November 1968 A. D . Belmont and D . G. Dartt 767
VARIATION WITH LONGITUDE OF THE QUASI-BIENNIAL OSCILLATION
' 3 '
A. D. BELMONT and D. G. DARTT
Research Division, Control Data Corporation, Minneapolis, Minn.
ABSTRACT
Daily data at 16 stations along five latitudes from 13"N. to 33"s. were carefully examined a t the 50-, lo&, and
500-mb. levels for evidence of longitudinal phase progression of the quasi-biennial oscillation (&BO). At 50 mb. there
is evidence of west to east progression although there are many irregularities and much uncertainty. The phase dates
differ by days a t low latitudes. At 100 and 500 mb., it appears that the &BO originates in tropical America and pro-
gresses both eastward and westward, occurring last in the Indian Ocean. The progression time ranges from 1 to 2 yr.
A t 500 and 100 mb., however, a cellular phase progression is possible due to the difficulty of identifying corresponding
waves with a very meager network.
It appears now that the &BO may not be simultaneous in longitude and that its speed and even direction of
propagation, like its other properties, may vary from cycle to cycle. The analysis is being expanded to other levels
and latitudes to obtain better continuity in following each wave.
1. INTRODUCTION
It has been generally assumed that the quasi-biennial
oscillation (QBO) in the zonal wind component, observed
f i s t in the tropical stratosphere and later at other lati-
tudes and levels, is simultaneous at all longitudes for a
given latitude. However, this impression is based on the
general use of monthly mean wind data, so if the phe-
nomenon actually has a longitudinal time variation in a
shorter period than 1 mo., one could not detect it from
monthly mean data. It is the purpose of this study to
determine phase dates of individual cycles of the QBO
as precisely as possible using daily data, and to see if
stations near a given latitude show consistent progression
of the wave with longitude. I n practice it became advis-
able not to restrict the study to individual latitudes but
t o map the phase dates so that the progression with
latitude and longitude could be observed.
The assumption of simultaneous occurrence implies a
global ring phenomenon whose influence is symmetric t o
the Equator and is a function only of latitude and altitude.
Such a pattern can best be described in terms of north-
south oriented standing or traveling waves. As observa-
tion has revealed nodal belts typical of standing waves and
phase progression characteristic of traveling waves, it is
reasonable that the variation along a meridian is a mix-
ture of both. However, if careful examination of data on a
daily, rather than a monthly, basis shows that there are
indeed longitudinal variations, a more complicated model
must be advanced. These variations, if evident, may be
1 Research supported under Contract Nonr 4700(00) with Oflice of Naval Research.
2 Presented in preliminary forms at American Geophysical Unionmeeting, Washington,
D.C., Apr. 17, 1967, and the Seventh Stanstead Seminar, July 1967.
due to the longitudinal variability of the properties of
north-south components or even possibly to an east-west
traveling component which spirals around the earth from
high to low latitudes with very rapid velocity.
No theory for the existence of the QBO is yet established,
although many tentative proposals have been advanced.
(A convenient review of the status of proposed QBO
causes can be found in [l].) To assist in ascertaining its
origin, its properties must be better known. Whether the
results of a detailed study of daily data reveals a regular
progression with longitude of this wave or not, they will
be of great help in focusing effort onto a reduced number
of possible causes.
Far from being a simple, regular, sinusoidal variation,
the QBO appears to be a highly irregular phenomenon
whose period, amplitude, and phase vary continually at a
given station, and which has noticeable intensity in various
regions such as the tropical stratosphere, the polar mid-
troposphere, and the polar midstratosphere, yet is not
seen clearly between these regions. A corresponding,
although less pronounced, variation in monthly mean
temperature is also noted. Despite its cycle-to-cycle
irregularity, long-term series of mean monthly surface
data also show an average period apparently near 26 mo.
on a worldwide basis (Landsberg et al. [2]). Shah and
Godson [3], also using monthly means, have mapped the
phase and amplitude of the biennial temperature cycle for
levels from 10 to 200 mb. on a global scale and recognize
a spacing of about 30" of lat. between maxima in ampli-
tude. They found that the tropical maximum (near 30")
is out of phase with the equatorial, temperate (SO"), and
polar (80") cycles, confirming results of Angel1 and
Korshover [4].
768 MONTHLY WEATHER REVIEW Vol. 96, No. 11
2. APPROACH
The type of analysis that has been chosen consists of
determining the calendrtr dates of maxima and minima
and magnitude of the QBO on an individual cycle basis.
Of the usual methods of periodic analysis-harmonic
analysis, spectral analysis, and filtering, the latter is the
most appropriate.
Harmonic and spectral techniques describe the phase
and amplitude of sinusoidal components mithin the data.
However, the quasi-biennial waveform being examined
contains appreciable energy which cannot be described
in terms of a single sine wave or in terms of harmonic
components primarily because of the time variations of
amplitude and frequency that are apparent. Therefore,
the amplitude and phase of a single quasi-biennial compo-
nent as given by the spectral techniques will not necessarily
describe the properties of the composite waveform.
