Extended Empirical Orthogonal Function Analysis Research Articles

Structure and Characteristics of Synoptic-Scale Waves in the Northern Eurasian Storm Track during Summer

Abstract This study examined the dominant structure and characteristics of synoptic-scale (2–8-day periods) waves over northern Eurasia during 40 summer seasons (June–August, 1979–2018). The synoptic-scale wave patterns are isolated using an extended empirical orthogonal function (EEOF) analysis on the 300-hPa geopotential height anomalies, and a composite based on atmospheric circulation fields and gridded precipitation product. The wave patterns are classified into two types from two pairs of EEOF modes. These two different wave types are defined as the polar frontal (PF) mode and Arctic frontal (AF) mode, respectively. The PF-mode waves are initiated in the North Atlantic sector to the west of the British Isles. They propagate eastward across Siberia into the North Pacific, and produce precipitation mainly over the Eurasian polar frontal zone. The AF-mode wave train arcs along the climatological Arctic frontal zone (AFZ). The AF-mode waves originate near the Scandinavian Peninsula. Their eastward passage brings precipitation along the AFZ. The development of the synoptic-scale waves is reflected by unique background conditions over northern Eurasia. The lower-tropospheric baroclinicity in southern Siberia and central Asia favored the baroclinic growth of the PF-mode waves. The AF-mode waves are trapped in the well-organized baroclinic zone along the north coast of the Eurasian continent. The baroclinic zone is coupled with a band of large meridional gradient of potential vorticity in the upper troposphere, suggesting that this band acts as a waveguide for the AF-mode waves. Significance Statement This study examines the synoptic-scale waves in the 2–8-day range of time scales over northern Eurasia during summer. The synoptic-scale waves are categorized into two distinct types at different latitude bands by the EEOF analysis on the 300-hPa z anomalies. They are defined as polar frontal (PF) mode and Arctic frontal (AF) mode. Then the EEOF-based composite analysis is conducted to detect the large-scale circulation anomalies associated with the propagation of different types of synoptic-scale waves. The structure and characteristics are examined. The roles of the mean background conditions in the development and propagation of the respective types are discussed. The behavior of these wave disturbances as rain-producing weather systems is also examined.

Evaluating Coupled Climate Model Parameterizations via Skill at Reproducing the Monsoon Intraseasonal Oscillation

Abstract Empirically generated indices are used to evaluate the skill of a global climate model in representing the monsoon intraseasonal oscillation (MISO). This work adapts the method of Suhas et al., an extended empirical orthogonal function (EEOF) analysis of daily rainfall data with the first orthogonal function indicating MISO strength and phase. This method is applied to observed rainfall and Community Earth System Model (CESM1.2) simulation results. Variants of the CESM1.2 including upper ocean parameterizations for Langmuir turbulence and submesoscale mixed layer eddy restratification are used together with the EEOF analysis to explore sensitivity of the MISO to global upper ocean process representations. The skill with which the model variants recreate the MISO strength and persistence is evaluated versus the observed MISO. While all model versions reproduce the northward rainfall propagation traditionally associated with the MISO, a version including both Langmuir turbulence and submesoscale restratification parameterizations provides the most accurate simulations of the time scale of MISO events.

Leading patterns of the satellite-era summer precipitation over West Africa and associated global teleconnections

Precipitation patterns over West Africa display a broad range of timescales, from the intraseasonal to decadal timescales, as well as multidecadal shifts. Here we investigate the dominant patterns of the July to September precipitation over the region and the related ocean-atmosphere anomalies during the satellite-era from 1983 to 2017. Using extended empirical orthogonal function analysis of an ensemble of nine precipitation datasets, we identify two dominant modes that together account for about 33% of the variance. The Sahel mode displays spatially coherent increases in precipitation over much of West Africa and a decrease at the Guinea Coast, and is closely reproduced by linear trend analysis. Linear trends explain 25–53% of the Sahel variance from the drier mid-1980s to the wetter mid-1990s. The Guinea Coast mode displays robust precipitation anomalies south of the Sahel, with strong interannual variability and a statistically non-significant trend. The Sahel mode is associated with a northerly displacement of the Inter-Tropical Convergence Zone (ITCZ), warm North Atlantic with cold blob in the subpolar gyre region, warm Mediterranean Sea, warm tropical southwest Indian Ocean and negative Pacific decadal variability pattern. The Atlantic Niño leads the Guinea Coast mode by two months. Both Sahel and Guinea Coast modes are substantially influenced by the interactions between meridional (displacements of the ITCZ) and zonal (variations of the Walker Circulation) atmospheric circulations. The southerly displacement of the ITCZ, convection, upper-level divergence and surface convergence in the equatorial Atlantic associated with the Guinea Coast mode is horizontally compensated by strong surface divergence and upper-level convergence over the equatorial Pacific where anomalous cooling prevails, implying a strong role for the Walker Circulation during this period.

