Showing papers on "Spatial analysis published in 1977"

A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling

Abstract: The paper describes a geographical solution to the scale and aggregation problems frequently encountered in studies of spatially aggregated data. Instead of trying to model the effects of scale and aggregation, the problem is inverted. An attempt is made to identify a set of zones which optimizes an objective function related in some way to the performance of a model subject to whatever constraints may be relevant. In this way scale and aggregation problems become one of optimal-zone design. A heuristic procedure is described which may solve this problem and it is demonstrated by reference to an empirical study. Finally, there is a brief discussion of some of the possible implications for the study of spatially aggregated data and of the role of the optimal-zone design approach in spatial model building. THE conventional approach to spatial analysis involves the application of a model to a study area which has been partitioned into zones. The definition of these zonal boundaries involves the selection of the scale of the study and the aggregation of data to match the choice of scale. In nearly all cases, there are an incredibly large number of alternative scales and aggregations which could be used. It follows, therefore, that spatial data and the patterns and processes they describe are the product of a particular set of zonal boundaries, and that qualitative or quantita- tive studies of spatial data are not invariant with the choice of these boundaries. Scale is an abstract concept which cannot be easily measured except in relative terms. The best surrogates are probably the size and number of zones used to partition a study area. The scale problem arises because of uncertainty about the number of zones needed for a particular study. The aggregation problem arises because of uncertainty about how the data is to be aggre- gated to form a given number of zones. These problems always occur in the design of zones for the study of spatial data; and the two together represent one of the greatest unsolved problems facing spatial study today. Current zone design procedures are typically haphazard. Zones are mainly based on considerations of convenience and the existence of readily available data, but on occasions may be selected at a certain scale in order to isolate a particular spatial pattern. However, in many cases current knowledge of spatial phenomena is insufficient to define with any precision the scale and the aggregation needed. In other studies zone design is not regarded as being very important, and the relationship between the choice of zones and the results is seldom investigated, even when the data is sufficient for such a study. It is suggested, therefore, that the distribution of zone-dependent results may be widespread throughout the geographical literature, wreaking havoc with at least some of it. The purpose of this paper is to provide a geographical solution to certain aspects of the

Detecting two-dimensional spatial structure in biological data.

Abstract: Cliff and Ord (1973) made versatile methods available for the direct utilization of location data in the analysis of dispersion patterns, but their monograph has as yet seen little use in the ecological literature. Application of their weighted forms of Geary's c and Moran's I indices of spatial autocorrelation to some marine benthos data demonstrates a diversity of population structure not anticipated on the basis of more common measures of pattern. These indices provide objective means to evaluate numerous recent spatial models and hypotheses in geographical ecology and genetics. The procedures are particularly attractive because (1) they efficiently utilize data which are often wasted (i.e., sample coordinates), (2) their application puts few constraints on sampling designs which would otherwise be employed, and (3) they reveal and quantify pattern differences which are not obvious to the untrained eye.

Alternative Approaches to Spatial Autocorrelation: An Improvement Over Current Practice

Abstract: THE ASSUMPTION THAT THE CORRELATION BETWEEN THE TEMPORAL ERROR TERMS ∈ t AND ∈t-n DECLINES AS n INCREASES CAN BE JUSTIFIED BY APPEALING TO FIRST OR SECOND ORDER MAR-KOV PROCESSES OR TO SPECTRAL ANALYSIS, BUT A SIMILAR ASSUMPTION CANNOT BE JUSTIFIED FOR SPATIAL ERROR TERMS. THIS INTRODUCES AMBIGUITY IN THE SPECIFICATION OF THE WEIGHTING MATRIX W. IN THIS PAPER WE PROPOSE THE JOINT GENERALIZED LEAST SQUARES, EQUICORRELATED ERROR TERMS, RANDOM ERROR COMPONENT MODELS, AND RANDOM COEFFICIENT REGRESSION MODELS AS ALTERNATIVE SOLUTIONS. THESE APPROACHES ARE SUBJECT TO FEW OR NO PERSONAL BIASES, YET THEY ARE ABLE TO RESOLVE THE PROBLEM OF SPATIAL AUTOCORRELATION.