The digital filter technique which we have chosen does
not depend on n single sinusoidal interpretation of the
biennial wave. By using a broad-band, low-pass filter, the
annual cycle and higher frequencies are greatly attenuated
so the lower frequency components with weak amplitude
can be identified. The frequency response of the filter in
the neighborhood of the biennial peak is almost uniform;
therefore, systematic variations of the quasi-biennial
waveform are evident in the filtered results. A logical
calendar interpretation of the dates of maxima and
minima of the filtered waveform is then easily accom-
plished. (Although it is recognized that the term “phase”
refers properly to a single sinusoidal wave, for lack of a
more convenient term it will be used here also to refer to
the maximum (or minimum) of a particular cycle.) The
use of digital filters in the analysis of the quasi-biennial
oscillation is not uncommon (Landsberg et al. [2] ; Edmond
[5]), and numerous investigators have made use of the
12-mo. running mean, another digital filter, for a variety
of descriptive analyses.
To obtain times of niaximum or minimum with finer
resolution than a month, daily data are required rather
than monthly means. However, in order to filter a time
series, all values must be equally spaced. Missing data
were therefore interpolated using a technique discussed
in the next section. I t is mainly to avoid the need for
interpolation that monthly means are commonly used,
and therefore there have been no findings concerning
shorter period variations in phase date. However, monthly
means contain an indeterminable bias due t o the 11011-
uniform distribution of few datn within a given month, and
also are aliased due to the infrequent sampling a t high
levels within the month.
Hence our approach mas t o prepare a serially complete
daily time series which was then subjected to a digital
filter to suppress the unwanted frequencies.
INTERPOLATION
Several techniques for estimating the missing data
were examined. These included the use of polynominals,
band-limited functions, and linear regression. Of these
methods, the latter was most appropriate because the
regression technique very nearly conserves most of the
statistical properties of the existing data, namely the
mean, variance, autocorrelation, and power spectrum.
Also, this interpolation is compatible with all time series
from different stations regardless of the density of sampled
data and gives a measure of interpolation error in terms
of the number and geometry of neighboring data utilized
to estimate the missing value.
As linear regression, commonly referred to as “optimum
interpolation,’’ has been discussed widely in various
texts and its application t o meteorological data has been
examined by Gandin [6], Peterson and Middleton [7],
and Buell [8], the analytic formulation is not given here.
Qualitatively, this technique utilizes the autocorrelation
function of the data to determine a set of optimum linear
weights to be attached to surrounding sample points to
give the best least squares estimate of the interpolated
value. A statistical estimate of interpolation error can
then be determined in terms of these optimum linear
weights and the variance and autocorrelation function
of the sampled data. The weights have the property of
point orthogonality, that is interpolation error vanishes
a t all sample points.
I n using this technique, the autovariance function of
a zonal wind time series was first determined for periods
somewhat greater than the longest gap in the wind data
record utilizing lags of 12- or 24-hr. multiples depending
on the basic sampling rate for a given station. (It is to be
noted that the autovariance function is equivalent to
to the autocorrelation function multiplied by the variance
of the data.) This was done by normalizing the resulting
correlations with respect to the number of data pairs
that were available from the incomplete data for that
given lag.
For each autovariance function, a pilot study of statisti-
cal interpolation errors was then made for various sample
configurations in the neighborhood of an interpolated
point. This was necessary to choose how many samples
might be utilized for the interpolation scheme for that
particular time series. (In practice, as a matrix inversion
is involved in determining the weighting functions for
each interpolated value, only a few samples can be eco-
nomically used.) As might be expected, interpolation
errors were most sensitive to the nearness of sample points
to the interpolated value. I n fact little improvement in
this statistical error was realized if other than the most
recent sample point was utilized. Naturally, smaller errors
occurred with two-sided interpolation than with one-
sided interpolation (extrapolation).
From this preliminary study, a method was obtained for
choosing the optimum number of observations to be
utilized in the interpolation program for each time series.
This consisted of an iterative technique for examining
observations on each side of the interpolated point SO
that: 1) a minimum number of observations were utilized
November 1968 A. 0. Belmont and 0. G. Dartt
0
769
0
--2 5
--5 0
as determined from the decay of interpolation error with
increased number of measurement, 2) more observations
than necessary are not used as the matrix inversion
determining regression coefficients can become a time
consuming operation, and 3) two-sided interpolation is
used whenever possible. Usually from four to 10 samples
were used for interpolating a missing data point; fewer
data are used when the samples are quite dense. The
optimum weights were then computed and the interpola-
tion in terms of existing data was accomplished. I n addi-
tion, statistical interpolation errors were determined for
each estimated value.
FILTERING
As discussed previously, it is desired to pass the combi-
nation of interpolated and sampled data through a digital
filter in order to isolate the quasi-biennial oscillation. This
filter must be chosen to attenuate the annual cycle and
higher frequencies where much of the spectral energy of
the wind is located. However, the selection of the filter
must also consider the number of weights involved because
the length of the transient-free filtered output is equivalent
to the length of the time series being analyzed minus the
number of filter weights. For many stations there are only
enough sampled data to contain one or two cycles of the
quasi-biennial oscillation, therefore the number of filter
weights must be conserved in order to examine any
maximum or minimum. This creates a further problem as
many filter weights are required to produce a filter whose
frequency response has a sharp cutoff without any un-
desirable side lobes.
