Testing Methods of Pattern Extraction for Climate Data Using Synthetic Modes

2021 ◽  
Vol 34 (18) ◽  
pp. 7645-7660
Author(s):  
D. James Fulton ◽  
Gabriele C. Hegerl
Keyword(s):  
Synthetic Data ◽  
Principal Component ◽  
Standard Technique ◽  
Extraction Methods ◽  
Empirical Orthogonal Functions ◽  
Alternative Methods ◽  
Climate Data ◽  
Pattern Extraction ◽  
Orthogonal Functions ◽  
Mode Decomposition

AbstractIn this paper we develop a method to quantify the accuracy of different pattern extraction techniques for the additive space–time modes often assumed to be present in climate data. It has previously been shown that the standard technique of principal component analysis (PCA; also known as empirical orthogonal functions) may extract patterns that are not physically meaningful. Here we analyze two modern pattern extraction methods, namely dynamical mode decomposition (DMD) and slow feature analysis (SFA), in comparison with PCA. We develop a Monte Carlo method to generate synthetic additive modes that mimic the properties of climate modes described in the literature. The datasets composed of these generated modes do not satisfy the assumptions of any pattern extraction method presented. We find that both alternative methods significantly outperform PCA in extracting local and global modes in the synthetic data. These techniques had a higher mean accuracy across modes in 60 out of 60 mixed synthetic climates, with SFA slightly outperforming DMD. We show that in the majority of simple cases PCA extracts modes that are not significantly better than a random guess. Finally, when applied to real climate data these alternative techniques extract a more coherent and less noisy global warming signal, as well as an El Niño signal with a clearer spectral peak in the time series, and more a physically plausible spatial pattern.

Extended-range predictability of sudden stratospheric warming events suggested by mode decomposition

2021 ◽  
Author(s):  
Zheng Wu ◽  
Bernat Jiménez-Esteve ◽  
Raphael de Fondeville ◽  
Eniko Székely ◽  
Guillaume Obozinski ◽  
...  
Keyword(s):  
Vortex Breakdown ◽  
Early Stage ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
The Arctic ◽  
Lead Times ◽  
Dynamical Process ◽  
Orthogonal Functions ◽  
Mode Decomposition ◽  
Advection Term

<p>Major sudden stratospheric warmings (SSWs) are extreme wintertime circulation events of the Arctic stratosphere that are accompanied by a breakdown of the polar vortex. The stratospheric anomalies can propagate downward to the lower stratosphere and influence the weather of the troposphere and the surface for up to two months after the onset of SSW events. Therefore, SSWs can be an important source of predictability on subseasonal to seasonal (S2S) time scales over the Northern Hemisphere (NH) mid- and high- latitudes. However, SSWs themselves are difficult to forecast, with a predictability limit of around one to two weeks. Therefore, understanding the dynamical process that leads to the vortex breakdown is crucial to improve the predictability of SSWs, and ultimately, the weather at the Earth’s surface. To this end, we employ a mode decomposition diagnosis to analyze Ertel's potential vorticity (PV) equation by decomposing each term using empirical orthogonal functions (EOFs) of PV to study the vortex weakening process. With this method, a principal component (PC) tendency equation can be derived, which includes the evolution of the linear and nonlinear PV advection terms and indicates how they contribute to the vortex weakening. The results show that the linear advection term is the main contributor to the increase of PC tendency in the early stage of the warming and contains distinct signals that indicate the weakening of the vortex as early as 25 days before the onset of SSWs using ERA-interim daily data. Our results indicate that both the lead times of the onset of SSW events as well as the type of the event may be extended beyond the current predictability limit, promising to provide longer lead times for the prediction of surface weather. </p>

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.

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 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.

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 Extended-range predictability of sudden stratospheric warming events suggested by mode decomposition

2021 ◽  
Author(s):  
Zheng Wu ◽  
Bernat Jiménez-Esteve ◽  
Raphaël de Fondeville ◽  
Enikő Székely ◽  
Guillaume Obozinski ◽  
...  
Keyword(s):  
Decomposition Analysis ◽  
Polar Vortex ◽  
Principal Component ◽  
Empirical Orthogonal Functions ◽  
Rate Of Change ◽  
The Arctic ◽  
Lead Times ◽  
Main Contributor ◽  
Budget Analysis ◽  
Mode Decomposition

Abstract. Major sudden stratospheric warmings (SSWs) are extreme wintertime circulation events of the Arctic stratosphere that are accompanied by a breakdown of the polar vortex and are considered an important source of predictability of tropospheric weather on subseasonal to seasonal time scales over the Northern Hemisphere mid- and high- latitudes. However, SSWs themselves are difficult to forecast, with a predictability limit of around one to two weeks. The predictability limit for determining the type of event, i.e., wave-1 or wave-2 events, is even shorter. Here we analyze the dynamics of the vortex breakdown and look for early signs of the vortex deceleration process with lead times beyond the current predictability limit of SSWs. To this end, we employ a mode decomposition analysis to analyze potential vorticity (PV) equation on the 850 K isentropic surface by decomposing each term in the PV equation using the empirical orthogonal functions of the PV. The first principal component (PC) is an indicator of the strength of the polar vortex and starts to increase from around 25 days before the onset of SSWs, indicating a deceleration of the polar vortex. We then use a budget analysis based on the mode decomposition to characterize the contribution of the linear and the nonlinear PV advection terms to the rate of change (tendency) of the first PC. The linear PV advection is the main contributor to the PC tendency at 15 to 25 days before the onset of both types of SSW events. The nonlinear PV advection becomes important between 1 to 15 days before the onset of wave-2 events, while the linear PV advection continues to be the main contributor for wave-1 events. By linking the PV advection to the PV flux, we find that the linear PV flux is important for both types of SSWs from 15 to 25 days before the events but with different wave-2 spatial patterns, while the nonlinear PV flux displays a wave-3 wave pattern, which finally leads to a split of the polar vortex. The signals found here indicate that both the lead times for predicting the SSW onset and the lead times for predicting the type of the SSW event could potentially be extended beyond the current predictability limit of one to two weeks.

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.

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