The Maximum Cross Correlation Method

The ocean surface velocity products provided on this site are generated by applying the Maximum Cross Correlation (MCC) method to sequential satellite imagery. The MCC method [1], [2] is an automated procedure that calculates the displacement of small regions of patterns from one image to another. The procedure, illustrated in Fig. 1, cross-correlates a template subwindow in an initial image with all possible subwindows of the same size that fall within the search window of a second image. The location of the subwindow in the second image that produces the highest cross-correlation with the subwindow in the first image indicates the most likely displacement of that feature. The velocity vector is then calculated by dividing the displacement vector by the time separation between the two images.

First Image                                                        Second Image
          

The size of the template subwindow is a balance between containing enough features for tracking (and hence having enough degrees of freedom for a statistically significant correlation) and smoothing out the structure of the flow.  A 22x22 pixel template subwindow is used for all realtime MCC processing. The search window in the second image must be large enough to accommodate the largest expected velocity. A maximum velocity of 70 cm/s is used for West Coast MCC processing, and 80 cm/s is used for Gulf of Mexico and East Coast processing.

A raw MCC output velocity field contains vectors at every grid point, many of which result from low correlations. To capture velocities that accurately depict the ocean surface currents, the raw MCC vectors are put through a strict filtering process. Velocities that meet the following filtering requirements are retained and considered accurate:
   
    - a cross-correlation coefficient > 0.8
    - the displacement of the subwindow in the second image (relative to that in the first image) must be greater than 1 pixel
    - the velocity must have 4 neighboring (within 2 grid points) velocities that have x- and y- components within 10 cm/s
    - the velocity must have 4 neighboring (within 2 grid points) velocities that have a direction within 50 degrees 

After the filtering process the accurate velocities are composited over a specified period of time. We provide both 3-day and 7-day composites. The composite velocities are also filtered using the following requirements as a final quality control:

    - 6 (west coast) or 8 (gulf and east coast) neighboring (within 3 grid points) velocities that have x- and y- components within 10 cm/s
    - 6 (west coast) or 8 (gulf and east coast) neighboring (within 3 grid points) velocities that have a direction within 50 degrees

Cloud-cover and isothermal/isochromatic ocean surface conditions drastically limit the spatial and temporal velocity coverage provided by the MCC method. Clouds block the ocean surface in both thermal and ocean color imagery, and there are no features for the MCC method to track in isothermal/isochromatic regions. As a result, it is common for there to be a limited number of MCC velocities in the composites.

For our realtime processing system, the MCC method is applied to thermal IR (11 micron) imagery acquired by the Advanced Very High Resolution Radiometers (AVHRR) on board the NOAA-class satellites, and to ocean color imagery acquired by the MODerate resolution Imaging Spectroradiometers (MODIS) on board the AQUA and TERRA satellites. Both the thermal and ocean color data products have a pixel size of ~1 km. The AVHRR images are geolocated using the method described in [3]. Crocker et al. 2007 have shown that MCC velocities derived from ocean color imagery are similar to those derived from thermal imagery, and these two MCC products can be merged to increase the overall spatial and temporal velocity coverage.

Fig. 2. Four sequential thermal images from the U.S. east coast, and the resulting MCC composite velocity field.