JUNE 1961 MONTHLY WEATHER REVIEW 197
ON VERIFICATION OF UPPER-AIR WINDS
BY VERTICAL SHEAR AND EXTREMES
OSKAR M. ESSENWANGER*
Research Laboratory, Army Ballistic Missile Agency, Huntsville, Ala.
ROBERT E. BRADFORD
National Weather Records Center, U.S. Weather Bureau, Asheville, N.C.
a n d
WILLIAM W. VAUGHAN**
Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, Ala.
[Manuscript received November 23, 1960; revised February 17, 19611
ABSTRACT
The existence of undetected errors in recorded wind observations may have a biasing influence on a statistical
study. In the progress of some studies it has been found necessary to reexamine the data being used. A series of
upper-air winds has been checked by using available listings of vertical shear and extreme winds. The developed
procedure permits correction for major errors and tolerates the minor (random) errors.
The test of data by maximum wind profiles uses the highest and second highest scalar wind speed for each station
and checks the data by profile scan. The test of data by vertical wind shear uses a critical value, theoretically
derived, exceedance of which marks the data as suspicious. A detailed check of the wind observation verifies this
suspicious value or it is corrected. In this program 3.5 percent of the observations proved suspicious and 85 percent
thereof, that is, 2.9 percent of the observations, required correction. Thus the critical value is highly efficient.
The errors were traced and split into clerical errors (1.1 percent), instrumental errors (1.3 percent), and computa-
tional errors (0.5 percent), which are quite within reasonable limits.
1. INTRODUCTION
For use in missile design and performance studies by
Army Ballistic Missile Agency, basic upper-air wind
observations were obtained for locations in the Pacific
Ocean, North America, and Europe. The stations are
listed in table 1. Preliminary analysis of the data revealed
that there were occurrences of apparent errors in the
observations as presented on punched cards. It was
decided that these data should be checked.
Although it was considered desirable to check and verify
all the upper-air data, this was not possible because of
the cost and the time required to review the mass af
observations. Instead it was decided to establish a
checking program which would permit a review eliminat-
ing major errors, yet tolerating minor (random) errors.
It was considered to be sufficient to restrict the checking
process to higher wind magnitudes and wind shears, where
the possibility exists that the reported extreme wind
velocity arises from the addition of wind data and error
with the same sign.
This method permitted the correction of the major items
‘Formerly associated with the Sational Weather Records Center, U.S. Weather
1 “Observation” used here refers to the entire ascent though sometimes only the value
**Formerly associated with the U.8. Army Ballistic Missile Agency, Huntsville, Ala.
Bureau, Asheville, N.C.
at a single level had to be corrected.
(maximum wind speed and wind shear) required for
missile design studies and verification of the wind data
a t the same time.
The mass of punched cards was converted to magnetic
t’apes for use on high-speed electronic computers (IBM 704
and 709). Use of these computers permitted the rapid
searching of the data and machine listings of all observa-
tions (plus the associated profile) which produced the
higher wind speeds and wind shear for each altitude level.
Also, it was possible to provide preliminary frequency
distributions of the wind shear and speed data for use in
further evaluation of suspicious data. The corrected
observations were subsequently incorporated into the
original data records and utilized on various statistical
programs for use in missile design and employment
studies.
2. THEORETICAL BACKGROUND
The problem existed that frequency distributions for
wind shears and extreme values had been programmed,
and tabulations similar to tabIe 2 (described later) had
been made before the necessity for critical review and
correction became apparent. Thus, the problem was not
to establish a suit’able statistical theory of fitting extreme
value data, but rather to develop an economical tech-
MONTHLY WEATHER REVIEW JUNE 1961 198
Job station No.
1
2
3
4
5
6
8
7
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23 24
TABLE 1.-Station listing of verified wind data 1
Station name
___
Cocoa (Patrick AFB) .......
Cape Canaveral .............
Tokyo (Haneda AFB)..-.-.
Nagoya .....................
Fairbanks ...................
Tripoli (Wheelus AB) .......
Berlin .......................
Wiesbaden". ...............
Bitburg .....................
Port Lyautey- ..............
Thule .......................
Lihue .......................
Grand Bahama IsL .........
International Falls- .........
Guam (Anderson AFB)."..
San Juan ....................
Balboa, C.Z. (Albrook AFB)
Johnston Isl. AFB ..........
Luzon (Clark AB)
~ ~-. ~. .-..
Santa Maria ................
Keflavik (Meeks Fld) .......
Silver Hill (Washington D.C.) .....................
Adak ........................
El Paso- ....................
Alert Barrow ......................
........................
- -
WBAN No.
