Principal component idealizations of the dominant modes of variability in the mechanics of the cutting process in metal turning

Abstract Principal component analysis (PCA), which is designed to look at internal modes of variability, has often been applied beyond its intended design to study coupled modes of variability in combined datasets, also referred to as combined PCA. There are statistical techniques better suited for this purpose such as singular value decomposition (SVD) and canonical correlation analysis (CCA). In this paper, a different technique is examined that has not often been applied in climate science, that is, redundancy analysis (RA). Similar to multivariate regression, RA seeks to maximize the variance accounted for in one random vector that is linearly regressed against another random vector. RA can be used for forecasting and prediction studies of the climate system. This technique has the added advantage that the time-lagged redundancy index offers a robust method of identifying lead–lag relations among climate variables. In this study, combined PCA and RA of global sea surface temperatures (SSTs) and sea level pressures (SLPs) are carried out for the National Centers for Environmental Prediction (NCEP) reanalysis data and a simulation of the Canadian Centre for Climate Modeling and Analysis (CCCma) climate model. A simplified state-space model is also constructed to aid in the diagnosis and interpretation of the results. The relative advantages and disadvantages of combined PCA and RA are discussed. Overall, RA tends to provide a clearer and more consistent picture of the underlying physical processes than combined PCA.

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Principal Metabolic Flux Mode Analysis

10.1101/163055 ◽

2017 ◽

Cited By ~ 1

Author(s):

Sahely Bhadra ◽

Peter Blomberg ◽

Sandra Castillo ◽

Juho Rousu

Keyword(s):

Metabolic Flux ◽

Principal Component ◽

Supplementary Information ◽

Mode Analysis ◽

Flux Analysis ◽

Large Set ◽

Elementary Mode Analysis ◽

Modes Of Variability ◽

Link Type ◽

Flux Mode

AbstractMotivationIn the analysis of metabolism using omics data, two distinct and complementary approaches are frequently used: Principal component analysis (PCA) and Stoichiometric flux analysis. PCA is able to capture the main modes of variability in a set of experiments and does not make many prior assumptions about the data, but does not inherently take into account the flux mode structure of metabolism. Stoichiometric flux analysis methods, such as Flux Balance Analysis (FBA) and Elementary Mode Analysis, on the other hand, produce results that are readily interpretable in terms of metabolic flux modes, however, they are not best suited for exploratory analysis on a large set of samples.ResultsWe propose a new methodology for the analysis of metabolism, called Principal Metabolic Flux Mode Analysis (PMFA), which marries the PCA and Stoichiometric flux analysis approaches in an elegant regularized optimization framework. In short, the method incorporates a variance maximization objective form PCA coupled with a Stoichiometric regularizer, which penalizes projections that are far from any flux modes of the network. For interpretability, we also introduce a sparse variant of PMFA that favours flux modes that contain a small number of reactions. Our experiments demonstrate the versatility and capabilities of our methodology.AvailabilityMatlab software for PMFA and SPMFA is available in https://github.com/ aalto-ics-kepaco/[email protected], [email protected], [email protected], [email protected] informationDetailed results are in Supplementary files. Supplementary data are available at https://github.com/aalto-ics-kepaco/PMFA/blob/master/Results.zip.

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Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems

Journal of Climate ◽

10.1175/jcli-d-20-0266.1 ◽

2021 ◽

Vol 34 (2) ◽

pp. 715-736

Author(s):

Clément Guilloteau ◽

Antonios Mamalakis ◽

Lawrence Vulis ◽

Phong V. V. Le ◽

Tryphon T. Georgiou ◽

...

Keyword(s):

Southern Oscillation ◽

Synthetic Data ◽

Principal Component ◽

High Sensitivity ◽

Frequency Resolution ◽

Robust Estimator ◽

Low Frequencies ◽

High Frequencies ◽

Modes Of Variability ◽

Spectral Principal Component Analysis

AbstractSpectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3–60-day periods) in both GPH and SST and El Niño–Southern Oscillation (ENSO) at low frequencies (2–7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics.

