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.

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 Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

2018 ◽  
Vol 22 (2) ◽  
pp. 1175-1192 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0) to Brown noise (β  =  2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

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 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 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.

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