January 1967 Marvin E. Miller 35
FORECASTING AFTERNOON MIXING DEPTHS AND TRANSPORT WIND SPEEDS
M A R V I N E. MILLER
Air Resources Field Research Office, ESSA, Cincinnati, Ohio
ABSTRACT
A method is presented to estimate the vertical extent of atmospheric mixing during the afternoon and the average
transport wind speed, i.e., the average wind speed within the mixing layer. Afternoon mixing depth is assumed to
be dependent upon the observed difference between the maximum afternoon surface temperature and the mean virtual
temperature of the standard atmospheric layer containing the top of the mixing depth. Transport wind speed is
assumed to be a function of the wind speed a t the level nearest the center of the mixing depth. Based on special
forecast material prepared by the National Meteorological Center, procedures are outlined for forecasting afternoon
mixing depths and transport wind speeds.
1, INTRODUCTION
The two most important meteorological variables that
determine the dilution of air pollutants over urban areas
are (1) the vertical depth through which the dispersion
takes place &e., the mixing depth), and (2) the mean
transport wind speed in that layer. An estimate of this
afternoons mixing depth is obtained by finding the height
above the surface of the dry adiabatic intersection of the
days observed maximum surface temperature with the
days 1200 GMT observed vertical temperature profile.
Holzworth [2] used mean radiosonde observations and
normal maximum surface temperatures to estimate
monthly mean afternoon mixing depths for 45 stations in
the conterminous United States. In the National Air
Pollution Potential Forecast Program (Miller and Nie-
meyer [SI), it is of special interest to anticipate the magni-
tude of mixing depths and transport wind speeds during
the afternoon. At that time they normally reach their
maximum values and hence represent the best dilution
conditions that will occur during the entire day. When
referred to established criteria, their values can then serve
as important indices or guides in the decision-making
process that may lead to the issuance of an air pollution
potential advisory. This report presents an objective
method for forecasting the afternoon mixing depths and
associated mean transport mind speeds.
2. AFTERNOON MIXING DEPTHS
DEVELOPMENT
Estimates of afternoon mixing depth are a function of
the 1200 GMT vertical temperature profile and the maxi-
1 Robert A. Tact Sanitary Engineering Center, Division of Air Pollution, Public
Health Service, US. Department of Health, Education, and Welfare. Authors present
affiliation: ESSA Weather Bureau State Climatologist, Columbus, Ohio.
mum afternoon temperature, but, in view of the inherent
difficulty in forecasting the detail of vertical temperature
profiles, it was decided to base mixing depth forecasts on
relationships between less direct but more readily fore-
castable parameters. An obvious relationship is that
between the mixing dept.h and the potential temperature
difference between the surface maximum temperature and
the temperature at some constant pressure surface aloft.
To test this relationship, surface and upper-air obser-
vations from Pittsburgh, Pa., were utilized; the 850-mb.
level was arbitrarily specified as the constant pressure sur-
face aloft. When mixing depths were plotted against the
differences between the afternoon maximum surface poten-
tial temperature, es,c, and the 850-mb. potential tem-
perature, ea50 (at 1200 GMT), the scatter expanded away
from the point where Os,c-B850=0. This variation was
essentially due to the occurrence of a wide range of lapse
rates in the layer between the top of the mixing depth and
the 850-mb. level. Thus, the more the top of the mixing
depth departed from the 850-mb. level, the wider was the
range of mixing depth values for es,c-e850. In addition,
however, even in cases when esfc-e850=o, i.e., when the
mixing depth coincided with the 850-mb. level, some varia-
tions in mixing depths occurred because of the daily and
seasonal variations of 850-mb. heights. Monthly mean
850-mb. heights, based on 10 yr. of data, have been given
by Ratner [4]; the maximum difference between any two
months at Pittsburgh mas 101 m.
