European Geophysical Society
XXVII General Assembly
Nice, France, 21 - 26 April 2002

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Modeling of ozone measurements monthly means or daily means?

Jörg A. Mäder, Gisela Koch and Johannes Stähelin
Institute for Atmospheric and Climate Science (IACETH), ETH Zürich


April 19. 2002

Introduction

large For it's function as UV filter, ozone is regarded as one of the most important gases in our atmosphere. Without it life as we know would not exist. Therefore, the detection of the depletion of the ozone layer was one of the most important events in natural monitoring and the reaction from public and politics were strong.
The most important factor for the depletion of ozone layer was relatively fast located (CFC) and the further possed resolutions now making impact. Nevertheless, the exact behavior and distribution of ozone in time and space is not completely understood. The corresponding chemical and physical models are still imperfect. Because of this, the measuring of ozone is still an important aspect in environmental research and monitoring.
In most cases, especially regression models, monthly values are used to reproduce trends in ozone distribution. The measurement itself is a single point event with a small amount in time. The Daily value is calculated of several single values, and in a second step monthly value can be determined. The calculation itself is a simple mean. But it looks as if this simplification generate problems in all succeeding analysis.


Data sources

This analysis bases on total ozone stations in the northern hemisphere with a long time series (more than 4600 daily values, see figure 1). The data set is available on the WOUDC. The other local data - tropopause pressure (Ptp) and the temperature levels on 300, 50 and 10 hPa (T300, T50, T10) - are calculated from the NCEP reanalysis which bases on different local measurements.
An overview of the correlation between ozone and the tropopause pressure is shown in figure 2.



Figure 1: used total ozone stations.


Figure 2: Correlations between total ozone and tropopause pressure.

Effects

The distrubution of ozone is not a normal distribution and it isn't symmetric too. In this case the calculation of the mean of the single months effects to a different distribution for the monthly means.
As shown in figure 3 (on the right side) both tails are shorter but shows higher probabilities near the balance point. In combination with the tropopause pressure, which shows stronger effects, this results in a rotation of the point cloud counterclockwise. In consequence of this the coefficients of the linear regressions, for example, are higher for monthly values than for daily values, and leads in this case to an overestimation of the influence to ozone concentrations.
This effect is also visible in many other variables, like the chlorine concentration or temperatures on different pressure levels. Figure 4 shows the daily and monthly coefficients from the linear regressions against each other. The effect depends also on the latitude and region of the different stations as shown in figure 5. 		Figure 3: Daily values of ozone and tropopause pressure at Arosa including the linear regression and distribution of the daily (black) and monthly (red) values. The colors of the points indicate their month.


Figure 4: Coefficients of linear regression based on monthly and daily values.


Figure 5: Difference of the coefficients against the latitude of the stations.




Mathematical aspects

Calculating the mean is the most common and often the only known method to combine values. But this process has an large effect to the data set, depending on ite distribution. The best known effect is the sensitivity to outliners, especially if there are not symmetric to the real focus. On the other side it's not possible to describe the characteristics of different values with a single number. But the distribution has major influencies to succeeding analysis.
Alternatives to mean like are, as example, the median (divides the data set in two parts of the same size), or the expected value (most likely value). Both of them are more stable against outliners, nevertheless they have the same effect on the distribution.

Advantages of monthly means

  • The size of the data set is strongly reduced. But this has only relevance for very complicated models.
  • The ozone time series is very inert. That means the current value depends strongly on his predecessors (high auto correlation). This aspect is weaker on monthly values.
  • To calculate proper models on autocorrelated models, it's better to have complete time series. With monthly means this is possible. However bad weather make it impossible to do this on the time scale of single days, since the measuring needs direct sunlight.
  • Other data sets are also often not available on daily values.

Conclusion and outlook

Calculating the monthly values from daily values using a simple mean changes the distribution of total ozone. This Modification has strong impact to all following analysis. Therefore is important to check this impact and search for better methods without the shown disadvantages. A possible solution may be the transformation of the data to a normal distribution, calculating the mean and retransforming back to the original distribution. A problem will be that the different months show different characteristics.

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