A GIs-Based Statistical Method to Analyze Spatial Change
Joel D. Schlagel and Carlton M. Newton
Abstract
A GIS-based statistical method to examine spatial change was developed and demonstrated. Each measurement occasion is mapped as a separate GIS coverage. Then, using a raster GIS, a nonparametric test for trend is performed on a per-pixel basis across the collection of coverages. The spatial component of the data set is maintained, allowing further spatial analysis of the derived coverage.
The method was applied to a subset of the animal waste management data collected as part of the St. Albans Bay, Vermont, Rural Clean Water Project. It was found that from 1983 to 1990, significant increases (P<O.30] in the rate of animal waste disposal occurred on 28 percent of the land within 100 metres of Jewett Brook, while significant decreases in application rate occurred on just 3 percent of the riparian land. This suggests that, despite widespread adoption of agricultural best management practices, agricultural activity was, to some extent, working against an improvement in water quality.
Introduction
Environmental research is frequently concerned with the measurement of variables whose magnitude and spatial distribution vary over time. Geographic information systems (GIS) are powerful tools for the analysis of such spatial changes (Johnson, 1990). Yet the ways in which GIS has been applied to the analysis of spatial change have been limited. Spatial change analysis with GIs is most commonly confined to the overlay of spatial data sets representing data at two points in time. Change is then represented as the difference of, or a ratio of, the two data sets (Lo and Shipman, 1990). Because only two data sets are used, the primary weakness of this method of change analysis is the inability to differentiate natural or random fluctuations over time from real trends.
This paper presents a GIS-based statistical method to examine spatial change. Given that the distribution and magnitude of a variable have been measured at evenly spaced time periods, each measurement occasion is mapped as a separate GIS coverage. Using a raster GIs, a nonparametric test is used to assess trend on a per-pixel basis, across the collection of these separate coverages (i.e., across the multitemporal data set).
Temporal Analysis Using GIs
When a multitemporal data set is of concern, mapping is often of limited value because it is difficult to visually interpret a map representing multitemporal data. Rather than present multitemporal data on a single map, the temporal di mension of the data is often summarized or eliminated. If the temporal dimension of a spatial database is to be summarized, that summarization should, in some way, assist in the interpretation of the data, so as to avoid basing conclusions about the spatial-temporal data set on non-significant or random variations (Choynowski, 1959). There are a variety of cartographic and computer-cartographic methods available to examine multitemporal spatial data.
The most common method of examining change is to overlay maps representing the spatial distribution of a variable of interest at two different time periods. This technique is widely used within both the raster GIS environment (Lo and Shipman, 1990) and the vector GIS environment (Ahern et al., 1990). The overlay method is also used in image processing to construct temporal difference images, or temporal ratio images (Avery and Berlin, 1985). The results of the overlay of two coverages are easily represented on one map, and are easilv intermeted visuallv. However. consideration of only two time periods may produce misleading or exaggerated results if there is any tendency of the variable of concern to cycle in either its spatial distribution, or in its magnitude. Cyclical variation may be incorrectly interpreted as either an upward or downward trend.
To overcome the limitations to understanding spatial change between two time periods, spatial data may be collected at multiple time periods. When data for multiple time periods are available for consideration, the meaningful use of overlay analysis becomes more difficult. A GIS may allow one to accurately overlay coverages representing data at many time periods, but a single map representing the results of the overlay of multiple coverages can be too complex to meaningfully interpret visually, so other techniques must be used.
One way to present a cartographic variable observed for multiple time periods is through the use af temporal "glyphs" (Monmonier, 1990). Temporal glyphs include bar charts or other complex symbols to portray change at a specific location.
McCord and Olson (1989) apply this concept by developing a data transfer method between ArcIInfo (ESRI, 1990) and SAS-Graph (SAS Institute, 1985), allowing graphs generated by SAS to be used as symbols in an ArcIInfo map. When using the temporal glyph or graph-in-map method, much of the data may be redundant, or may not describe meaningful change. Furthermore, the large amount of data that are presented as one map may overwhelm the map reader, hindering understanding (VonEssen and Walsh, 1989).
Computer animation is another way of presenting a multitemporal data set so as to portray change. Computer anima tion methods allow one to visualize change in a spatial data set over time as maps are displayed sequentially on a computer screen (MacEachren and DiBiase, 1991). While useful for many purposes, such a computer "flip book" does not assist in the quantification or the objective evaluation of spatial change. A more advanced conceptual approach to the problem of analyzing spatial change is to incorporate temporal-topology in a GIS, making temporal relationships as much a part of the data set as spatial relationships (Langran and Chrisman, 1990). Temporal topology does not, however, directly address the problem of quantification and representation of spatial change on a map.
An alternative to representing data measured at numerous time periods on a map is to statistically summarize the temporal data set. Descriptive statistics of a spatial data set could then be more easily presented and interpreted visually.
Maps of descriptive statistics of the data set, such as the maximum, mean, or median values, could then be generated.
However, maps of descriptive statistics can oversimplify or overgeneralize multitemporal data, reducing their usefulness (VonEssen and Walsh, 1989). Furthermore, descriptive statistics do not help one understand trends that may occur over time.
An improvement over the use of static descriptive statistics is the use of inferential statistics and hypothesis testing.
For instance, the statistical hypothesis of no change may be tested throughout a study area, and the resulting statistics may be presented as a map. The mapping of the results of statistical analysis is common. This is demonstrated in Taylor and Loftis (1977) and Robinson et al. (1985:. Both references demonstrate the mapping of predicted values and residuals from regression analysis, allowing one to consider the spatial relationships associated with the fit of a regression model.
If one wishes to explore statistically the relationship among GIs coverages, then the GIS data sets may be linked with other programs that possess more advanced statistical capabilities. For instance, image processing systems may be used to conduct principal components analysis of a raster based spatial data set. Principal components analysis of multitemporal spatial data sets has been used to reduce data redundancy and identify critical time periods (VonEssen and Walsh, 1989). Alternatively, one may transfer data from a series of GIS coverages to statistical packages, in order to conduct regression analysis among coverages (Ludeke et al., 1990).
Rather than mapping the results of statistical analysis,one may perform the statistical analysis with the GIs. A raster GIS that is capable of mathematical overlay, or map algebra functionality as described by Tomlin (1990), can be used to perform most calculations needed for statistical tests. The use of a statistical test is one way of summarizing several temporal coverages in a form which may be easily presented visually, and provides a way to objectively view patterns of spatial change.
School of Natural Resources, The University of Vermont,
Burlington, VT 05405-0088
J.D. Schlagel is presently with the Remote SensingIGIS Center, U.S. Army Cold Regions Research and Engineering Lab.,Hanover, MA 03755.
Photogrammetric Engineering & Remote Sensing, VO~. 62, NO. 7, July 1996, pp. 839-844.
0099-1112/96/6207-844$3.00/0 O 1996 American Society for Photogrammetry and Remote Sensing
PE&RS July 199
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