The colors of proxy noise

Abstract. The complex biological and physical processes that preserve paleoclimate information over centuries or longer introduce variations in proxy time series that are unrelated to the true climate. These non-climatic variations act on different timescales and are often referred to as “noise” of a specific color, based on similarities between a time series' power spectrum and the electromagnetic spectrum of light. For example, “white noise” equally affects all timescales, where “red noise” dominates only on long timescales, similar to longwave red light. Noise spectra in proxy records have far-reaching implications in paleoclimate research, but noise characteristics are often assumed based on first principles rather than estimated directly, risking either inflating or underestimating error at particular frequencies. Here, we provide concrete definitions of the various types of timescale-dependent errors that are present in proxy data, and review the literature on methods for quantifying noise terms. We then synthesize the results of several published studies that use a common empirical approach for estimating the noise spectrum in ice-core, coral, and tree-ring data. We posit that the colors of proxy noise are archive-specific, with white noise dominating in depositional archives such as ice cores and marine sediment cores, while red noise is more common in biological archives such as tree rings and corals. Our synthesis supports assigning specific colored noise terms in proxy system models, data assimilations and other experiments.