Gis Environmental Modeling And Engineering Second Edition 2nd Edition Allan Brimicombe
- 1. Gis Environmental Modeling And Engineering Second Edition 2nd Edition Allan Brimicombe download https://ebookbell.com/product/gis-environmental-modeling-and- engineering-second-edition-2nd-edition-allan-brimicombe-2106176 Explore and download more ebooks at ebookbell.com
- 2. Here are some recommended products that we believe you will be interested in. You can click the link to download. Gis Environmental Modelling And Engineering 1st Edition Allan Brimicombe https://ebookbell.com/product/gis-environmental-modelling-and- engineering-1st-edition-allan-brimicombe-2106166 Spatial Modeling In Gis And R For Earth And Environmental Sciences Hamid Reza Pourghasemicandan Gokceoglu https://ebookbell.com/product/spatial-modeling-in-gis-and-r-for-earth- and-environmental-sciences-hamid-reza-pourghasemicandan- gokceoglu-7398478 Environmental Modelling With Gis And Remote Sensing Geographic Information Systems Workshop 1st Edition Andrew Skidmore https://ebookbell.com/product/environmental-modelling-with-gis-and- remote-sensing-geographic-information-systems-workshop-1st-edition- andrew-skidmore-1472548 Modelling Interactions Between Vectorborne Diseases And Environment Using Gis Hassan M Khormi https://ebookbell.com/product/modelling-interactions-between- vectorborne-diseases-and-environment-using-gis-hassan-m-khormi-5090136
- 3. Gis Technology Applications In Environmental And Earth Sciences Tian https://ebookbell.com/product/gis-technology-applications-in- environmental-and-earth-sciences-tian-5699156 Gis For Environmental Decisionmaking 1st Edition Andrew A Lovett https://ebookbell.com/product/gis-for-environmental- decisionmaking-1st-edition-andrew-a-lovett-2206050 Gis And Environmental Monitoring Applications In The Marine Atmospheric And Geomagnetic Fields 1st Edition Stavros Kolios https://ebookbell.com/product/gis-and-environmental-monitoring- applications-in-the-marine-atmospheric-and-geomagnetic-fields-1st- edition-stavros-kolios-5882796 Gis For Environmental Applications A Practical Approach Xuan Zhu https://ebookbell.com/product/gis-for-environmental-applications-a- practical-approach-xuan-zhu-12199274 Gis In Environmental Engineering Shaheemath Suhara K K A K Haghi https://ebookbell.com/product/gis-in-environmental-engineering- shaheemath-suhara-k-k-a-k-haghi-231661624
- 8. Allan Brimicombe CRC Press is an imprint of the Taylor & Francis Group, an informa business Boca Raton London NewYork
- 9. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number: 978-1-4398-0870-2 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Brimicombe, Allan. GIS, environmental modeling and engineering / Allan Brimicombe -- 2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-1-4398-0870-2 (hardcover : alk. paper) 1. Geographic information systems. 2. Environmental sciences--Mathematical models. 3. Environmental engineering--Mathematical models. I. Title. G70.212.B75 2010 628.0285--dc22 2009035961 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 10. v Contents Acknowledgments..................................................................................................ix The Author...............................................................................................................xi Abbreviations....................................................................................................... xiii Statement on Trade Names and Trademarks.....................................................xv 1. Introduction......................................................................................................1 Metaphors of Nature........................................................................................2 A Solution Space?..............................................................................................4 Scope and Plan of This Book...........................................................................5 I Section 2. From GIS to Geocomputation..................................................................... 11 In the Beginning …........................................................................................12 Technological Facilitation.............................................................................. 14 Representing Spatial Phenomena in GIS. ....................................................19 Putting the Real World onto Media.............................................................24 Vector...........................................................................................................26 Tessellations................................................................................................28 Object-Oriented..........................................................................................31 Data Characteristics. .......................................................................................32 Data Collection Technologies........................................................................37 GPS and Inertial Navigation Systems.....................................................38 Remote Sensing..........................................................................................39 Ground Survey...........................................................................................41 Nontraditional Approaches to Data Collection.....................................42 Basic Functionality of GIS.............................................................................42 A Systems Definition of GIS..........................................................................44 Limitations of GIS and the Rise of Geocomputation and Geosimulation.................................................................................................46 3. GIScience and the Rise of Geo-Information Engineering...................49 Technology First … . .......................................................................................49 Science to Follow … .......................................................................................52 And Now … Geo-Information Engineering...............................................59
- 11. vi Contents I Section I 4. Approaches to Modeling..............................................................................63 Model of an x...................................................................................................64 Typology of Models........................................................................................66 Building Models. .............................................................................................69 Modeling Landslides.................................................................................70 Modeling Topography...............................................................................75 Spatio-Temporal Dimensions and the Occam–Einstein Dimension...................................................................................................77 Evaluating Models..........................................................................................81 Applying Models............................................................................................83 A Summary of Model Development............................................................87 5. The Role and Nature of Environmental Models.....................................91 Context of Environmental Modeling...........................................................92 Environmental Impact Assessment........................................................94 An Integrated Approach...........................................................................97 Sustainable Development.........................................................................99 Hazard, Vulnerability, and Risk............................................................ 101 Decision Environment................................................................................. 105 Conceptual Models....................................................................................... 107 Empirical Models.......................................................................................... 110 Models Incorporating Artificial Intelligence............................................ 117 Knowledge-Based Systems..................................................................... 117 Heuristics.................................................................................................. 118 Artificial Neural Networks. .................................................................... 119 Agent-Based Models................................................................................ 121 Process Models.............................................................................................. 124 Lumped Parameter Models....................................................................126 Distributed Parameter Models............................................................... 131 Discretization. ...................................................................................... 131 Routing across a Digital Elevation Model....................................... 132 Transport through a Medium...........................................................134 II Section I 6. Case Studies in GIS, Environmental Modeling, and Engineering.................................................................................................. 147 Modeling Approaches in GIS and Environmental Modeling................ 147 Spatial Coexistence.......................................................................................150 Source–Pathway Characterization............................................................. 157 Basin Management Planning.................................................................158
- 12. Contents vii Coastal Oil Spill Modeling..................................................................... 169 Cluster Detection..........................................................................................172 … and Don’t Forget the Web....................................................................... 182 7. Issues of Coupling the Technologies.......................................................185 Some Preconditions...................................................................................... 186 Initial Conceptualizations........................................................................... 189 Independent..............................................................................................190 Loosely Coupled. ......................................................................................190 Tightly Coupled........................................................................................ 191 Embedded................................................................................................. 191 An Over-Simplification of the Issues......................................................... 192 Maturing Conceptualizations..................................................................... 197 Integration versus Interoperability....................................................... 198 Environmental Modeling within GIS...................................................201 Model Management.................................................................................203 Maturing Typology of Integration.............................................................207 One-Way Data Transfer...........................................................................207 Loose Coupling........................................................................................207 Shared Coupling......................................................................................209 Joined Coupling. .......................................................................................209 Tool Coupling...........................................................................................209 De facto Practices........................................................................................... 210 8. Data and Information Quality Issues..................................................... 213 The Issue Is … Uncertainty......................................................................... 213 Early Warnings. ............................................................................................. 217 So, How Come … ?....................................................................................... 219 Imperfect Measurement.......................................................................... 219 Digital Representation of Phenomena..................................................220 Natural Variation.....................................................................................221 Subjective Judgment and Context. .........................................................223 Semantic Confusion. ................................................................................224 Finding a Way Forward...............................................................................224 Measuring Spatial Data Quality.................................................................226 Modeling Error and Uncertainty in GIS. ...................................................231 Topological Overlay.................................................................................231 Interpolation.............................................................................................236 Kriging..................................................................................................238 Fuzzy Concepts in GIS............................................................................242 Theory of Fuzzy Sets..........................................................................243 Example of Fuzzy Sets in GIS. ...........................................................244 Sensitivity Analysis.................................................................................256 Managing Fitness-for-Use...........................................................................259
- 13. viii Contents 9. Modeling Issues...........................................................................................263 Issues of Scale................................................................................................264 Issues of Algorithm......................................................................................277 Issues of Model Structure............................................................................285 Issues of Calibration.....................................................................................288 Bringing Data Issues and Modeling Issues Together..............................293 10. Decision Making under Uncertainty......................................................297 Exploring the Decision Space: Spatial Decision Support Systems. ........299 Communication of Spatial Concepts.........................................................304 Participatory Planning and the Web-Based GIS......................................307 All’s Well That Ends Well?. .......................................................................... 311 References............................................................................................................ 315 Index......................................................................................................................341
- 14. ix Acknowledgments First Edition First, a heartfelt thanks to my wife, Lily, for her unwavering support in this venture and for her hard work in preparing most of the figures. Second, I would like to thank my colleague, Dr. Yang Li, for his assistance with some of the figures and particularly for the preparation of the coastal oil-spill modeling examples. Third, I would like to thank Professor Li Chuan-tang for his invaluable insights into finite element methods. Fourth, I would like to thank my sequential employers—Binnie & Partners International (now Binnie Black & Veatch, Hong Kong); Hong Kong Polytechnic University; University of East London—for providing me with the opportunities and space to do so much. Second Edition Again I must thank my wife, Lily, for all her effort in recapturing the figures and for reformatting and preparing the publisher’s electronic copy of the first edition for me to work on. My thanks to Irma Shagla and other staff at Taylor & Francis for support- ing and seeing this project through.
- 16. xi The Author Professor Allan J. Brimicombe is the Head of the Centre for Geo- Information Studies at University of East London, United Kingdom. He holds a BA (Hons) in Geography from Sheffield University, an MPhil in Applied Geomorphology, and a PhD in Geo-Information Systems both from the University of Hong Kong. Professor Brimicombe is a chartered geog- rapher and is a Fellow of the Royal Geographical Society, the Geological Society, and the Royal Statistical Society. He was employed in the Far East for 19 years, first as an engineering geomorphologist with Binnie & Partners International (now Black & Veatch) including being general manager of a subsidiary company, Engineering Terrain Evaluation Ltd. In 1989, Professor Brimicombe joined the Hong Kong Polytechnic University where he founded the Department of Land Surveying and Geo-Informatics. Here he pioneered the use of geo-information systems (GIS) and environmental modeling as spatial decision support systems. In 1995, he returned to the United Kingdom as professor and head of the School of Surveying at the University of East London. His research interests include data quality issues, the use of GIS and numerical simulation modeling, spatial data mining and analysis, and location-based services (LBS).
- 18. xiii Abbreviations ABM: agent-based modeling AI: artificial intelligence ANN: artificial neural networks API: aerial photographic interpretation BMP: basin management plans CA: cellular automata CBR: case-based reasoning CN: runoff curve number DDE: dynamic data exchange DEM: digital elevation model DIME: dual independent map encoding DSS: decision support systems EIA: environmental impact assessment EIS: environmental impact statement fBm: fractional Brownian motion FDM: finite difference method FEM: finite element method FoS: factor of safety GI: geo-information GIS: geographical information systems GLUE: generalized likelihood uncertainty estimator GPS: global positioning system GPZ: Geo-ProZone, geographical proximity zones HKDSD: Drainage Services Department, Hong Kong Government HTML: hypertext markup language ICS: index of cluster size IDW: inverse distance weighted KBS: knowledge-based systems LBS: location-based services LiDAR: light distancing and ranging MAUP: modifiable areal unit problem MC: Monte Carlo (analysis) MCC: map cross-correlation NEC: no effect concentration NEPA: National Environmental Policy Act (U.S.) NIMBY: not in my back yard NVDI: normalized vegetation difference index OAT: one-at-a-time OLE: object linking and embedding OO: object-oriented
- 19. xiv Abbreviations ORDBMS: object-relational database management system PCC: proportion correctly classified PEC: predicted environmental concentration PDF: probability density function PGIS: participatory GIS QAE: quality analysis engine RAISON: regional analysis by intelligent systems on microcomputers RDBMS: relational database management system REA: representative elementary area RS: remote sensing SA: sensitivity analysis SCS: Soil Conservation Service (U.S.) SDSS: spatial decision support systems TIN: triangular irregular networks UA: uncertainty analysis WWW: world wide web
- 20. xv Statement on Trade Names and Trademarks In a book such as this, it is inevitable that proprietary or commercial prod- ucts will be referred to. Where a name is used by a company to distin- guish its product, which it may claim as a trade name or trademark, then that name appears in this book with an initial capital or all capital let- ters. Readers should contact the appropriate companies regarding com- plete information. Use of such names is to give due recognition to these products in illustrating different approaches and concepts and providing readers with practical information. Mention of proprietary or commercial products does not constitute an endorsement, or indeed, a refutation of these products.
