AUGUST 1985
ATMOSPHERIC DIFFUSION MODELING BASED ON BOUNDARY LAYER PARAMETERIZATION
ATMOSPHERIC SCIENCES RESEACH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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ATMOSPHERIC DIFFUSION MODELING BASED ON BOUNDARY LAYER PARAMETERIZATION
by
J. S. Irwin
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
Research Triangle Park, USA
S. E. Gryning
Ris«i National Laboratory
Roskilde, Denmark
A. A. M. Holtslag
Royal Netherlands Meteorological Institute
DeBilt, The Netherlands
B. Sivertsen
Norwegian Institute for Air Research
Lillestrjfa, Norway
ATMOSPHERIC SCIENCES RESEACH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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NOTICE
The information in this document has been funded in part by the United
States Environmental Protection Agency (EPA), under agreement DW-13931239
between the EPA and the Air Resources Laboratories (ARL), National Oceanic
and Atmospheric Administration (NOAA). It has been subjected to the Agency's
peer and administrative review, and it has been approved for publication as
an EPA document. Approval does not signify that mention of trade names or
commercial products constitute endorsement or recommendation for use.
AFFILIATION
Mr. John S. Irwin is on assignment from the National Oceanic and Atmospheric
Administration, U. S. Department of Commerce.
11
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PREFACE
During September 12-16, 1983 at the Royal Netherlands Meteorological Institute
and in June 25-29, 1984 at the Ris^ National Laboratory, a workgroup of scien-
tists from four air research and meteorological agencies met to review and
discuss methods for characterizing diffusion meteorology. The contents of
this report summarizes the discussions of these meetings. Based on this
report, the workgroup drafted two papers which were presented at the 15-th
International Technical Conference on Air Pollution Modeling and Its Appli-
cation (16-19 April 1985 at St. Louis, MO):
Parameterization of the atmospheric boundary layer for air pollution
dispersion models by A.A.M. Holtslag, S.E. Gryning, J.S. Irwin and
B. Sivertsen.
Atmospheric dispersion modeling based upon boundary layer parameter-
ization by B. Sivertsen, S.E. Gryning, J.S. Irwin and A.A.M. Holtslag.
These two papers extend the concepts presented in this report and demonstrate
the performance of the suggested dispersion modeling using nonbuoyant tracer
data from field experiments conducted in Denmark and Norway. A bound version
of the proceedings of the conference will be made available through Plenum
Press as Air Pollution Modeling and Its Application V.
iii
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ABSTRACT
The conclusions of a workgroup are presented outlining methods for
processing meteorological data for use in air quality diffusion modeling. To
incorporate the proper scaling parameters the discussion is structured in
accordance with the current concepts for the idealized states of the planetary
boundary layer. We recommend a number of models, the choice of which depends
on the actual idealized state of the atmosphere. Several of the models
characterize directly the crosswind integrated concentration at the surface,
thus avoiding whenever justified the assumption of a Gaussian distribution of
material in the vertical. The goal was to characterize the meteorological
conditions affecting the diffusion for transport distances on the order of 10
km or less. Procedures are suggested for estimating the fundamental scaling
parameters. For obtaining the meteorological data needed for estimating the
scaling parameters, a minimum measurement program to be carried out at a mast
is recommended. If only synoptic data are available, methods are presented
for the determination of the scaling parameters. Also, methods are suggested
for estimating the vertical profiles of wind velocity, temperature, and the
variances of the vertical and lateral wind velocity fluctuations.
iv
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CONTENTS
Notice ii
Preface iii
Abstract iv
List of Symbols vi
1. Introduction I
2. The Boundary Layer 3
2.1 The Unstable Boundary Layer 3
2.2 The Stable Boundary Layer 7
3. Parameters 9
3.1 The Surface Roughness Length 9
3.2 The Monin-Obukhov Length 10
3.3 Mixing Height and Inversion Height 14
4. Profiles 16
4.1 Wind Profile 16
4.2 Temperature Profile 18
4.3 Turbulence Profiles 19
5. Diffusion 23
5.1 The Surface Layer 26
5.2 The Mixed Layer 29
5.3 The Free Convection Layer 30
5.4 The Entrainment Layer 31
5.5 The Near Neutral Upper Layer 32
5.6 The Local Scaling Region 32
6. Discussion 34
7. References 37
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LIST OF SYMBOLS
a = an empirical constant, used in Eq (4-4) in the estimation of the
nighttime potential temperature profile
al»a2 = empirical constants used in shape parameter equations
t>i,b2
c,p
b = empirical constant, used in Eq (5-15)
A,B = shape constant functions used to describe general solution to the
two-dimensional diffusion equation
Aw = empirical constant, used in Eq (4-5) in the estimation of the
variance of the vertical wind speed fluctuations
d,di,d2 = empirical constants used in parameterization of the net radiation
c,ci,c2
c3
C4,C5 = empirical constant, used to determine mixing height in Eq (3-7)
C6 = empirical constant, used to determine mixing height in Eq (3-8)
Cp = specific heat capacity at constant pressure
d = empirical constant, used in Eq (4-5) in the estimation of the
variance of the vertical wind speed fluctuations
D = angle between the surface wind direction and the geostrophic wind
direction
f = Coriolis parameter
fs,fg = weighting functions used in the estimation of the vertical profile of
the wind
fy,fz = empirical functions describing the growth of the disperision
parameters, ay and az
F = plume buoyancy, gQa/^pCpTo
2
F* = plume buoyancy parameter, F/(UwAzi)
g = acceleration due to gravity
G = geostrophic wind speed
vi
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Go = soil heat flux
h = surface temperature inversion height
H = pcpw'0', sensible heat flux
Hj = integral of heat flux, Eq (4-4)
k = Von Karman constant
K = vertical eddy diffusivity of matter
L = Monin-Obukhov length
N = fraction of sky covered by cloud
N = Brunt-Vaisala frequency
P = fraction of material that stabilzes in capping inversion
Q = emission rate
QH = rate of output of heat from a chimney
Q* = net radiation
r = albedo of surface
R0 = Rossby number
'£) = Lagrangian autocorrelation function
s = shape parameter, Eq 5-13 and Eq 5-14
t0 = transition time, the instant when the net sensible heat flux at the
surface changes sign from positive to negative
T = air temperature
Te = empirical time scale, used in Eq (5-5)
TL = Lagrangian integral time scale
T0 = stack gas temperature
vi i
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u = horizontal wind speed
uf = free convection scaling velocity
u* = /t/p surface friction velocity
U = estimated horizontal wind speed assuming surface layer similarity
Ur = near-surface reference wind speed
UZ,VZ = components of horizontal wind in the vertical relative to a coordinate
system alined along the surface-layer reference wind direction
w* = mixed layer scaling velocity
x,y,z = rectangular coordinates, x usually along mean wind and z vertical
xo = integration constant used in describing variation of the mean height
of particles as a function of distance downwind
x' = typical distance to upwind obstacle
X = (x/zi)(w*/U)
X' = (x/zs)(w*/U)
z0 = surface roughness length
zr = measurement height of the near-surface reference wind speed
zs = release height above ground
z^ = mixing height
a = empirical constant, accounts for the strong correlation between
surface heat flux, net radiation and soil heat flux in Eq (3-2)
p = empirical constant, accounts the portion of the sensible heat flux
not related to the net radiation or the soil heat flux in Eq (3-2)
Yi = lapse rate above unstable mixed layer
Y/s = thermo-dynamic function of temperature
AT = vertical temperature difference
A9 = used in defining the nighttime potential temperature
profile, 0(t,z)-00
A0i = potential temperature jump at top of unstable mixed layer
viii
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A9S = 0s(t) - 00
C = z/L
Cr = zr/L
Q = potential temperature
0gL = mixed layer temperature
9(t,z) = nighttime potential temperature
d0/dz = potential temperature gradient
Qf = free convection scaling temperature
0m = mixed layer scaling temperature
Q0 = the potential temperature of the adiabatic profile at transition
time
Qs(t) = the surface potential temperature found at time t since transition
0* = surface layer scaling temperature
< = horizontal wave number
£ = the length scale, estimated as, (l/lg + l/Jln) where I is
the stable length scale and Jln is the neutral length scale,
2
As = y
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= induced lateral dispersion due to buoyancy effects
o"yO = lateral dispersion due to ambient turbulence
ays = induced lateral dispersion due to wind direction shear in the
vertical
azo = vertical dispersion due to ambient turbulence
°"zb = vertical dispersion due to buoyancy effects
T = -pu'w', momentum shear stress
= elevation of sun above horizon
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1. INTRODUCTION
The purpose of the following discussion is to outline a set of methods
for processing meteorological data for use in diffusion modeling. In this
discussion, the emphasis will be on those methods considered both physically
realistic and numerically efficient.
