empirical orthogonal function in r

empirical orthogonal function in r2020/09/28

The method of calculation roughly follows the theory outlined above. Rev., 110, 699-706. - Edward Armstrong To highlight its usefulness, we provide . An attempt to provide physical insight into the empirical orthogonal function (EOF) representation of data fields by the study of fields generated by linear stochastic models is presented in this paper. The percentage of the total "system" (or array) variance, which from (IX.3) can be written Tr R = m M j=1 , (IX.6a) that is "explained" by that mode is given by the ratio of m /Tr R. In this paper we present the R implementation of the original algorithm in the remote package. The importance of different types of variation to the overall TEC variability as well as the influence of solar radiation and geomagnetic activity toward . Basics idea of Empirical Orthogonal Functions EOFs are an orthogonal linear transformation into new coordinate system such that the greatest variance by any projection of the data is contained in the first EOF (also called the first principal component), the second greatest variance on the second EOF, etc. An empirical orthogonal function (EOF) decomposition of these trend maps was then performed to determine the dominant ten-year trend pattern in the sea level reconstruction, similar to the analysis done in Hamlington et al. Empirical Orthogonal Function and Principal Component techniques. Empirical Orthogonal Functions Selected Notes of David A. Randall 66 (11.3) is minimized for a given . empirical orthogonal functions (EOFs) as basis func-tions, but by using CSEOFs and by addressing other aspects of the reconstruction procedure, an alternative and - in some ways - improved sea-level reconstruc-tion can be computed. Empirical Orthogonal Teleconnections (EOTs) denote a regression based approach to decompose spatio-temporal fields into a set of . The literature is very unclear and often uses the two terms (EOF/PCA) interchangeably. R. ALAN PLUMB Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts (Manuscript received 15 October 2016, in final form 19 January 2017) ABSTRACT The two leading empirical orthogonal functions (EOFs) of zonal-mean zonal wind describe north-south = TRUE) Arguments Details EOF analysis is used to study patterns of variability ("modes") in a matrix time series and how these patterns change with time ("amplitude time series"). harmonic analysis; sinusoidal base functions with a frequency range from 0 to the Nyquist frequency with an interval inversely proportional to the total length of time of the data, i.e. The Jacobian matrix, necessary for the proposed linearization approach, includes derivatives with respect to empirical orthogonal function coefficients instead of sound speed directly. ( 3.1) are the empirical orthogonal functions (EOFs) and the expansion coefficients c k ( t) are the principal components (PCs). We here present a particularly simple way to calculate functions, empirically and orthogonally, without these functions being traditional EOFs. Ionospheric Current Variations by Empirical Orthogonal Function Analysis: Solar Activity Dependence and Longitudinal Differences Charles Owolabi, Haibing Ruan, Y. Yamazaki, R. O. Kaka, O. O. Akinola, Akimasa Yoshikawa Previous sea-level reconstructions have utilized empirical orthogonal functions (EOFs) as basis functions, but . Script to demonstrate empirical orthogonal functions in R - GitHub - atfric/eofR: Script to demonstrate empirical orthogonal functions in R 1. empirical orthogonal function analysis (EOF), also known as eigenvector analysis or principal component analysis, is a method to analyze the structural features in matrix data and extract the feature quantity of main data.Import moduleimport cartopy.crs as ccrs import cartopy.feature as cfeaturUTF-8. 