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. We present an approach for deriving a systematicmathematical representation of the statistically significant features of theaverage long-term changes and seasonal cycle of concentrations of tracetropospheric species. The results for two illustrative data sets (timeseries of baseline concentrations of ozone and N2O at Mace Head,Ireland) indicate that a limited set of seven or eight parameter valuesprovides this mathematical representation for both example species. Thismethod utilizes a power series expansion to extract more informationregarding the long-term changes than can be provided by oft-employed lineartrend analyses. In contrast, the quantification of average seasonal cyclesutilizes a Fourier series analysis that provides less detailed seasonalcycles than are sometimes represented as 12 monthly means; includingthat many parameters in the seasonal cycle representation is not usuallystatistically justified, and thereby adds unnecessary “noise” to therepresentation and prevents a clear analysis of the statistical uncertaintyof the results. The approach presented here is intended to maximize thestatistically significant information extracted from analyses of time seriesof concentrations of tropospheric species, regarding their mean long-termchanges and seasonal cycles, including nonlinear aspects of the long-termtrends. Additional implications, advantages and limitations of this approachare discussed.

Flexible approach for quantifying average long-term changes and seasonal cycles of tropospheric trace species