Journal ArticleDOI
Some Models for Rainfall Based on Stochastic Point Processes
TLDR
In this paper, the variation of rainfall intensity at a fixed point in space is discussed for the variation in rainfall intensity over a fixed period of time and the main properties of these models are determined analytically.Abstract:
Stochastic models are discussed for the variation of rainfall intensity at a fixed point in space. First, models are analysed in which storm events arise in a Poisson process, each such event being associated with a period of rainfall of random duration and constant but random intensity. Total rainfall intensity is formed by adding the contributions from all storm events. Then similar but more complex models are studied in which storms arise in a Poisson process, each storm giving rise to a cluster of rain cells and each cell being associated with a random period of rain. The main properties of these models are determined analytically. Analysis of some hourly rainfall data from Denver, Colorado shows the clustered models to be much the more satisfactory.read more
Citations
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Journal ArticleDOI
Models for exceedances over high thresholds
Anthony C. Davison,Richard Smith +1 more
TL;DR: In this article, the authors discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds, and the natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated.
Journal ArticleDOI
Precipitation downscaling under climate change: Recent developments to bridge the gap between dynamical models and the end user
Douglas Maraun,Douglas Maraun,Fredrik Wetterhall,Andrew Ireson,Richard E. Chandler,Elizabeth J. Kendon,Martin Widmann,S. Brienen,S. Brienen,Henning W. Rust,Tobias Sauter,M. Themeßl,Victor Venema,Kwok Pan Chun,Clare Goodess,Richard G. Jones,Christian Onof,Mathieu Vrac,I. Thiele-Eich +18 more
TL;DR: In this paper, the authors integrate perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps.
Journal ArticleDOI
Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art
TL;DR: The ability to predict urban hydrology has also evolved, to deliver models suited to the small temporal and spatial scales typical of urban and peri-urban applications as discussed by the authors. But despite the advances, many important challenges remain.
Journal ArticleDOI
Multiscaling properties of spatial rainfall and river flow distributions
Vijay K. Gupta,Edward C. Waymire +1 more
TL;DR: In this paper, a general class of continuous multiplicative processes is constructed to provide a theoretical framework for these observations, namely, the log-log linearity of moments with spatial scale and the concavity of corresponding slopes.
Journal ArticleDOI
A daily weather generator for use in climate change studies
Chris Kilsby,Philip Jones,A. Burton,A Ford,Hayley J. Fowler,C. Harpham,Philip James,A. P. Smith,Robert L. Wilby +8 more
TL;DR: The development of a weather generator for use in climate impact assessments of agricultural and water system management, which produces internally consistent series of meteorological variables including: rainfall, temperature, humidity, wind, sunshine, as well as derivation of potential evapotranspiration.
References
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Book
The theory of stochastic processes
David Cox,Hilton D. Miller +1 more
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
Journal ArticleDOI
Random Fields: Analysis and Synthesis.
J. K. Ord,Erik H. Vanmarcke +1 more
TL;DR: The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient."
Journal ArticleDOI
The mathematical structure of rainfall representations: 1. A review of the stochastic rainfall models
Edward C. Waymire,Vijay K. Gupta +1 more
TL;DR: The first part of a three-part series on the mathematical structure of rainfall models is presented in this article. But the mathematical structures that arise in the rainfall descriptions are not discussed.
Journal ArticleDOI
Scale considerations in the modeling of temporal rainfall
TL;DR: In this article, the authors employed three stochastic models having different dependence structures which range from complete independence and Markovian dependence to non-Markovian clustering dependence and showed that the problem of estimating the model parameters is also tied to the scale of measurements.