- 22. 1 1 Introduction I wish to begin by explaining why this book has been written. Peter Fleming, in writing about his travels in Russia and China in 1933, put the need for such an explanation this way: With the possible exception of the Equator, everything begins some- where. Too many of those who write about their travels plunge straight in medias res; their opening sentence informs us bluntly and dramatically that the prow (or bow) of the dhow grated on the sand, and they stepped lightly ashore. No doubt they did. But why? With what excuse? What other and anterior steps had they taken? Was it boredom, business, or a broken heart that drove them so far afield? We have a right to know. Peter Fleming One’s Company (1934) In 2003, I wrote in the first edition of this book: “At the time of writing this introduction, the President of the United States, George W. Bush, has already rejected the Kyoto Agreement on the control of greenhouse gas emissions; European leaders appear to be in a dither and ecowarriors alongside anti- capitalists have again clashed with riot police in the streets.” A key change since then has been the Stern Review (Stern, 2006) on the economics of cli- mate change. The likely environmental impact of climate change trajecto- ries—rising sea levels permanently displacing millions of people, declining crop yields, more than a third of species facing extinction—had already been well rehearsed. What had not been adequately quantified and understood was the likely cost to the global economy (a 1% decline in economic output and 4% decline in consumption per head for every 1°C rise in average tem- perature) and that the cost of stabilizing the situation would cost about 1% of gross domestic product (GDP). It seemed not too much to pay, but attention is now firmly focused on the “credit crunch”’ and the 2008 collapse of the financial sector. In the meantime, annual losses in natural capital worth from deforestation alone far exceed the losses of the current recession, severe as it is. Will it take ecological collapse to finally focus our attention on where it needs to be? This book has been written because, like most of its readers, I have a concern for the quality of world we live in, the urgent need for its maintenance and where necessary, its repair. In this book I set out what I believe is a key approach to problem solving and conflict resolution through the analysis and modeling of spatial phenomena. Whilst this book alone will
- 23. 2 GIS, Environmental Modeling and Engineering, Second Edition perhaps not safeguard our world, you the reader on finishing this book will have much to contribute. The phrase quality of world used above has been left intentionally broad, even ambiguous. It encompasses: Our natural environment—climate, soils, oceans, biological life • (plants, animals, bacteria)—that can both nurture us and be hazards to us. The built environment that we have created to protect and house • ourselves and to provide a modified infrastructure within which we can prosper. The economic environment that sustains our built environment and • allows the organization of the means of production. The social, cultural, and legal environments within which we con- • duct ourselves and our interactions with others. These environments are themselves diverse, continually evolving and having strong interdependence. Each of them varies spatially over the face of the globe mostly in a transition so that places nearer to each other are more likely to be similar than those farther apart. Some abrupt changes do, of course, happen, as, for example, between land and sea. They also change over time, again mostly gradually, but catastrophic events and revolutions do happen. Together they form a complex mosaic, the most direct visible mani- festation being land cover and land use—our evolved cultural landscapes. Furthermore, the interaction of these different aspects of environment gives enormous complexity to the notion of “quality of life” for our transient existence on Earth. Globalization may have been a force for uniformity in business and consumerism, but even so businesses have had to learn to be spatially adaptive, so-called glocalization. When it comes to managing and ameliorating our world for a sustainable quality of life, there is no single goal, no single approach, no theory of it all. Let’s not fight about it. Let us celebrate our differences and work toward a common language of understanding on how we (along with the rest of nature) are going to survive and thrive. Metaphors of Nature We often use metaphors as an aid in understanding complexity, none more so perhaps than in understanding nature and our relationship within it. These metaphors are inevitably bound up in philosophies of the environment, or knowledge of how the environment works and the technology available to us to modify/ameliorate our surrounding environment. Thus, for millennia,
- 24. Introduction 3 environmental knowledge was enshrined in folklore derived from the trial and error experiences of ancestors. Archaeology has revealed patterns of site selection that changed as we developed primitive technologies or adapted to new environments. Places for habitation had to satisfy the needs for water, food,rawmaterials,shelter,andsafety,andhumanslearnedtorecognizethose sites that offered the greatest potential for their mode of existence. Examples are numerous: caves near the feeding or watering places of animals; Neolithic cultivation of well-drained, easily worked river terraces; early fishing com- munities on raised beaches behind sheltered bays and so on. Undoubtedly mistakes were made and communities decimated, but those that survived learned to observe certain environmental truths or inevitabilities. Successful early civilizations were those that had social structures that allowed them to best use or modify the landforms and processes of their physical environment. Thus, the Egyptians, Mesopotamians, and Sumerians devised irrigation systems to regulate and distribute seasonally fluctuating water supplies, while the Chinese and Japanese included widespread terrac- ing as a means of increasing the amount of productive land. More than 2,500 years ago, the Chinese developed the Taoist doctrine of nature, in which the Earth and the sky had their own “way” or “rule” to maintaining harmony. Human beings should follow and respect nature’s way or risk punishment in the form of disasters from land and sky. Thus, even at that time there were laws governing, for example, minimum mesh size on fishing nets so that fish would not be caught too young. Of course, our stewardship has not always been a continual upward journey of success. Some human civilizations have collapsed spectacularly through environmental impact and loss of natural resources (Tickell, 1993; Diamond, 2005). These disasters aside, the dominant metaphor was of “Mother Earth”: a benevolent maker of life, a controlling parent that could provide for our needs, scold us when we erred, and, when necessary, put all things to right. The industrial revolution allowed us to ratchet up the pace of develop- ment. Early warnings of the environmental consequences, such as from Marsh (1864), were largely ignored as the Victorians and their European and North American counterparts considered themselves above nature in the headlong rush to establish and exploit dominions. Our technologies have indeed allowed us to ameliorate our lifestyle and modify our environ- ment on an unprecedented scale—on a global scale. But, from the 1960s, the cumulative effect of human impact on the environment and our increasing exposure to hazard finally crept onto the agenda and remains a central issue today. The rise of the environmental movement brought with it a new meta- phor—Spaceship Earth—that was inspired by photos from the Apollo moon missions of a small blue globe rising above a desolate moonscape. We were dependant on a fragile life-support system with no escape, no prospect of res- cue, if it were to irreparably break down. This coincided with the publication of seminal works, such as Rachel Carson’s (1963) Silent Spring, which exposed the effects of indiscriminate use of chemical pesticides and insecticides;
- 25. 4 GIS, Environmental Modeling and Engineering, Second Edition McHarg’s (1969) Design with Nature, which exhorted planners and designers to conform to and work within the capacity of nature rather than compete with it; and Schumacher’s (1973) Small Is Beautiful proposed an economics that emphasized people rather than products and reduced the squandering of our “natural capital.” The words fractal, chaos, butterfly effect, and complexity (Mandelbrot, 1983; Gleick, 1987; Lewin, 1993; Cohen and Stewart, 1994) have since been added to the popular environmental vocabulary to explain the underlying structure and workings of complex phenomena. Added to these is the Gaia hypothesis (Lovelock, 1988) in which the Earth is proposed to have a global physiology or may in fact be thought of as a superorganism capable of switching states to achieve its own goals in which we humans may well be (and probably are) dispensable organisms. A Solution Space? That we are capable of destroying our life support system is beyond doubt. As a species, we have already been responsible for a considerable number of environmental disasters. If I scan the chapter titles of Goudie’s (1997) The Human Impact Reader, the list becomes long indeed, including (in no par- ticular order): subsidence, sedimentation, salinization, soil erosion, desic- cation, nutrient loss, nitrate pollution, acidification, deforestation, ozone depletion, climate change, wetland loss, habitat fragmentation, and deser- tification. I could go on to mention specific events, such as Exxon Valdez, Bhopal, and Chernobyl, but this book is not going to be a catalog of dire issues accompanied by finger-wagging exhortations that something must be done. Nevertheless, worrying headlines continue to appear, such as: “Just 100 months left to save the Earth” for a piece on how greenhouse gases may reach a critical level or tipping point beyond which global warming will accelerate out of control (Simms, 2008). One can be forgiven for having an air of pessimism; the environment and our ecosystems are definitely in trouble. But, we are far from empty-handed. We have a rich heritage of science and engineering, a profound knowledge of environmental processes and expe- rience of conservation and restoration. The technologies that have allowed humankind to run out of control in its impact on the environment can surely be harnessed to allow us to live more wisely. Our ingenuity got us here and our ingenuity will have to get us out of it. As stated above, we need a common language and, in this regard, we have some specific technologies—drawing upon science—that can facilitate this. While humankind has long striven to understand the workings of the envi- ronment, it has only been in the past 30 years or so that our data collection and data processing technologies have allowed us to reach a sufficiently detailed understanding of environmental processes so as to create simulation
- 26. Introduction 5 models. I would argue that it is only when we have reached the stage of suc- cessful quantitative simulation, can our level of understanding of processes allow us to confidently manage them. This is the importance of environmental modeling. Facilitated by this in a parallel development has been environmental engineering. Engineering also has a rich history, but while traditionally engi- neering has focused on the utilization of natural resources, environmental engineering has recently developed into a separate discipline that focuses on the impact and mitigation of environmental contaminants (Nazaroff and Alvarez-Cohen, 2001). While most management strategies arising out of envi- ronmental modeling will usually require some form of engineering response for implementation, environmental engineering provides solutions for man- aging water, air, and waste. Engineering in the title of this book refers to the need to design workable solutions; such designs are often informed by com- putational or simulation modeling. The youngest technology I would like to draw into this recipe for a common language is geographic information systems (GIS). Because environmental issues are inherently spatial—they occur some- where, often affecting a geographic location or area—their spatial dimension needs to be captured if modeling and engineering are to be relevant in solv- ing specific problems or avoiding future impacts. GIS have proved successful in the handling, integration, and analysis of spatial data and have become an easily accessible technology. While the link between simulation modeling and engineering has been longstanding, the link between GIS and these technolo- gies is quite new, offers tremendous possibilities for improved environmental modeling and engineering solutions, and can help build these into versatile decision support systems for managing, even saving our environment. And that is why I have written this book. Scope and Plan of This Book From the early 1990s onwards, there has been an accelerating interest in the research and applications of GIS in the field of environmental modeling. There have been a few international conferences/workshops on the subject— most notably the series organized by the National Center for Geographic Information and Analysis (NCGIA), University of California, Santa Barbara in 1991, 1993, 1996, and 2000—and have resulted in a number of edited collec- tions of papers (Goodchild et al., 1993; 1996; Haines-Young et al., 1993; NCGIA, 1996; 2000) as well as a growing number of papers in journals, such as the International Journal of Geographical Information Science, Transactions in GIS, Hydrological Processes, Computers Environment and Urban Systems, ASCE Journal of Environmental Engineering, Photogrammetric Engineering and Remote Sensing, Computers and Geosciences, and so on. But, working with GIS and environ- mental simulation models is not just a case of buying some hardware, some
- 27. 6 GIS, Environmental Modeling and Engineering, Second Edition software, gathering some data, putting it all together and solving problems with the wisdom of a sage. While technology has simplified many things, there still remain many pitfalls, and users need to be able to think critically about what they are doing and the results that they get from the technology. Thus, the overall aim of this book is to provide a structured, coherent text that not only introduces the subject matter, but also guides the reader through a number of specific issues necessary for critical usage. This book is aimed at final-year undergraduates, postgraduates, and professional practitioners in a range of disciplines from the natural sciences, social sciences to engineer- ing, at whatever stage in their lifelong learning or career they need or would like to start working with GIS and environmental models. The focus is on the use of these two areas of technology in tandem and the issues that arise in so doing. This book is less concerned with the practicalities of software development and the writing of code (e.g., Payne, 1982; Kirkby et al., 1987; Hardisty et al., 1993; Deaton and Winebrake, 2000; Wood, 2002). Nor does it consider in detail data collection technologies, such as remote sensing, GPS, data loggers, and so on, as there are numerous texts that already cover this ground (e.g., Anderson and Mikhail, 1998; Skidmore, 2002). The overall thrust of this book can be summarized in the mapping: ƒ: Ω → ℜ (1.1) where Ω = set of domain inputs, ℜ = set of real decisions. In other words, all decisions (including the decision not to make a decision) should be ade- quately evidenced using appropriate sources of information. This is perhaps stating the obvious, but how often, in fact, is there insufficient information, a hunch, or a gut feeling? GIS, environmental modeling, and engineering are an approach to generating robust information upon which to make decisions about complex spatial issues. The subject matter is laid out in three sections. Section I concentrates uniquely on GIS: what they are, how data are structured, what are the most common types of functionality. GIS will be viewed from the perspective of a technology, the evolution of its scientific basis, and, latterly, its synergies with other technologies within a geocomputational paradigm. This is not intended to be an exhaustive introduction as there are now many textbooks that do this (e.g., Chrisman, 1997; Burrough and McDonnell, 1998; Longley et al., 2005; Heywood et al., 2006) as well as edited handbooks (e.g., Wilson and Fotheringham, 2008). Rather, its purpose is to lay a sufficient founda- tion of GIS for an understanding of the substantive issues raised in Section III. Section II similarly focuses on modeling both from a neutral scientific perspective of its role in simulating and understanding phenomena and from a more specific perspective of environmental science and engineering. Section III is by far the largest. It looks at how GIS and simulation modeling are brought together, each adding strength to the other. There are examples of case studies and chapters covering specific issues, such as interoperability,
- 28. Introduction 7 data quality, model validity, space-time dynamics, and decision-support systems. Those readers who already have a substantial knowledge of GIS or have completed undergraduate studies in GIS may wish to skip much of Section I and move quickly to Sections II and III. Those readers from a simu- lation modeling background in environmental science or engineering should read Section I, skim through Section II, and proceed to Section III. In a book such as this, it is always possible to write more about any one topic; there are always additional topics that a reader might consider should be added. There are, for example, as many environmental models as there are aspects of the environment. GIS, environmental modeling, and engineering are quite end- less and are themselves evolving. Also, I have tried not to focus on any one application of simulation modeling. Given its popularity, there is a tempta- tion to focus on GIS and hydrology, but that would detract from the overall purpose of this book, which is to focus on generic issues of using GIS and external simulation models to solve real problems. Presented in the following chapters is what I consider to be a necessary understanding for critical think- ing in the usage of such systems and their analytical outputs. Enjoy.
