Multichannel Singular Spectrum Analysis Research Articles

Reconstructing daytime and nighttime MODIS land surface temperature in desert areas using multi-channel singular spectrum analysis

The availability of continuous spatiotemporal land surface temperature (LST) with high resolution is critical for many disciplines including hydrology, meteorology, ecology, and geology. Like other remote sensing data, satellite–based LST is also encountered with the cloud issue. In this research, over 5000 daytime and nighttime MODIS–LST images are utilized during 2014–2020 for Yazd–Ardakan plain in Yazd, Iran. The multi–channel singular spectrum analysis (MSSA) model is employed to reconstruct missing values due to dusts, clouds, and sensor defect. The selection of eigenvalues is based on the Monte Carlo test and the spectral analysis of eigenvalues. It is found that enlarging the window size has no effect on the number of significant components of the signal which account for the most variance of the data. However, data variance changes for all the three components. Employing two images per day, window sizes 60, 180, 360, and 720 are examined for reconstructing one year LST, where these selections are based on monthly, seasonal, semi-annual, and annual LST cycles, respectively. The results show that window size 60 had the least computational cost and the highest accuracy with RMSE (root mean square error) of 2.6 °C for the entire study region and 1.4 °C for a selected pixel. The gap–filling performance of MSSA is also compared with the one by the harmonic analysis of time series (HANTS) model, showing the superiority of MSSA with an improved RMSE of about 2.7 °C for the study region. In addition, daytime and nighttime LST series for different land covers are compared. Lastly, the maximum, minimum, and average LST for each day and night as well as average and standard deviation of LST images in the seven-year-long time series are also computed.

SINGULAR SPECTRAL ANALYSIS OF TEMPERATURE MULTIDIMENSIONAL TIME SERIES

In the paper the algorithm of singular structural analysis and forecasting of a multidimensional series by the MSSA method is used. The program was developed, in which the steps of the method for the selection of singular decomposition components were implemented, the analysis and forecast of real time series was carried out. Singular spectrum analysis (SSA) is increasingly used in the study of time series. Unlike other methods of statistical research of time series, this method is used to study the structure, selection of individual components and forecast of both stationary and non-stationary time series. It does not require an analytical model of the series. In fact, this approach is based on the method of principal components. It is based on the transformation of a series into a matrix and its singular decomposition. After identifying the components of the singular decomposition, their grouping takes place, which leads to the decomposition of the original series into additive components, such as trend, oscillations (periodics), and noise. The SSA method allows you to continue the structure of the time series, thus building a forecast (continuation). An important direction of the development of the SSA method as a method of time series analysis is its generalization for the analysis of multidimensional time series. The method is known as MSSA (Multi-Channel SSA) or E-EOFs (Extended Empirical Orthogonal Functions). In this case, the expected result is the simultaneous decomposition of several series into interpreted components. However, a sufficiently complete theory for MSSA does not exist.

A New Paradigm for Active–Break Cycle in the Indian Summer Monsoon

Abstract A multichannel singular spectrum analysis of 121 years of daily rainfall over India and 43 years of outgoing longwave radiation and horizontal wind has revealed two dominant intraseasonal oscillations (ISOs) that describe the space–time variability of monsoon rainfall. The two nonlinear oscillations are not perfectly periodic but exhibit broadband spectra centered at 45 and 28 days. These modes have coherent and near-regular spatial structure and temporal variations. This study posits that the two nonlinear oscillations provide a consistent and comprehensive framework to study the variability and predictability of intraseasonal rainfall variations. The active and break cycles of monsoon rainfall over India have been traditionally defined by using an arbitrarily chosen duration of persistence of arbitrarily chosen amount of rainfall averaged over an arbitrarily chosen area. This study shows that the phases of the two objectively derived modes of variability provide an objective method for defining the active and break cycles. The two ISOs are further shown to make negligible contribution to the seasonal mean rainfall and its interannual variability. This study proposes that the investigations of the origins of these nonlinear modes, and modulations of their amplitudes and phases, provide a new paradigm for future research on validation and predictability of intraseasonal variations in climate models.

