Singular systems analysis as a moving-window spectral method

1998 ◽  
Vol 9 (1) ◽  
pp. 55-79 ◽  
Author(s):  
A. C. FOWLER ◽  
G. KEMBER
Keyword(s):  
Systems Analysis ◽  
Singular Systems ◽  
A Priori ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Moving Window ◽  
Window Length ◽  
Sampled Data ◽  
Orthogonal Functions ◽  
Local Filters

Singular Systems Analysis (SSA), or time domain Principal Component Analysis (PCA), is most appropriately analysed in terms of local, moving-window spectral analysis. The behaviour of Empirical Orthogonal Functions (EOF) of this theory are examined, for continuously sampled data, in the limits of large and small window length, and for centre or end projection. Filters obtained by projecting on to these EOFs are shown to approximate local, linear band pass filters, where the EOFs depend upon the correlation structure (or the power spectral density) of the signal and the window length. Power in the spectra is not generally conserved, and projection to the endpoints of a window may not converge to the underlying signal in the absence of noise. The filters are independent of the phase of the Fourier transform, and are therefore unable to distinguish dynamically between a signal and a surrogate (phase-randomized) transform of it. Iteration of such local filters using a prediction error-based stopping criterion can and does lead to improved results, but the choice of window length must be made a priori. Hence, we introduce an iterative local filter with the window length being determined as part of the filtering procedure. This involves the determination of the predictability of the projected time series, and hence allows SSA to be used in a genuinely nonlinear way.

scholarly journals On the Nonlinearity of Winter Northern Hemisphere Atmospheric Variability

2019 ◽  
Vol 76 (1) ◽  
pp. 333-356 ◽  
Author(s):  
A. Hannachi ◽  
W. Iqbal
Keyword(s):  
North Atlantic ◽  
Polar Vortex ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
The Arctic ◽  
Climate Change Signal ◽  
Two Dimensional ◽  
Orthogonal Functions ◽  
Local Flow ◽  
The North

Abstract Nonlinearity in the Northern Hemisphere’s wintertime atmospheric flow is investigated from both an intermediate-complexity model of the extratropics and reanalyses. A long simulation is obtained using a three-level quasigeostrophic model on the sphere. Kernel empirical orthogonal functions (EOFs), which help delineate complex structures, are used along with the local flow tendencies. Two fixed points are obtained, which are associated with strong bimodality in two-dimensional kernel principal component (PC) space, consistent with conceptual low-order dynamics. The regimes reflect zonal and blocked flows. The analysis is then extended to ERA-40 and JRA-55 using daily sea level pressure (SLP) and geopotential heights in the stratosphere (20 hPa) and troposphere (500 hPa). In the stratosphere, trimodality is obtained, representing disturbed, displaced, and undisturbed states of the winter polar vortex. In the troposphere, the probability density functions (PDFs), for both fields, within the two-dimensional (2D) kernel EOF space are strongly bimodal. The modes correspond broadly to opposite phases of the Arctic Oscillation with a signature of the negative North Atlantic Oscillation (NAO). Over the North Atlantic–European sector, a trimodal PDF is also obtained with two strong and one weak modes. The strong modes are associated, respectively, with the north (or +NAO) and south (or −NAO) positions of the eddy-driven jet stream. The third weak mode is interpreted as a transition path between the two positions. A climate change signal is also observed in the troposphere of the winter hemisphere, resulting in an increase (a decrease) in the frequency of the polar high (low), consistent with an increase of zonal flow frequency.

scholarly journals Using Lomb–Scargle Analysis to Derive Empirical Orthogonal Functions from Gappy Meteorological Data

2018 ◽  
Vol 57 (10) ◽  
pp. 2217-2229
Author(s):  
Christopher Dupuis ◽  
Courtney Schumacher
Keyword(s):  
Time Series ◽  
Meteorological Data ◽  
Tropical Rainfall Measuring Mission ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Complex Topography ◽  
Sampled Data ◽  
Orthogonal Functions ◽  
Hard Limit ◽  
Irregularly Sampled Data

AbstractThe Lomb–Scargle discrete Fourier transform (LSDFT) is a well-known technique for analyzing time series. In this study, a solution for empirical orthogonal functions (EOFs) based on irregularly sampled data is derived from the LSDFT. It is demonstrated that this particular algorithm has no hard limit on its accuracy and yields results comparable to those of complex Hilbert EOF analysis. Two LSDFT algorithms are compared in terms of their performance in evaluating EOFs for precipitation observations from the Tropical Rainfall Measuring Mission satellite. Both are shown to be able to capture the pattern of the diurnal cycle of rainfall over the complex topography and diverse land cover of South America, and both also show other consistent features in the 0–12-day frequency band.

