Mesoscale Meteorology in Midlatitudes E-Book

Paul Markowski

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Advancing Weather and Climate Science
• Sprache: Englisch

Seitenzahl: 937

Veröffentlichungsjahr: 2011

Beschreibung

Mesoscale Meteorology in Mid-Latitudes presents the dynamics of mesoscale meteorological phenomena in a highly accessible, student-friendly manner. The book's clear mathematical treatments are complemented by high-quality photographs and illustrations. Comprehensive coverage of subjects including boundary layer mesoscale phenomena, orographic phenomena and deep convection is brought together with the latest developments in the field to provide an invaluable resource for mesoscale meteorology students. Mesoscale Meteorology in Mid-Latitudes functions as a comprehensive, easy-to-use undergraduate textbook while also providing a useful reference for graduate students, research scientists and weather industry professionals. * Illustrated in full colour throughout * Covers the latest developments and research in the field * Comprehensive coverage of deep convection and its initiation * Uses real life examples of phenomena taken from broad geographical areas to demonstrate the practical aspects of the science

Leseprobe

Contents

Series Foreword

Advances in Weather and Climate

Preface

Acknowledgments

List of Symbols

PART I General Principles

Chapter 1: What is the Mesoscale?

1.1 Space and time scales

1.2 Dynamical distinctions between the mesoscale and synoptic scale

Chapter 2: Basic Equations and Tools

2.1 Thermodynamics

2.2 Mass conservation

2.3 Momentum equations

2.4 Vorticity and circulation

2.5 Pressure perturbations

2.6 Thermodynamic diagrams

2.7 Hodographs

Chapter:3 Mesoscale Instabilities

3.1 Static instability

3.2 Centrifugal instability

3.3 Inertial instability

3.4 Symmetric instability

3.5 Shear instability

PART II Lower Tropospheric Mesoscale Phenomena

Chapter 4: The Boundary Layer

4.1 The nature of turbulent fluxes

4.2 Surface energy budget

4.3 Structure and evolution of the boundary layer

4.4 Boundary layer convection

4.5 Lake-effect convection

4.6 Urban boundary layers

4.7 The nocturnal low-level wind maximum

4.7.1 Low-level jets versus jet streams

Chapter 5: Air Mass Boundaries

5.1 Synoptic fronts

5.2 Drylines

5.3 Outflow boundaries

5.4 Mesoscale boundaries originating from differential surface heating

Chapter 6: Mesoscale Gravity Waves

6.1 Basic wave conventions

6.2 Internal gravity wave dynamics

6.3 Wave reflection

6.4 Critical levels

6.5 Structure and environments of ducted mesoscale gravity waves

6.6 Bores

PART III Deep Moist Convection

Chapter :7 Convection Initiation

7.1 Requisites for convection initiation and the role of larger scales

7.2 Mesoscale complexities of convection initiation

7.3 Moisture convergence

7.4 Elevated convection

Chapter 8: Organization of Isolated Convection

8.1 Role of vertical wind shear

8.2 Single-cell convection

8.3 Multicellular convection

8.4 Supercellular convection

Chapter 9: Mesoscale Convective Systems

9.1 General characteristics

9.2 Squall line structure

9.3 Squall line maintenance

9.4 Rear inflow and bow echoes

9.5 Mesoscale convective complexes

Chapter 10: Hazards Associated with Deep Moist Convection

10.1 Tornadoes

10.2 Nontornadic, damaging straight-line winds

10.3 Hailstorms

10.4 Flash floods

PART IV Orographic Mesoscale Phenomena

Chapter 11: Thermally Forced Winds in Mountainous Terrain

11.1 Slope winds

11.2 Valley winds

Chapter 12: Mountain Waves and Downslope Windstorms

12.1 Internal gravity waves forced by two-dimensional terrain

12.2 Gravity waves forced by isolated peaks

12.3 Downslope windstorms

12.4 Rotors

Chapter 13: Blocking of the Wind by Terrain

13.1 Factors that govern whether air flows over or around a terrain obstacle

13.2 Orographically trapped cold-air surges

13.3 Lee vortices

13.4 Gap flows

PART V Appendix

Appendix A: Radar and Its Applications

A.1 Radar basics

A.2 Doppler radar principles

A.3 Applications

References

Index

This edition first published 2010, ©2010 by John Wiley & Sons, Ltd

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We dedicate this book to our familiesMarisa, Nolan, & ShaneandScott, Nick, & Sydney

