Peter Haggett

Trend-Surface Mapping in Geographical Research

ALTHOUGH GEOGRAPHERS are traditionally concerned with the description, analysis and explanation of areal distributions of phenomena, much of the most vigorous development of new techniques in this field has come from outside geography. The harnessing of the vast potential of computer systems to mapping problems has been pressed forward both in subjects like meteorology where mechanical graph-plotters, line printers, and cathode-ray tube displays are being used to map directly the output of digital computers (Sawyer, 1960; Wippermann, 1959), and in botany where field information on the occurrence of vascular plants are being rapidly processed and printed out (for example, the 1,623 maps of the Atlas of the British Flora (Perring and Walters, 1962)). The most striking adaptations of computer technology to traditional mapping problems are being employed in the earth sciences, however: for example, in geophysical prospecting, structural mapping and sedimentary petrology (Krumbein, 1958). Here the most fundamental developments in mapping techniques lie less in the automation of traditional techniques (a field reviewed for geographers by Tobler (1959)) but in the evolution of new ways of extracting more information from map data. This paper reviews developments in one of the most promising of these techniques, trend-surface mapping, and attempts to assess its significance for, and applications in, the wider field of geographical research.

Elements of spatial structure : a quantitative approach

1. Introduction Part I. Static Aspects of Regional Structure: 2. Regions as combinatorial structures 3. Regions as ordered series 4. Regions as surfaces Part II. Dynamic Aspects of Regional Structure: 5. Spatial comparison of time series: a framework 6. Spatial comparison of time series: I. Contagious processes 7. Spatial comparison of time series: II. Unemployment in South-West England Part III. Autocorrelation and Forecasting: 8. Spatial autocorrelation 9. The analysis of regional patterns by nearest-neighbour methods 10. Regional forecasting Appendices.

Hybridizing alternative models of an epidemic diffusion process

Seven alternative models of an epidemic diffusion model are compared using a binary autocorrelation statistic. The study area consisted of 28 local areas within an English county reporting measles ...

Geographical aspects of the emergence of infectious diseases

The historical geography of infectious diseases of humans shows a constantly changing pattern. In the late 20th century that pattern is being affected by strong population growth in the host population, by worldwide environmental changes associated with that growth, and by increased spatial mobility for both the disease-causing microorganisms and for the human host. The paper identifies some of the geographical factors that have shaped disease emergence in the past and those that appear to be playing a part today.

On the Efficiency of Alternative Aggregations in Region-Building Problems

It is clear that, whenever sub-areas are aggregated into regions, the set of regions obtained is only one of a large number of alternative groupings. To illustrate this, equations are derived which give the number of different ways n counties may be grouped to form k regions, k ≤ n, in two limiting situations: the totally unconstrained case, in which each county may be grouped with any other county; and the maximally constrained case, when each county can only be grouped with its physically contiguous neighbours. A measure of the efficiency, co, of any regional grouping is given, and the problem of finding the regional grouping with the ‘best’ value of co in the set of alternative grouping patterns is discussed.

Statistical modelling of measles and influenza outbreaks

This paper reviews the application of statistical models to outbreaks of two common respiratory viral diseases, measles and influenza. For each disease, we look first at its epidemiological characteristics and assess the extent to which these either aid or hinder modelling. We then turn to the models that have been developed to simulate geographical spread. For measles, a distinction is drawn between process-based and time series models; for influenza, it is the scale of the communities (from small groups to global populations) which primarily determines modelling style. Applications are provided from work by the authors, largely using Icelandic data. Finally we consider the forecasting potential of the models described.

Regional and Local Components in the Distribution of Forested Areas in South-East Brazil: A Multivariate Approach: Discussion

There are few sins in which geographers indulge with more relish than generalizing our field fi dings at a local level over the whole of an adjacent re ion. The writer was made keenly aware of this commission in returning in 1962 to travel more widely over the south-eastern part of Brazil. Speculations on the persistence of forested zones based on localized field-work in the Taubati area (Haggett, 1961) were only partly sustained when the survey was extended, via sampling methods over an adjacent area some hundreds of times larger. In this paper the results of a localized study based on a small 100-square-kilometrearea are reported alongside those of a wider regional study. It is shown that not only is the distribution different at the two levels but that the appropriate pattern of study changes in sympathy. Data available at one level are unobtainable at another, levels of measurement possible at one level are too fine at another, and statistical tests appro? priate at one level are inapplicable at another.

Prediction and predictability in geographical systems

Prediction plays an essential part in the building of models of geographical systems: it exposes weaknesses in our concepts, checks our credibility and encourages model reformulation. Despite this centrality, the notion of system predictability and the way it fits into model building is often weakly developed in the geographical literature. The nature of predictions is illustrated here by the attempts to build geographical models of the spread of epidemic waves. Three types of spatial models are explored and illustrated: (i) descriptive models of a spread process, (ii) predictive models of the future extent of spread and (iii) interdictive models which show how spread may be curtailed. From this review, the wider role of prediction and predictability in other areas of geographical model-building is explored.

The Use of Trend-Surface Parameters in Inter-Urban Comparisons

The general problem of comparing isarithmic maps of different urban areas is examined. Proposed solutions by Merriam and Sneath (1966) and Haggett (1967) are revised in the light of the indicated instability of coefficients under shifts in the grid systems for such maps. A number of stable classifications of city structures can be built up which are invariant under orthogonal grid rotations but most of these break down under non-orthogonal rotations. Variances accounted for by successive terms (linear, quadratic, cubic) appeared stable and are recommended for preliminary analysis. The fundamental problems of pattern analysis remain unresolved by trend-surface coefficients. The argument in the paper is largely empirical and is illustrated from simulated urban patterns and by fifteen sample metropolitan areas from the United States.

Regional and Local Components in the Areal Distribution of Surface Sand Facies in the Breckland, Eastern England

ABSTRACT The Breckland is a distinctive region of arenaceous deposits overlying the chalk escarpment of eastern England, covering an area of some 1000 sq km. The origin of these deposits is obscure, but it is commonly believed that they originated from the weathering of sandy till derived from the Neocomian Sandringham Sands to the north. This investigation, using both systematic- and nested-sample surveys, was designed to determine: (1) whether there are significant areal variations in the grain size of the surface sands; (2) if so, to what extent it is possible to disentangle regional and local components; and (3) which linear scale intervals are associated with the greatest grain size variance components. Trend-surface analysis pointed to significant regional variations in grain size, with a general coarsening towards the north-east. This was supported by a hierarchical variance analysis, which also indicated that: (1) variability in grain size increases successively with areal sub-division; (2) the total amount of variability is generally greater for coarse-grained facies; and (3) that the increments of variability differ at different areal levels. The greatest increments appeared at 17,000 m (contributing some 54 percent of the total variability), at about 8 m (22 percnt), and within the range of about 125 to 1000 m (18 percent). It is tentatively suggested that the regional variations (that is, at the scale of 17,000 m) might be explained by variations in the original till compositi n and/or by surface aeolian reworking. The variability at the most local level seems to accord with the dimensions of the periglacial polygon and stripe patterns which are characteristic of much of the Breckland, although the variability in the range [1]/[8] to 1 km is less obviously accounted for.