We present an approach for deriving a systematic mathematical representation of the statistically significant features of the average long-Term changes and seasonal cycle of concentrations of trace tropospheric species. The results for two illustrative data sets (time series of baseline concentrations of ozone and <span classCombining double low line"inline-formula">N2O</span> at Mace Head, Ireland) indicate that a limited set of seven or eight parameter values provides this mathematical representation for both example species. This method utilizes a power series expansion to extract more information regarding the long-Term changes than can be provided by oft-employed linear trend analyses. In contrast, the quantification of average seasonal cycles utilizes a Fourier series analysis that provides less detailed seasonal cycles than are sometimes represented as 12 monthly means; including that many parameters in the seasonal cycle representation is not usually statistically justified, and thereby adds unnecessary "noise" to the representation and prevents a clear analysis of the statistical uncertainty of the results. The approach presented here is intended to maximize the statistically significant information extracted from analyses of time series of concentrations of tropospheric species, regarding their mean long-Term changes and seasonal cycles, including nonlinear aspects of the long-Term trends. Additional implications, advantages and limitations of this approach are discussed.