Eigen-glaciers: elucidating hidden features in the flow of Sermeq Kujalleq (Jakobshavn Glacier), Greenland.

2021 ◽  
Author(s):  
David Ashmore ◽  
Douglas Mair ◽  
Jonathan Higham ◽  
Stephen Brough ◽  
James Lea ◽  
...  
Keyword(s):  
Flow Field ◽  
Environmental Flows ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Ice Dynamics ◽  
Relative Contribution ◽  
Glacier Terminus ◽  
Hydrological System ◽  
Ice Velocity ◽  
Value Decomposition

<p>The increasing volume and spatio-temporal resolution of satellite-derived ice velocity data has created new exploratory opportunities for the quantitative analysis of glacier dynamics. One potential technique, Proper Orthogonal Decomposition (POD), also known as Empirical Orthogonal Functions, has proven to be a powerful and flexible technique for revealing coherent structures in a wide variety of environmental flows: mapping hydraulic vortex shedding patterns, the dynamics of fluidised granular beds, and the magnetohydrodynamics of sunspots.</p><p>POD exactly describes a series of snapshots from a flow field with the product of ranked spatially orthogonal Eigenfunctions, or “modes” of spatial weighting, and one-dimensional “temporal” coefficients (Eigenvectors). In many cases the variance of the flow field is well described by just a few dominant modes. The orthogonal nature of each mode, by definition, means that the relative contribution of independent forcing mechanisms on the flow can, in theory, be separated.</p><p>In this study we investigate the applicability of POD to freely available TanDEM-X/TerraSAR-X derived ice velocity datasets of Sermeq Kujalleq (Jakobshavn Glacier), Greenland. We outline the POD procedure using the singular value decomposition of a rearranged and resampled velocity matrix and investigate the factors responsible for the dominant modes. We find dominant modes interpreted as relating to the stress-reconfiguration at the glacier terminus and the development of the glacier hydrological system, but also find that the POD is sensitive to data resampling and quality. With the proliferation of publicly available optical and radar derived velocity products (e.g. MEaSUREs/ESA CCI) we suggest POD, and potentially other modal decomposition techniques, will become increasingly useful in future studies of ice dynamics.</p>

scholarly journals Proper orthogonal decomposition of ice velocity identifies drivers of flow variability at Sermeq Kujalleq (Jakobshavn Isbræ)

2021 ◽  
Author(s):  
David W. Ashmore ◽  
Douglas W. F. Mair ◽  
Jonathan E. Higham ◽  
Stephen Brough ◽  
James M. Lea ◽  
...  
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Google Earth ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Decomposition ◽  
Ice Dynamics ◽  
Velocity Signal ◽  
Glacier Terminus ◽  
Hydrological System ◽  
Ice Velocity ◽  
Proper Orthogonal

Abstract. The increasing volume and spatio-temporal resolution of satellite-derived ice velocity data has created new exploratory opportunities for the quantitative analysis of glacier dynamics. One potential technique, Proper Orthogonal Decomposition (POD), also known as Empirical Orthogonal Functions, has proven to be a powerful and flexible technique for revealing coherent structures in a wide variety of environmental flows. In this study we investigate the applicability of POD to an openly available TanDEM-X/TerraSAR-X derived ice velocity dataset from Sermeq Kujalleq (Jakobshavn Isbræ), Greenland. We find three dominant modes with annual periodicity that we argue are explained by glaciological processes. Mode 1 is interpreted as relating to the stress-reconfiguration at the glacier terminus, known to be an important control on the glacier’s dynamics. Modes 2 and 3 together relate to the development of the spatially heterogenous glacier hydrological system and are primarily driven by the pressurisation and efficiency of the subglacial hydrological system. During the melt season, variations in the velocity shown in Modes 2 and 3 are explained by the drainage of nearby supraglacial melt ponds, as identified with a Google Earth Engine MODIS dynamic thresholding technique. By isolating statistical structures within velocity datasets, and through their comparison to glaciological theory and complementary datasets POD indicates which glaciological processes are responsible for the changing bulk velocity signal, as observed from space. With the proliferation of optical and radar derived velocity products (e.g. MEaSUREs/ESA CCI/PROMICE) we suggest POD, and potentially other modal decomposition techniques, will become increasingly useful in future studies of ice dynamics.

scholarly journals Ice dynamics during a surge of Sortebræ, East Greenland

2002 ◽  
Vol 34 ◽  
pp. 323-329 ◽  
Author(s):  
Tavi Murray ◽  
Tazio Strozzi ◽  
Adrian Luckman ◽  
Hamish Pritchard ◽  
Hester Jiskoot
Keyword(s):  
Synthetic Aperture Radar ◽  
Synthetic Aperture ◽  
Visual Interpretation ◽  
Ice Dynamics ◽  
East Greenland ◽  
Radar Images ◽  
Glacier Terminus ◽  
Hydrological System ◽  
Ice Velocity ◽  
Aperture Radar