Interpolated Fast Damped Multichannel Singular Spectrum Analysis for Deblending of Off-the-Grid Blended Data

Interpolated Fast Damped Multichannel Singular Spectrum Analysis for Deblending of Off-the-Grid Blended Data

Determination of dominant oscillation section in power system based on MSSA algorithm and dissipated energy

The identification of dominant oscillation paths is one of the key aspects in studying the stability of inter-area power grids. This paper proposes an improved multi-channel singular spectrum analysis (MSSA) algorithm combined with dissipative energy to identify dominant oscillation section in power systems. First, an improved MSSA method is introduced, which determines the order using the singular value energy spectrum and can effectively identify inter-area oscillation modes in power systems. Second, an energy function analysis method is proposed, which is well-suited for determining dominant oscillation section in power systems. This method is minimally affected by time-varying and nonlinear factors and allows for the visualization of generator states. Finally, the IEEE 68-bus system is used to construct an equivalent model, demonstrating the method's versatility. Simulation results validate the noise resistance, computational efficiency, and applicability to topology change scenarios of the proposed method. This method can accurately analyze inter-area oscillation modes and help to establish the dominant oscillation section.

The South Atlantic Dipole via multichannel singular spectrum analysis

This study analyzes coupled atmosphere–ocean variability in the South Atlantic Ocean. To do so, we characterize the spatio-temporal variability of annual mean sea-surface temperature (SST) and sea-level pressure (SLP) using Multichannel Singular Spectrum Analysis (M-SSA). We applied M-SSA to ERA5 reanalysis data (1959–2022) of South Atlantic SST and SLP, both individually and jointly, and identified a nonlinear trend, as well as two climate oscillations. The leading oscillation, with a period of 13 years, consists of a basin-wide southwest–northeast dipole and is observed both in the individual variables and in the coupled analysis. This mode is reminiscent of the already known South Atlantic Dipole, and it is probably related to the Pacific Decadal Oscillation and to El Niño–Southern Oscillation in the Pacific Ocean. The second oscillation has a 5-year period and also displays a dipolar structure. The main difference between the spatial structure of the decadal, 13-year, and the interannual, 5-year mode is that, in the first one, the SST cold tongue region in the southeast Atlantic’s Cape Basin is included in the pole closer to the equator. Together, these two oscillatory modes, along with the trend, capture almost 40% of the total interannual variability of the SST and SLP fields, and of their co-variability. These results provide further insights into the spatio-temporal evolution of SST and SLP variability in the South Atlantic, in particular as it relates to the South Atlantic Dipole and its predictability.

The Study on Anomalies of the Geomagnetic Topology Network Associated with the 2022 Ms6.8 Luding Earthquake

On 5 September 2022, the Ms 6.8 Luding earthquake occurred at 29.59°N and 102.08°E in China. To investigate the variations in geomagnetic signals before the earthquake, this study analyzes the geomagnetic data from nine stations around the epicenter. First, we apply the Multi-channel Singular Spectrum Analysis to reconstruct the periodic components of the geomagnetic data from multiple stations. Second, we employ K-means clustering to rule out the possibility of occasional anomalies caused by a single station. Subsequently, we construct a geomagnetic topology network considering the remaining stations. Network centrality is defined as a measure of overall network connectivity, where the higher the correlation between multiple stations, the greater the network centrality. Finally, we examine the network centrality 45 days before and 15 days after the Luding earthquake. The results show that several anomalies in network centrality are extracted about one week before the earthquake. We further validate the significance of the anomalies in terms of time as well as space and verify the utility of the centrality anomalies through the SEA technique. The anomalies are found to have a statistical correlation with the earthquake event. We consider that this study provides a new way and a novel observational perspective for earthquake precursor analysis of ground-based magnetic data.

