Stochastic Modelling of the Areal Extent of Weather Conditions


Book Description

If the probability of a 24-hour rainfall, exceeding 1/2 inch, is 10 percent over a small area like a barn, how much greater is the probability of such an amount falling somewhere within a 1000-sq mile region. The generalization of this problem is to relate the probability of a meteorological event at a single location to the problem of its occurrence within a specified area or along a specific line of travel. A Monte Carlo technique was applied to a variable that is normally distributed everywhere in a horizontal space. The procedure produced synoptic maps in which the correlation between the elements at two stations decreases determinably with increasing distance between the stations. On each synoptic map the minimum in various-sized areas or along line segments of various lengths was found. From a large number (like 10,000) of such synoptic fields it was possible to plot estimates of the probability distributions of areal minima (or maxima) or minima (or maxima) along lines of travel. This kind of modelling was tested and found effective on temperatures along flight-path segments of several hundred to several thousand miles in length at 100 mb and on New England 24-hour rainfall. (Author).




Stochastic Modelling of the Areal Extent of Weather Conditions


Book Description

If the probability of a 24-hour rainfall, exceeding 1/2 inch, is 10 percent over a small area like a barn, how much greater is the probability of such an amount falling somewhere within a 1000-sq mile region. The generalization of this problem is to relate the probability of a meteorological event at a single location to the problem of its occurrence within a specified area or along a specific line of travel. A Monte Carlo technique was applied to a variable that is normally distributed everywhere in a horizontal space. The procedure produced synoptic maps in which the correlation between the elements at two stations decreases determinably with increasing distance between the stations. On each synoptic map the minimum in various-sized areas or along line segments of various lengths was found. From a large number (like 10,000) of such synoptic fields it was possible to plot estimates of the probability distributions of areal minima (or maxima) or minima (or maxima) along lines of travel. This kind of modelling was tested and found effective on temperatures along flight-path segments of several hundred to several thousand miles in length at 100 mb and on New England 24-hour rainfall. (Author)




Modeling Climatology of Areal Coverage


Book Description

Several stochastic processes have been explored to simulate the areal climatic characteristics of the weather. The success or failure of a model of areal cover, or partial cover, has been judged partly by how well the resulting horizonal field of correlation resembles the natural field. The evaluation of each model, however, is based mostly on its efficiency in approximating the probability distribution of partial or complete coverage, by a weather condition, of an area. Emphasis, in application, is placed on the probability of cloud cover, that should vary from clear or zero cover, to partly cloudy, to overcast or 100% coverage. In addition to the size of the area, the probability distribution is directly related to the horizontal persistence of the weather element, which is parameterized in each model. The parameter is called scale distance. When the model successfully fits the observed areal extent, as viewed by a ground observer, it is then useful in application to other areal dimensions, as might be viewed by a satellite. With each of the several tested models, the snapshot picture of a field can be changed stochastically in a Markov process, simulating thereby a time sequence of weather patterns. Further investigation is well justified.




Areal Coverage Estimates by Stochastic Modelling


Book Description

The purpose of this paper is to relate the single-point probability of a meteorological event to the probability of its occurrence along a line or in an area of given size or fraction of the area. To make the problem tractable it was limited to modelling the probability estimates of the minimum or maximum condition along a line or in an area, or of the maximized minimum in a fraction of the area. In the absence of an analytical solution a Monte Carlo technique, applied to a Gaussian variable, was used to obtain answers that are presented graphically. Two models are described, one shown to be effective with macroscale events; the other, and more interesting model, is shown to be effective with the mesoscale phenomena of quantitative precipitation in areas ranging from a few hundred square kilometers to more than 50,000 sq. km. (Author).




Stochastic Climate Models


Book Description

A collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. Mathematicians will benefit from a survey of simple models, while physicists will encounter mathematically relevant techniques at work.




Areal Coverage Estimates by Stochastic Modelling


Book Description

The purpose of this paper is to relate the single-point probability of a meteorological event to the probability of its occurrence along a line or in an area of given size or fraction of the area. To make the problem tractable it was limited to modelling the probability estimates of the minimum or maximum condition along a line or in an area, or of the maximized minimum in a fraction of the area. In the absence of an analytical solution a Monte Carlo technique, applied to a Gaussian variable, was used to obtain answers that are presented graphically. Two models are described, one shown to be effective with macroscale events; the other, and more interesting model, is shown to be effective with the mesoscale phenomena of quantitative precipitation in areas ranging from a few hundred square kilometers to more than 50,000 sq. km. (Author)




Extreme Hydrology and Climate Variability


Book Description

Extreme Hydrology and Climate Variability: Monitoring, Modelling, Adaptation and Mitigation is a compilation of contributions by experts from around the world who discuss extreme hydrology topics, from monitoring, to modeling and management. With extreme climatic and hydrologic events becoming so frequent, this book is a critical source, adding knowledge to the science of extreme hydrology. Topics covered include hydrometeorology monitoring, climate variability and trends, hydrological variability and trends, landscape dynamics, droughts, flood processes, and extreme events management, adaptation and mitigation. Each of the book's chapters provide background and theoretical foundations followed by approaches used and results of the applied studies. This book will be highly used by water resource managers and extreme event researchers who are interested in understanding the processes and teleconnectivity of large-scale climate dynamics and extreme events, predictability, simulation and intervention measures. - Presents datasets used and methods followed to support the findings included, allowing readers to follow these steps in their own research - Provides variable methodological approaches, thus giving the reader multiple hydrological modeling information to use in their work - Includes a variety of case studies, thus making the context of the book relatable to everyday working situations for those studying extreme hydrology - Discusses extreme event management, including adaption and mitigation







Report on Research at AFCRL.


Book Description




Two-dimensional Modeling for Lineal and Areal Probabilities of Weather Conditions


Book Description

Single-point probabilities of weather conditions, which are easily estimated from climatic records, have been extended to lines and areas by means of Monte Carlo simulation. Simulation was accomplished using the Boehm Sawtooth Wave (BSW) model. This model was chosen because of its speed and simplicity, and because it has a spatial correlation function similar to that of many weather elements. The BSW model generates fields (or maps) of normally distributed values called Equivalent Normal Deviates (ENDs). The procedure was to obtain the cumulative probability distribution for threshold END values. To do this, a large number of maps had to be generated, 25,000 in all, to approximate the true probability distributions. This was done for 12 different sized square areas and lines. The results were put in graphical form by plotting the probabilities as a function of areal and lineal size, and fitting them to curves through hand analysis. The curves were then fitted by equations, making it possible to obtain solutions quickly by computer. Thus, a model has been produced that can be used to estimate the probability that a certain weather condition will cover a given area or length, or fraction of an area or length.