THIS POST IS A STUDY OF TRENDS IN STRATOSPHERIC OZONE CONCENTRATION 1979-2015 FROM SATELLITE DATA AND A TEST OF THE ROWLAND MOLINA THEORY OF ANTHROPOGENIC CHEMICAL OZONE DEPLETION DESCRIBED IN FARMAN ETAL 1985 AND THE MONTREAL PROTOCOL.

SUMMARY: Mean global total ozone is estimated as the latitudinally weighted average of total ozone measured by the TOMS and OMI satellite mounted ozone measurement devices for the periods 1979-1992 and 2005-2015 respectively. The TOMS dataset shows an OLS depletion rate of 0.65 DU per year on average in mean monthly ozone from January 1979 to December 1992. The OMI dataset shows an OLS accretion rate of 0.5 DU per year on average in mean monthly ozone from January 2005 to December 2015. The conflicting and inconsequential OLS trends may be explained in terms of the random variability of nature and violations of OLS assumptions that can create the so called Hurst phenomenon. These findings are inconsistent with the Rowland-Molina theory of ozone depletion by anthropogenic chemical agents because the theory implies continued and dangerous depletion of total ozone on a global scale until the year 2040.

POLICY IMPLICATION: THE APPARENT MONTREAL PROTOCOL SUCCESS THAT VAULTED THE UNITED NATIONS INTO A GLOBAL ROLE IN CLIMATE CHANGE HAS NO SUPPORTING EVIDENCE. IT SHOULD ALSO BE MENTIONED THAT THERE IS NO ROLE FOR THE OZONE HOLE IN THE ROWLAND MOLINA THEORY OF OZONE DEPLETION. THE OZONE HOLE IS A LOCALIZED EVENT. THE ROWLAND MOLINA THEORY OF OZONE DEPLETION RELATES ONLY TO LONG TERM TRENDS IN GLOBAL MEAN OZONE LEVEL. NO SUCH TREND HAS EVER BEEN PRESENTED AS EVIDENCE PROBABLY BECAUSE NO SUCH TREND IS FOUND IN THE DATA. THE OZONE DEPLETION CRISIS AND ITS MONTREAL PROTOCOL SOLUTION APPEARS TO BE AN IMAGINED CRISIS THAT WAS SIMPLY DECLARED TO HAVE BEEN SOLVED.

THE OZONE DEPLETION ISSUE: Atmospheric ozone plays an important role in protecting life on the surface of the earth from the harmful effects of UV-B radiation. The mechanism of this protection involves the Chapman Cycle that both forms and destroys ozone (Chapman, 1930) (Fisk, 1934). The essential reaction equilibrium between oxygen molecules (O2) and ozone molecules (O3) is 3O2↔2O3. In the absence of UVB (280-315 nm) and UVC (100-280 nm) radiation, O3 concentration is negligible and undetectable because the equilibrium heavily favors O2. In the presence of UVC, the equilibrium shifts towards O3 because UVC disintegrates O2 into charged oxygen free radicals. Their chance collision with O2 forms ozone and that with O3 destroys ozone. The much higher probability of collision with O2 favors an equilibrium inventory of O3. In the presence of both UVC and UVB, as in the ozone layer, the equilibrium shifts back towards O2 because UVB destroys O3 and lowers the equilibrium concentration of ozone. In this process UVB is almost completely absorbed and life as we know it on the surface of the earth is protected from the known harmful effects of UVB that include increased incidence of skin cancer (McDonald, 1971) (UNEP, 2000) and adverse effects on photosynthesis in plants (Allen, 1998) (Tevini, 1989). The importance of the ozone layer and environmental concerns with respect to man-made chemicals that may cause ozone depletion are understood in this context (Molina, 1974) (UNEP, 2000). Stratospheric ozone forms over the tropics where UVB irradiance is direct. It is distributed to the higher latitudes primarily by the Brewer-Dobson Circulation or BDC (Brewer, 1049) (Dobson, 1956). Mid latitude ozone concentration tends to be higher than that over the tropics partly because stratospheric ozone is more stable when UVB irradiance is at an inclination. The distribution of ozone to the extreme polar latitudes is asymmetrical and less efficient than that to the mid-latitudes (Kozubek, 2012) (Tegtmeier, 2008) (Weber, 2011). The high level of interest in atmospheric ozone today derives from the discovery in 1971 of a global distribution of synthetic halogenated hydrocarbons in the atmosphere (Lovelock, 1973) and the analysis of its implications by Molina and Rowland in terms of the ability of chlorine free-radicals from synthetic halogenated hydrocarbon to catalyze the destruction of ozone in the stratosphere (Molina, 1974). The discovery in 1985 that the mean monthly atmospheric ozone over the South Pole for the period 1980-1984 was dramatically lower than that in the period 1957-1973 (Farman, 1985) served as empirical evidence of the Rowland-Molina ozone depletion mechanism. A fatal flaw in the Farman 1985 paper is described in a related post: LINK: https://tambonthongchai.com/2019/03/12/ozone1966-2015/ Critical review and commentary provided by Kirk P. Fletcher and Mhehed Zherting helped to improve this presentation and they are greatly appreciated. .