- 30. I Section
- 32. 11 2 From GIS to Geocomputation The cosmological event of the Big Bang created the universe and in so doing space–time emerged (some would say “switched on”) as an integral aspect of gravitational fields. Space and time are closely interwoven and should more properly be thought of as a four-dimensional (4D) continuum in which time and space, over short durations, are interchangeable. Nevertheless, we con- ventionally think of separate one-dimensional (1D) time and three-dimen- sional (3D) space. The terrestrial space on which we live, the Earth, is at least 4.5 billion years old and has been around for about 40% of the time since time began. Since our earliest prehistory, we have grappled with the prob- lems of accurately measuring time and space. Crude measures of time prob- ably came first given the influences of the regular cycles of the day, tides, the moon, and seasons on our lives as we evolved from forager to agriculturist. With technology, we have produced the atomic clock and the quartz watch. Measuring position, distances, and area were less obvious in the absence of the type of benchmark that the natural cycles provided for time. Early mea- surements used a range of arbitrary devices—the pace, the pole, the chain— and longer distances tended to be equated with the time it took to get to destinations. Much later, the development of accurate clocks was the key to solving the problem of determining longitudinal position when coupled with observations of the sun. Measurement requires numerical systems, and 1D time requires either a linear accumulation (e.g., age) or a cyclical looping (e.g., time of day). Measurement of 3D space requires the development of higher order numerical systems to include geometry and trigonometry. Let us not forget that at the root of algebra and the use of algorithms was the need for precise partitioning of space (land) prescribed by Islamic law on inheritance. Calculus was developed with regard to the changing position (in time) of objects in space as a consequence of the forces acting upon them. Three fundamental aspects of determining position are: a datum, a coor- dinate system (both incorporating units of measurement), and an adequate representation of the curved (or somewhat crumpled) surface of the Earth in the two dimensions of a map, plan, or screen. The establishment of a datum and coordinate system is rooted in geodetic surveying, which aims to pre- cisely determine the shape and area of the Earth or a portion of it through the establishment of wide-area triangular networks by which unknown loca- tions can be tied into known locations. Cartographers aim to represent geo- graphic features and their relationships on a plane. This involves both the art of reduction, interpretation, and communication of geographic features
- 33. 12 GIS, Environmental Modeling and Engineering, Second Edition and the science of transforming coordinates from the spherical to a plane through the construction and utilization of map projections. The production of quality spatial data used to be a time-consuming, expensive task and for much of the twentieth century there was a spatial data “bottleneck” that held back the wider use of such data. Technology has provided solutions in the form of the global positioning system (GPS), electronic total stations, remote sensing (RS), digital photogrammetry, and geographic information systems (GIS). GPS, RS, and GIS are now accessible to every citizen through inexpensive devices and the Internet. Determining where is no longer dif- ficult and, through mobile devices such as GPS-enabled smartphones, deter- mining one’s geographic position and location has become no more difficult than telling the time. This chapter will chart the rise of the GIS as a technology, consider its main paradigms for representing the features of the Earth and structuring data about them. The basic functionality of GIS will be described with examples. A “systems” view of GIS will then be developed bringing us to the point where GIS can be formally defined. The limitations of modern GIS will be discussed leading us to consider the rise of geocomputation as a new para- digm and the role of GIS within it. In the Beginning … It would be nice to point to a date, a place, an individual and say, “That’s where it all started, that’s the father of GIS.” But no. As Coppock and Rhind put it in their article on the History of GIS (1991), ”unhappily, we scarcely know.” In the beginning, of course, there were no GIS “experts” and nobody specifically set out to develop a new body of technology nor a new scientific discipline for that matter. In the mid-1960s, there were professionals from a range of disciplines, not many and mostly in North America, who were excited by the prospect of handling spatial data digitally. There were three main focal points: the Harvard Graduate School of Design, the Canada Land Inventory, and the U.S. Census Bureau. In each of these organizations were small groups of pioneers who made important contributions toward laying the foundations for today’s GIS industry. The significance of the Harvard Graduate School of Design lies in its Laboratory for Computer Graphics and Spatial Analysis, a mapping pack- age called SYMAP (1964), two prototype GIS, called GRID (1967), and ODYSSEY (c. 1978), and a group of talented individuals within the labora- tory and the wider graduate school: N. Chrisman, J. Dangermond, H. Fisher, C. Steinitz, D. Sinton, T. Peucker, and W. Warntz, to name a few. The cre- ator of SYMAP was Howard Fisher, an architect. His use of line printers to produce three types of map—isoline, choropleth, and proximal—was a
- 34. From GIS to Geocomputation 13 way of visualizing or recognizing spatial similarities or groupings in human and physical phenomena (McHaffie, 2000). The other leap was a recognition (rightly or wrongly) that just about any such phenomenon, no matter how ephemeral or whether described quantitatively or qualitatively could be rep- resented as a map of surfaces or regions. The printing of these maps using equally spaced characters or symbols, line by line, naturally resulted in a “blocky,” cell-based map representation (Figure 2.1). David Sinton, a land- scape architect, took cell-based (raster) mapping forward with GRID, which allowed analyses to include several thematic data sets (layers) for a given area. Furthermore, by 1971 a rewrite of GRID allowed users to define their own logical analyses rather than being restricted to a limited set of prepack- aged procedures. Thus, a flexible user interface had been developed. By the late 1970s, ODYSSEY, a line-based (vector) GIS prototype had been written capable of polygon overlay. In this way, it can be seen that the overlay or co- analysis of several thematic layers occupied the heart of early GIS software strategies (Chrisman, 1997). In 1966, the Canada Geographic Information System (CGIS) was initiated to serve the needs of the Canada Land Inventory to map current land uses and the capability of these areas for agriculture, forestry, wildlife, and recre- ation (Tomlinson, 1984). Tomlinson had recognized some years earlier that the manual map analysis tasks necessary for such an inventory over such a large area would be prohibitively expensive and that a technological solution was necessary. Within this solution came a number of key developments: optical scanning of maps, raster to vector conversion, a spatial database man- agement system, and a seamless coverage that was nevertheless spatially partitioned into “tiles.” The system was not fully operational until 1971, but Figure 2.1 Sample of a SYMAP-type line printer contour map showing emphasis on similarities. The con- tour lines are perceived only through the “gap” between the areas of printed symbols.
- 35. 14 GIS, Environmental Modeling and Engineering, Second Edition has subsequently grown to become a digital archive of some 10,000 maps (Coppock and Rhind, 1991). The significance of the U.S. Bureau of Census in developing its Dual Independent Map Encoding (DIME) scheme in the late 1960s is an early example of inserting additional information on spatial relationships into data files through the use of topological encoding. Early digital mapping data sets had been unstructured collections of lines that simply needed to be plotted with the correct symbology for a comprehensible map to emerge. But the demands for analysis of map layers in GIS required a structuring that would allow the encoding of area features (polygons) from lines and their points of intersection, ease identification of neighboring features, and facilitate the checking of internal consistency. Thus, DIME was a method of describing urban structure, for the purposes of census, by encoding the topological relationships of streets, their intersection points at junctions and the street blocks and census tracts that the streets define as area features. The data structure also provided an automated method of checking the consis- tency and completeness of the street block features (U.S. Bureau of Census, 1970). This laid the foundation of applying topology or graph theory now common in vector GIS. Technological Facilitation The rise of GIS cannot be separated from the developments in information and communication technology that have occurred since the 1960s. A time- line illustrating developments in GIS in relation to background formative events in technology and other context is given in Table 2.1. Most students and working professionals today are familiar at least with the PC or Mac. I am writing the second edition of this book in 2008/09 on a notebook PC (1.2 GHz CPU, 1 GB RAM, 100 GB disk, wireless and Bluetooth connectivity) no bigger or thicker than an A4 pad of paper. My GIS and environmental mod- eling workhorse is an IBM M Pro Intellistation (dual CPU 3.4 GHz each, 3.25 GB RAM, 100 GB disk). They both run the same software with a high degree of interoperability, and they both have the same look and feel with toolbars, icons, and pull-down menus. Everything is at a click of a mouse. I can eas- ily transfer files from one to the other (also share them with colleagues) and I can look up just about anything on the Internet. Even my junk mail has been arriving on CD and DVD, so cheap and ubiquitous has this medium become, and USB data sticks are routinely given away at conferences and exhibitions. It all takes very little training and most of the basic functions have become intuitive. I’m tempted to flex my muscles (well, perhaps just exercise my index finger) for just a few minutes on the GIS in this laptop … and have indeed produced Figure 2.2—a stark contrast to Figure 2.1.
- 36. From GIS to Geocomputation 15 Table 2.1 Timeline of Developments in GIS in Relation to Background Formative Events in Technology and Other Context Year GIS Context 1962 Carson’s Silent Spring 1963 Canadian Geographic Information System 1964 Harvard Lab for Computer Graphics & Spatial Analysis GPS specification 1966 SYMAP WGS-66 1967 U.S. Bureau of Census DIME 1968 Relational database defined by Codd 1969 ESRI, Intergraph, Laser-Scan founded Man on the noon; NEPA; McHarg’s Design with Nature 1970 Acronym GIS born at IGU/UNESCO conference Integrated circuit 1971 ERTS/Landsat 1 launched 1973 U.K. Ordnance Survey starts digitizing 1974 AutoCarto conference series; Computers & Geosciences UNIX 1975 C++; SQL 1978 ERDAS founded First GPS satellite launched 1980 FEMA integrates USGS 1:2 m mapping into seamless database 1981 Computers, Environment & Urban Systems; Arc/Info launched 8088 chip; IBM PC 1983 Mandelbrot’s The Fractal Geometry of Nature 1984 1st Spatial Data Handling Symposium 80286 chip, RISC chip; WGS-84 1985 GPS operational 1986 Burrough’s Principles of Geographical Information Systems for Land Resources Assessment; MapInfo founded SPOT 1 launched Internet; mobile phones 1987 International Journal of Geographical Information Systems; GIS/LIS conference series; “Chorley” Report 80386 chip 1988 NCGIA; GIS World, U.K. RRL initiative Berlin Wall comes down 1989 U.K. Association for Geographic Information 1990 Berners–Lees launches WWW 1991 USGS digital topo series complete 1st International Symposium on Integrating GIS and Environmental Modeling Dissolution of Soviet Union 1992 Rio Earth Summit – Agenda 21 1993 GIS Research U.K. conference series Pentium chip; full GPS constellation 1994 Open GIS Consortium HTML Continued
- 37. 16 GIS, Environmental Modeling and Engineering, Second Edition To fully comprehend the technological gulf we have crossed, let me briefly review a late 1970s GIS-based land capability study in South Dakota (Schlesinger et al., 1979). The project was carried out on an IBM 370/145 main- frame computer using 10 standalone program modules written in FORTRAN IV and IBM Assembler. A digitizing tablet and graphics terminal were avail- able, but all hardcopy maps were produced using a line printer. Maps wider than a 132-character strip had to be printed and glued together. The study area covered 115 km2; size of cell was standardized at one acre (~0.4 ha). With the objective to identify land use potential, four base data layers were digi- tized: 1969 and 1976 land use from aerial photographic interpretation (API), soils, and underlying geology from published map sheets. Through a process Table 2.1 (Continued ) Timeline of Developments in GIS in Relation to Background Formative Events in Technology and Other Context Year GIS Context 1995 OS finished digitizing 230,000 maps Java 1996 1st International Conference on GeoComputation; Transactions in GIS 1997 IJGIS changes “Systems” to “Science”; last AutoCarto; Geographical and Environmental Modeling Kyoto Agreement on CO2 reduction 1998 Journal of Geographical Systems; last GIS/LIS GPS selective availability off 2000 “Millennium Bug” 2003 1st ed.: GIS, Environmental Modeling & Engineering 2005 Google Maps; Google Earth 2006 Stern Review: The economics of climate change 2008 Google Street View Figure 2.2 Laptop GIS of today: 3-D topographic perspective of a landscape.
