Showing papers on "Spatial analysis published in 1998"

Multidimensional access methods

Abstract: Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.

Geographically Weighted Regression: A Natural Evolution of the Expansion Method for Spatial Data Analysis

Abstract: Geographically weighted regression and the expansion method are two statistical techniques which can be used to examine the spatial variability of regression results across a region and so inform on the presence of spatial nonstationarity. Rather than accept one set of 'global' regression results, both techniques allow the possibility of producing 'local' regression results from any point within the region so that the output from the analysis is a set of mappable statistics which denote local relation­ ships. Within the paper, the application of each technique to a set of health data from northeast England is compared. Geographically weighted regression is shown to produce more informative results regarding parameter variation over space. 1 Spatial nonstationarity A frequent aim of data analysis is to identify relationships between pairs of variables, often after negating the effects of other variables. By far the most common type of analysis used to achieve this aim is that of regression, in which relationships between one or more independent variables and a single dependent variable are estimated. In spatial analysis the data are drawn from geographical units and a single regression equation is estimated. This has the effect of producing 'average' or 'global' parameter estimates which are assumed to apply equally over the whole region. That is, the relationships being measured are assumed to be stationary over space. Relationships which are not stationary, and which are said to exhibit spatial nonstationarity, create problems for the interpretation of parameter estimates from a regression model. It is the intention of this paper to compare the results of two statistical techniques, Geographically weighted regression (GWR) and the expansion method (EM), which can be used both to account for and to examine the presence of spatial nonstationarity in relationships .

Landscape ecology and epidemiology of vector-borne diseases: tools for spatial analysis

Abstract: Geographic information systems (GIS), global positioning systems (GPS), remote sensing, and spatial statistics are tools to analyze and integrate the spatial component in epidemiology of vector-borne disease into research, surveillance, and control programs based on a landscape ecology approach. Landscape ecology, which deals with the mosaic structure of landscapes and ecosystems, considers the spatial heterogeneity of biotic and abiotic components as the underlying mechanism which determines the structure of ecosystems. The methodologies of GIS, GPS, satellite imagery, and spatial statistics, and the landscape ecology--epidemiology approach are described, and applications of these methodologies to vector-borne diseases are reviewed. Collaborative studies by the author and colleagues on malaria in Israel and tsetse flies in Kenya, and Lyme disease, LaCrosse encephalitis, and eastern equine encephalitis in the north-central United States are presented as examples for application of these tools to research and disease surveillance. Relevance of spatial tools and landscape ecology to emerging infectious diseases and to studies of global change effects on vector-borne diseases are discussed.

Land-Use Changes in Southern Appalachian Landscapes: Spatial Analysis and Forecast Evaluation

Abstract: Understanding human disturbance regimes is crucial for developing effective conservation and ecosystem management plans and for targeting ecological research to areas that define scarce ecosystem services We evaluate and develop a forecasting model for land-use change in the Southern Appalachians We extend previous efforts by (a) addressing the spatial diffusion of human populations, approximated by building density, (b) examining a long time period (40 years, which is epochal in economic terms), and (c) explicitly testing the forecasting power of the models The resulting model, defined by linking a negative binomial regression model of building density with a logit model of land cover, was fit using spatially referenced data from four study sites in the Southern Appalachians All fitted equations were significant, and coefficient estimates indicated that topographic features as well as location significantly shape population diffusion and land use across these landscapes This is especially evident in the study sites that have experienced development pressure over the last 40 years Model estimates also indicate significant spatial autocorrelation in land-use observations Forecast performance of the models was evaluated by using a separate validation data set for each study area Depending on the land-use classification scheme, the models correctly predicted between 68% and 89% of observed land uses Tests based on information theory reject the hypothesis that the models have no explanatory power, and measures of entropy and information gain indicate that the estimated models explain between 47% and 66% of uncertainty regarding land-use classification Overall, these results indicate that modeling land-cover change alone may not be useful over the long run, because changing land cover reflects the outcomes of more than one human process (for example, agricultural decline and population growth) Here, additional information was gained by addressing the spatial spread of human populations Furthermore, coarse-scale measures of the human drivers of landscape change (for example, population growth measured at the county level) appear to be poor predictors of changes realized at finer scales Simulations demonstrate how this type of approach might be used to target scarce resources for conservation and research efforts into ecosystem effects

Spatial Cognition, An Interdisciplinary Approach to Representing and Processing Spatial Knowledge

