Application of ordinary and complex methods for filling random gaps in total ozone data

Ozone gas has a major controlling factor for solar radiation of the shortest wavelength that reaches the earth surface. This gas is formed by chemical reaction and its formation process has been considered in various researches. Ozone is closely related to sun radiation time, relative air humidity and temperature. So ozone gas has been investigated from various interests. But one of remarkable problems challenge scientists is missing data or even unmeasured data in some periods. Hence suggesting a technique to solve this problem has a high degree of importance. Therefore, the main aim of this paper was formed.
In this study, six years observed data (2005-2010) of total ozone measured both by Dobson and TOMS satellite were used.  Dobson spectrophotometer (D109) has been installed at the Institute of Geophysics of University of Tehran. This institute situated in the north of Tehran with geographical characteristics of 35.44 ^oN and 51.23 ^oE and elevation of 1418.6 m above sea level. The correlation coefficient between the observational Dobson and measured satellite data has been calculated. The results show that the maximum value of the determination coefficient occurred in spring, winter, autumn and summer, respectively. Also the minimum value of the determination coefficient (R²=0.0596) happened in autumn of the year of 2005, while the maximum value of this coefficient (R²=0.9623) computed in autumn of the year of 2010. Following to investigate the accuracy of each ordinary interpolation methods to fill total ozone data gaps, some interpolation methods were selected. These methods includes Nearest, Linear, Spline and Pchip.
Data investigation showed that frequent gaps last 1, 2, 3, 4 and 5 days. To clarify the accuracy of each method, first randomly missing periods were produced with the same length. Then to evaluate the performance of the four interpolation methods, Index of Agreement (IOA) was computed. In this evaluation method, the predicted values are compared with the measured values. Values of IOA greater than 0.5 indicate that the applied method for predicting performs well (Willmott 1981). In this paper, values of IOA were calculated using the results of interpolation methods and the original observed data for each period.
The present paper indicates that the Spline method produces the more acceptable IOA, but this method creates least accuracy in estimating missed data, compare with other methods. It is also worthwhile to note that other interpolation methods produced similar IOA.
In second step, the operation of a complex method, namely wavelet transform, for filling real gaps was studied. It should be noted that the wavelet transform has also been used in other meteorological fields such as the time series analysis of soil changes, the relationship between rainfall and runoff, simulations of photochemical reactions, mountain waves, ENSO and predicting floods and droughts.
For this aim, missed data in signal of total ozone data for 2009 were constructed using wavelet theory. The outcomes of applying this theory to the observed data were compared with satellite data at the same time. The results showed that the reconstructed signal and the signal measured by satellite were consistent.