Because of the necessity of masking almost entirely the
annual cycle, it appeared that filters with side lobes would
have to be considered. Examination of several filters
showed one particular truncated cosine filter to be prom-
ising because of its zero response at the frequency of the
annual variation and because of thwelatively few weights
required. The weights of this slter are given by:
0
wt(n)=1.65(.rr/2N) cos (1~/2N) (N-2n)
n=O, 1, 2, . . ., N, (1)
-7 5 - --7 5
0 where N is the total number of weights required over an
18-mo. period. The frequency response of the filter, R(w),
is given by:
--2 5
---50
R(w)=1.65(~/4) (cos 9W+T/2 (9w) - cos 9W-.rr/2 (9"') ' (2)
where w is radial frequency. Both the above equations
have been normdized so that the frequency response of
the filter at w=2~/26 mo. is 1. Figure 1 indicates the
weighting and response functions of the cosine filter. This
filter and a 365-day running mean were considered for
analysis of the data. Figure 2 shows the result of passing
a time series of data for Nairobi through both filters. As
higher frequencies are significantly more evident in the
filtered output of the running mean, the cosine filter was
chosen for use on all data.
321-265 0-68---3
FILTER WEIGHTS
5r
18 18 18 18 - 2r - -2 7 0 - - 5r -
RADIAL FREOUENCY ( rad. /mo. 1
FIGURE 1.-(A) Cosine filter weights and (B) frequency response of
cosine filter.
+3 0 ~
t20 I I
1
- 40
770 MONTHLY WEATHER REVIEW Vol. 96, No. 11
Quantanamo'. _______.._
Swan Island* _____.__._._
San Andreas'.. . ______..
Niamey ____....._.....__
Aden ______......_____...
Bangkok ....._.._.___...
Guam--. - -. . -. - -
~
-
~
~. . . .
Kwajalein. __...._.______
Balboa* __.......______..
Canton' ...-- -. - - -. -. . . - -
~U8y8qUfi* ____._.______
Nairobi ___..____......__
Lima*--.. - - -. . . . . -. - -. . -
cocos _.__...___.......__
Danvin __.__......__....
Quintero' _.___...._...__
Capetown _._.__......___
Willismtown __...____..
~
the extreme values will vary accordingly. The mean square
error, 2, of a single point in the filtered time series can be
represented (after Cramer [9]) as:
19"54'N.
17"24'N.
12'35".
13°29'N.
12°50'N.
13'44".
13'33".
08'43".
08'56'N.
02'46's.
02'12's.
0lo18'S.
12°00'S.
12005'5.
12'26's.
32'47%
33O58'S.
32'49'5.
where E is the statistical expectation, ai are the N filter
weights, et are the interpolation errors for the N data
points underneath the filter and hik is the covariance
error matrix of the N data points. A property of the op-
timum interpolation method utilized is that the inter-
polation errors are orthogonal among themselves and also
to the existing observational points. As a result only the
diagonal of the covariance error matrix needs to be
considered and equation (3) may be written:
N
i= 1
g2= a:hti. (4)
Thus the error of a single-filtered output value can be
simply represented as a weighted average of the mean
square errors, e:, of the interpolated points underneath
the filter. It is to be noted that where observational points
occur, their mean square error is zero.
The above technique was utilized to determine the
accuracy of extreme values in the filtered time series.
Instrumental errors were not considered, as their magni-
tude and behavior are not generally known. These errors,
if known, could be incorporated into the analysis; how-
ever, a correlation would then exist between the errors in
the interpolated values and the instrumental errors as-
sociated with sample points. As a result, the error in the
filtered output would be tedious to compute as equation
(3) must be used.
It is desirable that the RMS error of extreme values in
the filtered time series, u, be transformed into correspond-
ing errors in time, of the calendar dates of these minima
and maxima. This would permit a direct comparison
among time series of the reliability of respective extremes.
However, to do this, it is necessary to know the joint
probability density function of the filtered data. This
requires knowledge of the true functional form of the
zonal wind data and of the joint probability density func-
tion of the errors associated with the points in the filtered
time series. As these are not known, the assumption was
made that the density function of an element of the
filtered time series was "Gaussian normal'' with a mean
equivalent to the value of that element, and with a stand-
ard deviation, u. When applied to extremes, the probabil-
ity that a maximum (minimum) is greater (less) than the
mean minus u (plus u) is therefore 84 percent. The time
interval in which the extreme value is known with 84-per-
cent confidence is then found by examining the filtered
data in the neighborhood of this point. For a maximum,
this interval is defined as the time differexe between
those filtered values equal to the extreme value minus u,
located on either side of the extreme point. (For a mini-
mum, the filtered values involved are equivalent to the
extreme value plus u.) Because the filtered data are not
necessarily locally symmetric with respect to the extreme
point, the time difference may not be equally distributed
with respect to this point.
TABLE 1.-Available percentage of all scheduled 12- or 24-hr. observa-
tions, for the time interval from 9 mo. before to 9 mo. after the periods
of record shown i n figures S and 4 . An asterisk indicates stations
taking 12-hr. observations.
Percentage of Complete Data
75~06' w .
