Evaluation of physically based computer models for air quality
applications is crucial to assist in control strategy selection. The
high risk of getting the wrong control strategy has costly economic and
social consequences. The objective comparison of modeled concentrations
with observed field data is one approach to assessment of model
performance. For dry deposition fluxes and concentrations of
air pollutants there is a very limited supply of evaluation data sets.
We develop a formal method for
evaluation of the performance of numerical models, which can be
implemented even when the field measurements are very sparse. This
approach is applied to a current U.S. Environmental Protection Agency
air quality model. In other cases, exemplified by an ozone study from
the California
Central Valley, the observed field is relatively data rich,
and more or less standard geostatistical tools can be used to compare
model to data. Yet another situation is when the cost of model runs is
prohibitive,
and a statistical approach to approximating the model output is needed.
We describe two ways of obtaining such approximations.
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footnote: This research was sponsored by a National Science Foundation grant DMS 0002790 and by a US EPA award R-8287801.
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A common technical issue in the assessment of environmental numerical models
is the need for tools to estimate nonstationary spatial covariance
structures. We describe in detail two such approaches.