Abstract: Spatial Knowledge Acquisition and Spatial Memory.- Allocentric and Egocentric Spatial Representations: Definitions, Distinctions, and Interconnections.- The Route Direction Effect and its Constraints.- Spatial Information and Actions.- The Impact of Exogenous Factors on Spatial Coding in Perception and Memory.- Judging Spatial Relations from Memory.- Relations between the mental representation of extrapersonal space and spatial behavior.- Representational Levels for the Perception of the Courses of Motion.- Formal and Linguistic Models.- How Space Structures Language.- Shape Nouns and Shape Concepts: A Geometry for 'Corner'.- Typicality Effects in the Categorization of Spatial Relations.- The Use of Locative Expressions in Dependence of the Spatial Relation between Target and Reference Object in Two-Dimensional Layouts.- Reference Frames for Spatial Inference in Text Understanding.- Mental Models in Spatial Reasoning.- Formal Models for Cognition - Taxonomy of Spatial Location Description and Frames of Reference.- Spatial Representation with Aspect Maps.- A Hierarchy of Qualitative Representations for Space.- Spatial Reasoning with Topological Information.- Navigation in Real and Virtual Worlds.- A Taxonomy of Spatial Knowledge for Navigation and its Application to the Bremen Autonomous Wheelchair.- Human Place Learning in a Computer Generated Arena.- Spatial Orientation and Spatial Memory Within a 'Locomotor Maze' for Humans.- Behavioral experiments in spatial cognition using virtual reality.- Spatial orientation in virtual environments: Background considerations and experiments.

Measures of spatial pattern for counts

Abstract: SADIE (Spatial Analysis by Distance IndicEs) is a new methodology to detect and measure the degree of nonrandomness in the two-dimensional spatial patterns of populations. It applies the same principles to data in the form of maps as to data in the form of counts at specified locations, but with different techniques. This paper considers data in the form of counts such as occur commonly in ecology. For such data the method has an advantage over traditional approaches that measure only statistical variance heterogeneity, because all the spatial information in the sample is used. Two indices and associated tests are reviewed, one based on the total distance of the sample from a completely regular arrangement, the other from a completely crowded arrangement. A new diagnostic plot is presented to aid interpretation. Results from some artificial data are studied to survey the properties of both indices for defined patterns of clustering. Indices based on the distance to regularity are powerful at detecting aggregation when several clusters are present; those based on the distance to crowding have the power to detect aggregation only when a single cluster is present. Methods are presented to estimate the typical cluster size and intercluster distance, suitable for data from sample units in the form of a contiguous grid. Examples are given for cyst-nematode field data and plant virus disease.

Modelling risk from a disease in time and space.

Abstract: This paper combines existing models for longitudinal and spatial data in a hierarchical Bayesian framework, with particular emphasis on the role of time- and space-varying covariate effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by a tentative re-analysis of Ohio lung cancer data 1968-1988. Two approaches that adjust for unmeasured spatial covariates, particularly tobacco consumption, are described. The first includes random effects in the model to account for unobserved heterogeneity; the second adds a simple urbanization measure as a surrogate for smoking behaviour. The Ohio data set has been of particular interest because of the suggestion that a nuclear facility in the southwest of the state may have caused increased levels of lung cancer there. However, we contend here that the data are inadequate for a proper investigation of this issue.

Incremental distance join algorithms for spatial databases

Abstract: Two new spatial join operations, distance join and distance semi-join, are introduced where the join output is ordered by the distance between the spatial attribute values of the joined tuples. Incremental algorithms are presented for computing these operations, which can be used in a pipelined fashion, thereby obviating the need to wait for their completion when only a few tuples are needed. The algorithms can be used with a large class of hierarchical spatial data structures and arbitrary spatial data types in any dimensions. In addition, any distance metric may be employed. A performance study using R-trees shows that the incremental algorithms outperform non-incremental approaches by an order of magnitude if only a small part of the result is needed, while the penalty, if any, for the incremental processing is modest if the entire join result is required.

Geostatistics and remote sensing

Abstract: In geostatistics, spatial autocorrelation is utilized to estimate optimally local values from data sampled elsewhere. The powerful synergy between geostatistics and remote sensing went unrealized until the 1980s. Today geostatistics are used to explore and describe spatial variation in remotely sensed and ground data; to design optimum sampling schemes for image data and ground data; and to increase the accuracy with which remotely sensed data can be used to classify land cover or estimate continuous variables. This article introduces these applications and uses two examples to highlight characteristics that are common to them all. The article concludes with a discussion of conditional simulation as a novel geostatistical technique for use in remote sensing.