12867
12868
43311
43312
26411
33123
35140
35010
34049
13017
17605
22536
12712
14918
41414
11631
107111
21601
41207
23236
23273
16204
16201
93722
25704
23044
2750:
18601
Period of record
10/52-11/56
1/51- 9/52
11/56-12/57
1/51- 4/52
4/52-12/53
7/55-12/55
8/57-12/57
1/54-6/55
1 /5 6 5/57
1/51-12/57
5/53-12/57
1/51- 4/53
lj51- 6/55
1/51- 3/53
4/53- 6/55
1/56-12/57
12/51-12/52
1/53-12/57
1151- 3/54
1/5612/57
1/51-12/57
10/54-12/57
1/51- 9/54
5153-12/57
1/51- 4/53
1/51- 5/55
1/5612/57
1/51-11/53
11/53- 4/55
6/55- 7/55
9155-12/57
5153- 2/54
1151- 4/53
3154-12157
1/51- 8/53
9/53-12/57
11/54-12/57
1151- 8/51
9/51-12/57
1/51-1215?
1153-12/55
6153-12/55
1/51-5/52
1/51- 4/54
5/54-12/55
1/51-12/57
7/53- 6/51
1/51-10/51
5/55
1151-12/57
1/51-10/54
no, 12
no, 12
on, 12
n9,21
00,12
00,12
06,18
00,12
00,12
00,12
00,12
.......
no, 12
........
no, 12
on, 12
on, 12
on, 12
on, 12
no, 12
on, 12
00,12
no, 12
00,12
........
........
~"
........
.......
........
........
........
........
........
no, 12
00,12
00,12
00.12
........
........
........
........
".~ ""
00,12
00,12
on, 12
00,12
00,12
"" ~".
........
- - -. -. -.
4,6.8 8
2,6
8
8
8
8
8
8
6
8
6
6
8
8
6
6
8
6
8
8
6
8
6
8
6
8
6
6
6
8
8
8
6,s
6
8 6
8 6
6
8
8
6
6
8
2
6
6
6
2, 6
' 8
1 The sequence of stations is not identical with that in tables 2 or 4.
a Prior to May 1957 observations were taken at 03 and 15 instead of 00 and 12. This is
3 Type of equipment: 2=Rabal, single theodolite 4=SCR-584 and SCR-545
6=SCR-658
8=QMD-1 and GMD-1A
not listed here.
nique with minimum amount of time and cost using
these available tabulations for selection and checking
procedures.
From the statistical point of view it must be pointed
out that the problem of establishing profiles of maximum
wind speed (magnitude of wind vector) or distributions
of maximum wind shears should be approached otherwise
than shown in this report by employing an ext'reme value
statistic. However, frequency distributions of maximum
wind speed and wind shear in the upper air are not com-
pletely known and application of techniques similar to
Thom's [2, 31 method or Gumbel's [I] theory would have
made necessary the careful evaluation of several such
statistical systems. This time-consuming basic study
could not have been completed within the limitation of
the available time and funds.
The first part of the verification program, checking
maximum wind profiles, was relatively simple. The listed
and plotted profiles were scanned for suspicious values.
Verification of those values considered suspicious was per-
formed by reference to the original data records. Details
of the procedures employed are presented in section 3.
The selection of suspicious values for wind shear data
appeared very complicated in the beginning. Distribu-
tions of wind component shear frequencies were available
in the form of table 2 without the column marked "Essen-
wanger's sum". In the form shown in table 2, frequency
distributions were given without regard to algebraic sign
of the wind shear. The problem was to find a value
which separated the acceptable values from suspicious
values without reviewing too many observations or ac-
cepting a large amount of unreliable data. This value
will be called the critical value ec.
The column marked "99.865" was practically identical
with the maximum shear value. There is no reason to
expect all maximum shear values to be wrong. On the
other hand, the value listed in the column marked "97.72"
was assumed to be acceptable since regularly it was ex-
ceeded by 2 out of every 100 values. Thus we may
contemplate the following ideas.
We start with the assumption that zonal and meridional
wind components are normal (Gaussian) distributions, or
approximately normal. Departures from normality will
be introduced later in the discussion. The wind shear
data must then also follow a normal distribution. The
shear distribution, disregarding the sign, then is a folded
distribution. This folding occurs at the zero wind shear
value. The mean value of the frequency distribution of
zonal or meridional shear values, not disregarding the sign,
usually will not coincide with zero. The question is now:
Which portion of u (standard deviation) corresponds to
the listed percentage frequencies, 50, 84.1, 97.72, etc.?
