Thus, uncertainty studies appear desirable to provide information about the effect of the parameter variations on the structure dynamics. Overall, we propose that the concepts of hydrological systems acting similarly and thus giving rise to redundancy or displaying unique functionality and thus being irreplaceable are not mutually exclusive. We analyze the degree of similarity of simulated discharge and storage among the hillslopes as a function of time by examining the Shannon information entropy. Our approach is neither restricted to the model nor to model targets or the data source we selected in this study. 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. Based on an extended thermodynamic approach, the authors explain which economic assumptions are acceptable for constructing a dynamic model that is consistent with the natural sciences. 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.
Based on the spatial distribution of mutual information, the whole study area was divided into five sub-regions. This study uses secondary data from Bank Indonesia and Indonesian Statistics Center from December 2005 to November 2017. On the contrary, the Shannon entropy as measure for diversity in the simulation ensemble shows a distinct annual pattern, with periods of highly redundant simulations, reflecting coherent and organized dynamics, and periods where hillslopes operate in distinctly different ways. Our results reveal that, within our given model environment, only a portion of the entire amount of topographic information stored within a digital elevation model is relevant for the simulation of distributed runoff and storage dynamics. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging.
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. They are in fact of complementary nature, and systems operate by gradually changing to different levels of organization in time. In the oasis regions, groundwater was also an important factor driving vegetation growth, and the rise of the groundwater level contributed to the growth of vegetation. The utility of the procedures is demonstrated with extreme sea level and precipitation data. Spatial and inverse spatial entropy are important for urbanplanning and are presented with clarity. This paper provides an overview of Tsallis entropy theory in water engineering. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory.
The calibrated hydrologic models simulated discharges using the updated snow water equivalent data from the Pareto-optimal networks. To such aim, flow entropy, maximum flow entropy, link density and average path length have been evaluated for a set of 22 networks, both real and synthetic, with different size and topology. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. 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. In this study we propose and demonstrate a data-driven approach in an information-theoretic framework to estimate precipitation quantitatively. . A complete discussion of the theory is presented by Kapur and Kesavan 1992 and Singh 2013.
Discusses the theory and its various aspects in both univariate and bivariate cases. The increasing diversity and resolution of spatially distributed data on terrestrial systems greatly enhance the potential of hydrological modeling. The results gained the accuracy of 96,38% and mean-squared error of 0. The Dual Entropy and Multiobjective Optimization is applied to design snow monitoring networks in La Grande River Basin in Québec and Columbia River Basin in British Columbia. Complete details are provided for the full range of ecosystems and models. The range of applications of entropy is constantlyexpanding and new areas finding a use for the theory arecontinually emerging. Shannon entropy, permutation entropy and Kullback-Leibler divergence were introduced, and former studies in which they were used in the turbulent analysis were then reviewed.
Maximum entropy spectralanalysis and minimum cross entropy spectral analysis are powerfultechniques for addressing a variety of problems faced byenvironmental and water scientists and engineers and are describedhere with illustrative examples. The strategy is based on an energetic approach. Giving a thorough introduction to the use of entropy to measurethe unpredictability in environmental and water systems this bookwill add an essential statistical method to the toolkit ofpostgraduates, researchers and academic hydrologists, waterresource managers, environmental scientists and engineers. First, several data quantization cases and their effects on the snow network design problems were explored. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Specifically, we subdivide a meso-scale catchment into 105 hillslopes and represent each by a two dimensional numerical hillslope model.
As hydraulic systems become more complex, entropy theory enables hydraulic engineers to quantify uncertainty, determine risk and reliability, estimate parameters, model processes, and design more robust and dependable water hydraulic systems. Results showed that the hybrid model produced better results in estimating the hydrograph properties than the latter models. The best model incorporated distance to the nearest otter release site, beaver occupancy, and flow rate. The results show that the degree of balance among water consumption sectors has increased from 0. How- ever, calculations of multivariate joint entropy from continuous dis- tribution functions have essential limitations at this time.
This book bridges the divide between the deterministic and the stochastic schools in hydrology, and is well suited as a textbook for hydrology courses. 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. Several measures of diversity have been proposed by different authors, but Shannon's, Simpson's and Brillouin's indices are the most widely used ones. For each method, the presentation includes a description of the conceptual basis and examples of applications in hydrology. Optimal and parsimonious use of these data sources requires, however, that we better understand a which system characteristics exert primary controls on hydrological dynamics and b to what level of detail do those characteristics need to be represented in a model. Therefore, reliable observations from an optimal snow monitoring network are necessary for an efficient management of snowmelt water for flood prevention and hydropower generation.