Since in the relationship between 6sfc-ess0 and the
mixing depth, minimum scatter was observed about the
point where Bs,c-0850= 0, it was hypothesized that the
scatter of all points would be minimized if the mixing
depths were separated into smaller layers and related to
the difference between the temperature of the surface
(tslc) a t the time of maximum, and the 1200 GMT mean
36
3400
3300
3200
3100
3000
2900
2800
2700
2600
2500
2400
E 2300-
2200-
F a
w 2100- 0
0 2ooo-
.-
g 1900-
x 1800-
0 0
W
E 1100-
5 l a -
I500
1400
MONTHLY WEATHER REVIEW Vol. 95, No. 1
-
-
-
-
-
-
-
-
- -
-
-
-
I400
l3oC
1200
I I O 0
- IO00
E
I
w k 900
5 100
n 800
0
x
E 600
2
8 500
z
5 400 I- LL
a 300
200
IO0
I I I I I I I I I I I I
n = 42 R = 0.76
Y - 230 + 208.5 X-8.6 X 2
MIXING DEPTH
-- - - - - - 90 % CONFIDENCE LIMITS
./ /
/
/
/
/ I I 1 I I I I I 1 I ,,
0 I 2 3 4 5 6 7 8 9 1011 1 2 1 3
+SfC - T1lOOO -850 - mb , "C
FIGURE 1.-Afternoon mixing depths whose upper limits were
below the 850-mb. level, as a function of (tsjc-T'1000--850 mb.) a t
Dayton, Ohio.
virtual temperature, T', of the layer (1000-850 mb., 850-
500 mb., etc.) that included the top of the mixing depth.
These layers were selected to coincide with the basic
levels used by the National Meteorological Center (NMC)
in their prognostic models. Further subdivision of the
layers was not recommended, since all other levels axe
linear interpolations of the basic levels. A computer pro-
gram was written to obtain statistical information on the
relationships between mixing depth and temperature dif-
ference (tsZc-T') at 67 rawinsonde stations within the
conterminous United States. Input data from daily raw-
insonde runs during calendar year 1964 were used to
determine coefficients for several types of regression equa-
tions; data for days with more than a trace of precipitation
were excluded from the computations because of differ-
ences in the physical processes experienced by rising
saturated air parcels as compared with rising dry parcels.
The best least squares fit of the data was obtained with
parabolic regression equations. Table 1 summarizes the
resulting correlation coefficients for the mixing depths as
I n - 83 R = 0.84 I
I Y = 6021 - 4 6 4 x +l l .B Y e I
I
- MIXING DEPTH I
I
------- 9ox CONFIDENCE LIMITS I
I
I
I
/' ..
.I
1 3 4 .
/-
FIGURE 2.-Afternoon mixing depths whose upper limits were
within the 850-500-mb. layer, as a function of (talc- T 650-500 mb.)
at Dayton, Ohio. .
TABLE 1.-Summary of correlation coeficients for the parabolic relationship between afternoon mixing de ths, whose upper limits were below the 850-mb. level, and (t 8 f e - T 1wo--850 ,,,b). P
Index of correlation < .56 .56-.60 .61-.65 .Mi-.70 .71-.75 .76-2.0 .SI-.85 > .85
Numberofstations--l 2
1
1 1 o
I
4
1
8
1
12
1
14
1
9
- --_____~
TABLE 2.--Summary of standard errors of mixing depths for the parabolic relationship between afternoon mixing depths, whose upper limits were below the 850-mb. level and (t s f O - Tflw-gm mb).
--
Number of stations--.-.
January 1967 Marvin E. Miller 31
FIGURE 3.-Isopleths of standard errora of mixing depth (meters) for the relationship between afternoon mixing depth within the 850-500-
mb. layer and (t 8 f c - Teso-sw mb.).
parabolic functions of (tslc-TJ) when the tops of the
mixing layers were below the 850-mb. level. Table 2
summarizes the standard errors of mixing depths about
these equations. The standard errors of mixing depths
were less than 200 m. at 44 of the 50 stations for which
comparisons were made. Stations with elevation 750 m.
or higher were excluded from these summaries because of
ttheir nearness to the 850-mb. level.
Figures 1 and 2 show the individual observations used
in deriving the statistical equations and the 90 percent
confidence limits for the relationship between mixing
depth and tslc-TJ when the top of the mixing depth fell
respectively within the 1000-850-mb. and 850-500-mb.
I layers a t Dayton, Ohio. Similar information was obtained
for all stations shown in figure 3.
Table 3 summarizes the computed correlation coeffi-
cients for the parabolic relationship between afternoon
mixing depths and tsfc-T when the tops of the mixing
depths fell between 850 and 500 mb. Figure 3 shows the
geographical distribution of the calculated standard errors
of mixing depths when the tops of the mixing layers fell
within the 850-500-mb. layer.
Figure 4 shows the confidence limits (plus or minus)
within which a mixing depth of 2000 m. occurred 90 per-
cent of the time during 1964 over the conterminous
United States. Maximum error was observed a t those
locations with higher station elevations.
