Abstract: This article presents a new approach to cartographic classification of univariate, quantitative polygonal data. The proposed method adapts to the degree of spatial autocorrelation in data by utilizing the Moran's I scatter plot in combination with the Fisher–Jenks algorithm. When data are spatially autocorrelated, the resulting maps are visually less complex than those derived using equivalent nonspatial classification approaches. However, the resulting classes might overlap in the value domain. The cartographic concept that we present therefore combines the advantages of traditional classification with those of our proposed method: it allows the visual assignment of individual polygons to mutually exclusive value ranges, while still preserving visual clarity of patterns.

Abstract: When landmasses and shapes. we look If (e.g., at it is a countries) a map, thematic we expect reflecting map; this to see is, their a the map actual portrayed that sizes dislandmasses (e.g., countries) reflecting their actual sizes and shapes. If t is a thematic ma ; hi is, a p that d splays information about a specific theme; the different units are colored according to the information displayed (what is known as a choropleth map), or with symbols representing either quantitative or qualitative information (for example, a proportional symbol map). In the case of the insular Caribbean, logically, the Greater Antilles occupy a larger extent than the Lesser Antilles and the small islands in the northern Caribbean (Map 1). Oftentimes, geographic patterns displayed on regional maps are not easily discernible, particularly for those islands with smaller sizes (this will depend, of course, on the scale and extent of the map). This can be problematic because the information, and ultimately the message that wants to be conveyed through a map, can be overlooked or missed due to the inherent size differences.

Abstract: This paper examines the adaptation of dasymetric mapping methodologies to agricultural data, including their testing and transposition, in order to recover the underlying statistical surface (i.e., an approximation of the real distribution of data). A methodology based on the ideas of Gal- lego and Peedell (2001) and on the binary method is proposed. It has several steps: (i) the ex- clusion of target zones for which no observations exist (binary method), (ii) the application of an iterative process to define the most precise densities for data distribution, and (iii) the stratification/definition of sub-units with homogenous characteristics if the results of the previ- ous step are not satisfactory, and the subsequent application of step two.The methodology was applied in the Alentejo region of Portugal, using data from the 1999 Agricultural Census. Several counties are used as source zones. The aim was to generate a dis- tribution of agro-forestry occupations as close as possible to reality. Two lines of analysis were followed: (i) application of the methodology simultaneously to all counties (definition of regional densities), and (ii) application of the methodology separately to the different sub- areas with similar characteristics (definition of sub-regional densities). For an easy application of the methodology, a computer tool was created, which allowed the easy optimization, vali- dation, and exportation of the data into a Geographic Information System (GIS).The results were validated using several error indicators at the county level, as well as in a sample of parishes. We show that the second variant of the methodology yielded more precise results, and is superior for the types of data available. This method yielded maps in which the distribution of the most relevant agro-forestry occupations is closest to reality.Key Words: dasymetric mapping, agricultural data, spatial disaggregation, iterative process, Alentejo(ProQuest: ... denotes formulae omitted.)Population density data are available to the Euro- pean Commission at the level of the county or parish. However, this level of spatial resolution may be insufficient, in many cases, for planning or modeling purposes or to assess the impact of European Union policies. In some countries, as in France, where most counties have a rather small area (approximately 15 km2 on average), the reso- lution may be sufficient, but it is clearly insuffi- cient in other countries where the counties tend to be larger (Gallego and Peedell 2001).Therefore, maps produced have limited utility in detailed spatial analysis, especially where human populations are concentrated in a relatively small number of villages and cities (Bielecka 2005). Choropleth maps by administrative units give the impression that population is distributed homoge- neously throughout each areal unit, even when portions of the region are, in actuality, uninhab- ited. Openshaw (1984) described these limitations as the modifiable areal unit problem (MAPU)- defined as a situation in which modifying the boundaries and scale of data aggregation signifi- cantly affects the result of spatial data analysis- and stated that it is often unclear whether the re- sults of statistical data analysis indicate some re- ality about the individuals living in that region or are rather strictly a function of the particular areal unit used in the analysis.As regards agricultural data, the situation is the same. Agricultural data is available at the NUTS II, NUTS III, county, and parish levels, but no information is available regarding the true spatial distribution of the available agricultural variables. In Portugal, for instance, data for these levels of analysis are available only from official statistics and from studies on agricultural data disaggrega- tion (Martins, Fragoso, and Xavier 2010, Frag- oso, Martins, and Lucas 2008). However, agricul- tural policies, in many cases, correspond to terri- torial areas that do not conform to county or parish boundaries. …

