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Optimal interpolation was used to create daily gridded ice motion fields from SMMR, SSM/I-SSMIS, AMSR-E, AVHRR, IABP buoy data, and NCEP/NCAR wind data. A cokriging estimation method described by Isaaks and Srivastava (1989) was employed for the interpolation. This method utilizes the cross-correlation between several variables—in this case, the vectors derived from SMMR, SSM/I-SSMIS,AMSR-E, AVHRR, IABP buoy data, and NCEP/NCAR winds—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.

**AVHRR autocorrelation**

The plot shows discontinuity near 50 km distance. If discontinuity is ignored, the autocorrelation line would cross the zero 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 zero km distance. The table below summarizes starting points for each of the auto- and cross-correlations. The autocorrelations for the ice motions for AMSR-E were very similar to AVHRR, and the vectors from the wind data were very close to the 37 GHz vectors.

BUOY | AVHRR/AMSR-E | SSM/I-SSMIS 85 GHz | SMMR or SSM/I-SSMIS 37 GHz/Winds | |

BUOY | .95 | .70 | .70 | .40 |

AVHRR/AMSR-E | .85 | .65 | .30 | |

85 GHz | .80 | .40 | ||

37 GHz/Winds | .45 |

A simple exponential function was used to model the correlation (dotted line) in the above figure. This function provided the best model to approximate the vector data. Cross-correlations between the u and v components were performed over the entire Arctic and Antarctic regions, and it was found that they were nearly independent. The u and v components were thus treated independently and were interpolated separately for simplicity. Using the modeled correlation functions, vectors for each ice-covered area on the 25 km EASE-Grid werre interpolated.

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 data 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 percentage of sea ice grid cells that contain vectors.

**Percent coverage of sea ice grid cells**

The following plot shows the average number of vectors available from each source.

**Number of 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 can affect a satellite's ability to discern sea ice, and thus, the number and location of available vectors on each day.

Data users should use the summer vector plots with caution due to the low number of vectors resulting from surface melt and increased cloud cover in the summer. As individual summer daily plots contain significant noise, weekly- and monthly-mean plots are more reliable.

Several years of vectors were interpolated to the same grid for comparison, 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 3.36 cm/sec. For the v component, the mean was 0.4 cm/sec with an RMS error of 3.40 cm/sec.

Isaaks, E., and R. M. Srivastava. 1989. *An Introduction to Applied Geostatistics*. New York: Oxford University Press.