Multichannel Singular Spectrum Analysis Research Articles

Multi-annual modes in the 20th century temperature variability in reanalyses and CMIP5 models

Abstract. A performance expectation is that Earth system models simulate well the climate mean state and the climate variability. To test this expectation, we decompose two 20th century reanalysis data sets and 12 CMIP5 model simulations for the years 1901–2005 of the monthly mean near-surface air temperature using randomised multi-channel singular spectrum analysis (RMSSA). Due to the relatively short time span, we concentrate on the representation of multi-annual variability which the RMSSA method effectively captures as separate and mutually orthogonal spatio-temporal components. This decomposition is a unique way to separate statistically significant quasi-periodic oscillations from one another in high-dimensional data sets.The main results are as follows. First, the total spectra for the two reanalysis data sets are remarkably similar in all timescales, except that the spectral power in ERA-20C is systematically slightly higher than in 20CR. Apart from the slow components related to multi-decadal periodicities, ENSO oscillations with approximately 3.5- and 5-year periods are the most prominent forms of variability in both reanalyses. In 20CR, these are relatively slightly more pronounced than in ERA-20C. Since about the 1970s, the amplitudes of the 3.5- and 5-year oscillations have increased, presumably due to some combination of forced climate change, intrinsic low-frequency climate variability, or change in global observing network. Second, none of the 12 coupled climate models closely reproduce all aspects of the reanalysis spectra, although some models represent many aspects well. For instance, the GFDL-ESM2M model has two nicely separated ENSO periods although they are relatively too prominent as compared with the reanalyses. There is an extensive Supplement and YouTube videos to illustrate the multi-annual variability of the data sets.

Retracted: Multi-step damped multichannel singular spectrum analysis for simultaneous reconstruction and denoising of 3D seismic data

Multichannel singular spectrum analysis (MSSA) is an effective approach for simultaneous seismic data reconstruction and denoising. MSSA utilizes truncated singular value decomposition (TSVD) to decompose the noisy signal into a signal subspace and a noise subspace and weighted projection onto convex sets (POCS)-like method to reconstruct the missing data in the appropriately constructed block Hankel matrix at each frequency slice. However, there still exists some residual noise in signal space due to two major factors: the deficiency of traditional TSVD and the iteratively inserted observed noisy data during the process of weighted POCS like iterations. In this paper, we first further extend the recently proposed damped MSSA (DMSSA) for random noise attenuation, which is more powerful in distinguishing between signal and noise, to simultaneous reconstruction and denoising. Then combined with DMSSA, we propose a multi-step strategy, named multi-step damped MSSA (MS-DMSSA), to efficiently reduce the inserted noise during the POCS like iterations, thus can improve the final performance of simultaneous reconstruction and denoising. Application of the MS-DMSSA approach on 3D synthetic and field seismic data demonstrates a better performance compared with the conventional MSSA approach.

Cleaning Financial Data Using SSA and MSSA

We introduce a powerful method for cleaning time series - Multi-Channel Singular Spectrum Analysis (MSSA). “Cleaning” means filling data gaps and removing unphysical spikes, which are chronic problems. MSSA utilizes all available information in “time” and “space” with autocorrelations, correlations, and lagged correlations. MSSA performs demonstrably better than other methods. Here we present tests using MSSA to fill data gaps, with positive results. Spike removal is in a separate paper.

A fast rank-reduction algorithm for three-dimensional seismic data interpolation

Rank-reduction methods have been successfully used for seismic data interpolation and noise attenuation. However, highly intense computation is required for singular value decomposition (SVD) in most rank-reduction methods. In this paper, we propose a simple yet efficient interpolation algorithm, which is based on the Hankel matrix, for randomly missing traces. Following the multichannel singular spectrum analysis (MSSA) technique, we first transform the seismic data into a low-rank block Hankel matrix for each frequency slice. Then, a fast orthogonal rank-one matrix pursuit (OR1MP) algorithm is employed to minimize the low-rank constraint of the block Hankel matrix. In the new algorithm, only the left and right top singular vectors are needed to be computed, thereby, avoiding the complexity of computation required for SVD. Thus, we improve the calculation efficiency significantly. Finally, we anti-average the rank-reduction block Hankel matrix and obtain the reconstructed data in the frequency domain. Numerical experiments on 3D seismic data show that the proposed interpolation algorithm provides much better performance than the traditional MSSA algorithm in computational speed, especially for large-scale data processing.

