Mid-Latitude Weather Systems

Early chapters focus on the mathematics necessary to construct simple models, which are subsequently used to describe and interpret the movement, evolution, and structure of particular weather patterns. Carlson discusses specific meteorological phenomena using schematic illustrations in conjunction with actual weather charts for explanation. The charts are an original and powerful feature of the text and display parameters routinely issued by the United States Weather Service.

With its fusion of the mathematical and descriptive fields of meteorology and its integrated coverage of synoptic and dynamic approaches, Mid-Latitude Weather Systems is an invaluable course text and reference source for students.

Toby N. Carlson is Professor Emeritus of Meteorology at The Pennsylvania State University.

Preface

Synoptic and dynamic meteorology are both concerned with the motions of the atmosphere and their effect on weather and climate. Synoptic meteorology is primarily concerned with putting together observations in order to understand or predict the weather. Dynamic meteorology is more concerned with quantitative relationships (equations), particularly those equations that govern the motion of the air. Because of the vast wealth of material that must be taught in graduate and undergraduate programs in meteorology, and in order for the student to be presented with at least the rudiments of this science, courses are often divided artificially into separate compartments. Such compartmentalization tends to fragment meteorology into seemingly mutually exclusive branches. On one hand, dynamics tends to introduce the mathematical framework of atmospheric motions without adequately showing their relation to weather maps. On the other hand, synoptic meteorology often is concerned with description, analysis and forecasting of large-scale atmospheric motions, but without detailed physical or mathematical explanations. Much of the material in both disciplines can be bewildering to the novice.

After a year of courses in synoptic and dynamic meteorology, most students are able to grasp individual concepts, although the whole remains to be integrated. This course attempts to provide a fusion in which the behavior of synoptic-scale weather patterns is described in relation to the governing equations. In order to see clearly how the dynamics operate, it is necessary to remain as simple as possible without violating mathematical principles or ignoring important components in the equations.

A proper integration of the material covered by this course means that there must be omissions in the development of the equations and in describing all the interesting aspects of a particular weather situation or case study. To do otherwise infers an integration as extensive as its derivative material. This text, therefore, begins with a set of assumptions concerning the atmosphere, such as the quasi-geostrophic constraint, and proceeds to make further assumptions in order to arrive at certain simple expressions. The aim of this book is to describe these patterns and their evolution using mathematics. The key to understanding is the interpretation of the equations of motion. Because the total system of atmospheric motions implicitly describes everything, and therefore nothing in particular, we must attempt to simplify both what we observe and how we formulate these observations mathematically. We will do that through the use of simplistic models based on the equations set forth in this book.

Although there are some elementary definitions in this course and even some repetition of basic equations throughout the text, this course presumes that the student is well acquainted with the basic dynamics and with elementary map analysis. Thus no effort will be made to derive in detail the fundamental equations (such as the equations of motion and of thermodynamics); they will be merely stated and students will be provided with the assumptions needed to derive all the missing steps in the derivations.

This book was written for the benefit of advanced undergraduate or beginning graduate students in meteorology. Its material has evolved over more than 10 years of teaching at The Pennsylvania State University, in response to a need to fill in some gaps in meteorological pedagogy. While there are a number of very fine books on dynamics and a few concerning synoptic meteorology, there are virtually none that use conventional weather charts and equations to illustrate the behavior and evolution of weather patterns. I hope that this work will redress the balance and place synoptic meteorology squarely within the realm of a quantitative science.

The subject matter is mid-latitude synoptic weather systems, by which I imply a scale of motion that can be treated adequately using quasi-geostrophic theory. The material is subject to some constraints: the subjects would take one or two semesters to cover and the illustrations focus on case studies and topics with which I am intimately familiar. The book does not represent an unbiased survey of the literature but concentrates on selected concepts that I feel are supremely important if one is to gain a deep understanding of mid-latitude, synoptic-scale weather systems.

The text constitutes a suitable reference source for working scientists with some background in physics and mathematics. It assumes some basic knowledge of synoptic meteorology, dynamics and thermodynamics, although the relevant basic equations customarily elaborated upon in dynamics texts are encapsulated in this book. Given the quantitative nature of the material, I must assume that the reader is familiar with the basic equations and relationships (such as the geostrophic wind) outlined in Chapter 1. The purpose of the mathematics is to construct simple models from which one can describe the movement, development and structure of a particular feature or phenomenon.

The presence of so many equations may distress some people and please others. Purists may also fret because complete rigor may be set aside in favor of developing a semi-empirical relationship. Where possible, I have tried to give the reader a sense of what assumptions have been made and where the relationships might differ from a rigorous treatment. Many of the derivations are not absolutely complete in the sense that not all of the steps are given. In some cases, well-known formulae, such as the conservation of potential vorticity, are simply stated where I feel that the mathematical relationships can be found in other texts and the derivation is not essential to the understanding of the discussion that follows. The student is encouraged to recognize the similarities in the underlying physics as expressed in the various models.

If it is an inescapable fact that the language of science is mathematics, then the particular dialect used in meteorology is dynamics. To me, dynamics is happily wedded to observations, and an understanding of how observations relate to equations is an absolute necessity for any modeler or theoretician. I have therefore tried to temper models with observations and mathematical interpretation with empiricism, with just a dash of speculation. A unique aspect of this book is the abundance of weather charts, which feature parameters routinely issued by the United States Weather Service. These charts are used to illustrate the workings of the mathematical models. Students not familiar with weather maps should find this text useful as an introduction to patterns customarily analyzed on weather charts. I hope that those already familiar with the charts will find that this text serves as a means for interpretation of the conventional weather maps within the framework of a simplified dynamics. In the matter of mathematical notation, I have followed normal conventions, but I must point out that there are some superficial differences between this and other texts. For the most part, these differences reflect personal preference of the author. Except where noted by quotation marks, all terms are defined as in the Glossary of meteorology (American Meteorological Society, Boston, 1959).