TABLE 3.--Summary of the correlation coeficients for the parabolic relationship between afternoon mixing depths, whose upper limits were between 860 and 600 rnb., and (talc- T850-soo mb.).
38 MONTHLY WEATHER REVIEW Vol. 95, No. 1
FIGURE 4.-Isopleths of 90 percent confidence limits (meters) about 2000-m. mixing depths.
FORECASTING PROCEDURE above 850 mb., and the computer proceeds to calculate
T~ estimate tomomow depth at e50a-esfc and to test its sign. Similarly, if this difference ..
.. .. ..
~
-. -- some location, NMC first makes a forecast of tomorrow
afternoons maximum surface potential temperature, e s f o
based on forecasts of tomorrows 1200 GMT station pressure
and maximum afternoon surface temperature.
Indirect 24-hr. temperature forecasts for the 850- and
numerical weather prediction forecasts. The computer
converts these temperatures to potential temperatures.
If es5,,-esfc is positive, the top of the mixing depth is
expected to occur below 850 mb. If, however, essO-esrc
is negative, the top of the mixing depth is expected to occur
I
500-mb. levels are then obtained from this mornings
2 An estimate of this afternoons mixing depth is obtained by finding the height above
the surface of the dry adiabatic intersection of todays forecast maximum surface tem-
perature with todays 1200 GMT observed vertical temperature profile.
is positive, the top of the mixing depth is expected to
occur in the layer 850-500 mb. and if negative, the top of
the mixing depth is forecast to extend above 500 mb.
After finding the standard layer that includes the top
of the mking depth, the computer calculates the forecast
thickness and then the mean virtual temperature of this
layer for 1200 GMT tomorrow. Once the independent
variable, tsfc-T, is known, a forecast of tomorrow after-
noons mixing depth is obtained from the parabolic re-
gression equation appropriate for the layer that contains
the top of the mixing layer. For purposes of the air
pollution potential forecast program i t is unnecessary to
know the value of the mixing depth when it extends above
500 mb. In such cases, the mixing depth forecast indi-
cates only that the depth will be deeper than the height of
the 500-mb. surface above the ground.
January 1967 Marvin E. Miller 39
1200 GYP mean wind speed through the
0000 GMT 85CLmb. wind speed ____.___._____.
oo00 QHT wind speed nearest the center of the afternoon mixing depth ______________.
afternoon mixing depth __________________.
3. TRANSPORT WIND SPEEDS
DEVELOPMENT
0.74 0.65 0.82
0.90 0.82 0.86
0.92 0.95 0.96
Since wind speed normally varies to some extent with
height, the average wind speed through the mixing depth
was chosen as a convenient representation of the hori-
zontal transport of air within the mixing layer. At most
Weather Bureau rawinsonde stations, winds aloft are not
observed during the normal diurnal time of maximum
atmospheric mixing, i.e., mid-afternoon. Observations
from Salt Lake City, Pittsburgh, and Nashville were used
to determine the observation time best describing the
afternoon transport wind. For each of the observation
times, wind speeds were averaged through the afternoon
mixing depth. These mean wind speeds were correlated
with the observed daily average afternoon (1200-1600
LST) surface wind speeds. Table 4 summarizes these
results. Winds aloft data a t 0000 GMT were near the usual
times of maximum afternoon heating and gave the highest
correlation coefficients. Therefore, wind information a t
0000 GMT was assumed to give the best estimates of after-
noon average wind speed through the mixing depths within
the conterminous United States.
In a search for a suitable relationship between the
transport wind speed and a forecastable parameter, three
different variables were related to the 0000 GMT average
wind speed through the afternoon mixing depth. These
variables were the 1200 GMT transport wind speed, the
0000 GMT 850-mb. wind speed, and the 0000 GMT wind
speed a t the level nearest the center of the afternoon
mixing layer. Table 5 shows the results of these correla-
tions for the test locations. Clearly, the best correlations
were attained with the 0000 GMT wind speeds a t the level
nearest the center of the mixing depth.
For each station shown in figure 5, parabolic regression
equations were calculated from 1964 data for the relation-
ship between the wind speed a t the level nearest the center
of the afternoon mixing depth and the average wind
speed through this layer. Table 6 summarizes the cor-
relation coefficients for this relationship. Sixty of the
67 correlations were greater than 0.85. Figure 5 shows
the geographical distribution of the standard errors of
mean transport wind speeds when the wind speed nearest
the center of the mixing layer was used as the independent
variable.