If the folding occurs outside the f3 u value in refer-
ence to the mean, then practically all shear values have
the same sign. Then the shear distribution follows a
normal distribution and the 50 percent value (median)
virtually coincides with the mean. This statement holds
for folding above f 1.5 u (fig. la) if we assume that the
frequency of data above 3 u is negligible. If the folding is
within f1.5 u, then the mean value of the unfolded
normal distribution must be smaller than the 50 percent
value (fig. 1b). Thus the listed 50 percent value permits
evaluation of the magnitude of this mean value. We recog-
nize (see also table 2) t,hat for practical purposes this value
is so close to the zero wind shear that we can continue our
discussion about the folded distribution as if it were
folded a t t h e mean value zero. Then the 84.1 percent
value corresponds to 1.41 u, the 97.72 percent to 2.28 U ,
and the 99.865 percent to 3.20 u.
We build the ratio
99.865 percentage value-3.20~
97.72 percentage value 2 .2 8 ~ - 1.40
Thus, theoretically we should expect the factor 1.4. A
2 Some statisticians may want to use the symbol s, the estimate of the population
standard deviation u. This has no influenceupon the development io this paragraph
insofar as later the 84.1 or 97.72 value may express the empirical replacement for c o r 8.
JUNE 1961 M O N T H L Y W E A T 199
TABLE 2.-Meridional wind shear (set.") distributions at KeJEaoik, Iceland, for J a n u a r y . S t a t i o n a l t i t u d e , 54 m. M S L ; lalitude, 65'57' N .;
longitude, 2d0S7' W . : period of observations, January 1961-December 1957
~
~
Suspi- cious values
-
T A l t i t u d e k m . (MSL) of OBS
Number
I-
Cumulative Percentage Frequency wanger's Essen-
sum Max shear Pct. freq.
15.9 50.0
,0026 . nogo . no08 ,11037
n n m
68.0
~
,0131
.0055
.0042
.0057
,0038
,0042
.0042
,0055
. on46
. on40
. on49
. on43 .on38
. on47
,0042
,0054
. on40 ,0042
,0049
,0035
0046 ,0042 ,0035
,0042
.0049
.0042
,0045
.0033
,0042
84. 1
I-
97.72 99.865 I ,1 3 5 2 .2 8 15.9 50.0
,0026 . nogo . no08 ,11037
. no30
,0028
,0037
. no03 . noit . on04 .on27
. on02 ,0025
,0023
. on04 . 0028 ,0003 . no28
. oozn
,0001 ,0028
,0004 .OW27
.0028
,0027
,0027
,0202 ,0093
,0077 ,0090 .no92
,0085 ,0061 ,0064
. nnxo
,0074
,0069
. no74
.on88
. 00x5
,0085
,0074
,0085
.0071 ,0073
. no77 no92
. 0069 .0071 ,0099 ,0085
,0064
,0074
. 0058
. on92
,0369
,0227 ,0199
,0176
,0204 ,0103 .0139 ,0164
,0157 .0159
,0243 ,0199 ,0176
,0142
,0162
. 01 72 .0142
.01 .XI ,0157
,0176
. 01 63 ,0214
.o n 1
,0222
,0153
. 0166
,0172
.n ~ 40
,0126
.27 .27 .27 .27 .27 .27 .27 .27 .27 .28 .28 .3n
372 370 368 369 372 374 375 373 371
359 351 335 303 278 262
249 231 207 187 170 156
138
115
89
65 75
46 36
12 19
8
6 2 2
2
2
2
2
2 1 1
loo
. OR21
.0342
. (1316
.0339
,0253
,0294
.0281
.n369
. nzsn
,0214
.m x 5
,0283 ,0206
,0334
,0275
,0381
,0311
,0265 ,0247 ,0289
,0261 .0271
.n314
,0306 ,0311 ,0277
.n33n ,0338
,0353
.....................
0.5-1.0 SFC-O.5
1.0-1.5 .......................
2.0-2.5 .......................
.......................
1 .~2 .n .......................
3.0-4.0 2.5-3.0
5.0-6.0 .......................
6.0-7.0 .......................
7.0-8.0 .......................
9.0-10.0 8.0-9.0
lo.n-ll.o.-.--.-- .............
ll.o-u.o.-.---- ..............
14.0-15.0.-.--- ...............
15.0.16.0 .....................
17.0-18.0 .....................
20.0-21.0.. ...................
21 .n-zz.o.. ...................
22.0-23.n .....................
23.0-~.0.. ...................
27.n-28.n 26.n-27.0
28.n-29.0 .....................
30.0-31.0.. ...................
31.0-32.0 .....................
33.0-34.0.. ...................
35.0-36.0. 34.0-35.0
36.0-37.0 .....................
37.0-38.0 .....................
39.0-40.0.-.-.--- .............
4o.n-41.0 .....................
.......................
.......................
4.0-5.0 .......................
.......................
......................
.....................