- 38. From GIS to Geocomputation 17 of either reclassification of single layers or a logical combination (overlay) of two or more layers with reclassification, a total of 19 new factor maps were created (Table 2.2) to answer a range of spatial questions where certain char- acteristics are concerning land suitability for development. Typical of the many pioneering efforts of the time, this study achieved its goals and was well received in the community despite the rudimentary hardware and soft- ware tools available. Some of the changes are obvious. Over the intervening 30 years, the action of Moore’s Law, by which the hardware price to performance ratio is expected to double every 18 months, means that the laptop I’m writing on far outstrips the IBM mainframe of that time in terms of power, performance, and storage by several orders of magnitude at a fraction of the cost in real terms. Instead of using a collection of software modules that may need to be modified and recompiled to satisfy the needs of the individual project, we have a choice of off-the-shelf packages (e.g., MapInfo, ArcGIS) that combine a wide range of functionality with mouse- and icon/menu-driven interfaces. For project-spe- cific needs, most of these packages have object-oriented scripting languages Table 2.2 Multiple Layer Production from Three Source Data Sets Base Maps → ↓ Factor Maps 1969 Land Use 1976 Land Use Soils Geology Slope Flood hazards Potential for building sites Potential for woodland wildlife habitat Potential for rangeland habitat Potential for open land habitat Limitations to road and street construction Limitations for septic tank absorption fields Soils of statewide importance for farmland Sliding hazards Groundwater recharge areas Land use change Limitations to sewage lagoons Important farmland Important farmland lost to urban development Limitations to urban development Land suitable for urban development, but not important agricultural land Limitations for septic tanks Limitations for new urban development Source: Based on Schlesinger, J., Ripple, W., and Loveland, T.R. (1979) Harvard Library of Computer Graphics 4: 105–114.
- 39. 18 GIS, Environmental Modeling and Engineering, Second Edition that facilitate customization and the addition of new functionality with many such scripts available over the Internet. Moreover, analysis can now be vastly extended to include external computational models that communicate either through the scripting or use of common data storage formats. Although the availability of digital map data is uneven across the world, particularly when it comes to large-scale mapping, off-the-shelf digital data ready for use in GIS are much more common today to the point where, certainly for projects in North America and Europe, there is hardly the need anymore to manually digitize. As mentioned above, the bottleneck in the production of digital spa- tial data has been burst not only by technologies, such as GPS, RS, and digital photogrammetry, but through palm-top data loggers, high-speed scanners, digital data transfer standards, and, above all, the computer capacity to cost- effectively store, index, and deliver huge data sets. In contrast to Table 2.2 in which only four data sources were used, Figure 2.3 summarizes the many input sources and output derivative data sets designed by the British Geological Survey in a recent project to build an integrate 3D geological and hydrogeological model. This model is to support development in the Thames Gateway, U.K., which at the time of writing is Europe’s largest regeneration program. Nevertheless, despite the technological advancement that has made spatial tools and particular GIS more widespread, sophisticated, and easier to use, many of the underlying principles have remained largely the same. Mineral assessment maps Geochemical surveys Land use map Map plans Digital geological maps Mineral assessment maps Borehole data Site investigation data Geotechnical data DTM Groundwater levels Bespoke attributed volume models Geotechnical attributes Environmental information system Geotechnical characteriza- tion of the ground at depth of build Archaeological potential maps Contaminated land risk assessment tools SUDS initial assessment tool Geohazard maps Site Investigation design tool Automated Georeports Risk maps Hydro- geological domain maps Urban aquifer vulnerability maps Underground asset management systems Mineral assessment maps Infrastructure planning tool Hydrogeological data Input Output Historic maps 3D Attributed Geological model Figure 2.3 A contemporary geological application using spatial modeling tools. (Adapted from Royse, K.R., Rutter, H.K., and Entwisle, D.C. (2009) Bulletin of Engineering Geology and the Environment 68: 1–16.)
- 40. From GIS to Geocomputation 19 Representing Spatial Phenomena in GIS The dominant paradigm in the way GIS data are structured comes from the idea that studies of landscape (both human and physical) and the solution to problems concerning the appropriate use of land can be achieved by describ- ing the landscape as a series of relevant factor maps or layers that can then be overlaid to find those areas having particular combinations of factors that would identify them as most suited to a particular activity. The methodology in its modern GIS context derives from the seminal work of McHarg (1969) as well as the conventional cartographic tradition of representing spatial phe- nomena. Although the use of manual overlay of factor maps considerably predates McHarg (Steinitz et al., 1976), he provided a compelling case for the methodology as a means of organizing, analyzing, and visualizing multiple landscape factors within a problem-solving framework. Consider the land- scape shown in Figure 2.4. This landscape can be viewed both holistically as a piece of scenery and as a seriesofconstituentelements,suchasitstopography,geology,hydrology,slope processes, flora, fauna, climate, and manmade (anthropomorphic) features, to Figure 2.4 A view of a sample landscape. (Photo courtesy of the author.)
- 41. 20 GIS, Environmental Modeling and Engineering, Second Edition name but a number that could be separated out. At any place within this land- scape there are several or all constituents to be considered: stand on any point and it has its topography, geology, hydrology, microclimate, and so on. Any comprehensive map of all these constituents would quickly become cluttered and complex—almost impossible to work with. So, consider then the mapped constituents of a very similar landscape in Figure 2.5(a–i). Although this particular landscape has been artificially created to demon- strate a number of issues throughout this book, it illustrates well a number of aspects of the layer or coverage paradigm and the graphic primitives used in any one layer. First, in order for a selection of layers to be used together, superimposed and viewed as a composite, they must all conform to the same coordinate system and map projection. This is critically important, otherwise the layers will be distorted and wrongly positioned in relation to one another. Individual layers, however, need not necessarily cover exactly the same area of the landscape in their extent as may happen, for example, if they have been derived from different surveys or source documents. Each layer can neverthe- less be clipped to a specific study area as has happened in Figure 2.5. Second, some of the layers are given to represent discrete objects in the landscape (e.g., landslides, streams, land cover parcels) while others represent a continuous field (e.g., topography, gradient, rainfall), which varies in its value across the landscape. What aspects of the landscape should be treated as continuous or discrete and how they should be presented cartographically is an old, but significant problem, which can still be debated today (Robinson and Sale, 1969; Peuquet, 1984; Goodchild, 1992a; Burrough, 1992; Burrough and Frank 1996; Spiekermann and Wegener, 2000; Goodchild et al., 2007). To a consider- able extent, it is a matter of data resolution, scale of representation, conven- tion, and convenience. For example, landslides can be quickly mapped at a regional level as individual points representing each scar in the terrain (as in Figures 2.5(h) and 2.6(a)). Another approach would be to represent each landslide as a line starting at the scarp and tracing the down slope extent of the debris to the toe (Figure 2.6(b)). Clearly any laterally extensive landslide in Figure 2.5(h) would represent a methodological problem for which a sin- gle point or a line would be an oversimplification. So, yet another approach would be to represent either the whole landslide or its morphological ele- ments according to a consistent scheme (e.g., source, transport, deposition) as polygons (Figure 2.6(c)). This latter approach, while providing more informa- tion, is more time consuming and expensive to produce. Finally, these land- slides could be represented as a field of varying numbers of landslides within a tessellation of cells (Figure 2.6(d)), or as densities (Figure 5.11(a)). To pursue this issue just a bit further, topography is a continuous field, but is conventionally represented by contours that in geometric terms are nested polygons. Gradient on the other hand is also a continuous field, but would generally be confusing to interpret if drawn as contours and, thus, is usually represented by a tessellation of cells, each having its own gradient value. Soils are conventionally classified into types and each type is represented
- 42. From GIS to Geocomputation 21 Degrees <5 5–10 10–5 15–20 >20 Geology Alluvium Colluvium Granite Vein Volcanic Land Cover Agriculture Bare Grassland Shrub Village Woodland 45 50 55 60 80 75 70 65 Hydrology Stream Tributary Roads Major Minor (a) (b) (d) (f) (h) (c) (e) (g) (i) Figure 2.5 Mapped constituents of an example landscape in eight layers (coverages): (a) oblique view of topography, (b) contours, (c) slope gradient, (d) geology, (e) land cover, (f) rainfall isohyets from a storm event, (g) drainage network, (h) landslide scars, (i) transport.
- 43. 22 GIS, Environmental Modeling and Engineering, Second Edition by discrete polygons wherever they occur. This is despite the fact that many boundaries between soil types are really gradations of one dominant char- acteristic (say, clay content or structure of horizons) to another. Land uses are similarly defined as homogenous discrete polygons on the basis of dominant land-use type despite perhaps considerable heterogeneity within any poly- gon. We will return to these issues later in Chapter 8 when we consider the implications of this on spatial data quality. Fundamentally then, any point within a landscape can be viewed as an array containing the coordinates of location {x, y} and values/classes for n defined attributes a. The first two of these attributes may be specifically defined as elevation z and time t. Therefore, the whole landscape L can be described by a large number of such points p in a matrix: L = x1 y1 z1 t1 a14 a15 a1n a13 ap3 xp yp zp tp ap4 aps apn (2.1) (a) (b) (c) 1 1 1 (d) Figure 2.6 Four possible methods of representing landslides in GIS: (a) as points, (b) as lines, (c) as poly- gons, (d) as a tessellation (raster).
- 44. From GIS to Geocomputation 23 In practical terms, time t is often fixed and the matrix is taken to be a single snapshot of the landscape. Also, because the number of points used to describe the landscape is usually only a tiny proportion of all possible points, L is considered to be a sample of one. Elevation z is taken to be an attribute of a location and, therefore, is not really a third dimension in the traditional sense of an {x, y, z} tuple. GIS are commonly referred to as 2½D rather than 3D. The points themselves can be organized into a series of points, lines, or polygons, that is, discrete objects of 0, 1, and 2 dimensions, respectively, to form vector layer(s). Usually, objects that are points, lines, and polygons are not mixed within a layer, but are kept separate. This describes the planar geometry and disposition of the objects within the landscape. The attributes of each object are stored in a database (either as flat files or in a relational database management system (RDBMS)) and are linked to the graphics via a unique identifier (Figure 2.7). The other approach to L is for the landscape to be tessellated, that is, split into a space-filling pattern of cells and for each cell to take an attribute value according to the distribution of points to form a raster layer. Thus, there may be n layers, one for each attribute. Although the objective in both vector and raster approaches is to achieve spatially seam- less layers that cover an entire area of interest; it may be that for large areas the data volume in each layer becomes too large and cumbersome to handle conveniently (e.g., response times in display and analysis). When this occurs, layers are usually split into a series of nonoverlapping tiles, which when used give the impression of seamless layers. Thus far, I have described the mainstream approach to representing spatial phenomena in GIS. Since the early 1990s, an alternative has emerged—the object-oriented (OO) view of spatial features, which should not be confused with the above object-based approach of vector representation. Spatial objects as discernible features of a landscape are still the focus, but rather than split- ting their various aspects or attributes into layers (the geology, soils, vegeta- tion, hydrology, etc., of a parcel of land), an object is taken as a whole with its properties, graphical representation, and behavior in relation to other spa- tial objects embedded within the definition of the object itself (Worboys et Vector Polygons RDBMS ID A1 A2 A3 A1 A2 A3 Raster Fields 1 1 2 3 2 3 Figure 2.7 Basic organization of geometry and attributes in layered GIS: vector and raster.
