Optimal Fingerprints for the Detection of Time-dependent Climate Change

Abstract An optimal linear filter (fingerprint) is derived for the detection of a given time-dependent, multivariate climate change signal in the presence of natural climate variability noise. Application of the fingerprint to the observed (or model simulated) climate data yields a climate change detection variable (detector) with maximal signal-to-noise ratio. The optimal fingerprint is given by the product of the assumed signal pattern and the inverse of the climate variability covariance matrix. The data can consist of any, not necessarily dynamically complete, climate dataset for which estimates of the natural variability covariance matrix exist. The single-pattern analysis readily generalizes to the multipattern case of a climate change signal lying in a prescribed (in practice relatively low dimensional) signal pattern space: the single-pattern result is simply applied separately to each individual base pattern spanning the signal pattern space. Multipattern detection methods can be applied either t...