[...]... vector g* and gravity g For an idealized homogeneous spherical earth, g* would be directed toward the center of the earth In reality, g* does not point exactly to the center except at the equator and the poles Gravity, g, is the vector sum of g* and the centrifugal force and is perpendicular to the level surface of the earth, which approximates an oblate spheroid surfaces slope upward toward the equator... a distance r (1.3) January 27, 2004 13:54 Elsevier/AID 8 aid 1 introduction In dynamic meteorology it is customary to use the height above mean sea level as a vertical coordinate If the mean radius of the earth is designated by a and the distance above mean sea level is designated by z, then neglecting the small departure of the shape of the earth from sphericity, r = a + z Therefore, (1.3) can be... techniques and ensemble forecasting Acknowledgments: I am indebted to a large number of colleagues and students for their continuing interest, suggestions, and help with various figures I am particularly grateful to Drs Dale Durran, Greg Hakim, Todd Mitchell, Adrian Simmons, David Thompson, and John Wallace for various suggestions and figures January 27, 2004 13:54 Elsevier/AID aid C H A P T E R 1 Introduction. .. force proportional to their masses and inversely proportional to the square of the distance separating them Thus, if two mass elements M and m are separated by a distance r ≡ |r| (with the vector r directed toward m as shown in Fig 1.2), then the force exerted by mass M on mass m due to gravitation is GMm r Fg = − 2 (1.2) r r where G is a universal constant called the gravitational constant The law of... still fundamental to the understanding of large-scale extratropical motions This chapter has been revised to provide increased emphasis on the role of potential vorticity and potential vorticity inversion The presentation of the omega equation and the Q vector has been revised and improved In Chapter 9, the discussions of fronts, symmetric instability, and hurricanes have all been expanded and improved... of view of an observer in inertial space the speed of the ball is constant, but its direction of travel is continuously changing so that its velocity is not constant To compute the acceleration we consider the change in velocity δV that occurs for a time increment δt during which the ball rotates through an angle δθ as shown in Fig 1.5 Because δθ is also the angle between the vectors V and V + δV,... Therefore, in order to apply Newton’s second law to describe the motion relative to this rotating coordinate system, we must include an additional apparent force, the centrifugal force, which just balances the force of the string on the ball Thus, the centrifugal force is equivalent to the inertial reaction of the ball on the string and just equal and opposite to the centripetal acceleration To summarize,... of important derived units have special names and symbols Those that are commonly used in dynamic meteorology are indicated in Table 1.2 In addition, the supplementary unit designating a plane angle, the radian (rad), is required for expressing angular velocity (rad s−1 ) in the SI system.1 In order to keep numerical values within convenient limits, it is conventional to use decimal multiples and submultiples... must change Thus, the object behaves as though a zonally directed deflection force were acting on it The form of the zonal deflection force can be obtained by equating the total angular momentum at the initial distance R to the total angular momentum at the displaced distance R + δR: + u R2 = R + u + δu R + δR (R + δR)2 where δu is the change in eastward relative velocity after displacement Expanding... (h), and day (d) may be used in preference to the second in order to express quantities in convenient numerical values 2 The hectopascal (hPa) is the preferred SI unit for pressure Many meteorologists, however, are still accustomed to using the millibar (mb), which is numerically equivalent to 1 hPa For conformity with current best practice, pressures in this text will generally be expressed in hectopascals . Paris San Diego San Francisco Singapore Sydney Tokyo January 24, 2004 12:0 Elsevier/AID aid Senior Editor, Earth Sciences Frank Cynar Editorial Coordinator Jennifer Helé Senior Marketing Manager. Elsevier/AID aid AN INTRODUCTION TO DYNAMIC METEOROLOGY Fourth Edition JAMES R. HOLTON Department of Atmospheric Sciences University of Washington Seattle,Washington Amsterdam Boston Heidelberg. publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission