Arguez, A. (2005). *Indexing, Mode Definition, and Signal Extraction in Climate Research: Analysis and Applications Involving the MJO, the AO, and ENSO*. Ph.D. thesis, Florida State University, Tallahassee, FL.

There are two objectives of the present study. The primary objective is to undertake the following research projects involving the Arctic Oscillation (AO), the El NiĆ±o Southern Oscillation (ENSO), and the Madden Julian Oscillation (MJO): (1) an assessment of the utility of using Cyclo-stationary empirical orthogonal function (CSEOF) analysis to define the AO, (2) an empirical analysis of ENSO impacts based on varying indicator and impact regions, (3) detection and extraction of the MJO signal from QuikSCAT, and (4) the development of a general algorithm for determining optimal filter weights for time series endpoints. A secondary objective is to enumerate the statistical and analytical treatments of the AO, ENSO, and the MJO. This will include comparisons of how these three modes are defined (including their indices) and extracted from geophysical data sets. The AO is defined using empirical orthogonal function (EOF) analysis of sea level pressure north of 20'N. The resulting spatial pattern and time series captures the regional influence of its precursor, the North Atlantic Oscillation (NAO), which is a measure of mid-latitude zonal winds over the North Atlantic. ENSO was originally defined as the pressure difference between Tahiti and Darwin, Australia: the Southern Oscillation Index. Scientists now primarily use sea surface temperature (SST) anomalies averaged over one of the Ni'o regions as ENSO indices. The MJO was originally observed using spectral analysis of zonal wind time series in the Indian Ocean and Western Pacific. Present day researchers use extensions of EOF analysis to construct MJO time series. For all three climate modes, the creation of high quality space-time data sets has allowed for more sophisticated indices, supplanting the simpler point-based metrics. For the AO project, the cyclo-stationarity of Northern Hemisphere sea level pressure variability is considered. CSEOF analysis is an extension of EOF analysis that allows multiple spatial maps per mode. It accomplishes this by cyclically extending the covariance matrix based on a parameter called the nested period. By using a nested period of 12, a climate mode can be decomposed into a series of 12 monthly maps and an associated time series. Unlike EOF PC time series, which typically have larger amplitudes during winter months, CSEOF PC time series do not favor a particular season because the physical evolution of the climate mode is posited in the loading vectors (the maps) rather than the time series. This is impossible to accomplish with regular EOF analysis because it relegates each mode to one single map. A compelling case is made for a cyclo-stationary interpretation of AO variability. The leading CSEOF mode includes AO-type variability during a winter regime, as well as a summer regime characterized by pressure anomalies centered over Mongolia and associated with rainfall variability in the vicinity of the Ganges delta and eastern China. EOF modes that contribute to the resulting maps of the leading CSEOF mode are identified, including the eighth mode, which is deemed responsible for the summertime Asian pattern. CSEOF analysis of the AO mode only exemplifies the power of CSEOF analysis with regard to transferring a mode's physical evolution from a PC time series to a series of loading vectors. For the ENSO project, traditional ENSO impact analysis was recast to investigate the teleconnections between U.S. climate and varying indicator regions of SST anomalies in the tropical Pacific. This serves the dual purpose of finding a targeted indicator region for a particular impact zone (i.e. a localization of the teleconnection pattern) and indirectly assessing the viability of well-established ENSO indices (i.e. the Ni'o indices). Based on a selection of impact grid points with known ENSO responses, it appears that the most appropriate indicator region often varies from one impact grid point to another, as well as from warm SST phase to cold SST phase. In addition, air temperature composites behave differently than precipitation composites. In order to simultaneously consider the 'impact perspective' detailed above with the typical 'indicator perspective' (in which climate impacts are computed based on the well-established Ni'o indices), EOF analysis of composited climate fields, conditioned on SST phase, as functions of indicator region and impact zone was performed. The resulting modes represent indicator-impact pairs. Each mode has an impact amplitude function (a spatial temperature or precipitation anomaly signature over the impact region) and an associated indicator weighting function, which modulates the impact amplitude function based on the location of the indicator region. Based on this approach, the unusual yet well-established La Ni'a air temperature impact over the U.S. when using the Ni'o 1+2 region is accounted for as the superposition of two EOF modes. In addition, a teleconnection between tropical Pacific SST and Southeastern U.S. temperature anomalies is documented that is not related to ENSO. For the MJO project, wind data from the SeaWinds instrument on the QuikSCAT satellite are investigated to ascertain how well the surface manifestation of the MJO can be resolved. The MJO signal is detected in non-filtered gridded data using Extended EOF analysis of the zonal wind field, overshadowed by annual, semi-annual, and monsoon-related modes. After bandpass filtering with Lanczos weights, MJO signals are clearly detected in several kinematic quantities, including the zonal wind speed, the zonal pseudostress, and the velocity potential. Extraction of the MJO using QuikSCAT winds compares favorably with extraction using NCEP Reanalysis 2, except that the QuikSCAT signal appears to be more robust. For the filtering project, least squares techniques are utilized to retain endpoint intervals that are normally discarded due to filtering with convolutions in the time domain. The techniques minimize the errors between the pre-determined frequency response function (FRF) of interior points with FRF's that are to be determined for each position in the endpoint zone. The least squares techniques are differentiated by their constraints: (1) unconstrained, (2) equal-mean constraint, and (3) an equal-variance constraint. The equal-mean constraint forces the new weights to sum up to the same value as the pre-determined weights. The equal-variance constraint forces the new weights to be such that, after convolved with the input values, the expected variance is identical to the expected variance of the interior points. These 3 least squares methods are tested under three separate filtering scenarios and compared to each other as well as to the spectral filtering method, which is the standard of comparison. The results indicate that all 4 methods (including the spectral method) possess skill at determining suitable endpoints estimates. However, both the unconstrained and equal-mean schemes exhibit bias toward zero near the terminal ends due to problems with appropriating variance. The equal-variance and spectral techniques do not show evidence of this attribute and were never the worst performers. The equal-variance method showed great promise in the ENSO project involving a 5-month running mean filter, and performed at least on par with the other methods for virtually all time series positions in all three filtering scenarios.