Collecting Spatial Data: Optimum Design of Experiments for Random Fields

Abstract: Fundamentals of Spatial Statistics.- Fundamentals of Experimental Design.- Exploratory Designs.- Designs for Spatial Trend Estimation.- Design and Dependence.- Multipurpose Designs.

Imprecision in Finite Resolution Spatial Data

Abstract: An important component of spatial data quality is the imprecision resulting from the resolution at which data are represented. Current research on topics such as spatial data integration and generalization needs to be well-founded on a theory of multi-resolution. This paper provides a formal framework for treating the notion of resolution and multi-resolution in geographic spaces. It goes further to develop an approach to reasoning with imprecision about spatial entities and relationships resulting from finite resolution representations. The approach is similar to aspects of rough and fuzzy set theories. The paper concludes by providing the beginnings of a geometry of vague spatial entities and relationships.

Memory for Spatial Location: Role of the Hippocampus in Mediating Spatial Pattern Separation

Abstract: A paradigm based on measuring short-term memory for spatial location information as a function of spatial similarity between distal cues was developed to examine the role of pattern separation in the modulation of short-term memory for spatial information. A delayed-match-to-sample for spatial location task using a dryland version of the Morris water maze was used to assess spatial pattern separation in male Long–Evans rats. In the sample phase, animals were trained to displace an object that covered a baited food well in one of 15 spatial locations along a row of food wells perpendicular to a start box. In the ensuing choice phase, the animal was allowed to choose between two objects identical to the sample phase object. One covered the same baited food well as did the object in the study phase (correct choice), and another foil object (incorrect choice) covered a different unbaited food well along the row of wells. Five spatial separations were randomly used to separate the correct object from the foil object. After reaching a criterion before the operation, animals were given either hippocampal or cortical control lesions. In trials after the operation, control animals matched their performance before the operation across all spatial separations. In contrast, hippocampal-lesioned animals displayed impairments across all spatial separations with the exception of the longest (105 cm) spatial separation. The results suggest that the hippocampus may serve to separate incoming spatial information by temporarily storing one place separate from another. It is proposed that hippocampal lesions decrease efficiency in pattern separation, resulting in impairments in trials with increased spatial similarity among working-memory representations.

Selective Materialization: An Efficient Method for Spatial Data Cube Construction

Abstract: On-line analytical processing (OLAP) has gained its popularity in database industry. With a huge amount of data stored in spatial databases and the introduction of spatial components to many relational or object-relational databases, it is important to study the methods for spatial data warehousing and on-line analytical processing of spatial data. In this paper, we study methods for spatial OLAP, by integration of nonspatial on-line analytical processing (OLAP) methods with spatial database implementation techniques. A spatial data warehouse model, which consists of both spatial and nonspatial dimensions and measures, is proposed. Methods for computation of spatial data cubes and analytical processing on such spatial data cubes are studied, with several strategies proposed, including approximation and partial materialization of the spatial objects resulted from spatial OLAP operations. Some techniques for selective materialization of the spatial computation results are worked out, and the performance study has demonstrated the effectiveness of these techniques.

Natural-Language Spatial Relations Between Linear and Areal Objects: The Topology and Metric of English- Language Terms *

Abstract: relations are the basis for many selections users perform when they query geographic information systems (GISs). Although such query languages use natural-language-like terms, the formal definitions of those spatial relations rarely reflect the same meaning people would apply when they communicate among each other. To bridge the gap between computational models for spatial relations and people's use of spatial terms in their natural languages, a model for the geometry of spatial relations was calibrated for a set of 59 English-language spatial predicates. The model distinguishes topological and metric properties. The calibration from sketches that were drawn by 34 human subjects identifies ten groups of spatial terms with similar properties and provides a mapping from spatial terms onto significant geometric parameters and their values. The calibration's results reemphasize the importance of topological over metric properties in the selection of English-language spatial terms. The model provides a basis for high-level spatial query languages that exploit natural-language terms and serves as a model for processing such queries.

