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Appendix E
TREND ANALYSIS OF TOTAL OZONE
Hans A. Panofsky
Department of Meteorology
Pennsylvania State University
INTRODUCTION
Total ozone has been measured at Arosa for almost 50 years
by the Dobson spectrophotometer. The number of Dobson
stations in the global observing network increased slowly
at first, but more rapidly since the late 1950s. Measure-
ments made with instruments developed in the USSR were
included in the network system after 1958, but their
reliability approached that of the Dobson measurements
only since about 1972. Most of the observing stations
are on continents and in the northern hemisphere.
Analysis of these records by Angell and Korshover
(1981) reveals considerable differences in long-term
variations from region to region; but, on the average,
trends appear to be mostly positive in the 1960s and near
zero in the 1970s. As we will see, more recent analyses
based on sophisticated statistical models suggest positive
trends in the 1970s, which are, however, not significantly
different from zero.
Whereas it is relatively easy to estimate trends from
Dobson data, it is much more difficult to ascribe such
trends to specific causes. There may have been trends in
variables such as dust that influence the measured ozone
but not necessarily the actual ozone; there may have been
real changes of ozone due to changes in circulation of
the atmosphere; there may have been changes of temperature
or of various trace elements that influence the ozone
budget; and there may have been influences of solar varia-
tion. Further, the Dobson network may not be representa-
tive of global averages.
As we shall see, some causes of trends in Dobson-
measured ozone can be evaluated by sophisticated
statistical analysis; for other causes we can only make
some not very well educated guesses.
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Ultraviolet satellite measurements of total ozone
trend largely avoid the problem of spatial represent-
ativeness (not completely, because the dark polar cap
remains unobserved). However, satellite records so far
are relatively short and have other deficiencies. Esti-
mates of total ozone have been made by backscattered
ultraviolet (B W) on the Nimbus 4 satellite beginning in
April 1970. However, this instrument initially suggested
global averages 3 to 4 percent less than the total Dobson
averages. This difference increased further over 81
months due to instrumental drift. In addition, failure
of a solar panel in June 1972 reduced the number of
observations after that date, introducing a problem of
spatial representativeness of the trends over the whole
81 months. The Solar Back-Scatter (SB W) instrument on
Nimbus 7, operational since 1978, did not have these
problems (see Hudson et al. 1982). But the period of its
operation so far is too short to make reliable trend
estimates.
In principle, however, satellites should eventually
lead to better trend measurements than Dobson instruments
for two reasons: (1) there is better spatial
representation, and (2) only one instrument is used,
whereas the different Dobson instruments have separate
idiosyncrasies and errors. Gradual instrumental drift
could be estimated by comparison with a well-calibrated
Dobson network.
Pittock (see Hudson et al. 1982, p. 3-46) estimates
that eventually satellites will be able to detect True
global trends" with standard deviations of the order of 1
or ~2 percent from observations by the same satellite over
10 years. Such trends, of course, could have man-made as
well as natural causes. So far, satellites, just as
Dobson instruments, have not suggested any significant
trend in total ozone.
Most recent physical models also suggest very little
ozone change due to human interference. Therefore there
is, at present, no real disagreement between statisti-
cians and physical modelers.
The main disagreement remaining concerns the extent to
which statistical analysis can be used as an early
warning system for the future.
For the Dobson network, there are two main problems:
first, how representative is the Dobson network of the
global ozone distribution? This problem has been attacked
by use of satellite data. The results are somewhat
controversial, as we shall
see.
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The second difficulty involves the importance of
"natural" variations over long periods. This question
has been attacked by studying the relatively long Arosa
record. Again, the results are controversial. For
satellite early warning, only the second problem is
important.
STATISTICAL ANALYSIS OF THE DOBSON NETWORK
Three separate groups of statisticians (Bloomfield et ale
1981, Reinsel et al. 1981, St. John et al. 1981) have
analyzed monthly averages at 36 Dobson stations with
records over 10 years long. Their studies differ in
detail but have many common features: the results also
are quite similar.
All of the groups originally based their analyses on
the "hockey stick" or "boomerang" approach. They argued
that since there was no obvious cause for the upward
trend in the 1960s, the observed upward trend must be due
to "red noise"--natural long-period variations. Therefore
the "true" long-range trend up to 1970 was assumed to be
zero. Given this zero trend, estimates for the Dobson
mean trend in the 1970s were made by various statistical
procedures. Such trends were generally positive (Figure
E.1) but did not differ significantly from zero.
1960 1970 1980
YEAR
FIGURE E.1 Typical ozone variations with time, and "hockey stick" fit (solid line).
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Bloomfield et al. (1981) also produced separate trend
analyses for the 1960s and 1970s (no hockey stick
assumed), and obtained a near-zero trend for the 1970s.
Further possibilities tested by Bloomfield et al.
(1981) were based on assumed relationships between ozone
and nuclear tests, and between ozone and solar activity.
