scholarly journals Spatial Weighting and Iterative Projection Methods for EOFs

2009 ◽  
Vol 22 (2) ◽  
pp. 234-243 ◽  
Author(s):  
Mark P. Baldwin ◽  
David B. Stephenson ◽  
Ian T. Jolliffe

Abstract Often there is a need to consider spatial weighting in methods for finding spatial patterns in climate data. The focus of this paper is on techniques that maximize variance, such as empirical orthogonal functions (EOFs). A weighting matrix is introduced into a generalized framework for dealing with spatial weighting. One basic principal in the design of the weighting matrix is that the resulting spatial patterns are independent of the grid used to represent the data. A weighting matrix can also be used for other purposes, such as to compensate for the neglect of unrepresented subgrid-scale variance or, in the form of a prewhitening filter, to maximize the signal-to-noise ratio of EOFs. The new methodology is applicable to other types of climate pattern analysis, such as extended EOF analysis and maximum covariance analysis. The increasing availability of large datasets of three-dimensional gridded variables (e.g., reanalysis products and model output) raises special issues for data-reduction methods such as EOFs. Fast, memory-efficient methods are required in order to extract leading EOFs from such large datasets. This study proposes one such approach based on a simple iteration of successive projections of the data onto time series and spatial maps. It is also demonstrated that spatial weighting can be combined with the iterative methods. Throughout the paper, multivariate statistics notation is used, simplifying implementation as matrix commands in high-level computing languages.

Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2578
Author(s):  
Leonid Kulikov ◽  
Natalia Inkova ◽  
Daria Cherniuk ◽  
Anton Teslyuk ◽  
Zorigto Namsaraev

Satellite research methods are [DCh]actively involvedfrequently used in observations of water bodies. One of the most important problems in satellite observations is the presence of missing data due to internal malfunction of satellite sensors and poor atmospheric conditions. We proceeded on the assumption that the use of data recovery methods based on spatial relationships in data can increase the recovery accuracy. In this paper, we present a method for missing data reconstruction from remote sensors. We refer our method to as Tensor Interpolating Empirical Orthogonal Functions (TIEOF). The method relies on the two-dimensional nature of sensor images and organizes the data into three-dimensional tensors. We use high-order tensor decomposition to interpolate missing data [ZN] on chlorophyll a concentration in lake Baikal (Russia, Siberia). Using MODIS and SeaWiFS satellite data of lake Baikal we show that the observed improvement of TIEOF was 69% on average compared to the current state-of-the-art DINEOF algorithm measured in various preprocessing data scenarios including thresholding and different interpolating schemes.


2011 ◽  
Vol 24 (5) ◽  
pp. 1396-1408 ◽  
Author(s):  
B. D. Hamlington ◽  
R. R. Leben ◽  
R. S. Nerem ◽  
K.-Y. Kim

Abstract Extracting secular sea level trends from the background ocean variability is limited by how well one can correct for the time-varying and oscillating signals in the record. Many geophysical processes contribute time-dependent signals to the data, making the sea level trend difficult to detect. In this paper, cyclostationary empirical orthogonal functions (CSEOFs) are used to quantify and improve the signal-to-noise ratio (SNR) between the secular trend and the background variability, obscuring this trend in the altimetric sea level record by identifying and removing signals that are physically interpretable. Over the 16-yr altimetric record the SNR arising from the traditional least squares method for estimating trends can be improved from 4.0% of the ocean having an SNR greater than one to 9.9% when using a more sophisticated statistical method based on CSEOFs. From a standpoint of signal detection, this implies that the secular trend in a greater portion of the ocean can be estimated with a higher degree of confidence. Furthermore, the CSEOF method improves the standard error on the least squares estimates of the secular trend in 97% of the ocean. The convergence of the SNR as the record length is increased is used to estimate the SNR of sea level trends in the near future as more measurements become available from near-global altimetric sampling.


2009 ◽  
Vol 27 (9) ◽  
pp. 3663-3676 ◽  
Author(s):  
O. Martínez-Alvarado ◽  
L. Montabone ◽  
S. R. Lewis ◽  
I. M. Moroz ◽  
P. L. Read

Abstract. We use proper orthogonal decomposition (POD) to study a transient teleconnection event at the onset of the 2001 planet-encircling dust storm on Mars, in terms of empirical orthogonal functions (EOFs). There are several differences between this and previous studies of atmospheric events using EOFs. First, instead of using a single variable such as surface pressure or geopotential height on a given pressure surface, we use a dataset describing the evolution in time of global and fully three-dimensional atmospheric fields such as horizontal velocity and temperature. These fields are produced by assimilating Thermal Emission Spectrometer observations from NASA's Mars Global Surveyor spacecraft into a Mars general circulation model. We use total atmospheric energy (TE) as a physically meaningful quantity which weights the state variables. Second, instead of adopting the EOFs to define teleconnection patterns as planetary-scale correlations that explain a large portion of long time-scale variability, we use EOFs to understand transient processes due to localised heating perturbations that have implications for the atmospheric circulation over distant regions. The localised perturbation is given by anomalous heating due to the enhanced presence of dust around the northern edge of the Hellas Planitia basin on Mars. We show that the localised disturbance is seemingly restricted to a small number (a few tens) of EOFs. These can be classified as low-order, transitional, or high-order EOFs according to the TE amount they explain throughout the event. Despite the global character of the EOFs, they show the capability of accounting for the localised effects of the perturbation via the presence of specific centres of action. We finally discuss possible applications for the study of terrestrial phenomena with similar characteristics.


