Optimal Detection Using Cyclostationary EOFs

Abstract

Many climatic and geophysical processes are cyclostationary and exhibit appreciable cyclic (monthly, daily, etc.) variation of their statistics in addition to interannual fluctuations. Utilization of this nested variation of statistics will lead to a better chance of detecting a signal in such a varying background noise field, especially when the signal is strongly phase locked with the nested cycle. In this study, a detection technique is constructed in terms of cyclostationary empirical orthogonal functions, which take the nested periodicity of noise statistics into account. To investigate the improved performance of the cyclostationary approach the developed algorithm is applied to three specific detection examples: El Niño, greenhouse warming, and sunspot fluctuations. In all the test cases, signal-to-noise ratio is raised between 2% and 43% compared with that of a stationary detection technique. The variation of signal strength when a detection filter is constructed based on a different section of modeled noise is within the range of mean signal-to-noise ratio for small to moderate signals. There is a significant variation, however, of signal strength when a detection filter is constructed based on a different model dataset. This implies that model discrepancy is a more important factor than sampling error for the accuracy of the detection method and that climate models need to be improved further in their noise statistics.