83%'W.
81"40'W.
02°1VE.
45'01'E.
100'3VE.
144O5VE.
167'44'E.
79034' w.
171'43'W.
78053'W.
36'45'E.
77'07'W.
96053'E.
130'52'E.
71'32'W.
18'36'E.
151'50'E.
47
67
47
57
46
26
85
41
61
a4
45
10
46
49
62
68
18
40
11
2" s
100 mb. (55,000ft.)
53
76
59
67
71
33
92
53
73
92
53
77
54
86
87
68
45
79
500 mb. (20,000 ft.)
I L 4 d l
70
96
85
77
85
49
97
88
86
98
68
94
70
96
96
97
95
95
12" s
33"s
FIGURE 3.-Filtered zonal winds, 50 mb., for all stations, plus 100
and 500 mb. at Swan and Guantanamo.
3. DATA
Table 1 indicates the 16 stations at five selected
latitudes between 13"N. and 33"s. for which daily data
were examined at the 50-, loo-, and 500-mb. levels.
Because of the strong dependence of QBO phase on
latitude, stations were selected dong each latitude so
that each station was not more than 1" from that latitude.
Obviously this severely limited the stations which could
be used and they were not those with the longest and most
complete or reliable observations. Further, i t was neces-
November 1968 A. D. Belmont and D. G. Dartt 771
sary to limit analysis to common periods of record at
all stations along a given latitude as we intended to
compare phase dates of the same wave. Swan Island and
Guantanamo were originally included along 80"W. to
establish a latitudinal correction that could be used to
correct for small latitude variations within each station
group. However, the results showed so much time varia-
tion of the QBO with latitude from one cycle to the next
that it was decided such corrections were inadvisable.
Rather, phase dates of each cycle were plotted on maps.
This permitted isochrones to be drawn which showed the
progression of the wave both in longitude and latitude
without the need to make assumptions concerning rate
of latitudinal progression.
4. RESULTS
50 MB.
Graphs of the quasi-biennial oscillation at 50 mb. are
shown in figure 3 for those periods of record which were
common t o stations at the same latitude. The amplitudes
of the QBO have been restored (at 26 mo.) to compensate
for the attenuation of the filtering process, and are drawn
to the same scale so that stations and levels may be
compared directly. In doing this, however, the maxima
and minima at 100 mb. and 500 mb. become indistinct
a t times. As the Australian data were available only for
constant heights, the waves at the nearest 5,000-ft. level
both above and below the 50-mb. level are shown. All
phase dates were extrapolated for the mean 50-mb.
height which at Darwin was 67,850 ft., at Cocos 67,750
ft., and at Williamtown 67,950 ft.
The magnitudes of the 50-mb. filtered time series show
predominately the normal amplitude variation with lati-
tude described in the literature. The wave appears
strongest near the Equator and progressively weaker at
subtropical latitudes. However, there are some noticeable
exceptions to this general pattern. For instance, near the
Equator, Nairobi exhibits a magnitude (3 m./sec.) much
weaker than Canton Island (20-40 m./sec.). Further, at
32's. Williamtown's variation (5-10 m./sec.) is stronger
than the variation at either Quintero or Capetown (3
m./sec. or less). The apparent increase with time of the
magnitude of the QBO leading to extreme variations in
1962 and 1963 can be seen a t all stations; higher latitude
stations indicate this increase at somewhat later times.
The asymmetry of the amplitude about the Equator can
be seen by comparison of the magnitudes of the variation
at 13'N. (13 m./sec.) and 12's. (13-20 m./sec.). Further,
the magnitude a t those stations along 33's. (3-10 m./sec.)
is somewhat larger than at Guantanamo, 21'N.
(3-7 m./sec.).
The interpolation errors, when interpreted in terms of
days, result in uncertainties of the phase date which at 50
mb. ranges from about 15 days a t Guam, Balboa, and
Canton to as high as about 50 days at stations where the
amplitude of the wave is weak or where the data are
very incomplete, such as at Guantanamo, Aden, and
Quintero. At Capetown and Williamtown the possible
errors are so large as to make the filtered waveform highly
uncertain. So many observations are missing a t these
stations that the average time variation of a maximum or
minimum is about f 7 5 days. I n almost every instance the
uncertainty varies from cycle to cycle as the amplitude
of the wave changes and the density of observations
varies. These uncertainties make time and space variations
of the QBO very difficult to interpret. No solution to this
problem seems possible without complete and accurate
observations at high levels. Nor can these uncertainties
be ascribed to the interpolation methods used. In fact
Gandin [6] has shown that the optimum interpolation
technique utilized is superior to other methods, particularly
in regions of sparse data. Further, one of the merits of this
technique is that errors in interpolation may be approxi-
mated, whereas in several other interpolation or averaging
schemes, such errors are intrinsically present in the result
but cannot be determined. It should also be realized that
the calendar dates of the extreme values are still the most
probable times of occurrence.
In view of these problems one must rely as usual in
meteorology on consistent results from independent data
in a given area. Hence, we can only hope to suggest
directions of progression where the data appear to be
consistent and not to prove them. By the same token,
inconsistent results a t this time are simply inconclusive.
