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Oceanic Eddies. Byron Conley Work done at COAPS with: Dr. Brian Arbic Dr. Patrick Timko. Outline. I will address our goal: to use eddy tracks to explain persistent signals Clarify relevant concepts Introduce the previous work that has led to our project Describe our work

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## Oceanic Eddies

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**Oceanic Eddies**Byron Conley Work done at COAPS with: Dr. Brian Arbic Dr. Patrick Timko**Outline**• I will address our goal: to use eddy tracks to explain persistent signals • Clarify relevant concepts • Introduce the previous work that has led to our project • Describe our work • And, time–permitting: • Discuss the challenges, benefits, and related developments in our study of oceanic eddies**Goal**Want to know if tracks of eddies, initially assumed isotropic, found in Chelton et al. (2007) can explain anisotropic signals seen described in Scott et al. (2008).**Clarifications**• What is an eddy? • General Definition: rotational movement of fluid that occurs when a flow passes over/around an obstruction, between oppositely flowing currents, or along edges of permanent currents • Vortices • Contain most of the ocean’s kinetic energy • Inverse energy cascade of two-dimensional flows: nonlinear advection (loosely: transfer) shifts kinetic energy from small to large scales, resulting in persistent structures (our eddies) • Eddies generally contain much higher kinetic energy than the mean kinetic energy of the worlds ocean Convergence of Oyashio and Kuroshio currents, off Hokkaido, Japan**More on Eddies**• Ocean’s dynamic equivalent of synoptic (large-scale) weather systems • Organization of turbulent fluid motion • “Stirring” mechanism through turbulent diffusion • Transfers heat, momentum, mass, chemical constituents of ocean: process known as “advection” • Anisotropy: quantification of preferred direction in flows • u=zonal (E-W) velocity, v=meridional (N-S) velocity, <> denotes time-average • For our purposes, M=<u2-v2>/<u2+v2> gives us an idea of how well structured, isotropic, or elongated, anisotropic, the eddies are. • M=0 indicates isotropy, ie. <u2>=<v2>; |M|≤1 • Idealized models of ocean eddies usually see M > 0 (Arbic et al. 2004 and references therein)**Geostrophic Balance**• Geostrophic balance results from a balance between the pressure gradient and the Coriolis Effect • We use geostrophic approximation to determine the velocities that we have interest in for this project. (Useful poleward of ±5° Lat.) • How we get our zonal (u) and meridional (v) velocities These equations are derivations of the Navier-Stokes equations. “f” or Coriolis Parameter In these: Z = geopotential height, ie. our SSH (Sea Surface Height) measurements Approximation fails within a few degrees of the Equator The Coriolis Effect**Scott et al.**• What does it tell us? • Research done on the zonal vs. meridional velocity variance from satellite observations and ocean models • Found that, in general, <u2>≠<v2>, therefore, eddies are generally anisotropic • Eddies can leave persistent signals over large timescales, counterintuitive to the chaotic nature of turbulent fluid motion • Typically have a general westward propagation • Persistent small-scale patches arise if they [eddies] follow preferred paths, perhaps due to bottom topography**Chelton et al.**• Eddy tracking experiment • Uses data smoothed and filtered from original AVISO satellite data to accentuate the relevent eddy data, based on current eddy characterizations • Removes data for ssh anomalies with lifetimes < 21 days, with amplitudes < 5 cm • Typical eddy amplitudes ~5-25 cm • Typical eddy diameters ~100-200 km**Process**• Form data matrix from provided eddy data • Write a program to read in the data from the two files to build our data matrix • Sort the info into files for each date, containing cyclonic and anticyclonic eddy data • Construct SSH fields using effective and e-folding eddy radii. • Determine optimum radius size, type, and decay factor. • Use visual and mathematical (% Variance Captured—more later) methods for these purposes. • From reconstructed SSH fields, determine u and v for all available data • Differentiate the SSH to get u and v • Repeat process for AVISO satellite data • Using u and v, calculate M-fields (remember M=<u2-v2>/<u2+v2>) for desired time periods. • Compare our reconstruction-based M-fields to AVISO-based M-fields • Hopefully, we will get comparable results • If these results are adequately similar, then we can answer the following questions and satisfy our goal: • Why does an isotropic eddy field still leave an anisotropic M-field? • Why is there temporal persistence?