Chapter 1
Introduction to Spatio-Temporal
Statistics
“I feel all things as dynamic events, being, changing, and interacting with each
other in space and time even as I photograph them.” (Wynn Bullock, 1902–
1975, American photographer)
Wynn Bullock was an early pioneer of modern photography, and this quote captures the
essence of what we are trying to get across in our book – except in our case the “pho-
tographs” are fuzzy and the pictures are incomplete! The top panel of Figure 1.1 shows
the July 2014 launch of the US National Aeronautics and Space Administration (NASA)
Orbiting Carbon Observatory-2 (OCO-2) satellite, and the bottom panel shows the “pho-
tographer” in action. OCO-2 reached orbit successfully and, at the time of writing, is taking
pictures of the dynamic world below. They are taken every fraction of a second, and each
“photograph” is made up of measurements of the sun’s energy in selected spectral bands,
reflected from Earth’s surface.
After NASA processes these measurements, an estimate is obtained of the fraction of
carbon dioxide (CO
2
) molecules in an atmospheric column between Earth’s surface and the
OCO-2 satellite. The top panel of Figure 1.2 shows these estimates in the boreal winter at
locations determined by the geometry of the satellite’s 16-day repeat cycle (the time interval
after which the satellite retraces its orbital path). (They are color-coded according to their
value in units of parts per million, or ppm.) Plainly, there are gaps caused by OCO-2’s orbit
geometry, and notice that the higher northern latitudes have very few data (caused by the
sun’s low angle at that time of the year). The bottom panel of Figure 1.2 shows 16 days
of OCO-2 data obtained six months later, in the boreal summer, where the same comments
about coverage apply, except that now the higher southern latitudes have very few data.
Data incompleteness here is a moving target in both space and time. Furthermore, any
color-coded “dot” on the map represents a datum that should not be totally believed, since
1
Wikle, C. K., Zammit-Mangion, A., and Cressie, N. (2019), Spatio-Temporal Statistics with R, Boca Raton,
FL: Chapman & Hall/CRC. © 2019 Wikle, Zammit-Mangion, Cressie. https://spacetimewithr.org
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