Although the trends in the 1970s derived from this
analysis did change somewhat, they still are not
significantly different from zero.
With 36 individual trends, it has been possible to
assess the uncertainty in the mean trend of the 36
stations, based on the 10- to 20-year records.
Statistically, this variability from station to station
was split into (1) random effects at each station; (2)
variation among stations in each region (the regions are
large, e.g., North America is a single region); and (3)
variation among regions. However, it should be noted
that these three sets of differences cannot be associated
with physical causes on a one-to-one basis.
For example, "random" errors are introduced in the
monthly averages by missing data, by the effect of large
variations with periods of the order of a week, by local
air pollution episodes or clouds, or simply by observa-
tional error.
Variations in trends within regions are primarily due
to different weather at the stations in the same region.
Different weather implies real differences in ozone, and
also differences in observational accuracy; e.g., clouds,
which interfere with the accuracy of the ozone observa-
tions. Also, rates of deterioration of instrumental
parts may be different, and calibrations may have been
performed at different points in the solar cycle.
Weather differences are even more important in
different regions; further, each region uses different
secondary standards for instrument calibration.
All groups agree that the standard deviation of
average trend derived from these stations, due to a
combination of all these factors, is about 0.6 percent
per decade. However, the question of trend "bias" due to
the assumption of the "hockey stick" model has been
raised frequently and requires further analysis.
SPATIAL BIAS
In principle, it is possible that trend estimates from
the Dobson network would differ systematically from
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global trends; e.g., if ozone moved from land areas to
ocean areas for an extended period, there might be an
indicated ozone change but no real global trend.
Three techniques have been used to estimate the bias
of global trend estimated from the Dobson network. In
the first technique, Hasebe (1980) has estimated total
ozone values at grid points over the world from the
Dobson network by a process called "optimum interpola-
tion." However, since there are huge areas of no ozone
stations, particularly in the southern hemisphere, the
interpolated (and sometimes extrapolated) values in such
areas are extremely uncertain. Hasebe computes global
trends from these grid-point values. These do not differ
significantly from those estimated by Angell and
Korshover (1981). In any case, it is unlikely that
Hasebe's techniques for estimating global trends are
necessarily superior to the simpler methods used by the
earlier authors.
In a second technique, Moxim and Mahlman (1980)
compared global trends with Dobson location trends as
computed from a "simple" three-dimensional numerical
global model of the atmosphere, containing ozone. They
find differences between one-year trends computed from
monthly averages between global and Dobson location ozone
of the order of 1 percent.
Finally, several groups of authors have attempted
estimates of spatial bias by use of the B W satellite
observations, described in the introduction. Of course,
it is difficult to evaluate the accuracy of these
comparisons, since the B W instrument deteriorated after
several years, and reliable trends over periods longer
than three years or so could not be computed.
London and Ling (1981) compared global total ozone
with Dobson location ozone and found only small mean
differences, but large standard deviations of these
averages. However, they did not compare trends.
Reinsel et al. (1982) compared statistics of ozone
trends all over the world with data for April 1970 to May
1975 with those of ozone trends in small areas surrounding
a select group of 36 Dobson stations. They found no
statistically significant differences in this one small
sample covering only a few years. The authors concluded
from this result that there are no differences between
global trends and trends derived from Dobson station data.
Meteorologists are doubtful about this conclusion and
suggest standard deviations of global trends due to Dobson
location bias could well be of the order of 1 percent per
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decade. This order of magnitude is also suggested by
satellite records analyzed by A.J. Miller (see Hudson et
al. 1982), and is somewhat smaller than what would have
been expected from Moxim and Mahlman's model study. In
fact, the results of
significantly from an assumption of a bias of decadal
average Dobson trend of 1 percent. Hence, meteorologists
generally suggest a spatial bias in the Dobson network,
of the order of 1 percent per decade, but realize that
this is an extemely uncertain number.
.
~ . . . ~ · _ _ ~ ~ _ ~ . ,
Reinsel et al. do not differ
LOW-FREQUENCY VARIATIONS
Bishop and Hill (1981) used a partially inhomogeneous
Arosa record to estimate the trend uncertainty due to
low-frequency variations (not directly analyzable with
the record of the Dobson network) from the variation
among decadal trends. Their result was an uncertainty of
the order of 0.8 percent per decade.
The Arosa record used by Bishop and Hill is remarkable
for the absence of fluctuations with periods of the order
of a century, periods that are often quite apparent in
temperature records. In fact, the homogenized Arosa
ozone record for the period 1932-1980 (Dutsch, personal
communication to J. London, University of Colorado, 1981)
shows noticeable long-period variations (Figure E.2).
The figure also shows the sensitivity of 10-year trends
to the starting date of each decade. For example, the
360
350
c
c
o
o 340
at
o
o 330
~ 320
I'. 41
1 ~ 11 1
, \/ t1
I V `!
