Technical Note: Higher-order statistical moments and a procedure that detects potentially anomalous years as two alternative methods describing alterations in continuous environmental data

Statistics of central tendency and dispersion may
not capture relevant or desired characteristics of the distribution
of continuous phenomena and, thus, they may not
adequately describe temporal patterns of change. Here, we
present two methodological approaches that can help to identify
temporal changes in environmental regimes. First, we
use higher-order statistical moments (skewness and kurtosis)
to examine potential changes of empirical distributions
at decadal extents. Second, we adapt a statistical procedure
combining a non-metric multidimensional scaling technique
and higher density region plots to detect potentially anomalous
years. We illustrate the use of these approaches by examining
long-term stream temperature data from minimally
and highly human-influenced streams. In particular, 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
and patterns in variability through time, as well as spatial
variability linked to regional and local factors that influence
stream temperature. Our findings highlight the complexity of
responses of thermal regimes of streams and reveal their differential
vulnerability to climate warming and human-related
water uses. The two approaches presented here can be applied
with a variety of other continuous phenomena to address
historical changes, extreme events, and their associated
ecological responses.