Most of the early attempts to estimate the diffusion of air pollutants
were based on the Gaussian-plume model, for example see Sutton (1953).
Pasquill (1961) gave simple rules for obtaining the lateral spread based on
wind-direction trace data and suggested the effects of thermal stratification
in the lower atmosphere be represented in broad categories of stability,
defined in terms of meteorological data routinely available in surface
weather observations. By the early 1970's, air quality simulation models
were viewed as a means to estimate the relative magnitudes of concentration
distributions from various sources and thereby provide a rational basis for
strategies leading to air quality improvement or maintenance. Most of the
air quality simulation models developed in response to these modeling
requirements were based on the general Gaussian-plume model. Invariably the
models were constructed assuming that the dispersive characteristics of the
atmosphere were vertically and horizontally homogeneous.
Current concepts regarding the structure of an idealized boundary layer,
are briefly reviewed and the basic meteorological variables of interest to
diffusion modeling are identified. Methods are proposed for specifying each
of these basic variables. The goal is to characterize the meteorological
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conditions affecting the diffusion for trans-port distances on the order of 10
km or less over reasonably flat and homogeneous terrain. In this description
of turbulence, the effects of clouds and fog are only considered as far as
these affect the radiation and the surface energy balance. The relationship
and importance of the variables to diffusion processes are reviewed. The
final section reviews the conclusions and envisioned future research activi-
ties.
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1. INTRODUCTION
The purpose of the following discussion is to outline a set of methods
for processing meteorological data for use in diffusion modeling. In this
discussion, the emphasis will be on those methods considered both physically
realistic and numerically efficient.
Most of the early attempts to estimate the diffusion of air pollutants
were based on the Gaussian-plume model, for example see Sutton (1953).
Pasquill (1961) gave simple rules for obtaining the lateral spread based on
wind-direction trace data and suggested the effects of thermal stratification
in the lower atmosphere be represented in broad categories of stability,
defined in terms of meteorological data routinely available in surface
weather observations. By the early 1970's, air quality simulation models
were viewed as a means to estimate the relative magnitudes of concentration
distributions from various sources and thereby provide a rational basis for
strategies leading to air quality improvement or maintenance. Most of the
air quality simulation models developed in response to these modeling
requirements were based on the general Gaussian-plume model. Invariably the
models were constructed assuming that the dispersive characteristics of the
atmosphere were vertically and horizontally homogeneous.
Current concepts regarding the structure of an idealized boundary layer,
are briefly reviewed and the basic meteorological variables of interest to
diffusion modeling are identified. Methods are proposed for specifying each
of these basic variables. The goal is to characterize the meteorological
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conditions affecting the diffusion for trans-port distances on the order of 10
km or less over reasonably flat and homogeneous terrain. In this description
.of turbulence, the effects of clouds and fog are only considered as far as
these affect the radiation and the surface energy balance. The relationship
and importance of the variables to diffusion processes are reviewed. The
final section reviews the conclusions and envisioned future research activi-
ties.
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2. THE BOUNDARY LAYER
Atmospheric diffusion is controlled by the turbulence in the air. The
parameters describing the scales of turbulence are therefore of fundamental
importance in a description of atmospheric diffusion. Most air pollution
sources emit into the boundary layer which can be defined as the lower layer
of the atmosphere where the influence of the surface is present due to fric-
tion. The character and turbulent state of the boundary layer is strongly
affected by the diurnal heating and cooling cycle.
2.1 The Unstable Boundary Layer
The unstable boundary layer is directly affected by solar heating of the
ground. The layer has a very pronounced diurnal variation, and typically
reaches a height of 1-2 km over land in summertime. For the characterization
of turbulence within this layer three length scales are important. These are
the mixing height, z^, the height above the ground, z, and the Monin-Obukhov
stability length, L. The mixing height z^ defines the height above the
surface in which pollutants are mixed by presence of turbulence. From these
three parameters, two independent dimensionless parameters can be formed.
The unstable boundary layer can be divided into several layers defined in
terms of these parameters. Fig. 2-1 'is a schematic diagram showing idealized
limits of validity of the scaling techniques together with the corresponding
parameters for the turbulence. This figure is similar to those presented
by Nicholls and Readings (1979) and Olesen et al. (1984). Traditionally, the
boundaries between the individual layers have not been expressed in the same
set of dimensionless parameters. This makes any sketch of the boxes look
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EMTRAINMENT LAYER
MIXED LAYER
w»
Zj
g/T
FREE CONVECTION
LAYER
uf
*f
z
g/T
NEAR NEUTRAL
UPPER LAYER
Zj
z
u«
SURFACE LAYER
u»
0,
z
g/T
Z/Zj
1.0
0.8
0.1
-100
-1.0
Z/L
-0
LIMIT
LOCAL AND z-LESS
SCALING REGION
u*(local)
N(local)
g/T(local)
SURFACE LAYER
u*
0,
z
g/T
+0
1.0
Z/L
10.0
Figure 2-1. Idealized view of the states of the Planetary Boundary
Layer and the limits of validity of the scaling
techniques.
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fairly complicated. Here, we have sacrificed some of the detailed structure
that arises from the traditional way of describing the boundaries. Our pro-
posed simplified version in some cases slightly deviates from the viewpoints
traditionaly held of the boundaries.
