Time series processing
Correlation of time series can be caused by similarity in variations
occurring at different frequencies. To be able to identify the relative
effect due to long term trends (low frequency) and interannual
variability (high frequency), three types of data were used: original
data (combination of both effects), detrended data (only interannual
variability) and smoothed data (dominance of long term trend). Time
series subject to low frequency influence are usually strongly
auto-correlated, which violates the assumption of serial independence
required for correlation test. One way to account for autocorrelation is
to re-assess the number of degrees of freedom, which results in higher
p-value for the same correlation coefficient. Pyper and Peterman (1998)
developed the so-called ‘modified Chelton method’ that allows one to
calculate a critical correlation coefficient value associated with a
given p-value. This method was later adapted by Barker, Hannaford,
Chiverton, and Svensson (2016) to account for missing values in time
series. We applied this approach for calculation of the p-values for the
correlation test of original and smoothed data. Smoothing of the data
was conducted using the LOESS method with a span of 0.1-0.2, depending
on the time series length, and one degree polynomial. The map plotting
was done with the Matlab package M_Map (Pawlowicz, 2019).