Showing papers on "Spatial analysis published in 2003"

Hierarchical Modeling and Analysis for Spatial Data

Abstract: OVERVIEW OF SPATIAL DATA PROBLEMS Introduction to Spatial Data and Models Fundamentals of Cartography Exercises BASICS OF POINT-REFERENCED DATA MODELS Elements of Point-Referenced Modeling Spatial Process Models Exploratory Approaches for Point-Referenced Data Classical Spatial Prediction Computer Tutorials Exercises BASICS OF AREAL DATA MODELS Exploratory Approaches for Areal Data Brook's Lemma and Markov Random Fields Conditionally Autoregressive (CAR) Models Simultaneous Autoregressive (SAR) Models Computer Tutorials Exercises BASICS OF BAYESIAN INFERENCE Introduction to Hierarchical Modeling and Bayes Theorem Bayesian Inference Bayesian Computation Computer Tutorials Exercises HIERARCHICAL MODELING FOR UNIVARIATE SPATIAL DATA Stationary Spatial Process Models Generalized Linear Spatial Process Modeling Nonstationary Spatial Process Models Areal Data Models General Linear Areal Data Modeling Exercises SPATIAL MISALIGNMENT Point-Level Modeling Nested Block-Level Modeling Nonnested Block-Level Modeling Misaligned Regression Modeling Exercises MULTIVARIATE SPATIAL MODELING Separable Models Coregionalization Models Other Constructive Approaches Multivariate Models for Areal Data Exercises SPATIOTEMPORAL MODELING General Modeling Formulation Point-Level Modeling with Continuous Time Nonseparable Spatio-Temporal Models Dynamic Spatio-Temporal Models Block-Level Modeling Exercises SPATIAL SURVIVAL MODELS Parametric Models Semiparametric Models Spatio-Temporal Models Multivariate Models Spatial Cure Rate Models Exercises SPECIAL TOPICS IN SPATIAL PROCESS MODELING Process Smoothness Revisited Spatially Varying Coefficient Models Spatial CDFs APPENDICES Matrix Theory and Spatial Computing Methods Answers to Selected Exercises REFERENCES AUTHOR INDEX SUBJECT INDEX Short TOC

Spatial Data Analysis: Theory and Practice

Abstract: Preface Readership Acknowledgements Introduction Part I. The Context for Spatial Data Analysis: 1. Spatial data analysis: scientific and policy context 2. The nature of spatial data Part II. Spatial Data: Obtaining Data And Quality Issues: 3. Obtaining spatial data through sampling 4. Data quality: implications for spatial data analysis Part III. The Exploratory Analysis of Spatial Data: 5. Exploratory analysis of spatial data 6. Exploratory spatial data analysis: visualisation methods 7. Exploratory spatial data analysis: numerical methods Part IV. Hypothesis Testing in the Presence of Spatial Autocorrelation: 8. Hypothesis testing in the presence of spatial dependence Part V. Modeling Spatial Data: 9. Models for the statistical analysis of spatial data 10. Statistical modeling of spatial variation: descriptive modeling 11. Statistical modeling of spatial variation: explanatory modeling Appendices References Index.

Spatial autocorrelation and red herrings in geographical ecology

Abstract: Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates 'red herrings', such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro-scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least-squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north-south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non-detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de-emphasized predictors with strong autocorrelation and long-distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.

Spatial Databases: A Tour

Abstract: 1. Introduction to Spatial Databases. 2. Spatial Concepts and Data Models. 3. Spatial Query Language. 4. Spatial Storage and Indexing. 5. Query Processing and Optimization. 6. Spatial Networks. 7. Introduction to Spatial Data Mining. 8. Trends in Spatial Databases.

Proper multivariate conditional autoregressive models for spatial data analysis.