**SSH AVISO vs. Reconstruction**• At first glance, it might seem that we are missing much of the SSH anomaly data • Smoothing and filtering techniques performed by Chelton et al. (our source of data) removed much of the unwanted data • Filtering/smoothing brings out much of the useful eddy data, while discarding much of the “noise’ • Visibly, the patterns are still fairly apparent • When performing our mathematical comparison, percent variance captured, we achieved expected results (~15-30% for the most effective reconstruction methods)**M-fields**• Here is an example of an M-field construction • Image constructed by Scott et al. for 13 year time average (Oct. 11, 1992 – Jan. 21, 2006) • Our images (we hope) will look very similar**How persistent paths can leave signatures in the M field**• As eddies propagate, their tracks leave trails visible in the M-fields • If we contour M>0 and M<0 as different colors, we can see these tracks • If another eddy takes a similar track, time averaging shows the preferred track • As stated before, can eddies which are individually isotropic still leave anisotropic signatures locally as in Scott et al. (2008)? • Can we explain the temporal persistence of these anisotropic signatures by repeated eddy tracks?**Eddy Tracks**• Image shows tracks of individual eddies with lifetimes ≥16 weeks from Chelton et al. (2007)**Where We Are**• The long road of the setup process is nearly over • Final steps include mapping our M-fields, double checking our codes for errors, and finally, analysis of the data • Useful results may be in hand as early as next week**Challenges Faced**• Difficulties of program writing • Program writing is never a simple task • Determining the best methods to use requires long hours of trial and error • Conceptual complexities**More Explanations**• Effective Radius • Radius used if “stretched-out” eddy was reshaped, with same surface area, into a perfect circle • E-folding Radius • Radius at which declines by a factor of e-1 • Decay factors • Gaussian e-(x/r)^2 • “Proper” Gaussian e-.5(x/r)^2 • x/r … e-x/r • x = distance from eddy center to grid point, r = tested radius (3,3.5,4) ie. how far from eddy center we want to go; the further we went, past 2 radii, our pvc calculations did not change (significantly) • Percent Variance Captured: • [RMS] Discrepancy • [RMS] Signal • PVC=100% x (1-(D/S)²) -> the higher, better • Our PVCs ~18-31% for best results • Seems low, but, data smoothing and filtering process immediately trims ~50-60% Discrepancy (below), AVISO signal (top right), Recontruction signal (bottom right)**Interesting Notes**• As with many topics about the ocean, eddies have yet to be fully understood • Causes for preferred eddy tracks can be speculated but have yet to be determined, however Scott et al. (2008) gives us some suggestions: • Atmospheric forcing and oceanic mean flow cannot explain persistent tracks • Bottom topography is a likely candidate • Characterizations of eddies are not completely clear: • Initially assumed “Gaussian”, possibly more “paraboloid” • This means that the function which fits the eddy SSH fields may be closer to a parabola than a Gaussian; i.e. ssh=m-n*r^2, where m and n are constants**What I Have Gained**• Much better understanding of code writing and how to “tell” a computer what to do • Better understanding of the chaotic and unpredictable nature of fluid dynamics • Insight into the methods of analytical science and modelling • Careful, slow progress is much better than having to go back and make corrections • You’ll never get it right the first time, but the more care taken, the more time saved**In Summary**• Eddies appear to have preferred tracks. • Our goal is to see that even if we assume these eddies are isotropic, their tracks can explain anisotropies we see in the statistics of velocity variance (u2 versus v2)**References**• Wikipedia (Images) • Zonal vs. Meridional Velocity Variance in Satellite Observations and Realistic and Idealized Ocean Circulation Models, Scott et al. (2008), Ocean Modelling, Vol. 23 • Global Observation of Large Oceanic Eddies, Chelton et al. (2007), Geophysical Research Letter, Vol. 34 • Data sets provided by Dr. Dudley Chelton and Dr. Michael Schlax, Oregon State University • Satellite Altimeter data taken from AVISO ftp website: ftp://ftpsedr.cls.fr/pub/oceano/AVISO/SSH/duacs/global/dt/ref/msla/merged/h/

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