Geographical perspectives of space, time, and scale

This article reviews space and time scales from a geographer's point of view. Because spatial phenomena come in incredibly different size classes, geographers have conducted analyses across many orders of spatial magnitude. Geographers seem adept at moving from one scale to another, but they are not prone to explicitly state these scales a priori. Moreover, in spite of many appeals for multiscaler research (e.g., Abler 1987; Miller 1970; Stone 1968; Kirkby 1985), this is seldom done, although higher-level information is often used to predict lower levels. Good multiscale work apparently meets data-handling thresholds rather quickly. Most geographic research is now conducted with a relativistic view of space rather than a view of space as a ‘container.’ Spatial scales for relative space are more difficult to define, however, than those for the absolute space of cartography and remote sensing. The relevant, important, and useful variables from a modeling standpoint change with spatial scale. By reviewing the literature on a topic in a systematic way, as was done here for physical climatology and orographie precipitation, this scale change in variables can be seen. We do not as yet have models of the changes in models caused by changes in scale. Spatial data violate nearly every requirement for parametric statistical analysis (Meentemeyer and Box 1987), which is partially responsible for fallacies and erroneous inference. Many of these problems are scale dependent. Based on the work of Harvey (1969), we see that there are three primary methodological problems in spatial analyses. There are first of all the differences in inference and relevant variables caused by different scales or hierarchical levels. This has been called the ‘scale problem’ in geographic literature. Secondly, the description and modeling of spatial patterns, as noted above, may defy easy solutions, and finally the relationships between spatial patterns and process remain a challenge. The geographic literature contains many examples of extrapolations to lower levels from higher levels. Often the higher levels have been more widely sampled geographically (e.g., weather and climate, topography) and may be data rich. Models which predict spatial patterns and process often use the data-rich higher levels as driving variables for lower levels. Young (1978) argues that central place theory in geography should be a component of hierarchy theory. Indeed it can be argued here that space is inherently hierarchical and needs to be more fully incorporated into hierarchy theory. As the various disciplines under the umbrella of the environmental sciences more fully incorporate the spatial dimension into their research agendas, problems associated with spatial scale will be encountered. Many of these problems have in varying degrees been recognized if not solved. Nevertheless it is worth noting Clark's (1985) warning, ‘No simple rules can automatically select the “proper” scale for attention.’ Good geographic models require good geographic coverage, but this may mean that lower-level details are simply not needed. As mentioned earlier, the question of whether one is working at a ‘fundamental’ level is never discussed in geography. The Long-Term Ecological Reserve (LTER) sites are a step in the right direction, but a geographer would prefer much more intensive spatial sampling, even if that means a sacrifice in accuracy or detail. Otherwise a spatial analysis may not be possible. It remains to be seen to what degree the reductionist sciences can contribute to IGBP. More work with explicitly stated scales is needed, as well as across-scales research. Scale has been treated philosophically in this essay. But I am reminded of Couclelis's caution, ‘Philosophizing in an empirical discipline is a sure sign of trouble’ (cited in Abler 1987).