Examining the effect of sample size on the estimation of low-frequency signals in tree-ring chronologies

Dendrochronology utilizes mean values of individual tree-ring indices to average out noise and strengthen common signals, typically associated with climate. Expressed Population Signal (EPS) is commonly used to assess the degree to which a chronology represents the common signal. However, there is a lack of studies on how EPS reflects low-frequency signals. In this study, we propose a frequency-dependent EPS (FEPS) approach to evaluating the low-frequency signal strength. Extensive tests were conducted using tree rings from Chinese Loess Plateau. We found that as timescales lengthen, EPS decreases due to declining inter-series correlations, thus demanding larger sample sizes. This finding remains robust across different detrending methods, filtering methods, filter orders, and treatments for end effects. Determining sample sizes by standard EPS (common use of EPS with unfiltered series) has a limited impact on multi-year frequencies, but considerably influences timescales exceeding a decade. Our study reveals a prevalent underestimation of sample size requirements for robust multi-year and interdecadal signals estimation, and the FEPS approach is expected to potentially enhance our understanding of long-term climate dynamics.