Establishing and modeling the causality relationship of hydro-climatic and land cover change variables with water quality over Lake Tana, Ethiopia

Lakes, the most widespread inland water bodies in the globe, are highly susceptible to change in trophic state due to external factors. Changing hydro-climatic conditions and land cover changes (LCC) can cause lake water quality deterioration. This study establishes the quantitative relationship between variability in the water quality index and changes in hydro-climatic and LCC variables. Water quality is represented by the Forel-ule index (FUI) whereas the hydro-climatic variables considered in this study are lake bottom layer temperature (lblt), lake total layer temperature (ltlt), precipitation, runoff, evaporation, lake skin temperature (lskt), surface wind speed and air temperature. The LCC is quantified by lower and higher level leaf area index (Lv-lai and Hv-lai). FUI has a positive relationship with surface wind speed, precipitation, runoff, ltlt, lblt, and LCC and a negative relationship with evaporation, lskt, and air temperature with 95% confidence level over most parts of the Lake. The temporal correlation is also apparent from the long-term trend pattern. A significant decreasing trend is observed in FUI and lake bottom layer temperature (lblt). In contrast, an insignificant increasing trend is observed in air temperature and lake skin temperature (lskt). The changes in LCC, runoff, precipitation, and surface wind speed is insignificant between 2000 and 2020. Moreover, the phase composites of FUI and hydro-climatic and LCC variables derived from multichannel singular spectrum analysis (MSSA) show strong seasonal modulation of water quality by hydro-climatic and LCC variables. The annual cycle represented by the first two eigenmodes (except wind speed which is represented by the second and third eigenmodes) accounts for between 27.41% (wind speed) to 52.32% (precipitation) of the total joint spatiotemporal variability of FUI and the driving variables. The convergent cross-mapping (CCM) analysis shows that cross-map skill (ρ2) is increased with increasing library length (L) and time delay (τ), which suggests significant causal effects of hydro-climatic and LCC variables on FUI and the lagged causation is consistent with maximum values of ρ2. The significant feedback of FUI to changes in hydro-climatic and LCC variables shows the possibility of hindcast/forecast of the historical/future status of water quality from hydro-climatic and LCC variables. As a result, a multivariate nonlinear regression model (MNWQFM) is developed to forecast the lake water quality index from the hydro-climatic and LCC variables. The model has high performance with R2 of 83.6% and root means square error (RMSE) of 0.15 in FUI.

Filling the gap between GRACE and GRACE follow-on observations based on principal component analysis

SUMMARY The Gravity Recovery and Climate Experiment (GRACE) and its successor, GRACE Follow-On (GRACE-FO), have revolutionized the approach to monitoring global mass variations. However, the presence of several gaps, notably the continuous 11-month gap between the two missions, has generated a disruption in observations and hindered the analysis and application of the data. To address this problem, we have proposed a spectral domain gap-filling approach based on principal component analysis (PCA). Our simulation experiments demonstrate that the PCA gap-filling technique has significant potential to successfully reconstruct global mass variation and accurately capture real signals for most basins with an accuracy of less than 2 cm. When applied to actual missing data, our methodology delivers highly consistent results with previously published filling approaches, such as singular spectrum analysis and improved multichannel singular spectrum analysis method, for most of the global basins. Noteworthy, in the case of the Nelson basin, our PCA gap-filling method outperforms other methods in capturing seasonal signals and the return to a normal level of the terrestrial water storage changes in 2018. A comparison in the spectral domain indicates that the accuracy of the PCA-filling output is comparable to the original GRACE(-FO) data. Moreover, our method exhibits high generality, allowing for direct application to continuous GRACE(-FO) data without other additional data processing and without differentiating the types of missing data. Therefore, the proposed PCA gap-filling method offers exciting opportunities to guarantee the continuity of global mass change observations and benefit subsequent applications that require continuous data records.

A GPS multipath mitigation method in coordinate-domain considering the effects of gross errors and missing data

Multipath is a significant obstacle to achieving high-precision deformation monitoring using the Global Positioning System (GPS) technique. Sidereal filtering (SF) can mitigate GPS multipath effects based on the multipath models derived from historical measurements, but its practical application in complex scenarios is still challenging due to unavoidable gross errors and missing data problems. In this paper, an improved SF algorithm is proposed that accurately extracts multipath immune to the effects of gross errors and missing values in historical measurements, aiming to obtain accurate displacements in a harsh environment. Specifically, a gross error detection method is first developed based on the dynamic time warping (DTW) algorithm to filter gross errors. Then, we adopt the multichannel singular spectrum analysis (MSSA) algorithm to extract initial multipath errors. Finally, we propose a weighted fusion (WF) algorithm to eliminate the impact of missing values and obtain the final multipath sequences. Extensive experiments with datasets collected from a real-world landslide, including both stable and sliding stations, demonstrate the effectiveness of our proposed method. Results show that compared with the traditional SF method, our proposed method can effectively mitigate the effects of gross errors and missing values on multipath modeling, with the multipath filtering accuracy improving by approximately 12% and 21% for stable and sliding scenarios, respectively.

