Peter Halls & Paul Miller

Of todes and worms: An Experiment in bringing Time to ArcInfo

For many people the term "temporal GIS" means the use of GIS for predictive modelling of change over time. Much of this temporal analysis is based upon visualisation techniques which ultimately depend upon cartoon style animation for the presentation of "time slices" to display the nature of the change through time.
Many disciplines seeking to apply GIS require a capability to display and analyse 'historical' data, whether with a range measured in seconds, millennia or beyond. By their very nature, these data are often incomplete and collected irregularly, making comparisons across time difficult.
Research use of GIS in a variety of subject areas from Archaeology to Ecology has found the current "time slice" approach to temporal GIS inappropriate to their data, methodology and theoretical tenets. An alternative technique defining a temporal "topology" is now under investigation, using ArcInfo as the development platform.
For each temporal observation, additional attributes are stored in the FAT defining the time, a confidence factor and the parameters to the mathematical description of the "time curve" linking this observation to its temporal neighbours. Using this curve, controlled by the measured, or acceptable, rate of change, it is possible to predict the nature of intermediate unmeasured locations from the recorded data. It is also possible to investigate the effects of changes to rates, confidence factors, etc., upon the relative 'fit' of the curve and so further assess the accuracy of observations.
A research project at York is investigating the applicability of this approach in relation to environmental ecology data; it is also hoped shortly to be able to test this technique with archaeological and historical data.

Table of Contents


In the years since the development of such pioneering systems as CGIS and SYMAP (Tomlinson 1990), the spatial functionality of computer-based Geographic Information Systems has been greatly enhanced. The past few decades have seen previously inconceivable developments in the power and availability of computer hardware, and the GIS industry has been quick to utilise many of the advantages to good effect, with modern systems such as ArcInfo capable of manipulating and displaying huge complex data structures.

The current trend in GIS development would appear (eg Maguire & Dangermond 1994) to be towards increased usability, with the creation of systems such as ArcView and increased usability for ArcInfo through ArcTools.

This trend, although undeniably welcome, masks the lack of GIS functionality in an important area of spatial science -- the storage, display and analysis of data pertaining to those dimensions beyond the first two or, simply, the escape from representational flatland into threespace and beyond (Tufte 1990).

Understanding of methods by which spatial location may be represented or modelled is now well advanced, and has built upon an evolution of cartographic tradition stretching back many centuries. Current advances in the arena of virtual worlds mark just one more step in the progression from those early carved maps, and represent a far smaller evolutionary jump than the original conceptual leap required in order to record a permanent two-dimensional abstraction of three-dimensional reality.

Ongoing developments in the database world mean that techniques are becoming available which can manipulate both precise and fuzzy locational descriptions, as well as supporting 'fuzzy logic' for the handling of non-spatial components of the record for a given entity, object, or phenomenon.

The traditional map -- whether carved in stone, printed on paper, or viewed on the VDU -- inevitably represents no more than a snapshot of reality. It is ultimately selective, relying upon the skill with which the author translates their perception of the real world onto the mapping medium, and can often represent no more than the environment or topography as it existed at a single instant in time.

If every map represents a temporal snapshot, then the only way in which to study temporal progression is to compare a series of maps; one with the next. Both paper and electronic methods make this simple stacking of time slices possible, but neither truly enable the researcher to model progression through time, whether mapping the change or interpolating values that may be assumed to exist between snapshots. In order to truly manipulate data from the fourth dimension, a different method is required.

Temporal GIS - an overview

A current holy grail of GIS research is the tool required for true spatiotemporal consideration of spatial data. This tool, variously known as Temporal GIS, TGIS and 4D GIS, remains elusive, and it appears that we currently have difficulty even agreeing what such a tool should comprise, let alone how we might go about creating one.

What, then, might a Temporal GIS be, and can we identify a core element set from which an initial definition might be drawn?

For Newell (1994), Temporal GIS embodies the tools required for continuous update of spatial records and the generation of reports based upon those data at specific points in time. He is, therefore, very much concerned with tracking versions of data. Scott (1993), on the other hand, is concerned with the continuous development and spread of a particular species of bracken. For her, Temporal GIS facilitates the modelling of biological processes in order to enable a better understanding of those factors which are significant in controlling reproduction of the plant, and she is therefore in need of a system capable of modelling continua within data.

Langran (1992) produced the seminal work on Temporal GIS as long ago as 1992, reviewing in detail many of the possibilities and technologies. Other than in largely cosmetic ways, depressingly little has changed in more than four years and, as such, it is perhaps worth using Langran 's book as a basis for discussion.

