4.3 Trend/time series analysis

Time series or trend analysis was primarily conducted using the Mann-Kendall statistical test. Trends analyses using the Mann-Kendall tests were conducted using custom programming in R, an open source statistical package. Changes in ecosystem characteristics over time are an important type of analysis and one of the most valuable types of information conveyed with indicators. Somewhat counter-intuitively, they are also rarely conducted using appropriate statistical techniques. Analysis of trend in time series data is necessary to determine if conditions in a subwatershed are improving or deteriorating. One of the most common techniques for determining trend is linear regression. However, linear regression requires certain data characteristics, such as normal distribution of values, which are not easy to assess in small data sets. Distribution-free trend analysis is ideal due to the unknown nature of the data, so non-parametric tests are preferred. Of the various commonly used options, the Mann-Kendall rank correlation trend test is the strongest (Berryman et al. 1988). It is appropriate for data that are not normally-distributed, tolerates missing values, and is relatively unaffected by extreme values or skewed data. Although it is sensitive to autocorrelation, this is only an issue in very long datasets and was not considered for these indicators. The output of the Mann-Kendall analysis is an assessment of the trend slope and its statistical significance.

One weakness of the Mann-Kendall is an inability to adjust for seasonality or cycling in the time series. Almost all environmental data will have daily, seasonal, inter-annual, and/or inter-decadal cycles. This means that one cannot detect change in these data without taking into account and controlling for these cyclic effects. Full decomposition of a time series into its component parts (trend, oscillations, seasonal factors, and disturbances) is not always possible or practical (Jassby & Powell 1990). For these data, the Seasonal-Kendall test can be used to determine whether or not significant changes have occurred over time, while taking into account variation due to seasonal effects (Hirsch et al., 1982; Hirsch and Slack 1984; Esterby 1996). It retains the non-parametric strengths of the Mann-Kendall, but performs separate trends analysis for each season and compares the results. For certain indicators, there may have been infrequent data collection (e.g., annual), or only a few years of data collection (i.e., <5 years), in which case a seasonal trends analysis was not conducted and instead the standard Mann-Kendall was used.

Hess et al. (2001) ran simulations for six linear trend analysis techniques, and determined that the strongest are the Seasonal-Kendall test and a t-test adjusted for seasonality. France et al. (1992) also found the Seasonal-Kendall to be the strongest option, and the best when seasonality is unknown as well. For non-seasonal data, such as annual data, the Mann-Kendall is probably superior (Hamed & Rao 1998).

When assessing trend within a broad region with multiple sampling sites, the same principle applies as with seasonal data: it is better to compare trends across sites than to combine them into a single time series. The Regional Mann-Kendall is analogous to the Seasonal-Kendall, but compares individual locations rather than seasons (Helsel & Frans 2006). Because it is statistically identical, it has all the advantages of the Seasonal-Kendall. This approach was used frequently for subwatershed analysis.