scholarly journals TIEOF: Algorithm for Recovery of Missing Multidimensional Satellite Data on Water Bodies Based on Higher-Order Tensor Decompositions

Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2578
Author(s):  
Leonid Kulikov ◽  
Natalia Inkova ◽  
Daria Cherniuk ◽  
Anton Teslyuk ◽  
Zorigto Namsaraev
Keyword(s):  
Missing Data ◽  
Lake Baikal ◽  
Satellite Data ◽  
Three Dimensional ◽  
Tensor Decomposition ◽  
Empirical Orthogonal Functions ◽  
Water Bodies ◽  
Atmospheric Conditions ◽  
Order Tensor ◽  
Orthogonal Functions

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.

Filling in missing sea-surface temperature satellite data over the Eastern Mediterranean Sea using the DINEOF algorithm

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Andreas Nikolaidis ◽  
Georgios Georgiou ◽  
Diofantos Hadjimitsis ◽  
Evangelos Akylas
Keyword(s):  
Missing Data ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Eastern Mediterranean ◽  
Western Mediterranean ◽  
Empirical Orthogonal Functions ◽  
Sea Surface ◽  
Temperature Fields ◽  
Special Technique ◽  
Orthogonal Functions

AbstractThe Data Interpolating Empirical Orthogonal Functions method is a special technique based on Empirical Orthogonal Functions and developed to reconstruct missing data from satellite images, which is especially useful for filling in missing data from geophysical fields. Successful experiments in the Western Mediterranean encouraged extension of the application eastwards using a similar experimental implementation. The present study summarizes the experimental work done, the implementation of the method and its ability to reconstruct the sea-surface temperature fields over the Eastern Mediterranean basin, and specifically in the Levantine Sea. L3 type Satellite Sea-surface Temperature data has been used and reprocessed in order to recover missing information from cloudy images. Data reconstruction with this method proved to be extremely effective, even when using a relatively small number of time steps, and markedly accelerated the procedure. A detailed comparison with the two oceanographic models proves the accuracy of the method and the validity of the reconstructed fields.

scholarly journals Transient teleconnection event at the onset of a planet-encircling dust storm on Mars

2009 ◽  
Vol 27 (9) ◽  
pp. 3663-3676 ◽  
Author(s):  
O. Martínez-Alvarado ◽  
L. Montabone ◽  
S. R. Lewis ◽  
I. M. Moroz ◽  
P. L. Read
Keyword(s):  
Dust Storm ◽  
General Circulation ◽  
Thermal Emission ◽  
Three Dimensional ◽  
Circulation Model ◽  
Empirical Orthogonal Functions ◽  
State Variables ◽  
Orthogonal Functions ◽  
Teleconnection Patterns ◽  
Pressure Surface

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.

scholarly journals Enhancing temporal correlations in EOF expansions for the reconstruction of missing data using DINEOF

2009 ◽  
Vol 6 (2) ◽  
pp. 1547-1568 ◽  
Author(s):  
A. Alvera-Azcárate ◽  
A. Barth ◽  
D. Sirjacobs ◽  
J.-M. Beckers
Keyword(s):  
Missing Data ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Empirical Orthogonal Functions ◽  
Sea Surface ◽  
The Black Sea ◽  
Time Variability ◽  
Orthogonal Functions ◽  
Data Set ◽  
Temporal Correlations

Abstract. DINEOF (Data Interpolating Empirical Orthogonal Functions) is an EOF-based technique for the reconstruction of missing data in geophysical fields, such as those produced by clouds in sea surface temperature satellite images. A technique to reduce spurious time variability in DINEOF reconstructions is presented. The reconstruction of these images within a long time series using DINEOF can lead to large discontinuities in the reconstruction. Filtering the temporal covariance matrix allows to reduce this spurious variability and therefore more realistic reconstructions are obtained. The approach is tested in a three years sea surface temperature data set over the Black Sea. The effect of the filter in the temporal EOFs is presented, as well as some examples of the improvement achieved with the filtering in the SST reconstruction, both compared to the DINEOF approach without filtering.

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 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
Keyword(s):  
Spatial Patterns ◽  
Signal To Noise Ratio ◽  
Three Dimensional ◽  
Projection Methods ◽  
Large Datasets ◽  
Empirical Orthogonal Functions ◽  
Climate Data ◽  
Orthogonal Functions ◽  
Weighting Matrix ◽  
Maximum Covariance Analysis

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.

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