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SPARC/IOC/GAW

Assessment of Trends in the Vertical Distribution of Ozone

 

3.6.  Combined trend at northern mid-latitudes and uncertainty estimate

In this chapter we have calculated trends as a function of altitude from 4 different measurement systems, SAGE, Umkehr, SBUV, and sondes. Each trend calculation was derived with an associated estimate of the statistical uncertainty. An additional uncertainty is that due to the potential drift of the instrument system over time. Such uncertainties are not included in the standard uncertainty derived from the statistical time-series models. For each of the systems, an attempt was made in Chapter 1 of this report to estimate these instrument-drift uncertainties. This section takes those estimates and combines them with the estimate for the statistical sampling uncertainty from the time-series models. The result is an estimate of overall uncertainty for each of the instrument systems.

 

 
Sapporo
Edmonton
Uccle
Payerne
Alt
Drift
Stat
Tot
Drift
Stat
Tot
Drift
Stat
Tot
Drift
Stat
Tot
2.5
0.92
4.98
5.07
0.72
1.56
1.71
2.30
1.56
2.78
2.30
1.66
2.83
5.0
0.92
3.45
3.57
0.72
1.62
1.77
2.30
1.38
2.68
2.30
1.60
2.80
7.5
0.86
5.77
5.84
0.69
3.54
3.60
2.03
2.51
3.23
2.03
2.58
3.28
10.0
0.80
6.67
6.72
0.66
3.98
4.03
1.75
3.39
3.82
1.75
3.03
3.50
12.5
0.74
7.17
7.21
0.63
3.69
3.75
1.48
3.62
3.91
1.48
2.99
3.33
15.0
0.68
7.48
7.51
0.59
3.14
3.20
1.21
3.08
3.31
1.21
2.50
2.78
17.5
0.62
5.54
5.57
0.56
2.29
2.36
0.93
2.32
2.50
0.93
1.87
2.09
20.0
0.56
3.65
3.69
0.53
1.61
1.70
0.66
1.67
1.80
0.66
1.24
1.40
25.0
0.78
1.74
1.91
0.72
1.09
1.30
1.23
0.99
1.58
1.23
0.65
1.39

 
Boulder
Goose Bay
Hohenpeissenberg
Alt
Drift
Stat
Tot
Drift
Stat
Tot
Drift
Stat
Tot
2.5
0.72
1.72
1.87
0.72
1.89
2.02
2.30
1.32
2.65
5.0
0.72
1.87
2.01
0.72
1.66
1.81
2.30
1.15
2.57
7.5
0.69
3.13
3.21
0.69
3.64
3.71
2.03
2.22
3.01
10.0
0.66
4.50
4.55
0.66
4.10
4.16
1.75
2.79
3.30
12.5
0.63
5.12
5.16
0.63
3.77
3.82
1.48
2.76
3.13
15.0
0.59
4.51
4.54
0.59
3.12
3.17
1.21
2.19
2.50
17.5
0.56
2.72
2.78
0.56
2.39
2.45
0.93
1.75
1.98
20.0
0.53
1.79
1.87
0.53
1.76
1.84
0.66
1.25
1.42
25.0
0.72
0.66
0.98
0.72
1.11
1.33
1.23
0.68
1.41

 

Table 3.4. Estimated uncorrected-drift uncertainties (all 1s) for each station along with statistical uncertainties of trend analysis and combined uncertainties. The drift uncertainties were determined from estimates in Chapter 1 for each type of sonde. The totals were determined as a root sum of squares of the drift and statistical uncertainties.

 

For ozonesondes, 7 stations at northern mid-latitudes were used. These are indicated in Table 3.4 along with the estimate for the uncorrected-drift uncertainty and the statistical uncertainty in the trend fit. These were combined as a root sum of squares (rss) to give an estimate for the overall trend uncertainty of each sonde station. Combination by rss is a reasonable way to combine these errors but it is not the only way. The trends and uncertainties for these 7 stations were then combined by using weighted means with the weighting factor being the reciprocal of the square of the total standard error. These results are given in Table 3.5 along with the standard error of the mean calculated from the 7 trend values at each altitude. At altitudes of 20 km and below, the standard error of the mean is larger than the overall uncertainty estimated from the station characteristics. It was decided to use the larger of the two values as a first cut at the uncertainty in the trend estimate from the sondes. However, the estimates of individual instrument uncertainties are still used to determine weighting to get the mean trend.