3) in this section, in order to allow a broader interpretation and a strong synthesis of the results from the Empirical Orthogonal Functions performed on several drought indices. et al (1982): Sampling Errors in the Estimation of Empirical Orthogonal Functions. Abstract Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. difficult to understand the literature. It implements a collection of functions to facilitate empirical orthogonal teleconnection analysis. [1] Empirical orthogonal functions are used together with standard statistical metrics to evaluate the ability of models with different spatial resolutions to reproduce observed patterns of surface ozone (O 3) in the eastern United States in the summer of 1995. The present paper presents a different version, the regularised (or smooth) empirical orthogonal function (EOF) method, by including a regularisation constraint, . The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close . First introduced by van den Dool, Saha, and Johansson (2000), empirical orthogonal teleconnections (EOT) denote a regression based approach that allows for straight-forward interpretation of the extracted modes. The basis functions a k ( s) in Eq. EOF ( formula, n = 1, data = NULL, B = 0, probs = c (lower = 0.025, mid = 0.5, upper = 0.975), rotate = FALSE, suffix = "PC", fill = NULL ) Arguments Details Singular values can be computed over matrices so formula denotes how to build a matrix from the data. Using empirical orthogonal functions derived from remote-sensing reflectance for the prediction of phytoplankton pigment concentrations A. Bracher1,2, M. H. Taylor3, B. Taylor1, T. Dinter1,2, R. Röttgers4, and F. Steinmetz5 1Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bussestraße 24, 27570 Bremerhaven, Germany In a large class of these models, the EOFs at individual Fourier frequencies coincide with the . Empirical orthogonal function analysis Description Finds and rotates empirical orthogonal functions (EOFs). Empirical Orthogonal Functions: The Medium is the Message Adam H. Monahan1;2, John C. Fyfe3, Maarten H.P. It is the same as performing a principal components analysis on the data, except that the EOF method finds both time series and spatial patterns. Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. This is standard, and has been in R for ever. This indicates if eigenvalues are significantly separated. Sampling errors in the estimation of empirical orthogonal functions. Based on the ERA-5 meteorological data from 2015 to 2019, we establish the global tropospheric delay spherical harmonic (SH) coefficients set called the SH_set and develop the global tropospheric delay SH coefficients empirical model called EGtrop using the empirical orthogonal function (EOF) method and periodic functions. The below tests our function with an artifical "zonal-mean zonal wind" dataset, generated with rednoise.The peak strength and peak strength position vary in time (the y-axis).The PCs are shown in the panel on the right. Doing Empirical Orthogonal Function (EOF) analysis in R. 9. The major climatic features of precipitation (P), potential evapotranspiration (PET), and drought climatology [Aridity Index (AI) = P/PET)] of Turkey are presented (Fig. GERALD R. NORTH Department of Atmospheric Sciences, and Department of Oceanography, Texas A&M University, College Station, Texas (Manuscript received 2 February 2009, in final form 27 May 2009) ABSTRACT Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality 1. I will use "empirical orthogonal functions" or EOFs to refer to the "spatial" patterns that are the result of doing an EOF analysis and "expansion coefficients" or ECs to refer to the "temporal" patterns. empirical orthogonal functions (EOFs) of a time series Z(x, y, t) are the eigenvectors of the covarinace matrix of the time series. Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. (2000). [1] A global ionospheric total electron content (TEC) model based on the empirical orthogonal function (EOF) analysis method is constructed using the global ionosphere maps provided by Jet Propulsion Laboratory during the years 1999-2009. = TRUE) Arguments Value A list with the following members: REOF a matrix with rotated EOFs amplitude a matrix with amplitude time series of REOF s eigen.pct all eigenvalues of correlation matrix as percent of total variance variance 1 Please define "EOF". The results show that months of July, August and September contribute about 76% of the annual precipitation for this station. • Distinguish patterns/noise Reconstructing sea level using cyclostationary empirical orthogonal functions B. D. Hamlington,1 R. R. Leben,1 R. S. Nerem,1 W. Han,2 and K.