Statistical Downscaling with Spatial Misalignment: Application to Wildland Fire $$\hbox {PM}_{2.5}$$

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Key Words: Image registration; Public health; Smoothing; Warping.

The views expressed in this manuscript are those of the individual authors and do not necessarily reflect the views and policies of the US Environmental Protection Agency. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. S. Majumder (B)· B. J. Reich, Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695, USA (E-mail: [email protected]) (E-mail: [email protected]). Y. Guan, Department of Statistics, University of Nebraska–Lincoln, 340 Hardin Hall North Wing, Lincoln, NE 68583, USA (E-mail: [email protected]). S. O’Neill, Pacific Northwest Research Station, United States Forest Service, 400 N 34th Street, Suite 201, Seattle, WA 98103, USA (E-mail: [email protected]). A. G. Rappold, United States Environmental protection Agency, 101 Manning Drive, Chapel Hill, NC 27514, USA (E-mail: [email protected]). © 2020 International Biometric Society Journal of Agricultural, Biological, and Environmental Statistics https://doi.org/10.1007/s13253-020-00420-4

S. Majumder et al.

1. INTRODUCTION Air pollution associated with wildland fire smoke is an increasingly pressing health concern (Dennekamp and Abramson 2011; Rappold et al. 2011; Johnston et al. 2012; Dennekamp et al. 2015; Haikerwal et al. 2015, 2016; Wettstein et al. 2018). Reliable short-term forecasts of fire-associated health risk using numerical models facilitate informed decision making for local populations. Numerical models produce forecasts on a coarse grid and are prone to bias. Assimilating point-level monitor data with numerical-model output can reduce bias and provide more realistic uncertainty quantification (e.g., Berrocal et al. 2010a,b; Kloog et al. 2011; Zhou et al. 2011, 2012; Berrocal et al. 2012; Reich et al. 2014; Chang et al. 2014). However, most downscaling methods only correct additive and scaling biases and fail to guard against spatial misalignment errors where a forecasted event occurs in a different spatial location than forecasted. Spatial misalignment error in this context implies errors corresponding to predicting the location of a feature, such as fire plume, are wrong. Not accounting for it is problematic for wildland fire smoke forecasting because a common source of error is in predicting the direction of the fire plume which cannot be accounted for by additive and scaling correction to the forecast. This motivates us to develop a statistical downscaling method that accounts for spatial misalignment errors. Spatial misalignment correction can be achieved using standard image registration (or warping) techniques, ranging from simple affine and polynomial transformations to more sophisticated methods such as Fourier-based transforms (Kuglin 1975; De Castro and Morandi 1987), nonparametric approaches like elastic deformation (Burr 1981; Tang and Suen 1993; Barron et al. 1994) and thin-plate splines (Bookstein 1989; Mardia and Little 1994; Mardia et al. 1996). Such applicat