An Improved Sea-Ice Velocity Retrieval Algorithm Based on 89 GHz Brightness Temperature Satellite Data in the Fram Strait

Abstract

Fram Strait is the passageway where most drifting sea ice exits the Arctic Ocean into the North Atlantic, and the sea-ice velocity (SIV) is the most critical parameter for the variability of the sea ice area flux through Fram Strait. Sea ice flux estimates through the Fram Strait based on satellite remote sensing exist. However, they show discrepancies, which mainly result from the sparse valid satellite observations and the increased uncertainty of sea ice motion in the Fram Strait. In order to improve the sea ice flux estimates, we develop an improved sea-ice velocity retrieval algorithm from 89 GHz brightness temperature fields of Advanced Microwave Scanning Radiometer for EOS and AMSR2. The improved retrieval algorithm employs an adjusted size of the template window and performs bilinear interpolation on candidate windows before the matching procedure. Instead of depending on external data sources, we construct the SIV uncertainty fields depending only on the maximum correlation coefficients of the image itself. Compared with two similar Passive Microwave (PM) sea ice velocity datasets, the new sea-ice velocity has lower bias and root-mean-square error with respect to buoy observations. In addition, the data density of the new SIV is 14% and 36% higher than the two reference datasets, respectively. Monthly sea ice area flux estimates through the Fram Strait are acquired with the new daily sea-ice velocity data and the existed sea-ice concentration. And it indicates that the improved sea ice area flux estimated by PM sea ice velocity agrees well with the Synthetic-aperture radar-derived sea ice area flux.

Key Points

• An optimal sea ice motion tracking method based on passive microwave image in the Fram Strait has been investigated

• Uncertainty of sea ice velocity has been estimated based on the maximum correlation coefficient of template

• Improved sea ice area flux through Fram Strait during winter has been acquired based on improved sea ice velocity data sets

Plain Language Summary

The sea ice outflux through the Fram Strait is critical for the mass balance of Arctic sea ice cover. However, previous studies tend to underestimate ice flux based on satellite data sets due to the weaker southward ice velocity with respect to buoy measurements. In order to acquire the accurate ice velocity in the Fram Strait to improve the ice flux estimates, we improve a pattern-tracking sea ice retrieval algorithm derived from 89 GHz brightness temperature in the Fram Strait. Besides, we acquire the uncertainties with spatiotemporal variability of ice velocity based on the pattern features rather than any external data sources. This improved sea ice velocity data set will be helpful to future studies on data assimilation and model improvements.

1 Introduction

As a sensitive component of the ocean-atmosphere system, the Arctic sea-ice extent experienced prominent retreats in the past four decades, accompanied by the decrease of mean sea-ice thickness (Kwok, 2018; Stroeve & Notz, 2018). Simultaneously the near-surface atmospheric temperature increased, which in part is connected to the sea-ice extent shrinkage, and the ice-albedo feedback accelerates the sea-ice retreat during summer (Serreze & Barry, 2011). In addition to these thermodynamic processes, sea ice advection could also alter the sea ice distribution remarkably. The acceleration of the Arctic sea-ice drift is confirmed by in situ observations (Hakkinen et al., 2008; Rampal et al., 2009) as well as satellite measurements (Spreen et al., 2011) from 1979 to the end of 2000s. Rampal et al. (2009) indicate the increase of sea ice deformation due to its thinning rather than stronger atmospheric forcing driven the acceleration of sea ice motion (Vihma et al., 2012). Spreen et al. (2011) report that positive trend of wind speed can only regionally and partly explain the acceleration of sea ice motion in the Transpolar Drift Stream (TDS) and they also suggest the ice thinning is more likely the leading cause of sea ice motion acceleration in other regions. In addition, as it lies the downstream end of TDS, the sea ice outflow through the Fram Strait not only is an indicator of sea ice motion, but also will affect the sea ice extent in the Arctic (Smedsrud et al., 2017).