Following a detailed evaluation of the options, Langran concluded that a technique based upon the concept of a 'space-time composite' -- effectively an extension of the time slice concept, in which an original (full) definition is stored, together with definitions for describing subsequent change -- offered the greatest promise.

Langran sees Temporal GIS as intended to support work on the following questions:

and suggests mechanisms for achieving this in terms of seeking

Based upon these considerations, she suggests that Temporal GIS will require

"a conceptual model of spatial change, treatment of aspatial attributes, data processing logistics, a spatiotemporal data access model, and efficient algorithms to operate on the spatiotemporal data"

(Langran 1992, 4)

Langran's review of the attempts to develop a spatiotemporal database technology over the past few years concludes that most recent work has been geared to the needs of the CAD industry - for example, Katz et al (1986a; 1986b), Beech & Mahbod (1988). These are dismissed as offering no blueprint for a temporal GIS database despite their discussions of spatial or temporal database design. Langran feels that neither these, nor similar, approaches adequately resolve a means by which spatial change might be suitably identified for the computer in order to select 'changed' objects for storage. Yet the basic desire for temporal control in CAD is to do with versioning; maintaining the 'original' version at each update such that any given update, or updates, can be wound back to a precise point in time, and of quality control. For many essentially cartographic applications of GIS this is precisely what is meant by Temporal GIS; indeed it would appear that the majority of recent work in this field has concentrated on the concepts of versioning - for example Worboys (1993), MacEachren (1994), Maguire (1994) and Newell (1994).

Throughout the history of geography many workers have studied temporal progressions in an analytic manner. Thus we have the studies of diffusion (eg Hagerstrand 1952), which in turn led to the ideas of 'Cellular Geography' (Tobler 1979) and 'cellular automata' (Codd 1968; Couclelis 1985) and Hagerstrand's more qualitative study of the effects of time and space on people which he termed 'Time Geography' (1970). Most of the emphasis in his Time Geography is upon the concept of society evolving over time, and this development being influenced by intersecting external activities.

Perhaps one factor in this paucity of spatiotemporal analysis technique is the limited availability of truly spatiotemporal data. As a result there has been a tendency towards static theory prescribing optimum equilibrium states (eg Isard 1970; Morrill 1977). Many will, no doubt, feel a certain empathy with the underlying experience that led Langran to state that

"Aside from air photos and satellite images, very little temporal coverage data exist, and when they do, the collection intervals may not suit the needs of the researcher."

(Langran 1992, 17)

Especially when dealing with micro-scale temporal change, problems are compounded in that many of the change detection techniques developed for Remote Sensing do not adequately determine whether the measurement is of true change or of error carried over from processing or image registration.

Langran's proposed model has been followed by many of the workers in Temporal GIS since, such as Worboys (1993) and Yearsley & Worboys (1994). The essence of these -- and other -- projects has been to maintain versions or 'temporal snapshots' of the data in order to provide temporal checkpoints. Ellis' (1994) work with a quadtree-based system has perhaps come the closest in terms of published attempts to implement Langran's space-time composite model. Ellis' work is amongst those recognising some of the problems inherent in a version-based approach temporality, with his plea for people to remember

"the present debate on temporal GIS needs to consider that modelling the past is subtly different from modelling future change"

(Ellis 1994, 12.2.4)

An important aspect of GIS functionality is the ability to display data based upon some spatial - or spatially related - component, and this underlying emphasis upon visualisation may serve to explain many of the problems that those attempting temporal descriptions are creating for themselves. Muehrcke (1978), for example, presented a list of temporal constructs likely to require mapping;

From these, Grelot & Chambon (1984) identified correlations between the perceived requirements of Muehrcke and the capabilities of most modern GIS, deriving a list of four display mechanisms felt to encompass the scope of Muehrcke's typology;

Langran derives a series of techniques for cartographic modelling, based upon time series methods and animation, in order to explore questions of change over time. This leads her to explore the role of maps in aiding an understanding of geographic process and Borchert's

"Many time series of maps are in one sense statements of theories, in cartographic language, about geographic development processes, about the functioning and the past and future evolution of some global or regional system. Interpretations of the map patterns involve logical interpolation or extrapolation from mapped observations, in both space and time. Distinctively geographic models are also cartographic generalisations. As four-dimensional descriptions of the geographic evolution of resource and settlement systems, time series of maps are a fundamental element of geographical explanation."