2.1.1 The surface layer (zo « z , Min(0.lz±;-L))
This is the layer where wind shear plays a dominant role. The control-
ling parameters are the height, z, the momentum shear stress, T = -pu'w',
the sensible heat flux at the ground, H = pCpW'0", and the buoyancy parameter,
g/T (Businger, 1973). From these parameters we can form the equivalent
o
parameters, z, L, u* and Q* where L is the Monin-Obukhov length, L = -u*/
[k(g/T)(H/pcp)], k the Von Karman constant (~0.4), the friction velocity u*
= /T/p and the scaling temperature Q* = -H/(pcpu*). Monin-Obukhov similarity
theory postulates that dimensionless local groups formed with u* and 0*
become universal functions of z/L. The surface layer is confined to the
layer 20z0 < z < -L and z < O.lz^, where zo is the surface roughness length.
2.1.2 The free convection layer (-L < z < O.lz.^)
Above z = -L, is a layer where T is no longer important in describing
the atmospheric turbulence and z.£ is not yet important, thus the controlling
parameters are z and the surface layer values of w'0' and g/T. The free
convection layer exists for -L < z < O.lz^. Tennekes (1970) described the
scaling velocity and temperature as,
uf = (w^T z g/T)1/3,
0f = w'0'/uf .
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2.1.3 The mixed layer (O.lz.^ < z < O.Sz^ and Z/-L > 1)
In this layer the turbulence structure is insensitive to i as in the
free convection layer, but also the height loses its importance as a scaling
parameter. Hence the mixing height, z-£, emerges as the controlling length
scale. The scaling velocity and temperature become, Deardorff (1970),
w* = (z± g/T ^r9r
9m = W'QS/W*.
where w'0' and g/T are surface layer values.
2.1.4 The entrainment layer (O.Sz^ < z < l.2z^_ )
The turbulence structure is dominated by entrainment processes from
the overlying stable air in the capping inversion. The turbulence structure
in this region is poorly understood. Recent measurements suggest that the
distance to the inversion, | z^ - z| enters as a scaling length, see Driedonks
and Tennekes (1984). The scaling velocity and temperature relevant to this
layer have not as yet been proposed.
2.1.5 Near neutral upper layer (O.lz^ < z < 0.8z-^ and Z/|L| < 1)
The layer will only rarely be found over land but is not unusual over
the sea. The scaling parameters for'the surface layer are relevant for the
near neutral upper layer; in addition the height of the inversion, z^, is
also important. For profiles of mean quantities the Rossby number, Ro =
G/fzo (G the geostrophic wind speed and f the Coriolis parameter) might be
of importance.
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2.2 The Stable Boundary Layer
.The stable boundary layer is created by cooling of the air adjacent to
the ground. The depth of the inversion layer, h, is often taken as the
height at which the (negative) heat flux has fallen to a certain (low)
proportion of its surface value. The study of the stable boundary layer is
much less advanced than its unstable counterpart. As buoyancy forces
suppress the turbulence under stable conditions, the magnitude of fluctua-
tions generally are very low and consequently difficult to measure. Also
the structure of the turbulence is masked by other physical processes that
are supported in a stable atmosphere. Such processes are gravity waves,
drainage and slope flows, intermittent turbulence and radiation divergence.
The coexistence of these processes and turbulence complicate the interpre-
tation of the data. No simple relation exists between the depth of the
surface inversion, h, and the mixing height, z^, through which the turbu-
lence exchange processes take place. The depth, z^, of the turbulent stable
boundary layer can become progressively smaller at the same time as the depth
of the surface based inversion h grows.
2.2.1 The surface layer (zo « z , Min (O.lz^L))
This layer is the stable counterpart of the unstable surface boundary
layer, and the same scaling parameters apply. The layer is in principle lower
than the height, z - L or z < 0.1 z^, whichever is smaller. Most times the
limit is given by O.lz-j_.
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2.2.2 Local and z-less scaling region (Min(0.Iz^jL) < z < z-^ and z/L < 10)
The range where local scaling applies is still unsettled and a matter
•
of discussion. We define it as the whole stable boundary layer except the
surface layer part. The local scaling approach is an extension of Monin-
-Obukhov similarity theory to the whole stable boundary layer (Nieuwstadt,
1984). Here A is called the local Monin-Obukhov length, defined as A =
-u*/[k(g/T)w'0'] where u* and -w'0" are the local values of the kine-
matic momentum flux and heat flux. The temperature scale for this region
can be defined as 0^ = (w'0')/u*. In the local scaling region only two
length scales arise, z and A. Nieuwstadt"s (1980b) model of the stable
boundary layer suggests that A ~ L (l-z/h)^/^. As z/A •* 1, local scaling
conforms to z-less scaling (Wyngaard, 1973), where z is no longer an impor-
tant length scale for the turbulence. This results from the stable tempera-
ture stratification becoming increasingly more effective in inhibiting
vertical motions. The turbulence within the z-less region is intermittent
and difficult to characterize. Some success has been achieved in describing
the low frequency part of the horizontal velocity spectra using the local
value of the Brunt-Vaisala frequency N2 = (g/T)(50/dz).
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3. BASIC PARAMETERS
3.1 The Surface Roughness Length
The surface roughness length z0 forms the lower boundary in diffusion
models (Pasquill and Smith, 1983). The length zo is in principle the height
at which the wind speed is zero. The length zo is related to the roughness
characteristics of a homogeneous terrain or landscape. When the terrain is
homogeneous, the roughness length can be determined from wind profiles
observed in near-neutral conditions.
Very often, we have relatively smooth terrain disturbed by occasional
obstructions or by large perturbations. In such cases an effective rough-
ness length was found appropriate for use in the flux-profile relations
(Nieuwstadt, 1978; Beljaars, 1982). As discussed by Wieringa (1981) and
Beljaars (1982) for a rough to smooth transition, the turbulence adjusts more
slowly to the underlying surface than does the wind profile. For this reason
the roughness averaged over the upwind fetch can be better evaluated from
o"u/u or gustiness than from wind profiles (Wieringa, 1976, 1980). 0U is the
root mean squared (rms) variance of the wind speed u and u is the average
wind speed. Conversely, this means that the wind profile can be described
with the effective roughness length only above a certain height. Beljaars
(1982) estimates this height as 2£, where £ is the height of the major
obstacles. Closer to the surface the flux-profile relations differ from
those over uniform terrain (Beljaars et al., 1983) and are usually location
dependent (Wieringa, 1981). When no measurements are available, we can
obtain from a visual terrain description a crude value for the effective
roughness length (Hogstrom and Hogstrom, 1978; Davenport, 1960). In Table
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3-1 an example is given. For the application of the above methods for
determining zo, we select as many wind direction sectors as needed to
distinguish between major variations. In general, no sectors less than 30
degrees in angular extent are expected to be suitable in practice.
TABLE 3-1. TERRAIN CLASSIFICATION IN TERMS OF EFFECTIVE SURFACE ROUGHNESS
LENGTH z0. TABLE PARTLY EXTRACTED FROM DAVENPORT (1960).