AbstractSortebræ, a large tidewater-terminating glacier in East Greenland, underwent a major surge between 1992 and 1995 during which the glacier terminus advanced by nearly 10 km. In this paper, intensity tracking, interferometry and visual interpretation have been used to characterize the ice dynamics during the surge from satellite synthetic aperture radar images. The surge had a rapid initiation that saw velocities increase by 60–1500 times, and within 13 months the entire lower 53 km of the glacier was affected. Surge termination occurred very rapidly during summer, and ice velocity dropped from around 20 md–1 to around 2 md–1 in only 3 months. Uniquely, part of the upper glacier remained fast-flowing even after the main surge event had terminated. Ice dynamics together with observations of large turbid lakes at the glacier margins suggest that the surge resulted from a throttling of basal water by a switch in the hydrological system.

Stochastic dynamics and model reduction of amplifier flows: the backward facing step flow

2013 ◽  
Vol 719 ◽  
pp. 406-430 ◽  
Author(s):  
G. Dergham ◽  
D. Sipp ◽  
J.-Ch. Robinet
Keyword(s):  
Stochastic Dynamics ◽  
Empirical Orthogonal Functions ◽  
Backward Facing Step ◽  
Orthogonal Functions ◽  
Step Flow ◽  
Flow Response ◽  
Entire Flow ◽  
Random Flow ◽  
Value Decomposition ◽  
And Diffusion

AbstractMethods for investigating and approximating the linear dynamics of amplifier flows are examined in this paper. The procedures are derived for incompressible flow over a two-dimensional backward-facing step. First, the singular value decomposition of the resolvent is performed over a frequency range in order to identify the optimal and suboptimal harmonic forcing and responses of the flow. These forcing/responses are shown to be organized into two categories: the first accounting for the Orr and Kelvin–Helmholtz instabilities in the shear layer and the second for the advection and diffusion of perturbations in the free stream. Next, we investigate the dynamics of the flow when excited by a white in space and time noise. We compute the predominant patterns of the random flow which optimally account for the sustained variance, the empirical orthogonal functions (EOFs), as well as the predominant forcing structures which optimally contribute to the sustained variance, the stochastic optimals (SOs). The leading EOFs and SOs are expressed as a linear combination of the suboptimal forcing and responses of the flow and are related to particular instability mechanisms and/or frequency intervals. Finally, we use the leading EOFs, SOs and balanced modes (obtained from balanced truncation) to build low-order models of the flow dynamics. These models are shown to accurately recover the time propagator and resolvent of the original dynamical system. In other words, such models capture the entire flow response from any forcing and may be used in the design of efficient closed-loop controllers for amplifier flows.

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.

Empirical Methods in Short-Term Climate Prediction

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.

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

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.

Identifying VIV Vibration Modes by Use of the Empirical Orthogonal Functions Technique

2002 ◽  
Author(s):  
Gudmund Kleiven
Keyword(s):  
Model Test ◽  
Vibration Mode ◽  
Multivariate Data ◽  
Empirical Orthogonal Functions ◽  
Mode Shapes ◽  
Data Sets ◽  
Vibration Modes ◽  
Ocean Engineering ◽  
Orthogonal Functions ◽  
Related Technique

The Empirical Orthogonal Functions (EOF) technique has widely being used by oceanographers and meteorologists, while the Singular Value Decomposition (SVD being a related technique is frequently used in the statistics community. Another related technique called Principal Component Analysis (PCA) is observed being used for instance in pattern recognition. The predominant applications of these techniques are data compression of multivariate data sets which also facilitates subsequent statistical analysis of such data sets. Within Ocean Engineering the EOF technique is not yet widely in use, although there are several areas where multivariate data sets occur and where the EOF technique could represent a supplementary analysis technique. Examples are oceanographic data, in particular current data. Furthermore data sets of model- or full-scale data of loads and responses of slender bodies, such as pipelines and risers are relevant examples. One attractive property of the EOF technique is that it does not require any a priori information on the physical system by which the data is generated. In the present paper a description of the EOF technique is given. Thereafter an example on use of the EOF technique is presented. The example is analysis of response data from a model test of a pipeline in a long free span exposed to current. The model test program was carried out in order to identify the occurrence of multi-mode vibrations and vibration mode amplitudes. In the present example the EOF technique demonstrates the capability of identifying predominant vibration modes of inline as well as cross-flow vibrations. Vibration mode shapes together with mode amplitudes and frequencies are also estimated. Although the present example is not sufficient for concluding on the applicability of the EOF technique on a general basis, the results of the present example demonstrate some of the potential of the technique.

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