Local spatial autocorrelation characteristics of remotely sensed imagery assessed with the Getis statistic

Abstract: To enable data collection by remote sensing instruments the Earth's continuously varying surface is regularized into a grid of consistently sized and shaped pixels. Remotely sensed data, as a result, is often highly spatially autocorrelated. The characterization and quantification of spatial autocorrelation can provide a valuable source of information for both theoretical and applied studies in remote sensing. Consequently, various techniques have been developed to assess the spatial dependence characteristics of remotely sensed imagery. Typically such techniques yield summary measures which enable the identification of distinctive regions of spatial dependency within the image. In contrast, local indicators of spatial association (LISA) measures, focus upon variations within the regions of spatial dependence. This letter provides an introduction to one such LISA measure, the Getis statistic, and indicates how it may be used in remote sensing research and applications as a complement to existing approache...

Spatial Nonstationarity and Autoregressive Models

Abstract: Until relatively recently, the emphasis of spatial analysis was on the investigation of global models and global processes. Recent research, however, has tended to explore exceptions to general processes, and techniques have been developed which have as their focus the investigation of spatial variations in local relationships. One of these techniques, known as geographically weighted regression (GWR), developed by the authors is used here to investigate spatial variations in spatial association. The particular framework in which spatial association is examined here is the spatial autoregressive model of Ord, although the technique can easily be applied to any form of spatial autocorrelation measurement. The conceptual and theoretical foundations of GWR applied to the Ord model are followed by an empirical example which uses data on owner-occupation in the housing market of Tyne and Wear in northeast England where the problems of relying on global models of spatial association are demonstrated. This empir...

R-trees. a dynamic index structure for spatial searching

Abstract: In order to handle spatial data efficiently, as required in computer aided design and geo-data applications, a database system needs an mdex mechanism that ti help it retrieve data items quickly accordmg to their spatial locations However, traditional mdexmg methods are not well suited to data oblects of non-zero size located m multidimensional spaces In this paper we describe a dynarmc mdex structure called an R-tree winch meets this need, and give algorithms for searching and updatmg it. We present the results of a series of tests which indicate that the structure performs well, and conclude that it is useful for current database systems m spatial applications

GIS Research Infrastructure for Spatial Analysis of Real Estate Markets

Abstract: This article outlines the type of research infrastructure needed to complement existing commercial Geographic Information System (GIS) environments to perform state-of-the-art spatial analysis of r...

Spatial information retrieval from remote-sensing images. II. Gibbs-Markov random fields

Abstract: For pt.I see ibid., p.1431-45 (1998). The authors present Gibbs-Markov random field (GMRF) models as a powerful and robust descriptor of spatial information in typical remote-sensing image data. This class of stochastic image models provides an intuitive description of the image data using parameters of an energy function. For the selection among several nested models and the fit of the model, the authors proceed in two steps of Bayesian inference. This procedure yields the most plausible model and its most likely parameters, which together describe the image content in an optimal way. Its additional application at multiple scales of the image enables the authors to capture all structures being present in complex remote-sensing images. The calculation of the evidences of various models applied to the resulting quasicontinuous image pyramid automatically detects such structures. The authors present examples for both synthetic aperture radar (SAR) and optical data.

Spatial information retrieval from remote-sensing images-Part I: Information theoretical perspective

Abstract: Automatic interpretation of remote-sensing (RS) images and the growing interest for query by image content from large remote-sensing image archives rely on the ability and robustness of information extraction from observed data. In Parts I and II of this article, we turn the attention to the modern Bayesian way of thinking and introduce a pragmatic approach to extract structural information from RS images by selecting from a library of priori models those which best explain the structures within an image. Part I introduces the Bayesian approach and defines the information extraction as a two-level procedure: 1) model fitting, which is the incertitude alleviation over the model parameters, and 2) model selection, which is the incertitude alleviation over the class of models. The superiority of the Bayesian results is commented from an information theoretical perspective. The theoretical assay concludes with the proposal of a new systematic method for scene understanding from RS images: search for the scene that best explains the observed data. The method is demonstrated for high accuracy restoration of synthetic aperture radar (SAR) images with emphasis on new optimization algorithms for simultaneous model selection and parameter estimation. Examples are given for three families of Gibbs random fields (GRF) used as prior model libraries. Part II expands in detail on the information extraction using GRF's at one and at multiple scales. Based on the Bayesian approach, a new method for optimal joint scale and model selection is demonstrated. Examples are given using a nested family of GRF's utilized as prior models for information extraction with applications both to SAR and optical images.