Abstract: In the past decade conditional autoregressive modelling specifications have found considerable application for the analysis of spatial data. Nearly all of this work is done in the univariate case and employs an improper specification. Our contribution here is to move to multivariate conditional autoregressive models and to provide rich, flexible classes which yield proper distributions. Our approach is to introduce spatial autoregression parameters. We first clarify what classes can be developed from the family of Mardia (1988) and contrast with recent work of Kim et al. (2000). We then present a novel parametric linear transformation which provides an extension with attractive interpretation. We propose to employ these models as specifications for second-stage spatial effects in hierarchical models. Two applications are discussed; one for the two-dimensional case modelling spatial patterns of child growth, the other for a four-dimensional situation modelling spatial variation in HLA-B allele frequencies. In each case, full Bayesian inference is carried out using Markov chain Monte Carlo simulation.

Ecological Scale: Theory and Applications

Abstract: Ferret Releases Net Population Growth Rate Ferret Dispersal Spatial Definition Ferret Reintroduction in South Dakota The Spatial Optimization Model The Black-Footed Ferret: A Case Study Discussion The Modeling Approach Sustainability of Species Richness The Logistic Distribution Transformations Declining Monotonicity of Natural Logarithm Results Allocation Over Time and Space Results Continuous Choice Variables Results The Problem An Example The Model A Cellular Model of Wildlife Population Growth and Dispersal Methods Dynamic Movement Row-Total Variance Reduction An Example Post-Optimization Calculations Simulation Versus Optimization An Adaptive Management Context Synthesis A New Definition for a Regulated Forest Single-Species Emphasis Accounting for Mortality Sensitivity to Planning Horizon Length Sensitivity to Minimum Harvest Age Model Reduction Linear Approximation of Objective Functions A Coastal Douglas-fir Case Study Objective Functions Wildlife Habitat Fragmentation Effects Edge Effects A Cellular Model of Wildlife Habitat Spatial Relationships Static Spatial Relationships A Final Introductory Note Solvability of Nonlinear Programs Solvability of (0-1) Integer Programs Methods Organization Viewpoint Introduction The Problem Pragmatic Approaches to Handling Risk and Uncertainty Discussion Results The Problem An Example Rectangles Circles Optimization Chance Maximization Spatial Autocorrelation Connectivity Theory A Geometric Wildlife Model with Spatial Autocorrelation and Habitat Connectivity Discussion Results The Problem An Example A Cellular Timber Model with Spatial Autocorrelation Approximation of the CDF Total Probability Chance-Maximizing Programming Joint Probability Chance-Maximizing Programming MAXMIN Chance-Maximizing Programming Chance-Maximizing Programs Total Probability Chance Constraint Joint Probability Chance Constraint Individual Chance Constraints Chance-Constrained Programming Spatial Autocorrelation Discussion Results The Problem An Example A Spatial Recreation Allocation Model The Case of More Than One Proposed Site The Travel Cost Model Spatial Supply-Demand Equilibrium: A Recreation Example Discussion Results An Example Spatial Effects A Geometric Model of Wildlife Habitat Spatial Relationships Discussion Results The Problem An Example Wildlife Habitat Size Thresholds Results A Steady-State Example Determining the Optimal Steady State Species Richness Objective Functions Diversity and Sustainability Discussion Results Two Examples The Spatial Optimization Approach A Nested-Schedule Model of Stormflow Discussion Results The Problem An Example The Model A Cellular Model of Pest Management Model Results Ferret Carrying Capacity