Short terrain description zo(m)
Open sea, fetch at least 5 km 0.0002
Mud flats, snow; no vegetation, no obstacles 0.005
Open flat terrain; grass, few isolated obstacles 0.03
Low crops, occasional large obstacles, x'/£ > 20* 0.10
High crops, scattered obstacles, 15 < x'/C < 20 0.25
Parkland, bushes, numerous obstacles, x'/C - 10 0.5
Regular large obstacle coverage (suburb, forest) (0.5 - 1.0)
* x' = typical distance to upwind obstacle; £ = height of obstacle.
3.2 The Monin-Obukhov Length
From the surface fluxes of sensible heat and momentum, the Monin-Obukhov
length for dry air can be formed,
L = - uJ/[k(g/T)(H/pcp)], (3-1)
10
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Here we have Ignored the moisture influence"which is typically small above
a land surface. Values for u*, H and thus L can be obtained from turbulence
measurements.
•
When no turbulence measurements are available the fluxes can be obtained
from profiles of wind and temperature near the surface (Businger et al., 1971;
McBean, 1979; Irwin and Binkowski, 1981). The profile method gives good
agreement with turbulence measurements and energy budget measurements, if an
effective roughness length is used in the wind profile (Nieuwstadt, 1978).
These derived fluxes are representative for a larger area than would be
measured with an instrumented meteorological tower located on-site. This
becomes important, for instance, for the estimation of wind profiles at
larger heights from a single wind speed and the surface fluxes. In such
cases, the surface fluxes should be representative of the larger area. This
is demonstrated by Korrell et al. (1982) for the Boulder tower and by Beljaars
(1982) and Holtslag (1984a) for the Cabauw tower. Furthermore, the horizontal
velocity fluctuations scale on the friction velocity representative of the
larger area (Beljaars et al., 1983).
When a vertical temperature profile in the surface layer is not avail-
able, we must parameterize the sensible heat flux H. Holtslag and Van Ulden
(1983) and Van Ulden and Holtslag (1983) have given procedures for the deri-
vation of the sensible heat flux from routine weather data.
During daytime over land, H is obtained from a modified Priestley-
Taylor formula (De Bruin and Holtslag, 1982),
1 - a + Y/S
H = (Q* - G0) - p , (3-2)
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where Q* is net radiation, GQ is soil heat flux (typically 0.1Q*). y/s
equals Cp/(X.oqs/oT) where \ is the latent heat of water vaporization and qs
is the saturation specific humidity. For T between -5 and 35 C, y/s can be
approximated as exp [(279.57-T)/17.78] , T in degrees K. It can be shown that
when saturated air passes over a wet surface a -*• 1 and (3 -*• 0 (Priestley,
1959). For other climatological and surface conditions a and p must be
adjusted. Table 3-2 shows typical values for a and p as a function of sur-
face moisture availability. Reiff et al. (1984) use (3-2) with a. = 1 and
P as a varying function of time. Around sunrise, p = 0, but (3 increases
with time up to p = 20 Wm~2 in a few hours.
In Holtslag and Van Ulden (1983) procedures are discussed for the evalu-
ation of Q* from the fraction of sky covered by cloud, N, the elevation of
the sun above the horizon, , and the shelter temperature,
(1 - r)[d,sin<|> + do](l + cN) + ClT 4
Q* = - (3-3)
1 + C3
where r is the albedo of the surface (typically 0.26 for short grass). Values
_n
for the empirical constants in (3-3) [d,d^ ,&2> c>ci >C2^ are [3.4, 990Wm~ ,
-30Wm~2,-0.75,5.31xlO~13Wm~2K~6,60Wm~2]. Values for the surface heating
cofficient C3 are listed in Table 3-2. This parameter describes the
relative increase of surface temperature with net radiation Q*. As shown
by Holtslag and Van Ulden 03 depends primarily on a and air temperature T.
Therefore, a is the crucial parameter for the surface energy budget
parameterization (see De Bruin, 1983; Van Dop, 1983). In combination with
a, P and C3 the sensible heat flux is obtained from (3-2). Afterwards, u*
and L are obtained from (3-1) and a single wind speed observation and the
12
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integrated wind profile. The values of a, J3 and 03 should reflect the
site. At present, we suggest the values listed in Table 3-2 be used for
guidance.
TABLE 3-2. TYPICAL VALUES OF THE COEFFICIENTS a, p AND c3 FOR SEVERAL
CASES. NOTE THAT C3 IS A FUNCTION OF AIR TEMPERATURE T AS WELL (SEE
HOLTSLAG AND VAN ULDEN, 1983).
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A simple analysis indicates that a constant value of 9* can be assumed
during nighttime. The sensible heat flux can be obtained from an approx-
imation for the scaling temperature, Q*. A typical value for clear conditions
is 8* - O.IK (Venkatram, 1980). Van Ulden and Holtslag (1983) present
methods for estimating 9* as a function of total cloud cover.
3.3 Mixing Height And Inversion Height
The mixing height z^ defines the layer above the surface through which
pollutants are mixed by the presence of turbulence. During daytime convective
conditions or neutral stability conditions the mixing height may extend to
the height where vertical mixing is capped by the inversion (inversion height
h). During nighttime stable conditions, however, it is important to distin-
guish between the mixing height z-^ and the surface inversion depth h. In
part, the difference between z^ and h results because the turbulence is
supressed in the presence of a stable temperature gradient, which extends
above the mixing height.
For conditions of negligible synoptic scale mean vertical velocity, the
equations governing the rate of growth of the convectively driven mixed
layer are,
d9BL/dt = (l/zi)(w^90" - w^") (3-4)
dA0i/dt = yidzi/dt - d0BL/dt
- (w'0Q - w'9i)/Zi (3-5)
dz-j/dt = -w~70T/A0i (3-6)
. (3-7)
is the mixed layer temperature, the subscripts o and i refer to values
at the surface and the top of the mixed layer, A0^ is the temperature jump
14
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at the top of the mixed layer (A0£ > 0) and yi i-3 the lapse rate above the
mixed layer. Laboratory and atmospheric measurements suggest 04 = 0.2 and
05 = 5. The numerical solution to the set of equations, employing a morning
radiosonde and the shelter temperatures through the day, is discussed in
detail by Tennekes and Driedonks (1981) and Wilczak and Phillips (1984).
Driedonks (1982) discusses practical application of the above method for
cases with convective and mechanical entrainment into the mixed layer.
Based on dimensional arguments, many researchers speculate that the
mixing height during neutral conditions can be determined from,
Z£ - c6u*/f, (3-8)
where f is the Coriolis parameter and eg is an empirical constant (typically
0.2 - 0.3). As discussed by Yu (1978) and Wetzel (1982), the correlation of
estimates of z^ by (3-8) with values determined from the Wangara field data,
range between 0.2 and 0.5, indicating no more than 20% of the variability of
z^ is explained. When an inversion is present, z± is given by the inversion
base or (3-8), whichever yields the smallest value.
For nighttime stable conditions, we propose the mixing height be deter-
mined from (Zilitinkevich, 1972; Andre, 1983),
z± = 0.4 (u*L/f)1/2. (3-9)
As stated before, the turbulent mixing depth may differ from the surface
inversion depth during stable conditions. Several authors have worked on
the evolution of the nocturnal surface inversion depth in combination with
the temperature profile in the boundary layer (Yaraada, 1979; Nieuwstadt
1980a; Stull, 1983a,b). At present, we suggest the inversion depth be
estimated during stable conditions as suggested by Stull (1983a,b). This
will be discussed in section 4.2.
