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).