MJO Prediction Skill Using IITM Extended Range Prediction System and Comparison with ECMWF S2S

Eastward propagating Madden–Julian Oscillation (MJO) is a dominant mode of the intraseasonal variability and hence a potential source of intraseasonal predictability. Therefore, advancing MJO prediction using state-of-the-art dynamical model is of utmost importance for improving intraseasonal prediction. The prediction skill and predictability of MJO are assessed using 44 members ensemble hindcast (16 years data; 2001–2016) of CFSv2 based extended range prediction (ERP) system of IITM as well as 10 member ensemble hindcast (16 years data; 2001–2016) of ECMWF S2S dataset. The MJO is diagnosed using a newly developed Extended Empirical Orthogonal Function (EEOF) analysis. Near equatorial (15° S–15° N) model anomaly fields are projected onto the leading pair of observed eigen modes. The leading pair of observed eigen modes are obtained based on the EEOF analysis of the combined field of zonal wind at 200 hPa (U200), zonal wind at 850 hPa (U850) and velocity potential at 200 hPa (chi200). Model forecasted principal components (PCs) are quantitatively compared with observed PCs using bivariate correlation coefficient and root mean square error (RMSE). We find that MJO could be predicted up to around 22 days (around 31 days) for IITM ERP system (ECMWF S2S dataset) as measured by anomaly correlation coefficient remains larger than 0.5 and RMSE remains lower than 1.4. This prediction skill is quite low compared to potential predictability, which is estimated as more than 40 days both for IITM-ERP and ECMWF system. MJO prediction skill varies with initial MJO phase, particularly at the longer lead. This variation is more significant for the ECMWF system. Model (both for IITM-ERP and ECMWF) predicted amplitude drops at a faster rate and phase propagation speed for almost all initial phase is slower and amplitude is weaker compared to the observation. It could be concluded that even the state-of-the-art models [IITM-ERP (basically NCEP CFSv2) and ECMWF] are also not free from systematic errors/biases. Hence, there is an enormous space for improving MJO prediction skill by reducing these errors/biases in the dynamical model and error in the initial condition.

Extension of the bimodal intraseasonal oscillation index using JRA-55 reanalysis

This study aims to extend the bimodal intraseasonal oscillation (ISO) index, developed by Kikuchi et al. (Clim Dyn 38:1989–2000, 2012), using JRA-55 reanalysis back in time to 1958. The bimodal ISO index is composed of two distinct ISO indices: the Madden–Julian oscillation (MJO) index and the boreal summer ISO (BSISO) index, each aiming to capture the ISO behavior during boreal winter and summer, respectively. These indices are derived by means of extended empirical orthogonal function (EEOF) analysis applied to outgoing longwave radiation (OLR) during boreal winter and summer, respectively. By combining the MJO and BSISO indices, the state of the ISO can be reasonably represented over the course of the year. First, the original index is updated using observed OLR until recently (–Jan. 2017) with a modification of the use of extended winter and summer months (Dec.–Apr./Jun.–Oct.) instead of normal winter and summer months (Dec.–Feb./Jun.–Aug.) in EEOF analysis. The updated version is quite consistent with the original counterpart, whereas it is arguably able to represent the ISO more faithfully throughout the year. In the same manner, a JRA-55-based index is constructed. Although JRA-55 OLR has systematic biases, the resulting JRA-55-based bimodal ISO index is in excellent agreement with the observation-based index. A comparison between JRA-55 and its subset, JRA-55C (satellite observations are not assimilated at all) suggests that the JRA-55-based index is reliable even in the pre-satellite era. Interannual variability and long-term trend of the ISO activity are also discussed. The newly developed, long-term JRA-55-based index will be useful for a number of applications.

New real-time indices for the quasi-biweekly oscillation over the Asian summer monsoon region

The quasi-biweekly oscillation (QBWO), with a periodicity of 10–30 days, is one of the most important modes of intraseasonal variability over the Asian summer monsoon region. Unlike the lower frequency (30–60 days) Madden–Julian Oscillation, which has had several real-time indices proposed for monitoring and predicting its state, there are very few equivalents for the QBWO. Given that extended empirical orthogonal function (EEOF) analysis is arguably more suitable than empirical orthogonal function analysis for capturing the canonical spatial and temporal structure of a propagating wave system, we introduce two new indices for real-time monitoring of the QBWO over the tropical western North Pacific (WNP) and Indian Ocean (IO), separately, by projecting outgoing longwave radiation (OLR) anomalies onto the two leading modes of EEOF analysis for the 10–30-day-filtered OLR anomalies over the two basins during 1980–2012. The newly proposed QBWO indices faithfully represent the vigorous QBWO activities over the WNP and IO, which are underestimated and/or not necessarily well represented by existing indices. It is also shown that the indices are able to reveal the connections between the QBWO and other pronounced phenomena, such as the onset of the South China Sea and Indian monsoons, the occurrence of extreme rainfall events, and tropical cyclone genesis. Thus, monitoring and predicting the evolution of the QBWO in these two basins based on the new QBWO indices should help in the quest to mitigate future damage caused by weather-related disasters at an extended lead time.