15
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4. PROFILES
4.1 Wind Profile
In the atmospheric surface layer the wind profile can be described
successfully with Monin-Obukhov similarity theory (Yaglom, 1977). In the
mixed layer and free convection layer during daytime, the wind speed and
direction remain nearly uniform with height. For stable conditions, however,
the wind speed increases with height often to a maximum, or low-level jet,
near the top of the inversion layer.
A procedure is proposed for the derivation of the wind profile from a
single observation of wind speed near the surface (10 m), an estimate of
the roughness length zo and the Obukhov length L. If estimates of geo-
strophic wind speed or free atmospheric wind speed are available, these can
be employed as well.
For the mixed layer, we assume uniform distributions for wind speed.
In the free convection and surface layer, the variation of the wind speed
is given by,
In(z/z0 - ?(
U = Ur - , (4-1)
In(zr/z0) - Y(zr/L)
where a general expression for ¥ is given by Paulson (1970) and 2r is the
measurement height of the wind speed Ur.
For the near neutral upper layer, we assume U is given by (4-1). The
change of wind direction is expected to be quite small during these neutral
conditions, of the order of 10X over the first 200m. A procedure proposed
16
-------
by Van Dop et al. (1982) could be employed to approximate the wind profile
as,
uz * fs u + fg G cos D> (4-2a)
Vz = fg G sin D, (4-2b)
where U2 and Vz are the components of the wind speed, D is the angle
between the surface wind direction and the direction of the Geostrophic wind
and G is the Geostrophic wind speed. Note that we have chosen the x-axis
along the surface wind direction. The precise characterization of the
weighting functions (fs and fg) is of little concern so long as they are
continuous, vary smoothly as a function of z/z^ between 0 and 1 with fs +
fg = 1, and fs = 1 for z/z-^ = 0.
For stable conditions with z/L < 0.5, the wind speed can be estimated
using (4-1) and (4-2). When z/L > 0.5, U can be better estimated using a
semi-empirical extension of the log-linear profile given by Holtslag (1984a)
as,
ln(z/z ) + 7 InC + 4.25/C - 0.5/C2 + 0.852
U = Ur , (4-3)
In(zr/z0) + 5£r
where C = z/L and Cr = zr/~L. With this profile it was shown that relatively
good estimates can be obtained of the magnitude of U in very stable con-
ditions up to z^. A yet unresolved problem with the stable boundary layer is
a description of the significant~turning of wind with height. This turning
can be 40* or more over the first 200m.
In the above, we have used values of G. For G we may use the surface
geostrophic wind speed evaluated from surface pressure charts. Also, a free
atmospheric wind or the 850 mb wind obtained from linear interpolation between
17
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subsequent radiosondes may be used. Neither estimate of G is considered
very accurate.
4.2 Temperature Profile
The potential temperature is constant within the mixed layer and the
free convection layer (Tennekes and Driedonks, 1981). For heights greater
than z^, the temperature profile has to be obtained from radiosonde data.
For heights below z^, conditions are well mixed and the potential temperature
is that recorded at the highest level of a tower or in the case when such
measurements are not available at shelter height. This neglects the con-
ditions that occur during strong heating, where a strong temperature gradient
exists near the ground.
In the -absence of strong heating or cooling at the surface or when the
wind speeds are strong (6 m/s or more), day or night, the interpolated
radiosonde temperature can be used with no modifications.
During the nighttime with strong radiational cooling or weak winds,
the temperature profile and the inversion depth can be estimated using the
procedures proposed by Stull (1983a,b). The nighttime sensible heat-flux
history, together with the surface temperature decrease after sunset, are
used to define the potential temperature profile as,
A0/A0S = exp (-az/Hx), " . (4-4)
where A0S = Qs - 0O
0s(t) = the surface potential temperature found
at time t since transition,
00 = the potential temperature of the adiabatic
profile at transition time,
18
-------
A0 •- 0(t,z) - 00,
9(t,z) = the potential temperature at height z at time
t since transition,
t
HI = (1/A0S) / (w'0') dT,
to
a » an empirical constant found to be about 0.77 by
Stull for the Wangara and Koorin experiments (nearly
uninhabited sites that were relatively dry).
The time of transition to is defined as that instant when the net sensible
heat flux at the surface changes sign from positive to negative. Stull(1983b)
demonstrates using Wangara field data that h is well estimated as 5Hj. For
large-scale advection effects, the surface temperature 9S could be increased
(decreased) to account for increases (decreases) of the 700 mb temperatures
between successive radiosondes. Such a procedure was employed successfully
by Benkley and Schulman (1979) and Garrett (1981) to adjust for large-scale
advection effects in their estimates of the growth of the unstable boundary
layer.
4.3 Turbulence Profiles
In the mixed layer, Caughey (1982) notes that the observations of the
rms variance of the vertical velocity o"w suggest a broad maximum centered
o 9
at z./2 where ov, is 0.4w* . The numerical simulations of the convective
J_ W
boundary layer by Deardorff (1974) suggest the height of maximum variance
is ZjL/3. Caughey (1982) reports that near z-^, water tank and numerical
n e\
results indicate aw is O.lw* in agreement with the 1976 Ashchurch field
9 7
data. Above z^, Caughey reports that o"w decreases to O.Olw* near 1.5z^.
During the nighttime, when the atmosphere is stratified, the vertical
wind-speed fluctuations in theory decrease in amplitude as a function of
19
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height, to near-zero values at z^ (Caughey, 1982 and Yamada, 1979). A
reasonable fit to the 1973 Minnesota stable field data is,
crw2/u*2 = Aw(l - z/z.)d, (4-5)
where o*w is the standard deviation of the vertical wind-speed fluctuations,
AW - 2.2 and d = 3/2. Nieuwstadt (1983) using data collected from the 213 m
meteorological tower at Cabauw found Aw =» 1.7 and d = 3/2. The significance -
of Nieuwstadt's results is that he arrived at (4-5) using local scaling
o
arguments. Measurements of a^ may be considerably influenced by gravity
wave contributions. For that reason, Nieuwstadt employed high pass filtered
data for the determination of ^ and d.
The standard deviation of the cross wind-speed fluctuations, av, in
the surface layer is poorly characterized using Monin-Obukhov similarity
scaling, especially within the stable surface layer, see Panofsky et al.
(1977). During convective conditions, the numerical simulations of the
convective boundary layer and the atmospheric data suggest a. slight maximum
2
near O.Sz^ in a ; the average value over the entire profile for o~v is
0.4w*2.