Fram Strait is the main gate for the sea ice outflow from the Arctic Ocean, and its annual area export accounts for approximately 10% of sea-ice area and 14% of ice volume in the whole Arctic Ocean (Kwok, 2009; Smedsrud et al., 2017; Spreen et al., 2009, 2020). The sea ice volume flux mainly depends on the sea-ice velocity (SIV), then the sea-ice thickness and sea-ice concentration (Smedsrud et al., 2017). Today, existing sea ice area flux (products of SIV, sea-ice concentration and grid spacing) estimates of the Fram Strait still exhibit significant inconsistency in magnitude and trend mainly due to the difference of SIV products (Krumpen et al., 2016).

The most commonly used SIV products in the Arctic are derived from passive microwave (PM) sensors based on measured brightness temperatures (Tb) employing different frequency channels (Ezraty et al., 2007; Lavergne et al., 2010; Tschudi et al., 2019). PM sensors have an obvious advantage in their high spatial-temporal coverage due to their wide swath and high permeability to the atmosphere as well as independence on illumination. Currently, most of operational SIV products are based on data from PM sensor by feature-patterns tracking algorithms (Ezraty et al., 2007; Lavergne et al., 2010; Tschudi et al., 2019). Due to the simplicity, the maximum correlation coefficient (MCC) method became a common basis for the current PM SIV retrievals. Most of these SIV products use 37 GHz Tb as input. However, also retrievals at 89 GHz do exist. All have larger uncertainties in the Fram Strait region than in the Central Arctic Ocean (Hwang, 2013). Sumata et al. (2014) also pointed out that sea ice regions with higher ice speed or lower ice concentration have higher uncertainty. These conditions are met in Fram Strait and thus we aim to improve the SIV retrieval based on 89 GHz Tb in the Fram Strait.

As mentioned above, SIV in the Fram Strait has lower quality compared with that in Pan-Arctic regions due to the rapid feature patterns changes resulted from higher SIV and melting in the ice edge. Moreover, most SIV products derived from the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and 2 (AMSR2) have a 2 day time-span, which is too long to keep the fidelity of Tb pattern (we refer to them as template in the following) in the Fram Strait region high enough to allow correlation matching. In this paper, we propose an improved SIV retrieval algorithm in the Fram Strait based on AMSR-E and AMSR2 89 GHz satellite observations. In Section 2, we introduce the data used for SIV retrieval in the Fram Strait and the reference data used for evaluation. The details on the improved algorithm will be presented in Section 3. Then, this method is applied to 1 and 2 days SIV retrievals. In Section 4, we introduce the method to construct the uncertainty maps of SIV fields. Then, we present the main features of the new SIV results and also compare them with other comparable products. Besides, we will comprehensively compare the improved SIV fields with other PM SIV products from four different aspects in this section. The sea ice area flux through the Fram Strait based on the new SIV will be presented in Section 5 and the conclusion will be provided in Section 6.

2 Data

2.1 Satellite Microwave Radiometer Data

In this paper, we use daily-averaged Tb from AMSR-E (October 2002–April 2011) and AMSR2 (October 2012–December 2018) to retrieve SIV. We choose daily gridded 89 GHz Tb with a 6.25 km spatial resolution, which are distributed by University of Bremen (seaice.uni-bremen.de). The SIV retrieval should be performed on ice-covered regions. Therefore, we exclude the open water pixels before SIV retrieval based on daily sea-ice concentration, which is also derived from AMSR-E and AMSR2, with the same 6.25 km spatial resolution as the brightness temperature data set (Spreen et al., 2008).

2.2 Data for Evaluation and Comparison

We use higher resolution distributed SIV from Copernicus Marine Service (CMS) for data evaluation (Eastwood et al., 2020). However, this data is not covering the whole Arctic. These daily mean sea-ice velocities are derived from Sentinel-1 Synthetic-aperture radar (SAR) image, occasionally covering the Fram Strait from 2016 to present (Pedersen et al., 2015). According to the quarterly validation reports from 2017 to 2019, the winter (first and last quarter) averaged uncertainty of ice drift is 0.34 and 0.30 km/d in the X and Y directions, respectively. The SAR-derived SIV is an ideal evaluation data to our SIV by two reasons: first, its similar acquisition time as AMSR-E and AMSR2 from 12:00 on the first day to 12:00 in the next day; second, its lower error compared with PM SIV (Pedersen et al., 2015).