An Operational Tracking Method for the MJO Using Extended Empirical Orthogonal Functions

Several methods are available to track the intraseasonal oscillation, namely the Madden–Julian oscillation (MJO) and monsoon intraseasonal oscillation (MISO). However, no methods to track both the modes in a uniform framework for real-time application exist. A new method to track the smooth propagation of the MJO and MISO is proposed to use it for real-time monitoring. The new approach is based on extended empirical orthogonal function (EEOF) analysis of the combined field of meridionally averaged zonal wind at 850 hPa (U850), zonal wind at 200 hPa and the velocity potential at 200 hPa. The EEOF method does not merely capture the MJO but also smooths (i.e., filters out undesired modes) the temporal propagation in the phase space defined by first two leading principal components (PCs) of the EEOF. Using these leading PCs, we additionally introduce a seasonally varying regression coefficient to filter out the space time structure of the MJO in various fields (rainfall/outgoing long-wave radiation, etc.). These reconstructed fields are then used to link the bidirectional phase movement (i.e., northward propagating MISO and eastward propagating MJO) during boreal summer. The life cycle of the MJO and MISO could be captured with equal fidelity with this current method. MJO filtering could be carried out for any space–time data, not limited to the variables/fields used in EEOF analysis. Examples of the TOGA-COARE and DYNAMO period MJO as well as a few strong MISO events are discussed to check the robustness of the newly proposed method.

A new method to compute the principal components from self-organizing maps: an application to monsoon intraseasonal oscillations

The study develops a self-organizing map (SOM)-based local principal component analysis (PCA) to obtain the linearly decorrelated principal components (PCs) of monsoon intraseasonal oscillations (MISOs). Although the SOM-derived feature maps are not orthogonal like empirical orthogonal function (EOFs), we show that in the case of MISOs simple mathematical substitution can make the SOM-derived PCs linearly decorrelated to each other. Thus, the SOM-based local PCA is seen also to be statistically equivalent to extended EOF analysis when applied to MISO analysis. The life cycle and phase evolution of MISO through SOM-based PCA is robust and conforms to the results based on extended EOFs besides having potential to give new information. The remarkable similarity of results with the symmetric SOM configurations shows the effectiveness of these methods for use as empirical reduction models for climate patterns. The asymmetric SOM lattice configurations derive similar phase evolution as compared to a symmetric lattice, but asymmetric temporal evolutions in the PC-defined phase space. The results once again endorse the mathematical basis of PCA through SOM for geophysical applications.

Oscillatory and Propagating Modes of Temperature Variability at the 3–3.5- and 4–4.5-yr Time Scales in the Upper Southwest Pacific Ocean

Abstract This paper investigates oscillatory and propagating patterns of normalized surface and subsurface temperature anomalies (from the seasonal cycle) in the southwest Pacific Ocean using an extended empirical orthogonal function (EEOF) analysis. The temperature data (and errors) are from the Digital Atlas of Southwest Pacific upper Ocean Temperatures (DASPOT). These data are 3 monthly in time (January, April, July, and October), 2° × 2° in space, and 5 m in the vertical to 450-m depths. The temperature anomalies in the EEOF analysis are normalized by the objective mapping temperature errors at each grid point. They are also Butterworth filtered in the 3–7-yr band to examine interannual variations in the temperature field. The oscillating and propagating patterns of the modes are examined across four vertical levels: the surface, and 100-, 250-, and 450-m depths. The dominant mode EEOF (70% of the total variance of the filtered data) oscillates in a 4–4.5-yr quasi-periodic manner that is consistent with El Niño–Southern Oscillation (ENSO). Anomalies peak first at the surface in the subtropics between New Caledonia and Fiji (centered around 17°S, 177°E), then 6 months later in the tropical far west centered around the Solomon Islands (5°S, 153°–157°E), with a maximum at the base of the mixed layer (100 m) and upper thermocline (250 m), and then eastward in the northeast of the southwest Pacific region (0°–10°S, 160°E–180°). Mode 2 (25% variance of the filtered data) has a periodicity of 3–3.5 yr, with centers of action in all four vertical levels. The mode-2 patterns are consistent with variations in the subtropical gyre circulation, including the East Australian Current and its separation, and are continuous with the Tasman Front. Two spatial dipoles are apparent: (i) one in sea surface temperature (SST) at about 5°S, straddling west–east either side of the Solomon Islands, consistent with the classic Pacific-wide ENSO SST anomaly mode, and (ii) a subsurface dipole pattern, with centers in the Solomon Islands region at 100- and 250-m depths, and the western Tasman Sea (27°–33°S, 157°–161°E) at 250- and 450-m depths, consistent with dynamic changes in the gyre intensity.