13.0-14.0 12.0-13.0
.....................
16.0-17.0 .....................
19.0-20.0 18.0-19.0 .....................
.....................
24.0-25.0.. ...................
25.0-26.0 .....................
.....................
.....................
29.0-30.0 .....................
32.0-33.0 .....................
.....................
....................
38.0-39.0 .....................
,0001 ,0028
. ."
,0028
,0037
. on04 .on27
. no03 . noit ,0004 .OW27
.33 .36 .36
.43 .48
.53 .59
.64
.72
. 87
1. 12
1.33
2. 17 1. 54
2. 78 5.26 8.33 12. 50 16.67
.4n
I. on
So. no
50. no 50. no
50.00
50. n ion. o inn. n
50.00
50.00
. on04 . 0028 ,0003 . no28
. ""
,0027
,0027
ec=P84.1+P97.72+0.005 sec."
where P 8 4 .1 is the 84.1 percentage value and PQ7.,, the 97.72
review of the frequency tabulations showed that for the
meridional shear the average empirical value amount's to
1.8 and for the zonal shear it is between 1.5 and 1.7. The
factor 1.6 seems, therefore, a sound compromise between
theory and practice. This takes care of departures from
the normal distribution law and a mean value different
from zero.
We have now established a theoretically acceptable
critical value (e,) of 1.6 times 2.28 C, which equals 3.65 C.
If the c is known, we can easily compute this critical
value e,.
We also could use the 97.72 percentage value for the
2.28 c value. For the individual case, however, too manj-
random variations may influence the result. Therefore,
we may try to incorporate another procedure t'o decrease
this effect. When we add the 84.1 percent and t'he 97.72
percent values, we obtain 1 .4 1 ~ plus 2.28a, which equals
3.69~. This is very close to 3 .6 5 ~. T h u s we may
derive the critical value by employing the 84.1 and 97.72
percentage values.
Further consideration may be given to an observat'ion
tolerance error. An error of 5 m. sec." per 1000 m. for
those extreme values seems to be within the limitation of
measurements.3 Thus we tolerate this error for the
critical value and derive finally
3 The flrst 3000 m. in table 2 are listed in 500-m. layers. It was decided for simplicity
to adopt 0.005 set." for those 500-m. layers, too.
percentage value.
J - 5a
I I I I I I
-2 -I 0 1 2 3 u units
FINJRE 1.-Folding of normal distribution and relation to 50
percent line (median).
200 MONTHLY WEATHER REVIEW JUNE 1961
The unit of ec is the same as in table 2, namely inverse
seconds. From table 2 we may give a sample for compu-
tation of the critical value for the layer, surface to 0.5
km. It wouldbe
ec= .0202 + .0369 + .0050 = .062 1 sec.”
This value is listed in table 2 in the column titled “Essen-
wanger’s sum”. All shear observations exceeding this
value, as computed for each level were labeled suspicious.
They are marked by an asterisk in table 2. Further
description of the shear checking process willfollow in
section 4. Of the suspicious values, 85 percent had to be
corrected, which is considered as high efficiency for this
checking procedure.
Results of randomly picked shear values for checking
have damonstrated that efficiency drops sharply for values
below the critical value. Thus, by t,he outlined process
we have achieved the soal to eliminate major errors, and
tolerate (random) minor errors which have little bearing
upon the determination of missile design criteria.
3. TEST OF DATA BY MAXIMUM WIND PROFILES
The highest and second highest (scalar) wind speeds for
each of the stations a t each of the 45 levels (or to the
41
40
35
30
25
W
I- W
I
s i? 20 -
i“ I
W
I
‘3
15
10
5
0
00 20 40 60 00 100 120 140
WIND SPEED (METERS PER SECOND)
FIQURE 2.-Maximum wind profile before verification, station no. 1.
highest level attained if it was less than 41 km.) were
machine selected, and the observations containing these
high wind speed values were listed.
The verification of these speeds may be managed in
two ways: verify or correct each and every value, or locate
and correct the greater majority of the erroneous values,
particularly values that are very large or appear to be
inconsistent wit’h a smooth profile which would be ex-
pected if all observations were correct). Practical economic
considerations demanded that, the latter be the guiding
principle in the verification. One-third, or 8, of the sta-
tions received total verification; i.e., every high wind
speed value was checked to provide a basis of comparison
to determine the adequacy of the smooth profile verifica-
tion procedure.
The verification procedure was divided into three steps
or categories, namely: observation scan, terminating val-
ues, and profile scan. The sequence of the checking
process might have been arbitrarily established, however,
it appeared that the sequence listed above would provide
maximum assurance that the final product, the maximum
wind profile, was correct.
ascent as:one:taken observation and is in this way different from an observed value.
