Mathematical Modeling of Random and Deterministic Phenomena

Mathematical Modeling of Random and Deterministic Phenomena

Author: Solym Mawaki Manou-Abi

Publisher: John Wiley & Sons

Published: 2020-04-28

Total Pages: 308

ISBN-13: 1786304546

DOWNLOAD EBOOK

This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.


Stochastic Modelling of Space-Time Rainfall

Stochastic Modelling of Space-Time Rainfall

Author: Marie-Laure Segond

Publisher: LAP Lambert Academic Publishing

Published: 2010-10

Total Pages: 232

ISBN-13: 9783843355469

DOWNLOAD EBOOK

In the context of flood management, this thesis investigates the relationship between spatial rainfall and runoff production, for a range of scales and catchment types. A methodology for the spatial-temporal rainfall simulation of hourly rainfall is developed and the sensitivity of simulated flood runoff to the representation of observed and simulated spatial rainfall is evaluated. The study is based on 15 years of radar data, 21 raingauges and 12 flow stations from the 1400 km2 Lee catchment, UK. Results show a complex picture. The dominant effect is the spatial variability of the rainfall. No clear pattern emerges as a function of catchment scale, or response time, except that the impact of spatial variability is damped at the whole catchment scale. The sensitivity to spatial rainfall is enhanced on urbanised catchments. In conclusion, the thesis provides specific guidance concerning the importance of spatial rainfall for flood estimation.


A Stochastic Model of Space-Time Variability of Mesoscale Rainfall

A Stochastic Model of Space-Time Variability of Mesoscale Rainfall

Author: Prasun K. Kundu

Publisher: BiblioGov

Published: 2013-08

Total Pages: 22

ISBN-13: 9781289285388

DOWNLOAD EBOOK

A characteristic feature of rainfall statistics is that they depend on the space and time scales over which rain data are averaged. A previously developed spectral model of rain statistics that is designed to capture this property, predicts power law scaling behavior for the second moment statistics of area-averaged rain rate on the averaging length scale L as L right arrow 0. In the present work a more efficient method of estimating the model parameters is presented, and used to fit the model to the statistics of area-averaged rain rate derived from gridded radar precipitation data from TOGA COARE. Statistical properties of the data and the model predictions are compared over a wide range of averaging scales. An extension of the spectral model scaling relations to describe the dependence of the average fraction of grid boxes within an area containing nonzero rain (the "rainy area fraction") on the grid scale L is also explored.


A Stochastic Space-time Rainfall Model for Engineering Risk Assessment

A Stochastic Space-time Rainfall Model for Engineering Risk Assessment

Author: Michael Leonard

Publisher:

Published: 2010

Total Pages: 253

ISBN-13:

DOWNLOAD EBOOK

The temporal and spatial variability of Australia's climate affects the quantity and quality of its water resources, the productivity of its agricultural systems, and the health of its ecosystems. This variability should be taken into account when assessing the risks associated with flooding. Continuous simulation rainfall models are one means for doing this, whereby sequences of storms are generated for an arbitrarily long time period and over some region of interest. The simulated rainfall should reproduce observed statistics in time and space so that it can be used as a suitable input for hydrologic models at the catchment scale, with particular emphasis on extreme events. There are a variety of approaches to modelling rainfall, including a broad range of single-site and multi-site rainfall models. By way of contrast there are few models that aim to simulate rainfall across all points within a region at daily or sub-daily increments. This thesis focuses on models calibrated solely to rain gauges, and a specific type known as Neyman-Scott Rectangular Pulse (NSRP) models. Existing NSRP models have a mature history of modelling developments including calibration methodology and an ability to reproduce key statistics across a range of timescales. Nonetheless, these models also have several limitations (and other space-time models not withstanding) that are addressed in this thesis. These developments include improvements to the conceptual representation of rainfall and improvements to calibration and simulation techniques. Specifically these improvements include (i) the development of an efficient simulation technique, (ii) assessing the impact of monthly parameter changes on rainfall statistics, (iii) the use of simulated statistics within calibration to overcome reliance on derived model properties (iv) incorporating a storm extent parameter to better match spatial correlations, (v) incorporating long term climatic variability and developing a methodology to assess climatic and seasonal variability in simulated extremes (vi) incorporating inhomogeneity of rainfall occurrence across a region. Numerous case studies are used at various locations about Australia to illustrate these improvements and highlight the applicability of the model under varied climatic conditions.


Stochastic Methods In Hydrology: Rain, Landforms And Floods

Stochastic Methods In Hydrology: Rain, Landforms And Floods

Author: Ole E Barndorff-nielsen

Publisher: World Scientific

Published: 1998-03-31

Total Pages: 226

ISBN-13: 9814496499

DOWNLOAD EBOOK

This book communicates some contemporary mathematical and statistical developments in river basin hydrology as they pertain to space-time rainfall, spatial landform and network structures and their role in understanding averages and fluctuations in the hydrologic water balance of river basins. While many of the mathematical and statistical nations have quite classical mathematical roots, the river basin data structure has led to many variations on the problems and theory.


Spatiotemporal Random Fields

Spatiotemporal Random Fields

Author: George Christakos

Publisher: Elsevier

Published: 2017-07-26

Total Pages: 698

ISBN-13: 0128030321

DOWNLOAD EBOOK

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. - Contains applications in the form of examples and case studies, providing readers with first-hand experiences - Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas - Includes significant updates from the previous edition, including a focus on new theoretical and applied results