THE DATA AND DATA ANALYSIS: Satellite based measurements of total ozone began in late 1978 with the Total Ozone Mapping Spectrometer (TOMS) aboard the Nimbus-7 and continued on other spacecraft after 1992 (NASA, 1992) (NASA, 2015) but with some deterioration in the quality of the data since 1993 and particularly after the year 2000 due to instrument degradation (Ziemke, 2011) (NASA GISS, 2015). However, very high quality daily gridded total ozone data have been generated since 2005 on board the Aura satellite program by the Ozone Monitoring Instrument (OMI) provided by the Netherlands’s Agency for Aerospace Programs (NIVR) in collaboration with the Finnish Meteorological Institute (FMI) (NASA, 2015) (McPeters, 2015) (Ziemke, 2011) (NLR, 2016).

The OMI data provide complete global coverage in one-degree steps in both longitude and latitude on a daily basis. However, there are large gaps in the data particularly in the in the extreme latitudes during their respective winter months. For the purpose of our analysis these data are averaged across all longitudes in each one-degree latitude step for all 4,086 days in the sample period 1/1/2005 to 3/10/2016. Analysis of data availability across latitudes shows 100% data availability between 57S and 71N latitudes but that data are sparse in the more extreme latitudes particularly in the Southern Hemisphere. Gaps in the polar data are patterned and not random because they occur only in the respective polar winters. It is possible for this pattern to impose a bias in the results.

Data from TOMS (Total Ozone Mapping Spectrometer) satellite mounted instruments for the measurement of atmospheric ozone are maintained and made available online by the NASA Goddard Institute for Space Studies (NASA GISS, 2015) (Ziemke, 2011) (NASA, 2011) (NASA TOMS ARCHIVE, 1992). These data are available as gridded monthly means for the period 1979-1992 in one by 1.25-degree grids for all latitudes and longitudes. There are a total of 170 months in the data series. As in the OMI data (and in ground station data) the extreme latitude data are mostly absent during their respective winters. A comparison TOMS, OMI, and ground station data reveals some data anomalies. TOMS and OMI data are not comparable because they are very different from each other. Also, both TOMS and OMI are different from ground station data. Therefore, the two sample periods are tested for trends in mean monthly global ozone separately. Ground station data are presented in a related post on this site. Trends are estimated using simple OLS regression of monthly means against time. A deseasonalized series is not used for this purpose because the seasonal cycles of monthly means are irregular when defined in terms of calendar months. Imposing a common seasonal cycle on these data based on calendar months may impose a bias (Box, 1994) (Draper&Smith, 1998).

The Hurst Exponent of these time series: The second sample period, containing more than 4,000 days of gridded daily means, provides a sufficient sample size to use Rescaled Range analysis (R/S) to estimate the Hurst exponent H of daily mean global ozone (Hurst, 1951) (Mandelbrot-Wallis, 1969). R/S requires subsampling without replacement in multiple cycles. We use seven cycles of subsampling with 1, 2, 3, 4, 6, 8, and 10 subsamples taken in the seven cycles. Thus a total of 34 subsamples are subjected to R/S analysis. In each subsample, the range is computed as the difference between the maximum value and the minimum value of the cumulative differences from the mean. The value of R/S is computed as the range R divided by the standard deviation of the subsample S. The H-value for each subsample is then computed as H = ln(R/S)/ln(N) where N is the subsample size. The Hurst exponent of the time series is then estimated as the simple arithmetic average of all 34 values of H2. The value of H indicates whether the usual independence assumption of OLS regression is violated. Under conditions of independence and Gaussian random behavior in the time series the theoretical value of the Hurst exponent is H=0.50. Gaussian and independence assumptions are not seriously violated if the Hurst exponent lies between 0.40 and 0.6 but higher values indicate long term memory and persistence. Under these conditions random numbers can appear to form patterns and faux statistically significant trends. However, sample size and the sub-sampling structure used in Rescaled Range analysis can impose a bias in the value of H computed. It is therefore necessary to “calibrate” the subsample structure with a known Gaussian series. The Hurst exponent of the test series must then be compared with the value of H computed for the Gaussian series in the calibration set under identical estimation procedures and subsampling conditions. Once the Hurst exponent of the latitudinally averaged global ozone time series is determined it will be possible to evaluate the validity of OLS trends particularly when they appear over short periods of time and when they are not robust to changes in the time frame. Memory and persistence in a time series is known to be the source of chaotic behavior in time series data that appears to create patterns out of randomness. The usual research procedure of looking for cause and effect explanations for observed patterns in the data can go awry under these conditions.

