The Colors of Proxy Noise

Abstract. Uncertainty in paleoclimate time series is inherent to the complex biological and physical processes involved in forming and archiving them in the environment for centuries or longer. The timescale-dependency of this uncertainty is often referred to as "noise" of a particular color based on similarities between the power spectrum of a timeseries 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. In paleoclimate research, the frequency characteristics of proxy noise are often assumed based on first principles rather than estimated directly, which risks either inflating or underestimating error at particular frequencies. Here, we synthesize several studies that use a common method to estimate the spectrum of error in ice core, coral, and tree-ring data. We conceptualize how time-scale dependent noise in proxy time series is created through the archive formation and data processing. Our results suggest 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 likely more common in biological archives such as tree rings and corals. Our aim is to clarify these concepts and provide tools for assigning noise terms in proxy system models, data assimilations, and other experiments.