Series Foreword

Advances in Weather and Climate

Meteorology is a rapidly moving science. New developments in weather forecasting, climate science and observing techniques are happening all the time, as shown by the wealth of papers published in the various meteorological journals. Often these developments take many years to make it into academic textbooks, by which time the science itself has moved on. At the same time, the underpinning principles of atmospheric science are well understood but could be brought up to date in the light of the ever increasing volume of new and exciting observations and the underlying patterns of climate change that may affect so many aspects of weather and the climate system.

In this series, the Royal Meteorological Society, in conjunction with Wiley–Blackwell, is aiming to bring together both the underpinning principles and new developments in the science into a unified set of books suitable for undergraduate and postgraduate study as well as being a useful resource for the professional meteorologist or Earth system scientist. New developments in weather and climate sciences will be described together with a comprehensive survey of the underpinning principles, thoroughly updated for the 21st century. The series will build into a comprehensive teaching resource for the growing number of courses in weather and climate science at undergraduate and postgraduate level.

Series Editors

Peter Inness, University of Reading, UK

William Beasley,University of Oklahoma, USA

Preface

This text originated from course notes used in the undergraduate mesoscale meteorology class at Pennsylvania State University. We assume that students have already had courses in atmospheric dynamics, thermodynamics, and synoptic meteorology. A mesoscale meteorology textbook likely will always be a ‘‘work in progress’’, given that so much of what we teach is constantly evolving as observing and numerical modeling capabilities continually improve. Another obvious challenge in preparing a reference on mesoscale meteorology is that the specialty is extraordinarily broad, and in a way a catch-all for essentially all atmospheric phenomena that are not dominated at one extreme by quasigeostrophic dynamics or at the other extreme by the effects of small-scale turbulence. Thus, it is perhaps impossible to write a truly comprehensive mesoscale meteorology textbook that can adequately address all of the mesoscale processes that influence the weather in every corner of the world in important ways.

Our focus is midlatitude mesoscale phenomena. The thermodynamics and dynamics of tropical convective clusters and hurricanes are therefore not included, nor is a comprehensive treatment of polar lows. It is our experience that these topics tend to be covered in tropical meteorology and synoptic meteorology courses, respectively, rather than in mesoscalemeteorology courses. Other perhaps surprising omissions include jet streaks and lee cyclogenesis, and the treatment of fronts and frontogenesis might be considered by some to be rather abridged. Again, in our experience these topics also tend to be covered in courses on synoptic meteorology. We also did not include chapters on upslope precipitation events or mesoscale modeling. The most interesting aspects of the former topic are probably the microphysical aspects (e.g. the seeder-feeder process) rather than themesoscale dynamical aspects. Regarding mesoscale modeling, even though numerous figures throughout the text are derived from numerical simulations, we felt that this topic deserves an entire course by itself. It is possible that we might reconsider including these topics in an expanded future edition. We also caution the reader that the subject of atmospheric convection, particularly deep, moist convection, is what drew us to meteorology in the first place and its study is what puts food on our tables. It will be obvious to the casual reader that this bias has not been well concealed.