Damped multichannel singular spectrum analysis for 3D random noise attenuation

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation in seismic data, which decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition (TSVD). However, this signal subspace actually still contains residual noise. We have derived a new formula of low-rank reduction, which is more powerful in distinguishing between signal and noise compared with the traditional TSVD. By introducing a damping factor into traditional MSSA to dampen the singular values, we have developed a new algorithm for random noise attenuation. We have named our modified MSSA as damped MSSA. The denoising performance is controlled by the damping factor, and our approach reverts to the traditional MSSA approach when the damping factor is sufficiently large. Application of the damped MSSA algorithm on synthetic and field seismic data demonstrates superior performance compared with the conventional MSSA algorithm.

Monte Carlo data-driven tight frame for seismic data recovery

Seismic data denoising and interpolation are essential preprocessing steps in any seismic data processing chain. Sparse transforms with a fixed basis are often used in these two steps. Recently, we have developed an adaptive learning method, the data-driven tight frame (DDTF) method, for seismic data denoising and interpolation. With its adaptability to seismic data, the DDTF method achieves high-quality recovery. For 2D seismic data, the DDTF method is much more efficient than traditional dictionary learning methods. But for 3D or 5D seismic data, the DDTF method results in a high computational expense. The motivation behind this work is to accelerate the filter bank training process in DDTF, while doing less damage to the recovery quality. The most frequently used method involves only a randomly selective subset of the training set. However, this random selection method uses no prior information of the data. We have designed a new patch selection method for DDTF seismic data recovery. We suppose that patches with higher variance contain more information related to complex structures, and should be selected into the training set with higher probability. First, we calculate the variance of all available patches. Then for each patch, a uniformly distributed random number is generated and the patch is preserved if its variance is greater than the random number. Finally, all selected patches are used for filter bank training. We call this procedure the Monte Carlo DDTF method. We have tested the trained filter bank on seismic data denoising and interpolation. Numerical results using this Monte Carlo DDTF method surpass random or regular patch selection DDTF when the sizes of the training sets are the same. We have also used state-of-the-art methods based on the curvelet transform, block matching 4D, and multichannel singular spectrum analysis as comparisons when dealing with field data.

Modeling the relationship between photosynthetically active radiation and global horizontal irradiance using singular spectrum analysis

We report on the construction of generic models to calculate photosynthetically active radiation (PAR) from global horizontal irradiance (GHI), and vice versa. Our study took place at stations of the Greek UV network (UVNET) and the Hellenic solar energy network (HNSE) with measurements from NILU-UV multi-filter radiometers and CM pyranometers, chosen due to their long (≈1M record/site) high temporal resolution (≈1min) record that captures a broad range of atmospheric environments and cloudiness conditions. The uncertainty of the PAR measurements is quantified to be ±6.5% while the uncertainty involved in GHI measurements is up to ≈±7% according to the manufacturer. We show how multi-linear regression and nonlinear neural network (NN) models, trained at a calibration site (Thessaloniki) can be made generic provided that the input–output time series are processed with multi-channel singular spectrum analysis (M-SSA). Without M-SSA, both linear and nonlinear models perform well only locally. M-SSA with 50 time-lags is found to be sufficient for identification of trend, periodic and noise components in aerosol, cloud parameters and irradiance, and to construct regularized noise models of PAR from GHI irradiances. Reconstructed PAR and GHI time series capture ≈95% of the variance of the cross-validated target measurements and have median absolute percentage errors <2%. The intra-site median absolute error of M-SSA processed models were ≈8.2±1.7W/m2 for PAR and ≈9.2±4.2W/m2 for GHI. When applying the models trained at Thessaloniki to other stations, the average absolute mean bias between the model estimates and measured values was found to be ≈1.2W/m2 for PAR and ≈0.8W/m2 for GHI. For the models, percentage errors are well within the uncertainty of the measurements at all sites. Generic NN models were found to perform marginally better than their linear counterparts.