Figure 4 maps the dates of the four minima and maxima
a t 50 mb. given in columns 2-5 in table 2. The letters E
and L refer to relatively early and late phase dates.
Month and "dy are indicated at IO-day intervals. In
addition to the usual progression from subtropical toward
equatorial latitudes there is an apparently strong tendency
for a west to east movement from southern Asia toward
the South Pacific. Further, the dates in the Caribbean
appear to be consistently earlier than those anywhere else.
The stations near 33"S., if they can be believed a t all, are
in a completely different regime from lower latitude
stations.
100 MB:
Figure 5 shows the filtered time series at 100 mb. and
also 500 mb. Zonal winds a t 55,000 ft. were analyzed at
the Australian stations. As the mean 100-mb. heights for
these stations are within approximately 1,000 ft. of this
level, no interpolation was used.
It can be seen that the 100-mb. waveform is generally
weaker and intermittently biennial as compared to 50 mb.
For some periods the series at these two levels are well
correlated, i.e. Swan Island and Guantanamo, 1958-1960 ;
other time intervals show practically no similarity between
the 50- and 100-mb. levels, i.e. Balboa, 1956-1962. Near
the Equator the 100-mb. time series exhibit a fairly
regular QBO with a magnitude of about 5 m./sec. Farther
north, however, the time series are more irregular and with
generally a weaker variation. I n the Southern Hemisphere
the magnitude of the filtered waveform is much the same
as at the Equator, however, the biennial pattern is less
regular. For instance, Williamtown exhibits a marked 4-yr.
period for the segment of data analyzed.
Table 3 shows that the time separation among respec-
tive maxima and minima of various stations a t 100 mb.
772 MONTHLY WEATHER REVIEW Vol. 96, No. 11
5 0 MB
40 N
30 N
20 N
IO N
0
2 O I O s IO s
3
4
5
120W 9 0 W 6 o W 30W 0 3 0 E 60E 9 0 E 120E
. 130s 20 s
-L //-/%58
180 150W 120W I 5 0 E
40 N
30 N
20N
10 N
0
IO s
2 0 s
3 0 S
-. - .. . .. . - . .
120w 9ow 6ow 3ow 0 3 0 E 60E 9 0 E 120E 150E 180 150W 120W
40
30
20
IO
0
IO
2 0
30
I 2 0 w 9 o w 6 o w 3 o w 0 3 0 E 60E 90E 120E 150E 180 150W 12OW
IO s
20s
30 S
I O s
2 0 s
30 S
120w 9ow 6ow 3ow 0 3 0 E 60E 9 0 E 120E 150E 180 150W 120W
FIQTJRE 4.-Phase progression of the quasi-biennial oscillation at 50 mb. in the Tropics. The particular maximum or minimum analyzed is
indicated by a correspondence of map number in the above figure and column number in table 2.
is of the order of months rather than days as was evident
a t 50 mb. As a result there is more difficulty in identify-
ing corresponding extremes for different stations. This
selection of corresponding maxima and minima was done
subjectively by comparing the total time history of
extremes for neighboring stations and taking into account
the similarities of the filtered waveforms a t the 50-, loo-,
and 500-mb. levels. The uncertainty of phase dates is
larger at 100 mb. than at 50 mb. This reflects a propor-
tionally larger loss of amplitude of the QBO between 50
November 1968 A. D. Belmont and D. G. Dartt 773
Quantanamo _____ Swan-
San Andress. - Niamey
Aden
Bangkok
Quam
Balboa ..............................................
Kwajalein .....................................................
ouayaquil..~_-
Nairobi-
Canton..
Lima
Cocos-.
D ~n
Quintero
Capetown
willtamtown.
TABLE 2.-Calendar dates (yr., mo., and day) of 60-mb. maxima and minima
Phase Dates (+ Max; - Min)
.....................................................................................
................................................................................................
........................................................................................
................................................................................................
..................................................................................................
..............................................................................................
.................................................................................................
520610 530705 640903 551013 561216
530821 640902 551011 561205
..............................................................................................
.............................................................................................
..................................................................................................
...............................................................................................
..............................................................................................
.......................................................................................
...............................................................................................
.............................................................................................
........................................................................................
Stations 1 -1 +1 -1 +1 -
600929
601201
601201
601214
601212
601229
601129
601202
601112
601123
601206
600205
600512
600725
611130 620930 631213
611116 630208 640401
611222 630325 ..........
................... 630412 ..........
.......................................
.......................................
611225 630220 ..........
620106 ....................
611229 ....................
.......................................
..............................
620129 ....................
..............................
611210 630516 ..........
611220 630527 ..........
610504 620624 ..........
610706 630625 ..........
610907 621102 631227
I
590221
590101
571231 590118
.........
580107
580109
571227
.........
.........
.........
.........
._ ___ -. - -
.........
.........
.........
590106
5'20113
590117
590124
590129
590210
590222
590217
590125
590207
580903
581130
..................
..................
3+
580226
580211
571109
571104
571006
571110
580301
580511
580817
580828
581014
581203
571017
.........
- .-..__ ~.
.........
.........
