Complementary Use of Scalar,Directional, and Vector Statistics with an Application to Surface Winds

Vector data are not uncommon in geography, and include examples such as transportation flows, particulate transport, and cartographic distortion. The directional and vector means and variances of these types of data are easily computed using a complex-arithmetic extension of the equations for scalar mean and variance. The January surface wind field over the contiguous United States provides an example with which to compare the information provided by scalar, directional and vector-based statistics. Spatial patterns of the mean and variance of January wind velocity (the wind vector) resemble patterns of wind speeds and directions but are not a simple superposition of the two, and one cannot necessarily infer the nature of the velocity field from separately computed salar and directional statistics. However, scalar and directional means and variances can lend insight into the features contributing to the velocity mean and variance. Scalar, directional, and vector-based analyses thus provide complementary methods with which to examine the spatial patterns of wind, or of any flow field that can be represented as a vector.     

Spatial Dispersion of Intra-Urban Juvenile Delinquency

Abstract

Studies of the spatial distribution of juvenile delinquency have generally been of a correlational nature. It is felt that geostatistical techniques such as centrography can offer complementary insights into spatial patterns of urban delinquency. The spatial dispersion of delinquent activity of Phoenix, Arizona for 1968 was assessed centrographically to determine differences in the dispersion of groups within selected delinquent populations. Greatest differences in dispersion were found when both offense and residence locations of delinquents were arrayed by ethnic group membership. For most groups of delinquents, it was found that the dispersion of residence locations was greater than was the dispersion of offense locations. Suggestions are made for classroom adaptation of the spatial methodology presented.     

Measuring Global Spatial Autocorrelation with Data Reliability Information

Assessing spatial autocorrelation (SA) of statistical estimates such as means is a common practice in spatial analysis and statistics. Popular SA statistics implicitly assume that the reliability of the estimates is irrelevant. Users of these SA statistics also ignore the reliability of the estimates. Using empirical and simulated data, we demonstrate that current SA statistics tend to overestimate SA when errors of the estimates are not considered. We argue that when assessing SA of estimates with error, one is essentially comparing distributions in terms of their means and standard errors. Using the concept of the Bhattacharyya coefficient, we proposed the spatial Bhattacharyya coefficient (SBC) and suggested that it should be used to evaluate the SA of estimates together with their errors. A permutation test is proposed to evaluate its significance. We concluded that the SBC more accurately and robustly reflects the magnitude of SA than traditional SA measures by incorporating errors of estimates in the evaluation. Key Words: American Community Survey, Geary ratio, Moran’s I, permutation test, spatial Bhattacharyya coefficient.     

Uncertainty in the effects of the modifiable areal unit problem under different levels of spatial autocorrelation: a simulation study

ABSTRACT

The objective of this paper is to investigate uncertainties surrounding relationships between spatial autocorrelation (SA) and the modifiable areal unit problem (MAUP) with an extensive simulation experiment. Especially, this paper aims to explore how differently the MAUP behaves for the level of SA focusing on how the initial level of SA at the finest spatial scale makes a significant difference to the MAUP effects on the sample statistics such as means, variances, and Moran coefficients (MCs). The simulation experiment utilizes a random spatial aggregation (RSA) procedure and adopts Moran spatial eigenvectors to simulate different SA levels. The main findings are as follows. First, there are no substantive MAUP effects for means. However, the initial level of SA plays a role for the zoning effect, especially when extreme positive SA is present. Second, there is a clear and strong scale effect for the variances. However, the initial SA level plays a non-negligible role in how this scale effect deploys. Third, the initial SA level plays a crucial role in the nature and extent of the MAUP effects on MCs. A regression analysis confirms that the initial SA level makes a substantial difference to the variability of the MAUP effects.     

An assessment of surface and zonal models of population

Abstract

The advantages of handling population data in GIS as a raster surface rather than as zonal attributes are discussed, and a technique for creating such surfaces briefly reviewed. Existing models created by this method using the 1991 UK Census are then compared with equivalent zonal data and some weaknesses identified, in particular the poor association between enumeration districts and 200 m grid cells. A refined version of the surface generation technique is presented in which population totals are constrained within zone boundaries, while residential geography is retained with considerable success.     

APPRAISAL OF GEOGRAPHIC RESEARCH AND TRAINING PROGRAMS IN THE SOVIET UNION

Global distributions are commonly described by maps and tables which emphasize the dispersion of a distribution. The Mean Spheroidal Center (M.S.C.) defines the average location of a world distribution. It is an objectively determined point within the sphere's surface. The M.S.C. calculations are demonstrated using the world's 25 largest cities in each of four time periods.     

NCGIA education activities: the core curriculum and beyond

Abstract

Education has been part of the NCGIA's mission from the earliest discussions of the concept of the Center at the National Science Foundation. To respond to the need for short-term solutions to the shortage of adequately trained personnel in GIS, the Center developed a set of teaching materials or core curriculum. The steps in its development are described and an analysis of initial distribution statistics is presented. Current efforts to develop a framework for laboratory materials are outlined. The paper ends with an assessment of the project and comparison with other disciplines.     