Abstract: A choropleth map is a cartographic document. It shows a geographic study area tessellated by a set of polygons that differ in shape and size. Each polygon is depicted by a uniform symbol representing the manifestation of some phenomenon. This thesis focuses on socio-economic phenomena. We want to delineate a set of socio-economic regions within a study area. These regions are used for decision making about the delivery of specific goods and services and/or the provision of specific community infrastructure. However, we have identified three fundamental weaknesses associated with the use of choropleth maps for socio-economic regionalisation. Therefore, as an alternative to the choropleth map if we think explicitly in R , then the best representation of the spatial distribution of a socioeconomic phenomenon is a smooth surface. The socio-economic data we use are collected during a national census of population and are summarised for areas, i.e., polygons. To accommodate these data we have developed and applied a method for gridding and smoothing — termed regularisation — in order to build a smooth surface. We apply Green’s theorem and use path integrals with much simplification to compute a smoothed datum for each intersection of a, say, 100 by 100 grid that describes a surface. Mathematically, surface shape is interpreted through the comparison of curvatures. Surface shape analysis involves the measurement of the Gaussian and mean curvatures at the internal intersections of the grid. Curvature measurement requires at least a twice differentiable function. We have invented such a function based on Lagrange interpolation. It is called a Lagrange polynomial in x y. Each internal intersection of the grid is the (2, 2) element of a 3× 3 matrix extracted from the grid. We compute a Lagrange polynomial in x y for each 3 × 3 matrix. Then we use this polynomial to measure the curvatures and classify the shape. Contiguous grid intersections of the same shape class comprise a shape neighbourhoods region interpreted as a specific manifestation of a socio-economic phenomenon. Hence, we have the basis for describing the spatial distribution of the phenomenon. Three investigations into the construction of quadratic polynomials as alternative functions are described. Two of these quadratic polynomials are called ‘exact fit’ in the sense that the polynomial returns the exact z-datum associated with each xy-pair used in its construction. Construction of a ‘best fit’ quadratic polynomial based on least squares interpolation comprises the third investigation. We compare the four different types of polynomials and of these we choose the Lagrange polynomial in x y as most appropriate. Given a relatively high density grid, e.g., 250 by 250, regardless of the polynomial used the resulting maps of shape neighbourhoods regions are virtually identical. This surprising convergence in R is explained. Is a map of shape neighbourhoods regions an accurate description of the spatial distribution of a socio-economic phenomenon? We effect an indirect evaluation of a known phenomenon represented by the spatial distribution of f(x, y) = sin x sin y. We compute the true map of shape neighbourhoods regions of this phenomenon. An approximate map of shape neighbourhoods regions is computed by sampling with 100 randomly generated polygons. Comparison implies that the approximate map is an accurate representation of the true map. This conclusion is supported strongly by the results of a study of a nonperiodic–nonrandom known phenomenon, based on a combination of exponential functions in x and y. This has a surface similar to that of a socio-economic phenomenon. We review selected geographic studies in which mathematical tools have been used for analytical purposes. Mathematical analysis is gaining broader acceptance in geography. The innovative, high quality Surpop work of British geographers is described, and we comment on the strongly complementary nature of the research presented in this thesis to the Surpop work. We describe 18 future research directions and themes; suggestions are made on how each may be undertaken. Next, we summarise each of the ten results of the research presented in this thesis. The thesis concludes with a statement of the medium-term research directions of the researcher and his acknowledgements.