During stable conditions the mean wind direction show sizeable inter-
mittent sudden changes (meandering). This phenomenon may result from various
factors such as the slope of the terrain, location of hills in the upwind
fetch and movement of weather systems. Although meander is most often observed
during very stable conditions, this does not preclude its occurence during
other times. Strong mixing during unstable conditions might mask the contri-
butions due to meander to av but the contributions to the energy spectra are
20
-------
still present. Hjjjstrup (1981, 1982) and Berkowicz and Prahm (1982) found
success in modeling the velocity spectra as consisting of a buoyancy-produced
part and a shear-produced part. The modeled variances by H^jstrup (1982)
agree well with data from the Kansas and Minnesota field experiments. His
results for the w-spectra are valid only for the lower half of the boundary
layer, where the long-wavelength fluctuations can be assumed to be damped by
the presence of a solid lower boundary mechanically impeding the vertical
fluctuations. As a working hypothesis for modeling the vertical velocity
variance, we could combine the shear-produced variance, as modeled by H«5jstrup
(1982), with the buoyancy-produced variance, as modeled by Baerentsen and
Berkowicz (1984). The resulting characterizations of the lateral and vertical
variances would be,
2/3 2.7(l-z/z.)2
0.7(Zi/L)2/:i + - =~- for L < 0
(1+2.8Z/Z,)2/3
1 (4-6)
(1-z/z.)2
for L >0
(l+2.8z/zi)2/3
f 1.54[z/(-kL]2/3exp(-2z/z.) + 1.457(l-z/z.)2 for L < 0
' \ 7 (4'
^ 1.457(l-z/Z;L)2 for L >_ 0
The expression (4-7) fits quite well the 1973 Minnesota field data for
unstable conditions .
The estimate of the lateral variance neglects meander. The linear
decrease of aw with height, while appropriate during daytime neutral con-
ditions, would not reflect the height dependence observed during stable
conditions. This deficiency although noticeable in the mean under ideal
21
-------
conditions would likely not be noticeable in" practice, owing to the vari-
ations caused by conditions differing from ideal. Recently, the low fre-
quency part of the spectra of the velocity components under stable conditions
has been successfully modeled by Larsen et al. (1983). The low frequency
part of the horizontal velocity components were found to be fairly well .
described by a N2<~3 law, where N is the Brunt-Vaisala frequency and < the
horizontal wave number.
22
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5.0 DIFFUSION
The applicability of employing scaling parameters for describing the
turbulence in the air depends on the extent to which the actual circumstances
approach the idealized conditions specified in the basic theoretical and
experimental studies. Reliable specification of the turbulence and thereby
the diffusion cannot be expected if the airflow is uncertain or calm, or if
the airflow has been complicated by local circulations induced by heating or
cooling or hilly terrain. Little success can be expected in the immediate
vicinity of buildings and obstacles. The methods described here for diffusion
estimates do not account for effects of deposition or reactions in the atmos-
phere, and are only valid for distances less than 10 km.
Even when the actual conditions approach the ideal conditions, the prac-
tical problems of estimating the expected distribution of concentration are
significant. The comparison results summarized in Pasquill's (1974) Table
6.XI suggest that even under ideal circumstances 20 to 30% deviations from
the mean concentration values can be expected for ensemble average estimates
for particular meteorological conditions. For individual comparisons devi-
ations of about 50% appear likely (Gryning and Lyck, 1984).
This chapter summarizes some of the relationships of the basic scaling
parameters to diffusion processes. A description of the pollutant distribu-
tion necessarily includes (implicitly or explicitly) the shape of the distri-
bution, the dimensions of the diffusing cloud, and the boundary conditions.
The shape describes the vertical and horizontal profiles of the cloud. The
dimensions are often specified by the root mean squared deviations o~y and az
of the pollutant mass along the coordinate axes. The values ay and az are
23
-------
typically referred Co as the dispersion parameters. Often they are associated
with a Gaussian shaped distribution but, of course, this is not necessary.
A traditional basis for describing diffusion is the Taylor diffusion
2
theory which relates the mean square particle displacement, o"v , to the cross
2
wind velocity variance, cr,through,
t T
ov2 = 2 a 2 / / R(5) d^dT,
* oo (5-1)
where t is travel time and R (£) the Lagrangian autocorrelation function and,
T
Urn / R(5) d£ = TL,
T -» « o
the Lagrangian integral time scale. In the limit (5-1) becomes,
o-y =
-------
Sivertsen (1978) argues that fy responds to "the overall structure of the
turbulence; whereas, av describe the local features of the terrain.
A comparison was performed of five empirical forms suggested for fy
(Irwin, 1983) with field tracer data collected at 11 sites. Draxler's (1976)
scheme performed best, a finding which is in agreement with Gryning and Lyck
(1984). Irwin (1983) noted that selecting a simple expression for fy that is
invariant with height resulted in little overall loss in performance. We
recommend,
f - 1/[1 + 0.9 (t/Te)i/z], (5-5)
where Te = 1000 s.
If we view the total diffusion as the summation of individual effects of
each process [Hb'gstrom (1964) and Pasquill (1976)], then,
rt2_rt2,2,2 /C.N
y ~ y° yb ys' t-> o;
where oVo ^s estimated using (5-4) and (5-5), ayb is the induced diffusion
due to buoyant plume rise effects, and o"ys is the induced diffusion due to
wind direction shear in the vertical. At this time, the magnitude of the
buoyancy effects on the lateral diffusion is uncertain. It seems o~yO
dominates initially with 0ys becoming of increasing importance at large
downstream travel time. Pasquill and Smith (1983) investigated the effect
of wind shear on the horizontal diffusion and found the distance of travel
at which the effect of o"ys becomes important. They conclude that the effect
is not important within about 5 km from an elevated source or within about
12 km of a ground-level source.
In the following, expressions are provided for characterizing the dis-
persion for each of the regimes described in Chapter 2. In some cases,
expressions are given for estimating the crosswind integrated concentration,
25
-------
where x (x,y) is the surface concentration. The x-coordinate axis is aligned
along the surface wind direction. Given -^7 we can compute x assuming a
Gaussian distribution of the material in the crosswind as,
). (5-7)
o-y
Even though the vertical distribution of material may be other than Gaussian,
the lateral distribution is well approximated using (5-7), as discussed by
Deardorff and Willis (1975), Gryning and Lyck (1980) and Gryning et al.,
(1978).
In general, the total vertical diffusion is a combination of turbulent
diffusion and the effects of buoyant plume rise, azb> as
For elevated sources well above the surface and below the inversion, a
similar approach for estimating azo as shown above for ay, (5-4), could be
applied when o"w is available. Field data suggest that azb scales with plum
e rise (Briggs, 1975).
In the following, examples are given demonstrating the relationship of
the basic meteorological parameters to the description of vertical diffusion
for each of the regimes described in Chapter 2.
5.1 The Surface Layer (unstable and stable conditions)
A number of investigations have demonstrated the applicability of Monin-
Obukhov similarity theory to describing the diffusion of near surface
releases by use of K models, (Nieuwstadt and Van Ulden, 1978, Gryning et
al., 1983, Sivertsen et al., 1983).
26
-------
Within the surface layer, the vertical' eddy diffusivity of matter, K,
can be expressed generally as,
K = ku*z/«*h(z/L), (5-9)
where ^(z/L) is an empirical function that describes the dependency on
atmospheric stability, Table 5-1. When the wind and K profiles are
represented by power laws, a general solution of the two-dimensional
diffusion equation can be written as (Van Ulden, 1978),
Xy(z)/Q = (A/iu~) exp [-(Bz/F)S] (5-10)
A = s r(2/s)/[ r(l/s) ]2 (5-11)
B = F(2/s)/ F(l/s), (5-12)
where r is the gamma function. The following equations are suggested for
specifying the shape parameter s (Gryning et al., 1983) and the mean height
of particles z" (Van Ulden, 1978).