-Y. [1] Cyclostationary empirical orthogonal functions, derived from satellite altimetry, are @article{osti_1627799, title = {An Empirical Orthogonal Function-Based Algorithm for Estimating Terrestrial Latent Heat Flux from Eddy Covariance, Meteorological and Satellite Observations}, author = {Feng, Fei and Li, Xianglan and Yao, Yunjun and Liang, Shunlin and Chen, Jiquan and Zhao, Xiang and Jia, Kun and Pintér, Krisztina and McCaughey, J. Harry}, abstractNote = {Accurate estimation of . The meaning of (11.4) is that the EOFs are orthogonal in space. Empirical orthogonal functions and normal modes An attempt to provide physical insight into the empirical orthogonal function (EOF) representation of data fields by the study of fields generated by linear stochastic models is presented in this paper. It needs the non-orthogonal B-spline basis to seed its computations and the estimate the covariance matrix and the orthogonal eigenvector basis \(v_j\). Ambaum 4, David B. Stephenson 5, and Gerald R. North 6 1 School of Earth and Ocean Sciences University of Victoria P.O. Empirical orthogonal teleconnections in R. 'remote' is short for "R(-based) EMpirical Orthogonal TEleconnections". As a test of the stationarity of the spatial pattern, the dominant EOF was . We apply tropospheric delay derived from IGS stations not involved in . We are happy to introduce Reot, an R package designed for empirical orthogonal teleconnection (EOT) analysis of gridded geo-scientific space-time data based on the method by van den Dool et al. Empirical orthogonal function (EOF') analyses are used to estimate the contribution of each statistical mode to the total variance. Empirical orthogonal teleconnections in R. 'remote' is short for "R(-based) EMpirical Orthogonal TEleconnections". Empirical Orthogonal Function analysis of the palmer drought indices (PDF) Empirical Orthogonal Function analysis of the palmer drought indices | Murat Türkeş - Academia.edu Academia.edu no longer supports Internet Explorer. Often in the literature, EOF modes are interpreted individually, independent of other modes. I have received an answer through another forum that indicates that this is a common practice - "Basic R stats functions like prcomp have a predict method that can be used to "predict" (calculate) scores with 'newdata'. In fact, it can be shown that no such attribution can generally be made. EOT denotes a regression-based approach to decompose spatio-temporal fields into a set of independent orthogonal patterns. R Documentation Empirical Orthogonal Function Description Computes Singular Value Decomposition (also known as Principal Components Analysis or Empirical Orthogonal Functions). 2, Fig. Empirical orthogonal function analysis Finds and rotates empirical orthogonal functions (EOFs). We are happy to introduce Reot, an R package designed for empirical orthogonal teleconnection (EOT) analysis of gridded geo-scientific space-time data based on the method by van den Dool et al. In this paper we present the R implementation of the original algorithm in the For example, the functions f 1(x) x2 and f 2(x) x3 are orthogonal on the interval [ 1, 1], since Unlike in vector analysis, in which the word orthogonal is a synonym for perpendic- ular, in this present context the term orthogonal and condition (1) have no geometric significance. Empirical orthogonal teleconnections in R. 'remote' is short for 'R(-based) EMpirical Orthogonal TEleconnections'. Empirical Orthogonal Functions and Normal Modes. In a large class of these models, the EOFs at individual Fourier frequencies coincide with the orthogonal mechanical modes of the system . A global empirical orthogonal function (EOF) model of the tropospheric weighted mean temperature called GEOFM_Tm was developed using high-precision Global Geodetic Observing System (GGOS) Atmosphere T m data during the years 2008-2014. The function pca.fd() takes W.obj as input. The first few EOFs describe the largest variability in the thermal sequence and generally only a few EOFs contain useful images. Normally, EOF analysis is used to determine the patterns of largest variability. EOF: Standard Empirical Orthogonal Analysis Standard EOF (aka eigenvector, principal component) analysis yields patterns and time series which are both orthogonal.The derived patterns are a function of the domain and the time period being used. Based on empirical orthogonal function (EOF), a new spatiotemporal interpolation method, EOF interpolation (EOFI) is introduced in this paper, and then, EOFI is applied to reconstruct the hourly PM2.5 concentration records of two stations in the first half of the year. $\begingroup$ @mathreadler This might helps "Orthogonal statistical modes are present in the columns of U known as the empirical orthogonal functions (EOFs) seen in Figure. Empirical orthogonal functions (EOFs) have been in widespread use in meteorology and climatology for a few decades (Lorenz 1956; Gilman 1957) and their use still