Habitat association among Amazonian tree species: a landscape‐scale approach

Abstract: 1: Unravelling which factors affect where tropical trees grow is an important goal for ecologists and conservationists. At the landscape scale, debate is mostly focused on the degree to which the distributions of tree species are determined by soil conditions or by neutral, distance-dependent processes. Problems with spatial autocorrelation, sparse soil sampling, inclusion of species-poor sites with extreme edaphic conditions, and the difficulty of obtaining sufficient sample sizes have all complicated assessments for high diversity tropical forests. 2: We evaluated the extent and pervasiveness of habitat association of trees within a 10 000 km 2 species-rich lowland landscape of uniform climate in south-west Amazonia. Forests growing on two non-flooded landscape units were inventoried using 88 floristic plots and detailed soil analyses, sampling up to 849 tree species. We applied singlespecies and community-level analytical techniques (frequency-distributions of presence records, association analysis, indicator species analysis, ordination, Mantel correlations, and multiple regression of distance matrices) to quantify soil/floristic relationships while controlling for spatial autocorrelation. 3: Obligate habitat-restriction is very rare: among 230 tree species recorded in ≥ 10 localities only five (2.2%) were always restricted to one landscape unit or the other. 4: However, many species show a significant tendency to habitat association. For example, using Monte Carlo randomization tests, of the 34 most dominant species across the landscape the distributions of 26 (76.5%) are significantly related to habitat. We applied density-independent and frequency-independent estimates of habitat association and found that rarer species tend to score higher, suggesting that our full community estimates of habitat association are still underestimated due to the inadequate sampling of rarer species. 5: Community-level floristic variation across the whole landscape is related to the variation in 14 of 16 measured soil variables, and to the geographical distances between samples. 6: Multiple regression of distance matrices shows that 10% of the floristic variation can be attributed to spatial autocorrelation, but even after accounting for this at least 40% is attributable to measured environmental variation. 7: Our results suggest that substrate-mediated local processes play a much more important role than distance-dependent processes in structuring forest composition in Amazonian landscapes.

A Comparison of Urban Mapping Methods Using High-Resolution Digital Imagery

Abstract: Recent advances in digital airborne sensors and satellite platforms make spatially accurate, high-resolution multispectral imagery readily available. These advances provide the opportunity for a host of new applications to address and solve old problems. High-resolution imagery is particularly well suited to urban applications. Previous data sources (such as Landsat TM) did not show the spatial detail necessary to provide many urban planning solutions. This paper provides an overview of a project in which one-meter digital imagery was used to produce a map of pervious and impervious surfaces to be used by the city of Scottsdale, Arizona for storm-water runoff estimation. The increased spatial information in onemeter or less resolution imagery strains the usefulness of image classification using traditional supervised and unsupervised spectral classification algorithms. This study assesses the accuracy of three different methods for extracting land-cover/land-use information from high-resolution imagery of urban environments: (1) combined supervised/ unsupervised spectral classification, (2) raster-based spatial modeling, and (3) image segmentation classification using classification tree analysis. A discussion of the results and relative merits of each method is included.

Erosion models: quality of spatial predictions

Abstract: An overview is given on the predictive quality of spatially distributed runoff and erosion models. A summary is given of the results of model comparison workshops organized by the Global Change and Terrestrial Ecosystems Focus 3 programme, as well as other results obtained by individual researchers. The results concur with the generally held viewpoint in the literature that the predictive quality of distributed models is moderately good for total discharge at the outlet, and not very good for net soil loss. This is only true if extensive calibration is done: uncalibrated results are generally bad. The more simple lumped models seem to perform equally well as the more complex distributed models, although the latter produce more detailed spatially distributed results that can aid the researcher. All these results are outlet based: models are tested on lumped discharge and soil loss or on hydrographs and sedigraphs. Surprisingly few tests have been done on the comparison of simulated and modelled erosion patterns, although this may arguably be just as important in the sense of designing anti-erosion measures and determining source and sink areas. Two studies are shown in which the spatial performance of the erosion model LISEM (Limburg soil erosion model) is analysed. It seems that: (i) the model is very sensitive to the resolution (grid cell size); (ii) the spatial pattern prediction is not very good; (iii) the performance becomes better when the results are resampled to a lower resolution and (iv) the results are improved when certain processes in the model (in this case gully incision) are restricted to so called 'critical areas', selected from the digital elevation model with simple rules. The difficulties associated with calibrating and validating spatially distributed soil erosion models are, to a large extent, due to the large spatial and temporal variability of soil erosion phenomena and the uncertainty associated with the input parameter values used in models to predict these processes. They will, therefore, not be solved by constructing even more complete, and therefore more complex, models. However, the situation may be improved by using more spatial information for model calibration and validation rather than output data only and by using 'optimal' models, describing only the dominant processes operating in a given landscape.

