Mid-Latitude Atmospheric Dynamics: A First Course - Hardcover

Martin, Jonathan E.

Hardcover

ISBN 10: 0470864648 ISBN 13: 9780470864647

Verlag: Wiley, 2006

Inhaltsangabe

This exciting text provides a mathematically rigorous yet accessible textbook that is primarily aimed at atmospheric science majors. Its accessibility is due to the texts emphasis on conceptual understanding.

The first five chapters constitute a companion text to introductory courses covering the dynamics of the mid-latitude atmosphere. The final four chapters constitute a more advanced course, and provide insights into the diagnostic power of the quasi-geostrophic approximation of the equations outlined in the previous chapters, the meso-scale dynamics of thefrontal zone, the alternative PV perspective for cyclone interpretation, and the dynamics of the life-cycle of mid-latitude cyclones.

• Written in a clear and accessible style
• Features real weather examples and global case studies
• Each chapter sets out clear learning objectives and tests students’ knowledge with concluding questions and answers

A Solutions Manual is also available for this textbook on the Instructor Companion Site www.wileyeurope.com/college/martin.

 

“…a student-friendly yet rigorous textbook that accomplishes what no other textbook has done before… I highly recommend this textbook. For instructors, this is a great book if they don’t have their own class notes – one can teach straight from the book. And for students, this is a great book if they don’t take good class notes – one can learn straight from the book. This is a rare attribute of advanced textbooks.”

 

Bulletin of the American Meteorological Society (BAMS), 2008

 

Über diesen Titel

Über die Autorin bzw. den Autor

Jonathan E. Martin is a Professor in the Department of Atmospheric and Oceanic Sciences at the University of Wisconsin-Madison where he has taught since 1994.  He has received numerous accolades for his teaching including the Underkofler Excellence in Teaching Award and is a Fellow in the Teaching Academy of the University of Wisconsin.  His teaching excellence is allied with  research expertise in the study of mid-latitude weather systems. Professor Martin has published extensively in scholarly journals and was awarded the distinction of being named a Mark H. Ingraham Distinguished Faculty Member by the College of Letters and Science at UW-Madison.

Von der hinteren Coverseite

Mid-Latitude Atmospheric Dynamics: A First Course provides an introduction to the physical and mathematical description of mid-latitude atmospheric dynamics and its application to the diagnosis of extratropical cyclones. Requiring a background in physics and calculus but no prior knowledge of meteorology, this student-friendly text places the emphasis on conceptual understanding.

Written in a conversational tone, this text is an ideal companion for a first course in the subject, delving into greater depth as the book, and the student, progresses. Real weather examples are woven through the more mathematically focused early chapters, while later chapters introduce a range of case-studies from around the globe to illustrate theoretical and phenomenological aspects of the mid-latitude cyclone life cycle.

• features end of chapter bibliography and problems
• takes a conceptual building block approach
• includes numerous real weather examples from around the globe

Written in a conversational tone, this text is an ideal companion for a first course in the subject, delving into greater depth as the book, and the student, progresses. Real weather examples are woven through the more mathematically focused early chapters, while later chapters introduce a range of case-studies from around the globe to illustrate theoretical and phenomenological aspects of the mid-latitude cyclone life cycle.

• features end of chapter bibliography and problems
• takes a conceptual building block approach
• includes numerous real weather examples from around the globe

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

Mid-Latitude Atmospheric Dynamics

A First CourseBy Jonathan E. Martin

John Wiley & Sons

Copyright © 2006 John Wiley & Sons, Ltd.
All right reserved.
ISBN: 978-0-470-86464-7

Chapter One

The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions

Objectives

Regions of upward vertical motion are often associated with clouds and precipitation since rising air cools by expansion. This cooling increases the relative humidity of the air which can eventually lead to condensation and cloud formation. Regions of rising air are also often associated with mass divergence in an atmospheric column and, consequently, surface pressure falls and cyclogenesis. Regions of downward vertical motion are often cloud free as air dries and warms upon being compressed as it sinks to higher pressure. Mass convergence into an atmospheric column, characteristic of regions of downward vertical motion, results in surface pressure rises and surface anti-cyclogenesis. As a result of the fundamental nature of these relationships, it is not an exaggeration to say that determination of where, when, and to what degree the air is rising or sinking is of fundamental importance for accurately diagnosing the current weather or predicting its future state. In this chapter we will investigate a number of different methods for diagnosing synoptic-scale vertical motions in typical mid-latitude weather systems.

Some of these diagnostic methods will derive from careful consideration of the ageostrophic wind vector itself. Several others (the Sutcliffe development theorem as well as the traditional and [??]-vector forms of the quasi-geostrophic omega equation) will arise from simultaneously solving the quasi-geostrophic vorticity and thermodynamic energy equations for the vertical motion, [omega], and will make reference only to the instantaneous mass distribution. Taken together, the collection of diagnostics to be developed in this chapter will provide us with a formidable set of tools for understanding the synoptic-scale behavior of mid-latitude weather systems. We begin our investigation by considering the ageostrophic wind.

