Detection and Tracking of Mesoscale Eddies Ramprasad Bala Assistant Professor Computer and Information Science UMass Dartmouth

Fall 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 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 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 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 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 Bala Previous Work  Physical Oceanography Visualization Rochon et. al. digital elevation, wire-frame, color shading - Gulf of Mexico. Moorhead et. al. – OVIRT – Scalar-field volume rendering. Healey et. al. – perceptual cues and data mining – visualizing large scientific datasets. Other approaches – B-spline [Tuohy], feature-based [Yang], optic-flow [Barron]

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Poleward Heat Flux  P(y,l)=   C p v(x,y,l)T(x,y,l)dp(x,y,l)dx Ppoleward Heat Fluxxeastward direction ynorthward directionx w western boundary x e eastern boundary  density of the layer C p specific heatvmeridional velocity component (Northward) Ttemperaturellayer dplayer thickness of l Similarly Eastward Heat flux can be computed using u(x,y,l) xexe xwxw

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Poleward heat flux Latitude Watts

Fall 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 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 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 Bala Eddy Layer 5, Day 0

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Eddy Layer 6, Day 0

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Eddy Layer 7, Day 0

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala 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 Bala Jet Layer 6, Day 0

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Jet Layer 6, Day 3

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Jet Layer 6, Day 6

Fall 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 Bala

Scaled Velocity Data

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Log Velocity

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Clockwise and counterclockwise Eddy features

Fall 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 1/12 th of a degree ~ 8 km

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala show the movie of the heat index visualization

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Movie – moving eddies

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Eddy types and segmentation

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Weakening eddy

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

false positives /false negatives

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

Eddy types  Eddy centers are circular, the eddy itself need not be.

Fall 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 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 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 Bala Tracking movie

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala

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 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 Bala Conclusions  This automated detection can be used on datasets that have velocity direction information  Feature tracking can limit visualizations to area of interests  Tracking an eddy and simultaneously looking at it’s chlorophyll numbers may yield newer insights

Fall 2003 – CIS Seminar Series – Dr. Ramprasad Bala Conclusion & Future Work  We propose new metrics that prove to be very effective in visualizing heat transport in the MICOM data. We demonstrate the effectiveness of this approach in identifying key mesoscale structures such as jets and eddies.  We also present a robust approach to identifying regions of interest and non-interest through simple examination of the metrics that we have defined.  The approach can be extended to study other metrics such as momentum flux and to study temperature structures and salinity structures.

Fall 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 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 Bala Publications  CGIM Visualization methods for heat transport in Miami Isopycnic Circulation Ocean Model (MICOM) – August  VIIP Detecting and Tracking of Mesoscale Oceanic Features in the Miami Isopycnic Circulation Ocean Model – September 2003.