Some readers may express disappointment at not seeing very much surface weather detail, such as precipitation, snowfall amounts or storm destruction statistics. In fact, some of the examples contain rather unspectacular weather but are nevertheless presented to illustrate a particular point. The reader will note that most of the maps center over the eastern two-thirds of the United States. The reason for this parochial choice of maps was not jingoism but convenience. These data are easily available to me and I have become quite familiar, through classroom teaching, with most of the examples, some of which were originally brought to my attention by students.

I have tried to avoid a discussion of local mesoscale effects (mountain breezes, cold air damming, local peculiarities of cyclones, etc.), not simply because mesoscale meteorology is a vast topic in itself, but because the effects are often imposed by local topography. I prefer to generalize the physical arguments. I realize, for example, that lee-side cyclogenesis over the Alps produces different patterns than it does in the lee of the Rocky Mountains in North America, but I am confident that, if the reader comprehends the examples given in this book, it will be a simple matter to apply the concepts to cases of lee-side cyclogenesis in any region. An exception to the exclusion of mesoscale processes is the case of fronts: here I include three chapters devoted to the kinematics and dynamics of fronts and jet streaks, which are byproducts of large-scale processes. The reader will also note that I occasionally use the directions "south" and "north" when I mean to say "equatorward" and "poleward". In most instances I try to avoid hemspheric bias but it is not always feasible to do so; there are just no graceful substitutes for directions such as southwesterly or northwesterly. I hope that Southern Hemisphere readers will overlook this semantic difficulty and make the appropriate coordinate transformations in their minds.

The approach adopted also differs from other texts in that it does not serialize the topics in neat compartments but, instead, attempts to present a picture: subjects are not examined as collections of research results but as elements of a whole, and each topic is related to all others. I wish to explain the behavior of meteorological processes and to give the reader an insight into processes and mechanisms rather than to list facts. It is for this reason that I do not wish to discuss operational forecast models, trends in meteorological research and instrumentation, techniques of computer analysis or current schools of thought, except as part of the historical tapestry. Today's operational models are tomorrow's obsolescence and yesterday's arguments are scarcely memories today. It may ultimately prove to be the case that some arguments are incomplete or partially incorrect and in need of modification. Therefore, I urge the reader, after having considered all the ramifications of the theory, to review the work in the light of his or her own insights and understanding.

Not only do I wish to avoid discussions involving a survey of models or which parameterizations are in favor or which approach yields the best forecast results, but my aim is to avoid the entire subject of weather forecasting, which is an art best left for another book. The contribution of this book to weather forecasting is the body of insights contained herein. Of course, I do use models to illustrate the atmospheric behavior, and I constantly refer to the historical development of different concepts and models. Models are necessary to simplify reality, and without them it would be difficult to isolate the important factors and mechanisms. Their function is simply to explain as many aspects with as much simplicity as possible of a particular set of phenomena. Models, however, are only approximations to the real physics. A perfectly complete model implies a complete mathematical description of the phenomenon and such a description should be left for the computer. Even with the aid of a computer, however, I feel that it is preferable to understand the physics of the atmosphere on simple levels before undertaking to comprehend the difficult. Without an intuitive understanding of the scale and range of the possible answers, one cannot be sure of having performed the calculations correctly with the computer.

The general flow of the discussions is intended to adhere to a simple progression. First, the basic equations are discussed and then reduced to the form of a simplified model, often based on empirical parameters. Next, the model is discussed in reference to schematic illustrations and finally to actual weather charts. Although that sequence of presentation may vary considerably from subject to subject, I hope that a clear sense of this progression remains unbroken in the mind of the reader and that both weather forecasters and mathematical modelers can profit by appreciating the necessary link between empiricism and pure theory. I have tried to minimize meteorological jargon, which abounds in the literature. In some cases the use of popular terms, such as "comma cloud" or "conveyor belt", is inescapable. Such terms, where not fully accepted by the meteorological community or listed in the Glossary of meteorology, are surrounded in quotes when first introduced. Terms that have gained more general acceptance are printed in italics.

Among some students, the romantic (almost quixotic) notions of weather forecasting have bred resentment toward anything highly mathematical, as if the excitement of reading a weather map will be dissipated by exposing the mechanistic nature of the atmosphere. As a result, the synoptician faces an identity crisis. Once, weather forecasting was performed solely by visual inspection of observations laboriously entered manually on charts. Except in some private enterprises, though, the romance of the independent forecaster has vanished within the lifetime of most of my students. In a way the practitioner is justified in feeling frustrated. First, meteorology differs from other sciences (such as engineering or medicine) in that the theoretician tends to receive more acclaim and reward than the practitioner. Second, weather prediction has become the province of the modeler, who is more often than not a dynamist. Operational weather forecasting is today governed by technology, the high-speed computer and sophisticated measurement systems. Improvement in weather forecasting skill has come about through greater computer capabilities, speed and memory, as well as through better numerical schemes and more efficient automatic data collection. These developments obscure the role of the empiricist and the forecaster, and raise the question whether intuitive understanding of weather processes is of value.

Meteorology has at last arrived as a true branch of physics and today exists more in the realm of fluid mechanics and mathematics. Neither the everyday forecaster nor the modeler can fully comprehend the increasingly complex models upon which routine forecasts are based. This trend toward greater complexity in operational forecasting could lead to a stultification of creative thought. I foresee a day in which operational models, having been developed layer upon layer over many years, will become almost incomprehensible black boxes to all but a very few specialists. There is a possibility that the intuitive scientist in meteorology will become a relic unless a conceptual knowledge can be passed on to the coming generation of meteorologists.

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