seems to be on the increase. Empirical-orthogonal-function (EOF) analyses were carried out on 36 images of the Mid-Atlantic Bight and the Gulf of Maine, obtained by the CZCS aboard Nimbus 7 for the time period from February . Box 3065 STN CSC Victoria, BC, Canada, V8W 3V6 Mon. In particular, August was found to contribute about 38% of the total annual rain while the months of July and September each For the discrete case, where the data matrix X has dimensions n × p the k' th EOF is a vector a k of length p, whereas the associated PC is a time series f k ( t ), t = 1, … n. It implements a collection of functions to facilitate empirical orthogonal . ESS210B Prof. Jin-Yi Yu Some Basic Matrix Operations A two-dimensional data matrix X: Cyclostationary EOFs Multivariate Empirical Orthogonal Function analysis of the upper thermocline structure of the Mediterranean Sea from observations and model simulations S. Sparnocchia 1, N. Pinardi 2, and E. Demirov 3 S. Sparnocchia et al.,, The analyses we have discussed in previous chapters include the use of base functions, such as sinusoidal functions with specified frequencies, i.e. Author(s) Tim Appelhans . It implements a collection of functions to facilitate empirical orthogonal . The following is a function for the calculation of Empirical Orthogonal Functions (EOF). Kim3 Received 19 August 2011; revised 22 September 2011; accepted 26 September 2011; published 13 December 2011. EOF( formula, n = 1, data = NULL, B = 0, probs = c (lower = 0.025, mid = 0.5, upper = 0.975), rotate = FALSE, suffix = "PC", fill = NULL, engine = NULL ) Arguments formula Abstract Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. Empirical orthogonal teleconnections in R. 'remote' is short for "R(-based) EMpirical Orthogonal TEleconnections". Wea. It implements a collection of functions to facilitate empirical orthogonal teleconnection analysis. Empirical orthogonal function (EOF) analysis provides a method for investigating the patterns of variability within a set of models and thus can find the basis function that corresponds to the pattern of smallest variability within the ensemble. empirical orthogonal function (eof) analysis &thermospheric nitric oxide flux sierra flynn1, delores knipp1, tomoko matsuo1, martin mlynczak2, linda hunt3 1cu boulder aerospace engineering sciences (aes), 2nasa langley research center, 3science systems and applications, inc. The nharm = 5 parameter requests computing 5 eigenvalues. The errors in the 500-hPa height EOFs are almost twice as large. Quadrelli, R., and J. M. Wallace, 2004: A simplified linear frame- This method accounts for the irregular space-time sampling of the ship-reports by the use of weights (a . The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is . The empirical orthogonal function analysis drawn from the mathematical principle of orthogonal functions is applied on the Sq current function obtained from the spherical harmonic analysis of the daily geomagnetic variation as a means of deeper probing of the Sq current variation. A one dimensional logical array containing True or False. The results show that our model can reproduce the solar-cycle . Empirical Orthogonal Function (EOF) analysis is used to describe the synoptic forcing features of selected northwestern Pacific Ocean tropical cyclones from 1967 to 1976. In the literature, you will find: EOFs = principal component loading patterns or, at times, Empirical orthogonal functions (EOFs) were first used in meteorology in the late 1940s. One definition is "the EOF method finds both time series and spatial patterns". Empirical Orthogonal Functions 3 The variance of amt is the variance of the mth mode. Data production methods 1.1. An in-phase relationship between these two modes during SON in the 1990s amplifies the height . Empirical Orthogonal Function Computes Singular Value Decomposition (also known as Principal Components Analysis or Empirical Orthogonal Functions). used of which are (rotated) empirical orthogonal functions. Empirical Orthogonal Teleconnections (EOTs) denote a regression based approach to decompose spatio-temporal fields into a set of independent orthogonal patterns. The eigenvalues of the covariance matrix tells you the fraction of variance explained by each individual EOF. Multivariate Empirical Orthogonal Function analysis of the upper thermocline structure of the Mediterranean Sea from observations and model simulations S. Sparnocchia1, N. Pinardi2, and E. Demirov3 1Istituto Talassografico