Dynamic Models of Spatial Autocorrelation

Abstract: Dynamic models have been studied intensively during the last decade, particularly in the field of growth theory and diffusion analysis. Consequently, problems like temporal autocorrelation have received much attention. Recently the attention of econometricians has also concentrated on spatial autocorrelation, particularly in the field of spatial interaction models. The existence of spatial autocorrelation among spatially dispersed phenomena appears to lead to significant differences in the treatment of multiregional models. In this paper, attention will be focused on the formal aspects of dynamic spatial diffusion models. Some statistical measures for temporal-spatial autocorrelation will be constructed. In addition, a formal derivation of necessary extensions in estimation procedures for dynamic multiregional econometric models will be presented, particularly in the field of seemingly unrelated regressions and instrumental variables. The analysis will be illustrated by means of a dynamic explanatory mode...

Spatial representation and spatial interaction

Abstract: 1. Spatial representation and spatial interaction: an overview.- 1.1. Introduction.- 1.2. The multi-criteria aggregation problem.- 1.3. The multi-level specification problem.- I: Multi-Criteria Aggregation Problems.- 2. Sequential treatment of the multi-criteria aggregation problem: a case study of zoning system design.- 2.1. Introduction.- 2.2. The Wirral case study.- 2.3. Conclusions.- 3. An empirical investigation of the use of Broadbent's rule in spatial system design.- 3.1. Introduction.- 3.2. Broadbent's rule.- 3.3. The Merseyside study.- 3.4. Conclusions.- 4. A simplistic approach to the redistricting problem.- 4.1. Introduction.- 4.2. Electoral redistricting methods.- 4.3. The development of the simplistic algorithm.- 4.4. The redistricting algorithm.- 4.5. Application of the procedure to the West Midlands.- 4.6. Conclusions.- 5. An optimal zoning approach to the study of spatially aggregated data.- 5.1. Introduction.- 5.2. Alternative approaches to the design of zoning systems for spatial study.- 5.3. Solving the automatic zoning problem.- 5.4. Applications.- 5.5. Zone design and spatial study.- 6. Speculations on an information theoretic approach to spatial representation.- 6.1. Introduction.- 6.2. Spatial entropy functions.- 6.3. Measures of relative spatial information.- 6.4. The aggregation of information.- 6.5. Theoretical aggregation problems: in a population density model.- 6.6. Hierarchical aggregation.- 6.7. Information measures of spatial efficiency.- 6.8. Spatial probability models incorporating zone size.- 6.9. An empirical algorithm based on spatial information theory.- 6.10. Conclusions.- II: Multi-Level Specification Problems.- 7. The specification of multi-level systems for spatial analysis.- 7.1. Introduction.- 7.2. Slater's method.- 7.3. The Intramax procedure.- 7.4. An analytical framework for the specification of multi-level spatial systems.- 7.5. Conclusions.- 8. Hierarchical trip distribution models and the design of accounting systems.- 8.1. Introduction.- 8.2. The matching of hierarchical models.- 8.3. Compound accounting systems.- 8.4. Conclusion.- 9. Some suggestions for future research.- References.

Region Extraction and Description through Planning.

Abstract: : This paper examines several image segmentation algorithms which have been explored in the development of the VISIONS system. Each of these algorithms can be viewed as a variation on a basic theme: the clustering of activity in feature space via histogram analysis, mapping these clusters back onto the image, and then isolating regions by analysis of the spatial relationships of the cluster labels. It is shown that the interaction between these two representations of data (global feature information and spatial information) provides a view that is lacking in either. The scene segmentation algorithms contain the following stages: (1) PLAN: reduce the amount of detail in the scene to a bare minimum by performing a fast simple segmentation into primary areas using spatial and/or quantization compression. (2) REFINE: resegment the scene with careful attention directed to the textural complexities of each region. The primitive transformations which are used include histogram clustering, region growing, data reduction by narrowing the quantization range, and/or data reduction by spatially collapsing the data while extracting features. These algorithms have been implemented using a parallel, hierarchical computational structure. Comparisons of performance on several images are given. (Author)

Remote sensing inputs to landscape models which predict future spatial land use patterns for hydrologic models

Abstract: A tropical forest area of Northern Thailand provided a test case of the application of the approach in more natural surroundings. Remote sensing imagery subjected to proper computer analysis has been shown to be a very useful means of collecting spatial data for the science of hydrology. Remote sensing products provide direct input to hydrologic models and practical data bases for planning large and small-scale hydrologic developments. Combining the available remote sensing imagery together with available map information in the landscape model provides a basis for substantial improvements in these applications.