- 45. 24 GIS, Environmental Modeling and Engineering, Second Edition al., 1990; Milne et al., 1993; Brimicombe and Yeung, 1995; Wachowicz, 1999; Shekhar and Vatsavai, 2008). Thus, the modeling of “what” is separated from “where” and, in fact, both “where” and whether to use raster or vector (or both, or neither) as a means of graphical representation can be viewed as attributes of “what.” This then allows even abstract spatial concepts, such as sociocultural constructs to be included in GIS alongside more traditional physical features of a landscape (see Brimicombe and Yeung, 1995). Although from a personal perspective the OO view provides a superior, more robust approach to spatial representation in GIS, the market share for truly OO GIS (e.g., Smallworld, Laser-Scan) and database management systems (e.g., ObjectStore) has remained comparatively small. Instead, hybrid object-rela- tional database management systems (ORDBMS, e.g., Oracle Spatial) have emerged to combine the best of both approaches to database management and spatial query. Putting the Real World onto Media Having introduced the representation of geographic phenomena in GIS from a practical “what you see on the screen” perspective, it is now necessary to do so from a computer science “what technically underpins it” perspective. Essentially, we want to achieve a representation of a landscape that can be stored digitally on a machine in such a way that the representation is con- venient to handle and analyze using that machine. Ultimately, the intended purpose of the representation, the nature of software tools available and the types of analyses we wish to undertake will strongly influence the form of representation that is deemed appropriate. A machine representation of a landscape as a digital stream of binary zeros and ones on a hard disk or diskette necessitates a considerable amount of abstraction, to say the least. The process of abstraction and translation into zeros and ones needs to be a formally controlled process if the results are going to be of any use. This process is known as data modeling and is dis- cussed at some length by Peuquet (1984) and Molenaar (1998). Two diagram- matic views of the data modeling process are given in Figure 2.8. In general, four levels can be recognized within data modeling: 1. The first of these is reality itself, which is the range of phenomena we wish to model as they actually exist or are perceived to exist in all their complexity. 2. The second level is the conceptual model, which is the first stage abstraction and incorporates only those parts of reality considered to be relevant to the particular application. A cartographic map is a good metaphor for the conceptual model as a map only contains
- 46. From GIS to Geocomputation 25 those features that the cartographer has chosen to represent and all other aspects of reality are omitted. This provides an immediate simplification, though a sense of the reality can still be readily inter- preted or reconstituted from it. Just as a cartographer must decide in creating a map what symbologies should be used for the various features, so it is at the conceptual modeling stage that decisions are generally made as to whether to use raster or vector and what the theme for each layer is going to be. The conceptual model is often referred to as the data model, which in a data modeling process can give rise to confusion. 3. The third level is the logical model, often called the data structure. This is a further abstraction of the conceptual model into lists, arrays, and matrices that represent how the features of the conceptual model are going to be entered and viewed in the database, handled within the code of the software, and prepared for storage. The logical model can generally be interpreted as reality only with the assistance of software, such as by creating a display. 4. The fourth level is the physical model or file structure. This is the final abstraction and represents the way in which the data are physically stored on the hardware or media as bits and bytes. The third and fourth levels, the logical and physical models, are usually taken care of in practical terms by the GIS software and hardware being Reality Data Model Data Structure File Structure ID 1 2 3 A1 A2 Avenue Two Increasing Abstraction Application Domain Conceptual Model Spatial Reasoning Application Disciplines Geo- Information Science Computer Science Logical Model Physical Model Avenue One Street One Street Two Street Three A3 Figure 2.8 Stages in the data modeling process. (Partly based on Molenaar, M. (1998) An introduction to the theory of spatial object modeling. Taylor & Francis, London.)
- 47. 26 GIS, Environmental Modeling and Engineering, Second Edition used. Long gone are the days of programming and compiling your own GIS software from scratch when the designs of the logical and physical mod- els were important. De facto standards, such as Microsoft® Windows® are even leading to a high degree of interoperability allowing Excel® spread- sheets to be accessed in MapInfo, as just one example. The challenge then is in creating the conceptual model that will not only adequately reflect the phenomena to be modeled, but also lead to efficient handling and analysis. The choice between vector and tessellation approaches can be important, as they have their relative advantages and disadvantages. These, however, are not entirely straightforward as the logical model (as offered by the software) used to underpin any conceptual model has important bearing on the ease of handling and “added intelligence” of the data for particular types of analy- ses. This issue then needs some further discussion. Vector As already discussed, the primitives or basic entities of vector represen- tation are point, line, and polygon (Figure 2.9) where a point is a zero- dimensional object, a line is a linear connection between two points in one-dimension, and a polygon is one or more lines where the end point of the line or chain of lines coincides with the start point to form a closed two-dimensional (2D) object. A line need not be straight, but can take on any weird shape as long as there are no loops. Any nonstraight line, from a digital perspective, is in fact made up of a series of segments and each segment will, of course, begin and end at a point. In order to avoid confu- sion then, points at the beginning and end of a line or connecting two or more lines are referred to as nodes. Lines connected at their nodes into a series can form a network. Polygons (also known as area features) when adjacent to one another will share one or more lines. Because all lines have orientation from their start node to their end node, they have a direction and on the basis of this have a left and right side. Thus, within a logical model that records topology, which is explicitly recording connectivity (as in a network) or adjacency (as for polygons), the polygon to the left and right of a line can be explicitly recorded in the database (Figure 2.10). In this way, a fully topological database has additional intelligence so that locating neighboring lines and polygons becomes straightforward. Some desktop GIS do not go so far, leaving each feature to be recorded separately without reference to possible neighbors. These are commonly referred to as shape-files. Finally, by providing a unique identifier to each point, line, and polygon (usually done automatically by the software), a join can be made to a database containing relevant attributes for each object (see Figure 2.7). Thus, by selecting specific map features in a vector-based GIS, their attri- butes can be displayed from the database. Conversely, by selecting specific attributes from the database, their spatial representation on the map can be highlighted.
- 48. From GIS to Geocomputation 27 Point ID Y Label X (a) Segment Line Node Point 1 1 1 1 2 m compose begin / end compose ID ID Label Y X X Y (b) Segment Line Polygon Node Point 1 1 1 1 1 2 m m m compose compose L polygon ID R polygon ID begin / end compose ID ID ID Label Y X X Y Entity Attribute 1 Relationship (c) Figure 2.9 Entities of the vector model: (a) point, (b) line, (c) polygon.
- 49. 28 GIS, Environmental Modeling and Engineering, Second Edition Tessellations A tessellation is a space-filling mesh (Figure 2.11) either with explicit bound- aries as a mesh of polygons or with an implicit mesh as defined, say, by a matrix of values in the logical model. A tessellation can be either regular, in which case, mesh elements are all the same size and shape, or irregular. Elements of a regular mesh could be isosceles triangles, squares (raster), rectangles, or hexagons. One example of an irregular mesh is a triangulated irregular network or TIN (Mark, 1975) in which a point pattern is formed into a triangular mesh often as a precursor to interpolating contours. Another is Theissen polygons (Theissen, 1911), which is the dual of TIN and represents the area of influence of each point in a point pattern. Tessellations can also be recursive, that is, the basic mesh shape can be progressively split into a finer mesh in order to represent higher resolution 1 5 6 11 10 15 14 9 4 7 3 2 1 1 8 13 7 12 1 Polygon Line Node Node List ID 1 2 3 4 Line ID X, Y Pairs 1 2 3 4 122, 130 134, 72 95, 54 56, 60, 52, 71 5 6 ID 1 2 3 4 5 6 11 1 2 3 4 5 12 7 8 9 10 6 Line List 13 12 13 14 15 11 14 6 7 8 9 10 15 7 8 9 10 95 112 107 83 134 117 72 53 89 87 115 94 72 77 112 56 54 95 130 101 X Y Line List Segment List Polygon List ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 2 3 4 10 2 3 4 10 5 5 6 7 8 1 2 3 4 8 9 6 7 8 9 9 5 6 7 10 From Node To Node 1 2 3 4 5 2 6 2 3 4 6 Left Polygon 6 1 1 1 1 3 4 5 6 2 3 4 5 5 Right Polygon 1 3 4 6 6 2 2 1 10 4 3 5 9 8 5 Figure 2.10 Building topology into the vector model.
- 50. From GIS to Geocomputation 29 (a) (b) (c) (d) (e) Figure 2.11 Examples of mesh types within the tessellation model: (a) point data set from which the tessel- lations are derived, (b) Theissen polygons, (c) raster, (d) quadtree, (e) TIN.
- 51. 30 GIS, Environmental Modeling and Engineering, Second Edition features. An example of this type of tessellation is the quadtree (Samet, 1984), which seeks to subdivide in a hierarchy, subject to a predefined minimum resolution, in order to achieve homogeneity within cells. One clear advantage of quadtree data structure over the traditional raster approach is that redun- dancy is reduced and storage is more compact. Topology in tessellations can be either implicit or explicit (Figure 2.12). For regular meshes, neighbors can be easily found by moving one cell to the left, right, up, down, or diagonally in which case the topology is implicit. For a TIN, the topology can be made explicit just as it is in the vector model because each triangular element is a polygon. For structures such as quadtree, an explicit topology can be stored by use of Morton ordering (Morton, 1966) to produce a space-filling curve (in Xi–1, j–1 Xi–1, j+1 Xi–1, j j i Xi+1, j–1 Xi+1, j+1 Xi+1, j Xi, j–1 Xi, j+1 Xij (a) 32 30 12 10 33 3 2 1 0 31 13 11 111 113 131 133 311 313 331 333 110 112 130 132 310 312 330 332 101 103 121 123 301 303 321 323 100 102 120 122 300 302 320 322 011 013 031 033 211 213 231 233 010 012 030 032 210 212 230 232 001 003 021 023 201 203 221 223 000 002 020 022 200 202 220 222 22 20 02 00 23 21 03 01 (b) (c) Figure 2.12 Examples of implicit and explicit topology in the tessellation model: (a) implicit neighbors, (b) Peano scan, (c) Morton ordering.
- 52. From GIS to Geocomputation 31 this case an N-shaped Peano scan), which reflects position of a cell within a hierarchical decomposition. The generally accepted relative advantages and disadvantages of vector and tessellation approaches are given in Table 2.3. Even so, as will be discussed below, most GIS provide adequate functionality for transforming vector to raster and vice versa and for transforming point patterns to area features (Theissen polygons), areas to points (centroids), lines to areas, points to TIN, and so on. More often than not, choice of an initial conceptual model is by no means a straightjacket. Object-Oriented Object-oriented (OO) analysis seeks to decompose a phenomenon into iden- tifiable, relevant classes of objects and to explicitly relate them into a struc- tured theme (Coad and Yourdan, 1991). A class represents a group of objects having similar or shared characteristics. These are made explicit in the attri- butes and services of a class, where attributes that describe or characterize the class and the services (or methods) are computer coded for handling that class (e.g., transformation, visualization). Thus, the class pub includes all objects that can be called a pub; attributes would include general character- istics shared by all pubs (opening hours, license); services might include the code for plotting a symbol of appropriate size on a map or screen. A specific pub, say the George & Dragon, would be an instance of a class and would inherit the attributes and services of that class as well as having some attri- butes and services specific to itself. The way classes are structured in a theme is shown explicitly by the links between them and which determine the form of association and, in turn, the form that inheritance takes. is _ a denotes generalization–specification structures while part _ of denotes whole-to- part structures; other forms of association, such as possess, start, stop, and so on are possible. An example of an OO analysis is given in Figure 2.13 for Table 2.3 Relative Advantages and Disadvantages of Vector and Tessellation Models Vector Tessellations POSITIVE Good portrayal of individual object geometry: versatility of point, line, polygon primitives Portrayal of networks Explicit topology Multiplicity of object attributes in RDBMS Topological (polygon) overlay Good portrayal of spatially continuous phenomena (fields) Relatively simple data structures Map algebra (on raster) Better conformance with remote sensing imagery NEGATIVE Relatively complex data structure, requires conflation of common object boundaries between layers and edge matching of tiles Poor representation of natural variation Implicit and explicit topology only at cell, not feature level Single attribute layers only Blocky cartographic appearance
- 53. 32 GIS, Environmental Modeling and Engineering, Second Edition some classes that constitute a landscape. The top most class (or super class) is landscape, which, for the sake of simplicity has two parts: community and topography. The class community can be further partitioned into classes, one of which is village, which in turn can be further partitioned into classes, one of which is building. Class pub is _ a building is a specific class of building with the George & Dragon being an instance of pub. Within this structure there are mixtures of classes that can be physical objects (village, topography) or those that are social constructs (community). Clearly it is very difficult to map a “com- munity” and while it may physically consist, in this example, of a village and its surrounding hamlets and farms, it will have other dimensions that are nei- ther easily quantified nor easily portrayed in map form (e.g., degree of cohe- sion, social structure, political outlook). In a traditional vector or raster GIS, it is not possible to include abstract, conceptual features that are not distinctly spatial objects no matter how important they might be to planning and envi- ronmental decision making. In OO, it is possible to include such classes of features, and while they may not have distinct geographic boundaries they can be included in the data structure and analyzed alongside those classes of features that are geographically distinct. For a more detailed example of this, see Brimicombe and Yeung (1995). So far in our landscape example, we haven’t touched on the issue of geometry. Whether a class is portrayed by its services in a vector or tessellation representation (or both, or even as 3D virtual real- ity) will depend on the attributes and services that are encapsulated within a class or instance of a class. Thus, in Figure 2.13, the farm, hamlet, village, and its components may well be all represented by vector geometry while topography may be represented both as tessellations (raster, TIN) and vector (contours). Overall, while OO provides for much greater versatility, it is not so straight- forward to implement as a traditional vector and raster GIS. Data Characteristics Data sources for GIS are broadly classified as primary or secondary. Primary data are those collected through first-hand surveys and can be termed raw data if they are unprocessed observations. Secondary data are those collected by others, perhaps even for a different purpose, or have been derived from published/marketed sources. All data used in connection with GIS that have dimensionality can be categorized by measurement type and have charac- teristics of scale and resolution. Furthermore, the data may be an exhaustive compilation (e.g., census) or it may be a sample. With data so central to GIS, it is important to have an understanding of these issues. A GIS layer of data has a locational, temporal, and thematic dimension or component, usually represented as a cube, whereby one component is always
- 54. From GIS to Geocomputation 33 fixed, another is allowed to vary in a controlled manner, and the third is measured (Sinton, 1978). Some examples are given in Figure 2.14: For the land • cover layer, time is fixed as a snapshot; the theme is controlled through defining a fixed number of land cover catego- ries; location is measured in as much as the land cover is observed/ recorded at all places. &/$66 6(59,&(6 PART_OF IS_A 7232*5$3+< &20081,7< )$50 +$0/(7 9,//$*( *5((1 Vector 675((7 %8,/',1* &+85&+ +286( 38% George & Dragon /$1'6&$3( Tessellation and vector $775,%87(6 Figure 2.13 Object-oriented modeling of geographic features.