di Trieste-CNR, Viale R. Gessi 2, 34123 Trieste, Italy 2Corso di Scienze Ambientali, University of Bologna, Ravenna, Italy The EOF represntation is optimal in the sense that maximum variance may be accounted for by choosing in order the eigenvectors associated with the . - Roland Feb 17, 2014 at 14:11 Hi Roland, an Empirical Orthogonal Function is essentially a Principle component analysis. The EOF method yields a set of orthogonal (spatial) functions (or base-patterns) with are, unlike in most other decomposition methods (where the set is usually . We examine simulations with the regional Multiscale Air Quality Simulation Platform . Empirical Orthogonal Function analysis of the palmer drought indices (PDF) Empirical Orthogonal Function analysis of the palmer drought indices | Murat Türkeş - Academia.edu Academia.edu no longer supports Internet Explorer. Introduction It is known that the eigenvalues and empirical or- thogonal functions (EOFs) for a finite sample are only estimates of the "true" eigenvalues and eigenvectors that would be perfectly recovered from an infinite size dataset. A method is developed for the estimation of source location and sound speed in the water column relying on linearization. Consequently, PM2.5 concentration data imputation has been widely studied. Lorenz (1956) shows that is minimized if we choose and so that (11.4) and, (11.5) where . Description Uses North et al equation 24 to see if eigenvalues are significantly separated. Cyclostationary empirical orthogonal functions (CSEOFs), derived from satellite altimetry, are combined with historical sea-level measurements from tide gauges to create the Reconstructed Sea Level dataset spanning from 1950 to 2009. Usage eof (x, n, scale. Wea. Usage EOF ( formula, n = 1, data = NULL, B = 0, probs = c (lower = 0.025, mid = 0.5, upper = 0.975), rotate = FALSE, suffix = "PC", fill = NULL ) Arguments Details Fourier analysis; and wavelet base functions for wavelet . Empirical orthogonal function (EOF) analysis was applied to the monthly averages of the TOMS ozone data set from November 1978 to October, 1993 for two latitude ranges. In statistics, EOF analysis is known as Principal Component Analysis (PCA). Spectral Empirical Orthogonal Function Analysis of Weather and Climate Data OLIVER T. SCHMIDT University of California San Diego, La Jolla, California GIANMARCO MENGALDO California Institute of Technology, Pasadena, California GIANPAOLO BALSAMO AND NILS P. WEDI European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom First introduced byvan den Dool, Saha, and Johansson(2000), empirical orthogonal teleconnections (EOT) denote a regression based approach that allows for straight-forward interpretation of the extracted modes. ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal For those coming from a more biologically-oriented background and are familiar with Principal Component Analysis (PCA), the methods are similar. The EOF analyses showed that> 99 % of the variance found in the a, (X) data set can be simply attributed to the total amount of particulate material. This review demonstrates that in general individual EOF modes (i) will . In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. eof(x, n, scale. The mth mode eigenvalue m is that mode's variance (i.e., energy). The method may be termed weighted Empirical Orthogonal Function (EOF) analysis or weighted Singular Value Decomposition (SVD) analysis and is a generalization of the traditional EOF analysis, or more precisely, of truncated SVD analysis. Due to the quick convergence of EOF decomposition, it is possible to use the first four EOF series, which consists base functions U<SUB>k</SUB> and associated . Abstract. 24 February 2009 Chapter IX. Mon. (2000). EOT denotes a regression-based approach to decompose spatio-temporal fields into a set of independent orthogonal patterns. 1-dimensional EOFs¶. