Atmospheric Environment 39 (2005) 3611–3619 Mapping spatio-temporal variables: The impact of the time-averaging window width on the spatial accuracy Yuval à , David M. Broday, Yohay Carmel Department of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Haifa 3200, Israel Received 29 October 2004; received in revised form 8 February 2005; accepted 25 February 2005 Abstract Spatialmappingofvariablesthatvaryinspaceandtimeisacommonprocedureinmanyresearchfields.Veryoftenit is of interest to map the time-average or time-integration of the variable over the whole period of interest. Normally, suchamapisproducedbyspatiallyinterpolatingthewholeperiodaveragesoftheobserveddata.Analternativeoption is to first spatially interpolate narrow time slice averages of the variable and then sum the resultant maps. This paper discusses the latter option, and the accuracy of the spatio-temporal variable interpolation as a function of the width of the time-averaging window. Theoretically, using a linear and data-value independent operator to interpolate a complete data set (i.e. without missing data), the accuracy is independent of the width of the time-averaging window. However, usinganonlinearoradata-valuedependentinterpolationoperator,and/orinthepresenceofmissingdata,theaccuracy of the interpolation can vary with the averaging window width. The concept is demonstrated using a set of half-hourly SO 2 concentrations measured at 20 monitoring stations in Haifa Bay area, Israel, during the years 1996–2002. Cross- validated interpolation accuracy measures calculated for this data set vary significantly with the time-averaging window width, showing a clear minimum at daily averaging. The results and their general implications for the interpolation of spatio-temporal variables are discussed. r 2005 Elsevier Ltd. All rights reserved. Keywords: Mapping accuracy; Spatial interpolation; Time-averaging window 1. Introduction Often, the time-aggregation of spatio-temporal vari- ables, i.e. their temporal average or time-integration, is of interest. For example, climatologists are usually interested in meteorological variables averaged at a time resolution coarser than a season (Fasullo, 2004; Lucero and Rodrı´gues, 2004; Sherwood, 2000; Skirvin et al., 2003) and epidemilogists often look at the exposure to air pollutants (usually estimated as the time-integration of the pollutant concentration) over long periods in the orderofyears(Lalletal.,2004;Libliketal.,2003;Samet et al., 2000). Since researchers using time-aggregated data usually feel comfortable with the data’s temporal resolution, they mainly focus on the interpolation of the spatially sparse observations to a fine regular grid (De Cesare et al., 2001). Thus, it is not unusual that spatial maps of precipitation (e.g. Doggett et al., 2004; Karnieli, 1990) or exposure to air pollution are generated by spatially interpolating annually, or multi-annual averages of the observed variables (Nikiforov et al., 1998; Wong et al., 2004). An alternative option for mapping time-aggregated variables is to first compute averages of the data records ARTICLE IN PRESS www.elsevier.com/locate/atmosenv 1352-2310/$-see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2005.02.042 à Corresponding author. Tel.: +97248292676; fax: +97248292606. E-mail address: lavuy@tx.technion.ac.il ( Yuval).