Coherent Tropical Indo-Pacific Interannual Climate Variability

AbstractA multichannel singular spectrum analysis (MSSA) applied simultaneously to tropical sea surface temperature (SST), zonal wind, and burstiness (zonal wind variability) reveals three significant oscillatory modes. They all show a strong ENSO signal in the eastern Pacific Ocean (PO) but also a substantial SST signal in the western Indian Ocean (IO). A correlation-based analysis shows that the western IO signal contains linearly independent information on ENSO. Of the three Indo-Pacific ENSO modes of the MSSA, one resembles a central Pacific (CP) El Niño, while the others represent eastern Pacific (EP) El Niños, which either start in the central Pacific and grow eastward (EPe) or start near Peru and grow westward (EPw). A composite analysis shows that EPw El Niños are preceded by cooling in the western IO about 15 months earlier. Two mechanisms are discussed by which the western IO might influence ENSO. In the atmospheric bridge mechanism, subsidence over the cool western IO in autumn (year 0) leads to enhanced convection above Indonesia, strengthening easterlies over the western PO, and the creation of a large warm water volume. This is essential for the creation of (EP) El Niños in the following spring–summer. In the state-dependent noise mechanism, a cool western IO favors a strong intraseasonal zonal wind variability over the western PO in early spring (year 1), which can partly be attributed to the Madden–Julian oscillation. This intraseasonal variability induces Kelvin waves, which in early spring lead to a strong warming of the eastern PO and can initiate EPw El Niños.

A possible interrelation between Earth rotation and climatic variability at decadal time-scale

Using multichannel singular spectrum analysis (MSSA) we decomposed climatic time series into principal components, and compared them with Earth rotation parameters. The global warming trends were initially subtracted. Similar quasi 60 and 20 year periodic oscillations have been found in the global mean Earth temperature anomaly (HadCRUT4) and global mean sea level (GMSL). Similar cycles were also found in Earth rotation variation. Over the last 160 years multi-decadal change of Earth's rotation velocity is correlated with the 60-year temperature anomaly, and Chandler wobble envelope reproduces the form of the 60-year oscillation noticed in GMSL. The quasi 20-year oscillation observed in GMSL is correlated with the Chandler wobble excitation. So, we assume that Earth's rotation and climate indexes are connected. Despite of all the clues hinting this connection, no sound conclusion can be done as far as ocean circulation modelling is not able to correctly catch angular momentum of the oscillatory modes.

Data‐adaptive detection of transient deformation in geodetic networks

AbstractThe recent development of dense and continuously operating Global Navigation Satellite System (GNSS) networks worldwide has led to a significant increase in geodetic data sets that sometimes capture transient‐deformation signals. It is challenging, however, to extract such transients of geophysical origin from the background noise inherent to GNSS time series and, even more so, to separate them from other signals, such as seasonal redistributions of geophysical fluid mass loads. In addition, because of the very large number of continuously recording GNSS stations now available, it has become impossible to systematically inspect each time series and visually compare them at all neighboring sites. Here we show that Multichannel Singular Spectrum Analysis (M‐SSA), a method derived from the analysis of dynamical systems, can be used to extract transient deformations, seasonal oscillations, and background noise present in GNSS time series. M‐SSA is a multivariate, nonparametric, statistical method that simultaneously exploits the spatial and temporal correlations of geophysical fields. The method allows for the extraction of common modes of variability, such as trends with nonconstant slopes and oscillations shared across time series, without a priori hypotheses about their spatiotemporal structure or their noise characteristics. We illustrate this method using synthetic examples and show applications to actual GPS data from Alaska to detect seasonal signals and microdeformation at the Akutan active volcano. The geophysically coherent spatiotemporal patterns of uplift and subsidence thus detected are compared to the results of an idealized model of such processes in the presence of a magma chamber source.

Randomised multichannel singular spectrum analysis of the 20th century climate data

In this article, we introduce a new algorithm called randomised multichannel singular spectrum analysis (RMSSA), which is a generalisation of the traditional multichannel singular spectrum analysis (MSSA) into problems of arbitrarily large dimension. RMSSA consists of (1) a dimension reduction of the original data via random projections, (2) the standard MSSA step and (3) a recovery of the MSSA eigenmodes from the reduced space back to the original space. The RMSSA algorithm is presented in detail and additionally we show how to integrate it with a significance test based on a red noise null-hypothesis by Monte-Carlo simulation. Finally, RMSSA is applied to decompose the 20th century global monthly mean near-surface temperature variability into its low-frequency components. The decomposition of a reanalysis data set and two climate model simulations reveals, for instance, that the 2–6 yr variability centred in the Pacific Ocean is captured by all the data sets with some differences in statistical significance and spatial patterns.