Mutual information applications to estimate the solar/ geomagnetic signatures in the drought indices in the Danube basin

2020 ◽  
Author(s):  
Ileana Mares ◽  
Venera Dobrica ◽  
Constantin Mares ◽  
Crisan Demetrescu
Keyword(s):  
Mutual Information ◽  
Drought Index ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Drought Indices ◽  
Drought Severity ◽  
Orthogonal Functions ◽  
Danube Basin ◽  
The Difference ◽  
Geomagnetic Activities

<p>The climatic condition for the dry or wet situations from 15 meteorological stations in the Danube basin has been evaluated using four indices: Palmer Drought Severity Index (PDSI), Palmer Hydrological Drought Index (PHDI), Weighted PDSI (WPLM) and Palmer Z-index (ZIND).</p><p>The overall temporal characteristic of the four indices has been analysed by means of the principal component of the Multivariate Empirical Orthogonal Functions decomposition (PC1-MEOF). Also, a simple drought index (TPPI) calculated as the difference between PC1 of the standardized temperature and precipitation, was considered.</p><p>To find the simultaneous influence of both solar and geomagnetic activities on drought indices in the Danube basin, the difference between synergistic and redundant components for each season was estimated, using the mutual information between the analyzed variables. The greater this difference is, the greater the simultaneous signature of the two variables in the drought indices is more significant, than by taking each of the two variables separately.</p><p>The solar activity was highlighted by Wolf numbers for the period 1901-2000 and for 1948-2000 by solar radio flux. For both periods the geomagnetic activity was quantified by the aa index.</p><p>The most significant results for the 100-year period were obtained for the autumn season for which the two predictors representing solar and geomagnetic activities, if considered simultaneously could be one of the causes that produce extreme hydroclimatic events. The analysis from 1948-2000 revealed that the simultaneous consideration of the two external factors is more significant in the summer and autumn time.</p>

Physical insights into principal component thermography

2020 ◽  
Vol 62 (5) ◽  
pp. 277-280 ◽  
Author(s):  
K Kaur ◽  
A Sharma ◽  
A Rani ◽  
V Kher ◽  
R Mulaveesala
Keyword(s):  
Principal Component ◽  
Steel Specimen ◽  
Vital Role ◽  
Empirical Orthogonal Functions ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Orthogonal Functions ◽  
Pulsed Thermography ◽  
Physical Insight ◽  
Non Destructive

Among widely used non-destructive testing (NDT) methods, infrared thermography (IRT) has gained importance due to its fast, whole-field, remote and quantitative inspection capabilities for the evaluation of various materials. Being fast and easy to implement, pulsed thermography (PT) plays a vital role in the infrared thermographic community. This paper provides a physical insight into the selection of empirical orthogonal functions obtained from principal component pulsed thermography for the detection of subsurface defects located inside a mild steel specimen.

scholarly journals A Comparison Study of EOF Techniques: Analysis of Nonstationary Data with Periodic Statistics

1999 ◽  
Vol 12 (1) ◽  
pp. 185-199 ◽  
Author(s):  
Kwang-Y. Kim ◽  
Qigang Wu
Keyword(s):  
Time Series ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Second Mode ◽  
Nonstationary Data ◽  
Cyclic Statistics ◽  
Surface Temperature Field ◽  
Climate Studies ◽  
Moving Patterns

Abstract Identification of independent physical/dynamical modes and corresponding principal component time series is an important aspect of climate studies for they serve as a tool for detecting and predicting climate changes. While there are a number of different eigen techniques their performance for identifying independent modes varies. Considered here are comparison tests of eight eigen techniques in identifying independent patterns from a dataset. A particular emphasis is given to cyclostationary processes such as deforming and moving patterns with cyclic statistics. Such processes are fairly common in climatology and geophysics. Two eigen techniques that are based on the cyclostationarity assumption—cyclostationary empirical orthogonal functions (EOFs) and periodically extended EOFs—perform better in identifying moving and deforming patterns than techniques based on the stationarity assumption. Application to a tropical Pacific surface temperature field indicates that the first dominant pattern and the corresponding principal component (PC) time series are consistent among different techniques. The second mode and the PC time series, however, are not very consistent from one another with hints of significant modal mixing and splitting in some of derived patterns. There also is a detailed difference of intraannual scale between PC time series of a stationary technique and those of a cyclostationary one. This may bear an important implication on the predictability of El Niño. Clearly there is a choice of eigen technique for improved predictability.

scholarly journals Ozone profile climatology for remote sensing retrieval algorithms

