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empirical orthogonal functions and related techniques in atmospheric science: A review

INTERNATIONAL JOURNAL OF CLIMATOLOGY 2007年第9期27卷 1119-1152页

作者： Hannachi, A. Jolliffe, I. T. Stephenson, D. B. Univ Reading Dept Meteorol Reading RG6 6BB Berks England

Climate and weather constitute a typical example where high dimensional and complex phenomena meet. The atmospheric system is the result of highly complex interactions between many degrees of freedom or modes. In order to gain insight in understanding the dynamical/physical behaviour involved it is useful to attempt to understand their interactions in terms of a much smaller number of prominent modes of variability. This has led to the development by atmospheric researchers of methods that give a space display and a time display of large space-time atmospheric data. empirical orthogonal functions (EOFs) were first used in meteorology in the late 1940s. The method, which decomposes a space-time field into spatial patterns and associated time indices, contributed much in advancing our knowledge of the atmosphere. However, since the atmosphere contains all sorts of features, e.g. stationary and propagating, EOFs are unable to provide a full picture. For example, EOFs tend, in general, to be difficult to interpret because of their geometric properties, such as their global feature, and their orthogonality in space and time. To obtain more localised features, modifications, e.g. rotated EOFs (REOFs), have been introduced. At the same time, because these methods cannot deal with propagating features, since they only use spatial correlation of the field, it was necessary to use both spatial and time information in order to identify such features. Extended and complex EOFs were introduced to serve that purpose. Because of the importance of EOFs and closely related methods in atmospheric science, and because the existing reviews of the subject are slightly out of date, there seems to be a need to update our knowledge by including new developments that could not be presented in previous reviews. This review proposes to achieve precisely this goal. The basic theory of the main types of EOFs is reviewed, and a wide range of applications using various data sets are also provided

关键词： empirical orthogonal functions simplified EOFs extended EOFs complex EOFs North Atlantic Oscillation Madden Julian oscillation quasi-biennial oscillation

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empirical orthogonal functions AND ITS MODIFICATION IN THE TASK OF RETRIEVING OF THE TOTAL AMOUNT CO2 AND CH4 WITH HELP OF SATELLITE FOURIER TRANSFORM SPECTROMETER GOSAT (TANSO-FTS) 22

EMPIRICAL ORTHOGONAL FUNCTIONS AND ITS MODIFICATION IN THE T...

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22nd International Symposium on Atmospheric and Ocean Optics - Atmospheric Physics

作者： Kataev, Mikhail Yu. Lukyanov, Andrey K. Tomsk State Univ Control Syst & Radioelect Av Lenin 40 Tomsk 634050 Russia

ISBN: (数字)9781510605121

ISBN: (纸本)9781510605121

The article describes the modification of the empirical orthogonal functions method for solving of the inverse task (retrieving of the total amount CO2) of the real data processing of the satellite instrument (Fourier transform spectrometer medium resolution) GOSAT. Presents the results of the processing of the GOSAT data for the USA territory monitoring stations Lamont and Park Falls (TCCON network).

关键词： satellite data empirical orthogonal functions inverse task

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Partitioned modal extraction applied to power system wide-area measurements using empirical orthogonal functions

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ELECTRIC POWER SYSTEMS RESEARCH 2015年 123卷 185-191页

作者： Esquivel Prado, P. Castaneda, Carlos E. Jurado, Francisco Technol Inst La Laguna Torreon Mexico Univ Guadalajara Univ Ctr Los Lagos Guadalajara Jalisco Mexico

This paper presents a numerical algorithm in order to identify and extract the inter-area modal inestability presented in large interconnected power systems, which significantly decreases the computational burden and gives a distributed application in the analysis of collected data from wide-area measurement systems (WAMS) using the empirical orthogonal functions. The proposed algorithm is based on a spatio-temporal statistical identification method using both empirical orthogonal functions (EOF) analysis and partitioned network data approximation. Firstly, identification process is carried out separating the power system network into a number of subnetworks either geographically distributed or by containing the same load types. Then, EOF analysis is applied to the local data array which contains the space-time response for each subnetwork where modal extraction is determined. Afterward, the derived modal approximation sets are used to compute global predominant modes by correlation of its temporal coefficients, which yields to a refined global approximation of local and inter-area oscillations, and a model-order reduction removing spurious modes. An illustrative example involving a transmission system is presented in order to validate the proposed methodology. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Computational burden empirical orthogonal functions Inter-area oscillations Interconnected power systems Model-order reduction Statistical identification

