Optimizing significance testing of astronomical forcing in cyclostratigraphy

Abstract

The recognition of astronomically forced (Milankovitch) climate cycles in geological archives marked a major advance in Earth science, revealing a heartbeat within the climate system of general importance and key utility. Power spectral analysis is the primary tool used to facilitate identification of astronomical cycles in stratigraphic data, but commonly employed methods for testing the statistical significance of relatively high narrow-band variance of potential astronomical origin in spectra have been criticized for inadequately balancing the respective probabilities of type I (false positive) and type II (false negative) errors. This has led to suggestions that the importance of astronomical forcing in Earth history is overstated. It can be readily demonstrated, however, that the imperfect nature of the stratigraphic record and the quasiperiodicity of astronomical cycles sets an upper limit on the attainable significance of astronomical signals. Optimized significance testing is that which minimizes the combined probability of type I and type II errors. Numerical simulations of stratigraphically preserved astronomical signals suggest that optimum significance levels at which to reject a null hypothesis of no astronomical forcing are between 0.01 and 0.001 (i.e., 99–99.9% confidence level). This is lower than commonly employed in the literature (90–99% confidence levels). Nevertheless, in consonance with the emergent view from other scientific disciplines, fixed-value null hypothesis significance testing of power spectra is implicitly ill suited to demonstrating astronomical forcing, and the use of spectral analysis remains a difficult and subjective endeavor in the absence of additional supporting evidence.