- --..__ _-
591031
591119
591216
590311
590211
590212
590808
600127
601028
590820
590728
590910
590526
590321
591024
600808
600211
580512
590116
581003
no
591225
591222
600103
600110
600122
610116
610221
600625
611208
620107
620710
610403
610908
610211
600223
600116
600108
630612
621025
620521
621004
630417
630408
630116
.........
611202
600207
590604
590707
590701
630905
630228
630406
.....................
4- I 5+ I 6- I +
....................
..........
..........
..........
....................
.. ....................
....................
Quantanamo
Swan.
San Andreas.-.
Niamey-.
Aden
Bangkok--
Quam..
Balboa ..............................................
Kwajaleiu .....................................................
Guayaquil--.
Nairobi.
Canton
TABLE 3.-Calendar dates (y t ., mo., and day) of 100-mb. maxima and minima
Phase Dates (+Max; - Mixi)
..........................................................................................
................................................................................................
.......................................................................................
.............................................................................................
..................................................................................................
............................................................................................
...............................................................................................
530111 531111 550119 no no
640402 540813 551025 570726
..............................................................................................
..............................................................................................
.........................................................................................
Stations l -l +l -l +l -
630216
620401
630531
621021
....................
....................
....................
....................
....................
..........
630427
..........
-. - - -. . -. .
Lima ............................................... -1 ......... -1. ------.--I ......... -1. ......... I. ........
611209
610215
610825
620813
610821
591113
600429
no
.........
.........
620804
631104
620517
610507
620512
no
I+ 1 2-
cocos
Darwin-.
Quintero.
Capetown
williamtown _____ .- __ __,_ __ .- __ __ _____ .- .-- .- __ __ -__
................................................................................................
............................................................................................
............................................................................................
............................................................................................
- -. __ ___. - _-_. __ .- _. -. __ -.- -. - ___ __ __ .- __ ____ -.-
3+
591125
591212
591008
601026
601022
611010
600824
no
600525
601008
600422
601005
611003
601125
590522
590923
600818
,.... ......,..........
and 100 mb. than can be compensated for by the increased
sampling rate at the lower level. (The relative uncertainty
can be interpreted in terms of a simple signal-noise ratio.)
It is to be noted that even though the uncertainty is
larger at 100 mb. than a t 50 mb., wave progression may
be more reliable at 100 mb. because the time interval of
progression between stations generally exceeds the phase
date error, whereas at 50 mb. these time intervals are
about the same. The 100-mb. phase date variability is
also much more asymmetric with respect to the mean
extreme date than at 56 mb. This is due to the increased
irregularity of the filtered waveform. At 100 mb. the
QBO is not only weak, but apparently skips a cycle oc-
casionallly so that a 4-yr. cycle appears at Balboa (but
not at Kwajalein at the same latitude) and at Capetown
and WiUiamtown, during the limited period of record.
20s
12"s
FIGURE 5.-Filtered zonal winds, 100 and 500 mb.
774 MONTHLY WEATHER REVIEW Vol. 96, No. 11
2
3
4
5
I00 MB.
- - 40N
30 N
20N
IO N
0
7-59
3 0 E 60E 9 0 E 120E 150E 180 150W- 120W
. -- . . __
i 20N
. 3 0 s
-7 40 N
i 30N
I20N
1 ION
1 0
.
j 10s
120W 9 0 W 6 0 W 3 0 W 0 3 0 E 60E 9 0 E 120E 150E 180 150W - 120W
FIQURE 6.-Phase progression of the quasi-biennial oscillation at 100 mb. in the Tropics. The particular maximum or minimum analyzed is
indicated by a correspondence of map number in the above figure and column number in table 3.
Figure 6 shows that a t 100 mb., as a t 50 mb., the areas
of earliest occurrence are in the Caribbean, and possibly
southern South America. The wave progresses both east-
ward and westward and appears last over southern Asia,
with a time lag of 6 mo. to 2 yr. Neighboring stations
show continuity even in the presence of quite large statisti-
cal interpolation uncertainties. In general, the patterns
are more cellular than they are simple functions of lati-
tude or longitude.
The analysis of phase progression a t 33"s. is somewhat
complicated as Williamtown does not exhibit a biennial
wave at 100 mb. Rather, this station appears to have a
4-yr. cycle a t least during the interval from 1958 to 1963.
However, some of the extremes at 100 mb. appear well
November 1968 A. D. Belmont and D. G. Dartt .
TABLE 4.-Calendar dates (yr., mo., and day) of 600-mb. maxima and minima
4-
610324
610808
610223
611227
620403
620610
611228
610206
610121
610712
610501
620717
610804
600604
610618
610831
775
5+ 6- + -___-___
631024 ....................
630517 ....................
630503 ....................
620904 630423 ..........
..............................
..............................
630218 ....................
..............................
..............................
.......................................
.......................................
..............................
620730 630429 ..........
630519 ....................
620312 630215 ..........
610508 620623 ..........
620807 630530 640203
620925 630709 ..........
Phase Dates (+ Max; - Min)
Quantanamo .................................................
Swan ........................................................
San Andreas- ................................................
Niamey.. ....................................................
Aden- .......................................................
Bangkok .....................................................
Guam. .......................................................
Balboa ..............................................
Kwajalein-.-. ................................................