Besides, ice buoy positions data from the International Arctic Buoy Program (IABP) are also employed to evaluate the PM SIV. This data set provides locations of automatic buoys twice (0:00 UTC and 12:00 UTC) a day from 1978 to present (Rigor & Colony, 1991; Thorndike et al., 1983). In order to match the PM SIV vectors, we extract ice drift from buoy positions at 12:00 UTC. In this paper, the CMS SIV are applied to evaluate the SIV during AMSR2 period, while the IABP buoys data are used for both AMSR-E and AMSR2 periods.

Besides, we also compare our new SIV with four other PM SIV products. Two SIV products distributed by National Snow and Ice Data Center (NSIDC), derived from AMSR-E and multi-sources are named NSIDC-A and NSIDC-M (Tschudi et al., 2019) in this paper. The AMSR-E/AMSR2 SIV product distributed by Ocean and Sea Ice Satellite Application Facility (OSISAF) High Latitude Processing Center is named OSISAF-A (Lavergne et al., 2010). The AMSR-E/AMSR2 SIV from Institut français de recherche pour l'exploitation de la mer (Ifremer)/CERSAT is named Ifremer-A (Ezraty et al., 2007). More details of these three products are listed in Table 1. OSISAF-A SIV are based on 37 GHz Tb while NSIDC-A, NSIDC-M and Ifremer-A SIV are based on 89 GHz Tb. The NSIDC-M SIV is derived from multi-sources by merging process and has better spatial coverage than other data sets.

Table 1. Four SIV Products Used for Comparison

Product name in this paper	Sensors	Retrieval algorithm	Tb channel	Spatial resolution	Time span	Time-span
Ifremer-A	AMSR-E, AMSR2	MCC + Laplace filter	89 GHz V + H	31.25 km	2002–2011, 2012 to present	2 days
OSISAF-A	AMSR-E, AMSR2	CMCC + Laplace filter	37 GHz V + H	62.5 km	2009–2011, 2012 to present	2 days
NSIDC-M	AMSR-E, AVHRR, BUOYS, SMMR, SSM/I, SSMIS	MCC	Multi	25 km	1979 to present	1 day
NSIDC-A	AMSR-E	MCC	89 GHz V	37.5 km	2002–2011	1 day

• Note. AMSR-E, Advanced Microwave Scanning Radiometer for EOS; OSISAF, Ocean and Sea Ice Satellite Application Facility.

3 Improved SIV Retrieval Method in the Fram Strait

Using MCC method, one could determine the relative SIV by comparing the correlation between a template window from designated imagery, and all candidates search windows from sequential imagery at a fixed time-span. The location where the MCC reached is selected as the final position of the template window, and the SIV is calculated by dividing the offset distance of the template window by time-span.

Previous AMSR-E SIV data commonly use 11 × 11 as the size of template window mainly according to practical experience (Ezraty et al., 2007; Lavergne et al., 2010). Here, based on the SAR ice velocity from 2016 to 2019 over the Fram Strait, we estimate the standard deviation (SD) of U_diff (i.e., U_diff = |U_AMSR − U_SAR|) with different width of template window from 8 to 18. The SD of U_diff decreases steeply when the width is larger than 11 and converges to about 7.5 km/d for larger template windows (Figure 1a). The valid number of comparison pairs varies randomly with the increase of the width of template size. In order to reach a compromise between uncertainties and the amount of valid data (Figure 1a), we employ 14 as the width of the template window in our improved algorithm in the Fram Strait, because it has obviously higher number of valid data than that with width of 15 and lower SD of U_diff than that with width of 13.

Figure 1

(a) The relationship between the standard deviation (SD) of U_diff and the width of template window. The gray bar is the valid number of comparison pairs scaled by 1,000. (b) The relationship between the maximum correlation coefficient (MCC) and U_diff. The black dots correspond to the drift differences at every grid point and the red crosses represent the mean difference in a certain MCC bin with size of 0.1.

Another improvement of our retrieval algorithm compared to the classical MCC method is a bilinear interpolation on the search window before correlation calculation, which can improve the quantity of the MCC search. The bilinear interpolation was first proposed by Lavergne et al. (2010) in the continuous maximum correlation coefficient (CMCC) method on SIV retrieval. The method is confirmed to improve the direction estimate of sea ice motion with low ice speed derived from 37 GHz Tb imagery. Because our improved algorithm is based on 89 GHz Tb, which has finer spatial resolution and resolves more surface structures than 37 GHz Tb, we only perform bilinear interpolation once. This is different with CMCC method, which performed MCC calculation on visual continuous target window after preliminary selection.