11 I]
1 1
1~
_ 1 1 1 1 1 1
1926 1930 1940 1950 1960 1970 1980
YEAR
FIGURE E.2 Homogenized values for total ozone at Arosa (Hudson et al. 1982).
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312
trend for 1936-1945 is almost zero.
for 1940-1949 is -33 Dobson units.
In contrast, that
Hence, the estimate
of 0.8 percent for long-period variability is quite
uncertain. Further, this estimate is based on the record
from only one station.
A further indication of the magnitude of uncertainties
due to long-period fluctuations is the sensitivity of the
trends in the 1970s to the statistical model used. Thus,
the "hockey stick" approach and the hypotheses of separate
unknown trends in the 1960s and 1970s produce trends in
the 1970s differing by 1.5 percent. E.L. Scott
(University of California, Berkeley, personal communica-
tion, 1981) also has criticized the dependence of the
global trend estimates on the particular statistical
model chosen. For these reasons, we suggest that the
uncertainty of global decadal ozone trends due to long-
period natural variations with unknown causes is at least
of the order of 1 percent; but we consider this estimate
also as very uncertain.
SUMMARY AND RECOMMENDATIONS
Because of the various controversies, it is not possible
to arrive at a definite understanding of the uncertainties
of global decadal ozone trends derived from Dobson
stations or satellites. The statisticians using the
"hockey stick" models would estimate the standard devia-
tions of the decadal trends derived from Dobson stations
to be of the order of 1 percent. Most meteorologists and
at least one statistician would prefer standard deviations
of the order of 2 percent or larger.
Once long-lived satellites with good reliability
characteristics are available, the standard deviations
may perhaps be cut considerably.
As we consider periods longer than 10 years, the trends
are better determined but they have to be extrapolated to
a longer period. These two factors almost cancel; the
uncertainty of trend may decrease only slightly for longer
periods. Therefore, meteorologists would consider trend
analysis an unreliable early warning system for man-made
ozone changes; an observed average trend of 0 percent at
the Dobson stations, over, say 20 years, could be produced
by a man-made decrease of 4 percent or larger, compensated
by other factors, with a probability of 5 percent or so.
If remedial action is taken only after a "significant"
decrease of ozone, existing fluorocarbons could continue
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313
to decrease the ozone further to intolerable levels due
to their long lifetimes. Some statisticians would
consider a zero trend as an indication that the trend due
to fluorocarbons must have been much smaller than 4
percent. Our best hope for using total ozone trends as
early-warning systems rests on improved and well-
calibrated records of total ozone measured from
long-lived satellites.
REFERENCES
Angell, J.K. and J. Korshover (1981) Update of ozone
variations through 1979. Pages 393-396, Proceedings of
the Quadrennial International Ozone Symposium, August
4-9, 1980. Boulder, Colo.: National Center for
Atmospheric Research.
Bishop, L. and W.J. Hill (1981) Analyzing Stratospheric
Ozone for the Natural and Man-made Trend Variability.
Pages 304-305, Summaries of Conference Presentations.
(Available from the Society for Industrial and Applied
Mathematics, Philadelphia, Pa.)
Bloomfield, P., M.L. Thompson, G.S. Watson, and S. Zeger
(1981) Frequency Domain Estimation of Trends in
Atmospheric Ozone. Technical Report No. 182,
Department of Statistics, Princeton University.
(Submitted for publication to Journal of Geophysical
Research)
Hasebe, Fumio (1980) A global analysis of the fluctuations
of total ozone II nonstationary annual oscillation,
quasi-biennial oscillation, and long-term variations
in total ozone. Journal of the Meteorological Society
of Japan 58:104-117.
Hudson, R.D., et al., eds. (1982) The Stratosphere 1981:
Theory and Measurement. Geneva: World Meteorological
Organization. (Available from National Aeronautics and
Space Administration, Code 963, Greenbelt, Md. 20771)
London, J. and X. Ling (1981) The geographic bias in
determining average variations of total ozone from
ground-based observations. Pages 337-339, Proceedings
of the Quadrennial International Ozone Symposium,
August 4-9, 1980. Boulder, Colo.: National Center for
Atmospheric Research.
Moxim, W.J. and J.D. Mahlman (1980) Evaluation of various
total ozone sampling networks using the GFDL 3-D
tracer model. Journal of Geophysical Research 85
(C8):4527-4539.
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Reinsel, G., G.C. Tiao, M.N. Wang, R. Lewis, and D.
Nytchka (1981) Statistical analysis of stratospheric
ozone data for detection of trend. Atmospheric
Environment 15:1569-1578.
Reinsel, G., G.C. Tiao, and R. Lewis (1982) A statistical
analysis of total ozone data from the Nimbus B W
satellite experiment. Journal of Atmospheric Sciences
39.
St. John, D.S., S.P. Bailey, W.H. Fellner, J.M. Manor,
and R.D. Snee (1981) Time series analysis for trends
in total ozone measurements. Journal of Geophysical
Research 86:7299-7311.
Representative terms from entire chapter:
dobson network