4 The word “observation” in this report is used in the sense of characterizing the entire
41 r I
40
c
25
W
I-
I
W
0 1
- E 20
c
$I 5 l IO
- HIGH€ ST SPEED
”- AREAS OF NO DATA
00 20 40 60 80 100 120 140
WIND SPEED (METERS PER SECOND)
FIQURE 3.-Maximum wind profile after verification, station no. 1.
JUNE 1961 MONTHLY WEATHER REVIEW 201
The observation sc,an was liberally a visual scan of the
observation. Each machine-selected observation was
searched for apparentr inconsistencies, such as a speed of
10 m.p.s. followed a t the next level by tt speed of 116
m.p.s., or similar rapid and large fluctuations in wind
speed. Those observations containing such inconsistencies
were checked and correct.ed as appropriate. This sub-
jective scanning sufficed for errors detectable by discon-
t>inuity. Were all errors of t,his type, no further checking
had been necessary. But, though some profiles showed
considerable smoothing from this process, most profiles
still contained irregular contours which appeared sus-
picious. The checking process was therefore continued.
Each value occurring as the terminating speed for a
given observation was considered suspicious. All observed
wind values are the result of 2- or 4-minute averages
except the last speed obtained which is allowed to be a
I-minute calculation if a 2- or 4-minute average is not
available. Terminating values were t,herefore checked for
representativeness. This eliminated t.he error from termi-
nating fluct,uations, but further smoothing was needed.
The profile scan necessitated the construction of the
vertical profiles of these highest and second highest wind
speeds. Figure 2 pictures the original profiles for station
no. 1 to serve as an example. The first move was to apply
to the profiles all corrections resulting from the first two
steps of the verification procedure. The profiles, after
this preliminary correction, were then examined and ques-
tionable values were "picked off" for verification. It is
obvious that a great deal of subjectivity was also encount-
ered here, but a system was utilized. The values were
chosen in sets, each set being verified and the resulting
corrections applied before the next set was chosen. Each
set consisted of those wind speed values which, if changed,
would most smooth the contours of the profile. This set
checking process was continued until no errors were found
or so few were found that the profilewas virtually un-
affected.
Figure 3 shows the maximum wind profile after veri-
fication. Since this investigation dealt with only the
highest and next to highest speeds, and values to replace
these when they were deleted or changed to a value below
that of the second highest were not included in this pro-
file, thus dashed areas of no data appear. This meant the
highest or second highest wind speed for a dashed
level would have to be obtained by going back to the
original records and selecting the now highest (or second
highest) value. As this would have had to be done by
hand at National Weather Records Center, it was decided
to leave the profile as in figure 3. The missing values
may easily be replaced by machine selection at Army
Ballistic Missile Agency. The corrected profile, in
TABLE 3.-Maximum wind verijication (observations checked and changed)
- I1 - 12 5 6 7 8 4
Percent of points checked, changed
Column 9
Column 8
Percent or observa-
checked tions
Column 2
Column 1
Percent of observa-
checked, tions
changed
Column 3
Column 2
Percent of observa-
changed tions
Column 3
Column 1
37
40
31
4
12 40
18 41
13
9 28
18 32 23 42 46
Percent of points changed
Column 9
Column 7
Station* Percent of points Points checked Vumber of profile
points
Number of
changed checked tions
Observa- Observa- observe- tions tions checked Points changed 1 Cohmn 8
procedure:
2....................... 1".
3.". ....................
4.... ....................
5 .......................
6 ........................
8
7
Y ........................
11 .......................
12". ....................
13 .......................
14 .......................
15 .......................
16 .......................
....................
.
........................
........................
I n .......................
23
27
3
19 9
23 n
6
18 9 19
31 20
33
18
n
50
43 56
43 32
41 56
71 56 44 56 42 53 41
62 58
74
10
71
72
26 32
26 5
24 41
12 41
13 7
27
1.5 36 30 45 54
58
n 60
12 43 55 21
54 11
39 22
55
56
63 73
38
02
68 69
75 48 51
56
4x
86 64
50
60
86 73 72
58
31
30 25
24
21 27
40
21
36 21 32 35 45 42
38
38
40 4s 40
40
55
69 53 69
37 56
61 36 58 39
63
67
831
90 70 90
76 86 73
73 72
630
1,461
38
i o 43
58 2'2 21 50 43
59 57 69 79
50 45 27
52
58 75 63
48
76
60 54
61
37
-~
1.326
90
90 70
86 76
73 73 72
630
.__
1,956
372 63
-~___ ~___
36 35
100
100 40
100 60
100
39 59 loo
43
100
26 100
338 100
710 75
ion
___-~
___ ~___
total verification:
17 .......................