The procedures of our improved retrieval algorithm are as follows:

1. The 89 GHz Tb image at start day and final day are both enhanced by a Laplacian filter (Ezraty et al., 2007).

2. The template window, including 14 × 14 pixels, is inspected for whether it contains enough sea ice pixels for the further steps (by using a sea ice concentration mask; see above). If the template window contains more than 70% of land pixels or open water pixels in the whole window, it will be discarded.

3. The daily maximum ice motion is set to seven pixels or 43.75 km. For the template window that meets the criteria, we will perform a 1 time spatial bilinear interpolation on the search window at final day with the size of 28 × 28 pixels. Then, the nominal resolution of the virtual search window is doubled.

4. The spatial interval of template window is set to five pixels. All locations of the MCC of research windows are determined. Similar to Ezraty et al. (2007), the results with a MCC less than 0.4 will be discarded.

5. The post-filter is employed by filtering the SIV vectors outliers that have different magnitude (relative difference greater than 100%) and direction (angle difference larger than 90°) with respect to neighboring eight vectors (Ezraty et al., 2007).

4 Results of Retrieval SIV and Comparison

4.1 Uncertainty of SIV Fields

The uncertainties of SIV are needed to meaningful compare or validate different SIV products and for data assimilation in model systems. Current daily SIV products only provide a constant uncertainty estimate for all SIV vectors (Ezraty et al., 2007; Lavergne et al., 2010). Inspired by the uncertainty estimates for four monthly SIV products proposed in Sumata et al. (2014), we proposed a similar method but for estimating daily SIV uncertainties. Different from Sumata et al. (2014), who use sea ice concentration and sea ice velocity as the basis of their uncertainties, we find U_diff between our SIV and the SAR data decreases with the increase of the MCC (Figure 1b). We assume that the higher resolution SAR SIV has higher accuracy and use it as reference. Figure 1b shows that if the similarity of a sea ice template (i.e., a pattern of ice floes) is high on different days (i.e., has high MCC) then the accuracy of our SIV product increases, which is expressed by the decrease of U_diff. Previous studies didn't associate the MCCs magnitude with the uncertainties of SIV but only used it to keep SIV vectors with MCC larger than a specific value (0.4 in Ezraty et al. (2007) or 0.6 in Lavergne et al. (2010)).

Following Equation 4 of Sumata et al. (2014), we estimate the probability distribution function (PDF) of the U_diff with seven MCC bins of width 0.1. The PDF of the first bin (0.3–0.4; not shown) is apart from the Gaussian distribution, while the other PDFs mainly show a Gaussian distribution (Figure 2a; shows three distributions as example, the other three (besides 0.3–0.4) also show Gaussian shape). The mean and SD of U_diff is estimated by:

(1)

(2)

Figure 2

(a) Probability density function of ice velocity difference between our improved maximum correlation coefficient (MCC) and Synthetic-aperture radar with bin width of 0.15 for different MCC ranges (purple: 0.4–0.5; green: 0.6–0.7; yellow: 0.8–0.9). The dashed lines depict corresponding Gaussian distribution. (b) Mean and standard deviation (SD) of the ice velocity difference in certain MCC bins with 0.1 width. The green dots denote the uncertainties of the MCC bins.

The μ and σ correspond to the mean and SD of fitted Gaussian distributions for the six different bin ranges (0.4–0.5 to 0.9–1.0). The uncertainty is defined as + . Sumata et al. (2014) associate the uncertainty of SIV with sea ice concentration, sea ice thickness and sea ice velocity. Different from them, we relate the uncertainty with the MCC, which can be referred as surface feature. The higher MCC usually means more easily identifiable feature of the template window and also means the higher accuracy of the ice velocity. Figure 2b shows that the uncertainty decreases with the increase of the MCC. The uncertainty of the 0.4–0.5 bin of 15.57 km/d has almost twice the size than the spatial resolution of Tb pixels of 6.25 km. In this paper, the uncertainties of SIV are estimated by the magnitude of the MCC of the template window, which is present in Figure 2b. For example, if the MCC of template window equal to 0.55, which is located at the range of 0.5–0.6, the corresponding uncertainty is 9.44 km/d.