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Characterization of the resilience and variability of vegetation during the Holocene using a large database of pollen data

10.5194/egusphere-egu21-15259 ◽

2021 ◽

Author(s):

Raphael Hébert ◽

Chenzhi Li ◽

Thomas Laepple ◽

Ulrike Herzschuh

Keyword(s):

Forest Ecosystems ◽

Principal Component ◽

Vegetation Composition ◽

The Holocene ◽

Modes Of Variability ◽

Millennial Time Scale ◽

Fire Disturbances ◽

Palynological Records ◽

Stability Of Forest Ecosystems

Global climatic changes which are expected in the 21st century are likely to create unparalleled disturbances on vegetation. In addition, human activities also increase the risk of fire disturbances and insect epidemies. We investigate the resilience of different biomes by examining their behaviour during the Holocene using a taxonomically harmonized and temporally standardized global fossil pollen datasets,synthesized from 2821 palynological records from the Neotoma Paleoecology Database and additional literature. Specifically, we study the composition variability on millennial time-scale and timescale-dependant scaling of variability from centennial to multi-millennial timescales. A principal component analysis was performed in order to characterize the principal modes of variability of the pollen assemblages. We find coherent regional signals of vegetation variability and scaling of variability from the pollen assemblages, indicating significant millennial scale variability which can be related to vegetation taxa and climates. Particularly, we observe more stability in North America and Northern Europe in areas dominated by boreal forest and deciduous forests. This may be linked to the greater stability of forest ecosystems and also a more stable climate over these areas which may be the result of stabilizing feedbacks. We find that diversity plays a key role in vegetation composition and that more diverse regions allow for greater variability.&#160;&#160;<div> <div>&#160;</div> </div>

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Interannual Variability of the Occurrence of MJO at Different Phases and Its Association with Two ENSO Modes

10.21203/rs.3.rs-112899/v1 ◽

2020 ◽

Author(s):

Panini Dasgupta ◽

Roxy Koll ◽

Rajib Chattopadhyay ◽

Chennu Naidu ◽

Abirlal Metya

Keyword(s):

Indian Ocean ◽

Interannual Variability ◽

Southern Oscillation ◽

Principal Component ◽

Western Indian Ocean ◽

Central Pacific ◽

Modes Of Variability ◽

Central Pacific Ocean ◽

Second Mode ◽

The Western Pacific

Abstract In the present study, we investigate the interannual variability of the occurrence of the Madden Julian Oscillation (MJO) at different Real-time Multivariate MJO (RMM) phase regions (MJO frequency) and its association with the El Niño Southern Oscillation (ENSO). Evaluating the all-season data, we identify the dominant zonal patterns of MJO frequency exhibiting prominent interannual variability. Using Principal Component Analysis Biplot (PCA Biplot) technique, we demonstrate that the MJO frequency has two distinct modes of variability related to RMM1 and RMM2 spatial patterns. The first spatial mode of MJO frequency related to RMM1 is associated with a higher frequency of MJO active days over the Maritime Continent and a lower frequency over the central Pacific Ocean and the western Indian Ocean, or vice versa. The second mode related to RMM2 is associated with a higher frequency of MJO active days over the eastern Indian Ocean and a lower frequency over the western Pacific, or vice versa. We find that these two types of MJO frequency patterns are associated with the central Pacific and eastern Pacific ENSO modes, respectively. These MJO frequency patterns are the lag response of the underlying ocean state.

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Northern Hemisphere Modes of Variability and the Timing of Spring in Western North America

Journal of Climate ◽

10.1175/2011jcli4069.1 ◽

2011 ◽

Vol 24 (15) ◽

pp. 4003-4014 ◽

Cited By ~ 44

Author(s):

Toby R. Ault ◽

Alison K. Macalady ◽

Gregory T. Pederson ◽

Julio L. Betancourt ◽

Mark D. Schwartz

Keyword(s):