FORECASTING PROCEDURE
Forecasts of mean transport wind speeds are obtained
from the parabolic relationship between the average
wind speed through the mixing layer and the wind speed
nearest the center of the mixing layer. Estimates of
wind direction and speed for any geographical point in
the United States and at any height are available through
linear interpolation of the FD winds aloft forecasts
(Badner and Kulawiec [I]) prepared by NMC. Hence,
estimates of wind speeds nearest the center of the mixing
depths are obtained directly from the FD forecasts.
I
TABLE 4.-Correlation coeficients for the relationship between average transport wind speed through the afternoon mixing depth and the average afternoon surface wind speed.
aloft observation time (GMT)
City
1200 I 1800 I m
Salt Lake City, Utah- _..___...__..____..__
I
0.68
1
'0.77
1
0.83 085
Pittsburgh, Pa- _...____.___ ...__.._ ___..__. 0.74 ___.-__._.-___
Nashville, Tenn ___. . ..__ .-. - __ .__ - - ...__ ... 0.67 ...___..____.. 0.82
I I I
*Salt Lake City is one.of the few rawinsonde stations within the United States for which atmospheric soundings are available every 6 hours.
TABLE 5.--Correlation coeficients for relationships between various wind speed parameters and the 0000 QMT average transport wind speed.
Wind speed parameter S a l t Lake Nashville, Pittsburgh,
1 City, Utah 1 Tenn. 1 Pa.
TABLE 6.-Summary. of the correlation coeficients for the derived parabolic relatzonshzp between the 0000 QMT wind speed nearest thecenter of the afternoon mixing depth and the OOOOQMT average transport wind speed.
N u m b e r o f S t a t i o ~------~~ 1
1
0
1
0
I
6
1
10
1
40
1
10
Index of correlation .6b.70 .71-.75 .76-.SO 31-35 .86-.90 .91-35 >.95
--______--
TABLE i'.-Summary of the correlation coeflcients for the relationship between the 0000 QMT average transport wind speed and the average afternoon surface wind speed.
~~
I I I I I I I I
Index of 56.60 .61-.65 .6!3-.70 .71-.75 .76-.80 .81-.85 .%-.90 31-.95
correlation I . I 1 1 1 I I I I- I- I- 1-1-
I I I I I I I I
TABLE 8.--Summary of the correlation coeficients for the relationship between average afternoon surface wind speed and the 24-hr. average surface wind speed.
40 MONTHLY WEATHER REVIEW Vol. 95, No. 1
FIGURE 5.-Isopleths of standard error8 of transport wiod speed (kt.) for the relationship between the transport wind speed and the wind
speed nearest the center of the mixing, depth.
RELATED WIND SPEEDS
Methods of estimating the afternoon (1200-1600 LST)
and 24-hr. average surface wind speeds were also developed
in this study. Average afternoon surface wind speeds
correlate highly with the 0000 GMT average wind speeds
through the mixing depths. In turn, the afternoon wind
speeds are useful in estimating 24-hr. average surface
wind speeds. Tables 7 and 8 summarize the correlation
coefficients about the derived parabolic equations for
these relationships.
4. VERIFICATION
A test period was conducted from April 20 through May
9, 1966 t o examine results from the methods of forecasting
afternoon mixing depths and transport wind speeds.
Figure 6 shows an example of such forecasts made from
the derived statistical regression equations, NMC forecast
material, and, forecast surface temperatures. It was
assumed that forecast and observed maximum surface
temperatures occurred during afternoon hours. Estimates
of mixing depth and transport wind speed, derived by use
of the above products, were called RADAT forecasts.
The RADAT forecasts shown in figure 6 verified on the
afternoon of May 5, 1966; they were prepared on the
morning (EST) of May 4 when the latest upper-air obser-
vations were for 1200 GMT. Figure 7 shows the calculated
values on May 5, 1966. Afternoon mixing depths were
computed as the height above ground at which the poten-
tial temperature of the 24-hr. observed maximum surface
temperature intersected the observed 1200 GMT vertical
temperature profile; observed transport wind speeds were
conputed as the 0000 GMT (1900 EST) mean wind speed
through the observed afternoon mixing depth. For veri-
fication purposes all forecast and calculated values of
mixing depths greater than 3 km. were treated as if they
were 3-km. depths.
