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In Ch. 8 the whole system of arithmetical operations is reviewed in order. With regard to the horizontal differential coefficients the general method may be briefly described in the following four sentences Take the differential equations and replace everywhere the infinitesimal operator 6 by the finite difference operator 6. Use arith metic instead of symbols. Attend carefully to the centering of the differences. Leave the errors due to the finiteness of the differences over for consideration at the end of the process. With regard to the vertical differential coefficients, on the contrary, it is oft-en possible to effect an exact transformation to differences, by means of a vertical integration. In arranging the computing, it has constantly to be borne in mind that the rate of change with time of every one of the discrete values of the dependent variables must be calculable from their instantaneous distribution in time and space, excepting' only those values near the edge of the horizontal area represented in the table. We may refer to this necessary property by saying, for brevity, that the system must be lattice-reproducing.
In Ch. 9 will be found an arithmetical table showing the state of the atmosphere observed over middle Europe at 1910 May 20 d. 7 h. G.m.t. This region and instant were chosen because the observations form the most complete set known to me at the time of writing, and also because V. Bjerknes has published large scale charts of the isobaric surfaces, together with collated data for wind, cloud and precipitation. Starting from the table of the initially observed state of the atmosphere at this instant, the method described in the preceding paragraphs is applied, and so the rates of change of the pressures, winds, temperatures, etc. Are obtained. Unfortunately this forecast is spoilt by errors in the initial data for winds. These errors appear to arise mainly from the irregular distribution of pilot balloon stations, and from their too small number.
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Excerpt from Weather Prediction by Numerical Process
In Ch. 7 the arrangement of the tabular numbers in space and time is discussed with a view to securing the best representation of differential coefficients by difference ratios.
In Ch. 8 the whole system of arithmetical operations is reviewed in order. With regard to the horizontal differential coefficients the general method may be briefly described in the following four sentences Take the differential equations and replace everywhere the infinitesimal operator a by the finite difference operator 6. Use arith metic instead of symbols. Attend carefully to the centering of the differences. Leave the errors due to the finiteness of the differences over for consideration at the end of the process. With regard to the vertical differential coefficients, on the contrary, it is oft-en possible to effect an exact transformation to differences, by means of a vertical integration. In arranging the computing, it has constantly to be borne in mind that the rate of change with time of every one of the discrete values of the dependent variables must be calculable from their instantaneous distribution in time and space, excepting' only those values near the edge of the horizontal area represented in the table. We may refer to this necessary property by saying, for brevity, that the system must be lattice-reproducing.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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- EditorialForgotten Books
- Año de publicación2018
- ISBN 10 1334260494
- ISBN 13 9781334260490
- EncuadernaciónTapa blanda
- Número de páginas258
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Weather Prediction by Numerical Process (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book presents a groundbreaking approach to weather prediction, offering a revolutionary method for understanding and forecasting atmospheric changes. The author builds upon the emerging field of numerical analysis, employing a system of finite differences to translate complex differential equations into a series of numerical calculations. This approach, reminiscent of the meticulous procedures used to generate astronomical almanacs, allows for the prediction of weather patterns based on observed initial conditions. The book meticulously details the author's methodology, using a simplified example to illustrate the process of calculating atmospheric pressure, velocity, and density over time. The author challenges traditional assumptions about weather forecasting, particularly the limitations of the geostrophic wind model, and advocates for a more nuanced understanding of atmospheric dynamics. This work, published in 1922, represents a significant departure from prevailing methods of weather prediction and anticipates the rise of modern computational meteorology. Forgotten Books publishes hundreds of thousands of rare and classic books. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Nº de ref. del artículo: 9781334260490_0
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