Methodological uncertainties in multi-regression analyses of middle-atmospheric data series

Multi-regression analyses have often been used recently to detect trends, in particular in ozone or temperature data sets in the stratosphere. The confidence in detecting trends depends on a number of factors which generate uncertainties. Part of these uncertainties comes from the random variability and these are what is usually considered. They can be statistically estimated from residual deviations between the data and the fitting model. However, interferences between different sources of variability affecting the data set, such as the Quasi-Biennal Oscillation (QBO), volcanic aerosols, solar flux variability and the trend can also be a critical source of errors. This type of error has hitherto not been well quantified. In this work an artificial data series has been generated to carry out such estimates. The sources of errors considered here are: the length of the data series, the dependence on the choice of parameters used in the fitting model and the time evolution of the trend in the data series. Curves provided here, will permit future studies to test the magnitude of the methodological bias expected for a given case, as shown in several real examples. It is found that, if the data series is shorter than a decade, the uncertainties are very large, whatever factors are chosen to identify the source of the variability. However the errors can be limited when dealing with natural variability, if a sufficient number of periods (for periodic forcings) are covered by the analysed dataset. However when analysing the trend, the response to volcanic eruption induces a bias, whatever the length of the data series. The signal to noise ratio is a key factor: doubling the noise increases the period for which data is required in order to obtain an error smaller than 10%, from 1 to 3-4 decades. Moreover, if non-linear trends are superimposed on the data, and if the length of the series is longer than five years, a non-linear function has to be used to estimate trends. When applied to real data series, and when a breakpoint in the series occurs, the study reveals that data extending over 5 years are needed to detect a significant change in the slope of the ozone trends at mid-latitudes.     

Indirect prediction of surface ozone concentration by plant growth responses in East Asia using mini-open top chambers

We developed small and mobile open top chambers (mini-OTC) measuring 0.6 m (W)?×?0.6 m (D)?×?1.2 m (H) with an air duct of 0.6 m (W)?×?0.23 m (D)?×?1.2 m (H). The air duct can be filled with activated charcoal to blow charcoal filtered air (CF) into the chamber, as opposed to non-filtered ambient air (NF). Ozone sensitive radish Raphanus sativus cv. Red Chime and rosette pakchoi Brassica campestris var. rosularis cv. ATU171 were exposed to NF and CF in mini-OTCs at different locations in East Asia. A total of 29 exposure experiments were conducted at nine locations, Shanghai, China, Ha Noi, Vietnam, Lampang, Phitsanulok and Pathumtani, Thailand, and Hiratsuka, Kisai, Abiko and Akagi, Japan. Although no significant relationships between the mean concentrations of ambient O₃ during the experimental period and the growth responses were observed for either species, multiple linear regression analysis suggested a good relationship between the biomass responses in each species and the O₃ concentration, temperature, and relative humidity. The cumulative daily mean O₃ (ppb/day) could be indirectly predicted by NF/CF based on the dry weight ratio of biomass, mean air temperature, and relative air humidity.