Two-tier analysis in palaeomagnetism

Summary. The statistical analysis necessary for isolating the between-site dispersion in palaeomagnetic studies is presented, both for the case of a common within-site precision and for variable within-site precision.
Approximate distributions are derived for all the relavant statistics. It is shown that if it is necessary to perform a two-tier analysis the overall true mean direction should be estimated as the mean of individual site mean directions and an equation for the semi-angle of the cone of confidence about this mean direction is derived.
The last section of the paper lays out the process by which a two-tier analysis should be performed together with relevant equations.     

Modeling Near-Surface Air Temperature From Solar Radiation and Lapse Rate: New Development on Short-Term Monthly and Daily Approach

Short-term monthly mean temperature (T_m ) and short-term daily mean temperature (T_d ) rather than long-term monthly and daily mean temperature (T_m and T_d ) are preferred for some ecosystem studies such as carbon source and sink, pine beetle mortality, and snow melting. The recent progress of modeling T_m and T_d (based on the previous work on T_m ) supported by climatologically aided interpolation (CAI) is reported over the mountainous Yellowstone National Park. With the spatial scale of a 30 m digital elevation model (DEM), the slope, aspect, and shadows cast by surrounding topography, which could not be well captured by very coarse DEM, could be taken into account. Data from 12 months (Jan-Dec 2008) and 12 dates (25 Jan-Dec 2008) were used to demonstrate the approach. Inverse distance weighting (IDW) interpolations of limited temperature anomalies were adopted to represent the deviations from normality. T_m , as a preexisting climatology surface, was added to deviations in order to model T_m . Linear temporal interpolation of adjacent T_m was used to create a climatology surface, which was then added to deviations in order to model T_d . Results show the mean absolute errors (MAEs) for T_m ranged from 0.75° C to 1.78° C, while the MAEs for T_d ranged from 1.14° C to 2.02° C. The four factors of elevation, seasonal change of lapse rate, temperature difference caused by variation in solar radiation, and preexisting climatology surface for the CAI approach were comprehensively considered in this approach.     

Spatial strategies for parallel spatial modelling

Abstract

Abstract. To achieve high levels of performance in parallel geoprocessing, the underlying spatial structure and relations of spatial models must be accounted for and exploited during decomposition into parallel processes. Spatial models are classified from two perspectives, the domain of modelling and the scope of operations, and a framework of strategies is developed to guide the decomposition of models with different characteristics into parallel processes. Two models are decomposed using these strategies: hill-shading on digital elevation models and the construction of Delaunay Triangulations. Performance statistics are presented for implementations of these algorithms on a MIMD computer.     

Design and Usability of an Enhanced Geographic Information System for Exploration of Multivariate Health Statistics

Abstract

The multidimensional nature of many types of data in modern geography calls for creative and innovative approaches to their analysis. Statisticians have recently developed methods for exploring and visualizing large, multivariate datasets, but cartographers and geographers in general have only recently begun to integrate these methods for use with spatial and spatiotemporal datasets that are multivariate in character. This article will present an example of such an integration—an environment for visualization of health statistics—as a case study to demonstrate the philosophical and practical advantages of geovisualization systems for the exploration of complex spatiotemporal information. Emphasis is placed on the encouragement of creative thinking about geographic phenomena through the use of such data-rich graphical tools.

     

Terrain Pattern Recognition and Spatial Decision Making for Regional Slope Stability Studies

A terrain partition scheme is presented that allows the identification of regions with high landslide risk in natural terrain zones on the basis of geomorphometric criteria from moderate resolution DEMs. The key factor being the terrain segmentation to aspect regions (regions formed by points preserving the same aspect direction) instead of using an artificial regular-grid terrain partition scheme. The study area is in western Greece (NW Peloponnesus) whereas a moderate resolution digital elevation model with spacing 75 m is used. Landslide inventory analysis and knowledge conceptualization identified that the landslide susceptibility of a particular aspect region is high, if the mean elevation is low and the mean gradient is high. Each aspect region was parametrically represented on the basis of its mean gradient and elevation. The domain of each parameter was divided to seven slices (classes) on the basis of the observed density. Subsequent knowledge based mapping identified aspect regions with high landslide susceptibility for the following spatial rule: (a) “mean slope in class 6 or 7” and (b) “mean elevation in class 1 to 5”. Alternatively the rule is expressed as mean slope to be equal or greater than 15^∘ whereas mean elevation to be in the range 0 to 750 m. These identified zones correspond to regions where historical landslides occurred (populated coastal areas in the North) as well as to south regions (natural terrain zone) where no landslide record is available, because of the limitations posed by the natural terrain landslide mapping program in Greece. The presented terrain segmentation technique combined to the spatial decision-making process, provided both an object framework for integrating geomorphometric parameters and a method for landslide risk analysis in natural terrain zones.     

