Variability of the Atlantic thermohaline circulation described by three-dimensional empirical 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.

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Modes of the BiOS-driven Adriatic Sea thermohaline variability

10.21203/rs.3.rs-990898/v1 ◽

2021 ◽

Author(s):

Cléa Lumina Denamiel ◽

Iva Tojčić ◽

Petra Pranić ◽

Ivica Vilibić

Keyword(s):

Time Series ◽

Thermohaline Circulation ◽

Climate Model ◽

Adriatic Sea ◽

Decadal Variability ◽

Current Speed ◽

Empirical Orthogonal Functions ◽

Climate Simulation ◽

Orthogonal Functions ◽

The Impact

Abstract In this study the impact of the Adriatic-Ionian Bimodal Oscillating System (BiOS) on the interannual to decadal variability of the Adriatic Sea thermohaline circulation is quantified during the 1987-2017 period with the numerical results of the Adriatic Sea and Coast (AdriSC) historical kilometer-scale climate simulation. The time series associated with the first five Empirical Orthogonal Functions (EOFs) computed from the salinity, temperature and current speed monthly detrended anomalies at 1-km resolution are correlated to the BiOS signal. First, it is found that the AdriSC climate model is capable to reproduce the BiOS-driven phases derived from in-situ observations along a long-term monitoring transect in the middle Adriatic. Then, for the entire Adriatic basin, high correlations to the 2-year delayed BiOS signal are obtained for the salinity and current speed first two EOF time series at 100 m depth and the sea-bottom Finally, the physical interpretation of the EOF spatial patterns reveals that Adriatic bottom temperatures are more influenced by the dense water circulation than the BiOS. These findings confirmed and generalized the known dynamics derived previously from observations, and the AdriSC climate model can thus be used to better understand the past and future BiOS-driven physical processes in the Adriatic Sea.

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

Annales Geophysicae ◽

10.5194/angeo-27-3663-2009 ◽

2009 ◽

Vol 27 (9) ◽

pp. 3663-3676 ◽

Cited By ~ 13

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.

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

Volume 5: Ocean Engineering ◽

10.1115/omae2013-10745 ◽

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.

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Spatial Weighting and Iterative Projection Methods for EOFs

Journal of Climate ◽

10.1175/2008jcli2147.1 ◽

2009 ◽

Vol 22 (2) ◽

pp. 234-243 ◽

Cited By ~ 42

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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Reconstruction of Objects from their Projections Using Orthogonal Functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100071788 ◽

1973 ◽

Vol 31 ◽

pp. 268-269

Author(s):

Elrnar Zeitler

Keyword(s):

Unit Area ◽

Three Dimensional ◽

One Dimension ◽

Spatial Density ◽

Dimensional Representation ◽

Orthogonal Functions ◽

Object A ◽

Plane Normal ◽

Dimensional Object ◽

Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

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SPATIO-TEMPORAL VARIATIONS OF BACKWARD SCATTERING COEFFICIENT OF SEAWATER IN JAPANESE OPEN COASTAL SEA BASED ON EMPIRICAL ORTHOGONAL FUNCTIONS ANALYSIS

Journal of Japan Society of Civil Engineers Ser B2 (Coastal Engineering) ◽

10.2208/kaigan.76.2_i_1069 ◽

2020 ◽

Vol 76 (2) ◽

pp. I_1069-I_1074

Author(s):

Hiroshi YAGI ◽

Hiroshi MURAKAMI ◽

Yoshiyuki ISOZAKI

Keyword(s):

Temporal Variations ◽

Empirical Orthogonal Functions ◽

Scattering Coefficient ◽

Orthogonal Functions ◽

Coastal Sea ◽

Spatio Temporal

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Empirical Methods in Short-Term Climate Prediction

10.1093/oso/9780199202782.001.0001 ◽

2006 ◽

Author(s):

Huug van den Dool

Keyword(s):

Climate Prediction ◽

Empirical Orthogonal Functions ◽

Data Sets ◽

Seasonal Forecasts ◽

Short Term ◽

Orthogonal Functions ◽

Ocean Atmosphere Interaction ◽

Global Coverage ◽

Atmosphere Interaction ◽

Global Data

This clear and accessible text describes the methods underlying short-term climate prediction at time scales of 2 weeks to a year. Although a difficult range to forecast accurately, there have been several important advances in the last ten years, most notably in understanding ocean-atmosphere interaction (El Nino for example), the release of global coverage data sets, and in prediction methods themselves. With an emphasis on the empirical approach, the text covers in detail empirical wave propagation, teleconnections, empirical orthogonal functions, and constructed analogue. It also provides a detailed description of nearly all methods used operationally in long-lead seasonal forecasts, with new examples and illustrations. The challenges of making a real time forecast are discussed, including protocol, format, and perceptions about users. Based where possible on global data sets, illustrations are not limited to the Northern Hemisphere, but include several examples from the Southern Hemisphere.

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Spatio-Temporal Patterns of Mass Changes in Himalayan Glaciated Region from EOF Analyses of GRACE Data

Remote Sensing ◽

10.3390/rs13020265 ◽

2021 ◽

Vol 13 (2) ◽

pp. 265

Author(s):

Harika Munagapati ◽

Virendra M. Tiwari

Keyword(s):

Temperature Anomaly ◽

Mass Gain ◽

Snow Accumulation ◽

Empirical Orthogonal Functions ◽

Total Water ◽

Orthogonal Functions ◽

Grace Data ◽

Grace Satellite ◽

Spatio Temporal ◽

Gravity Recovery

The nature of hydrological seasonality over the Himalayan Glaciated Region (HGR) is complex due to varied precipitation patterns. The present study attempts to exemplify the spatio-temporal variation of hydrological mass over the HGR using time-variable gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite for the period of 2002–2016 on seasonal and interannual timescales. The mass signal derived from GRACE data is decomposed using empirical orthogonal functions (EOFs), allowing us to identify the three broad divisions of HGR, i.e., western, central, and eastern, based on the seasonal mass gain or loss that corresponds to prevailing climatic changes. Further, causative relationships between climatic variables and the EOF decomposed signals are explored using the Granger causality algorithm. It appears that a causal relationship exists between total precipitation and total water storage from GRACE. EOF modes also indicate certain regional anomalies such as the Karakoram mass gain, which represents ongoing snow accumulation. Our causality result suggests that the excessive snowfall in 2005–2008 has initiated this mass gain. However, as our results indicate, despite the dampening of snowfall rates after 2008, mass has been steadily increasing in the Karakorum, which is attributed to the flattening of the temperature anomaly curve and subsequent lower melting after 2008.

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