DATA ANALYSIS AND RESULTS FOR TOMS NIMBUS7 DATA:

The monthly mean gridded total ozone data from archives of the now de-commissioned TOMS Nimbus7 program are converted into latitudinally weighted global means and these global means are depicted graphically in Figure 5. The data show that the seasonal cycle is irregular when described in terms of calendar months. The monthly means show a gradual decline in mean global total ozone at a rate of 0.0542 DU per month or 0.65 DU per year. The observed rate of decline is inconsequential in the ozone depletion context. Though statistically significant, the practically insignificance of the decline is in sharp contrast to the claim of a catastrophic anthropogenic destruction of the ozone layer and its dangerous consequences including an alleged epidemic of skin cancer. Also, the ozone time series may violate the independence assumption of OLS regression and the Hurst phenomenon in the ozone time series can create apparent patterns out of randomness that may be mistaken for trends. We should also take note that that the TOMS/Nimbus program has been decommissioned and that the OMI/Aura ozone measurement program that was started in 2005 and which continues to this day (2016) is considered to provide much better measurements of total ozone than the discontinued TOMS/Nimbus program. The mean meridional pattern of mean monthly ozone for 1979-1992 in the TOMS dataset shows the efficiency of ozone distribution by atmospheric circulation. In the tropics, the only place where ozone is formed, the average ozone concentration is about 280 DU. At the mid-latitudes ozone concentration is higher – as high as 370 DU in the Northern Hemisphere and 340 DU in the Southern Hemisphere – because at these latitudes UVB irradiance is at an inclination and it is therefore less efficient in destroying ozone. At the extreme latitudes, the ozone level drops because atmospheric circulations are less efficient in distributing ozone to these latitudes. The distributional efficiency to the extreme latitudes is asymmetrical and is less efficient in the Sothern Hemisphere than in the Northern Hemisphere. Changes in ozone levels at these extreme latitudes – both seasonal and decadal – are therefore more likely to be the result of natural variations in atmospheric circulations than ozone destruction by anthropogenic chemical agents. The implication of these patterns is that polar “ozone holes” cannot serve as evidence of ozone depletion.

DATA ANALYSIS AND RESULTS FOR THE OMI DATA:

The OMI gridded daily total ozone data are smoothed and converted into latitudinally weighted global means with cosine weighting. These daily global means are depicted graphically in Figure 7. Smoothing was necessary because the raw data contain spikes that occur irregularly about once a month. Each spike consists of two anomalous values in adjacent days- one high and one low. The left panel of Figure 8 shows these spikes for the year 2005. They occur in all years. These spikes are assumed to be anomalous and they are removed by replacing them with the mean value for day-7 to day-2. The data shown in Figure 7 are the smoothed values. The right panel of Figure 8 shows the average meridional pattern in the data from the South Pole to the North Pole. There is a trough of about 280 DU in the tropics with higher values in the mid-latitudes that drop again as we enter the Polar Regions. The drop is more severe in the South Pole than in the North Pole. The graphic indicates the extreme asymmetry between the two hemispheres and the uniqueness of the South Pole in terms of atmospheric total ozone and supports the findings in a prior study that ozone behavior in the South Pole cannot be generalized on a global scale (Munshi, An empirical test of the chemical theory of ozone depletion, 2016).

For ease of comparison with the TOMS mean monthly data series 1979-1992, the OMI daily data in Figure 7 are converted into monthly means from January 2005 to December 2015. The monthly means and their OLS trend are shown in Figure 9 below. OLS regression shows a rising trend of 0.0416 DU per month or about 0.5 DU per year. Though statistically significant this trend is of little practical consequence and is more likely to be the result of natural variability than the implementation of the Montreal Protocol particularly since the effect of the Protocol’s ban on ozone depleting substances is not expected for many decades to come because of the long life halogenated hydrocarbons in the atmosphere; and the size and direction of this trend is almost the exact opposite of the OLS trend observed in the 14-year period from 1979-1992 where we found global ozone declining at a rate of 0.65 DU per year. Yet, both of these study periods fall in a regime in which the Rowland-Molina theory predicts continued and sustained ozone depletion by long-lived anthropogenic ozone depleting substances.