- 55. Other documents randomly have different content
- 56. clara, cantando a Mandolinata: Amici, la notte é bella, La luna va spontari... —Fica tão só, coitada!...—disse Jorge. Deu alguns passos pelo escriptorio, fumando, com a cabeça baixa: —Todo o casal bem organisado, Sebastião, deve ter dous filhos! Deve ter pelo menos um!... Sebastião coçou a barba em silencio—e a voz de Luiza, elevando-se com um certo esforço aspero, nos altos da melodia : Di cà, di là, per la cità Andiami a transnottari... Era uma tristeza secreta de Jorge—não ter um filho! Desejava-o tanto! Ainda em solteiro, nas vesperas do casamento, já sonhava aquella felicidade: o seu filho! Via-o de muitas maneiras: ou gatinhando com as suas perninhas vermelhas, cheias de rôscas, e os cabellos annelados, finos como fios de sêda; ou rapaz forte, entrando da escóla com os livros, alegre e d'olho vivo, vindo mostrar-lhe as boas notas dos mestres: ou, melhor, rapariga crescida, clara e rosada, com um vestido branco, as duas tranças cahidas, vindo pousar as mãos nos seus cabellos já grisalhos... Vinha-lhe, ás vezes, um medo de morrer sem ter tido aquella felicidade completadora! Agora, na sala, a voz aguda de Ernestinho perorava, depois, no
- 57. piano Luiza recomeçou a Mandolinata, com um brio jovial. A porta do escriptorio abriu-se, Julião entrou: —Que estão vossês aqui a conspirar? Vou-me safar, que é tarde! Até á volta, meu velho, hein? Tambem ia comtigo tomar ar, respirar, vêr campos, mas... E sorriu com amargura.—Addio! Addio! Jorge foi alumiar-lhe ao patamar, abraçal-o outra vez. Se quizesse alguma cousa do Alemtejo!... Julião carregou o chapéo na cabeça: —Dá cá outro charuto, por despedida! Dá cá dous! —Leva a caixa! Eu em viagem só fumo cachimbo. Leva a caixa, homem! Embrulhou-lh'a n'um Diario de Noticias; Julião metteu-a debaixo do braço, e descendo os degraus: —Cuidado com as sezões, e descobre uma mina d'ouro! Jorge e Sebastião entraram na sala. Ernestinho, encostado ao piano, torcia as guias do bigodinho, e Luiza começava uma valsa de Strauss —o Danubio Azul. Jorge disse, rindo, estendendo os braços: —Uma valsa, D. Felicidade? Ella voltou-se, com um sorriso. E porque não? Em nova era fallada! Citou logo a valsa que dançára com o sr. D. Fernando, no tempo da Regencia, nas Necessidades. Era uma valsa linda, d'essa época: A
- 58. Perola d'Ophir. Estava sentada ao pé do conselheiro, no sophá. E como retomando um dialogo mais querido—continuou, baixo para elle, com uma voz meiga: —Pois creia, acho-o com optimas côres. O conselheiro enrolava vagarosamente o seu lenço de sêda da India. —Na estação calmosa passo sempre melhor. E D. Felicidade? —Ai! Estou outra, conselheiro! Muito boas digestões, muito livre de gazes... Estou outra! —Deus o queira, minha senhora, Deus o queira—disse o conselheiro, esfregando lentamente as mãos. Tossiu, ia levantar-se, mas D. Felicidade pôz-se a dizer: —Espero que esse interesse seja verdadeiro... Córou. O corpete flaccido do vestido de sêda preta enchia-se-lhe com o arfar do peito. O conselheiro recahiu lentamente no sophá,—e com as mãos nos joelhos: —D. Felicidade sabe que tem em mim um amigo sincero... Ella levantou para elle seus olhos pisados, d'onde sahiam revelações de paixão e supplicas de felicidade: —E eu, conselheiro!... Deu um grande suspiro, pôz o leque sobre o rosto.
- 59. O conselheiro ergueu-se seccamente. E com a cabeça alta, as mãos atraz das costas, foi ao piano, perguntou a Luiza curvando-se: —É alguma canção do Tyrol, D. Luiza? —Uma valsa de Strauss—murmurou-lhe Ernestinho, em bicos de pés, ao ouvido. —Ah! Muita fama! Grande author! Tirou então o relogio. Eram horas, disse, de ir coordenar alguns apontamentos. Aproximou-se de Jorge, com solemnidade: —Jorge, meu bom Jorge, adeus! Cautela com esse Alemtejo! O clima é nocivo, a estação traiçoeira! E apertou-o nos braços com uma pressão commovida. D. Felicidade punha a sua manta de renda negra. —Já, D. Felicidade?—disse Luiza. Ella explicou-lhe, ao ouvido: —Já, sim, filha, que tenho estado a abarrotar, comi umas bajes e tenho estado!... E aquelle homem, aquelle gêlo! O snr. Ernesto vem para os meus sitios, hein? —Como um fuso, minha senhora! Tinha vestido o seu paletot d'alpaca clara, fumava chupando, com as faces encovadas, por uma boquilha enorme, onde uma Venus se torcia sobre o dorso d'um leão domado. —Adeus, primo Jorge, saudinha e dinheiro, hein? Adeus. Quando fôr
- 60. a Honra e Paixão cá mando um camarote á prima Luiza. Adeus! Saudinha! Iam a sahir. Mas o conselheiro, á porta, voltando-se subitamente, com as abas do paletot deitadas para traz, a mão pomposamente apoiada no castão de prata da bengala que representava uma cabeça de mouro, disse, com gravidade: —Esquecia-me, Jorge! Tanto em Evora, como em Beja, visite os governadores civis! E eu lhe digo porquê: deve-lh'o como primeiros funccionarios do districto, e podem-lhe ser de muita utilidade nas suas peregrinações scientificas! E curvando-se profundamente: —Al rivedere, como se diz em Italia. Sebastião tinha ficado. Para arejar do fumo de tabaco Luiza foi abrir as janellas; a noite estava quente e immovel, de luar. Sebastião pozera-se ao piano, e com a cabeça curvada, corria devagar o teclado. Tocava admiravelmente, com uma comprehensão muito fina da musica. Outr'ora, compozera mesmo uma Meditação, duas Valsas, uma Ballada: mas eram estudos muito trabalhados, cheios de reminiscencias, sem estylo.—Da cachimonia não me sahe nada— costumava elle dizer com bonhomia, batendo na testa, sorrindo— mas lá com os dedos!... Pôz-se a tocar um Nocturno de Choppin. Jorge sentára-se no sophá ao pé de Luiza. —Já tens prompto o teu farnelzinho!—disse-lhe ella.
- 61. —Bastam umas bolachas, filha. O que quero é o cantil com cognac. —E não te esqueças de mandar um telegramma logo que chegues! —Pudera! —Tu d'aqui a quinze dias, vens! —Talvez... Ella teve um gesto amuado. —Ah, bem! Se não vieres, vou ter comtigo! A culpa é tua. E olhando em redor: —Que só que vou ficar! Mordeu o beicinho, fitou o tapete. E de repente, com a voz ainda triste: —Pst, Sebastião! A malaguenha, faz favor? Sebastião começou a tocar a malaguenha. Aquella melodia calida, muito arrastada, encantava-a. Parecia-lhe estar em Malaga, ou em Granada, não sabia: era sob as laranjeiras, mil estrellinhas luzem; a noite é quente, o ar cheira bem; por baixo d'um lampeão suspenso a um ramo, um cantador sentado na tripeça mourisca faz gemer a guitarra; em redor as mulheres com os seus corpetes de velludilho encarnado batem as mãos em cadencia: e ao largo dorme uma Andaluzia de romance e de zarzuela, quente e sensual, onde tudo são braços brancos que se abrem para o amor, capas romanticas que roçam as paredes, sombrias viellas onde luz o nicho do santo e se repenica a viola, serenos que invocam a Virgem Santissima cantando as horas...
- 62. —Muito bem, Sebastião! Gracias! Elle sorriu, ergueu-se, fechou cuidadosamente o piano, e indo buscar o seu chapéo desabado: —Então ámanhã ás sete? Cá estou, e vou-te acompanhar até ao Barreiro. Bom Sebastião! Foram debruçar-se na varanda para o vêr sahir. A noite fazia um silencio alto, d'uma melancolia placida; o gaz dos candieiros parecia mortiço; a sombra que se recortava na rua, com uma nitidez brusca, tinha um tom quente e dôce; a luz punha nas fachadas brancas claridades vivas, e nas pedras da calçada faiscações vidradas; uma clara-boia reluzia, a distancia, como uma velha lamina de prata; nada se movia; e instinctivamente os olhos erguiam-se para as alturas, procuravam a lua branca, muito séria. —Que linda noite! A porta bateu, e Sebastião de baixo, na sombra: —Dá vontade de passear, hein? —Linda! Ficaram á varanda preguiçosamente, olhando, detidos pela tranquillidade, pela luz. Puzeram-se a fallar baixo da jornada. Áquella hora onde estaria elle? Já em Evora, n'um quarto d'estalagem, passeando monotonamente sobre um chão de tijolo. Mas voltaria breve; esperava fazer um bom negocio com o Paco, o hespanhol das minas de Portel, trazer talvez alguns centos de mil reis, e teriam então a doçura do mez de setembro; poderiam fazer uma jornada ao Norte, irem ao Bussaco, trepar aos altos, beber a agua fresca das
- 63. rochas, sob a espessura humida das folhagens: irem a Espinho, e pelas praias, sentar-se na arêa, no bom ar cheio d'azote, vendo o mar unido, d'um azul metallico e faiscante, o mar do verão, com algum fumo de paquete que passa para o Sul ao longe muito adelgaçado. Faziam outros planos com os hombros muito chegados: uma felicidade abundante enchia-os deliciosamente. E Jorge disse: —Se houvesse um pequerrucho, já não ficavas tão só! Ella suspirou. Tambem o desejava tanto! Chamar-se-hia Carlos Eduardo. E via-o no seu berço dormindo, ou no collo, nú, agarrando com a mãosinha o dedo do pé, mamando a ponta rosada do seu peito... Um estremecimento d'um deleite infinito correu-lhe no corpo. Passou o braço pela cinta de Jorge. Um dia seria, teria um filho de certo! E não comprehendia o seu filho homem nem Jorge velho: via-os ambos do mesmo modo: um sempre amante, novo, forte; o outro sempre dependente do seu peito, da maminha, ou gatinhando e palrando, louro e côr de rosa. E a vida apparecia-lhe infindavel, d'uma doçura igual, atravessada do mesmo enternecimento amoroso, quente, calma e luminosa como a noite que os cobria. —A que horas quer a senhora que a venha acordar?—disse a voz secca de Juliana. Luiza voltou-se: —Ás sete, já lhe disse ha pouco, creatura. Fecharam a janella. Em torno das velas uma borboleta branca esvoaçava. Era bom agouro! Jorge prendeu-a nos braços: —Vai ficar sem o seu maridinho, hein?—disse tristemente.
