Detection and Tracking of Mesoscale Eddies

Ramprasad Bala

Assistant Professor

Computer and Information Science

UMass Dartmouth

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Abstract

The process of identifying and tracking oceanic eddies over space and time, and their relationship to the net poleward heat transport are of fundamental importance for Climate studies.

The visualization provides a better understanding of the structural behavior of the eddies (and other mesoscale features) and their role in the heat transport.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Abstract – cont.

In this work we propose approaches inspired by physical metrics (heat flux) for visualizing heat transport.

We propose a metric, heat index, that enables the viewing of heat transport at individual latitude-longitude points by combining temperature, depth and velocity.

Visualizing the heat index provides the range of latitudes and longitudes where there is significant activity.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Introduction

Measurements done to-date have suggested that the mesoscale eddies and mesoscale features play a strong role in carrying heat poleward (and eastward).

MICOM is one of a few suite of models, where the resolution of the numerical experiments is high enough to resolve the mesoscale eddies.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Miami Isopycnic Coordinate Ocean Model

A 3-D general circulation model whose vertical coordinate is potential density.

The ocean is divided into 18 layers, each of which maintains its own density -- hence the term isopycnic, meaning constant density.

Temperature, Velocity, Salinity data are available in spatial resolution of 1/12th of a degree, and temporal resolution of every 3 days.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Questions

To what spatial extent must we resolve the features to get an accurate description of the Poleward heat flux in individual isopycnal layers?

How to detect and track these mesoscale structures in order to understand their role in the net poleward heat transport?

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Poleward Heat Flux

P(y,l)= Cp v(x,y,l)T(x,y,l)dp(x,y,l)dx

P poleward Heat Flux x eastward directiony northward direction xw western boundaryxe eastern boundary density of the layerCp specific heat v meridional velocity

component (Northward)T temperature l layerdp layer thickness of l

Similarly Eastward Heat flux can be computed using u(x,y,l)

xe

xw

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Poleward heat flux

Latitude

Wat

ts

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Limitations While the Poleward and Eastward heat fluxes

are a good measure of heat transport, we deemed them insufficient for visualization for the following reasons: The heat flux produces a graph as shown earlier that

provides very few cues about the heat transport in specific regions.

The heat flux represents a cumulative sum for individual latitude and longitude i.e. it provides a single value per latitude or longitude. This provides no sense of the heat transport at different areas of the same latitude or longitude.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Heat Index

Heat_Content(i,j,l)=v(i,j,l) * T(i,j,l) * dp (i,j,l);

Heat_Index(i,j,l)= Heat_Content(i,j,l)/ P(i,l);

Heat_Index_Northward(i,j)= Heat_Index+(i,j)/P+(i,l)

Heat_Index_Southward(i,j)= Heat_Index-(i,j)/P-(i,l) Where i=latitude, j=longitude, l=layer.

Similar metric is defined for the Eastward flow using u(i,j) instead of v(i,j)

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Heat Index Visualization

The heat index represents the percentage contribution of individual lat-lon heat content to the net poleward heat flux.

The direction is represented by the color-coding. Experiments were conducted on spatial data to

track the eddy through the various layers to observe its structure.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Eddy Layer 5, Day 0

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Eddy Layer 6, Day 0

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Eddy Layer 7, Day 0

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Temporal Data

This technique was applied temporally i.e. for the same layer over time.

In this, we tracked the gulf stream that transports heat poleward along the east coast of the Unites States.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Jet Layer 6, Day 0

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Jet Layer 6, Day 3

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Jet Layer 6, Day 6

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Goals

While the heat index provides a way to visualize the heat flux, we still had to answer the bigger question - the role of these mesoscale structures in the heat transport.

To accomplish this, we needed to Automate detection of eddies Be able to view variability of eddy structures. Automatically track eddies – temporally and spatially. Extend to other structures.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

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Scaled Velocity Data

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Log Velocity

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Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Clockwise and counterclockwise Eddy features

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Structuring Element to look for areas that are likely to be the center of an eddy

Resolution of each cell is 1/12th of a degree ~ 8 km

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

show the movie of the heat index visualization

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Movie – moving eddies

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Eddy types and segmentation

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Weakening eddy

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false positives /false negatives

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Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Eddy tracking – algorithm

Use the structuring element to identify the eddy centers in the first frame and mark it.

From the small-motion assumption, we can restrict the search space for the eddy center in the next frame to a small grid (10 x 10 points).

Search in the small neighborhood to find the next eddy center using the structuring element

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Correspondence Problem

Establishing the correspondence between objects under going motion is a fundamental and open problem in motion analysis.

One way to overcome this problem here is to use brute force in a couple of frames to establish manual correspondence and know direction of motion.

Once the direction of the eddy is know, again due to small motion assumption, correspondence can be established in the small search space.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Small Motion Assumption

The small motion assumption states that most naturally occurring motion tend to be smooth within short periods of time.

Even if the motion tends to non-uniform or even non-rigid, with short enough rate of sampling of data acquisition, this assumption tends to be true.

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Tracking movie

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Complexity

Brute Force – search complexity (60 x 120 x 12 x 12) ~1200K

Number of eddies ~ 1700 Tracking algorithm – search complexity

(1100 x 10 x 10) ~110K A factor improvement of ~ 11

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Results

We have presented methods of

Automatically detect mesoscale eddies

Segment (and classify) the eddies

Track eddies

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Future Work

Sensitivity studies on false positives, tolerance to the structuring element angles

Detection of new eddies – understand the cause and effect of phenomenon that result in the formation of eddies

Detect other mesoscale structures such as jets. Quantification of heat “trapped” in these structures from

the heat index. Apply described methods to satellite images – SST (in

progress)

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Collaborators

Dr. Amit Tandon, Physics/SMAST Dr. Avijit Gangopadhyay, Physics/SMAST Students

Bin John Vishal Sood Ayan Chaudhuri Sourish Ray Ramana Andra

Fall 2003 – CIS Seminar Series – Dr. Ramprasad BalaFall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Publications

CGIM 2002 - Visualization methods for heat transport in Miami Isopycnic Circulation Ocean Model (MICOM) – August 2002.

VIIP 2003 - Detecting and Tracking of Mesoscale Oceanic Features in the Miami Isopycnic Circulation Ocean Model – September 2003.