I recently returned from the annual meetings of the Association of American Geographers, which convened in Seattle in April, 2011. While there I had the opportunity to attend a few of the featured sessions on space-time geography. This special series, with concurrent sessions that ran for most of the conference, addressed salient research questions and issues when dealing with dynamic geographic systems. There is a large and rapidly expanding literature on this topic, and a long mathematical tradition for modeling space-time systems. What is novel about the contribution of geographers to this problem is their emerging synthesis that addresses the many facets of space-time dynamics, from semantics and ontology (how we think about the system), to representation of space-time objects and space-time fields (how they move, morph and change) to the statistical and mathematical modeling of time-dynamic geographic systems. A lot of this is really nifty stuff, and you may want to visit www.AAG.org to take a peek at the abstracts.

I’ve been thinking about different aspects of space-time, and attending this meeting prompted me to pen this blog on the temporal and spatio-temporal extensions of what is known as the “modifiable areal unit problem”, called MAUP for short. MAUP arises when a summary statistic (for example) is calculated at one geographic scale (say counties), but the value of the summary statistic changes when it is calculated at a different geographic scale (say zip codes). Consider, for example, that the variance of an estimate usually increases as the sample size decreases. Since smaller areas often comprise smaller sample sizes (e.g. households), the variance of an estimate (say household income) is usually larger when calculated for smaller areas. And because variance and covariance enter into the calculation of the Pearson product-moment correlation coefficient, measures of association may change quite dramatically when calculated for two variables at different spatial scales. The literature on MAUP is extensive; when I searched “Modifiable Areal Unit Problem” on Google 56,700 hits were returned.

What about MTUP? I then searched for “Modifiable Temporal Unit Problem” and **zero** hits were returned – hopefully this blog entry will change that! The modifiable temporal unit problem is something we have observed in practice in our research at BioMedware and when using SpaceStat to analyze time-dynamic geographic data. In a fashion analogous to MAUP, we find that the variance of estimates calculated from a time series of data (say prices of homes purchased in a given area) increases as the duration of the time period considered shortens. We also find, however, that the phenomena we study may have temporal trends and/or cycles imposed on them. Hospital admissions for acute myocardial infarction peak on Mondays, for example, while beer sales in convenience outlets are highest on weekends. We also may see seasonality as well as daily cycles, depending on what we are studying and the time resolution of the data. The temporal resolution of the data turns out, not surprisingly, to be key when working with cyclic or periodic data. Consider, for example, time series of temperatures from ground sampling stations. Temperature shows strong daily cycles (lower at night, higher during the day), seasonal cycles (lowest in winter, higher in summer months) and a longer term trend since 1990 that is attributable to global warming. If our temporal sampling frame is every 24 hours at noon we will miss the daily cycle entirely. If we choose to sample once a year we will completely miss seasonal variation as well as the daily cycle. Yet many of us are still not accustomed to thinking about “temporal sampling frames”, and rarely if ever consider the “Modifiable Temporal Unit Problem”.

If you believe MTUP is underserved, consider the state of the “Modifiable Spatio-Temporal Unit Problem” (MSTUP). Like MTUP, “Modifiable Spatio-Temporal Unit Problem” returned **zero** hits in a Google search, so as a potential research problem MSTUP is wide open and waiting. MSTUP arises as the intersection of MAUP and MTUP, it considers not only that the spatial sampling frame may be changing, but that the temporal sampling frame is changing as well. What happens to estimates of mean and variance when one goes from county to zip code, and from weekly to annual sampling frames? How much, if any, bias is introduced into our estimates of underlying parameters and variables, and what happens to measures of association (such as correlation)? To my knowledge these questions have yet to be addressed in a systematic fashion, but will come quickly to the fore as temporal GIS and space-time information systems become commonly available.