4.2 Seasonal Variation of SIV

In Figure 3, we present the climatology of monthly averaged SIV fields during the winter period (from October to April) as well as the corresponding uncertainty maps. All these fields are averaged by daily SIV/uncertainty fields from 2012 to 2018. The SIV increases from October to November and again from February to March. In general, there is an area of fast ice velocities close to the east coast of Greenland and a region with maximum SIV mainly located in the region between 78°N and 81°N. In general, the closer to the sea ice edge, the greater the uncertainty; the further south, the greater the uncertainty. From October to April, the uncertainty becomes lower when sea ice cover becomes more stable in the region north of 79°N.

Figure 3

Monthly average SIV fields in the Fram Strait region averaged from October 2012 to April 2018. The background represents the climatology uncertainty corresponding to the sea ice velocity.

4.3 Evaluation by SAR-Based Data Sets

We evaluated our results against daily SAR-based SIV. To guarantee the representativeness of SAR-based SIV vectors, we selected 27 scenes of SAR SIV fields. Each scene has more than 1,800 pairs of SIV vectors from October 2016 to April 2018 (Figure 4). AMSR2 SIV vectors are interpolated to the SAR-based 10 km polar stereographic grid by bilinear interpolation. Compared with SAR-based ice velocity, the zonal and meridional mean difference of the AMSR2 SIV and SAR SIV using original MCC algorithm with a 1 day time-span is −0.11 and −0.31 km/d, respectively. Their SD of the difference is 1.71 and 1.95 km/d, respectively. The mean difference of the improved SIV algorithm is −0.03 and −0.36 km/d, respectively. Their SD of the difference is 1.43 and 1.62 km/d. This means that both the mean differences and their SD became lower for the improved SIV algorithm. Of all 27 SAR scenes, in 26 cases the SD of the zonal component got improved (i.e., smaller) and in 21 cases also the SD of the meridional component got improved (Table 2). Thus, in general, there is a clear improvement for the new algorithm. The improvement in zonal component is better than that in the meridional component. We think the better performance of our algorithm in the zonal component is closely related to its lower ice velocity. Because as indicated by Lavergne et al. (2010), the spatial interpolation scheme works better in sea ice regions with low velocity.

Figure 4

Exemplary SIV fields showing the cases with highest difference to Synthetic-aperture radar (SAR) SIV in zonal δU (2017-04-04) (a) and meridional δV (2017-03-27) (b) components. The black, blue and red arrows represent the results from SAR, maximum correlation coefficient and improved retrieval algorithm, respectively. All vectors are twice enlarged and drawn only for every third vector on the 10 km grid.

Table 2. Standard Deviation (σ) of the SIV Difference Between AMSR2 and SAR Using the Improved Algorithm and MCC Algorithm (Parentheses) for 27 SAR Scenes Between Oct 2016 and Apr 2018

Start date	σU	σV	Sample number	Start date	σU	σV	Sample number
2017-03-06	1.99(2.00)	1.42(1.56)	2295	2017-04-05	1.66(1.97)	1.58(1.79)	2105
2017-03-19	1.21(1.49)	1.88(1.72)	2092	2017-04-06	1.38(1.61)	1.72(2.05)	2042
2017-03-20	1.40(1.61)	1.75(2.13)	2520	2017-04-07	1.29(1.42)	1.68(1.95)	2320
2017-03-23	1.57(2.01)	2.22(2.18)	2506	2017-04-08	1.47(1.73)	1.40(1.52)	2243
2017-03-26	1.35(1.46)	1.96(2.01)	2195	2017-04-09	1.41(1.80)	1.59(1.58)	2215
2017-03-27	1.36(1.77)	1.31(2.06)	2644	2017-04-10	1.27(1.69)	1.44(1.75)	2181
2017-03-28	1.79(1.99)	1.74(1.75)	2360	2017-04-12	1.64(1.82)	1.59(1.62)	2259
2017-03-29	1.45(1.57)	1.56(1.78)	2048	2017-04-17	1.39(1.85)	1.53(1.61)	1988
2017-03-30	1.31(1.73)	1.52(1.57)	2045	2017-04-18	1.09(1.35)	1.32(1.42)	1946
2017-03-31	1.38(1.50)	1.83(1.66)	2684	2017-04-19	1.38(1.48)	2.11(2.20)	2336
2017-04-01	1.36(1.72)	1.35(1.64)	2677	2018-03-28	1.38(1.48)	1.69(1.55)	2208
2017-04-02	1.29(1.79)	1.49(1.78)	2657	2018-04-10	1.48(1.73)	1.31(1.68)	2139
2017-04-03	1.20(1.66)	1.42(1.90)	2630	2018-04-17	1.70(1.62)	1.72(1.65)	2000
2017-04-04	1.33(2.29)	1.68(1.79)	2281	Average	1.43(1.71)	1.62(1.65)	-