Algorithms for characterization and trend detection in spatial databases

Abstract: The number and the size of spatial databases, e.g. for geo-marketing, traffic control or environmental studies, are rapidly growing which results in an increasing need for spatial data mining. In this paper, we present new algorithms for spatial characterization and spatial trend analysis. For spatial characterization it is important that class membership of a database object is not only determined by its non-spatial attributes but also by the attributes of objects in its neighborhood. In spatial trend analysis, patterns of change of some non-spatial attributes in the neighborhood of a database object are determined. We present several algorithms for these tasks. These algorithms were implemented within a general framework for spatial data mining providing a small set of database primitives on top of a commercial spatial database management system. A performance evaluation using a real geographic database demonstrates the effectiveness of the proposed algorithms. Furthermore, we show how the algorithms can be combined to discover even more interesting spatial knowledge.

The DEDALE system for complex spatial queries

Abstract: This paper presents DEDALE, a spatial database system intended to overcome some limitations of current systems by providing an abstract and non-specialized data model and query language for the representation and manipulation of spatial objects. DEDALE relies on a logical model based on linear constraints, which generalizes the constraint database model of [KKR90]. While in the classical constraint model, spatial data is always decomposed into its convex components, in DEDALE holes are allowed to fit the need of practical applications. The logical representation of spatial data although slightly more costly in memory, has the advantage of simplifying the algorithms. DEDALE relies on nested relations, in which all sorts of data (thematic, spatial, etc.) are stored in a uniform fashion. This new data model supports declarative query languages, which allow an intuitive and efficient manipulation of spatial objects. Their formal foundation constitutes a basis for practical query optimization. We describe several evaluation rules tailored for geometric data and give the specification of an optimizer module for spatial queries. Except for the latter module, the system has been fully implemented upon the O2 DBMS, thus proving the effectiveness of a constraint-based approach for the design of spatial database systems.

Metric details for natural-language spatial relations

Abstract: Spatial relations often are desired answers that a geographic information system (GIS) should generate in response to a user's query. Current GIS's provide only rudimentary support for processing and interpreting natural-language-like spatial relations, because their models and representations are primarily quantitative, while natural-language spatial relations are usually dominated by qualitative properties. Studies of the use of spatial relations in natural language showed that topology accounts for a significant portion of the geometric properties. This article develops a formal model that captures metric details for the description of natural-language spatial relations. The metric details are expressed as refinements of the categories identified by the 9-intersection, a model for topological spatial relations, and provide a more precise measure than does topology alone as to whether a geometric configuration matches with a spatial term or not. Similarly, these measures help in identifying the spatial term that describes a particular configuration. Two groups of metric details are derived: splitting ratios as the normalized values of lengths and areas of intersections; and closeness measures as the normalized distances between disjoint object parts. The resulting model of topological and metric properties was calibrated for 64 spatial terms in English, providing values for the best fit as well as value ranges for the significant parameters of each term. Three examples demonstrate how the framework and its calibrated values are used to determine the best spatial term for a relationship between two geometric objects.

Testing for Spatial Autocorrelation in Ecological Studies

Abstract: We describe a statistical method appropriate for the analysis of spatial autocorrelation in data varying in time as well as space. In particular, the technique was developed lo address the issue of geographic synchrony in ecological variables that may change markedly from year to year such as population density of animals or seed production of trees. The method yields ‘modified correlograms” that test for significant autocorrelation between sites located within any given range of distances apart. This technique facilitates detecting and understanding spatial processes m a variety of ecological phenomena, including testing the plausibility of causational hypotheses using cross-correlational analyses. Several examples are discussed, including population densities of squirrels in Finland, winter densities of two hawk species in California, and acorn production and radial growth by individual blue oak Quercus douglasii trees in central coastal California.