The book is divided into four parts. Part I, General Principles, begins by defining what is meant by the term mesoscale (Chapter 1). This requires the introduction of some basic dynamical concepts, such as the Rossby number, hydrostatic approximation, and pressure perturbations. In Chapter 2 we present a more detailed review of the tools that will be needed for the rest of the book. Some readers may wish to skip Chapter 2. Itmight seem somewhat awkward to introduce some dynamics in Chapter 1 and then review the basic governing equations more thoroughly in Chapter 2, but the alternative—forcing readers to trudge through a lengthy review chapter to open a book before getting to a description of the types of phenomenon that are the focus of the book—seemed even less attractive. One of the concepts in Chapter 1 is that mesoscale phenomena can be driven by a variety of instabilities, unlike synoptic-scale motions, which are driven almost exclusively by baroclinic instability, at least inmidlatitudes. Chapter 3 discusses these mesoscale instabilities.

The remaining chapters in the book (Parts II–IV) deal with mesoscale phenomena. The phenomena can be attributed to either instabilities, topographic forcing, or, in the case of air mass boundaries such as fronts and drylines, frontogenesis. There no doubt are a number of ways to organize mesoscale meteorology topics, as is evidenced by the fact that we did things differently at least the first four times we taught the course at Penn State. In Part II we explore mesoscale phenomena that are confined principally to the lower troposphere, for example, boundary layer convection, air mass boundaries (e.g. fronts, drylines, sea breezes, outflow boundaries), and ducted gravity waves. Part III treats the subject of deep moist convection, including its initiation, organization, and associated hazards. Part IV contains mountain meteorology topics. The basic idea in Part IV is to treat each of the following in a separate chapter, in this order: (i) the simplest case—no ambient flow and only heating/cooling of sloped terrain, which results in thermally forced mountain and valley circulations; (ii) the case of wind flowing over a topographic barrier, which excites gravity waves and occasionally leads to severe, dynamically induced downslope winds; (iii) phenomena resulting when winds that impinge on a topographic barrier experience significant blocking, such as cold-air damming, wake vortices, and gap winds.

We lament that each of Parts II–IV themselves could be the basis for entire textbooks. The scope of each chapter purposely has been limited somewhat to facilitate the examination of a wide range ofmesoscale topics within the course of a typical semester. In part for this reason, a ‘‘further reading’’ list also appears at the end of each chapter, which contains supplemental references not specifically cited in the bibliography. We speculate that these listings might be most valuable to graduate students seeking to supplement the contents herein with more advanced readings. Finally, a ‘‘crash course’’ on radar meteorology is provided in an appendix. Radars are arguably the most important instrument in the observation of mesoscale phenomena. After all, the term mesoscaleoriginated in a review paper on radar meteorology.

Acknowledgments

Weare grateful for all of the discussionswith our friends and colleagues over the years: Mark Askelson, Peter Bannon, Howie Bluestein, Harold Brooks, George Bryan, Don Burgess, Fred Carr, John Clark, Bill Cotton, Bob Davies- Jones, Chuck Doswell, David Dowell, Kelvin Droegemeier, Dale Durran, Evgeni Fedorovich, Bill Frank, Mike Fritsch, Kathy Kanak, Petra Klein, Sukyoung Lee, Doug Lilly, Matt Parker, Erik Rasmussen, Dave Schultz, Alan Shapiro, Nels Shirer, Todd Sikora, Dave Stensrud, Jerry Straka, Jeff Trapp, Hans Verlinde, Tammy Weckwerth,MorrisWeisman, Lou Wicker, JoshWurman, JohnWyngaard, George Young, and Conrad Ziegler.We are especially appreciative of those who reviewed earlier versions of this book: George Bryan, John Clark, Chuck Doswell, Dale Durran, Evgeni Fedorovich, Bart Geerts, Thomas Haiden, Jerry Harrington, Steve Koch, Dennis Lamb, Sukyoung Lee, Doug Lilly,Matt Parker, Dave Schultz, Russ Schumacher, Alan Shapiro, Nels Shirer, Todd Sikora, Hans Verlinde, Dave Whiteman, Josh Wurman, John Wyngaard, George Young, and Fuqing Zhang.