 

Alt
Sappo
Edmon
Uccle
Bould
Goose
Hohen
Payer
Comb
SE Mean
2.5
5.07
1.71
2.78
1.87
2.02
2.65
2.83
0.87
2.48
5.0
3.57
1.77
2.68
2.01
1.81
2.57
2.80
0.85
1.99
7.5
5.84
3.60
3.23
3.21
3.71
3.01
3.28
1.32
2.72
10.0
6.72
4.03
3.82
4.55
4.16
3.30
3.50
1.52
1.84
12.5
7.21
3.75
3.91
5.16
3.82
3.13
3.33
1.48
1.96
15.0
7.51
3.20
3.31
4.54
3.17
2.50
2.78
1.25
2.28
17.5
5.57
2.36
2.50
2.78
2.45
1.98
2.09
0.93
1.68
20.0
3.69
1.70
1.80
1.87
1.84
1.42
1.40
0.66
1.07
25.0
1.91
1.30
1.58
0.98
1.33
1.41
1.39
0.51
0.47

 

Table 3.5. Combined drift and statistical uncertainties for each sonde station as a function of altitude (1s). The weighted combined uncertainty is also shown along with the standard error of the mean for the trend at each station. Because the standard error of the mean was larger for most altitudes, the total uncertainty was taken as the larger of the combined uncertainties and the standard error of the mean. At all altitudes except 25 km this means that the standard error of the mean was used to estimate the combined sonde uncertainty.

 

The fact that the standard error of the mean for the 7 sonde stations is larger than the estimated combined statistical uncertainty highlights an issue that is most important for the interpretation of tropospheric ozone trends. The trends obtained in various geographical regions are sufficiently different from one another that they are likely measures of geophysical changes in the regions which are the result of different combinations of cause. We will go through the formality of creating a combined trend in the troposphere, but advise caution on interpreting this trend as a true zonal mean. Specifically, the sonde mean is obtained here by weighting each station inversely by its total variance, including estimates for instrument drift. These uncertainty estimates in the troposphere are largest for the Brewer-Mast ozonesondes in use at the European stations. They are thus accorded less weight in this analysis, while the Canadian ECC sondes are accorded more weight. This weights the mean more towards the negative trends found at the Canadian stations since 1980 and yields a somewhat different result than obtained above in section 3.5. There is a further issue in forming the mean in the troposphere when the results seem to indicate that the processes leading to change are different in different regions. We cannot be sure that the distribution of the locations of the sonde stations is correctly representing the area of the globe which has undergone change due to a particular set of causes. The station distribution may overestimate or underestimate the importance of the negative tropospheric trends found at the Canadian stations to a zonal mean effect.

 

 

 
Sonde
SAGE
SBUV
Umkehr
Mean
Alt(km)
Trend
Unc
Trend
Unc
Trend
Unc
Trend
Unc
Trend
Unc
2.5
-1.87
2.48
-
-
-
-
-
-
-1.87
2.48
5.0
-1.55
1.99
-
-
-
-
-
-
-1.55
1.99
7.5
-0.23
2.72
-
-
-
-
-
-
-0.23
2.62
10.0
-3.33
1.84
-
-
-
-
-
-
-3.33
1.84
12.5
-6.40
1.96
-
-
-
-
-
-
-6.40
1.96
15.0
-7.34
2.28
-
-
-
-
-
-
-7.34
2.28
17.5
-6.81
1.68
-
-
-
-
-
-
-6.81
1.68
20.0
-5.99
1.07
-4.90
2.84
-
-
-1.10
2.34
-5.12
0.92
25.0
-3.67
0.51
-1.90
1.39
-0.90
1.71
0.30
2.13
-3.12
0.45
30.0
-
-
-2.20
1.24
-1.70
1.77
-1.90
2.04
-2.01
0.91
35.0
-
-
-5.00
1.03
-3.50
2.41
-6.00
2.04
-4.99
0.86
40.0
-
-
-8.30
1.23
-4.70
2.64
-6.60
2.05
-7.42
0.98
45.0
-
-
-7.20
2.02
-4.00
2.75
-
-
-6.08
1.63
50.0
-
-
-4.50
3.28
-
-
-
-
-4.50
3.28

 

Table 3.6. Trends and uncertainties in %/decade for each measurement system for northern mid-latitudes. All uncertainties are given as 1s. Derivation of mean trend and uncertainty is described in text.

