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Guarino for their prompt responses to my questions. Third, to all my colleagues and friends in the Department of Spatial Information Science I would like to thank you for sharing the good and bad moments of my study life. I feel fortunate for having being part of a friendly environment that made my Ph.D. program an enjoyable and unforgettable experience. iii Fourth, I thank the support and funding from the University of Concepcin, Chile, and the initial funding from the Fulbright foundation. Further funding from the National Center of Geographic Information and Analysis, the National Imagery and Mapping Agency, and Lockheed Martin are gratefully acknowledged. Most important, I thank the continuous support, love, and patience of Christian and Alicia. This long journey would not have been possible without them. iv Table of Contents Acknowledgments .......................................................................................................ii List of Figu

Environmental modeling with GIS: A strategy for dealing with spatial continuity by Karen Kathleen Kemp Linking a GIS to a spatially distributed, physically-based environmental model offers many advantages. However, the implementation of such linkages is generally problematic. Many problems arise because the relationship between the reality being represented by the mathematical model and the data model used to organize the spatial data in the GIS has not been rigorously defined. In particular, while many environmental models are based on theories that assume continuity and incorporate physical fields as independent variables, current GISs can only represent continuous phenomena in a variety of discrete data models. This document develops and outlines a strategy in which field variables are used to enable modelers to work directly with the spatial data as spatially continuous phenomena. Field variables are declared like other data types in standard computing languages. Specifications...

This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church’s (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme).

Discussion of geographic information systems (GIS) has taken professional and academic planning forums by storm within the last decade. Examples of fundamental organizational topics for understanding a GIS include system definition (Leno 1989), improved

In 1999, the NASA Jet Propulsion Lab presented a proposal for a six satellite navigation and communication network for Mars called the Mars Network. This thesis investigates the performance of the Mars Network both theoretically, using figures of merit commonly applied to satellite navigation systems on Earth, and in the position domain using simulated observations.

Statistical analyses provide a means for assessing relationships between landscape spatial pattern and errors in the estimates of cover-type proportions as land-cover data are aggregated to coarser scales. Results from a multiple-linear regression model suggest that as patch sizes, ratio, and initial proportions of cover types increase, the proportion error moves in a positive direction and is governed by the interaction of the spatial characteristics and the scale of aggregation. However, the standard linear model does not ac- count for the different directions of scale-dependent proportion error since some classes become larger and others become smaller as the scene is aggregated. Addition of indicator variables representing class-type sig- nificantly improves the performance by allowing the model to respond differently to different classes. A regression tree model provides a much simpler fit to the complex scaling behavior through an interaction be- tween patch size and aggregation scale. An understanding of the relationships between landscape pattern, scale, and proportion error may advance methods for correcting land-cover area estimates. Such methods could also facilitate high-resolution calibration and validation of coarse-scale remote-sensing-based land- cover mapping algorithms. Ongoing initiatives to produce global land-cover datasets from remote sensing, such as efforts within the IGBP and the EOS Land-Team, include significant emphasis on high level calibration and validation activities of this nature.

These notes may not be reproduced by any means (mechanical or electronic or any other) without the express written permission of Hanan Samet

These notes may not be reproduced by any means (mechanical or electronic or any other) without express written permission of Hanan Samet

Digital elevation models (dems) provide the basic information required to characterise the topographic attributes of terrain. The primary derived topographic parameters associated with DEMs are slope and aspect. Slope and aspect can be used to calculate other significant topographic parameters such as upslope area and topographic index. The topographic index, in turn, can be used by distributed hydrological models, such as Topmodel, to characterise the spatial distribution of terrain. Many algorithms have been developed to calculate slope, aspect and upslope area from dems - specifically from gridded dems - but little work has gone into determining the uncertainty in these parameters, or the effect of this uncertainty in further applications. The accuracy of these parameters is dependent both on the algorithm used to generate them, and on the errors associated with the dem itself. Since it is almost impossible to model all the errors associated with a given slope, aspect or upslope area algorithm, and since a dem is normally only provided with a single rms error, simple error propagation is not adequate to determine the error associated with the derived topographic parameters. A more rigorous method of determining the effect of dem errors on derived topographic parameters is with statistical analysis using Monte Carlo simulation and error realisations of the dem. In this research, a comparison of slope, aspect, upslope area, and topographic index algorithms are presented along with an examination of how errors in dems e#ect the reliability of the derived topographic parameters. The effect of errors in the derived topographic parameters on the Topmodel hydrological model is also examined.