We also thank those who provided us with their original photographs or figures (all photographs are copyrighted by the those credited in the figure captions): Nolan Atkins, Peter Blottman, Harold Brooks, George Bryan, Fernando Caracena, Brian Colle, Chris Davis, Chuck Doswell, Jim Doyle, Dale Durran, Charles Edwards, Roger Edwards, Craig Epifanio, Marisa Ferger, Brian Fiedler, Jeff Frame, Bart Geerts, Roberto Giudici, Joel Gratz, Vanda Grubiˇsi´c, Jessica Higgs, Richard James, Dave Jorgensen, PatKennedy, Jim LaDue, Bruce Lee, Dave Lewellen, Amos Magliocco, Jim Marquis, Brooks Martner, Al Moller, Jerome Neufeld, Eric Nguyen,Matt Parker, Erik Rasmussen, Chuck Robertson, Paul Robinson, Chris Rozoff, Thomas Sävert, Dave Schultz, Jim Steenburgh, Herb Stein, Jeff Trapp, Roger Wakimoto, Nate Winstead, Josh Wurman, Ming Xue, and Conrad Ziegler. A number of staff at Penn State helped us acquire several archived datasets that were used to construct some of the figures within the book, in addition to providing virtually ‘‘24/7’’ computer support: Chad Bahrmann, Chuck Pavloski, Art Person, and Bill Syrett. We also are grateful for the support and patience of Wiley, especially Rachael Ballard and Robert Hambrook. Some of the figures contain numerical model output generated by the Advanced Regional Prediction System (ARPS), developed by the Center for the Analysis and Prediction of Storms at the University of Oklahoma, and the Bryan Cloud Model, developed by George Bryan. Much of the radar imagery appearing in figures was displayed using the SOLOII software from the NationalCenter for Atmospheric Research.

Paul MarkowskiYvette Richardson

Work on this book began in the spring of 2001 when I began preparing to teach the undergraduate mesoscale meteorology course at Penn State for the first time. Much of the inspiration at that time came from reviewing Greg Forbes’ lecture notes from the class, which I took from Dr. Forbes in 1995 as an undergraduate meteorology major at Penn State. Dr. Forbes’ influence on my early development—through his formal classroom lectures, undergraduate honors thesismentorship, and simply shared interests in convective storms—cannot be overstated. I also likely would not be where I am today if not for the opportunity to spend the summer after my junior year in Norman, Oklahoma, as a Research Experiences for Undergraduates (REU) student. My mentor there, Dave Stensrud, is one of the reasons I decided to pursue a Ph.D. Another important aspect of my REU experience in Norman was the opportunity to participate in the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX). My experience in the field forever sealed my fate to follow a career path to research. It was through VORTEX that I met Jerry Straka and Erik Rasmussen, who convinced me to attend the University of Oklahoma and who served as my advisors. They were superb advisors, and it’s hard to say what their biggest contribution was. It was either their trust in me to allow me to work so independently right from the start, or it was their tireless and selfless willingness to discuss prettymuch any aspect of my research or theirs at virtually any hour of the day. I also single-out Bob Davies-Jones, with whom I chased storms for a number of years while doing field work as a part of my graduate research. Hours upon hours of watching the sky and listening to Bob’s assessments, in addition to discussing dynamics problems, benefited me in immeasurable ways. Finally, I am forever grateful for the support of my wife (also a meteorologist) throughout the project.