For L > 0:
1 + 2 bi cz/L 1 + b2 cz/L
1 + bj cz/L In(cz/z0) + b2 cz/L
(5-13a)
x + XQ = (F/k) [{ln(czVz0) + (5-13b)
2 b2PF/(3L)} (1 + blPF/(2L) + (bj/4 - b2/6)PF/L)].
For L < 0:
1 - ai cz~/(2L) (1 - a2cF/L
s = - ~ + - - - : - ~ — , (5-14a)
1-a cz/L
x + XQ = (/k) [ In (c/zQ) - y (cF/L) ] [1 - p aj_ /(4L)]~. (5-14b)
x0 is an integration constant and is determined with x = 0 and z equal to the
release height zs.
For stable conditions (L > 0), we solve for the crosswind integrated
concentration by first determining z (iteratively from 5-13b) for the given
27
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distance downwind. With z, we can solve for A and B for use in 5-10. A
similar approach is followed for unstable conditions (L < 0).
Dyer(1974) proposed a^ = a2 = 16; bj = b2 = 5 with k = 0.41. These
coefficients were used by Gryning et al. (1983) and Holtslag (1984b). In
the original derivation, Van Ulden (1978), used the coefficients proposed
by Businger et al,, 1971). In Table 5-1, the «$m and ^ functions are given
together with the expression for the mean wind speed, u, over the plume.
The coefficients p and c are in fact dependent on s. For practical appli-
cations we propose p = 1.55 (Van Ulden, 1978) and c = 0.6 (Gryning et al.,
1983).
TABLE 5-1. THE ^, «5m AND u FUNCTIONS NEEDED FOR THE APPLICATION OF
EQUATIONS (5-9) THROUGH (5-14).
For L < 0:
z/L)~1/2
z/L)-1/4
¥(z/L) = 21n {(1 + x)/2} + In {(1 + x2)/2} - 2 tan"1(x) +
where x = (l/«*m),
ku7u* = In(cz7z0) - ?(cz/L).
For L > 0:
<$h(z/L) = d(l + b! z/L),
«$m(z/L) = 1 + b2 z/L,
ku/u* = In(cz/z0) + l>2 z/L .
28
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Elliott (1961) found the shape parameter ranged from s = 1.0 from un-
stable conditions to about s = 2.0 for stable conditions. For a Gaussian
concentration distribution s = 2, hence under unstable and neutral conditions
a Gaussian concentration profile does not fit the observed vertical distri-
bution.
5.2 The Mixed Layer
The mixed layer scaling is appropriate when zs/z^ > 0.1 and zs/-L > 1,
where zs is the release height. Deardorff and Willis (1975), Willis and
Deardorff (1978), Lamb (1978, 1979) reported the results of a series of
laboratory and numerical simulations of dispersion of nonbuoyant material in
a well developed mixed layer. Deardorff and Willis presented tabulations of
the dimensionless mean crosswind integrated concentration values at various
heights and distances from the release at zs/z^ of 0.067.
As an extension of these results, Briggs (1985) reanalyzed the dimension-
less cross-wind integrations both from the laboratory and the numerical
simulations. It was found that the mean cross-wind integrated concentration
results at the surface could be well characterized as,
0.9 X 9/2 Z -11/2
y U/Q .
[Z -J/* + 0.4 X y// Zc
j S
9/2
^s J
(5-15)
Z + 50
S
where X = (x/Zj_) (w*/U) and Zs = Zg/z-^. This expression applies for nonbuoyant
releases when 1 > Zs > 0.04.
Recently, Willis and Deardorff (1983) reported the findings of a series
of laboratory simulations of buoyant releases within a well developed
convective boundary layer. They found that plume buoyancy effects became
29
-------
noticeable in the diffusion results where the plume buoyancy parameter F* =
f\
F/(Uw^z^), exceeded about 0.02, where F .is the standard definition of plume
buoyancy. The vertical distribution of concentration within the plume was
highly skewed and non-Gaussian. Tabulations of •%? are not available for a
wide variety of values of F* and a suitable number of release heights for a
recharacterization of (5-15) including buoyant plume rise effects.
5.3 The Free Convection Layer
Free convection exists in the layer above z = -L and and below z ~ O.lz^
where z, Uf and 9f are the controlling parameters. Nieuwstadt (1980b) ana-
lyzed the portion of the Prairie Grass data measured under convectively
unstable conditions and found that free convection similarity scaling was
appropriate for those cases downwind when 0.03 < X < 0.23. The normalized
crosswind integrated concentration is then given by,
X^U/Q = bX~3/2 (5-16)
where b is 0.9. Holtslag (1984b) compared the surface similarity pre-
dictions by (5-10) versus the free convection predictions by (5-15) using
the Prairie Grass data. At x = 50 m it was seen that the surface layer
model performed better than the free convection model, comfirming that at x
= 50 m the plume was still within the surface layer. At x = 200 m and 800
m the surface layer model and the free convection model predictions were
similar. This would suggest that both scaling principles can be applied to
these distances. Deposition was not considered in the analyses by Nieuwstadt
(1980b) and Holtslag (1984b). Gryning et al. (1983) show that consideration
of deposition significantly improves the predictions of Che surface layer
model, especially at x = 800 m.
30
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5.4 The Entrainment Layer
For unstable conditions, the entrainment layer extends between z >
O.Sz^ and z < 1.2z^. For strongly buoyant releases, the possibility exists
for material to become stabilized in the layer above z^. The amount of
material which "penetrates" into the stable layer capping the mixed layer
is dependent on (Briggs, 1975),
PS = F/(UYi.z£3) (5-17) *
where z^' = z^ - zs and yi = the potential temperature gradient in the
capping inversion. The fraction of material, P, that stabilizes in the
capping inversion is estimated by Weil and Brower (1982) as,
P - 1.5 - (l/2.6)/ps1/3. (5-18)
This penetration estimate suggests that full penetration occurs when ps >
0.44. Penetration of 50 % is estimated when ps = 0.129. These estimates
suggest that it requires only 13% as much buoyancy to achieve 50% penetration
as that required to penetrate fully. Laboratory simulations for a strongly
buoyant effluent (F* > 0.1) with a strong capping density jump (ps < 0.05),
suggest that the plume tends to loft against the capping inversion (Willis
and Deardorff, 1983). It appears that the plume still retains sufficient
buoyancy to resist mixing down towards the surface.
5.5 Near Neutral Upper Layer
Knowledge of the diffusion in the near neutral upper layer is very
limited. For releases in the near neutral upper layer we therefore recommend
the use of the traditional Gaussian plume model for estimating concentrations.
31
-------
Measurement of crw and where Y ' 0.522,
An = ocz, where a = 0.36,
32
-------
N = the local value at z of the Brurit-Vaisala frequency,
[(g/TXae/az)]1/2,
o*w = the local value at z of the standard deviation of the vertical
velocity fluctuations.
