Empirical Orthogonal Functions: The Medium is the Message

2009 ◽  
Vol 22 (24) ◽  
pp. 6501-6514 ◽  
Author(s):  
Adam H. Monahan ◽  
John C. Fyfe ◽  
Maarten H. P. Ambaum ◽  
David B. Stephenson ◽  
Gerald R. North
Keyword(s):  
Dimensionality Reduction ◽  
Data Compression ◽  
Empirical Orthogonal Function ◽  
Degrees Of Freedom ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Entire Domain ◽  
Orthogonal Function

Abstract Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

scholarly journals Long range forecasting parameters vis-a-vis sub-divisional summer rainfall over India

MAUSAM ◽  
2022 ◽  
Vol 44 (2) ◽  
pp. 185-190
Author(s):  
S.S. SINGH ◽  
S.V. DATAR ◽  
H.N. SRIVASTAVA
Keyword(s):  
Interannual Variability ◽  
Long Range ◽  
Empirical Orthogonal Function ◽  
Monsoon Rainfall ◽  
Summer Rainfall ◽  
Summer Monsoon Rainfall ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Orthogonal Function ◽  
Global Parameters

Interannual variability of Empirical Orthogonal Functions (EOF) based upon regional/global parameters, associated with the summer monsoon rainfall over different meteorological sub-divisions of the country have been discussed, based upon the data during the years 1958 to 1990 enabling us to identify three broad  sub-divisions of the country.   It was interesting to note that the first empirical orthogonal function did not show significant correlation with monsoon rainfall over most SUB-DIVISIONS of the NE and SE parts of the country. However, this EOF was found to be significantly correlated with the rainfall over the remaining meteorological sub-divisions of the country.  

Empirical Orthogonal Function Analysis of 2D Current Transects in the Fehmarn Belt

2013 ◽  
Author(s):  
Maziar Golestani ◽  
Jacob Tornfeldt Sørensen
Keyword(s):  
Time Series ◽  
Degrees Of Freedom ◽  
Function Analysis ◽  
Spatial Coherence ◽  
Three Dimensional ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Orthogonal Functions ◽  
Relative Contribution ◽  
Adcp Measurements

Describing spatial coherence of hydrodynamic conditions typically includes analysis of long time series of model results and site specific bathymetric and hydrodynamic features. This complex task often involves a time-consuming qualitative analysis to identify the critical physical processes for normal and extreme conditions. A methodology for skillful reduction of the system dimensions and determination of the most important current patterns can provide a more quantitative analysis of the coherence and variability of complex spatial time series. The objective of this study is to decompose transects of velocity in the hydrodynamically complex Fehmarn Belt area into Empirical Orthogonal Functions (EOF) and determine their relative contribution to the total variance. This will help marine engineers and contractors to gain a more quantitative and accessible picture of the changes in the current transects and to obtain an overview of current shear pattern while performing complex and exquisite operations. 18 years of hindcast data from a three-dimensional flow model are used for performing the EOF analysis. After performing the EOF analysis, the most important and dominant current patterns are extracted. The analysis reveals that the first eigenmode explains about 89 % of the variance and resembles the barotrpic flow at the cross-section while other EOF modes represent various modes of the baroclinic flow. The results are compared to EOF analysis of two ADCP measurements installed on the seabed and comparisons with similar analysis of model output are performed. It is shown that the whole time series can be reconstructed with much fewer degrees of freedom and almost no data loss by using only the first five EOF modes.

scholarly journals Eddy Trains and Striations in Quasigeostrophic Simulations and the Ocean

2016 ◽  
Vol 46 (9) ◽  
pp. 2807-2825 ◽  
Author(s):  
Changheng Chen ◽  
Igor Kamenkovich ◽  
Pavel Berloff
Keyword(s):  
North Pacific ◽  
Empirical Orthogonal Functions ◽  
Eof Analysis ◽  
Sea Level Anomaly ◽  
Orthogonal Functions ◽  
The North ◽  
Temporal Averaging ◽  
Low Pass ◽  
The Relationship ◽  
The North Pacific

AbstractThis study explores the relationship between coherent eddies and zonally elongated striations. The investigation involves an analysis of two baroclinic quasigeostrophic models of a zonal and double-gyre flow and a set of altimetry sea level anomaly data in the North Pacific. Striations are defined by either spatiotemporal filtering or empirical orthogonal functions (EOFs), with both approaches leading to consistent results. Coherent eddies, identified here by the modified Okubo–Weiss parameter, tend to propagate along well-defined paths, thus forming “eddy trains” that coincide with striations. The striations and eddy trains tend to drift away from the intergyre boundary at the same speed in both the model and observations. The EOF analysis further confirms that these striations in model simulations and altimetry are not an artifact of temporal averaging of random, spatially uncorrelated vortices. This study suggests instead that eddies organize into eddy trains, which manifest themselves as striations in low-pass filtered data and EOF modes.

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.

scholarly journals Statistical characteristics of the total ion density in the topside ionosphere during the period 1996-2004 using empirical orthogonal function (EOF) analysis

2005 ◽  
Vol 23 (12) ◽  
pp. 3615-3631 ◽  
Author(s):  
B. Zhao ◽  
W. Wan ◽  
L. Liu ◽  
X. Yue ◽  
S. Venkatraman
Keyword(s):  
Empirical Orthogonal Function ◽  
Original Data ◽  
Statistical Characteristics ◽  
Topside Ionosphere ◽  
Eof Analysis ◽  
Data Set ◽  
Ion Density ◽  
Orthogonal Function ◽  
Solar Declination ◽  
Close Relationship

Abstract. We have applied the empirical orthogonal function (EOF) analysis to examine the climatology of the total ion density Ni at 840 km during the period 1996-2004, obtained from the Defense Meteorological Satellite Program (DMSP) spacecraft. The data set for each of the local time (09:30 LT and 21:30 LT) is decomposed into a time mean plus the sum of EOF bases Ei of space, multiplied by time-varying EOF coefficients Ai. Physical explanations are made on the first three EOFs, which together can capture more than 95% of the total variance of the original data set. Results show that the dominant mode that controls the Ni variability is the solar EUV flux, which is consistent with the results of Rich et al. (2003). The second EOF, associated with the solar declination, presents an annual (summer to winter) asymmetry that is caused by the transequatorial winds. The semiannual variation that appears in the third EOF for the evening sector is interpreted as both the effects of the equatorial electric fields and the wind patterns. Both the annual and semiannual variations are modulated by the solar flux, which has a close relationship with the O+ composition. The quick convergence of the EOF expansion makes it very convenient to construct an empirical model for the original data set. The modeled results show that the accuracy of the prediction depends mainly on the first principal component which has a close relationship with the solar EUV flux.

Significance test for empirical orthogonal function (EOF) analysis of meteorological and oceanic data

2000 ◽  
Vol 18 (1) ◽  
pp. 10-17 ◽  
Author(s):  
Li Xiao-feng ◽  
L. Pietrafesa ◽  
Lan Shu-fang ◽  
Xie Li-an
Keyword(s):  
Empirical Orthogonal Function ◽  
Significance Test ◽  
Eof Analysis ◽  
Orthogonal Function
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