncertainties in the statistical evaluation is provided below:  The distribution and pattern of stormwater analyte concentrations may be much more complicated than observed. For example, the analyte distribution plots, presented in Attachment C3, often do not show distinct breaks between subpopulations (i.e., groups), but rather a continuous spread of concentrations. This indicates the use of a three- component model may be an oversimplification of a much more complex system. However, the three-component model is useful as a data driven method for identifying groups of basins that are most similar in order to simplify a complex system for policy purposes (i.e., source tracing).  Stormwater sample results for individual sampling events are assumed to be random samples of the underlying distribution of analyte concentrations in each outfall basin. To the extent that these samples are not random, they may provide a biased view of the conditions in each basin.  The model fits well enough to represent the stormwater data set for the purpose of identifying basins for consideration of additional source tracing activities. Inferences obtained from a faulty or ill fitting model may be misleading. There is no gross evidence of lack of fit in the model for the analytes evaluated. However, some variances were noted. For example, the stormwater sample concentrations from one non-City outfall were noted to be more variable than concentrations in other outfall basins; all four copper concentrations in this basin were outside the model estimated 95% confidence intervals for copper. The chance for this condition to have occurred randomly if the variances were the same in each basin is small. It is more likely that the variance of analyte concentrations varies from basin to basin according to other factors. However, investigating factors (grab versus composite sampling, size of basin) that might affect concentration variance did not reveal any way to explain this excess variance in some basins. In addition, the problem seems to affect a small number of basins, with most basins having variability that is consistent from basin to basin.  In the model, composite a...
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