Substituting typical values into (5-19) and solving for TL, shows T^ is
approximately 8 to 12 s. The expressions (5-5) and (5-19) for fz are nearly
equivalent when Te = 4.861^. Hence, these results reported by Venkatram et al,
(1983) are in accord with the findings reported by Irwin (1983) for Te = 50 s
for stable conditions. The information provided by Venkatram et al. (1983)
shows that local z-less scaling arguments can be employed to describe the
diffusion processes.
33
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6.0 DISCUSSION
An outline of methods for processing meteorological data for use in
diffusion modeling has been presented. To incorporate the proper scaling
parameters the discussion was structured in accordance with current concepts
for the idealized states (regimes) of the planetary boundary layer. The
goal was to characterize the meteorological conditions affecting the
diffusion for transport distances on the order of 10 km or less. The
distance to the maximum ground-level concentration is often within this
range.
The diffusion is routinely found to be other than Gaussian in the
vertical (Gryning and Lyck, 1984). Therefore, whenever justified we have
recommended the use of techniques that characterize directly the crosswind
integrated concentrations at the surface. For elevated releases within the
near neutral upper layer and the stable (local scaling region) we recommend
use of the Gaussian plume model, where the dispersion parameters are
estimated using statistical methods. Little is known regarding diffusion
within the entrainment layer.
A special complication in the use of the suggested methods arises when
the proper state of the diffusion process is at the border line between two
regimes. Such cases will give rise to a jump in concentration dependent on
the choice. No procedures have been devised to avoid these jumps in calcu-
lated concentration.
34
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For obtaining the meteorological data "needed for estimating the
fundamental meteorological scaling parameters, we recommend as a minimum a
measurement program as presented in Table 6-1. The measurements should be
carried out at a mast. The upper measurement level should be at a height
100zo, but not less than 10m. The lower measuring level should be at 20zo,
but not less than 1m. Here, zo is the effective surface roughness length
and can be estimated from Table 3.1. Also discussed in this report are
methods for determining the fundamental scaling parameters if only synoptic
meteorological data are available.
We anticipate that the suggested characterizations of the diurnal
variation of the wind speed and direction profiles are too simplistic and
will need further development. Furthermore, the turbulence profiles are
highly idealized as the assumption is made that above the mixed layer the
turbulence is negligible. To complete the development of a meteorological
processor, the methods outlined should be tested using available data.
With the test results, future research can focus on those estimation methods
requiring the greatest improvement and on developing methods to characterize
the spatial variations in the meteorological variables.
35
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TABLE 6-1. RECOMMENDED MINIMUM "MEASUREMENT PROGRAM
THE TYPICAL SAMPLING DURATION SHOULD BE 10 MINUTES.
PARAMETER
SAMPLING
RATE (sec)
MEASURING
HEIGHT
EXAMPLE
INSTRUMENTS
**
Wind speed
Wind direction
Longitudinal
Turbulence
Wind direction
fluctuation
1 to 5
1 to 5
Upper level Cup anemometer
Upper level Wind vane
Upper level Cup anemometer
Upper level Wind vane
Temperature
Temperature
difference
10
10
Upper level
Upper level
to
lower level
Resistance
Fast
Thermocouples
* Estimated from wind speed and direction measurements.
** Instruments should be well designed for the purpose.
Minimum instrument requirements are given in Hoffnagle et al.
(1981) Table 1.
36
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7.0 REFERENCES
Andre, J. C., 1983: On the variability of the nocturnal boundary-layer depth.
J. Atmos. Sci., 40, 2309-2311.
Baerentsen, J. H., and R. Berkowicz, 1984: Monte Carlo simulation of plume
dispersion in the convective boundary layer. Atmos. Environ., 18, 701-712.
Beljaars, A.C.M., 1982: The derivation of fluxes from profiles in perturbed
areas, Bound.-Layer Meteorol., 24, 35-55.
Beljaars, A.C.M., P. Schotanus, and F.T.M. Nieuwstadt, 1983: Surface layer
similarity under non-uniform fetch conditions. J. Glim. Appl. Meteor., 22,
1800-1810.
Benkley, C.W. and L.L. Schulman, 1979: Estimating hourly mixing depths
from historical meteorological data. J. Appl. Meteor., 18, 772-780.
Berkowicz, R., and L.P. Prahm, 1982: Spectral representation of the vertical
structure of turbulence in the convective boundary layer. National Agency
of Environmental Protection, Riso National Laboratory, Roskilde, Denmark,
47pp.
Binkowski, F.S., 1979: A simple semi-empirical theory for turbulence in the
atmospheric surface layer. Atmos. Environ., 13, 247-253.
Briggs, G.A., 1975: Plume rise predictions. In: Lectures On Air Pollution
And Environmental Impact Analysis (Edited by D. A. Haugen). Amer. Meteor.
Soc., Boston, MA, pg. 59-111.
Briggs, G.A., 1985: Analytical parameterizations of diffusion: the CBL. J_.
Glim. Appl. Meteor., [In Press].
Businger, J.A., 1973: In: Workshop on Micrometeorology. (Edited by D. A. Haugen),
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
2.
3. RECIPIENT'S ACCESSION NO.
. TITLE AND SUBTITLE
ATMOSPHERIC DIFFUSION MODELING BASED ON
BOUNDARY LAYER PARAMETERIZATION
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
. AUTHOH(S)
J.S. Irwin1, S.E. Gryning2, A.A.M. Holtslag3,
B. Siversten*
8. PERFORMING ORGANIZATION REPORT NO.
PERFORMING ORGANIZATION NAME ANO ADDRESS
1. ASRL, RTP, NC, USA
2. Ris«J National Laboratory, Roskilde, DENMARK
3. KNMI, DeBilt, THE NETHERLANDS
4. LILU, Lillestrrfn, NORWAY
10. PROGRAM ELEMENT NO.
CDTA1D/08 - 2182(FY85)
1 1. CONTRACT/GRANT NO.
2. SPONSORING AGENCY NAME AND ADDRESS
Atmospheric Sciences Research Laboratory - RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/09
5. SUPPLEMENTARY NOTES
6. ABSTRACT
The conclusions of a workgroup are presented outlining methods for
processing meteorological data for use in air quality diffusion modeling. To
incorporate the proper scaling parameters the discussion is structured in
accordance with the current concepts for the idealized states of the planetary
boundary layer. We recommend a number of models, the choice of which depends
on the actual idealized state of the atmosphere. Several of the models
characterize directly the crosswind integrated concentration at the surface,
thus avoiding whenever justified the assumption of a Gaussian distribution of
material in the vertical. The goal was to characterize the meteorological
conditions affecting the diffusion for transport distances on the order of 10
km or less. Procedures are suggested for estimating the fundacental scaling
parameters. For obtaining the meteorological data needed for estimating the
scaling parameters, a minimum measurement progrSn to be carried out at a mast
is recommended. If only synoptic data are available, methods are presented
for the determination of the scaling parameters. Also, methods are suggested
for estimating the vertical profiles of wind velocity, temperature, and the
variances of the vertical and lateral wind velocity fluctuations.
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