Practical Handbook of Spatial Statistics

Abstract: Introduction: The Need for Spatial Statistics, DA Griffith Components of Geographic Information and Analysis Background: The Importance of Locational Information Background: Statistical Estimator Properties Organization of the Book Summary References Visualization of Spatial Dependence: An Elementary View of Spatial Autocorrelation, IR Vasiliev Editorial Note Introduction The Spatial Mean and Other Basic Concepts Spatial Autocorrelation Map Complexity Map Representations of Changes in Space and Time Summary: Rules-of-Thumb for Spatial Autocorrelation References Spatial Sampling, SV Stehman and WS Overton Introduction Spatial Universes and Populations Sampling Fundamentals Sampling a Continuous Universe Sampling Spatially Distributed Objects via Areal Samples of the Continuous Universe Inference in Spatial Sampling Applications of Spatial Sampling Empirical Evaluation of Sampling Strategies Summary References Some Guidelines for Specifying the Geopraphic Weights Matrix Contained in Spatial Statistical Models, DA Griffith Introduction Background Evaluation Criteria Rules-of-Thumb Implications References Aggregation Effects in Geo-Referenced Data, DWS Wong Spatial Dependency of Spatial Data Analysis Source of the MAUP: Spatial Dependence and the Averaging Process General Impacts of the MAUP on Spatial Data Approaches to "Solving" the MAUP Guidelines for Analyzing Data From Different Scales Conclusions References Implementing Spatial Statistics on Parallel Computers, B Li Introduction A Brief Introduction to Parallel Processing Software Models for Parallel Processing Parallel Implementations Performance Summary References Appendix I: Test Statistics for Spatial Autocorrelation Coefficients Appendix II: Source Code Spatial Statistics and GIS Applied to Internal Migration in Rwanda, Central Africa, DG Brown Introduction Study Area Database Description GIS Data Management Traditional Regression Analysis Mapping Residuals Spatial Statistical Model Conclusions References Spatial Statistical Modeling of Regional Fertility Rates: A Case Study of He-Nan Province, China, HM Feng Introduction Preliminary Considerations of the Spatial Statistical Application The Dataset and the Model Specification Explicit Variables A Classical Linear Regression Model of Explicit Variables In Search of a Spatial Pattern Interpretation and Conclusions References Appendix I: Description of Data Set Appendix II: Maps Appendix III: Scatter-Plots Spatial Statistical/Econometric Versions of Simple Urban Population Density Models, DA Griffith and A Can Introduction and Background The Selected Metropolitan Landscapes Preliminaries for Estimating the Autoregressive Model The Estimated Population Density Models Implementation Findings References Spatial Statistics for Analysis of Variance of Agronomic Field Trials, DS Long The Example Data Set Goals of the Case Study The Autoregressive Response Model Calculating the Moran Coefficient Calculating the Necessary Eigenvalues Estimating the Jacobian Term Estimating an Autoregressive Response Model Comparison of AR-based ANOVA and Conventional ANOVA Conclusions Acknowledgments References Index

Scale detection in real and artificial landscapes using semivariance analysis

Abstract: Semivariance analysis is potentially useful to landscape ecologists for detecting scales of variability in spatial data. We used semivariance analysis to compare spatial patterns of winter foraging by large ungulates with those of environmental variables that influence forage availability in northern Yellowstone National Park, Wyoming. In addition, we evaluated (1) the ability of semivariograms to detect known scales of variability in artificial maps with one or more distinct scales of pattern, and (2) the influence of the amount and spatial distribution of absent data on semivariogram results and interpretation. Semivariograms of environmental data sets (aspect, elevation, habitat type, and slope) for the entire northern Yellowstone landscape clearly identified the dominant scale of variability in each map layer, while semivariograms of ungulate foraging data from discontinuous study areas were difficult to interpret. Semivariograms of binary maps composed of a single scale of pattern showed clear and interpretable results: the range accurately reflected the size of the blocks of which the maps were constructed. Semivariograms of multiple scale maps and hierarchical maps exhibited pronounced inflections which could be used to distinguish two or three distinct scales of pattern. To assess the sensitivity of semivariance analysis to absent data, often the product of cloud interference or incomplete data collection, we deliberately masked (deleted) portions of continuous northern Yellowstone map layers, using single scale artificial maps as masks. The sensitivity of semivariance analysis to random deletions from the data was related to both the size of the deleted blocks, and the total proportion of the original data set that was removed. Small blocks could be deleted in very high proportions without degrading the semivariogram results. When the size of deleted blocks was large relative to the size of the map, the corresponding variograms became sensitive to the total proportion of data removed: variograms were difficult or impossible to interpret when the proportion of data deleted was high. Despite success with artificial maps, standard semivariance analysis is unlikely to detect multiple scales of pattern in real ecological data. Semivariance analysis is recommended as an effective technique for quantifying some spatial characteristics of ecological data, and may provide insight into the scales of processes that structure landscapes.