Paul Markowski

My path to authoring this book was somewhat circuitous. I majored in physics as an undergraduate at the University of Wisconsin-River Falls. The professors I had there were incredible teachers and mentors, and I will always be indebted to Drs. Shepherd, Larson, Paulson, and Blodgett for providing me with a solid foundation. My journey into meteorology began with the Summer Institute on Atmospheric Science at NASA-Goddard Space Flight Center between my junior and senior year. It was there that my husband (also a physics major) and I both realized that atmospheric science was an extremely interesting application of our physics backgrounds, and it is where we met Kelvin Droegemeier, who represented the University of Oklahoma graduate program with such enthusiasm we could not help but go there! I am grateful to Fred Carr who served as the thesis advisor for my masters degree and did his best to teach a physics student to understand actual weather! For my Ph.D., I decided to study severe storms with Kelvin, and I am ever grateful for his undying support and encouragement. It was through him that I learned to be a numerical modeler, and his markups of my manuscripts taught me the essence of scientific writing. I also will never forget having the opportunity to sit at the feet of theoretical giants Douglas Lilly and Robert Davies-Jones, both of whom always were willing to discuss difficult concepts and pass along their incredible insight. As I was finishing my Ph.D., the University of Oklahoma allowed me to get my feet wet in teaching as a Visiting Assistant Professor, and through this I determined that was the career path for me. Following my Ph.D., I had the wonderful opportunity of a post-doc position with Joshua Wurman, who did his best to help a numerical modeler become an observationalist, before landing at the Pennsylvania State University as an assistant professor. It has been an interesting path, and one made possible through the support of family and all of the friendships developed along the way. In particular, this path was possible because of my husband who started out as my study partner in my Freshman year of college and has fully supported my endeavors ever since.

Yvette Richardson

List of Symbols

α specific volume, angle a parcel displacement makes with respect to the horizontal, angle of axis of dilatation with respect to the x axis, inclination angle of sloping terrain

α0 constant reference specific volume

αd specific volume of dry air

β angle between v and dl, latitudinal variation of Coriolis parameter, angle between isentropes and the axis of dilatation, between-beam angle

γenvironmental lapse rate

Γd dry adiabatic lapse rate

Γm moist adiabatic lapse rate

Γp parcel lapse rate

Γps pseudoadiabatic lapse rate

Γrm reversible moist adiabatic lapse rate

δ horizontal divergence, displacement of a streamline

δc displacement of the dividing streamline

vertically averaged horizontal divergence

ε ratio of gas constants for dry air and water vapor, dissipation

ζ vertical vorticity component

mean (environmental) vertical vorticity

ζ′ vertical vorticity perturbation

η meridional vorticity component

〈η〉 cross-section-averaged meridional vorticity

mean (environmental) meridional vorticity

ξ zonal vorticity component

mean (environmental) zonal vorticity

θ potential temperature, radar beam azimuth angle

mean (environmental) potential temperature

〈〉 layer-averaged environmental potential temperature

a mean potential temperature at anemometer level

θ′ potential temperature perturbation

amplitude of potential temperature perturbation

θ0 constant reference potential temperature, potential temperature at the height of the roughness length

θc potential temperature in well-mixed region between split streamlines in flow over a barrier

θe equivalent potential temperature

equivalent potential temperature if air is saturated at its current temperature and pressure

mean (environmental) equivalent potential temperature if air is saturated at its current temperature and pressure

θep pseudoequivalent potential temperature

θv virtual potential temperature

mean (environmental) virtual potential temperature

virtual potential temperature perturbation

θw wet-bulb potential temperature

θρ density potential temperature

θρ mean (environmental) density potential temperature

density potential temperature perturbation

κ wave vector

κ thermal diffusivity

κe moisture diffusivity

λ longitude, wavelength

λx zonal wavelength

λz vertical wavelength

μ a real number

ν kinematic viscosity

π 3.141 592 65, Exner function

mean (environmental) Exner function

π′ perturbation Exner function

ρ air density

ρ0 constant reference density

ρa density of an adiabatic reference state

ρd density of dry air

ρi density of ice hydrometeor

ρv density of water vapor

mean (environmental) air density

ρ′air density perturbation

σ static stability parameter, growth rate of isentropic surface

τ lifetime of a convective cell

φ latitude, radar beam elevation angle, phase of radar transmission

Φ geopotential

mean geopotential

Φ′ geopotential perturbation

imaginary part of the geopotential perturbation

real part of geopotential perturbation

Φ′ * complex conjugate of the geopotential perturbation

ψ streamfunction

ψ0 angular constant designating the orientation of the ageostrophic wind at the start of the inertial oscillation that leads to the nocturnal low-level wind maximum

