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The evaluation of complex geophysical models, such as large scale
Eulerian acid deposition models and regional photochemical models,
involves a variety of tasks, including sensitivity studies, diagnostic testing,
mechanistic testing, and operational evaluation (Dennis et al., 1990). It is
computationally infeasible to simulate these complex models repeatedly to
utilize the types of procedures just discussed, so there is a considerable
emphasis on operational evaluation, the process of comparing model
predictions against environmental monitoring data. (We note, however,
recent developments in ``automatic differentiation'' of large scale
models for sensitivity analysis; Hwang, et al., 1997.) There are two
primary elements to our proposed methodology.
- Repeatedly, the literature on model evaluation notes two particular
problems: the difficulty of comparing spatial point observations from
monitoring networks with spatial averages from grid-based air quality models,
and the need to assess better the ability of a model to simulate the spatial
(and temporal) patterns of pollutant concentrations (see Seinfeld, 1988,
Schere, 1988, Dennis et al, 1990). Given realistic spatio-temporal models of
the dynamic variation for the quantities of interest, we can estimate areal
(grid cell) averages from point source data (block kriging in the
kriging/geostatistics literature; Journel and Huijbregts, 1978; Cressie, 1991;
Meiring, 1995). This approach is operationally inverse to the currently
recommended EPA procedure (EPA 1994), which mandates a linear combination of
neighboring model grid cell values to compare to a monitoring point
observation. Because of the smoothing involved in calculating grid cell
averages, it is fundamentally impossible to use the model output to
determine values that are (stochastically) comparable to point
observations.
- Numerical summaries of comparisons between grid cell model predictions
and point monitoring data can be insufficient for model assessment, and
possibly even misleading, particularly when the model has been tweaked
to match monitoring data. Far more diagnostic information is available
through consideration of the multivariate nature of the modeled and
observed spatial fields and through consideration of the second order
properties of these fields (cf. Barchet and Dennis, 1995). More
specifically, we propose to compare estimated spatio-temporal
correlation structures for field monitoring data and for gridded
model output, as well as the cross-correlation structure between pairs of
species (e.g. ozone, NO, NO
).
The calculations just discussed for the operational assessment of model
predictions rely on spatio-temporal modeling, and in particular, a
spatio-temporal correlation model. Estimation of such a model is
based on residuals from estimated long-term (hourly) means or
``trends'' that vary in space and at various temporal scales.
Methods for the estimation of both the spatio-temporal correlation
structure and the spatio-temporal trends are discussed in the following.
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