Coupling VMD and MSSA denoising for dam deformation prediction

The measured data of dams in complex environments are influenced by factors such as external forcing and instrumentation errors and inevitably contain noise, which makes accurately predicting dam deformation challenging. Traditional denoising methods suffer from both excessive denoising and incomplete denoising, resulting in limited improvement in prediction accuracy. To better address these problems, this paper proposes a denoising method that combines adaptive variational modal decomposition (VMD) with improved multichannel singular spectrum analysis (MSSA). The algorithm denoises the decomposed subsequence while accounting for the covariance between the subsequence and extracts valid information from the residual sequences. A concrete panel rockfill dam is used as an example for validation. The results show that the proposed algorithm effectively preserves the intrinsic components and coupling relationships between the decomposed subsequence. Based on machine learning models with different sensitivities to noise, the prediction accuracy of the proposed denoising algorithm model is better than that of the traditional denoising algorithm model. It is more suitable for deformation prediction modelling in complex situations involving actual dams, which further enhances the generalization ability of the prediction model.

Combining unsupervised deep learning and Monte Carlo dropout for seismic data reconstruction and its uncertainty quantification

Many methods, such as multichannel singular spectrum analysis (MSSA) and deep seismic prior (DSP), have been developed for seismic data reconstruction, but they do not quantify the uncertainty of reconstructed traces, relying on the subjective visual inspection of results. Our goal is to quantify the reconstructed uncertainty while recovering missing traces. We develop a framework including an unsupervised deep-learning-based seismic data reconstruction method and the existing Monte Carlo dropout method to achieve this goal. The only information required by our framework is the original incomplete data. A convolutional neural network trained on the original nonmissing traces can simultaneously denoise and reconstruct seismic data. For uncertainty quantification, the Monte Carlo dropout method treats the well-known dropout technique as Bayesian variational inference. This refers to the fact that the dropout technique can be regarded as an approximation to the probabilistic Gaussian process and thus can be used to obtain an approximate distribution (Bernoulli variational distribution) of the posterior distribution. The reconstructed result and uncertainty of the trained model are yielded through multiple Monte Carlo dropout simulations. The analysis of the reconstructed uncertainty quantifies the confidence to use reconstructed traces. Tests on synthetic and field data illustrate that our framework outperforms the MSSA and DSP methods on reconstructed accuracy and quantifies the reconstructed uncertainty as an objective benchmark to guide decision making.

An Antijamming Method Based on Multichannel Singular Spectrum Analysis and Affinity Propagation for UWB Ranging Sensors

Ultra-wideband impulse radio system has received extensive attention due to their high resolution and poor interception possibility. But the specific electromagnetic threat posed by its complex work environment cannot be ignored. In all kinds of active jamming signals, smart noise jamming plays an important role in modern radar electronic warfare, and most traditional anti-jamming methods have less suppression effect. In this paper, the mechanism of smart noise jamming on the UWB ranging sensor is discussed first. On this basis, an anti-smart noise jamming method based on multichannel singular spectrum analysis and kurtosis characteristic is proposed. Experiments show that smart noise jamming is more threatening to the UWB system than other noise modulation jamming. And the improved algorithm proposed in this paper can suppress the jamming better. After the anti-jamming processing, the average detection probability can reach more than 95%. Meanwhile, the method is improved by adding the affinity propagation (AP) clustering algorithm to solve the underdetermined signal separation problem in the case of compound jamming. The advantage is that it does not have to estimate the number of signals first. Even if the SJR is -10 dB, the waveform similarity between the separation signal and the source signal can reach 0.7 or more.

