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.

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.

ADAPTIVE FILTERING AND PREDICTION OF NOISY MULTIVARIATE SIGNALS: AN APPLICATION TO SUBANNUAL VARIABILITY IN ATMOSPHERIC ANGULAR MOMENTUM

1993 ◽  
Vol 03 (03) ◽  
pp. 625-634 ◽  
Author(s):  
CHRISTIAN L. KEPPENNE ◽  
MICHAEL GHIL
Keyword(s):  
Time Series ◽  
Angular Momentum ◽  
Multivariate Time Series ◽  
Singular Spectrum Analysis ◽  
Predictive Ability ◽  
Principal Component ◽  
Entropy Method ◽  
Empirical Orthogonal Functions ◽  
Atmospheric Angular Momentum ◽  
Orthogonal Functions

Principal component analysis (PCA) in the space and time domains is applied to filter adaptively the dominant modes of subannual (SA) variability of a 12-year long multivariate time series of Northern Hemisphere atmospheric angular momentum (AAM); AAM is computed in 23 latitude bands of equal area from operational analyses of the U.S. National Meteorological Center. PCA isolates the leading empirical orthogonal functions (EOFs) of spatial dependence, while multivariate singular spectrum analysis (M-SSA) yields filtered time series that capture the dominant low-frequency modes of SA variability. The time series prefiltered by M-SSA lend themselves to prediction by the maximum entropy method (MEM). Whole-field predictions are made by combining the forecasts so obtained with the leading spatial EOFs obtained by PCA. The combination of M-SSA and MEM has predictive ability up to about a month. These methods are essentially linear but data-adaptive. They seem to perform well for short, noisy, multivariate time series, to which purely nonlinear, deterministically based methods are difficult to apply.

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 The Influence of European Climate Variability Mechanism on Air Temperatures in Romania

2014 ◽  
Vol 8 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Nicoleta Ionac ◽  
Monica Matei
Keyword(s):  
Time Series ◽  
Climate Variability ◽  
Large Scale ◽  
Empirical Orthogonal Functions ◽  
Spatial And Temporal Variability ◽  
Orthogonal Functions ◽  
Mean Values ◽  
European Climate ◽  
Air Temperatures ◽  
And Shifts

Abstract The present paper investigates on the spatial and temporal variability of maximum and minimum air-temperatures in Romania and their connection to the European climate variability. The European climate variability is expressed by large scale parameters, which are roughly represented by the geopotential height at 500 hPa (H500) and air temperature at 850 hPa (T850). The Romanian data are represented by the time series at 22 weather stations, evenly distributed over the entire country’s territory. The period that was taken into account was 1961-2010, for the summer and winter seasons. The method of empirical orthogonal functions (EOF) has been used, in order to analyze the connection between the temperature variability in Romania and the same variability at a larger scale, by taking into consideration the atmosphere circulation. The time series associated to the first two EOF patterns of local temperatures and large-scale anomalies were considered with regard to trends and shifts in their mean values. The non- Mann-Kendall and Pettitt parametric tests were used in this respect. The results showed a strong correlation between T850 parameter and minimum and maximum air temperatures in Romania. Also, the ample variance expressed by the first EOF configurations suggests a connection between local and large scale climate variability.

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.

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