January 1967 Marvin E. Miller 41
RADAT .. in mixing depth calculations. '
Mean absolute errors of forecast surface maximum ---
Excluding stations with precipitation.. _.....__...._.._.._
Including stations with precipitation --.._..--_..-..--..--.
5.9' F. 6.3' F. temperatures during the test days axe summarized in table
FIGURE 6.-RADAT forecasts of afternoon mixing depth (m.) and transport wind speeds (m. sec.-l) made on May 4, 1966. (Isopleths
of mixing depth are in kilometers.)
.RAOB
___-
3.5" F. 4.0 F.
' MIXING DEPTHS TABLE 9.-Mean absolute errors of afternoon mixing depth from RADAT and RAOB forecasts: April 80 through May 9 , 1966
Table 9 shows that for the verification test deriod the
observed mean mixing depth mas 1790 m.; the mean
absolute error of RADAT forecasts for non-precipitation
stations was 600 m. and for all stations it mas 635 m.
These errors may be compared with those for shorter lead
time forecasts, i.e., mixing depth forecasts based on
today's observed 1200 GMT vertical temperature profiles
and forecasts prepared this morning of maximum surface
temperatures for today. Such forecasts are called RAOB
forecasts and, as shown in table 9, the mean absolute
errors were only about half those for RADAT forecasts.
In the first comparison of table 9, stations where measurable
Observed mean mixing depth
Mean absolute error of forecast mixing depth
-___
Excluding stations with precipitation-. -. - - - .. . -. ..
Including stations with precipitation ..._._.___...__.. .
1790 meters
-t--------
RADAT -RAOB
i-- 600 m. 310 m. 635m. 1 360m.
42 MONTHLY WEATHER REVIEW Vol. 95, No. 1
April21,1966
8.6 m.see.-l
3.1
2.5
Observed mean transport wind speed.-. __.....___ _--___
Mean absolute error of transport wind speed: 36-hr. RADAT forecast. ______________..____---..----- 12-hr. RADAT forecast-.. __..._.______________
~
______
Mean absolute error of transport wind speed when persis- tence of the average 1200 GMT wind speed through the observed mixin depth is used to indicate the afternoon transport wlndspeed ______
~
_____._.............~.~~~.. __ 3.6
FIGURE 7.-Observed afternoon mixing depths (m.) and transport wind speeds (m. sec.-l) on May 5, 1966. (Isopleths of mixing
depth are in kilometers.)
May 5,1966
11.1 m.sec.-*
3.7 3.0
4. 5
tures used in RADAT mixing depth forecasts were 24 hr.
longer than those for RAOB mixing depth forecasts.
Table 10 shows that errors in forecast temperatures were
considerably larger for the longer than for the shorter
forecast lead time. The data in tables 9 and 10 suggest
that a considerable portion of the error in forecast mixing
depths was due to inaccurate forecasts of maximum
were for mixing depths forecast with a lead time of 30 hr.
or more. The 12-hr. RADAT forecasts of average trans-
port wind speed mere somewhat better than the 36-hr.
RADAT forecasts.
Table 11 also shows that if the 1200 GMT observed
average wind speeds through the observed afternoon
I temperature.
TRANSPORT WIND SPEEDS
Transport wind speed forecasts as calculated from the
parabolic regression equations and winds aloft forecasts
were verified for only April 21 and May 5. Table 11
summarizes this verification. The 36-hr. RADAT fore-
casts of average wind speed through tjhe mixing layer
utilized NMC wind forecasts with a lead time of 36 hr.,
i.e., forecasts were based on 1200 GMT upper-air observa-
tions yesterday and verified at 0000 GMT tomorrow (1900
EST today). These forecasts of transport wind speed
January 1967 Marvin E. Miller 43
TABLE l2.-Comparisons of mixing depth estimates (meters) obtained from 1964 parabolic regression equations for the relationship between mixing depth and (t a l c - T) with estimates for similar equations derived from 1966 data.
t.,,--Tlwo-8so ( C.) h- Tsro-Jar ( C.)
_______-_- City
j
Year
j 4 6 10 14 20 27 26 30
Albany, N.Y .....................................
Bismarck, N. Dak ................................
Columbia, Mo-. ...................................
Montgomery, Ala- ................................
Oakland, Calif. ...................................
Pittsburgh, Pa ....................................
Salem, Oreg .......................................
Salt Lake City, Utah .............................
San Antonio, Tex .................................