(Borchert 1987, 388)

Cartography remains a two-dimensional activity, although cartographers have developed means of displaying additional dimensions by means of symbols and tones. Conventionally, cartography is about the mapping of boundaries, and Langran suggests extending this concept from space to time;

"While temporal boundaries are no more discrete than spatial ones, sharp lines also prove useful in their representation... temporal episodes can simplify time"

(Langran 1992, 30, emphasis added)

The main body of literature offers five 'standard' conceptions of time for storage and modelling purposes, which Langran deals with in order;

The data storage and processing implications of modelling geographic space in this manner are enormous, even before trying to resolve the added complications brought by disciplines such as Archaeology which would require the mapping of three dimensional volumes over time; thus requiring a four dimensional cube. The space-time cube would therefore appear to be incapable of aiding studies such as these.

Given that temporal visualisation techniques are currently time-slice oriented, this might well be regarded as the most pragmatic approach, regardless of the obvious limitations.

This is, essentially, the space-time cube flattened into two dimensions, and it suffers from the same set of defects.

This technique is clearly based within the cartographic concept of time upon which Langran, and so many others, have concentrated. The emphasis is upon defining a modelling framework in terms of the limitations of 2D display technology, rather than upon seeking the most appropriate means of conceptualising and recording the actual data. Perhaps it is time for researchers to worry less about the display medium and more about the underlying modelling techniques.

Langran's implementation of a Temporal GIS, based upon her conclusions, results in a cartographically oriented system which defines a temporal topology of objects and features based, ultimately, upon the space-time composite outlined above. This approach may be suitable for small areas with short temporal spans, but its efficacy must be called into question when applied to realistic geographic data volumes. Langran feels that the intersection capabilities integral to the technique are vital in aiding the facilitation of effective error detection, and goes on to argue that;

"Information systems can model temporality in two ways. The first is termed 'process modelling'... Process modelling allows a system to respond to such historical or trend analysis queries as

(Langran 1992, 56)

The approach proposed by Langran is, perhaps, too simplistic for application to real situations. Her definition of process modelling seems very close to that for version management and although scheduling is a part of the administrative process, it is also a crucial aspect of simulation visualisation; often the scheduling data provides the trigger controlling animation or numeric modelling processes. By dismissing this, Langran and those who base their work closely upon hers have discarded much of the support required for environmental process modelling and the modelling of truly temporal processes.

A lot of other work has concentrated upon the problems of reducing the data storage and/or computational implications of these approaches and into attempting to provide mechanisms for content-based searches. Stewart et al (1994) proposed an object oriented database model for managing temporal change, but this suffers from the same problem as Langran's approach; that of assuming that only two dimensional space needs to be modelled. Worboys' work (1994) utilised the object oriented Smallworld GIS. Whilst an elegant model, Stewart et al admit that their implementation is limited and, whilst extensible, is unlikely to fulfil the requirements of diverse application areas.

Taking a different approach, Openshaw (1994) suggests a tri-space approach in which he recognises the existence of three core 'data spaces' handled within GIS;

(Openshaw 1994, 88)

He then seeks algorithms to explore each of the data spaces simultaneously without preselection. For Openshaw's specific applications, crime and disease, the purpose of the research is to seek patterns of commonality across time. This is an interesting approach for such analytic tasks for which pattern seeking is appropriate, but does not seem to offer generality.

Newell (1994) has concentrated on the management of continuous update schemes based upon observing data points at specific points in time. He is principally concerned with managing versions of data, but his concern is primarily with rendering temporal change within an environment of cartographic visualisation.

Relatively little effort appears to have been invested in taking any of this recent work on Temporal GIS beyond the pilot phase; indeed several have not even progressed beyond the stage of a design concept presented on paper.

Langran concludes;

"A capability to treat temporal spatial information would release cartography from the confines of the two-dimensional page in which it has been trapped over the years."

(Langran 1992, 163)

Much of the current work on Temporal GIS has a remarkable reliance upon cartography and, whilst at times attempting a broader basis, continually falls back upon old cartographic ideas. As a result, the only temporal issue which is really addressed is that of versioning. The concept of time slicing is never far from the surface, and most applications appear primarily concerned with two dimensional visualisations.

This focus upon presentation, and the corresponding lack of consideration for the dynamic nature of the objects and processes under study, is undoubtedly a matter for concern. It appears that, in terms of spatiotemporal issues, existing work has barely scratched the surface; indeed, there has been a tendency for the spatial and temporal problems to be addressed in isolation such that there remains a clear lack of a coherent conceptual framework within which to model geographic change.