• Note. U for the zonal and V for the meridional difference. In general, σ got reduced for the improved algorithm. MMC, maximum correlation coefficient; SAR, Synthetic-aperture radar.

We further specifically check the cases with the highest mean difference at zonal component δU (2017-04-04) and highest mean difference at meridional component δV (2017-03-27, Figure 4)., For the δU case it shows that the improved algorithm present similar ice motion as the SAR-based SIV in the region north to 81°N, but the direction of the MCC-derived ice SIV is 10° to the right to the southeastward ice motion of SAR SIV (Figure 4a). In the case with the highest δV (Figure 4b), the differences are mainly resulted from the MCC's underestimation of southward ice motion south to 78°N by 12%.

4.4 Evaluation by Buoy Data Sets

We also evaluate the 1 day SIV against daily buoy-based SIV from the IABP data sets. We selected all available buoy SIV records from the Fram Strait region from October 2002 to December 2017. All AMSR-E/AMSR2 sea ice velocities are interpolated to the location of the buoys by linear interpolation before comparison. These 2,733 buoy records are mainly located in the main stream of the East Greenland Current between 15°W and 0°W while seldomly some buoys get stuck in the land-fast ice close to the east coast of Greenland (not shown). The error of the MCC algorithm with a 1 day time-span in zonal (U) and meridional (V) component is −0.04 ± 3.93 and 1.33 ± 5.51 km/d, respectively. While those of the improved algorithm are −0.02 ± 3.76 and 1.34 ± 5.47 km/d, respectively. Thus, the improved algorithm shows a lower uncertainty in zonal direction while in meridional direction the results are very similar to the classical MCC algorithm. However, the scatter plot of U and V biases shows an overall reduced scatter for the improved algorithm than that of the MCC results, and it has a larger sample percentage lower than 0.5 σ (53%) than MCC (48%) (Figure 5).

Figure 5

Scatterplot of sea-ice velocity (SIV) bias with respective to buoy motion by maximum correlation coefficient (MCC) (a) and improved algorithm (b). The red and blue cycle outlines the half and one range of the standard deviation (SD) error of MCC ice velocity, respectively. δ and σ represent the mean difference and the SD difference of the AMSR2 SIV and buoy SIV vectors. ρ represent the correlation between the zonal and meridional difference of the AMSR2 SIV and buoy SIV vectors.

4.5 Comparison With Other Passive Microwave SIV Products

In this section, we performed inter-comparison between four kinds of monthly SIV results from Ifremer (Ezraty et al., 2007), OSISAF (Lavergne et al., 2010), NSIDC (Tschudi et al., 2019) and our improved algorithm, respectively. Limited by the length of the OSISAF data sets, we only use the data from October 2015 to April 2018. All monthly SIV are averaged based on the daily SIV fields and the data with records length less than 20 was excluded. In order to make the vectors more distinct for the Figures, each SIV field present ice motion vectors for every second vector only, except OSISAF-A where we keep every vector because of its relatively low spatial resolution.

