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Briggs, K. (2006). ENSO Event Reproduction: A Comparison of an EOF vs. A Cyclostationary (CSEOF) Approach. Master's thesis, Florida State University, Tallahassee, FL.
Abstract: In past studies, El Niño-Southern Oscillation (ENSO) events have been linked to devastating weather extremes. Climate modeling of ENSO is often dependent on limited records of the pertinent physical variables, thus longer records of these variables is desirable. Noisy signals, such as monthly sea surface temperature, are good candidates for reproduction by several existing auto-regression techniques. Through auto-regression, influential principal component modes are broken down into a series of time points that are each dependent upon an optimal weighting of the surrounding points. Using these unique numerical relationships, a noisy signal can be reproduced by thus processing the leading modes and adding an artificial record of properly distributed noise. Statistical measures of important ENSO regions suggest that the nature of oceanic and atmospheric anomalous events is cyclic with respect to certain timescales; for example, the monthly timescale. To detect ENSO signals in the presence of a varying background noise field, the detection method should take into account the signal's strong phase-locking with this nested variation. Cyclostationary Emperical Orthogonal Functions (CSEOFs) are built upon the idea of nested cycles, unlike traditional EOFs, which incorporate a design that is better detailed for stationary processes. In this study, both EOF and CSEOF modes of a 50-year Pacific SST record are processed using an auto-regression technique, and several sets of artificial SST records are constructed. Appropriate statistical indices are applied to these artificial time series to ensure an acceptable consistency with the real record, and then artificial data is produced using the artificial time series. In all cases, the cyclostationary approach produces more realistic warm ENSO events with respect to timing, strength, and other traits than does the stationary approach. However, both methods produce only a fair representation of cold events, suggesting that further study is necessary for improvement of La Niña modeling. Shorter records of variables such as sea level height and Pacific wind stress anomalies can hinder the usefulness of auto-regression, owing to time point dependence on surrounding points. Using a regression technique to find an evolutionary consistency (i.e. physically consistent patterns) between one of these variables and a variable with a longer record (such as SST) can eliminate this problem. Once a regression relationship is found between two variables, the variable with the shorter record can be re-written to match the time evolution of the variable with the longer record. Here regression, both EOF and CSEOF, is performed on both sea surface temperature and sea level height (a 20-year record), and sea surface temperature and wind stress (a 39-year record). Once the regression relationships are found, artificial SST time series are incorporated in place of the original time series to produce several artificial 50-year SLH and wind stress data sets. 5 Pacific regions are chosen, and statistics and behavior of the artificial sets within these regions are compared to those of the original data. Once again the cyclostationary approach fares better than the stationary. In particular the EOF assumption of cross correlational symmetry fails to capture the direction-dependence of ENSO evolution, causing inconsistent ENSO behavior. This renders an EOF method insufficient for climate modeling and prediction, and implies that a better aim is to incorporate physical cyclic features via a cyclostationary method.
Keywords: EOF, Autoregression, Wind Stress, Sea Level Height, SST, ENSO, Regression, CSEOF, Cyclostationary
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