The nature of the problem

Temporal visualisation currently draws upon the animation technology of multiple snap shots recorded in sequence and replayed to create an impression of motion. Unlike much of the work in scientific simulation, temporal modelling in GIS remains constrained by essentially static representations and data models that make little effort to recognise dynamism. Scott (1993), studying the spread and development of the bracken fern, Pteridium aquilinum, seeks to model the biological processes involved in order to understand which factors are significant in controlling the reproduction of the plant. Scott is by no means alone in seeking dynamic techniques to solve dynamic problems. Bagg & Ryan (1996) noted that current GIS and database products remain tied to a snapshot-oriented approach capable of only static representations of data. Change through time, although central to many applications, may only be modelled by simplistic methods.

Current temporal techniques can be extremely effective for predictive assessment, especially in fields such as meteorology and related applications of fluid dynamics where precise values and locations may be calculated for any arbitrary frame rate. A case in point is Miller's work (1994) on the modelling of groundwater pollution. The allied concepts of versioning (which provide roll-back access to data recording change) are appropriate to new collections of data, for example within organisations such as the Land Registry. Such methods are, however, ill suited to investigations of the past, whether working with historical, archaeological or geological timescales. In these cases, the available data inevitably refer to irregularly spaced - and often imprecise - units of time or space.

Langran, as mentioned above, notes that temporal data are rarely collected under a regular sampling strategy. Bagg (1996), too, draws attention to the imprecise nature of much of this data. This lack of knowledge has implications for other studies - whether one event influenced another, what the interactions between people or environments were, etc. Adding to the complication, the data are often incomplete and fail to include all of the factors which might shed light upon control rates and directions of change.

The fossil record, for example, is notably incomplete due to differential preservation of the various organic materials making up past flora and fauna. Shells, bones, and other calcareous materials are common amongst the remains whilst soft tissue normally decays too rapidly for preservation. As a result, data are available on the skeletal structure of creatures such as the dinosaurs while little, if anything, is known about other aspects of them. The archaeological record is also prone to differential preservation, being prey to soil chemistry, aerobic action and both natural and human transformations of the deposition environment. A study that fails to take account of these preservation issues will be seriously flawed.

The traditional Temporal GIS approach is to treat the time-space relationship between objects as Langran suggests (Figure 1 & Figure 2).

Figure 1

Figure 1: A traditional approach to mapping object lifespans in time and space (after Langran 1992, figure 4.5)

Figure 2

Figure 2: A traditional approach to mapping feature lifespans in time and space (after Langran 1992, figure 4.6)

We would contend that this is too simplistic an approach to an extremely complex problem, and is probably only really applicable to such instances as examining different versions of a map. Most researchers are concerned with spatio-temporal relationships between objects, entities, and even ideas, which have a life cycle, and that life cycle is related to those of other objects in both space and time (Figure 3).

Figure 3

Figure 3: hypothetical object life cycles

A life cycle begins with birth or creation, continues through growth or stagnation to eventual death or destruction, and may last many millions of years as easily as a shorter time span. In some cases, the cycle may include periods of decline and resurgence (Figure 4) or else incorporate metamorphoses or other major changes (Figure 5).

Figure 4

Figure 4: Life cycles including periods of decline and resurgence; the example of a volcano

Figure 5

Figure 5: Life cycles including instances of metamorphosis; the example of a butterfly

Archaeologists are concerned with all aspects of space, including horizontal and vertical location as well as stratigraphic relationships. Data may well be gathered by means of excavation, which of necessity represents a series of isolated and often spatially discrete interventions with the Past. They do not have the luxury of anything approaching a temporal snapshot as may be afforded by an aerial photograph or satellite image, but must instead draw conclusions from a far less coherent vision of an area.

Even in situations where evidence is recovered, it is necessary to painstakingly piece together the sequence of events, based upon temporal information for certain objects and a carefully constructed inference for undated materials based upon their stratigraphic relationship to 'known' dates. Layers and stratigraphic sequences are rarely neatly horizontal, but instead thicken and thin across a site, present in some areas and not in others. Even dating an artefact as 'Roman' merely confines it to a period of 500 years. Few would claim a similarity between today and the time of the Civil War, yet this involves a similar level of generalisation to that considering all Roman material as comparable.

Geologists have similar problems, albeit over longer periods of time, whilst Environmental studies tend to encounter similar issues over a more compacted temporal span. For all such disciplines, there is an important issue relating to the precision of any temporal reference, especially as this may vary greatly. In archaeology, for example, a temporal reference may be derived from coinage and be precise to plus or minus 10 years. Alternatively, the reference may derive from dendrochronology (tree ring dating) and date the felling to within a growth season. The less precise, but common, radiocarbon dating is unlikely to improve upon a date within plus or minus 60 years of any event.