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Estimating temperature and salinity profiles using empirical orthogonal functions and clustering on historical measurements

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OCEAN DYNAMICS 2013年第7期63卷 809-821页

作者： Hjelmervik, Karl Thomas Hjelmervik, Karina Norwegian Def Res Estab FFI N-2027 Kjeller Norway Vestfold Univ Coll Fac Technol & Maritime Sci N-3103 Tonsberg Norway

Oceanographic climatology is normally estimated by dividing the world's oceans into geographical boxes of fixed shape and size, where each box is represented by a climatological salinity and temperature profile. The climatological profile is typically an average of historical measurements from that region. Since an arbitrarily chosen box may contain different types of water masses both in space and time, an averaged profile may be a statistically improbable or even non-physical representation. This paper proposes a new approach that employs empirical orthogonal functions in combination with a clustering technique to divide the world's oceans into climatological regions. Each region is represented by a cluster that is determined by minimising the variance of the state variables within each cluster. All profiles contained in a cluster are statistically similar to each other and statistically different from profiles in other clusters. Each cluster is then represented by mean temperature and salinity profiles and a mean position. Methods for estimating climatological profiles from the cluster information are examined, and their performances are compared to a conventional method of estimating climatology. The comparisons show that the new methods outperform conventional methods and are particularly effective in areas where oceanographic fronts are present.

关键词： Oceanography Climatology empirical orthogonal functions Clustering

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Reduced models for linear groundwater flow models using empirical orthogonal functions

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ADVANCES IN WATER RESOURCES 2004年第1期27卷 57-69页

作者： Vermeulen, PTM Heemink, AW Stroet, CBMT Delft Univ Technol Fac Informat Technol & Syst NL-2600 GA Delft Netherlands TNO Natl Geol Survey Netherlands Inst Appl Geosci NL-2600 JA Delft Netherlands

In this paper we describe two reduced models that describe the hydraulic head h within three-dimensional groundwater flow models. We defined a reduced model structure as a linear combination of a set of spatial patterns P with time-varying coefficients r. The patterns were obtained by a data-driven indentification technique (empirical orthogonal functions, EOFs), and they span a subspace of model results that captures most of the relevant information of the original model. Due to those patterns, we constructed two different formulations for dr/dt, by applying different projections: (1) a State-Space Projection (SSP) that projects a state-space formulation for groundwater flow;and (2) a Galerkin Projection (GP) that substitutes h within the PDE for groundwater flow by the reduced model structure P-T r, and projects the outcome onto the patterns. The SSP and GP have been both applied to a realistic case study with a negligible loss of model accuracy (Relative Mean Absolute Error< 0.5%). The dimension of r (16) was significantly reduced compared to the dimension of h (32,949) and hence we achieved a maximal reduction in computational time for the SSP approximate to 1/625 and for the GP approximate to 1/70 of the original time. Both reduced models have a promising prospect as their time reduction increases whenever the number of grid cells increases and the parameterization of the original model grows in complexity. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： groundwater MODFLOW empirical orthogonal functions reduced model galerkin projection state-space projection

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Global retrieval of phytoplankton functional types based on empirical orthogonal functions using CMEMS GlobColour merged products and further extension to OLCI data

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REMOTE SENSING OF ENVIRONMENT 2020年第0期240卷 111704-000页

作者： Xi, Hongyan Losa, Svetlana N. Mangin, Antoine Soppa, Mariana A. Garnesson, Philippe Demaria, Julien Liu, Yangyang D'Andon, Odile Hembise Fanton Bracher, Astrid Helmholtz Ctr Polar & Marine Res Alfred Wegener Inst Bremerhaven Germany Russian Acad Sci Shirshov Inst Oceanol Moscow Russia ACRI ST F-06904 Sophia Antipolis France Univ Bremen Fac Biol & Chem Bremen Germany Univ Bremen Inst Environm Phys Bremen Germany

