Fowler used optimal interpolation to create daily gridded ice motion fields from SMMR, SSM/I, AVHRR, and buoy data. He used a cokriging estimation method described by Isaaks and Srivastava (1989) for interpolation. This method utilizes the cross-correlation between several variables -- in this case, the vectors derived from SMMR, SSM/I, AVHRR, and buoys -- to minimize the estimation error variance. The following figure shows an example of autocorrelation (jagged line) for the u component of the vectors derived from AVHRR.
The plot shows discontinuity near 50 km distance. If discontinuity is ignored, the autocorrelation line would cross the "0" distance line at about 0.8. This value, which is related to measurement error, is often referred to as the "nugget effect" in geostatistics. The shape of the curve is similar for both u and v vector components, and for all of the auto-correlation and cross-correlation functions among all of the data sets. The major difference is the starting point at 0-km distance. The table below summarizes starting points for each of the auto- and cross-correlations.
|BUOY||AVHRR||85 GHz||37 GHz|
Fowler used a simple exponential function to model the correlation (dotted line) in the above figure. This function provided the best model to approximate the vector data. He performed cross-correlations between the u and v components over the entire Arctic and Antarctic regions, and found that they were nearly independent. The u and v components were then treated independently and were interpolated separately for simplicity. Using the modeled correlation functions, he interpoloated vectors for each ice-covered area on the 25-km EASE-Grid.
Following is a sample vector plot for 20 April 2000, where every fourth vector is plotted.
Sample daily-averaged vector plot
The number of vectors from the buoy, passive microwave, and AVHRR varies. A plot of monthly average percent coverage of ice-covered areas shows that summer weather conditions affect the ability of satellites to track ice.
The following plot shows the average number of vectors available from each source.
Total vectors from each source
Similarly, the following plot shows the percentage of available vectors from each source.
Percentage of vectors from each source
Note that the vectors from the 85-GHz channels began in 1987 with the launch of the SSM/I instrument.
Gridded vector fields are not the optimal data set for everyone. They are best used for evaluating climatological patterns and changes in sea ice motion over the last 25 years. Various assumptions were factored into the production of gridded vector fields. For optimal interpolation, the data should be stationary, homogenous, and isotropic. Sea ice does not have these characteristics. Changes in ice concentration and thickness may negate the assumptions. In an ideal case, two-dimensional correlation functions are found at every grid location on each day to help alleviate some of these problems.
Another limitation of the data is cloud cover, which affects a satellite's ability to discern sea ice, and thus, the number and location of available vectors on each day.
Users should view the summer vector plots with caution because of the low number of vectors resulting from surface melt and increased cloud cover in the summer. Weekly- and monthly-mean plots are fairly reliable, but individual summer daily plots contain significant noise.
Fowler interpolated several years of vectors to the same grid but without using the buoy data. The mean difference between the interpolated u components and the buoy vectors was 0.1 cm/sec with a Root Mean Square (RMS) error of 3.364 cm/sec. For the v component, the mean was 0.4 cm/sec with an RMS error of 3.39722.