Tucson, Ariz ......................................
1964 ............... 1965--. ............ 1964 ............... 1965 ____ - __ __ - - - ._.
1964 ............... 1965 ............... 1964 ............... 19 65. ..............
1964 ............... 1965. .............. 1964 ............... 1965 ............... 1964 ............... 1965 ............... 1964 ...............
1965 ............... 1964 ...............
1965.-. ............ 1964 ............... 19 65. ..............
575 77.5
394 687 411 507 429 490 550 719 668 743 599 846 507 784
590 74 1 582 730 619 726 574 692 548 704 586 738 (*) ....
____ ..__
455 692 681 813
(*) ....
1140 1131 690
61 0 997 874 1208 1241 1173 1158 958 1016 1087 1111 ....
.__.
1059 1045
1457 1388 859 72s 1195 978 1391 1565 1781 1764 1215 1459 1565 1575
....
_.__
1283 1150
....
....
1652 1715 1467 1606 1539 1535 1629 1519 1571 1707 1589 1579 1634 1705 2529 2429 1540 1483 1717 1767
Values not calculated because of the nearness of the station elevation to the 850-mb level.
mixing depths had been used to represent the afternoon
transport wind speeds, the mean absolute transport
wind speed errorsmould have been 3.6 m. set.-' on April
21 and 4.5 m. set.-' on May 5. Thus 12-hr. persistence
forecasts of the observed morning wind speeds would
have given poorer est.imates of the afternoon transport
wind speeds than the 12- and 36-hr. RADAT forecasts,
which were based on the derived statistical equations
and NMC winds aloft forecasts.
5. SUMMARY
To determine objective forecasts of afternoon mixing
depth and the average wind speed through this depth,
parabolic regression equations of relationships between
these quantities and selected independent variables were
derived for 67 rawinsonde stations. Although the methods
of obtaining estimates of mixing depths and transport
wind speeds were developed specifically for use in the
National Air Pollution Potential Forecast Program, the
byproducts from this study, statistical equations for
estimating average afternoon and 24-hr. surface wind
speeds, can be beneficial to synoptic and fie-weather
meteorologists.
Methods of forecasting the vertical extent above the
surface of atmospheric mixing during the afternoon and
the average wind speed through this mixing depth have
been presented. Sample forecasts, made during April and
May 1966, have shown that the products are satisfactory
enough to be incorporated into the National Air Pollution
Potential Forecast Program.
6. EPILOGUE
Further justifkation for using the 1964 derived parabolic
regression equations for estimating mixing depths is given
in table 12. This table shows, for selected stations, esti-
mates of mixing depths obtained from regression equations
derived from 1965 data and similar estimates obtained
from the 1964 equations. The values of mixing depths
from these equations are not significantly different.
Hence, either equations calculated for the two different,
years or new equations derived from the combination of
1964 and 1965 data can be expected to give similar esti-
mates of mixing depths. At present the 1964 regression
equations are used to forecast mixing depths through the
year. It is planned to derive parabolic regression equations
based on seasonal breakdown of the data. Some improve-
ment in the quality of the forecasts might then be
expected.
ACKNOWLEDGMENTS
The author is indebted to Mr. Robert A. McCormick and Mr.
George C. Holeworth for their comments and suggestions. The
efforts of Mr. Mike Yanolko, who assisted in compiling the data,
and Miss Phyllis Polland and Dr. John Stackpole, who wrote the
computer programs used to obtain the data, are also acknowledged.
1.
REFERENCES
J. Badner and M. Kulawiec, FD Program: Winds Aloft and
Temperature Forecasts, Notes to Forecasiers, Technical Proce-
dures Branch, WXAP Division, U.S. Weather Bureau, Wash-
ington, D.C., May 1965.
44 MONTHLY WEATHER REVIEW Vol. 95, No. 1
2. G. Holzworth, Estimates of Mean Maximum Mixing Depths A Years Experience, Journal of the A i r Pollution Control
in the Contiguous United States, Monthly Weather Review, Association, vol. 13, No. 5, May 1963, pp. 205-210.
vol. 92, No. 5, May 1964, pp. 235-242. 4. B. Ratner, Upper Air Climatology of the United States,
3. M. Miller and L. Niemeyer, Air Pollution Potential Forecasts- Technical Paper No. 38, Part I, U.S. Weather Bureau, June 1957.
[Received October 3, 1966; rewised November 21, 19661
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