Quayaquil- ..................................................
Nairobi. .....................................................
Canton. .....................................................
Lima .........................................................
cocos ........................................................
Darwin ......................................................
Quintero. ....................................................
Capetown ....................................................
Williamtown. ................................................
Stations ~-~+~-l +l -l 1 +l 2 -
520201 521112
540414
........................................ 580226
........................................ 680111
........................................ 571013
.............................. 580331 600101
.................... 570815 580410 590308
........................................ 590211
.............................. 580124 590214
530803 55097.4 560725 570603
550122 560519 570218 571220
.............................. 581116 590804
........................................ 580713
........................................ 590313
........................................ 580709
.............................. 580415 590325
.................................................
.................................................
.................................................
........................................ 580421
590427
590213
590111
600502
601216
601107
591109
580910
590705
590727
610329
590719
591030
590803
600217
580718
590619
3+
600527
600404
600404
610218
610512
610830
600911
600503
600505
- - - - -. . -.
.........
600312
600531
610616
601026
590617
600418
correlated in time with the quasi-biennial oscillation at
50 mb. Also, these extremes appear to be more closely
related t o the neighboring stations, Darwin and Canton,
than to Quintero and Capetown. It can be noted that for
every extreme the filtered waveform a t Quintero leads that
a t Capetown.
500 MB.
Figure 5 and table 4 indicate the filtered time series a t
500 mb. zonal winds a t 20,000 ft. were analyzed for the
Australian stations. The mean 500-mb. height is generally
800-1,300 f t . lower than this level.
The 500-mb. filtered time series shows intermittent
quasi-biennial features similar to those a t 100 mb. However,
the 100-mb. levels a t Balboa and Williamtown did not
exhibit quasi-biennial waveforms, yet these stations do
have quasi-biennial features at 500 mb. Also, the magni-
tude of the QBO is somewhat weaker a t 500 mb. as com-
pared to the higher level. A tendency exists for the
magnitude of this fluctuation to increase with latitude,
the reverse of what is normally found in the stratosphere.
The relative errors a t 500 mb. are somewhat smaller
than a t 100 mb. Thus, the increase of measurements
at the lower level overcompensates for the slight decrease
in magnitude of the QBO, but the lack of vertical corre-
lation of this level with 100 and 50 mb. makes it more
difficult to identify corresponding maxima and minima.
In figure 7, the features are quite similar to those
observed a t 100 mb. Extremes appear to originate in
either or both the Northern and Southern Hemisphere
in the vicinity of 8O"W. andpropagate both eastward and
westward, finally occurring latest in the Indian Ocean.
It should be realized that the large-scale map features
at 500 and 100 mb. depend a great deal on how the stations
along 32"s. are incorporated into the analysis. At 500 mb.
Williamtown is in phase with Capetown but out of phase
with Quintero. Further, Williamtown is approximately in
phase with stations at other latitudes in the southwestern
Pacific. However, Quintero is out of phase with Lima,
the closest neighboring station. As a result, several
interpretations of extreme progression are possible:
(a) Williamtown and Capetown lagging Quintero, (b)
Williamtown and Capetown leading Quintero, and (c)
Williamtown leading Quintero leading Capetown. Which
one of these interpretations is preferred depends on
whether one assumes vertical continuity, horizontal
continuity, or a combination of both. For instance, (a)
is the analysis we have chosen and utilizes vertical
continuity to establish the relationship between Lima
and Quintero and primarily horizontal continuity to fit
Williamtown to neighboring stations. An analysis based
on (b) would tend to establish more or less uniform hori-
zontal progression from Northern to Southern Hemisphere
and does not take into account vertical continuity. The
pattern (c) would produce a more or less uniform pro-
gression pattern in both hemispheres, but, with separate
areal origins and terminations in each hemisphere. This
case demands that horizontal continuity be maintained
in a certain preconceived fashion. As the QBO exists at
higher latitudes than is shown on these maps, the global
pattern cannot be described at this time. Data from all
available upper air stations are now being plotted,
however, and the analysis will be reported in a later
paper.
5. SUMMARY
At 50 mb. evidence of longitudinal progression of
maxima and minima of the quasi-biennial zonal wind is
present. The progression generally appears to be from
west to 'east, although many irregularities from one cycle
to the next are apparent. Differences in phase dates for
stations located at approximately .the same latitude
range from a few days for equatorial stations to 5 mo.
for locations along 32"s. Uncertainties in phase dates
due to the use of interpolated data are usually larger
than the differences in arrival times of maxima or minima
at neighboring stations. However, because consistent
progression behavior is found within certain areas, even
in the presence of such large errors, the analysis may still
suggest real features of the circulation.
7 76
...........
~. --y
1-63
\ / \ ---lo
-'
....