- 64. Ela deixou pesar o corpo sobre as mãos d'elle cruzadas, olhou-o com um longo olhar que se ennevoava e escurecia, e envolvendo-lhe o pescoço com o gesto lento, harmonioso e solemne dos braços, pousou-lhe na bocca um beijo grave e profundo. Um vago soluço levantou-lhe o peito. —Jorge! Querido!—murmurou. III Havia doze dias que Jorge tinha partido e, apesar do calor e da poeira, Luiza vestia-se para ir a casa de Leopoldina. Se Jorge soubesse, não havia de gostar, não! Mas estava tão farta de estar só! Aborrecia-se tanto! De manhã, ainda tinha os arranjos, a costura, a toilette, algum romance... Mas de tarde! Á hora em que Jorge costumava voltar do ministerio, a solidão parecia alargar-se em torno d'ella. Fazia-lhe tanta falta o seu toque da campainha, os seus passos no corredor!... Ao crepusculo, ao vêr cahir o dia, entristecia-se sem razão, cahia n'uma vaga sentimentalidade: sentava-se ao piano, e os fados tristes, as cavatinas apaixonadas gemiam instinctivamente no teclado, sob os seus dedos preguiçosos, no movimento abandonado dos seus braços molles. O que pensava em tolices então! E á noite, só, na larga cama franceza, sem poder dormir com o calor, vinham- lhe de repente terrores, palpites de viuvez. Não estava acostumada, não podia estar só. Até se lembrára de chamar a tia Patrocinio, uma velha parenta pobre que vivia em
- 65. Belem: ao menos era alguem: mas receou aborrecer-se mais ao pé da sua longa figura de viuva taciturna, sempre a fazer meia, com enormes oculos de tartaruga sobre um nariz d'aguia. N'aquella manhã pensára em Leopoldina, toda contente d'ir tagarellar, rir, segredar, passar as horas do calor. Penteava-se em collete e saia branca: a camisinha decotada descobria os ombros alvos d'uma redondeza macia, o collo branco e tenro, azulado de vêasinhas finas; e os seus braços redondinhos, um pouco vermelhos no cotovêlo, descobriam por baixo, quando se erguiam prendendo as tranças, fiosinhos louros, frisando e fazendo ninho. A sua pelle conservava ainda o rosado humido da agua fria: havia no quarto um cheiro agudo de vinagre de toilette: os transparentes de linho branco descidos davam uma luz baça, com tons de leite. Ah! positivamente devia escrever a Jorge, que voltasse depressa! Que o que tinha graça era ir surprehendel-o a Evora, cahir-lhe no Tabaquinho, um dia, ás tres horas! E quando elle entrasse empoeirado e encalmado, de lunetas azues, atirar-se-lhe ao pescoço! E á tardinha, pelo braço d'elle, ainda quebrada da jornada, com um vestido fresco, ir vêr a cidade. Pelas ruas estreitas e tristes admiravam-na muito. Os homens vinham ás portas das lojas. Quem seria? É de Lisboa. É a do Engenheiro.—E diante do toucador, apertando o corpete do vestido, sorria áquellas imaginações, e ao seu rosto, no espelho. A porta do quarto rangeu devagarinho. —Que é? A voz de Juliana, plangente, disse: —A senhora dá licença que eu vá logo ao medico? —Vá, mas não se demore. Puxe-me essa saia atraz. Mais. O que é
- 66. que vossê tem? —Enjôos, minha senhora, peso no coração. Passei a noite em claro. Estava mais amarella, o olhar muito pisado, a face envelhecida. Trazia um vestido de merino preto escoado, e a cuia da semana de cabellos velhos. —Pois sim, vá—disse Luiza.—Mas arranje tudo antes. E não se demore, hein ? Juliana subiu logo á cozinha. Era no segundo andar, com duas janellas de sacada para as trazeiras, larga, ladrilhada de tijolo diante do fogão. —Diz que sim, snr.a Joanna—disse á cozinheira—que podia ir. Vou- me vestir. Ella tambem está quasi prompta. Fica vossemecê com a casa por sua! A cozinheira fez-se vermelha, poz-se a cantar, foi logo sacudir, estender na varanda um velho tapete esfiado; e os seus olhos não deixavam, defronte, uma casa baixa, pintada d'amarello, com um portal largo,—a loja de marceneiro do tio João Galho, onde trabalhava o Pedro, o seu amante. A pobre Joanna «babava-se» por ele. Era um rapazola pallido e afadistado; Joanna era minhota, de Avintes, de familia de lavrador, e aquella figura delgada de lisboeta anemico seduzia-a com uma violencia abrazada. Como não podia sahir á semana, mettia-o em casa, pela porta de traz, quando estava só; estendia então na varanda para dar signal o velho tapete desbotado, onde ainda se percebiam os paus de um veado. Era uma rapariga muito forte, com peitos d'ama, o cabello como azeviche, todo lustroso do oleo de amendoas dôces. Tinha a testa curta de plebêa teimosa. E as sobrancelhas cerradas faziam-lhe parecer o olhar mais negro.
- 67. —Ai!—suspirou Juliana.—A snr.a Joanna é que a leva! A rapariga ficou escarlate. Mas Juliana acudiu logo: —Olha o mal! fosse eu! Boa! faz muito bem! Juliana lisongeava sempre a cozinheira: dependia d'ella: Joanna dava-lhe caldinhos ás horas de debilidade, ou, quando ella estava mais adoentada, fazia-lhe um bife ás escondidas da senhora. Juliana tinha um grande medo de «cair em fraqueza», e a cada momento precisava tomar a «sustancia». De certo, como feia e solteirona detestava aquelle «escandalo do carpinteiro»; mas protegia-o, porque elle valia muitos regalos aos seus fracos de gulosa. —Fosse eu!—repetiu—dava-lhe o melhor da panella! Se a gente ia a ter escrupulos por causa dos amos, boa! Olha quem! Vêem uma pessoa a morrer, e é como fosse um cão. E com um risinho amargo: —Diz que me não demorasse no medico. É como quem diz, cura-te depressa ou espicha depressa! Foi buscar a vassoura a um canto, e com um suspiro agudo: —Todas o mesmo, uma récua! Desceu, começou a varrer o corredor.—Toda a noite estivera doente: o quarto no sotão, debaixo das telhas, muito abafado, com um cheiro de tijolo cozido, dava-lhe enjôos, faltas d'ar, desde o começo do verão: na vespera até vomitára! E já levantada ás seis horas, não descançára, limpando, engommando, despejando, com a pontada no
- 68. lado e todo o estomago embrulhado!—Tinha escancarado a cancella, e com grandes ais, atirava vassouradas furiosas contra as grades do corrimão. —A snr.a D. Luiza está em casa? Voltou-se. Nos ultimos degraus da escada estava um sujeito, que lhe pareceu «estrangeirado». Era trigueiro, alto, tinha um bigode pequeno levantado, um ramo na sobrecasaca azul, e o verniz dos seus sapatos resplandecia. —A senhora vai sahir—disse ela olhando-o muito.—Faz favor de dizer quem é? O individuo sorriu. —Diga-lhe que é um sujeito para um negocio. Um negocio de minas. Luiza, diante do toucador, já de chapéo, mettia n'uma casa do corpete dous botões de rosa de chá. —Um negocio!—disse muito surprehendida—Deve ser algum recado para o snr. Jorge, de certo! Mande entrar. Que especie de homem é? —Um janota! Luiza desceu o véo branco, calçou devagar as luvas de peau de suède claras, deu duas pancadinhas fofas ao espelho na gravata de renda, e abriu a porta da sala. Mas quasi recuou, fez ah! toda escarlate. Tinha-o reconhecido logo. Era o primo Bazilio. Houve um shake-hands demorado, um pouco tremulo. Estavam ambos calados:—ella com todo o sangue no rosto, um sorriso vago;
- 69. elle fitando-a muito, com um olhar admirado. Mas as palavras, as perguntas vieram logo, muito precipitadamente:—Quando tinha elle chegado? Se sabia que elle estava em Lisboa? Como soubera a morada d'ella? Chegára na vespera no paquete de Bordeus. Perguntára no ministerio: disseram-lhe que Jorge estava no Alemtejo, deram-lhe a adresse... —Como tu estás mudada, Santo Deus! —Velha? —Bonita! —Ora! E elle, que tinha feito? Demorava-se? Foi abrir uma janella, dar uma luz larga, mais clara. Sentaram-se. Elle no sophá muito languidamente; ella ao pé, pousada de leve á beira d'uma poltrona, toda nervosa. Tinha deixado o degredo—disse elle.—Viera respirar um pouco á velha Europa. Estivera em Constantinopla, na Terra Santa, em Roma. O ultimo anno passára-o em Paris. Vinha de lá, d'aquella aldeola de Paris!—Fallava devagar, recostado, com um ar intimo, estendendo sobre o tapete, commodamente, os seus sapatos de verniz. Luiza olhava-o. Achava-o mais varonil, mais trigueiro. No cabello preto annelado havia agora alguns fios brancos: mas o bigode pequeno tinha o antigo ar moço, orgulhoso e intrepido; os olhos, quando ria, a mesma doçura amollecida, banhada n'um fluido. Reparou na ferradura de perola da sua gravata de setim preto, nas pequeninas estrellas brancas bordadas nas suas meias de sêda. A Bahia não o vulgarisára. Voltava mais interessante!
- 70. —Mas tu, conta-me de ti—dizia elle com um sorriso, inclinado para ela.—És feliz, tens um pequerrucho... —Não—exclamou Luiza rindo.—Não tenho! Quem te disse? —Tinham-me dito. E teu marido demora-se? —Tres, quatro semanas, creio. Quatro semanas! Era uma viuvez! Offereceu-se logo para a vir vêr mais vezes, palrar um momento, pela manhã... —Pudera não! És o unico parente, que tenho, agora... Era verdade!... E a conversação tomou uma intimidade melancolica: fallaram da mãi de Luiza, a tia Jójó, como lhe chamava Bazilio. Luiza contou a sua morte, muito dôce, na poltrona, sem um ai... —Onde está sepultada?—perguntou Bazilio com uma voz grave; e acrescentou, puxando o punho da camisa de chita:—Está no nosso jazigo? —Está. —Hei-de ir lá. Pobre tia Jójó! Houve um silencio. —Mas tu ias sahir!—disse Bazilio de repente, querendo erguer-se. —Não!—exclamou—Não! Estava aborrecida, não tinha nada que fazer. Ia tomar ar. Não saio, já. Elle ainda disse:
- 71. —Não te prendas... —Que tolice! Ia a casa d'uma amiga passar um momento. Tirou logo o chapéo; n'aquelle movimento os braços erguidos repuxaram o corpete justo, as fórmas do seio accusaram-se suavemente. Bazilio torcia a ponta do bigode devagar; e vendo-a descalçar as luvas: —Era eu antigamente quem te calçava e descalçava as luvas... Lembras-te?... Ainda tenho esse privilegio exclusivo, creio eu... Ella riu-se. —De certo que não... Bazilio disse então, lentamente, fitando o chão: —Ah! Outros tempos! E poz-se a fallar de Collares: a sua primeira idéa, mal chegára, tinha sido tomar uma tipoia e ir lá: queria vêr a quinta; ainda existiria o balouço debaixo do castanheiro? ainda haveria o caramanchão de rosinhas brancas, ao pé do Cupido de gesso que tinha uma aza quebrada?... Luiza ouvira dizer que a quinta pertencia agora a um brazileiro: sobre a estrada havia um mirante com um tecto chinez, ornado de bolas de vidro; e a velha casa morgada fôra reconstruida e mobilada pelo Gardé. —A nossa pobre sala de bilhar, côr d'oca, com grinaldas de rosas!— disse Bazilio; e fitando-a:—Lembras-te das nossas partidas de bilhar?
- 72. Luiza, um pouco vermelha, torcia os dedos das luvas; ergueu os olhos para elle, disse, sorrindo: —Eramos duas crianças! Bazilio encolheu tristemente os hombros, fitou as ramagens do tapete: parecia abandonar-se a uma saudade remota, e com uma voz sentida: —Foi o bom tempo! Foi o meu bom tempo! Ella via a sua cabeça bem feita, descahida n'aquella melancolia das felicidades passadas, com uma risca muito fina, e os cabellos brancos—que lhe dera a separação. Sentia tambem uma vaga saudade encher-lhe o peito: ergueu-se, foi abrir a outra janella, como para dissipar na luz viva e forte aquella perturbação. Perguntou-lhe então pelas viagens, por Paris, por Constantinopla. Fôra sempre o seu desejo viajar—dizia—ir ao Oriente. Quereria andar em caravanas, balouçada no dorso dos camêlos; e não teria medo, nem do deserto, nem das feras... —Estás muito valente!—disse Bazilio.—Tu eras uma maricas, tinhas medo de tudo... Até da adega, na casa do papá, em Almada! Ella córou. Lembrava-se bem da adega, com a sua frialdade subterranea que dava arripios! A candêa d'azeite pendurada na parede alumiava com uma luz avermelhada e fumosa as grossas traves cheias de têas d'aranha, e a fileira tenebrosa das pipas bojudas. Havia alli ás vezes, pelos cantos, beijos furtados... Quiz saber então o que tinha feito em Jerusalém, se era bonito. Era curioso. Ia pela manhã um bocado ao Santo Sepulchro; depois d'almoço montava a cavallo... Não se estava mal no hotel, inglezas bonitas... Tinha algumas intimidades illustres...
