A research paper submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in GEOGRAPHY Portland State University 2001



Time is inherent to all geographic data. Where spatial data are augmented with a temporal attribute, the information content of spatial data is extended. The benefits of evaluating spatial and temporal data together include a means of determining the evolution of spatial data in time. The usefulness of these temporal data depends on the way spatial data integrates time.

"The fundamental temporal attribute of duration may be compared to the spatial qualities of area or distance in that they are of finite and of measurable magnitude" (Thornes and Brunsden 1994 p.3). By this reasoning, one characteristic of temporal data is that time can be modeled into discrete objects.

Both time and space can be conceived as multi-dimensional, divided by intervals, measured, and classified. Though normally considered a continuum, time is usually sampled at discrete points or events usually sampled at regular or irregular intervals. Such "quantized measurement" divides continuous time into time states for which spatial or thematic data can be measured and queried. For example, gallons per minute are a quantized unit of thematic measurement used in continuous flow data. Such a moment can be modeled as valid for a moment in time, or assigned to a duration between sampled events. The alternative ways of assigning these attributes indicate different approaches to modeling, time, and spatial and thematic data. This paper compares two spatio-temporal approaches conditioned by the thematic behavior of geographic phenomenon.


1.1 Cartographic Time and Space

Cartographic time refers to the date for which a mapped representation is assumed to be valid. This may or may not be the map publication date. Temporal generalization inherent to cartographic time limits the accuracy of representing any specific event at a specific time. Change studies using historic map sources, associate cartographic object states with temporal duration. The accuracy of this association depends upon whether the state is assumed to be changing or defined as static until an event occurs to change it. Fuzzy transitions make it difficult in some cases to clearly define end-points of a state. Cartographic time ignores such fuzzy transitions by establishing points to occur at a transaction time, where one object is replaced by the next object as identified in a new map.

Map versions separated by time are the raw material for change study. Geographic features on a map version are symbolized by points, lines, or areas that represents the duration of a condition. Objects in a database represent physical features that exist at a particular time and location bound together in a condition Langran and Chrisman (1988) describe as a state, which can be altered by events that transform it from a past state to the present state and to future states.

Cartographic space is an abstraction of real space. Cartographic surfaces represent a continuous field of information interpolated from an assortment of sampled values. Cartographic objects represent geographical features modeled to point, line, or area entities. Both continuous and discontinuous change to cartographic space is initiated by events that happen as measured in cartographic time. Table 1 suggests certain parallel approaches to modeling spatial and temporal structure.

  Cartographic Space Cartographic Time
Overall Configuration Map State
Configurations Separated ByÉ Sheet Lines Events
Regular Sampling Units Cells Hours, Days, Decades, Etc.
Meaningful Units Objects Versions
Subdivisions Separated ByÉ Boundaries Mutations
Size Measured ByÉ Length, Area Duration
Positions Measured ByÉ Coordinates Date
Contiguous Neighbors Are Adjacent Objects Previous And Next Manifestations
Maximum Number Of Contiguous Neighbors Infinite Two

Table 1 Parallels in Spatial and Temporal Structure (Langran and Chrisman 1988)


1.2 Sampling Rates

The effect of time on space is demonstrated best by comparing one data source with another. The first consideration is to match the behavior of a mapped geographic feature to an appropriate sampling interval. Sampling intervals used in change studies must consider the periodic or episodic nature of the phenomena being measured (Thornes and Brunsden 1994).

Wilson (1996) suggests sampling can happen in one of three ways: real time, magnified time, or accelerated time. Sampling spatial themes in real time implies continuous sampling. Continuously occurring phenomena are usually not measured continuously -- this is why regularized or quantized time intervals are more commonly used. Unfortunately, these data cannot be collected continuously even though it would be ideal for time change studies.

The sample rate has interesting effects on the perceived magnitude of events that cause change. Time is apparently slowed down when the samples are very close together. A high sample rate causes the apparent magnitude of change between each sample to be proportionately low. A low sample rate alternately increases the apparent magnitude of change between samples because changes appear to happen all at once. Time can be slowed down or sped up to allow for observations that would be difficult otherwise. Various sampling rates have tremendous possibilities detecting and revealing change, but available map data are primarily oriented towards low sample rates, which favors increasing the apparent magnitude of changes.

There are certain nuances inherent to sample rates that must be considered in change detection applications, the most significant involves the behavior of the source data. The sample rate must be matched with the mechanism of operation inherent to the mapped phenomena. In general, lower sample rates correspond to slowly changing phenomena and high sample rates with fast changing phenomena. With low sample rates, the state of a feature is likely to change more rapidly than the map data can capture the new state.

In addition to the behavior of the geographic phenomena under study, another concern in change detection involves the availability of spatial data. Hooke and Redmond (1989) remind us that we sometimes have little control over sampling and we need to simply accept the available map evidence. Thus, while it may be ideal to study diurnal air temperatures, a daily average may only be available. While vegetative cover may vary weekly in a season, only imagery for every 30 days is available. While urban expansion occurs in small increments involving one lot or subdivision at a time, only yearly mapping representation of the built environment are obtainable. Thus, whether spatio-temporal data are modeled as continuous and therefore specific states interpolated from sampled evidence, or modeled discretely from events which definitively bound specific states is a matter of the practical availability of data as much as the nature of the phenomenon itself.

<-- Chapter 1
Return to Main Menu
Chapter 2-->