mean streamfunction

ψ′ streamfunction perturbation

complex amplitude of streamfunction

perturbation

Ω Earth’s angular velocity vector

Ω angular rotation rate of Earth, intrinsic frequency

ω relative vorticity vector

ωh horizontal vorticity vector

ω frequency

ωc crosswise vorticity component

ωk frequency of kth mode

ω streamwise vorticity component

A area of an arbitrary surface bounded by the circuit about which circulation is computed

Ae projection of A onto the equatorial plane

a radius of Earth, shape parameter for terrain profile

B buoyancy

Bu Burger number

C circulation, condensation rate, speed of bore relative to upstream density current, radar constant

Ca absolute circulation

Cp heat capacity at constant pressure

c storm motion vector

cg group velocity

c phase speed, speed of light

c∗ complex conjugate of the phase speed

cd drag coefficient

ce bulk transfer coefficient for moisture

cgx zonal group velocity component

cgz vertical group velocity component

ch bulk transfer coefficient for heat

ci imaginary part of phase speed

cl specific heat of liquid water for a constant pressure process

cp specific heat for a constant-pressure process

cpd specific heat at constant-pressure for dry air

cpv specific heat at constant-pressure for water vapor

cr real part of phase speed

cv specific heat for a constant-volume process

cvd specific heat at constant-volume for dry air

cvv specific heat at constant volume for water vapor

D characteristic depth scale, resultant deformation, depth of wave duct, depth of fluid layer, depth of outflow, duration of precipitation, hailstone diameter

D1 stretching deformation

D2 shearing deformation

d depth of control volume

dA element of an arbitrary surface having an area A

dl element of a circuit about which circulation is evaluated

E evaporation rate, precipitation efficiency

e vapor pressure, Euler’s number

mean vapor pressure, turbulent kinetic energy

eij deformation tensor

es saturation vapor pressure

F viscous force

Fh sum of horizontal forces acting on an air parcel

Fu viscous force acting on u

Fv viscous force acting on v, sum of vertical forces acting on an air parcel

Fw viscous force acting on w

Fr Froude number

Frm mountain Froude number

f Coriolis parameter, frequency

f0 constant reference Coriolis parameter

g gravitational acceleration vector

g gravitational acceleration

g′ reduced gravity

H scale height of atmosphere, undisturbed depth of fluid layer, far-field depth of cold pool

