Arya S.P.S. Introduction to Micrometeorology
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X Contents
Chapter 14 Nonhomogeneous Boundary Layers
14.1 Types of Surface Inhomogeneities
14.2 Step Changes in Surface Roughness
14.3 Step Changes in Surface Temperature
14.4 Air Modifications over Water Surfaces
14.5 Air Modifications over Urban Areas
14.6 Building Wakes and Street Canyon Effects
14.7 Other Topographical Effects
14.8 Applications
Problems and Exercises
Chapter 15 Agricultural and Forest Microrneteorology
15.1 Flux-Profile Relations above Plant Canopies
15.2 Radiation Balance within Plant Canopies
15.3 Wind Distribution in Plant Canopies
15.4 Temperature and Moisture Fields
15.5 Turbulence in Plant Canopies
15.6 Applications
Problems and Exercises
References
Index
International Geophysics Series
223
224
231
235
237
245
252
259
260
263
266
271
273
277
282
284
287
295
305
Preface
Many university departments of meteorology or atmospheric sciences
offer a course in micrometeorology as a part of their undergraduate cur-
ricula. Some graduate programs also include an introductory course in
micrometeorology or environmental fluid mechanics, in addition to more
advanced courses on planetary boundary layer (PBL) and turbulence.
While there are a number of excellent textbooks and monographs avail-
able for advanced graduate courses, there is no suitable text for an intro-
ductory undergraduate or graduate course in micrometeorology. My col-
leagues and I have faced this problem for more than ten years, and we
suspect that
other
instructors of introductory micrometeorology courses
have faced the same
problem-lack
of a suitable textbook. At first, we
tried to use R. E. Murin's "Descriptive Micrometeorology," but soon
found it to be much out-of-date. There has been almost an explosive
development
of
the field during the past two decades, as a result of in-
creased interest in micrometeorological problems and advances in com-
putational and observational facilities. When Academic Press approached
me to write a textbook, I immediately saw an opportunity for fillinga void
and satisfying an acutely felt need for an introductory text, particularly
for undergraduate students and instructors. I also had in mind some in-
coming graduate students having no background in micrometeorology or
fluid mechanics. Instructors may also find the latter half of the book
suitable for an introductory or first graduate course in atmospheric bound-
ary layer and turbulence. Finally, it may serve as an information source
for boundary-layer meteorologists, air pollution meteorologists, agricul-
xi
xii Preface
tural and forest micrometeorologists, and environmental scientists and
engineers.
Keeping in mind my primary readership, I have tried to introduce the
various topics at a sufficiently elementary level, starting from the basic
thermodynamic and fluid dynamic laws and concepts. I have also given
qualitative descriptions
based
on observations before introducing more
complex theoretical concepts and quantitative relations. Mathematical
treatment is deliberately kept simple, presuming only a minimal mathe-
matical background of upper-division science majors. Uniform notation
and symbols are used throughout the text, although certain symbols do
represent different things in different contexts. The list of symbols should
be helpful to the reader. Sample problems
and
exercises given at the end
of each
chapter
should be useful to students, as well as to instructors.
Many
of
these were given in homework assignments, tests, and examina-
tions for
our
undergraduate course in micrometeorology.
The book is organized in the form of fifteen chapters, arranged in order
of increasing complexity and what I considered to be a natural order of
the topics covered in the book. The scope and importance
of
micromete-
orology
and
turbulent exchange processes in the
PBL
are introduced in
Chapter
1. The next three chapters describe the energy budget near the
surface and its components, such as radiative, conductive, and convec-
tive heat fluxes.
Chapter
5 reviews basic thermodynamic relations and
presents typical temperature and humidity distributions in the PBL. Wind
distribution in the
PBL
and simple dynamics, including the balance of
forces on an air parcel in the PBL, are discussed in Chapter 6. The
emphasis, thus far, is on observations, and very little theory is used in
these early chapters. The viscous flow theory, fundamentals of turbu-
lence,
and
classical semiempirical theories
of
turbulence, which are
widely used in micrometeorology and fluid mechanics, are introduced in
Chapters 7, 8,
and
9. Instructors
of
undergraduate courses may like to
skip some of the material presented here, particularly the Reynolds-aver-
aged equations for turbulent motion. Chapters 10-12 present the surface-
layer similarity theory and micrometeorological methods and observa-
tions using the similarity framework. These three chapters would
constitute the core of any course in micrometeorology. The last three
chapters
cover
the
more specialized topics of the marine atmospheric
boundary layer, nonhomogeneous boundary layers, and micrometeorol-
ogy of vegetated surfaces. Since these topics are still hotly pursued by
researchers, the
reader
will find much new information taken from recent
journal articles. The instructor should be selective in what might be in-
cluded in an undergraduate course. Chapters
7-15
should also be suitable
for a first graduate course in micrometeorology or PBL.