North America ◽

Northern Hemisphere ◽

Principal Component ◽

Reanalysis Data ◽

Onset Date ◽

Western North America ◽

Spatial And Temporal Patterns ◽

Modes Of Variability ◽

Index Model ◽

Maximum Temperatures

Abstract Spatial and temporal patterns of variability in spring onset are identified across western North America using a spring index (SI) model based on weather station minimum and maximum temperatures (Tmin and Tmax, respectively). Principal component analysis shows that two significant and independent patterns explain roughly half of the total variance in the timing of spring onset from 1920 to 2005. However, these patterns of spring onset do not appear to be linear responses to the primary modes of variability in the Northern Hemisphere: the Pacific–North American pattern (PNA) and the northern annular mode (NAM). Instead, over the period when reanalysis data and the spring index model overlap (1950–2005), the patterns of spring onset are local responses to the state of both the PNA and NAM, which together modulate the onset date of spring by 10–20 days on interannual time scales. They do so by controlling the number and intensity of warm days. There is also a regionwide trend in spring advancement of about −1.5 days decade−1 from 1950 to 2005. Trends in the NAM and PNA can only explain about one-third (−0.5 day decade−1) of this trend.

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Observed snow depth trends in the European Alps: 1971 to 2019

The Cryosphere ◽

10.5194/tc-15-1343-2021 ◽

2021 ◽

Vol 15 (3) ◽

pp. 1343-1382

Author(s):

Michael Matiu ◽

Alice Crespi ◽

Giacomo Bertoldi ◽

Carlo Maria Carmagnola ◽

Christoph Marty ◽

...

Keyword(s):

Snow Depth ◽

Principal Component ◽

European Alps ◽

North West ◽

Modes Of Variability ◽

North East ◽

Regional Trends ◽

Spatial Coverage ◽

Snow Cover Duration ◽

Regional Analyses

Abstract. The European Alps stretch over a range of climate zones which affect the spatial distribution of snow. Previous analyses of station observations of snow were confined to regional analyses. Here, we present an Alpine-wide analysis of snow depth from six Alpine countries – Austria, France, Germany, Italy, Slovenia, and Switzerland – including altogether more than 2000 stations of which more than 800 were used for the trend assessment. Using a principal component analysis and k-means clustering, we identified five main modes of variability and five regions which match the climatic forcing zones: north and high Alpine, north-east, north-west, south-east, and south and high Alpine. Linear trends of monthly mean snow depth between 1971 and 2019 showed decreases in snow depth for most stations from November to May. The average trend among all stations for seasonal (November to May) mean snow depth was −8.4 % per decade, for seasonal maximum snow depth −5.6 % per decade, and for seasonal snow cover duration −5.6 % per decade. Stronger and more significant trends were observed for periods and elevations where the transition from snow to snow-free occurs, which is consistent with an enhanced albedo feedback. Additionally, regional trends differed substantially at the same elevation, which challenges the notion of generalizing results from one region to another or to the whole Alps. This study presents an analysis of station snow depth series with the most comprehensive spatial coverage in the European Alps to date.

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Observed snow depth trends in the European Alps 1971 to 2019

10.5194/tc-2020-289 ◽

2020 ◽

Author(s):

Michael Matiu ◽

Alice Crespi ◽

Giacomo Bertoldi ◽

Carlo Maria Carmagnola ◽

Christoph Marty ◽

...

Keyword(s):

Snow Depth ◽

Principal Component ◽

Alpine Region ◽

European Alps ◽

Climatic Forcing ◽

Climate Zones ◽

Modes Of Variability ◽

Regional Trends ◽

Spatial Coverage ◽

Regional Analyses

Abstract. The European Alps stretch over a range of climate zones, which affect the spatial distribution of snow. Previous analyses of station observations of snow were confined to regional analyses. Here, we present an Alpine wide analysis of snow depth from six Alpine countries: Austria, France, Germany, Italy, Slovenia, and Switzerland; including altogether more than 2000 stations. Using a principal component analysis and k-means clustering, we identified five main modes of variability and five regions, which match the climatic forcing zones: north and high Alpine, northeast, northwest, southeast and southwest. Linear trends of mean monthly snow depth between 1971 to 2019 showed decreases in snow depth for 87 % of the stations. December to February trends were on average −1.1 cm decade−1 (min, max: −10.8, 4.4; elevation range 0–1000 m), −2.5 (−25.1, 4.4; 1000–2000 m) and −0.1 (−23.3, 9.9; 2000–3000 m), with stronger trends in March to May: −0.6 (−10.9, 1.0; 0–1000 m), −4.6 (−28.1, 4.1; 1000–2000 m) and −7.6 (−28.3, 10.5; 2000–3000 m). However, regional trends differed substantially, which challenges the notion of generalizing results from one Alpine region to another or to the whole Alps. This study presents an analysis of station snow depth series with the most comprehensive spatial coverage in the European Alps to date.

