An improved optical flow method to estimate Arctic sea ice velocity (winter 2014−2016)
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Abstract: Sea ice velocity impacts the distribution of sea ice, and the flux of exported sea ice through the Fram Strait increases with increasing ice velocity. Therefore, improving the accuracy of estimates of the sea ice velocity is important. We introduce a pyramid algorithm into the Horn-Schunck optical flow (HS-OF) method (to develop the PHS-OF method). Before calculating the sea ice velocity, we generate multilayer pyramid images from an original brightness temperature image. Then, the sea ice velocity of the pyramid layer is calculated, and the ice velocity in the original image is calculated by layer iteration. Winter Arctic sea ice velocities from 2014 to 2016 are obtained and used to discuss the accuracy of the HS-OF method and PHS-OF (specifically the 2-layer PHS-OF (2LPHS-OF) and 4-layer PHS-OF (4LPHS-OF)) methods. The results prove that the PHS-OF method indeed improves the accuracy of sea ice velocity estimates, and the 2LPHS-OF scheme is more appropriate for estimating ice velocity. The error is smaller for the 2LPHS-OF velocity estimates than values from the Ocean and Sea Ice Satellite Application Facility and the Copernicus Marine Environment Monitoring Service, and estimates of changes in velocity by the 2LPHS-OF method are consistent with those from the National Snow and Ice Data Center. Sea ice undergoes two main motion patterns, i.e., transpolar drift and the Beaufort Gyre. In addition, cyclonic and anticyclonic ice drift occurred during winter 2016. Variations in sea ice velocity are related to the open water area, sea ice retreat time and length of the open water season.
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Figure 2. n-layer pyramid image construction process (a), and flow chart of the n-layer pyramid HS-OF method (b). The bottom layer (0 layer) represents the original image, and the top layer represents the smallest image. The thin arrows in b indicate the direction of sea ice drift.
Figure 3. Spatial distribution of the region where velocity data for buoys in the Arctic Ocean are obtained. The buoys are numbered as nbx with x being 1 to 7.
Figure 4. Scatterplots of the data obtained by the HS-OF, 2LPHS-OF and 4LPHS-OF methods versus the buoy data in the u (x) and v (y) directions. a, b and c. HS-OF velocity, 2LPHS-OF velocity and 4LPHS-OF velocity in the u-direction; and d, e and f. HS-OF velocity, 2LPHS-OF velocity and 4LPHS-OF velocity in the v-direction.
Figure 5. The daily sea ice velocity in winter from 2014 to 2016 in the u-direction and v-direction, which are obtained from buoys and by the HS-OF, 2LPHS-OF and 4LPHS-OF methods. a, c, e and g. Velocities at the nb2, nb4, nb5 and nb7 positions in the u-direction; and b, d, f and h. velocity at the nb2, nb4, nb5 and nb7 positions in the v-direction.
Figure 6. The daily sea ice velocity in winter from 2014 to 2016 in the u-direction and v-direction, which are obtained from buoys and the OSI SAF and CMEMS dataset. a, c, e and g. Velocities at the nb2, nb4, nb5 and nb7 positions in the u-direction; and b, d, f and h. velocities at the nb2, nb4, nb5 and nb7 positions in the v-direction.
Figure 7. Spatial distribution of the sea ice drift velocity on the 1st and 15th days of each month in the Arctic in 2016. The blue box indicates the occurrence of the Arctic cyclone, and the black box indicates the occurrence of the Arctic anticyclone, including the Beaufort Gyre.
Figure 8. The monthly sea ice velocity in nine subregions from January to March, 2016.