Preface xiii
Finally, I would like to acknowledge the contribution of my colleagues,
Jerry Davis, Al Riordan, and Sethu Raman, and of my students for re-
viewing certain parts of the manuscript and pointing out many errors and
omissions. I am most grateful to Professor Robert Fleagle for his thorough
and timely review of each chapter, without the benefit of the figures and
illustrations. His comments and suggestions were extremely helpful in
preparing the final draft. I would also like to thank the publishers and
authors
of
many
journal
articles, books, and monographs for their permis-
sion to reproduce many figures and tables in this book. The original
sources are acknowledged in figure legends, whenever applicable. Still,
many ideas, explanations, and discussions in the text are presented with-
out specific acknowledgments
of
the original sources, because, in many
cases, the original sources were not known and also because, I thought,
giving too many references in the
text
would actually distract the reader.
In the end, I wish to acknowledge the help of Brenda Batts and Dava
House
for typing the manuscript and Pat Bowers and LuAnn Salzillo for
drafting figures and illustrations.
This page intentionally left blank
Symbols
A Amplitude of thermal wave
01
Empirical constant
in the subsurface medium
02
Empirical constant
(Chapter 4)
B Bowen ratio
A
Aerodynamic surface area
B Buoyancy production term
of vegetation
per
unit
in the turbulent kinetic
volume (Chapter 15)
energy equation (Chapter
As
Amplitude of thermal wave
8)
at the surface
b
Boltzmann constant
A
o
Mean advection terms in the
C
Heat
capacity
thermodynamic energy
C
A constant (Chapter 9)
equation
a
Albedo or shortwave reflec-
CD
Surface drag coefficient
tivity of the surface
Cd
Drag coefficient (Chapter
(Chapter 3)
15)
a
a
==
(j/2v)l/2
(Chapter 7)
C
DN
Drag coefficient in neutral
a
An empirical constant
stability
(Chapter 13)
C
H
Heat
transfer coefficient
°b
Acceleration due to buoy-
C
HN
Heat
transfer coefficient in
ancy
neutral stability
OJ
Empirical constant
C
w
Water vapor transfer coeffi-
00
Instantaneous advection
cient
terms in the thermody-
C
w
Wave speed
namic energy equation
C
w
A constant (Chapter 9)
xv
xvi
Symbols
C
8
An empirical constant
Eo
Rate of evaporation or con-
Co
Phase speed of dominant
densation at the surface
waves
e
Water vapor pressure
C Specific heat
e
s
Water vapor pressure at
C
Speed of light (electromag-
saturation
netic waves) in vacuum
eo
Water vapor pressure at the
(Chapter 3) surface or at
z =
ZO
C
m
Electromagnetic wave speed
F
Function of certain variables
in a medium (Chapter 3) (Chapter 9)
C
m
A constant (Chapter 14) F
Froude
number (Chapters 13
c
p
Specific heat at constant
and 14)
pressure
F
c
Critical
Froude
number
C
y
Specific heat at constant F
L
Froude
number based on
volume length of the
hill
D Reference depth in the sub-
F
u
A similarity function
medium (Chapter 4)
F
y
A similarity function
D
Viscous dissipation term in
f
Coriolis parameter
the turbulent kinetic en-
f
Function of variables (Chap-
ergy equation (Chapter 8)
DlDt Total derivative
ter 9)
d
Distance
of
the earth from
f'
Normalized velocity as a
the sun (Chapter 3)
function
of
YJ
G
Magnitude
of
geostrophic
d
Damping depth of thermal
wind
wave in the submedium
(Chapter 4)
G
Geostrophic wind vector
dH
Heat
added to a parcel
Gr
Grashof number
d
m
Mean distance between the
Go
Magnitude of surface geo-
earth and the sun
strophic wind
dP
Change in the air pressure
Go
Surface geostrophic wind
dT
Change in the air tempera-
vector
ture
g
Acceleration due to gravity
do
Zero-plane displacement
H
Sensible (direct) heat flux
E Rate of evaporation or con-
H
Wave height (Chapter 13)
densation
H
Building height (Chapter 14)
E
a
Drying
power
of
air
H
Mean wave height
E
p
Potential evaporation or
tt,
Anthropogenic heat flux in
evapotranspiration
an urban area
Symbols
XVll
H
G
Ground heat flux to or from
k
Thermal conductivity
the subsurface medium (Chapter 4)
Hi
Heat
flux at the inversion
k
m
Hydraulic conductivity of
base
the subsurface medium
H
io
Energy coming in
L
Obukhov length
H
L
Latent
heat flux
L A characteristic length scale
n.;
Energy going
out
(Chapter 9)
u, Height of the dividing
L Wavelength (Chapter 13)
streamline
LA!
