Jingxiong Zhang

Scale in Spatial Information and Analysis

Introduction Issue of Scale Models of Scale Scaling Up and Down Book Chapters Geographic Representations Geo-Atoms Geo-Fields Geo-Objects Hierarchical Data Structures Discussion Geospatial Measurements Framework for Spatial Sampling Optical Remote Sensing and Resolution Microwave Remote Sensing and Resolution Discussion Geostatistical Models of Scale Geostatistical Fundamentals and Variograms Variogram Regularization and Deregularization Statistics for Determining Measurement Scales Discussion Lattice Data and Scale Models Lattice Data Spatial Autocorrelation and Its Measures Local Models Discussion Geostatistical Methods for Scaling Kriging Indicator Approaches Upscaling by Block Kriging Downscaling by Area-to-Point Kriging Geostatistical Inverse Modeling Discussion Methods for Scaling Gridded Data Upscaling Downscaling Discussion Multiscale Data Conflation Multivariate Geostatistics Image Fusion Other Multiscale Methods Discussion Scale in Terrain Analysis Digital Elevation Data and Their Scales Terrain Derivatives Models of Scale in Topography Methods for Scaling Terrain Variables Discussion Scale in Area-Class Mapping Area-Class Mapping Spatial Scales and Patterns in Area Classes Scaling Area-Class Information Discussion Information Content Information Theory Information Content in Remotely Sensed Images Image Resolution and Information Content Information Content in Map Data Discussion Uncertainty Characterization Accuracy Metrics and Assessment Geostatistical Approaches to Validation Analytical Approaches to Error Propagation Geostatistical Simulation Discussion Epilogue References Index

Discriminant Models of Uncertainty in Nominal Fields

Despite developments in error modeling in discrete objects and continuous fields, there exist substantial and largely unsolved conceptual problems in the domain of nominal fields. This article explores a novel strategy for uncertainty characterization in spatial categorical information. The proposed strategy is based on discriminant space, which is defined with essential properties or driving processes underlying spatial class occurrences, leading to discriminant models of uncertainty in area classes. This strategy reinforces consistency in categorical mapping by imposing class-specific mean structures that can be regressed against discriminant variables, and facilitates scale-dependent error modeling that can effectively emulate the variation found between observers in terms of classes, boundary positions, numbers of polygons, and boundary network topology. Based on simulated data, comparisons with stochastic simulation based on indicator kriging confirmed the replicability of the discriminant models, which work by determining the mean area classes based on discriminant variables and projecting spatially correlated residuals in discriminant space to uncertainty in area classes.

Geostatistical approaches to conflation of continental snow data.

Information on snow cover extent and mass is important for characterization of hydrological systems at different spatial and temporal scales, and for effective water resources management. This paper explores geostatistics for conflation of ground-measured and passive microwave remotely sensed snow data, here referred to as primary and secondary data, respectively. A modification to conventional cokriging is proposed, which first estimates differenced local means between sparsely distributed primary data and densely sampled secondary data by cokriging, followed by a best linear estimation of the primary variable based on the primary data and bias-corrected secondary data, with variogram models revised in the light of corrections made to the original secondary data. An experiment was carried out with snow depth (SD) data derived from the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) instrument and the World Meteorological Organization (WMO) SD measurement, confirming the effectiveness of the proposed methodology.

Positional accuracy in RPC point determination based on high-resolution imagery

The rational function model (RFM), also known as rational polynomial coefficients (RPCs) or rational polynomial camera (RPC) model, is a generalized sensor model. Different from rigorous sensor model, RFM does not need to obtain the interior and exterior orientation geometry and other physical properties associated with the physical sensor. RFMs were first adopted by Space Imaging company as a replacement for rigorous sensor models, and it drew much attention from the commercial satellite data vendors who rapidly followed the suit in order to protect the confidential information of the sensors. This paper focuses on the solution for rational polynomial coefficients, RFM-based stereo-model reconstitution, and positional accuracy analysis. As RPCs do not have obvious physical meanings and their solution is iterative, analytical approaches to accuracy analysis may not be feasible; computer simulation is thus adopted to quantify accuracy in RPC-determined positional data. The simulation-based strategy is efficient in mapping local features in positional errors, which contain both the systematic and random components.

A discriminant space-based framework for scalable area-class mapping

Earlier research has introduced the concept of discriminant space, which is spanned by the covariates underlying area-class occurrences, for increased consistency, interpretability, and replicability in area-class mapping and uncertainty characterization. While simple univariate cases with b=1 (b being the dimension of the discriminant space) were investigated previously using simulated data, real world applications are usually multivariate with b>1, thus giving rises to the need for developing discriminant models in spaces of higher dimensionality for increased applicability. This paper describes combined use of generalized linear modeling and kriging for area-class mapping, with the former deterministically predicting mean class responses while the latter making use of spatially correlated residuals in the predictive class models. Scalability in area-class mapping is facilitated by flexible implementation of scale-dependent prediction of mean class responses and point- vs. area-support kriging of the residuals. This is followed by an empirical study concerning land cover mapping in central western Montana, which confirmed the effectiveness of the proposed strategy combining regression and kriging for scale-dependent mapping of area classes.

Discriminant models for scaling area-class maps

Earlier research has discussed the concept of discriminant space and its applications in area-class mapping and uncertainty characterization. Both simple univariate cases with b=1 (b being the dimension of the discriminant space) and multivariate cases with b>1 were analyzed with simulated and real data sets, respectively. This paper describes combined use of generalized linear models and kriging for scalable area-class mapping, with the former deterministically predicting mean class responses and the latter making use of spatially correlated residuals in the predictive class models. Scalability in area-class mapping is facilitated by scale-dependent prediction of mean class responses and kriging of the residuals over specific gridding cells. The methodology was implemented with topographic data and Landsat TM imagery concerning land cover mapping in central western Montana, which confirmed the effectiveness of the proposed strategy combining regression and kriging for scalable mapping of area classes.