This study presents an algorithm for globally retrieving chlorophyll a (Chl-a) concentrations of phytoplankton functional types (PFTs) from multi-sensor merged ocean color (OC) products or Sentinel-3A (S3) Ocean and Land Color Instrument (OLCI) data from the GlobColour archive in the frame of the Copernicus Marine Environmental Monitoring Service (CMEMS). The retrieved PFTs include diatoms, haptophytes, dinoflagellates, green algae and prokaryotic phytoplankton. A previously proposed method to retrieve various phytoplankton pigments, based on empirical orthogonal functions (EOF), is investigated and adapted to retrieve Chl-a concentrations of multiple PFTs using extensive global data sets of in situ pigment measurements and matchups with satellite OC products. The performance of the EOF-based approach is assessed and cross-validated statistically. The retrieved PFTs are compared with those derived from diagnostic pigment analysis (DPA) based on in situ pigment measurements. Results show that the approach predicts well Chl-a concentrations of most of the mentioned PFTs. The performance of the approach is, however, less accurate for prokaryotes, possibly due to their general low variability and small concentration range resulting in a weak signal which is extracted from the reflectance data and corresponding EOF modes. As a demonstration of the approach utilization, the EOF-based fitted models based on satellite reflectance products at nine bands are applied to the monthly GlobColour merged products. Climatological characteristics of the PFTs are also evaluated based on ten years of merged products (2002-2012) through inter-comparisons with other existing satellite derived products on phytoplankton composition including phytoplankton size class (PSC), SynSenPFT, OC-PFT and PHYSAT. Inter-comparisons indicate that most PFTs retrieved by our study agree well with previous corresponding PFT/PSC products, except that prokaryotes show higher Chl-a concentration in low latit

关键词： Retrieval algorithm Chlorophyll a Phytoplankton functional types empirical orthogonal functions Remote sensing reflectance HPLC pigments CMEMS GlobColour OLCI

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Interpolation of monthly runoff along rivers applying empirical orthogonal functions: Application to the Upper Magdalena River, Colombia

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JOURNAL OF HYDROLOGY 2015年 528卷 177-191页

作者： Gottschalk, Lars Krasovskaia, Irina Dominguez, Efrain Caicedo, Fabian Velasco, Andres Univ Oslo Inst Geosci N-0315 Oslo Norway IGC SE-26352 Lerberget Sweden Pontificia Univ Javeriana Dept Ecol & Terr Bogota Colombia

An approach for interpolation of discharge along rivers is presented applying empirical orthogonal functions. From a theoretical point of view this approach for hydrological applications should be looked upon as a generalisation of a Karhunen-Loeve expansion. The eigenvalue problem is then represented by a Fredholm integral equation of the second kind over the spatial domain, which in a hydrological application is defined by the principal drainage area. Most methods for numerical solution of this equation entail reduction to an approximately equivalent algebraic problem. The problem is to correctly account for drainage areas and drainage patterns, as the irregularity in sizes of drainage areas might violate the orthogonality if not accounted for correctly. A basic solution to the problem is developed and demonstrated on discharge observations from the Upper Magdalena drainage basin, Colombia. Seven discharge time series are used to determine the empirical orthogonal functions and principal components and four series are used for validation of the application for gap filling and estimation at ungauged sites. The results show a high accuracy for larger basins while those for mountain headwater stations are moderately good. For these latter stations the gain of a short period of observations compared to no observations at all is 5% increase in the coefficient of determination. The results confirm the plausibility of the theoretical approach. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Interpolation of discharge Karhunen-Loeve expansion empirical orthogonal functions Spatial variance-covariance

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Geoacoustic profile estimation using empirical orthogonal functions for propagation applications

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IEEE JOURNAL OF OCEANIC ENGINEERING 2001年第4期26卷 795-808页