Abstract: The cartographic community has taken a renewed interest in evaluating the effectiveness of automated map displays, given their increasing prevalence among general map users. The changing values of the mapped area from frame to frame in a dynamic thematic map constitute its main element of visual complexity, while many of the peripheral map components often change little (titles) or not at all (scale bars, color ramps). Building on recent research into visual complexity as it relates to dynamic thematic mapping, this study developed a raster-based GIS model for evaluating the graphical variability between sequences of choropleth maps as they would appear as scenes in a dynamic map. The evaluation of visual complexity is based on two previously established metrics, Basic Magnitude of Change (BMOC) and Magnitude of Rank Change (MORC), for describing the variability and average class 'jump' for enumeration units across map scenes. The model presented in this paper uses a neighborhood focal operator that sequentially moves across the entire map, replicating the user's viewing perspective as it divides the scene to instantaneously focus only on the part of the map within the foveal viewing area, a zone of enhanced visual-cognitive acuity. This model accepts a single vector map, uses its class membership attribute data as inputs, computes the BMOC and MORC variability, and writes the value to the focus. The model output is two smoothed map images depicting relative visual complexity values for the sequence of maps. While the neighborhood paradigm can theoretically be used to quantify change on either a vector or raster map, the raster-based approach suggests several improvements over one based on vector polygons. These include a potentially higher degree of accuracy in modeling the user's perspective, especially if enumeration units vary widely in size within the foveal area and map itself, plus the ability to use (with minimal customization) existing image-processing software such as ERDAS Imagine, ArcGIS Spatial Analyst and ENVI to perform analysis of dynamic map complexity.

Abstract: description and analysis of geographically indexed health data with respect to demographic, environmental, behavioural, socioeconomic, genetic, and infectious risk factors (Elliott andWartenberg 2004). Disease maps can be useful for estimating relative risk; ecological analyses, incorporating area and/or individual-level covariates; or cluster analyses (Lawson 2009). As aggregated data are often more readily available, one common method of mapping disease is to aggregate the counts of disease at some geographical areal level, and present them as choropleth maps (Devesa et al. 1999; Population Health Division 2006). Therefore, this chapter will focus exclusively on methods appropriate for areal data...

Abstract: Abstract The online Atlas kartograficznych metod prezentacji [Atlas of cartographic presentation methods, hereinafter the Atlas] is a research project being carried out at the Department of Cartography of the University of Warsaw. The aim of the project is to systematize knowledge about the use of cartographic presentation methods. This study discusses selected issues related to two of the five presentation methods analysed in the project, viz. the choropleth map and the diagram map. A rational application of two quite commonly-used presentation methods leads to a number of problems. These problems are most easily visible during attempts to program its implementation in the web-based Atlas and are largely due to the difficulties with drawing a clear boundary between what is a good and a bad map. For this reason, the system operator’s skill and eye for the graphics of semi-automated visualisation seem to be of key importance.

Abstract: Rozwój technologii komputerowych sprawił, że opracowanie mapy – zwłaszcza statystycznej – jest dziś dostępne dla każdego. Zaistniała zatem potrzeba przygotowania i udostępnienia szerszym kręgom zainteresowanych opracowania, które byłoby więcej niż tylko podręcznikiem lub instrukcją użytkowania programu. Atlas skierowany jest do wszystkich pragnących poznać podstawowe zasady redagowania map statystycznych, a więc studentów geografi i, specjalistów w zakresie gospodarki przestrzennej i ochrony środowiska, geodetów oraz tych, któ-

Abstract: Despite the utility of these maps, R has lacked a consistent interface for creating choropleth maps. In the R Graphics Cookbook [1], Winston Chang explains how to create a state choropleth map in the popular ggplot2 graphing library. His method requires several lines of code and is a different technique than that required for creating a choropleth of US Counties. And that, in turn, is a different technique than that required for creating a map of US ZIP codes. choroplethr provides a consistent, one-line, interface to create maps at these three different levels of detail. Currently choroplethr renders ZIP level maps as scatterplots; technically they are no longer choropleths because they do not show geographic boundaries. A discussion of this design decision is provided.

Abstract: The demand for small-scale population data is increasing in a variety of fields. Spatial techniques including Geographic Information Systems (GIS) and Remote Sensing (RS) have been more often used for the population study in recent years, which makes it possible to conduct the dasymetric mapping, a vital technique transforming a traditional choropleth map into a continuous statistical surface with values at all locations rather than solely aggregated values over the existing units.

Abstract: The EVALIDator Web application, developed in 2007, provides estimates and sampling errors for many user selected forest statistics from the Forest Inventory and Analysis Database (FIADB). Among the statistics estimated are forest area, number of trees, biomass, volume, growth, removals, and mortality. A new release of EVALIDator, developed in 2012, has an option to select two statistics and generate a ratio estimate of the pair. The new feature can estimate statistics such as volume or growth per acre or the growth to removals ratio. Also, the program now makes county choropleth maps of all estimates. We provide information on the data and methods used along with sample output from a simple query that demonstrates these new features.