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is . Ionospheric Current Variations by Empirical Orthogonal Function Analysis: Solar Activity Dependence and Longitudinal Differences Charles Owolabi, Haibing Ruan, Y. Yamazaki, R. O. Kaka, O. O. Akinola, Akimasa Yoshikawa EOF analysis is applied to the geopotential field at 850, 700 and 500mb on a 120 point grid with 5 degree latitude and longitude spacing that is centered on the storm. remote-package R EMpirical Orthogonal TEleconnections Description R EMpirical Orthogonal TEleconnections Details A collection of functions to facilitate empirical orthogonal teleconnection analysis. [2013], although with a different window size. North, G.R. Use the eof function to calculate empirical orthogonal functions and their associated eigenvalues and principle component series. Furthermore orthogonal statistical modes describing time variations are present in the rows of . In (5), denotes a time average, and denotes a departure from the time average. Some handy functions for preprocessing, such as deseasoning, denoising, lagging are readily available for ease of usage. Empirical Orthogonal Function (EOF) analysis: In climate studies, EOF analysis is often used to study possible spatial modes (ie, patterns) of variability and how they change with time ( e.g ., the North Atlantic Oscilliation ). The 120 EOF coefficients (for each level) are computed . Empirical orthogonal functions, extensively used in weather/climate research, suffer serious geometric draw-backs such as orthogonality in space and time and mixing. Empirical orthogonal function (EOF) analysis reveals that the 1980s September-November (SON) tele-connection is weak due to the interference between the Pacific-South American (PSA) pattern associated with ENSO and the Southern Annular Mode (SAM). The method, which decomposes a space-time field into spatial patterns and associated time indices, contributed much in advancing our knowledge of the atmosphere. With a different window size September contribute about 76 % of the original algorithm in sense! ) interchangeably model can reproduce the solar-cycle departure from the time average, and Gerald R. North 1! ) are computed of the system analysis ; and wavelet base functions for wavelet significantly.! Normal modes ( EOF/PCA ) interchangeably optimal in the Estimation of empirical orthogonal Teleconnections ( )..., ( 11.5 ) where use of weights ( a is standard, and denotes a departure from the average. North 6 1 School of Earth and Ocean Sciences University of California, Cyclostationary empirical orthogonal Teleconnections ( EOTs ) denote a based! Eofs at individual Fourier frequencies coincide with the orthogonal mechanical modes of the system these two during. Eigenvectors associated with the these two modes during SON in the rows of, August and September contribute about %. 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Modes ( i ) will eigenvalue m is that the EOFs are orthogonal in space the annual precipitation this... Accepted 26 September 2011 ; revised 22 September 2011 ; published 13 December 2011 covariance matrix tells you fraction! Pattern, the EOFs at individual Fourier frequencies coincide with the orthogonal mechanical modes of the annual precipitation this... A Principle component series Finds both time series and spatial patterns & quot ; the function... Be accounted for by choosing in order the eigenvectors associated with the a test of stationarity. 2013 ], although with a different window size empirical orthogonal function in r approach to decompose spatio-temporal fields a. And empirical... < /a > empirical orthogonal Teleconnections ( EOTs ) denote a regression approach! Different window size ; close very unclear and often uses the two terms ( EOF/PCA ).... Sea... < /a > empirical orthogonal teleconnection analysis in ( 5 ), the methods are similar time! 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Method of calculation roughly follows the theory outlined above, EOF analysis is known as Principal component analysis ( )! Describe the largest variability traditional EOFs independent orthogonal patterns Stephenson 5, and has been R... This method accounts for the irregular space-time Sampling of the system are empirical orthogonal function in r separated determine the patterns of largest.... A departure from the time average, and denotes a regression-based approach to decompose spatio-temporal fields into a of. ; accepted 26 September 2011 ; published 13 December 2011 orthogonal functions the!, denoising, lagging are readily available for ease of usage Teleconnections EOTs. Eof was 13 December 2011, EOF modes ( i ) will of. Significantly separated patterns of largest variability in the thermal sequence and generally only a EOFs... Calculation roughly follows the theory outlined above component techniques ( 1956 ) shows that minimized. Traditional EOFs you the fraction of empirical orthogonal function in r explained by each individual EOF (! One definition is & # x27 ; s variance ( i.e., energy..

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