H0 original height of dividing streamline

H1 nadir height of dividing streamline

h specific enthalphy, height above ground

h0 depth of stable layer

h1 depth of bore

hI inertial height scale

hm height of mountain summit

ht height of terrain

Iδ vertical integral of the displacement of potential temperature surfaces

i unit vector in positive xdirection

i

j unit vector in positive ydirection

Ke eddy diffusivity for moisture

Kh eddy diffusivity for heat

Km eddy viscosity

k unit vector in positive zdirection

k zonal wavenumber, von Karman’s constant, wave mode

KE kinetic energy

LR Rossby radius of deformation

LRm mountain Rossby radius of deformation

Lx distance between mountain crests

l meridional wavenumber, mixing length, cross-gap length scale, Scorer parameter

lf specific latent heat of fusion

ls specific latent heat of sublimation

lv specific latent heat of vaporization

M angular momentum, absolute (or pseudoangular) momentum

mean angular momentum

M′angular momentum perturbation

Mg geostrophic absolute (or geostrophic pseudoangular) momentum

m vertical wavenumber

N Brunt-Väisälä frequency, refractivity

Nm moist Brunt-Väisälä frequency

N0 constant Brunt-Väisälä frequency

n unit vector that points to the left of the horizontal wind velocity

n coordinate in the n direction, an integer, refractive index

Pr received backscattered power

p pressure

mean (environmental) pressure

p0 reference pressure

pd pressure of dry air

p∗ saturation pressure

p′ pressure perturbation

amplitude of pressure perturbation

p′b buoyancy pressure perturbation

p′d dynamic pressure perturbation

p′h hydrostatic pressure perturbation

p′nh nonhydrostatic pressure perturbation

p′dl linear dynamic pressure perturbation

p′dnl nonlinear dynamic pressure perturbation

complex amplitude of pressure perturbation

p∞ ambient far-field pressure away from a tornado

PV Ertel’s potential vorticity

PVg geostrophic potential vorticity

Q heating rate

Qe surface latent heat flux

Qh surface sensible heat flux

Qg ground heat flux

q specific heating rate

R gas constant, radius of circulation circuit, reflection coefficient, rainfall rate

R∗ complex conjugate of reflection coefficient

Rd gas constant for dry air

Rf flux Richardson number

Rn net radiation

Rt radius of curvature of a trajectory

Rv gas constant for water vapor

r position vector

r distance to center of Earth, radial coordinate, range to radar target, linear correlation coefficient, aspect ratio of a mountain

rh hydrometeor mixing ratio

rt total water mixing ratio

rv water vapor mixing ratio

rv0 water vapor mixing ratio at the height of the roughness length

mean water vapor mixing ratio

mean water vapor mixing ratio at anemometer level

r′v water vapor mixing ratio perturbation

rvs saturation water vapor mixing ratio

Ra Rayleigh number

Rac critical Rayleigh number

Re Reynolds number

Ri Richardson number

Ro Rossby number

RH relative humidity

S mean vertical wind shear vector

S swirl ratio

Si sources and sinks of water vapor s unit vector that points in the direction of the horizontal wind velocity

s coordinate in the s direction

T absolute temperature, characteristic timescale

mean (environmental) absolute temperature

T′ absolute temperature perturbation

T0 constant reference absolute temperature

Td dew-point temperature

Te equivalent temperature

Tv virtual temperature

mean (environmental) virtual temperature

T′ v virtual temperature perturbation

Tw wet-bulb temperature

T∗ saturation temperature

Tρ density temperature

t time

U along-gap wind speed

u zonal wind component, radial wind component, cross-mountain wind component, cross-gap wind speed

u mean (environmental) zonal wind component

mean zonal wind at anemometer level

u′ zonal wind perturbation

amplitude of zonal wind perturbation

u∗ friction velocity

ua zonal ageostrophic wind component

u0 constant reference zonal wind component, wind speed far upstream of a mountain

ua0 zonal ageostrophic wind at the start of the inertial oscillation that leads to the nocturnal low-level wind maximum

ug zonal geostrophic wind component

ugc along-front geostrophic wind component on cold side of front

ugw along-front geostrophic wind component on warm side of front

V characteristic velocity scale, horizontal wind speed, volume of air

Vg geostrophic wind speed

v wind velocity vector

mean (environmental) wind velocity vector

v′ perturbation wind velocity vector

va ageostrophic wind vector

va0 ageostrophic wind vector at the start of the inertial oscillation that leads to the nocturnal low-level wind maximum

vg geostrophic wind vector

vh horizontal wind velocity vector

vT thermal wind vector

v meridional wind component, tangential wind component, mountain-parallel wind component

mean (environmental) meridional wind component

mean meridional wind at anemometer level

v′ meridional wind perturbation

vR radial velocity

va meridional ageostrophic wind component

va0 meridional ageostrophic wind at the start of the inertial oscillation that leads to the nocturnal low-level wind maximum