2019 ◽  
Vol 12 (9) ◽  
pp. 4745-4778 ◽  
Author(s):  
Kai Yang ◽  
Xiong Liu
Keyword(s):  
Remote Sensing ◽  
A Priori ◽  
Uv Spectra ◽  
Empirical Orthogonal Functions ◽  
Ozone Monitoring Instrument ◽  
Orthogonal Functions ◽  
Monitoring Instrument ◽  
Retrieval Algorithms ◽  
Ozone Monitoring ◽  
Priori Information

Abstract. New ozone (O3) profile climatologies are created from the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) O3 record between 2005 and 2016, within the period of Aura Microwave Limb Sounder (MLS) and Aura Ozone Monitoring Instrument (OMI) assimilation. These two climatologies consist of monthly mean O3 profiles and the corresponding covariances dependent on the local solar time, longitude (15∘), and latitude (10∘), which are parameterized by tropopause pressure and total O3 column. They are validated through comparisons, which show good agreements with previous O3 profile climatologies. Compared to a monthly zonal mean climatology, both tropopause- and column-dependent climatologies provide improved a priori information for profile and total O3 retrievals from remote sensing measurements. Furthermore, parameterization of the O3 profile with total column O3 usually reduces the natural variability of the resulting climatological profile in the upper stratosphere further than the tropopause parameterization, which usually performs better in the upper troposphere and lower stratosphere (UTLS). Therefore tropopause-dependent climatology is more appropriate for profile O3 retrieval for complementing the vertical resolution of backscattered ultraviolet (UV) spectra, while the column-dependent climatology is more suited for use in total O3 retrieval algorithms, with an advantage of complete profile specification without requiring ancillary information. Compared to previous column-dependent climatologies, the new MERRA-2 column-dependent climatology better captures the diurnal, seasonal, and spatial variations and dynamical changes in O3 profiles with higher resolutions in O3, latitude, longitude, and season. The new MERRA-2 climatologies contain the first quantitative characterization of O3 profile covariances, which facilitate a new approach to improve O3 profiles using the most probable patterns of profile adjustments represented by the empirical orthogonal functions (EOFs) of the covariance matrices. The MERRA-2 daytime column-dependent climatology is used in the combo O3 and SO2 algorithm for retrieval from the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) satellite, the Ozone Mapping and Profiler Suite Nadir Mapper (OMPS-NM) on the Suomi National Polar Partnership (SNPP), and the Ozone Monitoring Instrument (OMI) on the Aura spacecraft.

scholarly journals Metastable Decomposition of High-Dimensional Meteorological Data with Gaps

2008 ◽  
Vol 65 (11) ◽  
pp. 3479-3496 ◽  
Author(s):  
Illia Horenko ◽  
Stamen I. Dolaptchiev ◽  
Alexey V. Eliseev ◽  
Igor I. Mokhov ◽  
Rupert Klein
Keyword(s):  
Markov Models ◽  
Transition Probabilities ◽  
Meteorological Data ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Metastable States ◽  
High Dimensional ◽  
Observation Data ◽  
Orthogonal Functions ◽  
Mean Values

Abstract This paper presents an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series. The modified approach is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space (guaranteeing that the overall dynamics will be Markovian). The main advantage of the modified method is its ability to deal with the gaps in the high-dimensional observation data. The proposed method allows for (i) the separation of the data according to the metastable states, (ii) a hierarchical decomposition of these sets into metastable substates, and (iii) calculation of the state-specific extended empirical orthogonal functions simultaneously with identification of the underlying Markovian dynamics switching between those metastable substates. The authors discuss the introduced model assumptions, explain how the quality of the resulting reduced representation can be assessed, and show what kind of additional insight into the underlying dynamics such a reduced Markovian representation can give (e.g., in the form of transition probabilities, statistical weights, mean first exit times, and mean first passage times). The performance of the new method analyzing 500-hPa geopotential height fields [daily mean values from the 40-yr ECMWF Re-Analysis (ERA-40) dataset for a period of 44 winters] is demonstrated and the results are compared with information gained from a numerically expensive but assumption-free method (Wavelets–PCA), and the identified metastable states are interpreted w.r.t. the blocking events in the atmosphere.

scholarly journals Annual Cycle of Surface Longwave Radiation

2011 ◽  
Vol 50 (6) ◽  
pp. 1212-1224 ◽  
Author(s):  
Pamela E. Mlynczak ◽  
G. Louis Smith ◽  
Anne C. Wilber ◽  
Paul W. Stackhouse
Keyword(s):  
Annual Cycle ◽  
Water Cycle ◽  
Thermal Inertia ◽  
Longwave Radiation ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Surface Radiation ◽  
Radiation Budget ◽  
Orthogonal Functions ◽  
Annual Cycles