6.1 The Nature of the Ageostrophic Wind: Isolating the Acceleration Vector

Recall that the geostrophic wind is non-divergent on an f plane. In fact, under such conditions only departures from geostrophy contribute to horizontal divergence and, through the continuity of mass, to vertical motions as shown in (4.9). For this reason it is extremely important to examine means by which the ageostrophic motions in the mid-latitude atmosphere might be diagnosed. We begin with the frictionless equation of motion

d[??]/dt = -f [??] [??] - [nabla][empty set], (6.1)

and take the vertical cross-product of this expression to obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6.2a)

The right hand rule dictates that [??] [??] [??] = -[??], and [[??].sub.g] = ([??]/ f) [nabla][empty set, so

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6.2b)

The famous British meteorologist R. C. Sutcliffe reasoned that surface pressure falls resulted from vertical differences in mass divergence in a column. Larger mass divergence aloft than at the surface resulted in surface pressure falls and vice versa for surface pressure rises. Such differences in divergence could be related to differential accelerations at the surface and aloft through application of (6.2b). Thus, Sutcliffe argued that isolation of the acceleration vector could give insights into the sense of the vertical motion in an atmospheric column. Before presenting the elegant theory of Sutcliffe (1939), let us endeavor to isolate the acceleration vector, and its ageostrophic consequences, in two rather simple cases. These cases correspond to the two broad classes of circumstances in which geostrophic balance is violated: the presence of along-flow speed change and curvature in the flow.

The canonical synoptic example of along-flow speed change is the isolated jet streak. Shown in Figure 6.1 is the isotach distribution associated with an isolated wind speed maximum at 300 hPa in the northern hemisphere. The dashed line drawn perpendicular to the jet axis divides the jet into the so-called entrance region to its left and the exit region to its right. A parcel of air located on the western edge of the entrance region (indicated by the solid circle in Figure 6.1) would quite obviously experience an acceleration in the direction of the flow at that location. Hence, the vector d[??]/dt points eastward toward the center of the jet streak. Consequently, the ageostrophic wind vector, [[??].sub.ag], points northward at the indicated point. The result of this distribution of ageostrophic winds in the entrance region of the jet is that there is convergence of air at 300 hPa to the north of the indicated position and divergence of air at 300 hPa to the south of the indicated position. Given that 300 hPa is nearly at the top of the troposphere, upper-level divergence (convergence) is associated with upward (downward) vertical motion in the intervening column and so a thermally direct vertical circulation generally exists in the entrance region of a straight jet streak.

A parcel of air located on the eastern edge of the exit region (indicated by the open circle in Figure 6.1) would quite obviously experience a deceleration in the direction opposite the flow at that location. Hence, the vector d[??]/dt points westward toward the center of the jet streak. Consequently, the ageostrophic wind vector, [[??].sub.ag], points southward at the indicated point. The result of this distribution of ageostrophic winds in the exit region of the jet is that there is convergence of air at 300 hPa to the south of the indicated position and divergence of air at 300 hPa to the north of the indicated position. Upward vertical motion occurs in the column beneath the upper divergence maxima and, thus, a thermally indirect vertical circulation generally exists in the exit region of a straight jet streak.

Curvature in the flow is also a circumstance that violates the geostrophic assumption. Consider flow through an upper tropospheric trough-ridge couplet where the wind speed is constant and everywhere parallel to the geopotential height lines as shown in Figure 6.2. Under such circumstances, the acceleration of the wind will be entirely a consequence of directional changes. Thus, between points A and B in Figure 6.2, a southwestward-directed acceleration is required to turn the wind from westerly at point A to northwesterly at point B. There is no direction change between points B and C and, thus, no acceleration vector. A northeastward-directed acceleration is required to turn the northwesterly wind at point C to a westerly direction at point D. In order to turn the westerly at point D to a southwesterly at point E, a northwestward-directed acceleration is required. No change in direction exists between points E and F but a change from southwesterly at F to westerly at point G requires a southeastward-directed acceleration as shown. Given the four acceleration vectors drawn in Figure 6.2, it is simple to draw the ageostrophic winds in this trough-ridge couplet. The ageostrophic winds clearly converge on the western side of the upper trough (on its upstream side) leading to downward vertical motion in the column in that location. Meanwhile, the divergence of the ageostrophic winds on the downstream side of the upper trough is associated with upward vertical motions in the column in that location. This result provides a first...

Details zur Ausgabe

• Verlag: Wiley
• Erscheinungsdatum: 2006
• Sprache: Englisch
• ISBN 10: 0470864648
• ISBN 13: 9780470864647
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 352
• Kontakt zum Hersteller: Wiley-VCH GmbH; product_safety@wiley.com; ; Boschstrasse 12; Weinheim; 69469; Deutschland