Objective landslide detection and surface morphology mapping using high-resolution airborne laser altimetry

A map of extant slope failures is the most basic element of any landslide assessment. Without an accurate inventory of slope instability, it is not possible to analyze the controls on the spatial and temporal patterns of mass movement or the environmental, human, or geomorphic consequences of slides. Landslide inventory maps are tedious to compile, difficult to make in vegetated terrain using conventional techniques, and tend to be subjective. In addition, most landslide inventories simply outline landslide boundaries and do not offer information about landslide mechanics as manifested by internal deformation features. In an alternative approach, we constructed accurate, high-resolution DEMs from airborne laser altimetry (LIDAR) data to characterize a large landslide complex and surrounding terrain near Christchurch, New Zealand. One-dimensional, circular (2-D) and spherical (3-D) statistics are used to map the local topographic roughness in the DEMs over a spatial scale of 1.5 to 10 m. The bedrock landslide is rougher than adjacent unfailed terrain and any of the statistics can be employed to automatically detect and map the overall slide complex. Furthermore, statistics that include a measure of the local variability of aspect successfully delineate four kinematic units within the gently sloping lower half of the slide. Features with a minimum size of surface folds that have a wavelength of about 11 to 12 m and amplitude of about 1 m are readily mapped. Two adjacent earthflows within the landslide complex are distinguished by a contrast in median roughness, and texture and continuity of roughness elements. The less active of the earthflows has a surface morphology that presumably has been smoothed by surface processes. The Laplacian operator also accurately maps the kinematic units and the folds and longitudinal levees within and at the margins of the units. Finally, two-dimensional power spectra analyses are used to quantify how roughness varies with length scale. These results indicate that no dominant length scale of roughness exists for smooth, unfailed terrain. In contrast, zones with different styles of landslide deformation exhibit distinctive spectral peaks that correspond to the scale of deformation features, such as the compression folds. The topographic-based analyses described here may be used to objectively delineate landslide features, generate mechanical inferences about landslide behavior, and evaluate relatively the recent activity of slides.     

Association affairs

Segregation and diversity measures are meant to reflect extent of integration. Based on population counts gathered for enumeration units, these areal-based measures are sensitive to the spatial scale at which the data are tabulated. They are also not effective in capturing various types of assimilation affected by spatial distance among ethnic groups. This paper proposes to use the multiethnic household as a measure of ethnic integration and social assimilation. Using 1990 Public Use Microdata Samples (PUMS), the percentage of multiethnic households is derived for each state and Public Use Microdata Area (PUMA) to indicate integration. Based upon the results, Hawaii and Alaska have extremely high levels of integration. The west and southwest are more integrated than the rest of the U.S., with the exceptions of Oklahoma and several states along the east coast. The least integrated region includes several Appalachian states. The PUMA-level analysis reveals a great deal of variation in ethnic integration within states.     

Artificial neural networks and geostatistical models for housing valuations in urban residential areas

Property valuation studies often use classical statistics techniques. Among these techniques, the Artificial Neural Networks are the most applied, overcoming the inflexibility and the linearity of the hedonic models. Other researchers have used Geostatistics techniques, specifically the Kriging Method, for interpreting spatial-temporal variability and to predict housing unit prices. The innovation of this study is to highlight how the Kriging Method can help to better understand the urban environment, improving the results obtained by classical statistics. This study presents two different methods that share the general objective of extracting information regarding a city’s housing from datasets. The procedures applied are Ordinary Kriging (Geostatistics) and Multi-Layer Perceptron algorithm (Artificial Neural Networks). These methods were used to predict housing unit prices in the municipality of Pozuelo de Alarcon (Madrid). The implementation of both methods provides us with the urban characteristics of the study area and the most significant variables related to price. The main conclusion is that the Ordinary Kriging models and the Neural Networks models, applied to predicting housing unit prices are necessary methodologies to improve the information obtained in classical statistical techniques.

Abbreviations: ANN: Artificial Neural Networks; OK: ordinary Kriging; MLP: multi-layer perceptron     

Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning

One of the major sources of uncertainty associated with geographical data in GIS arises when they are the outcome of a sampling process. It is well known that when sampling from a spatially autocorrelated homogeneous surface, stratification reduces the error variance of the estimator of the population mean. In this study, we evaluate the efficiency of different spatial sampling strategies when the surface is not homogeneous. When the surface is first-order heterogeneous (the mean of the surface varies across the map), we examine the effects of stratifying it into first-order homogeneous zones prior to the usual stratification for a systematic or stratified random sample. We investigate the effect of this form of spatial heterogeneity on the performance of different methods for estimating the population mean and its error variance. We do so by distinguishing between the real surface to be surveyed (?), the sampling frame (?) including the choice of zoning, and the statistical estimators (Ψ). The study shows that zoning improves estimator efficiency when sampling a heterogeneous surface. Systematic comparison provides rules of thumb for choice of sample design, sample statistics and uncertainty estimation, based on considering different spatial heterogeneities on real surfaces.