vg meridional geostrophic wind component

vt hydrometeor fall speed

W work, width, sum of vertical velocity of air plus hydrometeor fall speed

W↓ work required to displace parcel downward

W↑ work required to displace parcel upward

w vertical wind component

w mean vertical wind component

w′ vertical velocity perturbation

amplitude of vertical velocity perturbation

complex amplitude of the vertical velocity perturbation

kth mode of the complex amplitude of the vertical velocity perturbation

imaginary part of the kth mode of the complex amplitude of the vertical velocity perturbation

real part of the kth mode of the complex amplitude of the vertical velocity perturbation

x coordinate in the i direction

y coordinate in the j direction

Z impedance, logarithmic reflectivity factor

Zhh reflectivity factor associated with horizontally polarized transmitted and backscattered pulses

Zvv reflectivity factor associated with vertically polarized transmitted and backscattered pulses

ZDR differential reflectivity factor

z coordinate in the k direction, reflectivity factor

z′ characteristic distance a parcel travels before mixing with its surroundings

z0 roughness length, height of a streamline far upstream of a mountain

zi height of the inversion at the top of the boundary layer

zinv height of inversion

zr height of interface separating two layers of fluid

PART I: General Principles

1

What is the Mesoscale?

1.1 Space and time scales

Atmospheric motions occur over a broad continuum of space and time scales. The mean free path of molecules (approximately 0.1 μm) and circumference of the earth (approximately 40 000 km) place lower and upper bounds on the space scales of motions. The timescales of atmospheric motions range from under a second, in the case of small-scale turbulent motions, to as long as weeks in the case of planetary-scale Rossby waves. Meteorological phenomena having short temporal scales tend to have small spatial scales, and vice versa; the ratio of horizontal space to time scales is of roughly the same order ofmagnitude for most phenomena (~10m s−1) (Figure 1.1).

Before defining the mesoscale it may be easiest first to define the synoptic scale. Outside of the field of meteorology, the adjective synoptic (derived from the Greek synoptikos) refers to a “summary or general view of a whole.” The adjective has a more restrictive meaning to meteorologists, however, in that it refers to large space scales. The first routinely available weathermaps, produced in the late 19th century, were derived from observations made in Europeancities having a relatively coarse characteristic spacing. These early meteorological analyses, referred to as synoptic maps, paved the way for the Norwegian cyclone model, which was developed during and shortly afterWorld War I. Because only extratropical cyclones and fronts could be resolved on the early synoptic maps, synoptic ultimately became a term that referred to large-scale atmospheric disturbances.

The debut of weather radars in the 1940s enabled phenomena to be observed that were much smaller in scale than the scales of motion represented on synoptic weather maps. The term mesoscale appears to have been introduced by Ligda (1951) in an article reviewing the use of weather radar, in order to describe phenomena smaller than the synoptic scale but larger than the microscale, a term that was widely used at the time (and still is) in reference to phenomena having a scale of a few kilometers or less.1 The upper limit of the mesoscale can therefore be regarded as being roughly the limit of resolvability of a disturbance by an observing network approximately as dense as that present when the first synoptic charts became available, that is, of the order of 1000 km.

At least a dozen different length scale limits for the mesoscale have been broached since Ligda’s article. The most popular bounds are those proposed by Orlanski (1975) and Fujita (1981).2 Orlanski defined the mesoscale as ranging from 2 to 2000 km, with subclassifications of meso-, meso-, andmeso- scales referring to horizontal scales of 200–2000 km, 20–200 km, and 2–20 km, respectively (). Orlanski defined phenomena having scales smaller than 2 km as microscale phenomena, and those having scales larger than 2000 km as macroscale phenomena. Fujita (1981) proposed a much narrower range of length scales in his definition of mesoscale, where the mesoscale ranged from 4 to 400 km, with subclassifications of meso- and meso- scales referring to horizontal scales of 40–400km and 4–40 km, respectively (Figure ).