Y
MONTHLY WEATHER REVIEW Vol. 96, No. 11
40N
30 N
20N
IO N
IO s
20s
30 S
I
2
3
4
5
500 MB. ..... 40N
i 30N
i20N
j ION
10
~
13s
1 7 5 9 , 20s
30 S
.~. -----_I 0 3 0 E 60E 90E ' 120E 150E 180 150W 120W
30 N
20N
ION
0
76/
120w 9ow 6Ow 3ow 0 3 0 E 60E 90E 120E 1 5 0 E 180 1 5 0 W 120W
n E
20 s
30 S
120w 9 o w €ow 3ow 0
I
3 0 E 60E 90E
I I
: 120E 150E 180 1 5 0 W 120W
FIGURE 7.-Phase progression of the quasi-biennial oscillation a t 500 mb. in the Tropics. The particular maximum or minimum analyzed
is indicated by a correspondence of map number in the above figure and column number in table 4.
November 1968 A. D. Belmont and D. G. Dartt 8
777
At 500 and 100 mb., although the quasi-biennial
oscillation is intermittent and weak in magnitude, progres-
sion is still evident. Tentatively, at these levels, the wave
appears to originate in subtropical latitudes in the vicinity
of 80”W. of both hemispheres and progresses both east-
ward and westward, occurring last in the Indian Ocean.
The entire progression time generally ranges from 1 to
2 Yr*
Due to the irregularity at these levels and slow speed
of the QBO between stations, it is sometimes quite
difficult to trace corresponding maxima and minima on a
global basis. It is quite possible that the QBO at 100 and
500 mb. has a cellular rather than a continuous pattern
of phase progression. Analyses of additional stations will
clarify the interpretation. In general, interpolation un-
certainties at 500 and 100 mb. are somewhat larger than
at 50 mb. The decrease in magnitude of the QBO with
decreasing altitude is not completely compensated for by
the increase in the number of observations available for
analysis at the lower levels. However, the results may
still be more significant at the lower levels than at 50 mb.
because of the much longer transit time of the QBO
be tween stations.
The above analysis apparently does not indicate any
new properties that confirm or deny either an external or
internal origin of the QBO in the atmosphere. Rather, it
shows the natural irregularity in the atmosphere at low
frequencies that of course has been observed many times
at shorter time scales.
Future work includes the expansion of the analysis to
higher latitudes and other levels utilizing a more dense
station network to obtain better continuity and to help
identify corresponding waves.
It is recommended that a series of long-term, scientific,
upper air stations be arranged carefully along a few
chosen latitudes and one meridian to obtain more com-
patible, accurate and complete data concerning this
global phenomenon whose properties are still poorly
described and whose cause is still completely unknown.
Perhaps after 10 or 20 yr. with such data its properties
can be described properly.
REFERENCES
1. R. J. Reed, “The Present Status of the 26-Month Oscillation,”
Bulletin of the American Meteorological Society, Vol. 46, No. 7,
July 1965, pp. 374-387.
2. H. E. Landsberg, J. M. Mitchell, Jr., H. L. Crutcher, and F. T.
Quinlan, “Surface Signs of the Biennial Atmospheric Pulse,”
Monthly Weather Review, Vol. 91, No. 10-12, 0ct.-Dec. 1963,
3. G. M. Shah and W. L. Godson, “The 26-Month Oscillation in
Zonal Wind and Temperature,” Journal of the Atmospheric
Sciences, Vol. 23, No. 6, Nov. 1966, pp. 786-790.
4. J. K. Angel1 and J. Korshover, “Harmonic Analysis of the
Biennial Zonal- Wind and Temperature Regimes,” Monthly
Weather Review, Vol. 91, No. 10-12, Oct.-Dec. 1963, pp. 537-
548.
5. G. E. Edmond, “An Analysis of Tropical Stratospheric Winds
by Means of a Band Pass Filter Technique,” Meteorological
Magazine, Vol. 94, No. 1119, Oct. 1965, London, pp. 304-308.
6. L. S. Gandin, “Objective Analysis of Meteorological Fields,”
(Translated from Russian book, Gidrometeorologicheskoe
Izdatel’stvo, published in Leningrad, 1963), Israel Program
for Scientific Translations, Jerusalem, 1965, 242 pp.
7. D. P. Peterson and D. Middleton, “Linear Interpolation,
Extrapolation, and Prediction of Random Space-Time Fields
With a Limited Domain of Measurement,” IEEE (Institute
of Electrical and Electronic Engineers, Inc.) Transactions on
Information Theory, Vol. IT-11, No. 1, New York, Jan.
8. C. E. Buell, “Two-Point Variability of Wind,” Kaman Nuclear
Report, (AFCRL-62-889), No. KN-173-62-2 (FR), Vol. 1-3,
Kaman Nuclear, Colorado Springs, Colo., July 1962, 152,
205, and 165 pp.
9. H. Cramer, Mathematical Methods of Statistics, Princeton
University Press, N.J., 1961, 575 pp.
pp. 549-556.
1965, pp. 18-29.
[Received January 11 , 1968; rewised May 1 , 19681
NOTICE TO AUTHORS
Miles F. Harris, Chief of the Scientific Review Group in ESSA’s Scientific
Information and Documentation Division, was appointed Editor of the
Monthly Weather Review on September 1, 1968. The January 1969 number
(Vol. 97, No. 1) will be the first issue under his editorship. Manuscripts and
correspondence should be addressed to :
MILES F. HARRIS, Editor
Monthly Weather Review
Scientific Information and Documentation Division
Environmental Science Services Administration
Rockville, Maryland 20852
321-266 %6 8 4