2021 ◽  
Vol 28 (3) ◽  
pp. 347-370
Author(s):  
Camille Besombes ◽  
Olivier Pannekoucke ◽  
Corentin Lapeyre ◽  
Benjamin Sanderson ◽  
Olivier Thual

Abstract. This paper investigates the potential of a Wasserstein generative adversarial network to produce realistic weather situations when trained from the climate of a general circulation model (GCM). To do so, a convolutional neural network architecture is proposed for the generator and trained on a synthetic climate database, computed using a simple three dimensional climate model: PLASIM. The generator transforms a “latent space”, defined by a 64-dimensional Gaussian distribution, into spatially defined anomalies on the same output grid as PLASIM. The analysis of the statistics in the leading empirical orthogonal functions shows that the generator is able to reproduce many aspects of the multivariate distribution of the synthetic climate. Moreover, generated states reproduce the leading geostrophic balance present in the atmosphere. The ability to represent the climate state in a compact, dense and potentially nonlinear latent space opens new perspectives in the analysis and handling of the climate. This contribution discusses the exploration of the extremes close to a given state and how to connect two realistic weather situations with this approach.


2008 ◽  
Vol 15 (1) ◽  
pp. 159-167 ◽  
Author(s):  
A. Bernacchia ◽  
P. Naveau

Abstract. In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF) decomposition, is often applied for this purpose, it provides meaningful results only if the underlying multivariate distribution is Gaussian. Indeed, PCA is based on optimizing second order moments, and the covariance matrix captures the full dependence structure of multivariate Gaussian vectors. Whenever the application at hand can not satisfy this normality hypothesis (e.g. precipitation data), alternatives and/or improvements to PCA have to be developed and studied. To go beyond this second order statistics constraint, that limits the applicability of the PCA, we take advantage of the cumulant function that can produce higher order moments information. The cumulant function, well-known in the statistical literature, allows us to propose a new, simple and fast procedure to identify spatial patterns for non-Gaussian data. Our algorithm consists in maximizing the cumulant function. Three families of multivariate random vectors, for which explicit computations are obtained, are implemented to illustrate our approach. In addition, we show that our algorithm corresponds to selecting the directions along which projected data display the largest spread over the marginal probability density tails.


2015 ◽  
Vol 28 (19) ◽  
pp. 7857-7872 ◽  
Author(s):  
Baird Langenbrunner ◽  
J. David Neelin ◽  
Benjamin R. Lintner ◽  
Bruce T. Anderson

Abstract Projections of modeled precipitation (P) change in global warming scenarios demonstrate marked intermodel disagreement at regional scales. Empirical orthogonal functions (EOFs) and maximum covariance analysis (MCA) are used to diagnose spatial patterns of disagreement in the simulated climatology and end-of-century P changes in phase 5 of the Coupled Model Intercomparison Project (CMIP5) archive. The term principal uncertainty pattern (PUP) is used for any robust mode calculated when applying these techniques to a multimodel ensemble. For selected domains in the tropics, leading PUPs highlight features at the margins of convection zones and in the Pacific cold tongue. The midlatitude Pacific storm track is emphasized given its relevance to wintertime P projections over western North America. The first storm-track PUP identifies a sensitive region of disagreement in P increases over the eastern midlatitude Pacific where the storm track terminates, related to uncertainty in an eastward extension of the climatological jet. The second PUP portrays uncertainty in a zonally asymmetric meridional shift of storm-track P, related to uncertainty in the extent of a poleward jet shift in the western Pacific. Both modes appear to arise primarily from intermodel differences in the response to radiative forcing, distinct from sampling of internal variability. The leading storm-track PUPs for P and zonal wind change exhibit similarities to the leading uncertainty patterns for the historical climatology, indicating important and parallel sensitivities in the eastern Pacific storm-track terminus region. However, expansion coefficients for climatological uncertainties tend to be weakly correlated with those for end-of-century change.


Author(s):  
Maziar Golestani ◽  
Jacob Tornfeldt Sørensen

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.


2021 ◽  
Vol 34 (18) ◽  
pp. 7645-7660
Author(s):  
D. James Fulton ◽  
Gabriele C. Hegerl

AbstractIn this paper we develop a method to quantify the accuracy of different pattern extraction techniques for the additive space–time modes often assumed to be present in climate data. It has previously been shown that the standard technique of principal component analysis (PCA; also known as empirical orthogonal functions) may extract patterns that are not physically meaningful. Here we analyze two modern pattern extraction methods, namely dynamical mode decomposition (DMD) and slow feature analysis (SFA), in comparison with PCA. We develop a Monte Carlo method to generate synthetic additive modes that mimic the properties of climate modes described in the literature. The datasets composed of these generated modes do not satisfy the assumptions of any pattern extraction method presented. We find that both alternative methods significantly outperform PCA in extracting local and global modes in the synthetic data. These techniques had a higher mean accuracy across modes in 60 out of 60 mixed synthetic climates, with SFA slightly outperforming DMD. We show that in the majority of simple cases PCA extracts modes that are not significantly better than a random guess. Finally, when applied to real climate data these alternative techniques extract a more coherent and less noisy global warming signal, as well as an El Niño signal with a clearer spectral peak in the time series, and more a physically plausible spatial pattern.


Sign in / Sign up

Export Citation Format

Share Document