32 59 59 L'4 .......................
30 50 60 23 .......................
28 58 58 %2 .......................
42 55 55 21 .......................
46 73 73 ........................
45 60 60 19 .......................
37 64 64 18 .......................
23 44 44
Totals ................. 463 463 283
Grand Totals ......... 1.489 975 558
-~______ -~______
100 100 100 100
100
100
loo mo
40 50
53 67
69
53
36 59
54
36
-__
40
50
67 53 69
53
36 59
54
49 -
52 58 7.5 63 76
48
60 54
61
57 65
'The sequence of stations is mot ideutical with station listing in table 1
202 MONTHLY WEATHER REVIEW JUNE 1961
general, takes on a smoother appearance with one distinct
layer of maximum wind speed. This is true with all of the
stations.
Table 3 denotes the amount of checking and changing
done in the maximum wind profile verification program.
The data are subdivided into two groups; the first being
for the 16 stations for which the verification was accom-
plished by the procedure described in the preceding para-
graphs, the second for the 8 stations which received total
verification. The combination of these yields the overall
results. Table 3 is self explanatory.
As can be seen from table 3, there is some question
concerning the efficiency of this three-step procedure,
particularly when the percentage of values changed be-
comes very large. It would seem that there still are a
significant number of erroneous observations unchecked.
It must be remembered, however, that the criterion for
terminating verification was that the contours of the pro-
file remain virtually unchanged, since the original goal of
the verification was to obtain a representative maximum
windprofile. This goal was attained in all cases where
the profilewas not completedly destroyed. Three sta-
tions lacked sufficient data and for one the entire profile
would have needed reconstruction.
This method was designed for adequacy, with efficiency
being second in importance. Methods aspiring toward
high efficiency may be similar t o the above procedures but,
would necessarily include more objectivity and less sub-
jectivity. The method outlined for vertical wind shear
verification with objective selection may be adaptable to
wind speeds using similar frequency distributions.
4. TEST OF DATA BY WIND SHEAR
Selections were made from the shear distribution tables
similar to table 2. These tables list the vertical shear by
l-km. layers, beginning at 3 km. Below 3 km., 500-m.
layers were taken. The first attempt at selection was by
picking out values that seemed to be erratic. This was
abandoned almost immediately since it was too laborious
and uncertain (nearly 14,000 observations contained all
of the maximum shear values).
Then it was decided to use the method outlined in
section 2. This method is as follows. Obtain the sum of
the shear values a t the cumulative percentage frequencies
of 84.1 percent and 97.72 percent plus 0.0050 sec.”,
then select shears for checking on the basis that any shear
value greater than this sum is suspicious. In addition, a
selection by observations was made: any value that had
been obtained a t a level reached ten or less times during
the period of record was considered as suspicious, regard-
less of magnitude.
The selection of the suspicious values is demonstrated in
table 2. This tabular form portrays layer versus curnu-
lative percentage frequency with supplementary columns
for observations counts and the observed maximum shear.
The vertical wind shear (henceforth shear) values were
computed for both the zonal and meridional components.
Listings of the profile for the maximum wind shear ac-
companied the listings of the form of table 2.
In the first set of tabulations maximum shear values
only were subjected to verification. Later all shear val-
ues exceeding the “critical” threshold (Essenwanger’s
sum) were listed as a review program. I t was understood
that, regardless of what portion or portions of an obser-
vation first raised suspicion, the entire observation was
to be subjected to a checking process.
Secondary review was limited to a review check program
which was designed to encompass not only highly suspi-
cious observations not contained in the first phase, but
also observations in which errors may have occurred or
been overlooked during previous verification. The latter,
fortunately, occurred very fewt’imes. Even with this,
some few errors undoubtedly still escaped detection.
The combination of these methods has proven accept-
ably efficient in that 85 percent of the observations
selected as suspicious were found to be erroneous.
The errors have been tabulated in three categories:
clerical, instrumental, and computational. The clerical
errors were based on the premise that no technical ob-
server training was required t o perform the work classified
as clerical. They were subdivided into three types:
punching, extraction (or transcription) , and plotting of
Form WBAN 20A. The punching was, of course, the
production of the cards constituting the original card
decks. The extraction was the “picking off” of values
from the WBAN 20A, a plot of the observed data in the
form of wind speed and direction versus height. Plotting
refers to wrong plots of WBAN 20A.
Instrumental error may be defined as large and rapid
fluctuations in angles (azimuth and elevation) incompat-
ible wit’h the calculated height changes.
The computational error was subdivided into two types:
Calculations on WBAN 20 (the observer’s work sheet)
and fictitious ascension rates (of the balloon) as calculated
from erroneous pressure-temperature-time measurements.