Spatial analysis of employment and population density: the case of the agglomeration of dijon, 1999

Abstract: The aim of this paper is to analyze the intra-urban spatial distributions of population and employment in the agglomeration of Dijon (regional capital of Burgundy, France). We study whether this agglomeration has followed the general tendency of job decentralization observed in most urban areas or whether it is still characterized by a monocentric pattern. In that purpose, we use a sample of 136 observations at the communal and at the IRIS (infra-urban statistical area) levels with 1999 census data and the employment database SIRENE (INSEE). First, we study the spatial pattern of total employment and employment density using exploratory spatial data analysis. Apart from the CBD, few IRIS are found to be statistically significant, a result contrasting with those found using standard methods of subcenter identification with employment cut-offs. Next, in order to examine the spatial distribution of residential population density, we estimate and compare different specifications: exponential negative, spline- exponential and multicentric density functions. Moreover, spatial autocorrelation, spatial heterogeneity and outliers are controlled for by using the appropriate maximum likelihood, generalized method of moments and Bayesian spatial econometric techniques. Our results highlight again the monocentric character of the agglomeration of Dijon.

GIS and spatial data analysis: Converging perspectives

Abstract: This article identifies some of the important developments in GIS and spatial data analysis since the early 1950s. Although GIS and spatial data analysis started out as two more or less separate areas of research and application, they have grown closer together over time. We argue that the two areas meet in the field of geographic information science, with each supporting and adding value to the other. The article starts off providing a critical retrospective of developments over the past 50 years. Subsequently, we reflect on current challenges and speculate about the future. Finally, we comment on the potential for convergence of developments in GIS and spatial data analysis under the rubric of geographic information science (GIScience).

Representation and Spatial Analysis in Geographic Information Systems

Abstract: A common—perhaps modal—representation of geography in spatial analysis and geographic information systems is native (unexamined) objects interacting based on simple distance and connectivity relationships within an empty Euclidean space. This is only one possibility among a large set of geographic representations that can support quantitative analysis. Through the vehicle of GIS, many researchers are adopting this representation without realizing its assumptions or its alternatives. Rather than locking researchers into a single representation, GIS could serve as a toolkit for estimating and exploring alternative geographic representations and their analytical possibilities. The article reviews geographic representations, their associated analytical possibilities and relevant computational tools in the combined spatial analysis and GIScience literatures. The discussion identifies several research and development frontiers, including analytical gaps in current GIS software.

Spatial Information Theory: Foundations of Geographic Informa­tion Science

Abstract: Ontologies of Space and Time.- Desiderata for a Spatio-temporal Geo-ontology.- Scale in Object and Process Ontologies.- Landscape Categories in Yindjibarndi: Ontology, Environment, and Language.- Layers: A New Approach to Locating Objects in Space.- Reasoning about Distances and Directions.- Spatial Reasoning about Relative Orientation and Distance for Robot Exploration.- Structuring a Wayfinder's Dynamic Space-Time Environment.- Systematic Distortions in Cognitive Maps: The North American West Coast vs. the (West) Coast of Israel.- Spatial Reasoning: Shapes and Diagrams.- Tripartite Line Tracks Qualitative Curvature Information.- Linearized Terrain: Languages for Silhouette Representations.- Maintaining Spatial Relations in an Incremental Diagrammatic Reasoner.- Computational Approaches.- MAGS Project: Multi-agent GeoSimulation and Crowd Simulation.- "Simplest" Paths: Automated Route Selection for Navigation.- A Classification Framework for Approaches to Achieving Semantic Interoperability between GI Web Services.- Reasoning about Regions.- Relative Adjacencies in Spatial Pseudo-Partitions.- A Geometry for Places: Representing Extension and Extended Objects.- Intuitive Modelling of Place Name Regions for Spatial Information Retrieval.- Convexity in Discrete Space.- Vagueness.- Stratified Rough Sets and Vagueness.- Communicating Vague Spatial Concepts in Human-GIS Interactions: A Collaborative Dialogue Approach.- Visualization.- Wayfinding Choremes.- Testing the First Law of Cognitive Geography on Point-Display Spatializations.- Constructing Semantically Scalable Cognitive Spaces.- Landmarks and Wayfinding.- Route Adaptive Selection of Salient Features.- Referring to Landmark or Street Information in Route Directions: What Difference Does It Make?.- Extracting Landmarks with Data Mining Methods.- Visual Attention during Route Learning: A Look at Selection and Engagement.