Table 1. Statistics for three sea ice drift datasets
Data provider NSIDC OSI SAF CMEMS Sensor AMSR-E, AVHRR, drifting buoys,
SMMR, SSM/I, SSMISAMSR-2, SSMIS, ASCAT AMSR-E, AMSR-2, SSM/I, SSMIS,
QuickSCAT, ASCATSpatial resolution 25 km×25 km 62.5 km×62.5 km 12.5 km×12.5 km Method MCC CMCC CMCC, model 
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Table 2. Accuracy evaluation of the HS-OF, 2LPHS-OF and 4LPHS-OF methods for the buoy velocity positions (in the u-direction and v-direction) through RMSE, ME, MAE, and P from 2014 to 2016 (winter)
unb1 vnb1 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 4.83 4.79 4.88 4.20 3.99 3.96 ME/(cm·s–1) –1.12 –0.79 –0.76 1.60 1.37 1.26 MAE/(cm·s–1) 3.63 3.63 3.72 3.10 2.97 2.91 P 0.44 0.62 0.58 0.58 0.70 0.71 unb2 vnb2 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 5.57 5.11 5.18 4.46 4.65 4.71 ME/(cm·s–1) –1.95 –1.19 –1.17 0.74 0.47 0.35 MAE/(cm·s–1) 4.40 3.98 4.00 3.35 3.46 3.43 P 0.79 0.84 0.83 0.52 0.66 0.68 unb3 vnb3 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 5.06 4.23 4.28 3.84 4.67 5.34 ME/(cm·s–1) –0.49 –0.29 -0.31 –1.78 –1.04 –0.99 MAE/(cm·s–1) 4.01 3.31 3.33 3.04 3.50 3.91 P 0.89 0.93 0.92 0.67 0.73 0.69 unb4 vnb4 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 3.86 4.08 4.27 4.90 4.53 5.14 ME/(cm·s–1) –0.29 –0.62 –0.59 2.24 1.92 2.03 MAE/(cm·s–1) 3.06 3.20 3.32 3.80 3.47 3.84 P 0.64 0.69 0.72 0.64 0.76 0.62 unb5 vnb5 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 4.48 4.40 4.37 3.39 3.39 3.48 ME/(cm·s–1) 1.57 1.47 1.44 –1.48 –1.36 –1.33 MAE/(cm·s–1) 3.37 3.30 3.27 2.53 2.58 2.62 P 0.34 0.48 0.50 0.30 0.42 0.39 unb6 vnb6 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 4.92 5.25 8.12 4.20 4.67 6.80 ME/(cm·s–1) 1.41 1.14 1.16 0.61 0.44 0.76 MAE/(cm·s–1) 3.69 3.92 5.80 3.34 3.59 4.49 P 0.35 0.44 0.36 0.43 0.52 0.61 unb7 vnb7 HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 4.72 4.70 5.30 5.92 5.99 6.17 ME/(cm·s–1) 2.86 2.37 2.37 2.30 2.42 2.54 MAE/(cm·s–1) 4.13 4.04 4.45 5.36 5.42 5.55 P 0.38 0.54 0.52 0.25 0.37 0.33
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Table 3. Overall accuracy evaluation of the HS-OF, 2LPHS-OF and 4LPHS-OF methods in the u-direction and v-direction through the RMSE, ME, MAE, and P based on buoy velocity from 2014 to 2016 (winter, a total of 1 829 matchup data)
u v HS-OF 2LPHS-OF 4LPHS-OF HS-OF 2LPHS-OF 4LPHS-OF RMSE/(cm·s–1) 4.89 4.76 5.45 4.56 4.70 5.29 ME/(cm·s–1) 0.19 0.22 0.23 0.54 0.54 0.59 MAE/(cm·s–1) 3.74 3.61 3.97 3.44 3.48 3.76 P 0.61 0.70 0.65 0.50 0.60 0.59 Note: The bolded values are the 2LPHS-OF volocity.
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Table 4. Accuracy evaluation of the OSI SAF and CMEMS vectors in the u- and v-directions through the RMSE, ME, MAE, and P values based on buoy velocity
u v OSI SAF CMEMS OSI SAF CMEMS RMSE/(cm·s–1) 6.28 (24%) 6.36 (25%) 6.98 (33%) 5.60 (16%) ME/(cm·s–1) 0.57 (60%) 0.15 (–56%) 1.22 (56%) 0.35 (–55%) MAE/(cm·s–1) 4.50 (20%) 4.93 (27%) 4.73 (26%) 4.16 (16%) P 0.64 (8%) 0.87 (–25%) 0.43 (41%) 0.78 (–29%) Note: The values in brackets indicate the percentage improvement of the accuracy indices of the 2LPHS-OF velocity relative to the accuracy indices of the other data.
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Table 5. Evaluation of the 2LPHS-OF vectors in the u- and v-directions through the RMSE, ME, MAE, and P based on NSIDC velocity data from 2014 to 2016
RMSE/(cm·s−1) ME/(cm·s−1) MAE/(cm·s−1) P u 1.90 0.90 1.45 0.62 v 1.99 0.91 1.64 0.80
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Table 6. Statistics for sea ice velocity in nine subregions of the Arctic
Region Mean
/(cm·s−1)SD
/(cm·s−1)Speed rate
/(cm·s−1·d−1)Arctic Ocean 1.39 0.70 –0.0030 Canadian Archipelago 0.14 0.08 –0.0002 Bering Sea 1.20 1.26 0.0050 Seas of Okhotsk and Japan 1.91 1.26 0.02501) Kara and Barents seas 2.07 1.10 –0.0060 Greenland Sea 1.15 0.74 –0.0030 Hudson Bay 0.77 0.92 0.00902) Baffin Bay/Labrador Sea 1.20 0.56 –0.0010 Gulf of St. Lawrence 0.62 1.00 0.0150 Note: 1) Probability value < 0.01. 2) Probability value < 0.05. Bolded values indicate a speed rate greater than 0.
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