Prediction of daily modes of South Asian monsoon variability and its association with Indian and Pacific Ocean SST in the NCEP CFS V2

The prediction capability of daily modes of variability for South Asian monsoon from climate forecast system version 2 of national centers for environmental prediction with respect to observed precipitation has been assessed. The space–time structure of the daily modes for summer monsoon rainfall has been identified by using multi-channel singular spectrum analysis (MSSA). The MSSA is applied on daily anomalies of rainfall data over the South Asian monsoon region (40°E–160°E, 30°S–35°N) for the period of 2001–2013 with a lag window of 61 days for June–July–August–September season. The broad spectrum around 45 and 50 days was obtained from the observed and model data during the time domain of our study. The space–time structure of the modes obtained from the model shows good resemblance with respect to the observation. The observed northeastward propagation of oscillatory mode is well simulated by the model. The significant improvement in the space–time structure, period of oscillation, and propagation of oscillatory modes was found in the model. The observed connectivity of oscillatory and persisting modes with the sea surface temperature of Indian and Pacific Ocean has also been investigated and it was found that the model is able to predict it reasonably well.

An Adaptive-MSSA-Based Algorithm for Detection of Trapped Victims Using UWB Radar

Postdisaster search and rescue is an important application of ultrawideband (UWB) radar systems, which mainly detect trapped victims by their respiratory-motion response. The development of a respiratory-motion detection (RMD) algorithm that can eliminate nonstationary clutter and noise is a challenging task for the application. A new algorithm is proposed to deal with the task in this letter. It uses the multichannel singular spectrum analysis (MSSA) technique to reconstruct the respiratory-motion response detected by a UWB radar. During the reconstruction, the periodicity and range interrelation characteristics of the response are exploited to adaptively identify signal subspaces. The performance of the algorithm is verified both by simulated and real data. The results show its improved performance over the reference algorithms, e.g., a singular-value-decomposition-based algorithm. The adaptive-MSSA-based RMD algorithm has great promise not only in practical use but also for future research of UWB-radar-based human being remote sensing.

A high-resolution δ&amp;lt;sup&amp;gt;18&amp;lt;/sup&amp;gt;O record and Mediterranean climate variability

Abstract. A high-resolution, well-dated foraminiferal δ18O record from a shallow-water core drilled from the Gallipoli Terrace in the Gulf of Taranto (Ionian Sea), previously measured over the last two millennia, has been extended to cover 707 BC–AD 1979. Spectral analysis of this series, performed using singular-spectrum analysis (SSA) and other classical and advanced methods, strengthens the results obtained analysing the shorter δ18O profile, detecting the same highly significant oscillations of about 600, 380, 170, 130 and 11 years, respectively explaining about 12, 7, 5, 2 and 2% of the time series total variance, plus a millennial trend (18% of the variance). The comparison with the results of multi-channel singular-spectrum analysis (MSSA) applied to a data set of 26 Northern Hemisphere (NH) temperature-proxy records shows that NH temperature anomalies share with our local record a~long-term trend and a bicentennial (170-year period) cycle. These two variability modes, previously identified as temperature-driven, are the most powerful modes in the NH temperature data set. Both the long-term trends and the bicentennial oscillations, when reconstructed locally and hemispherically, show coherent phases. Furthermore, the corresponding local and hemispheric amplitudes are comparable if changes in the precipitation–evaporation balance of the Ionian sea, presumably associated with temperature changes, are taken into account.