Data‐Driven Gap Filling and Spatio‐Temporal Filtering of the GRACE and GRACE‐FO Records

AbstractGravity Recovery And Climate Experiment and Follow On (GRACE/‐FO) global monthly measurements of Earth's gravity field have led to significant advances in quantifying mass transfer. However, a significant temporal gap between missions hinders evaluating long‐term mass variations. Moreover, instrumental and processing errors translate into large non‐physical North‐South stripes polluting geophysical signals. We use Multichannel Singular Spectrum Analysis (M‐SSA) to overcome both issues by exploiting spatio‐temporal information of Level‐2 GRACE/‐FO solutions, filtered using the DDK7 decorrelation and a new complementary filter, built based on the residual noise between fully processed data and a parametric fit to observations. Using an iterative M‐SSA on Equivalent Water Height (EWH) time series processed by Center of Space Research, GeoForschungsZentrum, Institute of Geodesy at Graz University of Technology, and Jet Propulsion Laboratory, we replace missing data and outliers to obtain a combined evenly sampled solution. Then, we apply M‐SSA to retrieve common signals between each EWH time series and its same‐latitude neighbors to further reduce residual spatially uncorrelated noise. Comparing GRACE/‐FO M‐SSA solution with Satellite Laser Ranging and Swarm low‐degree Earth's gravity field and hydrological model demonstrates its ability to satisfyingly fill missing observations. Our solution achieves a noise level comparable to mass concentration (mascon) solutions over oceans (3.0 mm EWH), without requiring a priori information nor regularization. While short‐wavelength signals are challenging to capture using highly filtered spherical harmonics or mascons solutions, we show that our technique efficiently recovers localized mass variations using well‐documented mass transfers associated with reservoir impoundments.

Three dimensional seismic data reconstruction based on truncated nuclear norm

The rank reduction method is widely used to reconstruct three dimensional (3D) seismic data. The traditional multichannel singular spectrum analysis (MSSA) utilizes truncated singular value decomposition (TSVD) to approximately solve the rank function of the block Hankel structure matrix constructed by frequency slices of seismic data. However, the TSVD algorithm discards all nonzero singular values except a few largest singular values and ignores the useful seismic information in small nonzero singular values. To further utilize the seismic data information contained in these small singular values, this paper proposes a method to recover 3D seismic data with truncated nuclear norm (TNN). The proposed method imposes different constraints on large singular values and small singular values. Essentially, the TNN is closer to the rank function than the TSVD. Finally, the proposed model is addressed by the alternating direction method of multipliers, and closed-form solutions are used to update the optimization variables. The experimental results demonstrate that the proposed method achieves superior reconstruction results than the traditional MSSA method.

Irregularly sampled seismic data interpolation with self-supervised learning

Supervised convolutional neural networks (CNNs) are commonly used for seismic data interpolation, in which a recovery network is trained over corrupted (input)/complete (label) pairs. However, the trained model always suffers from poor generalization when the target test data are significantly different from the training data sets. To address this issue, we have developed a self-supervised deep learning method for interpolating irregularly missing traces, which uses only the corrupted seismic data for training. This approach is based on the receptive field characteristic of CNNs, and the training pairs are extracted from the corrupted seismic data through a random trace mask. After network training, all target data are recovered using the trained model. This self-supervised learning interpolation (SSLI) method can be easily integrated into commonly used CNNs. Synthetic and field examples demonstrate that SSLI not only significantly outperforms traditional multichannel singular spectrum analysis and unsupervised deep seismic prior methods but also competes with supervised learning methods.

Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis

Previous studies of GNSS-IR mainly focused on the legacy L1C signal; the potential of modernized signals (L2C and L5Q) has not yet been fully exploited. In this paper, we applied the Multichannel Singular Spectrum Analysis (M-SSA) method to extract common interference patterns from different frequencies simultaneously. The three-frequency (L1C, L2C, and L5Q) signal-to-noise ratio (SNR) measurements from a total of 840 satellite rising and setting arcs, occurring between day of year 250 to 279 in year 2020 and 2021, were used. By comparing GNSS-IR reflector heights obtained from the original and M-SSA-reconstructed SNR time series, we found that M-SSA significantly improves the between-frequency consistency, as shown by an increase in the values of R-squared of linear regression from (0.69, 0.67, 0.89) to (0.95, 0.96, 0.98), and a decrease in RMSE from (0.10 m, 0.10 m, 0.06 m) to (0.04 m, 0.04 m, 0.02 m) for S1C-S2C, S1C-S5Q, and S2C-S5Q pair, respectively. Our results validate (1) the effectiveness of the M-SSA method in extracting common interference patterns from multi-frequency SNR time series, and (2) the superiority of modernized civil signals L2C and L5Q over the legacy L1C signal in GNSS-IR studies. We also emphasize the important role that the L5 signal will play in future GNSS-IR research because of its compatibility and interoperability among different satellite navigation systems.