Leaf
area
index
H
o
Sensible heat flux at the
L
e
Latent
heat of evaporation/
surface
condensation
Fluctuating mixing length
Hl/3
Significant wave height
'
m
Mean mixing length
h
Boundary layer thickness
M
Soil moisture flow rate
h
Depth of channel flow or
u,
Soil moisture flow rate at
distance between two
the bottom of layer
parallel planes (Chapter 7)
u,
Mass of dry air
hE
Ekman
depth
M
w
Mass
of
water vapor
hi
Internal boundary layer
M
o
Soil moisture flow rate at
thickness
the surface
h
p
Planck's constant
m
Mean molecular mass of air
h
o
Average height of roughness
(Chapter 5)
elements or plant canopy
m
Exponent in the power-law
1
Insolation at the surface
wind profile equation
1
0
Insolation at the top of the
(Chapter 10)
atmosphere
m
A coefficient (Chapter 15)
Imaginary number
v=I
md
Mean molecular mass of dry
air
K
Effective viscosity
m
w
Mean molecular mass of
K
h
Eddy diffusivity of heat
water vapor
K
m
Eddy
viscosity or diffusivity
N
Brunt-
Vaisala frequency
of momentum
Nu
Nusselt number
K
mr
Eddy viscosity at the refer-
n
Exponent in the power-law
ence height
eddy viscosity profile
K
w
Eddy
diffusivity of water
(Chapter 10)
vapor
n
Wave frequency (Chapter
k
von Karman constant
13)
xviii
Symbols
n
A coefficient (Chapter 15)
RLj
Outgoing (upward)
P
Mean air pressure
longwave radiation
P
Period of the wave (Chapter
R
N
Net
radiation
4)
R
s
Shortwave radiation (flux)
PAl
Plant
area
index
Rst
Incoming (downward) short-
Pe Peclet number
wave radiation
Pr Prandtl number
R
st
Outgoing (upward) short-
Po
Pressure of the reference
wave radiation
atmosphere
R
s
Solar radiation flux at the
surface
P
Instantaneous pressure
Absolute gas constant
Po
Pressure of the reference
R*
state
R)...
Radiative energy flux den-
PI
Deviation of pressure from
sity
per
unit wavelength
the reference state
R
o
Solar radiation flux at the
Q Mean specific humidity
top of the atmosphere
Qs
Mean specific humidity at
rH
Aerial resistance to heat
saturation
transfer
Qo
Specific humidity at z = Zo
rM
Resistance to momentum
transfer
q Specific humidity fluctuation
rw
Resistance to water vapor
q*
Specific humidity scale for
transfer
the surface layer
S
Shear
production term in
R Radiative energy flux or
the turbulent kinetic en-
radiation (Chapter 3)
ergy equation (Chapter 8)
R
Specific gas constant (Chap-
S
Soil moisture content
ter
5)
(Chapter 12)
Ra Rayleigh number
SF
Speed-up factor
R
D
Diffuse radiation
So
Solar constant
R
d
Specific gas constant for dry
s Static stability
air
T
Mean air temperature
Re
Reynolds number
T Temperature of the subsur-
Ri
Richardson number
face medium (Chapter 4)
RiB
Bulk Richardson number
T
Wave period (Chapter 13)
Ric
Critical Richardson number
t.;
Equivalent black body tem-
R
L
Longwave radiation (flux)
perature
RLt
Incoming (downward)
T
m
Mean temperature of the
longwave radiation
I
surface and submedium
Symbols
XIX
t;
Turbulent transport of tur-
U
IO
Wind speed at a reference
bulent kinetic energy
height of
10m
t,
Surface temperature (Chap-
U Fluctuating velocity compo-
ter
4)
nent in
x direction
t,
Sea-surface temperature
U
Characteristic velocity scale
(Chapter 13)
of turbulence (Chapter 8)
T
u
Urban
air temperature
U
Instantaneous velocity in x
Tv
Mean virtual temperature of
direction
moist air
Uf
Local free convective veloc-
t.,
Mean virtual temperature of
ity scale
the parcel
U*
Friction velocity
T
vo
Virtual temperature at the
V Mean velocity component in
reference state
y direction
T*
Convective temperature
V
Volume (Chapter 2)
scale
V Characteristic velocity scale
To
Air temperature at the refer-
(Chapter 9)
ence state
V Wind vector
T
I
Deviation in the tempera-
V
g
Geostrophic wind compo-
ture from the reference
nent in
y direction
state
Fluctuating velocity compo-
u
T
IO
Air temperature at
10m
nent in y direction
above the surface
v
Instantaneous velocity in y
t
Time
direction
U
Mean velocity component in
W
Mean velocity component in
x direction
z (vertical) direction
U
g
Geostrophic wind compo-
W Building width (Chapter 14)
nent in
x direction
W
AI
Woody-element area index
U
h
Velocity at z = h
W*
Convective velocity scale
U
h
Velocity of the moving sur-
w
Fluctuating velocity compo-
face (Chapter 7)
nent in z (vertical) direc-
Urn
Mixed-layer averaged wind
tion
speed
W
Instantaneous velocity in z
o,
Wind speed at the reference
direction
height
z
Height above or depth be-
U'"
Ambient wind speed
low the surface or an
U
o
Mean velocity in the ap-
appropriate reference
proach flow
plane