Generalized common spatial factor model

Abstract: There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.

Soil sampling strategies for spatial prediction by correlation with auxiliary maps

Abstract: The paper evaluates spreading of observations in feature and geographical spaces as a key to sampling optimisation for spatial prediction by correlation with auxiliary maps. Although auxiliary data are commonly used for mapping soil variables, problems associated with the design of sampling strategies are rarely examined. When generalised least-squares estimation is used, the overall prediction error depends upon spreading of points in both feature and geographical space. Allocation of points uniformly over the feature space range proportionally to the distribution of predictor (equal range stratification, or ER design) is suggested as a prudent sampling strategy when the regression model between the soil and auxiliary variables is unknown. An existing 100-observation sample from a 50 by 50 km soil survey in central Croatia was used to illustrate these concepts. It was re-sampled to 25-point datasets using different experimental designs: ER and 2 response surface designs. The designs were compared for their performance in predicting soil organic matter from elevation (univariate example) using the overall prediction error as an evaluation criterion. The ER design gave overall prediction error similar to the minmax design, suggesting that it is a good compromise between accurate model estimation and minimisation of spatial autocorrelation of residuals. In addition, the ER design was extended to the multivariate case. Four predictors (elevation, temperature, wetness index, and NDVI) were transformed to standardised principal components. The sampling points were then assigned to the components in proportion to the variance explained by a principal component analysis and following the ER design. Since stratification of the feature space results in a large number of possible points in each cluster, the spreading in geographical space can also be maximised by selecting the best of several realisations.

Spatial Autocorrelation Or Model Misspecification

Abstract: A Monte Carlo experiment illustrates one of the pitfalls of spatial modeling. Specification tests indicate spatial autocorrelation when functional form misspecification is actually the only problem with the model. Incorrect functional forms and omitted variables that are correlated over space produce spurious spatial autocorrelation.

Developing local measures of spatial association for categorical data

Abstract: This paper describes a procedure for extending local statistics to categorical spatial data. The approach is based on the notion that there are two fundamental characteristics of categorical spatial data; composition and configuration. Further, it is argued that, when considered locally, the latter should be measured conditionally with respect to the former. These ideas are developed for binary, gridded data. Local composition is measured by counting the numbers of cells of a particular type, while local configuration is measured by join counts. The approach is illustrated using a small, empirical data set and an ad hoc procedure is developed to deal with the impact of global spatial autocorrelation on the local statistics.

Spatial Statistics in the Presence of Location Error with an Application to Remote Sensing of the Environment

Abstract: Techniques for the analysis of spatial data have, to date, tended to ignore any effect caused by error in specifying the spatial locations at which measurements are recorded. This paper reviews the methods for adjusting spatial inference in the presence of data-location error, particularly for data that have a continuous spatial index (geostatistical data). New kriging equations are developed and evaluated based on a simulation experiment. They are also applied to remote-sensing data from the Total Ozone Mapping Spectrometer instrument on the Nimbus-7 satellite, where the location error is caused by assignment of the data to their nearest grid-cell centers. The remote-sensing data measure total column ozone (TCO), which is important for protecting the Earth's surface from ultraviolet and other radiation.

Spatial cognition III: Routes and navigation, human memory and learning, spatial representation and spatial learning