Space–Time Structure of Diabatic Heating in Monsoon Intraseasonal Oscillation

Abstract The space–time structure of the leading monsoon intraseasonal oscillation (MISO) in three-dimensional diabatic heating is studied. Using the ERA-Interim data of the European Centre for Medium-Range Weather Forecasts, the diabatic heating data were constructed by the residual method of the thermodynamic equation. The MISO was extracted by applying multichannel singular spectrum analysis on the daily anomalies of three-dimensional diabatic heating over the South Asian monsoon region for the period 1979–2011.The diabatic heating MISO has a period of 45 days, and exhibits eastward propagation in the equatorial Indian and Pacific Oceans and northward propagation over the entire monsoon region. The horizontal structure shows a long tilted band of heating anomalies propagating northeastward. The period, horizontal pattern, and propagation properties of the diabatic heating MISO are similar to those found in precipitation, outgoing longwave radiation, and circulation in earlier studies. The vertical structure of the diabatic heating MISO indicates deep columns, with maximum values at about 450 hPa, propagating northeastward. The vertical structure of the heating anomalies has good correspondence with that of the moisture anomalies but with a phase difference. The moisture anomalies lead the heating anomalies and may provide a preconditioning process for the propagation mechanism. The temperature anomalies also show oscillatory behavior corresponding to the diabatic heating MISO but the phase difference between the two varies from region to region.

Stochastic modeling of decadal variability in ocean gyres

AbstractDecadal large‐scale low‐frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data driven approach that addresses this challenge. Proposed is non‐Markovian low‐order methodology with stochastic closure and use of mode decomposition by multichannel Singular Spectrum Analysis. The multilayer stochastic linear model is obtained from the coarse‐grained eddy‐resolving ocean model solution, and with high accuracy it reproduces the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data.

Forecasting natural inflow energy series with multi-channel singular spectrum analysis and bootstrap techniques

The NIE time series have great importance for the Brazilian energy long term planning, as the decisions about the optimal dispatch of hydroelectric and thermoelectric plants are highly dependent on them. Therefore, reliable and accurate long term forecasts and simulations for the NIE series are crucial. To develop such forecasts, the proposed approach relies on the decomposition of NIE series from the South subsystem into signal and noise using the MSSA technique. After that, synthetic series are generated from the noise using the Bootstrap procedure, forecasts of 60 months ahead for each series using the traditional Holt Winters are calculated to arrive at the final predictions obtained by taking the average of the individual series forecasts. The results indicate that the proposed methodology significantly improved the results when compared with forecasts achieved by directly applying the Holt Winters model to the original series, and prove to be more effective for lead time of more than 36 months than others techniques applied in series without simulation.

Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models

Abstract The present paper is the second part of a two-part study on empirical modeling and prediction of climate variability. This paper deals with spatially distributed data, as opposed to the univariate data of Part I. The choice of a basis for effective data compression becomes of the essence. In many applications, it is the set of spatial empirical orthogonal functions that provides the uncorrelated time series of principal components (PCs) used in the learning set. In this paper, the basis of the learning set is obtained instead by applying multichannel singular-spectrum analysis to climatic time series and using the leading spatiotemporal PCs to construct a reduced stochastic model. The effectiveness of this approach is illustrated by predicting the behavior of the Jin–Neelin–Ghil (JNG) hybrid seasonally forced coupled ocean–atmosphere model of El Niño–Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction methodology is applied. Critical transitions in the hybrid periodically forced coupled model are successfully predicted on time scales that are substantially longer than the duration of the learning sample.

Multispectral analysis of Northern Hemisphere temperature records over the last five millennia

Aiming to describe spatio-temporal climate variability on decadal-to-centennial time scales and longer, we analyzed a data set of 26 proxy records extending back 1,000–5,000 years; all records chosen were calibrated to yield temperatures. The seven irregularly sampled series in the data set were interpolated to a regular grid by optimized methods and then two advanced spectral methods—namely singular-spectrum analysis (SSA) and the continuous wavelet transform—were applied to individual series to separate significant oscillations from the high noise background. This univariate analysis identified several common periods across many of the 26 proxy records: a millennial trend, as well as oscillations of about 100 and 200 years, and a broad peak in the 40–70-year band. To study common NH oscillations, we then applied Multichannel SSA. Temperature variations on time scales longer than 600 years appear in our analysis as a dominant trend component, which shows climate features consistent with the Medieval Warm Period and the Little Ice Age. Statistically significant NH-wide peaks appear at 330, 250 and 110 years, as well as in a broad 50–80-year band. Strong variability centers in several bands are located around the North Atlantic basin and are in phase opposition between Greenland and Western Europe.

Oscillatory Climate Modes in the Indian Monsoon, North Atlantic, and Tropical Pacific

This paper explores the three-way interactions between the Indian monsoon, the North Atlantic, and the tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation index for the tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands.The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors.A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggests that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes.Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air–sea interaction as well.