- 73. Fallava d'ellas, devagar, traçando a perna: o seu amigo o patriarcha de Jerusalém, a sua velha amiga a princeza de La Tour d'Auvergne! Mas o melhor do dia era de tarde—dizia—no Jardim das Oliveiras, vendo defronte as muralhas do templo de Salomão, ao pé a aldêa escura de Bethania onde Martha fiava aos pés de Jesus, e mais longe, faiscando immovel sob o sol, o mar Morto! E alli passava sentado n'um banco, fumando tranquillamente o seu cachimbo! Se tinha corrido perigos? De certo. Uma tempestade de arêa no deserto de Petra! Horrivel! Mas que linda viagem, as caravanas, os acampamentos! Descreveu a sua toilette:—uma manta de pelle de camêlo ás listras vermelhas e pretas, um punhal de Damasco n'uma cinta de Bagdad, e a lança comprida dos Beduinos. —Devia-te ficar bem! —Muito bem. Tenho photographias. Prometteu dar-lhe uma, e acrescentou: —Sabes que te trago presentes? —Trazes?—E os seus olhos brilhavam. O melhor era um rosario... —Um rosario? —Uma reliquia! Foi benzido primeiro pelo patriarcha de Jerusalém sobre o tumulo de Christo, depois pelo papa... Ah! Porque tinha estado com o papa! Um velhinho muito aceado, já todo branquinho, vestido de branco, muito amavel!
- 74. —Tu d'antes não eras muito devota—disse. —Não, não sou muito caturra n'essas cousas—respondeu rindo. —Lembras-te da capella de nossa casa em Almada? Tinham passado alli lindas tardes! Ao pé da velha capella morgada havia um adro todo cheio de altas hervas floridas,—e as papoulas, quando vinha a aragem, agitavam-se como azas vermelhas de borboletas pousadas... —E a tilia, lembras-te, onde eu fazia gymnastica? —Não fallemos no que lá vai! Em que queria ella então que elle fallasse? Era a sua mocidade, o melhor que tivera na vida... Ella sorriu, perguntou: —E no Brazil? Um horror! Até fizera a côrte a uma mulata. —E porque te não casaste?... Estava a mangar! Uma mulata! —E de resto—acrescentou com a voz d'um arrependimento triste—já que me não casei quando devia,—encolheu os hombros melancolicamente—acabou-se... Perdi a vez. Ficarei solteiro. Luiza fez-se escarlate. Houve um silencio. —E qual é o outro presente, então, além do rosario?
- 75. —Ah! Luvas. Luvas de verão, de peau de suède, de oito botões. Luvas decentes. Vossês aqui usam umas luvitas de dous botões, a vêr-se o punho, um horror! De resto pelo que tinha visto, as mulheres em Lisboa cada dia se vestiam peor! Era atroz! Não dizia por ella; até aquelle vestido tinha chic, era simples, era honesto. Mas em geral, era um horror. Em Paris! Que deliciosas, que frescas as toilettes d'aquelle verão! Oh! mas em Paris!... Tudo é superior! Por exemplo, desde que chegára ainda não pudera comer. Positivamente não podia comer!—Só em Paris se come—resumiu. Luiza voltava entre os dedos o seu medalhão de ouro, preso ao pescoço por uma fita de velludo preto. —E estiveste então um anno em Paris? Um anno divino. Tinha um appartamento lindissimo, que pertencera a lord Falmouth, rue Saint Florentin, tinha tres cavallos... E recostando-se muito, com as mãos nos bolsos: —Emfim, fazer este valle de lagrimas o mais confortavel possivel!... Dize cá, tens algum retrato n'esse medalhão? —O retrato de meu marido. —Ah! deixa vêr! Luiza abriu o medalhão. Elle debruçou-se; tinha o rosto quasi sobre o peito d'ella. Luiza sentia o aroma fino que vinha de seus cabellos. —Muito bem, muito bem!—fez Bazilio. Ficaram calados.
- 76. —Que calor que está!—disse Luiza.—Abafa-se, hein! Levantou-se, foi abrir um pouco uma vidraça. O sol deixára a varanda. Uma aragem suave encheu as pregas grossas das bambinellas. —É o calor do Brazil—disse elle.—Sabes que estás mais crescida? Luiza estava de pé. O olhar de Bazilio corria-lhe as linhas do corpo; e com a voz muito intima, os cotovêlos sobre os joelhos, o rosto erguido para ella: —Mas, francamente, dize cá, pensaste que eu te viria vêr? —Ora essa! Realmente, se não viesses zangava-me. És o meu unico parente... O que tenho pena é que meu marido não esteja... —Eu—acudiu Bazilio—foi justamente por elle não estar... Luiza fez-se escarlate. Bazilio emendou logo, um pouco corado tambem: —Quero dizer... talvez elle saiba que houve entre nós... Ella interrompeu: —Tolices! Eramos duas crianças. Onde isso vai! —Eu tinha vinte e sete annos—observou elle, curvando-se. Ficaram calados, um pouco embaraçados. Bazilio cofiava o bigode, olhando vagamente em redor. —Estás muito bem installada aqui—disse.
- 77. Não estava mal... A casa era pequena, mas muito commoda. Pertencia-lhes. —Ah! estás perfeitamente! Quem é esta senhora, com uma luneta d'ouro? E indicava o retrato por cima do sophá. —A mãi de meu marido. —Ah! vive ainda? —Morreu. —É o que uma sogra póde fazer de mais amavel... Bocejou ligeiramente, fitou um momento os seus sapatos muito aguçados, e com um movimento brusco, ergueu-se, tomou o chapéo. —Já? Onde estás? —No Hotel Central. E até quando? —Até quando quizeres. Não disseste que vinhas ámanhã com o rosario? Elle tomou-lhe a mão, curvou-se: —Já se não póde dar um beijo na mão d'uma velha prima? —Porque não? Pousou-lhe um beijo na mão, muito longo, com uma pressão dôce. —Adeus!—disse.
- 78. E á porta, com o reposteiro meio erguido, voltando-se: —Sabes, que eu, ao subir as escadas, vinha a perguntar a mim mesmo, como se vai isto passar? —Isto quê? Vêrmo-nos outra vez? Mas, perfeitamente. Que imaginaste tu? Elle hesitou, sorriu: —Imaginei que não eras tão boa rapariga. Adeus. Ámanhã, hein? No fundo da escada accendeu o charuto, devagar. —Que bonita que ella está!—pensou. E arremessando o phosphoro, com força: —E eu, pedaço d'asno, que estava quasi decidido a não a vir vêr! Está de appetite! Está muito melhor! E sósinha em casa, aborrecidinha talvez!... Ao pé da Patriarchal fez parar um coupé vazio; e estendido, com o chapéo nos joelhos, em quanto a parelha esfalfada trotava: —E tem-me o ar de ser muito aceada, cousa rara na terra! As mãos muito bem tratadas! O pé muito bonito! Revia a pequenez do pé, poz-se a fazer por elle o desenho mental de outras bellezas, despindo-a, querendo adivinhal-a... A amante que deixára em Paris era muito alta e magra, d'uma elegancia de tisica; quando se decotava viam-se as saliencias das suas primeiras costellas. E as fórmas redondinhas de Luiza decidiram-no: —A ella!—exclamou com appetite:—A ella, como S. Thiago aos
- 79. mouros! Luiza, quando o sentiu em baixo fechar a porta da rua, entrou no quarto, atirou o chapéo para a causeuse, e foi-se logo vêr ao espelho. Que felicidade estar vestida! Se elle a tivesse apanhado em roupão, ou mal penteada!... Achou-se muito afogueada, cobriu-se de pós de arroz. Foi á janella, olhou um momento a rua, o sol que batia ainda nas casas fronteiras. Sentia-se cançada. Áquellas horas, Leopoldina estava a jantar já, de certo... Pensou em escrever a Jorge «para matar o tempo», mas veio-lhe uma preguiça; estava tanto calor! Depois não tinha que lhe dizer! Começou então a despir- se devagar diante do espelho, olhando-se muito, gostando de se vêr branca, acariciando a finura da pelle, com bocejos languidos d'um cansaço feliz.—Havia sete annos que não via o primo Bazilio! Estava mais trigueiro, mais queimado, mas ia-lhe bem! E depois de jantar ficou junto á janella, estendida na voltaire, com um livro esquecido no regaço. O vento cahira, e o ar, de um azul forte nas alturas, estava immovel; a poeira grossa pousára, a tarde tinha uma transparencia calma de luz; passaros chilreavam na figueira brava; da serralheria proxima sahia o martellar continuo e sonoro de folhas de ferro. Pouco a pouco o azul desbotou; sobre o poente, laivos de côr de laranja desmaiada esbateram-se como grandes pinceladas desleixadas. Depois tudo se cobriu de uma sombra diffusa, calada e quente, com uma estrellinha muita viva que luzia e tremia. E Luiza deixára-se ficar na voltaire esquecida, absorvida, sem pedir luz. —Que vida interessante a do primo Bazilio!—pensava.—O que elle tinha visto! Se ella podesse tambem fazer as suas malas, partir, admirar aspectos novos e desconhecidos, a neve nos montes, cascatas reluzentes! Como desejaria visitar os paizes que conhecia dos romances—a Escocia e os seus lagos taciturnos, Veneza e os seus palacios tragicos; aportar ás bahias, onde um mar luminoso e
- 80. faiscante morre na arêa fulva; e das cabanas dos pescadores, de tecto chato, onde vivem as Graziellas, vêr azularem-se ao longe as ilhas de nomes sonoros! E ir a Paris! Paris sobretudo! Mas, qual! Nunca viajaria de certo; eram pobres; Jorge era caseiro, tão lisboeta! Como seria o patriarcha de Jerusalém? Imaginava-o de longas barbas brancas, recamado d'ouro, entre instrumentações solemnes e rolos de incenso! E a princeza de La Tour d'Auvergne? Devia ser bella, de uma estatura real, vivia cercada de pagens, namorára-se de Bazilio.—A noite escurecia, outras estrellas luziam.—Mas de que servia viajar, enjoar nos paquetes, bocejar nos wagons, e, n'uma diligencia muita sacudida, cabecear de somno pela serra nas madrugadas frias? Não era melhor viver n'um bom conforto, com um marido terno, uma casinha abrigada, colxões macios, uma noite de theatro ás vezes, e um bom almoço nas manhãs claras quando os canarios chalram? Era o que ella tinha. Era bem feliz! Então veio-lhe uma saudade de Jorge; desejaria abraçal-o, tel-o alli, ou quando descesse ir encontral-o fumando o seu cachimbo no escriptorio, com o seu jaquetão de velludo. Tinha tudo, elle, para fazer uma mulher feliz e orgulhosa: era bello, com uns olhos magnificos, terno, fiel. Não gostaria de um marido com uma vida sedentaria e caturra: mas a profissão de Jorge era interessante; descia aos poços tenebrosos das minas, um dia aperrára as pistolas contra uma malta revoltada; era valente, tinha talento! Involuntariamente, porém, o primo Bazilio fazendo fluctuar o seu burnous branco pelas planicies da Terra Santa; ou em Paris, direito na almofada, governando tranquillamente os seus cavallos inquietos—davam-lhe a idéa d'uma outra existencia mais poetica, mais propria para os episodios do sentimento. Do céo estrellado cahia uma luz diffusa: janellas alumiadas sobresahiam ao longe, abertas á noite abafada: vôos de morcegos passavam diante da vidraça. —A senhora não quer luz?—perguntou á porta a voz fatigada de Juliana.
- 81. —Ponha-a no quarto. Desceu. Bocejava muito, sentia-se quebrada. —É trovoada—pensou. Foi á sala, sentou-se ao piano, tocou ao acaso bocados da Lucia, da Somnambula, o Fado; e parando, os dedos pousados de leve sobre o teclado, poz-se a pensar que Bazilio devia vir no dia seguinte: vestiria o roupão novo de foulard côr de castanho! Recomeçou o Fado, mas os olhos cerravam-se-lhe. Foi para o quarto. Juliana trouxe o rol e a lamparina. Vinha arrastando as chinellas, com um casabeque pelos hombros, encolhida e lugubre. Aquella figura com um ar de enfermaria irritou Luiza: —Credo, mulher! Vossê parece a imagem da morte! Juliana não respondeu. Pousou a lamparina; apanhou, placa a placa, sobre a commoda, o dinheiro das compras; e com os olhos baixos: —A senhora não precisa mais nada, não? —Vá-se, mulher, vá! Juliana foi buscar o candieiro de petroleo, subiu ao quarto. Dormia em cima, no sotão, ao pé da cozinheira. —Pareço-te a imagem da morte!—resmungava, furiosa. O quarto era baixo, muito estreito, com o tecto de madeira inclinado; o sol, aquecendo todo o dia as telhas por cima, fazia-o
- 82. Welcome to our website – the perfect destination for book lovers and knowledge seekers. We believe that every book holds a new world, offering opportunities for learning, discovery, and personal growth. That’s why we are dedicated to bringing you a diverse collection of books, ranging from classic literature and specialized publications to self-development guides and children's books. More than just a book-buying platform, we strive to be a bridge connecting you with timeless cultural and intellectual values. With an elegant, user-friendly interface and a smart search system, you can quickly find the books that best suit your interests. Additionally, our special promotions and home delivery services help you save time and fully enjoy the joy of reading. Join us on a journey of knowledge exploration, passion nurturing, and personal growth every day! ebookbell.com