AbstractThe annual cycles of upward and downward longwave fluxes at the earth’s surface are investigated by use of the NASA Global Energy and Water Cycle Experiment (GEWEX) Surface Radiation Budget Dataset. Principal component analysis is used to quantify the annual cycles. Because of the immense difference between the heat capacity of land and ocean, the surface of the earth is partitioned into these two categories. Over land, the first principal component describes over 95% of the variance of the annual cycle of the upward and downward longwave fluxes. Over ocean the first term describes more than 87% of these annual cycles. Empirical orthogonal functions show the corresponding geographical distributions of these cycles. Phase-plane diagrams of the annual cycles of upward longwave fluxes as a function of net shortwave flux show the thermal inertia of land and ocean.

On the Nature of Zonal Jet EOFs

2006 ◽  
Vol 19 (24) ◽  
pp. 6409-6424 ◽  
Author(s):  
Adam H. Monahan ◽  
John C. Fyfe
Keyword(s):  
Time Series ◽  
Covariance Structure ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Physical Processes ◽  
Linear Combinations ◽  
Orthogonal Functions ◽  
The Mean ◽  
Systematic Perturbation ◽  
The Individual

Abstract Analytic results are obtained for the mean and covariance structure of an idealized zonal jet that fluctuates in strength, position, and width. Through a systematic perturbation analysis, the leading empirical orthogonal functions (EOFs) and principal component (PC) time series are obtained. These EOFs are built of linear combinations of basic patterns corresponding to monopole, dipole, and tripole structures. The analytic results demonstrate that in general the individual EOF modes cannot be interpreted in terms of individual physical processes. In particular, while the dipole EOF (similar to the leading EOF of the midlatitude zonal mean zonal wind) describes fluctuations in jet position to leading order, its time series also contains contributions from fluctuations in strength and width. No simple interpretations of the other EOFs in terms of strength, position, or width fluctuations are possible. Implications of these results for the use of EOF analysis to diagnose physical processes of variability are discussed.

scholarly journals Sea level variability at Adriatic coast and its relationship to atmospheric forcing

2005 ◽  
Vol 23 (6) ◽  
pp. 1997-2010 ◽  
Author(s):  
K. Bergant ◽  
M. Sušnik ◽  
I. Strojan ◽  
A. G. P. Shaw
Keyword(s):  
Sea Level ◽  
Large Scale ◽  
Tide Gauge ◽  
Grid Point ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Seasonal Cycles ◽  
Atmospheric Forcing ◽  
Orthogonal Functions ◽  
Adriatic Coast

Abstract. Sea level (SLH) variability at the Adriatic coast was investigated for the period 1872–2001 using monthly average values of observations at 13 tide gauge stations. Linear trends and seasonal cycles were investigated first and removed afterwards from the data. Empirical Orthogonal Functions (EOF) analysis was used further on remaining anomalies (SLA) to extract the regional intermonthly variability of SLH. It was found that the leading EOF and its principal component (PC) explain a major part of SLA variability (92%). The correlation between the reconstructed SLA, based on leading EOF and its PC, and overlapping observed SLA values for selected tide gauge stations is between 0.93 and 0.99. Actual SLH values at tide gauge stations can be reconstructed and some gaps in the data can be filled in on the basis of estimated SLA values if reasonable estimates of long-term trends and seasonal cycles are also available. A strong, seasonally dependent relationship between SLA at the Adriatic coast and atmospheric forcing, represented by sea level pressure (SLP) fields, was also found. Comparing the time series of leading PC and gridded SLP data for the period 1948–2001, the highest correlation coefficients (r) of –0.92 in winter, –0.84 in spring, –0.66 in summer, and –0.91 in autumn were estimated for a SLP grid point located in northern Italy. The SLP variability on this grid point contains information about the isostatic response of the sea level at the Adriatic coast, but can also be treated as a sort of teleconnection index representing the large-scale SLP variability across central and southern Europe. To some extent the large-scale SLP variability that affects the SLA at the Adriatic coast can be related to the North Atlantic Oscillation (NAO), because significant correlations were found between the NAO index and the first PC of SLA (rwinter=–0.56, rspring=–0.45, rsummer=–0.48, and rautumn=–0.43) for the period 1872–2001. The use of partial least-squares (PLS) regression between large-scale SLP fields and SLA only slightly improved the description of the SLA dependence on SLP forcing in comparison to the single grid point approach. A strong relationship between atmospheric pressure and the sea level could represent an additional possibility for filling in the gaps in the tide gauge data. Keywords. Oceanography: general (Climate and interannual variability) – Oceanography: physical (Air-sea interactions; sea level variations)

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