Dynamical data mining captures disc–halo couplings that structure galaxies

ABSTRACTStudying coupling between different galactic components is a challenging problem in galactic dynamics. Using basis function expansions (BFEs) and multichannel singular spectrum analysis (mSSA) as a means of dynamical data mining, we discover evidence for two multicomponent disc–halo dipole modes in a Milky-Way-like simulated galaxy. One of the modes grows throughout the simulation, while the other decays throughout the simulation. The multicomponent disc–halo modes are driven primarily by the halo, and have implications for the structural evolution of galaxies, including observations of lopsidedness and other non-axisymmetric structure. In our simulation, the modes create surface density features up to 10 per cent relative to the equilibrium model stellar disc. While the simulated galaxy was constructed to be in equilibrium, BFE + mSSA also uncovered evidence of persistent periodic signals incited by aphysical initial conditions disequilibrium, including rings and weak two-armed spirals, both at the 1 per cent level. The method is sensitive to distinct evolutionary features at and even below the 1 per cent level of surface density variation. The use of mSSA produced clean signals for both modes and disequilibrium, efficiently removing variance owing to estimator noise from the input BFE time series. The discovery of multicomponent halo–disc modes is strong motivation for application of BFE + mSSA to the rich zoo of dynamics of multicomponent interacting galaxies.

Identification and Removal of Reaction Wheel Interference From In‐Situ Magnetic Field Data Using Multichannel Singular Spectrum Analysis

AbstractIn situ magnetic field measurements are critical to our understanding of a variety of space physics phenomena including field‐aligned currents and plasma waves. Unfortunately, high‐fidelity magnetometer measurements are often degraded by stray magnetic fields from the host spacecraft, its subsystems, and other instruments. One dominant source of magnetic interference on many missions are reaction wheels—spinning platters of varying rates used to control spacecraft attitude. This manuscript presents a novel approach to the mitigation of reaction wheel interference on magnetometer measurements aboard spacecraft where multiple magnetometer sensors are deployed. Specifically, multichannel singular spectrum analysis is employed to decompose multiple time series simultaneously. A technique for automatic component selection is proposed that classifies the decomposed signals into common geophysical signals and disparate locally generated signals enabling the robust estimation and removal of the local interference without requiring any assumptions about its characteristics or source. The utility of this proposed method is demonstrated empirically using in situ data from the CASSIOPE/Swarm‐Echo mission, and a data interval with near‐constant background field was shown to have its local reaction wheel interference reduced from 1.90 nT RMS, for the uncorrected outboard sensor, to 0.21 nT RMS (an 89.0% reduction). This technique can be generalized to arrays of more than two sensors, and should apply to additional types of magnetic interference.

Experimental detection of train wheel defects using wayside vibration signal processing

While many studies have been used onboard monitoring methods to detect train wheel defects, this paper aims to extract damage features from vibrational signals obtained by the wayside monitoring system. To provide an appropriate tool for the decomposition of experimental nonstationary vibration signals containing impacts, an analytical amplitude-based signal decomposition method is provided. A two-axle motor car with a flat wheel defect is studied at different operating conditions. Vibrational signals arising from wheel-rail interactions are gathered by the Wayside Data Collection Setup (WDCS) with five piezoelectric accelerometers. The tests are performed at the constant speeds of 10, 20, 30, and 40 km/h. The acquired signals are decomposed by the Multi-channel Singular Spectrum Analysis (MSSA) into the contributing components. Based on the results, increases in the amplitudes of the second reconstructed components (RCs) of the vibrational signals sensed by all the accelerometers can be observed at a specific time instance as a repeating pattern. Similar patterns are obtained at different motor car positions relative to the measurement area, as well as different motor car speeds. To verify the consistency of the second RCs, the crest factors are obtained for all the angular positions. The results show sudden increases in the crest factor at a fixed angular position that indicate the existence of a defect at that specific angular position of the wheel.