Abstract: Routes and Navigation.- Navigating by Mind and by Body.- Pictorial Representations of Routes: Chunking Route Segments during Comprehension.- Self-localization in Large-Scale Environments for the Bremen Autonomous Wheelchair.- The Role of Geographical Slant in Virtual Environment Navigation.- Granularity Transformations in Wayfinding.- A Geometric Agent Following Route Instructions.- Cognition Meets Le Corbusier - Cognitive Principles of Architectural Design.- Human Memory and Learning.- The Effect of Speed Changes on Route Learning in a Desktop Virtual Environment.- Is It Possible to Learn and Transfer Spatial Information from Virtual to Real Worlds?.- Acquisition of Cognitive Aspect Maps.- How Are the Locations of Objects in the Environment Represented in Memory?.- Priming in Spatial Memory: A Flow Model Approach.- Context Effects in Memory for Routes.- Spatial Representation.- Towards an Architecture for Cognitive Vision Using Qualitative Spatio-temporal Representations and Abduction.- How Similarity Shapes Diagrams.- Spatial Knowledge Representation for Human-Robot Interaction.- How Many Reference Frames?.- Motion Shapes: Empirical Studies and Neural Modeling.- Use of Reference Directions in Spatial Encoding.- Spatial Reasoning.- Reasoning about Cyclic Space: Axiomatic and Computational Aspects.- Reasoning and the Visual-Impedance Hypothesis.- Qualitative Spatial Reasoning about Relative Position.- Interpretation of Intentional Behavior in Spatial Partonomies.

Spatial Effects within the Agricultural Land Market in Northern Ireland

Abstract: The importance of dealing properly with spatial effects, such as spatial autocorrelation, in cross-sectional econometric estimation has become more widely recognised in recent years. Spatial autocorrelation is similar in many ways to serial correlation, but while the latter is ordered on a one-dimensional time axis, the former is ordered in two dimensions. The multi-directional nature of spatial dependence means that specialised techniques are needed for diagnostic testing and estimation purposes. This paper uses these specialised diagnostics to test for spatial effects within a hedonic pricing study of the agricultural land market. The tests indicate that spatial autocorrelation (in the form of spatial lag dependence) and spatially distinct sub-markets (or spatial heterogeneity) are present. Ignoring these effects in the estimation process is likely to lead to biased parameter estimates. Consequently, we re-specify the hedonic model to allow for these spatial effects. The presence of spatial lag dependence suggests that there is circularity of price setting within the agricultural land market. This means that agricultural land prices are not solely determined by the inherent characteristics of the land, but tend to reflect also the average local price per acre.

A comparison of stochastic models for spatial rainfall downscaling

Abstract: [1] We explore the performance of three types of stochastic models used for spatial rainfall downscaling and assess their ability to reproduce the statistics of precipitation fields observed during the GATE radar experiment. We consider a bounded multifractal cascade, an autoregressive linear process passed through a nonlinear static filter (sometimes called a meta-Gaussian model), and a model based on the presence of individual rainfall cells with power law profile. As test statistics we use the low-order moments of the amplitude distribution, the distribution of generalized fractal dimensions, the generalized scaling exponents, the slope of the power spectrum, and the properties of the spatial autocorrelation. The results of the analysis indicate that all models provide, on average, a satisfactory representation of the statistical properties of the GATE rainfall fields (including the anomalous scaling behavior), with a slightly better performance of the model based on individual rainfall cells. All models, however, display large scatter in the field-to-field comparison with the data. These results indicate that data analysis alone does not allow, at the moment, for preferring one downscaling approach over another.

Towards unified 3D city models

Abstract: An increasing number of municipalities decide nowadays to build up 3D city models. Often the main purpose of such a model is to support urban planning processes. However, in most cases this support currently is restricted to the visualization of virtual scenes. The first reason is that there are still no commercial 3D geoinformation systems available. Thus, city models typically are implemented on top of CAD systems or visualization software which all offer only limited modeling capabilities. The second reason is that there does not exist a standard for 3D city models yet. Only few investigations about multifunctional and multiscale modeling, storage and analysis have been carried out so far. In this paper we propose a unified model for the representation of spatial objects in 3D city and regional models. It constitutes a base schema providing patterns for application specific 3D models. It is shown how real world objects are represented by features with geometric, topological and thematic (i.e. non-spatial) properties. We explicitly cope with the problem of multiscale representations. A special level-detail-of-relation between features and their geometry is introduced ensuring spatial consistency between 3D models at different scales. Furthermore, issues concerning the integration of features below surface with the digital terrain model are discussed. Finally, we show how interoperability at system level can be achieved by mapping the proposed model to GML3, the new standard for the representation and exchange of spatial data developed by the OpenGIS Consortium.