Analyses of such data must take this variable temporal precision into account in order to derive any worthwhile results whatsoever.

As noted, above, many of the objects likely to be modelled within a GIS have a life cycle which moves from creation - through a possible cycle of growth and decline - to eventual demise. Given the manner in which most temporal data are gathered, it may be presumed that these data are primarily discontinuous and that the dating of any given point may well be inferred or interpolated, rather than measured.

The York Approach

Recent work at York, reported by Halls & Miller (1995), seeks to explore a GIS capable of manipulating the temporal dimension by proposing a mechanism for recording and modelling the rate and 'direction' of temporal variance, together with an assessment of confidence in any measured point.

A key difference between this and other approaches is that it is not based upon an attempt to map an ill-suited display technique onto an existing GIS database, but rather aims to model the actual processes at work. As such, it should be possible to interpolate the stored temporal data in such a way as to display the state of the model at any point in time, rather than being constrained by predetermined time slices.

The concept for this technique arose from difficulties encountered in trying to map more traditional schemes to the real world problems of environmental studies (Scott 1993) and archaeology (Miller 1996). In both cases, the essentially uncontrolled access to temporal data of greatly varying quality made the application of time slices and related techniques totally inappropriate.

In order to overcome the non-linearity in the distribution of so much temporal data - and to cope with the observed nature of behaviour through time - Halls & Miller (1995) proposed the use of mathematical curves (or worms) to model the temporal trends. A curve fitting technique is proposed that will generate curves based upon a number of temporal nodes - or todes - plus associated information on their relative precision and the effect this should have upon constraining the curve fitting algorithm. The use of normal statistical descriptors, such as standard deviation, may be applied to the curve, enabling the precision of the fit to be represented graphically along the length of the curve itself by modulating line thickness, colour, etc. By moving backwards and forwards along the curve from the known points, the todes, it is easily possible to interpolate a value for any unknown point and to derive a measure of how probable this value is based upon the available evidence.

Research into applying these concepts to a working model within ArcInfo are, as yet, at an early stage, although an MSc dissertation in Biological Computation at the University of York is presently (Summer 1996) working to extend elements of Scott's work on bracken in this direction, examining ecological problems facing the staff of the North York Moors National Park.

The proposed model makes use of existing curve description techniques as provided by the Numerical Algorithms Group (NAG) libraries (NAG 1990). Specifically, the weighted cubic spline algorithms discussed within NAG's E02BxF routines are under examination.

An important benefit offered by these routines is the manner in which different todes affect the shape of the curve; rather than laying a curve through each tode, the todes exert a 'pull' upon the curve with the strength of the pull related to the defined precision of the temporal attribute. For example, a tode defined as being +/- 1 year would pull the curve towards it with greater strength than a tode defined as +/- 50 years. Implementation appears more straightforward than it might at first appear, with the only required additions to ArcInfo databases likely to be the temporal value (a date, for example) itself and a measure of error or precision in that value in a form such as a standard deviation or a minimum and maximum allowable value.

Discontinuities in the smoothness of the fitted curve (or 'knots' in NAG terminology) may either represent a lack of precision in the todes before or after the discontinuity or, perhaps more importantly, a temporally related event that could be of interest to the researcher. It may, for example, prove possible to detect periods and phases within an archaeological excavation by studying these discontinuities in the curve. Scott (1993), working with the invasion rates of the bracken fern, noted that there were clearly factors other than those she had modelled involved in the process, and that by locating these factors and building them into her model she could greatly have increased its efficacy. We believe that the technique discussed here, which will emphasise those temporal points at which some additional factor has been involved, may offer benefits in the evaluation of temporal models and in the further study of spatiotemporal phenomena.


The significance of the York work would appear to be its recognition of the nature of the data available for analysis, together with its attempt to extract the maximum potential from any given data source, rather than trying to coerce the data to fit some abstract technique removed from the realities of data and data collection. There is no difficulty in generating time slices for use in visualisation, or any other construct, from data stored using these techniques; all of the data are available for reuse, together with a measure of precision and other associated attributes.


The authors would like to thank Gail Langran, Mike Worboys, Eric Miller, Pat McKay and Nick Ryan for thought-provoking discussions of these - and other - ideas at various times.


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Peter J. Halls (link to pages in York)
GIS Advisor
Computing Service
University of York

Telephone: (+44 1904) 43 3806
Fax: (+44 1904) 43 3740

Paul Miller (link to pages in Newcastle)
Graphics & GIS Adviser
University Computing Service
University of Newcastle
Claremont Tower
Claremont Road

Telephone: (+44 191) 222 8212
Fax: (+44 191) 222 8765