A potential problem with extended EOF analysis of standing wave fields

The extended empirical orthogonal function (EEOF) analysis of signals containing a standing wave component is considered. It is shown using a simple analytical model that for a single time‐lag EEOF analysis, two EEOF patterns describe the standing wave, and that their associated eigenvalues become degenerate if the lag chosen is close to a zero of the sample autocovariance function of the standing wave time series. This degeneracy strongly affects the relative magnitudes of the two sectors of each EEOF pattern and the structure of the associated spatial pattern. A set of EEOF analysis of varying lags is performed on a tropical Pacific sea level pressure (SLP) dataset, known to be dominated by standing variance, and the predictions of the analytical model are verified. As well, it is seen that at degeneracy there is a reduction in the quality of the spatial patterns produced by the EEOF analysis.

Extended EOF Analysis of Tropical Disturbances: TOGA COARE

Empirical orthogonal function (EOF) analyses are performed of time‐height series of zonal and meridional winds and of cumulonimbus heating and drying in the Tropics. The data are from a rawinsonde array in the western Pacific located between the equator and 108S during the intensive observation period of the Tropical Ocean Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment (TOGA COARE). The EOF analyses are performed by applying a window of 20 days to the data and thus calculating the EOFs of the time development of the vertical structure. The wind time series is found to be well represented by two pairs of EOFs, each representing an oscillation. The first oscillation has a period of approximately 40 days, is predominantly in the zonal wind component, and has a first internal mode vertical structure with westerly anomalies in the lower troposphere corresponding to easterly perturbations in the upper troposphere. This pair describes 48.3% of the variance. A second EOF pair in the wind is a zonal variation that occurs predominantly in the upper troposphere. It has a period of approximately 24 days and describes 13.9% of the variance. The heating‐drying series is described by a dominant oscillation of period 40 days representing 41% of the variance. The structure is maximum in the middle troposphere and is associated with the same physical phenomeon as the dominant (u, y) oscillation. The second EOF pair for heating‐drying has a period of 13 days, so there is a large time separation in periodiocities for heating‐drying compared to that for winds. The second (13 day) oscillation in heating‐drying has the same vertical structure as the dominant (40 day) oscillation.

Modes of North Atlantic Decadal Variability in the ECHAM1/LSG Coupled Ocean–Atmosphere General Circulation Model

Abstract The climate variability in the North Atlantic sector is investigated in a 325-yr integration of the ECHAM1/ LSG coupled ocean–atmosphere general circulation model. At the interannual timescale, the coupled model behaves realistically and sea surface temperature (SST) anomalies arise as a response of the oceanic surface layer to the stochastic forcing by the atmosphere, with the heat exchanges both generating and damping the SST anomalies. In the ocean interior, the temperature spectra are red up to a period of about 20 years, and substantial decadal fluctuations are found in the upper kilometer or so of the water column. Using extended empirical orthogonal function analysis, two distinct quasi-oscillatory modes of ocean–atmosphere variability are identified, with dominant periods of about 20 and 10 years, respectively. The oceanic changes in both modes reflect the direct forcing by the atmosphere through anomalous air–sea fluxes and Ekman pumping, which after some delay affects the intensity of t...

複素経験直交関数(CEOF)を用いた時空間データ解析

The usefulness of complex empirical orthogonal function (EOF) analysis for quasi-periodic propagating phenomena is discussed using the sea surface temperature data in the equatorial Pacific. The features of the complex EOF analysis are as follows: 1) It is easy to interpret physically a propagating phenomenon since it can be explained with a complex eigenmode in the complex EOF analysis. The usual EOF analysis, however, most likely extracts plural eigenmodes for the propagating phenomenon. 2) The complex EOF analysis has the advantage of separating some propagating modes with near frequency domain. 3) Time-space structure of the quasi-periodic propagating mode can be reconstructed by the extracted principal complex eigenmode. This analysis is also compared with the extended EOF analysis.

An Efficient Approach for Statistical Calculations with Globally Gridded Filtered Time Series

The formulas for performing several statistical calculations based on Fourier coefficients are presented for use in atmospheric observational studies. The calculations discussed include a method for estimating the degree of temporal freedoms of two correlated time series and a method for performing seasonal analyses using a half-year summer/winter projection operator in the frequency domain. A modified lag-correlation calculation is proposed for obtaining lag correlations in the frequency domain. Also, a spectral approach for Empirical Orthogonal Function (EOF) and Extended EOF analysis is given which reduces the size of the matrix to be solved in the eigenproblem.