Entropy Theory and its Application in Environmental and Water Engineering responds to the need for a book that deals with basic concepts of entropy theory from a hydrologic and water engineering perspective and then for a book that deals with applications of these concepts to a range of water engineering problems. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging. The applications of concepts and techniques vary across different subject areas and this book aims to relate them directly to practical problems of environmental and water engineering. The book presents and explains the Principle of Maximum Entropy (POME) and the Principle of Minimum Cross Entropy (POMCE) and their applications to different types of probability distributions. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. Maximum entropy spectral analysis and minimum cross entropy spectral analysis are powerful techniques for addressing a variety of problems faced by environmental and water scientists and engineers and are described here with illustrative examples. Giving a thorough introduction to the use of entropy to measure the unpredictability in environmental and water systems this book will add an essential statistical method to the toolkit of postgraduates, researchers and academic hydrologists, water resource managers, environmental scientists and engineers. It will also offer a valuable resource for professionals in the same areas, governmental organizations, private companies as well as students in earth sciences, civil and agricultural engineering, and agricultural and rangeland sciences. This book: Provides a thorough introduction to entropy for beginners and more experienced users Uses numerous examples to illustrate the applications of the theoretical principles Allows the reader to apply entropy theory to the solution of practical problems Assumes minimal existing mathematical knowledge Discusses the theory and its various aspects in both univariate and bivariate cases Covers newly expanding areas including neural networks from an entropy perspective and future developments.

Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network design, river flow forecasting, floods and droughts, river network analysis, infiltration, soil moisture, sediment transport, surface water and groundwater quality modeling, ecosystems modeling, water distribution networks, environmental and water resources management, and parameter estimation. Such applications have used several different entropy formulations, such as Shannon, Tsallis, Rényi, Burg, Kolmogorov, Kapur, configurational, and relative entropies, which can be derived in time, space, or frequency domains. More recently, entropy-based concepts have been coupled with other theories, including copula and wavelets, to study various issues associated with environmental and water resources systems. Recent studies indicate the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering, including establishing and explaining physical connections between theory and reality. The objective of this Special Issue is to provide a platform for compiling important recent and current research on the applications of entropy theory in environmental and water engineering. The contributions to this Special Issue have addressed many aspects associated with entropy theory applications and have shown the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering.

Focuses On an Emerging Field in Water EngineeringA broad treatment of the Tsallis entropy theory presented from a water resources engineering point of view, Introduction to Tsallis Entropy Theory in Water Engineering fills a growing need for material on this theory and its relevant applications in the area of water engineering. This self-contained

Overview of systems of frequency distributions, their properties, applications to the fields of water resources and environmental engineering.

This book provides a comprehensive approach to all aspects of water-related subjects affected by climate change that expand readers' attitudes toward future of the management strategies and improve management plans. It summarizes climate change scenarios, models, downscaling methods, and how to select the appropriate method. It also introduces practical steps in assessing climate change impacts on water issues through introducing hydrological models and climate change data applications in hydrologic analysis. The book caters to specialist readers who are interested in analyzing climate change effects on water resources, and related issues can gain a profound understanding of the practical concepts and step-by-step analysis, which is enriched with real case studies all around the world. Moreover, readers will be familiar with potential mitigation and adaptation measures in sustainable water engineering, considering the results of hydrologic modeling.

This authoritative book presents a comprehensive account of the essential roles of nonlinear dynamic and chaos theories in understanding, modeling, and forecasting hydrologic systems. This is done through a systematic presentation of: (1) information on the salient characteristics of hydrologic systems and on the existing theories for their modeling; (2) the fundamentals of nonlinear dynamic and chaos theories, methods for chaos identification and prediction, and associated issues; (3) a review of the applications of chaos theory in hydrology; and (4) the scope and potential directions for the future. This book bridges the divide between the deterministic and the stochastic schools in hydrology, and is well suited as a textbook for hydrology courses.

This book analyses the physics of complex systems to elaborate the problems encountered in teaching and research. Inspired by the of Kurt Gödel (including his incompleteness theorems) it considers the concept of time, the idea of models and the concept of complexity before trying to assess the state of physics in general. Using both general and practical examples, the idea of information is discussed, emphasizing its physical interpretation, debates ideas in depth using examples and evidence to provide detailed considerations on the topics. Based on the authors’ own research on these topics, this book puts forward the idea that the application of information measures can provide new results in the study of complex systems. Helpful for those already familiar with the concepts who wish to deepen their critical understanding, Physics of Complex Systems will be extremely valuable both for people that are already involved in complex systems and also readers beginning their journey into the subject. This work will encourage readers to follow and continue these ideas, enabling them to investigate the various topics further.

The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.

Precipitation drives the dynamics of flows and storages in water systems, making its monitoring essential for water management. Conventionally, precipitation is monitored using in-situ and remote sensors. In-situ sensors are arranged in networks, which are usually sparse, providing continuous observations for long periods at fixed points in space, and due to the high costs of such networks, they are often sub-optimal. To increase the efficiency of the monitoring networks, we explore the use of sensors that can relocate as rainfall events develop (dynamic sensors), as well as increasing the number of sensors involving volunteers (citizens). This research focusses on the development of an approach for merging heterogeneous observations in non-stationary precipitation fields, exploring the interactions between different definitions of optimality for the design of sensor networks, as well as development of algorithms for the optimal scheduling of dynamic sensors. This study was carried out in three different case studies, including Bacchiglione River (Italy), Don River (U.K.) and Brue Catchment (U.K.) The results of this study indicate that optimal use of dynamic sensors may be useful for monitoring precipitation to support water management and flow forecasting.

With majority of the Earth’s people now urban dwellers, and cities being the most efficient habitat for the utilisation of resources, it is imperative that we continue to support standards of living and efficiencies of urban areas. However, the urbanisation process has not been without its problems. While much has been done to address the original issues surrounding the quality of urban life, new challenges continue to arise. It is no longer sustainable to achieve improvements by means that require greater and greater energy consumption as we did in the past. Despite their complexity, however, cities are a great laboratory for architects, engineers, and other key professionals to apply new ideas and new technology to meet our requirements for more sustainable city environments. Containing papers presented at the latest in a series of conferences organised by the Wessex Institute of Technology, these proceedings, split in to two volumes address not just environmental, architectural, and engineering concerns, but also quality of life, security, risk, and heritage. The diversity of topics and the case studies based on existing projects make the book an important contribution to the literature on urban planning.