 

Figure 3.53 Estimates of mean trend and combined statistical and instrument drift uncertainty estimates at northern mid-latitudes for a) Umkehr, b) SAGE I/II, c) SBUV/SBUV2, and d) sondes. Estimates were made at 2.5 km intervals from 2.5 to 20 km and 5 km intervals from 20 to 50 km. Uncertainties shown are 1s. Note that the sonde results were obtained as variance-weighted means. In the troposphere there is an additional unquantified uncertainty about the representativeness of the small number of stations. See text and Tables 3.4-3.6 for details.

 

The statistical uncertainties and instrument-drift uncertainties for the other measurement systems were also combined by rss. The result for each of the systems for northern mid-latitudes is given in Table 3.6 and shown in the 4 panels of Figure 3.53. This figure shows the mean trend and one standard error calculated for these systems as a function of altitude and the mean trend plus or minus one standard error. All estimates were interpolated to 2.5 km altitude intervals starting at 2.5 km and going through 20 km and 5 km intervals from 20 km through 50 km. Sonde results are shown down to 2.5 km but caution should be exercised in interpreting the meaning of any trends in the troposphere.

Once the estimates for trend and uncertainty were obtained for each system, these were combined into one trend versus altitude plot as shown in Figure 3.54. At altitudes where only one system has measurements, the trend and uncertainty estimates from this system were used. At altitudes where more than one system has measurements, these were combined as a weighted mean and weighted uncertainty using the square of each system’s standard error.

The trends shown in Figure 3.54 for the upper stratosphere are dominated by those determined from the SAGE instruments because these have the smallest estimated uncertainty. The result of this estimation of the trend at 40 km is -7.4%/decade ±2.0%/decade, a highly significant trend. The trend at 50 km is estimated from the SAGE instruments only and is not significant at the 2s level because an uncertainty has been estimated at this altitude for SAGE which includes the observed sunrise-sunset differences in ozone from SAGE II.

 

Figure 3.54 Estimate of mean trend using all 4 measurement systems at northern mid-latitudes (heavy solid line). Combined uncertainties are also shown as 1s (light solid line) and 2s (dashed line). Combined trends have not been shown in the troposphere because the small sample of sonde stations have an additional unquantified uncertainty concerning their representativeness of mean trends.

 

Below 20 km the trend estimate comes from the sondes alone. Data at 12.5 km is generally in the stratosphere while that at 10 km is generally in the troposphere, except during winter. Trends have not been shown in this figure below 10 km because of the issues concerning the unquantified uncertainty in their representativeness in the troposphere. At 20 km the trend is from sondes, SAGE, and Umkehr. The Umkehr trend at 20 km is actually that for layer 4 which is centred a little above 20 km. This trend is quite different from that derived from the sondes or SAGE. The uncertainty estimate is large enough that, after weighting, it only reduces the estimated trend from about -6% to about -5%. It could be argued to not use Umkehr at this low level, but the overall conclusion would not change significantly. The estimated SAGE I/II uncertainties at 20 km are quite large. They are dominated by the uncertainty estimated for correcting the altitude offset of SAGE I. This will need more study if we are to be able to give trends at other latitudes in the lowest stratosphere with reasonably small uncertainties.

It must be emphasised that this is a first attempt to put together an overall trend versus altitude with instrumental and statistical uncertainties. A number of assumptions had to be made to estimate the instrument drift uncertainties. More assumptions had to be made to determine how to combine the various uncertainties. This was done only for the northern mid-latitudes where the data is most plentiful. It is hoped that this exercise will stimulate others to examine the input to these calculations and the assumptions made so that they can improve upon this first attempt.

 

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