Fictitious ascension rates may be thought of as instru-
mental, but only the tracking equipment was considered
an instrument in this study. The trac,king equipment
consisted mainly of the theodolite (visual tracking), the
SCR-658 (manual radiosonde tracking), and the GMD-1
and GMD-1A (automatic radiosonde tracking).
Table 4 shows the error statistics resulting from the
verification of the shear selected observations. The head-
ings are self explanatory. Some observations contained
more than one type of error so t.hat the occurrence of
errors exceeds the number of observations changed. The
end results in this tabulation prove interesting in the
predominance of the instrumental and clerical errors.
The relatively small computational error is gratifying.
We note in table 4 that from all observations only 3.5
percent were found to contain suspicious values; from the
suspicious Observations 85 percent, i.e., 2.9 percent of all
JUNE 1961 MONTHLY WEATHER REVIEW
TABLE 4.--T.'ertical wind shear cerification (error statistics)
203
Observations Perccntagr of Number of rrrors
""
3
""
Suspi- cious
"_
226 223 169 208
106 215 112
146 124 103
182 178
112 182
226 150
n3 129 251 127 217
162 77
103
3, 951
""
2
Contain- ing maxi
mum shear
___
595 556
626 537
m02
550
542 51 5
504 608 627 535 612 fil9
640
622
591
6.50
541 549 486
509
521 502
13,639
"
I
"
I 5 6 I 8 Total ob- servations containing maximum shear
Column 2
Column 1
1
Station'
number Total
servstions
Total oh-
containing
suspicious
Column 3
Column 1
4
""~
Changed
159 194 133 159 87 195
118
83
91
80 162 121 167
132 90
219 195 117 237
198 116
61 146 80
3,310
"
-1-
Suspi- cious changed
3nlumn
aolumn,
:hanged of total Clerical
:olumn4 Column
X u m n 1 Column ____
Compu- tation
2olumn 8
:olumn 5
Instru- mental
3nlumn'
2olumn !
Instru- mental
57 93 100 58 50 73
53
15
26 35
66
58
G9
48
60
86 104
120
91
139
113 46
49
1, 713
104
"_
Cornpu- tatinn
18
5;
30
40 24
44
52
4
3
R3
17
59
34 34
6Y
58
12 51
41
12
6
9
750
8
"_
Total Clcrical
167
249 134 166
219
107
152 97
102 75 189 152 212 121 167 287 267 127 300
227 121
64 164 93
3,959
"
92
101 27 78 33
106
38 47 72 37
60
77
39 84
132 73
105 24
12Y 9
47 12 39 35
1,496
""
11.6 11.1
10. 5
12.2
11.8 15.1
35.2
IO. 7 12.9 11.9 12. 3
10. 5
13. 2 12.0
12. 5 12.5
12.7 11.6 10. 6
10. 7 9.5 10.0 10. 2 13. 7
11.9
4.4 4. 5
3.3 4.1
4. 2 2.9
7.7 2.9 3.2 2.0 3.5
3. 6
3.6 2.4 3.0 4.4 4. 4
2.5 4.9 2.5 4. 2
1.5 3. 2 2.8
3. 5
"_
34 37
35
75
47 34
35 16
47 25
35
38
40 32
30 36
39
72 40 86 61 72 69 52
43
11
22
18 5
22
18 45 34 4 4
33 11
28 28
M 24 22
9 17
7 18
9
10 7
70 87
80
76 82
74
91
81 73
91
78
66 92
XU
88 97
87 91 94 91 91
79
90
78
85
3. 1
3. 9 55
2. 6
41
20 3 .1 2.4 47
3.8 48 31
2.3 5.7 31 39
2.3 1. 6 71
3.2 49 32
3.3 2.4 51
1.9 40 32
4. 3 2. 6 44
3.8 46
2.3 39 19 4. 6 43 2.3 3.0 7 21 1.2 2.8
19
2.2 24
38
2. 9 38
"" "_ I- Grand total..-! 114,208 I- 19
*The sequence of stations is not identical with station listing in table I.
considerations on Forms WBAN 31 A and B. Errone-
ously low pressure or high temperat'ure readings result in
erroneously high height det'ernlinations, whichwhen
considered with ascension time, may present unduly
large ascension rates. This norrnally occurred in the
topmost layers of the higher ascents. This same reason-
ing can also account for highly erratic or incompatible
height cllangcs at' any level with t'he erroneous pressure
or temperatures being high or low. Highly erratic
angles are caused mainly by equipment malfunction and
limitjation. Any appreciable influence of turbulence
would be confined to t'he lowest levels except under rare
conditions such as balloon entry into a thunderstorm or
possibly clear air turbulence. The first event was
eliminated by consideration of the weather reports. The
latter event, generally not t'oo frequent in occurrenc,e, is
not known at' the present in sufficient detail to make an
unequivocal decision. It' was felt, however, that when
low ascension rat'es are involved, it is more likely that
the data are erroneous due to instrumental errors. This
conclusion may be due for revision after knowledge of
clear air turbulence has improved.