CHAOTIC BEHAVIOR OF THE OMI DAILY DATA TIME SERIES: A a possible explanation for the apparent contradiction in the OLS trends observed in the two data series is chaotic behavior of the time series. Here we look at the Hurst exponent of the daily global ozone series 2005-2015. If it turns out that the series contains memory and persistence and that it therefore violates the OLS assumption of independence we would expect the random behavior of the series to generate faux patterns of this nature. The deseasonalized and detrended standardized residuals of the OMI daily data in Figure 7 are shown in Figure 10 below. They are examined with Rescaled Range analysis. A total of 34 sub-samples are taken in 7 cycles. Subsampling is without replacement in each cycle. The Hurst exponent of the deseasonalized and detrended residuals of the latitudinally weighted daily mean global ozone series 2005-2015 is found to be H=0.784, a high value much greater than H=0.5 indicative of memory and persistence in the series. However, it is known that empirical values of H cannot be compared directly with the theoretical Gaussian value of H=0.5 because of the effect of the subsampling strategy on the empirical value of H. It is necessary to perform a calibration with a Gaussian series using the same sample size and subsampling strategy for comparison. The calibration test with a random Gaussian series inserted into the same sub-sampling structure yielded a Hurst exponent of H=0.5217. The comparison of this neutral value with H=0.784 provides strong evidence of the existence of memory, dependence, persistence, and therefore of chaotic behavior in the daily mean global ozone time series. This behavior is depicted graphically below.

CONCLUSION: Satellite based total ozone gridded data from the TOMS instrument (1979-1992) and the OMI instrument (2005-2015) are used to estimate latitudinally weighted global mean ozone levels. The global mean ozone values are found to have a regular seasonal cycle for daily data and irregular seasonal cycles for monthly mean data. The monthly mean data are examined for trends with OLS regression. In both datasets, statistically significant but practically insignificant trends are found that are contradictory. The older TOMS data show a depletion of mean monthly global ozone at a rate of 0.65 DU3 per year. The newer and possibly more reliable OMI data show an accretion of mean monthly global ozone at a rate of 0.5 DU per year. According to the chemical theory of ozone depletion subsumed by the UNEP and the Montreal Protocol, both of the sample periods tested lie within a regime of continuous destruction of total ozone on a global scale by long lived anthropogenic chemical agents. The weak and contradictory OLS trends found in this study cannot be explained in terms of this theory. The OLS assumption of independence is investigated with Rescaled Range analysis. It is found that the deseasonalized and detrended standardized residuals of daily mean global ozone levels in the OMI dataset 2005-2015 contain a high value of the Hurst exponent indicative of dependence, persistence, and long term memory.

The weak and contradictory OLS trends observed in the TOMS and OMI datasets can therefore be explained as artifacts of the Hurst phenomenon which is known to create apparent patterns and OLS trends out of randomness. These results are inconsistent with the Rowland-Molina theory of anthropogenic ozone depletion on which the Montreal Protocol is based.

POLICY IMPLICATION: THE APPARENT MONTREAL PROTOCOL SUCCESS THAT VAULTED THE UNITED NATIONS INTO A GLOBAL ROLE IN CLIMATE CHANGE HAS NO SUPPORTING EVIDENCE. IT SHOULD ALSO BE MENTIONED THAT THERE IS NO ROLE FOR THE OZONE HOLE IN THE ROWLAND MOLINA THEORY OF OZONE DEPLETION. THE OZONE HOLE IS A LOCALIZED EVENT. THE ROWLAND MOLINA THEORY OF OZONE DEPLETION RELATES ONLY TO LONG TERM TRENDS IN GLOBAL MEAN OZONE LEVEL. NO SUCH TREND HAS EVER BEEN PRESENTED AS EVIDENCE PROBABLY BECAUSE NO SUCH TREND IS FOUND IN THE DATA. THE OZONE DEPLETION CRISIS AND ITS MONTREAL PROTOCOL SOLUTION APPEARS TO BE AN IMAGINED CRISIS THAT WAS SIMPLY DECLARED TO HAVE BEEN SOLVED.