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A factorial, computational experiment was conducted to compare the spatial interpolation accuracy of ordinary and universal kriging and two types of inverse squared-distance weighting. The experiment considered, in addition to these four interpolation methods, the effects of four data and sampling characteristics: surface type, sampling pattern, noise level, and strength of small-scale spatial correlation. Interpolation accuracy was measured by the natural logarithm of the mean squared interpolation error. Main effects of all five factors, all two-factor interactions, and several three-factor interactions were highly statistically significant. Among numerous findings, the most striking was that the two kriging methods were substantially superior to the inverse distance weighting methods over all levels of surface type, sampling pattern, noise, and correlation.[PUBLICATION ABSTRACT]

The process of creating printed statistical maps in the predigital era was expensive and time consuming. These and other interacting factors constrained the number of design alternatives, such as color choices, that a cartographer might reasonably have been able to consider. In this article, we develop an approach to map deconstruction that enables researchers to investigate the statistical choices made by cartographers by placing each printed map into the universe of all possible choices available to them. We place a particular focus on the specification of choropleth map class intervals for maps produced in the early twentieth century. Three published choropleth maps are used as case studies to illustrate the approach, using four evaluation criteria to evaluate the accuracy of the data classifications. The results indicate that the class interval selection choices made for the examined maps are inferior when compared with available alternatives and that, in one case, classification errors are not only evident, they are abundant.

During the Second World War, the U.S. Bureau of the Census published a novel population density map for the U.S. that used minor civil divisions as its areal basis. Prior to that time, the national-level area measurements required to calculate densities for such sub-county units were unavailable. The data that enabled the production of the map published in 1942 were collected by clerical workers who were employed as part of a joint project between the Census Bureau and the Works Progress Administration. The area measurements, made using planimeters, were used with 1940 Census of Population data to compute densities that are represented on the map using a choropleth technique.

During the past three decades a large body of research has investigated the problem of specifying class intervals for choropleth maps. This work, however, has focused almost exclusively on placing observations in quasi-continuous data distributions into ordinal bins along the number line. All enumeration units that fall into each bin are then assigned an areal symbol that is used to create the choropleth map. The geographical characteristics of the data are only indirectly considered by such approaches to classification. In this article, we design, implement, and evaluate a new approach to classification that places class-interval selection into a multicriteria framework. In this framework, we consider not only number-line relationships, but also the area covered by each class, the fragmentation of the resulting classifications, and the degree to which they are spatially autocorrelated. This task is accomplished through the use of a genetic algorithm that creates optimal classifications with respect to multiple criteria. These results can be evaluated and a selection of one or more classifications can be made based on the goals of the cartographer. An interactive software tool to support classification decisions is also designed and described.

Geographers have been specifying and testing models for decades and are well positioned to make significant contributions to interdisciplinary computational-science teaching and research initiatives. Many types of geographic models are intrinsically computationally intensive.

Public policies with geographical consequences are often difficult to analyze because they affect multiple stakeholders with competing objectives. While such problems fall conceptually into the domain of multiobjective evaluation, associated analytical techniques often search for a single optimum solution. Within the context of geographical problems, optimality often means different things to different stakeholders and, thus, an optimum optimorum may not exist. In this article, we present a new technique based on an evolutionary algorithm (EA) that produces a large number of optimal and near-optimal solutions to a large class of land management problems. As implemented for this article, solutions represent landscape patterns that produce services that meet stakeholder needs to varying degrees. The construction of curves that illustrate the trade-offs among various services given limited resources is central to this approach. Decision makers can use these curves to help find solutions that strike a balance among conflicting objectives and, thus, meet stakeholder needs. To provide context to this work we consider the impact of the U.S. Department of Agriculture's (USDA) Conservation Reserve Program on rural landscapes. Three objectives are assumed: (1) maximize farm income, (2) maximize environmental quality, (3) minimize public investment in conservation programs; the first two are viewed as services desired by stakeholders. Analytical and visualization tools are developed to reduce the burden associated with exploring the large number of solutions that are produced by this technique. The results illustrate that the EA-based approach can produce results equal to and significantly more diverse than conventional integer programming techniques.

Geographic information systems (GIS) are now widely used to manage and visualize transportation and other network information and to plan for changes in network infrastructure. As GIS technology becomes more portable and as planning styles evolve, these network data and derived analyses will be presented, sometimes interactively, not only to professional analysts but also to a wider audience of administrators, planners, and the general public. Such presentations require the effective communication of a combination of static and dynamic attributes of complex spatial networks to a diverse audience for a variety of purposes. A large quantity of data that describes the geometry and attributes of network infrastructures is already accumulated on a regular basis and is readily available in digital formats. Like most raw data, however, this massive digital resource is often not used to its fullest potential because methods for rendering it and synthesizing it for visual display are not well developed or implemented within standard GIS software. In this paper we develop a framework in which the formal functions of networks are tied to the information that must be communicated given a set of demands that influence the choice of a basic representational strategy.

Many types of geospatial analyses are computationally complex, involving, for example, solution processes that require numerous iterations or combinatorial comparisons. This complexity has motivated the application of high performance computing (HPC) to a variety of geospatial problems. In many instances, HPC assumes even greater importance because complexity interacts with rapidly growing volumes of geospatial information to further impede analysis and display. This chapter briefly reviews the underlying need for HPC in geospatial applications and describes different approaches to past implementations. Many of these applications were developed using hardware systems that had a relatively short life-span and were implemented in software that was not easily portable. More promising recent approaches have turned to the use of distributed resources that includes cyberinfrastructure as well as cloud and fog computing.

The pace of improvement in the performance of conventional computer hardware has slowed significantly during the past decade, largely as a consequence of reaching the physical limits of manufacturing processes. To offset this slowdown, new approaches to HPC are now undergoing rapid development. This chapter describes current work on the development of cutting-edge exascale computing systems that are intended to be in place in 2021 and then turns to address several other important developments in HPC, some of which are only in the early stage of development. Domain-specific heterogeneous processing approaches use hardware that is tailored to specific problem types. Neuromorphic systems are designed to mimic brain function and are well suited to machine learning. And then there is quantum computing, which is the subject of some controversy despite the enormous funding initiatives that are in place to ensure that systems continue to scale-up from current small demonstration systems.