Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events

This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.