作者： Jaye, M Badiey, M Siegmann, WL Rensselaer Polytech Inst Dept Math Sci Troy NY 12180 USA Univ Delaware Grad Coll Marine Studies Newark DE 19716 USA

The use of empirical orthogonal functions (EOFs) for the direct estimation of sediment sound speed, density and attenuation profiles is described, when extensive data sets such as those from the Atlantic Generating Station (AGS) site are available. Interpolations are generated based on minimizing mean square errors and their construction is modified here to incorporate lateral terrain orientations as occur at the AGS site. Uncertainties in the geoacoustic fields can then be modeled by stochastic variations of the EOF coefficients. The field representations are used to produce gcoacoustic input for propagation calculations for fluid or elastic sediment models in the AGS region. Statistics of transmission loss (TL) variations are discussed in terms of geoacoustic variability, source frequency and resolution provided by the number of interpolating EOFs. Preliminary results show that sediment sound speed uncertainties can produce a significant uncertainty envelope for TL predictions in the AGS area.

关键词： broadband empirical orthogonal functions geoacoustic interpolation shallow water stochastic propagation transmission loss statistics

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Modelling ionospheric vertical drifts over Africa low latitudes using empirical orthogonal functions and comparison with climatological model

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ADVANCES IN SPACE RESEARCH 2018年第1期61卷 326-336页

作者： Dubazane, Makhosonke Berthwell Habarulema, John Bosco Uwamahoro, Jean Claude South African Space Agcy SANSA Space Sci ZA-7200 Hermanus South Africa Rhodes Univ Dept Phys & Elect Grahamstown South Africa

For the first time, empirical model of daytime vertical E x B drift based on empirical orthogonal functions (EOF) decomposition technique is presented. Day-to-day variability of E x B drift inferred from horizontal (H) geomagnetic field data around dip latitude for the period of 2008-2013 is used to both develop and validate the model. Results show that the EOF technique is promising with modelled values and data giving correlation coefficient values of at least 0.90 for geomagnetic conditions of both K-p <= 3 and K-p > 3 within 2008-2013. Independent model validation shows that in situ E x B values from ion velocity meter (IVM) instrument on-board C/NOFS satellite are closer to model E x B estimates than the climatological Scherliess-Fejer (SF) model incorporated within the International Reference Ionosphere (IRI). (C) 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.

关键词： Vertical E x B drift Low latitude ionosphere empirical orthogonal functions

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On the Sensitivity of Field Reconstruction and Prediction Using empirical orthogonal functions Derived from Gappy Data

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JOURNAL OF CLIMATE 2013年第22期26卷 9194-9205页

作者： Taylor, Marc H. Losch, Martin Wenzel, Manfred Schroeter, Jens Alfred Wegener Inst Polar & Marine Res Bremerhaven Germany

empirical orthogonal function (EOF) analysis is commonly used in the climate sciences and elsewhere to describe, reconstruct, and predict highly dimensional data fields. When data contain a high percentage of missing values (i.e., gappy), alternate approaches must be used in order to correctly derive EOFs. The aims of this paper are to assess the accuracy of several EOF approaches in the reconstruction and prediction of gappy data fields, using the Galapagos Archipelago as a case study example. EOF approaches included least squares estimation via a covariance matrix decomposition [least squares EOF (LSEOF)], data interpolating empirical orthogonal functions (DINEOF), and a novel approach called recursively subtracted empirical orthogonal functions (RSEOF). Model-derived data of historical surface chlorophyll-a concentrations and sea surface temperature, combined with a mask of gaps from historical remote sensing estimates, allowed for the creation of true and observed fields by which to gauge the performance of EOF approaches. Only DINEOF and RSEOF were found to be appropriate for gappy data reconstruction and prediction. DINEOF proved to be the superior approach in terms of accuracy, especially for noisy data with a high estimation error, although RSEOF may be preferred for larger data fields because of its relatively faster computation time.

关键词： empirical orthogonal functions Interpolation schemes Principal components analysis Singular vectors Statistical techniques

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