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Using the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) for 1958 to 2001, adjusted for bias over the southern oceans prior to 1979, an analysis is made of global patterns of monthly mean anomalies of atmospheric mass, which is approximately conserved globally. It differs from previous analyses of atmospheric circulation by effectively area weighting surface or sea level pressure that diminishes the role of high latitudes. To examine whether global patterns of behavior exist requires analysis of all seasons together (as opposite seasons occur in each hemisphere). Empirical orthogonal function (EOF) analysis, R-mode varimax-rotated EOF analysis, and cyclostationary EOF (CSEOF) analysis tools are used to explore patterns and variability on interannual and longer time scales. Clarification is given of varimax terminology and procedures that have been previously misinterpreted. The dominant global monthly variability overall is associated with the Southern Hemisphere annular mode (SAM), which is active in all months of the year. However, it is not very coherent from month to month and exhibits a great deal of natural unforced variability. The third most important pattern is the Northern Hemisphere annular mode (NAM) and associated North Atlantic Oscillation (NAO), which is the equivalent Northern Hemisphere expression. Neither of these is really a global mode, although they covary on long time scales in association with tropical or external forcing. For monthly data, the second mode is coherent with Niño-3.4 sea surface temperatures and thus corresponds to El Niño–Southern Oscillation (ENSO), which is truly global in extent. It exhibits more coherent evolution with time and projects strongest onto the interannual variability, where it stands out by far as the dominant mode in the CSEOF analysis. The CSEOF analysis extracts the patterns phase locked with annual cycle and reveals their evolution throughout the year. Standard EOF and varimax analyses are not able to evolve with time of year unless the analysis is stratified by season. Varimax analysis is able to extract the SAM, NAM, and ENSO modes very well, however.

The misleading aspect of the statistical analyses used in Dommenget and Latif, which raises concerns on some of the reported climate modes, is demonstrated. Adopting simple statistical techniques, the physical existence of the Indian Ocean dipole mode is shown and then the limitations of varimax and regression analyses in capturing the climate mode are discussed.

The authors analyzed climate data, seasonal averages of precipitation, and maximum, mean, and minimum temperatures over the years 1960–90, from 18 stations spread around the island of Puerto Rico in the Caribbean, to determine whether these distinguish the existence of climate zones in Puerto Rico. An R-mode principal components analysis (PCA), with varimax rotation to the seasonal data in order to reduce their dimensionality, was applied. The first five principal components, found by cross validation to be statistically significant, account for 99% of the variability in the 16 variables included in the analysis. These five components are related to annual variation in mean and minimum temperature (first PC), annual maximum temperature (second PC), and spring, summer, and fall precipitation (third through fifth PCs). A self-organizing map, an artificial neural network algorithm, was then employed to classify the first five PC scores in an optimal fashion. The scores were classified by the neural ...

Singular value decomposition (SYD) analysis is frequently used to identify pairs of spatial patterns whose time series are characterized by maximum temporal covariance. It tends to compress complicated temporal covariance between two fields into a relatively few pairs of spatial patterns by maximizing temporal covariance explained by each pair of spatial patterns while constraining them to be spatially orthogonal to the preceding ones of the same field. The resulting singular vectors are sometimes complicated and difficult to interpret physically. This paper introduces a method, an extension of SVD analysis, which linearly transforms a subset of total singular vectors into a set of alternative solutions using a varimax rotation. The linear transformation (known as “rotation"), weighting singular vectors by the square roots of the corresponding singular values, emphasizes geographical regions characterized by the strongest relationships between two fields, so that spatial patterns corresponding to...

Empirical orthogonal function (EOF) analysis has been applied to nine years of daily 500-hPa data for the Southern Hemisphere from which synoptic-scale variations had been removed by application of a 10-day low-pass fitter. This resulted in 11 principal modes, accounting for 66% of the variance, which were then regionalized through application of a Varimax rotation. These rotated patterns included a high-latitude mode covering the Antarctic, eight others defining regional perturbation in the principal storm tracks at high latitudes, and two residual patterns not used for this investigation. Persistent anomalies were defined as spells where the time coefficient of the rotated EOF was greater than 1 standard deviation or less than −1 standard deviation for a period of 10 days or more, and 220 of these spells were obtained for the nine EOFs used in the analysis. Storm tracks were identified in two ways: 1) from high-pass filtering of the daily 5OO-hPa geopotential height anomalies to include periods...

18 pages, 12 figures, 2 tables, 2 appendixes, A proper description of ocean–atmosphere interactions is key for a correct understanding of climate evolution. The interplay among the different variables acting over the climate is complex, often leading to correlations across long spatial distances (teleconnections). On some occasions, those teleconnections occur with quite significant temporal shifts that are fundamental for the understanding of the underlying phenomena but that are poorly captured by standard methods. Applying orthogonal decomposition such as maximum covariance analysis (MCA) to geophysical datasets allows us to extract common dominant patterns between two different variables, but generally suffers from (i) the nonphysical orthogonal constraint as well as (ii) the consideration of simple correlations, whereby temporally offset signals are not detected. Here we propose an extension, complex rotated MCA, to address both limitations. We transform our signals using the Hilbert transform and perform the orthogonal decomposition in complex space, allowing us to correctly correlate out-of-phase signals. Subsequent varimax rotation removes the orthogonal constraints, leading to more physically meaningful modes of geophysical variability. As an example, we have employed this method on sea surface temperature and continental precipitation; our method successfully captures the temporal and spatial interactions between these two variables for (i) the seasonal cycle, (ii) canonical ENSO, (iii) the global warming trend, (iv) the Pacific decadal oscillation, (v) ENSO Modoki, and finally (vi) the Atlantic meridional mode. The complex rotated modes of MCA provide information on the regional amplitude and, under certain conditions, the regional time lag between changes on ocean temperature and land precipitation, The authors gratefully acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement 813844, and also from the Spanish government through the ‘‘Severo Ochoa Centre of Excellence’’ accreditation (CEX2019-000928-S)