Higher statistical moments and an outlier detection technique as two alternative methods that capture long-term changes in continuous environmental data

Abstract

Central tendency statistics may not capture relevant or desired characteristics about the variability of continuous phenomena and thus, they may not completely track tem- poral patterns of change. Here, we present two methodological approaches to iden- 5 tify long-term changes in environmental regimes. First, we use higher statistical mo- ments (skewness and kurtosis) to examine potential changes of empirical distributions at decadal scale. Second, we adapt an outlier detection procedure combining a non- metric multidimensional scaling technique and higher density region plots to detect anomalous years. We illustrate the use of these approaches by examining long-term 10 stream temperature data from minimally and highly human-influenced streams. In par- ticular, we contrast predictions about thermal regime responses to changing climates and human-related water uses. Using these methods, we effectively diagnose years with unusual thermal variability, patterns in variability through time, and spatial variabil- ity linked to regional and local factors that influence stream temperature. Our findings highlight the complexity of responses of thermal regimes of streams and reveal a differ- entiated vulnerability to both the climate warming and human-related water uses. The two approaches presented here can be applied with a variety of other continuous phe- nomena to address historical changes, extreme events, and their associated ecological responses.