In general, erratic data were determined subjectively
since there were 110 adequat'e objective methods available.
Ascension rat,es were, in general, declared fictit'ious in a
subject,ive manner since time limitations and unavailable
observation data precluded thorough chec,king. There
are two conlpensnting factors, however, in t'hat observa-
tion data were always given the benefit of the doubt, and
all decisions were made by qualified meteorologists.
observations, had t.0 be changed. This means that one
or several values had to be correct'ed in 2.9 percent of t'he
observations. As one observution contains numerous
levels, t'he actual percentage of errors in relation to t'lle
wind dat'a of all levels is far less. The clerical error con-
t,ribut)ed 1.1 percent, the inst'rurnental error 1.3 percent,
and the cornputational error 0.5 percent. A perfect curd
deck wouldbe the ideal goal, of course. As one should
expect, this goal cannot be reached without a thorough
check of the produced d a h . Thus, the magnitude of
percentage of the larger error discovered by the met'hod
outlined above stays well within reasonable tolerance
limits.
A few brief remarks may be in order concerning the
difficulties involved in verificat'ion. First, the major
division of errors is not as clear-cut a s it appears. Prior
to 1956, the extracted values were not always entered
in the allotted space on WBAN 2OA. Errors occurring
subsequent to plotting were att'ributed to extraction in
such cases. Then, beginning on January I , 1956, WBAN
20A was no longer a filed form so that plotting errors
were undetectable. WBAN 20B had come int'o being,
onwhich was allotted space for t'he "extracted" values.
Again, arbitrarily, errors occurring between calculation
(WBAN 20) and punching were att'ributed to extraction,
so that nn overlap occurred. Fortunately, plotting errors
contributed very lit'tle to the mass of clerical errors.
Perha,ps the most difficult' problems arose with erratic
inst'rurnent data and fictit'ious ascension rat'es. Balloon
heights are determined through pressure-temperature
5. CONCLUSION
This st'udy has discussed the possibilit'y of checking
wind d a h by nu&munl wind profiles and wind shear dis-
taibutions. While t'he maximum wind profiles were cvalu-
at'ed for suspicious values by profile scan, tllc checking
process by wind shears was based upon cornputation of a
crit'ical value E,. Exceedance of this critical value ~nutle
the shear value suspicious and subject to verification.
The derivat>ion of t'he critical vtrlue E , was dcvclopctl
and the application to 24 stations showed an effic,icr~cy of
85 percent, which may be considercd very high. Although
3.5 percent of the observat'ions proved t'o be suspicious,
and 2.9 percent had t'o be correct'ed, the act'ual corrections
are less, as one obscrvation in the average contains he-
tween 20 and 30 levcl values, not all of which h:td to he
corrected.
The errors were trrtccd and divided into 1.1 pcrcent
clerical errors, 1.3 percent inst'rurnental Errors, and 0.5 2. H.
percent computational errors. Thesc :we within rcusonnble
limitation.
It may be stressed that establisllrnent, of maxi~nunl
wind profiles or r~laxinlum wind shears may be better ap-
proxhed by thcoretic,al statistical proresscs in orcicr to
3. H.
elirnirlate the efect of the relatively short period of avail-
able d a h rccord. Time and cost, lirnitat'ions, however,
prevented further investigation in t'his direction.
ACKNOWLEDGMENTS
The aut'hors wish to exprcss their special appreciation to
A h . Earl 11. Ritchic of NWRC, who started work on the
r~~axi~nurn wind speed procedure and completed most, o f
this phase of the project. We would like also to rccognizc
tlw outstanding efforts of Mr. S o r r n ~n Graham of SWRC
for the technical work in the accornplishrnent of the
project.
REFERENCES
I . $;. J. Gurnhcl and P. G. Carlson, "Extreme Values in Aeronau-
tics," Journal of the Aeronautical Sciences, vol. 21, K O . 6,
June 1954, pp. 380498.
C'. S. Thorn, "Freyucncy of Mssinlurn Wind Speeds," Pro-
ceedings oJ the American Society of Civil Engineers, Sgs. K O .
C'. S. Thorn, "lXst,ributiorl of Extreme Winds in the Grlited
States," Journal of the Struclwal Dicision, Proceedings of the
American Society of Civil Engineers, vo1. 86, S o . ST 4, hpr.
1060, pp. 11-24
530, 1854, pp. 1-11.