Statistical assessment of numerical models

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. 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. 1Montserrat Fuentes is an assistant professor at the Statistics Department, North Carolina State University (NCSU), Raleigh, NC 27695-8203, and a visiting scientist at the US Environmental Protection Agency (EPA). Tel.:(919) 515-1921, Fax: (919) 515-1169, E-mail: [email protected]. This research was sponsored by a National Science Foundation grant DMS 0002790 and by a US EPA award R-8287801. 2Peter Guttorp is professor of Statistics, University of Washington, Seattle, WA 98195-4322. Tel.:(206) 543-6774, Fax: (206) 685-7419 , E-mail: [email protected] 3Peter Challenor is Head of Satellite Remote Sensing, James Rennell Division for Ocean Circulation and Climate, Southampton Oceanography Centre, Southampton, SO14 3ZH, UK. Tel: (+44)23 80596413, Fax: (+44) 23 80596400, E-mail: [email protected]