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Vertical crustal deformations and climate variability through PCA and SVD

10.5194/egusphere-egu21-13013 ◽

2021 ◽

Author(s):

Letizia Elia ◽

Susanna Zerbini ◽

Fabio Raicich

Keyword(s):

Time Series ◽

Principal Component ◽

Space Time ◽

Time Variability ◽

Large Network ◽

Coupled Modes ◽

Entire Study ◽

Modes Of Variability ◽

Multivariate Enso Index ◽

Enso Index

We investigated a large network of permanent GPS stations to identify and analyse common patterns in the series of the GPS height, environmental parameters, and climate indexes.The study is confined to Europe, the Mediterranean, and the North-eastern Atlantic area, where 114 GPS stations were selected from the Nevada Geodetic Laboratory (NGL) archive. The GPS time series were selected on the basis of the completeness and the length of the series.In addition to the GPS height, the parameters analysed in this study are the atmospheric surface pressure (SP), the terrestrial water storage (TWS), and a few climate indexes, such as MEI (Multivariate ENSO Index). The Principal Component Analysis (PCA) is the methodology adopted to extract the main patterns of space/time variability of the parameters.Moreover, the coupled modes of space/time interannual variability between pairs of variables was investigated. The methodology adopted is the Singular Value Decomposition (SVD).Over the study area, main modes of variability in the time series of the GPS height, SP and TWS were identified. For each parameter, the main modes of variability are the first four. In particular, the first mode explains about 30% of the variance for GPS height and TWS and about 46% for SP. The relevant spatial patterns are coherent over the entire study area in all three cases.The SVD analysis of coupled parameters, namely H-AP and H-TWS, shows that most of the common variability is explained by the first 3 modes, which account for almost 80% and 45% of the covariance, respectively.Finally, we investigated the relation between the GPS height and a few climate indexes. Significant correlations, up to 50%, were found between the MEI (Multivariate Enso Index) and about half of the stations in the network.

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Observed snow depth trends in the European Alps 1971 to 2019

10.5194/egusphere-egu21-3287 ◽

2021 ◽

Author(s):

Michael Matiu ◽

Alice Crespi ◽

Giacomo Bertoldi ◽

Carlo Maria Carmagnola ◽

Christoph Marty ◽

...

Keyword(s):

Snow Depth ◽

Principal Component ◽

European Alps ◽

Climatic Forcing ◽

Modes Of Variability ◽

Regional Trends ◽

Spatial Coverage ◽

Trend Assessment ◽

Snow Cover Duration ◽

Regional Analyses

The European Alps stretch over a range of climate zones, which affect the spatial distribution of snow. Previous analyses of station observations of snow were confined to regional analyses, which complicates comparisons between regions and makes Alpine wide conclusions questionable. Here, we present an Alpine wide analysis of snow depth from six Alpine countries: Austria, France, Germany, Italy, Slovenia, and Switzerland; including altogether more than 2000 stations, of which more than 800 were used for the trend assessment. Using a principal component analysis and k-means clustering, we identified five main modes of variability and five regions, which match the climatic forcing zones: north & high Alpine, northeast, northwest, southeast, and south & high Alpine. Linear trends of monthly mean snow depth between 1971 and 2019 showed decreases in snow depth for most stations for November to May. The average trend among all stations for seasonal (November to May) mean snow depth was -8.4 % per decade, for seasonal maximum snow depth -5.6 % per decade, and for seasonal snow cover duration -5.6 % per decade. However, regional trends differed substantially after accounting for elevation, which challenges the notion of generalizing results from one region to another or to the whole Alps. This study presents an analysis of station snow depth series with the most comprehensive spatial coverage in the European Alps to date.

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