For the data sets with a a-day time interval, the climatology meridional ice velocity of NSIDC and our results is −2.35 and −2.46 km/d, respectively. Our zonal ice velocity (−9.93 km/d) is significantly lower than that of NSIDC (−6.56 km/d), which means our results present stronger southward ice motion generally. For the data sets with a 2 day time interval, the climatology meridional ice velocity of Ifremer-A, OSISAF-A and our results is −3.07, −1.87 and −1.58 km/d, respectively. The climatology zonal ice velocity of Ifremer-A, OSISAF-A and our results is −12.08, −10.31 and −11.58 km/d, respectively. The results (Figure 6) also show that in NSIDC-M results, the ice motion slow down and become more homogeneous from November to March. The results of all other products do not show this behavior and have no significant seasonal variations of SIV. In general, SIV of NSIDC-M is lower than the other data sets. This could be associated with the relative low-resolution Tb (37 GHz) they used. NSIDC-M has the lowest SIV and a comparably smooth SIV distribution, which partly could result from its merging methods, which include wind estimated SIV results and interpolation to grid cells without observation. Ifremer-A, OSISAF-A and the improved SIV results with 2 day time-spans have similar SIV vector distributions. Their high ice speed area centers in the region of 78°N–81°N (from November to March) and region around 78°N (January and March). Ifremer-A has a wider area with SIV with more than 25 km/d magnitude than the other SIV results with 2 day time-span. Consistent with Haarpaintner and Spreen (2007), the improved SIV with 1 day time-span are highly consistent with that of improved SIV with 2 day time-span but lower ice velocity, which infers that the longer time-span may ignore fast ice motion.

Figure 6

Three-winter mean (October 2015 to April 2018 SIV fields in the Fram Strait from derived from National Snow and Ice Data Center (NSIDC), Ocean and Sea Ice Satellite Application Facility (OSISAF), Ifremer-AMSR2, and improved SIV with 1 and 2 day time-span in this paper, respectively. The colors represent the magnitude of SIV. SIV vectors are shown for every two grid cell, except OSISAF for every grid cell due to its relatively low spatial resolution.

In order to further compare the quality of SIV data set above with other SIV data sets, we compare the errors of three 2 day SIV data sets (OSISAF, Ifremer, this study) with the SIV from buoy observations. Limited by the temporal coverage of OSISAF AMSR SIV, we only collected 147 available buoys records to evaluate the error of the three data sets from October 2015 to December 2017 (Figure 7). All three SIV results were interpolated to the buoy locations by linear interpolation. In the zonal direction, all mean differences of the three data sets are lower than 0.2 km/d, and the SD of the difference of OSISAF-A, Ifremer-A and improved SIV are 1.62, 1.31 and 1.24 km/d, respectively.; In the meridional direction, OSISAF-A has significant larger mean difference (1.27 km/d) than Ifremer-A (0.35 km/d) and improved SIV (0.28 km/d), which is comparable with its SD difference of 1.95 km/d. The SD of differences of OSISAF-A, Ifremer-A and improved SIV are 1.95, 1.54 and 1.69 km/d, respectively. The scatterplots in Figure 7 shows that OSISAF samples are more dispersed than the other two data sets because its original spatial resolution of 12.5 km is half of other two AMSR-E/AMSR2 data sets with 6.25 km. For our improved algorithm, more samples are among the 1σ range, which indicates that the improved algorithm can improve the quality of SIV.

Figure 7

Scatterplot of SIV bias from Ocean and Sea Ice Satellite Application Facility-A (OSISAF-A) (a), Ifremer-A (b) and our improved algorithm (c) with respect to buoy measurements. The red and blue cycle outlines the half and full range of one standard deviation error of the improved algorithm ice velocity, respectively.

