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Stat Med. 2016 Jun 30;35(14):2422-40. doi: 10.1002/sim.6867. Epub 2016 Jan 21.

Spatiotemporal calibration and resolution refinement of output from deterministic models.

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School of Public Health, University of Michigan, Ann Arbor, MI 48109, U.S.A.
Yale School of Public Health, Yale University, New Haven, CT 06520, U.S.A.
Yale School of Forestry and Environmental Studies, Yale University, New Haven, CT 06511, U.S.A.
Department of Management Sciences, University of Miami, Coral Gables, FL 33124, U.S.A.


Spatiotemporal calibration of output from deterministic models is an increasingly popular tool to more accurately and efficiently estimate the true distribution of spatial and temporal processes. Current calibration techniques have focused on a single source of data on observed measurements of the process of interest that are both temporally and spatially dense. Additionally, these methods often calibrate deterministic models available in grid-cell format with pixel sizes small enough that the centroid of the pixel closely approximates the measurement for other points within the pixel. We develop a modeling strategy that allows us to simultaneously incorporate information from two sources of data on observed measurements of the process (that differ in their spatial and temporal resolutions) to calibrate estimates from a deterministic model available on a regular grid. This method not only improves estimates of the pollutant at the grid centroids but also refines the spatial resolution of the grid data. The modeling strategy is illustrated by calibrating and spatially refining daily estimates of ambient nitrogen dioxide concentration over Connecticut for 1994 from the Community Multiscale Air Quality model (temporally dense grid-cell estimates on a large pixel size) using observations from an epidemiologic study (spatially dense and temporally sparse) and Environmental Protection Agency monitoring stations (temporally dense and spatially sparse).


Kalman filter; calibration; dynamic space-time modeling; environmental pollutant; integrated exposure; spatial misalignment

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