Mathematical Geosciences

, Volume 48, Issue 2, pp 107–121 | Cite as

Hot Enough for You? A Spatial Exploratory and Inferential Analysis of North American Climate-Change Projections

  • Noel CressieEmail author
  • Emily L. Kang


Climate models have become the primary tools for scientists to project climate-change into the future and to understand its potential impact. Continental-scale General Circulation Models (GCMs) oversimplify the regional climate processes and geophysical features such as topography and land cover. The consequences of local/regional climate change are particularly relevant to natural resource management and environmental-policy decisions, for which Regional Climate Models (RCMs) have been developed. RCMs simulate, for example, three-hourly “weather” over long time periods, from which long-run averages (e.g., over 30 years) are commonly computed to estimate a region’s future climate. With anthropogenic forcings incorporated, RCMs provide a means to assess a combination of natural and anthropogenic influences on climate variability. The North American Regional Climate Change Assessment Program ran RCMs into the future, until 2070, for 11,760 contiguous regions, each of which is approximately \(50~\mathrm {km}\times 50~\mathrm {km}\) in area. Using the 94,080 temperature changes projected to 2070 for all regions, for two RCMs, and for the four seasons, we present both an exploratory and a Bayesian inferential spatial analysis. Climate-model output is deterministic, but we capture its spatial variability using a hierarchy of conditional probability models. The exploratory Spatial Proportion Over Threshold (SPOT) function and the inferential PRedictive probability Over Threshold (PROT) function are defined and contrasted through videos available online in the Supplementary Materials, showing regions of North America that attain or exceed temperature change thresholds as a function of increasing threshold. The preponderance of our results throughout all regions of North America is one of warming by 2070, usually more (and sometimes much more) than \(2\,^\circ \mathrm {C}\).


ESDA PROT function Spatial hierarchical model SPOT function Temperature-change projections 



This research was partially supported by the NASA’s Earth Science Technology Office through its Advanced Information Systems Technology Program. We wish to thank the North American Regional Climate-Change Assessment Program (NARCCAP) for providing the data used in this article. NARCCAP is funded by NSF, DoE, NOAA, and EPA’s Office of Research and Development. Many thanks go to Andrew Holder for his assistance in preparation of this article, to the referees for their excellent suggestions, and to the Editor for his vision regarding new directions for mathematical geosciences.

Supplementary material

11004_2015_9607_MOESM1_ESM.mpg (4 mb)
Supplementary material 1 (mpg 4075 KB)
11004_2015_9607_MOESM2_ESM.mpg (2.4 mb)
Supplementary material 2 (mpg 2494 KB)
11004_2015_9607_MOESM3_ESM.docx (12 kb)
Supplementary material 3 (docx 11 KB)


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Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  1. 1.Centre for Environmental InformaticsUniversity of WollongongWollongongAustralia
  2. 2.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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