Multiscale Raster Map Analysis for Sustainble Environment and Development A Research and Outreach Prospectus of Advanced Mathematical, Statistical and Computational Approaches Using Remote Sensing Data. Development and Implementation of a Prototype and user-friendly MARMAP system. Remote Sensing Application, Technology and Education for Multiscale Advanced Raster Map Analysis Program.

Consider a 21st century digital government scenario of the following nature: What message does a remote sensing-derived land cover land use map have about the large landscape it represents? And at what scale and at what level of detail? Does the spatial pattern of the map reveal any societal, ecological, environmental condition of the landscape? And therefore can it be an indicator of change?

Consider a 21st century digital government scenario of the following nature: How do you automate the assessment of the spatial structure and behavior of change to discover critical areas, hot spots, and their corridors? Is the map accurate? How accurate is it? How do you assess the accuracy of the map? Of the change map over time for change detection?

Consider a 21st century digital government scenario of the following nature What are the implications of the kind and amount of change and accuracy on what matters, whether climate change, carbon emission, water resources, urban sprawl, biodiversity, indicator species, or early warning, or others. And with what confidence, even with a single map/change-map?

The needed partnership research is expected to find answers to these questions and a few more that involve multicategorial raster maps based on remote sensing and other geospatial data. It is also expected to design a prototype and user-friendly advanced raster map analysis system for digital governance.

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Partnership Research Issues

Geospatial Cell-based Data Kinds of Data Cell as a Unit (Regular grid layout) –Categorical –Ordinal –Numerical –Multivariate Numerical Cell as an Object (Irregular cell sizes and shapes) –Partially Ordered –Ordinal –Numerical –Multivariate Numerical

Approaches to Research Issues

Landscape Pattern Extraction Spectral data Empirical extraction Thematic data Empirical extraction Spectral data Model-based extraction Thematic data Model-based extraction

HMTM Model Hierarchical Transitions Model generates a hierarchical sequence of raster maps, all having the same spatial extent Hierarchical Level 0 Hierarchical Level 1 Hierarchical Level 2

Assigning Categories to Pixels Assignment at coarsest scale is a random draw from the marginal land-cover distribution:

Assigning Categories to Pixels Assignment at finer scales is via k by k row stochastic matrices G i Mother cell4 daughter cells The transition is determined by 4 draws from the ith row of G:

HMTM Model Fitting One matrix G for each transition in the hierarchy Estimated recursively from the auto-association matrices: Only matrix algebra and eigen-decomposition required

HMTM Simulation Alias-Urn Methods Quadtree Ordering of Pixels Very Fast

Applications of HMTM Model Fragmentation Profiles –Model predicted profiles –Confidence bands Variability of Landscape Metrics –Fragstats –Perimeter-Area exponents –Patch Structure

Applications of HMTM Model Self-Similarity –HMTM definition ( transition matrices G equal) –Formal Hypothesis Tests Parameter Reduction –Equally-spaced Eigenvalues

Applications of HMTM Model Eigenvectors as Landscape Metrics –Marginal land-cover distribution –Orthogonality (PCA) –Contrasts on land-cover categories

MARMAP System Partnership A primary purpose of MARMAP System Partnership is to develop sound methodology and appropriate software for the quantitative analysis and interpretation of multi- categorical raster maps and cellular surfaces (inferential geospatial informatics) involving landscape pattern analysis, multiscale landcover landuse change detection, accuracy assessment, critical area detection and delineation, disease mapping and geographic surveillance, prioritization and ranking without having to integrate multiple indicators, and a few more. It will be nice to see you participate in one capacity or the other.

Springer Monograph Series in Environmental and Ecological Statistics Series Editor: G. P. Patil The proposed series will be devoted to the cross-disciplinary subject area of environmental and ecological statistics discussing important topics and themes in statistical ecology, environmental statistics, and relevant risk analysis. Emphasis will be on the clarity of exposition of applied mathematical statistics, statistical methodology, data interpretation and improvement for future use, with a view to advance statistics for environment, ecology, and environmental health, and to advance environmental theory and practice using valid statistics. Besides clarity of exposition, a single most important criterion for publication of a monograph will be the appropriateness of the statistical methodology to the particular environmental and ecological problem area, within the context of contemporary environmental issues and the associated statistical tools, concepts, and methods.

Environmental and Ecological Statistics An international forum for cross-disciplinary discussion for statistical ecology and environmental statistics Editor-in-Chief Ganapati P. Patil Associate Editor Timothy Gregoire Managing Editor Stephen Rathbun Editorial Secretary Barbara Freed Environmental and Ecological Statistics publishes papers on practical applications of statistics and related quantitative methods to environmental science addressing contemporary issues. The emphasis is on applied mathematical statistics, statistical methodology and data interpretation and improvement for future use with a view to advance statistics for environment. Ecology and environmental health, and to advance environmental and ecological theory and practice using valid statistics.