4.6 Data Density of SIV Fields

Data density of SIV, which is the ratio of valid SIVs and valid templates (with valid mean sea ice concentration above a threshold of 70%), is another effective way to measure the improvement of our new SIV method. According to Figure 8, our improved algorithm could increase the data density of SIV effectively (the NSIDC data set is not shown because here SIV is interpolated to all ice-covered areas and the data density cannot be calculated). The data density improvement is especially high in the relatively lower latitude regions and land-fast ice zone close to the coast (not shown). This improvement is important for the application of these new SIV data sets for studies on sea ice flux estimates (next section) and ice deformation calculation. The time series of the daily data density of three kinds of SIV data sets during the winter of 2016–2017 and 2017–2018 shows strong short-time scale variation (Figure 8). The mean data density of the Ifremer, OSISAF and improved algorithm with 1 and 2 day time-span is 29%, 53%, 67% and 63%, respectively. In general, the data density of our improved algorithm is higher than that of the other two algorithms. Even though there are significant differences between the data density of these three data sets, they have similar daily variations, especially for the Ifremer and our SIV. Compared with OSISAF-A, Ifremer-A's lower data density probably mainly results from the fact that 89 GHz Tb is used for tracking for Ifremer-A, which are more sensitive to atmospheric influences, which thus lowers the MCC coefficient. Both of our improved SIV datasets have higher data density than OSISAF-A and Ifremer-A. We associate this with the looser post-process condition used, which includes keeping templates with water pixels less than 30% and not performing a wind consistency test (wind datasets from atmospheric reanalysis are not totally consistent with ice motion in the Fram Strait Van Angelen et al., 2011). Compared with the improved 2 SIV, the 1 day SIV generally has higher data density except for the period from end of January to beginning of March in 2018.

Figure 8

Times series of daily data density of SIV fields derived from Ifremer, Ocean and Sea Ice Satellite Application Facility (OSISAF) and improved algorithm in the winter of 2016–2017 (a) and 2017–2018 (b).

5 Sea Ice Area Flux Through the Fram Strait

Sea ice flux through the Fram Strait is a key component to influence the mass balance of the Arctic sea ice. Smudsrud et al. (2017) pointed out that the SIV is the leading parameter in estimating either ice volume or area flux. Here, we estimate the sea ice area flux out of Arctic Ocean using our new SIV and compare it with estimates of previous studies. In the literature, there are more area flux estimates (Bi et al., 2016; Kwok, 2009; Kwok et al., 2004; Smedsrud et al., 2017) than volume flux (Min et al., 2019; Ricker et al., 2018; Spreen et al., 2009, 2020; Zamani et al., 2019). Besides, in order to avoid the errors derived from ice thickness estimates, we focus on the sea ice area flux through the Fram Strait. The choice of location of the sea ice flux gate is different in previous studies. Smedsrud et al. (2017) and Spreen et al. (2009) use the gate of 79°N–80°N, while Zamani et al. (2019) use their gate at 81°N and 82°N. The gate at higher latitude is less affected by the northward warm current as well as ice melting. However, our improved SIV present higher ice velocity uncertainty in the region east to 0°W and at 80°N (not shown here), which is consistent with their low MCC in the marginal ice zone. Besides, the center of high SIV is mainly located in the region between 76°N and 79°N (Figure 6). Therefore, in this paper, we use the 79°N gate to estimate the sea ice area flux.

To readily compare with NSIDC-M estimate, we choose 1-day SIV to estimate the daily sea ice area flux. All daily SIV are reprojected into the grids along the 79°N gate from −16°W to approximately 7.5°E. Daily sea ice area flux is then calculated by 3:

(3)

The sea ice concentration (SIC) is the ARTIST Sea Ice sea ice concentration product derived from AMSR-E/AMSR2 satellite observations at 89 GHz distributed by the University of Bremen (Melsheimer & Spreen, 2019a, 2019b; Spreen et al., 2008); V southward ice velocity (unit: km/d); L is the grid spacing. In order to facilitate the flux calculation, we regrid the AMSR2 grid into equal-distance grid strictly along 79°N section. The SIV and SIC are also regridded into these equal-distance grids. N is the grid number of 16. All SICs and V are gridded into equidistant grids with 31.25 km spatial interval before calculation. Due to the different spatial coverage between these data sets on daily basis, we interpolate SIV along the 79°N transect by following rules: (a) If the number of valid ice velocity grid cells is lower than four (out of 16), the sea ice area flux is labeled as missing for that day; (b) If there are repeated missing values in the east part of the transect till the easternmost grid cell of the transect, these missing values are set equal to the easternmost valid value until the edge of open water (SIC < 0.15). (c) The missing values in the middle of the transect are interpolated by adjacent grid cells linearly.

We use the “valid data density” for statistics of the ratio of days of valid daily area flux based on above-mentioned rules and days per month. All monthly valid data densities are higher than 0.65 (Figure 9) and the minimum of 0.65 happen in January 2005. The median density per months is 0.91.

Figure 9

Spatial-temporal variation of monthly valid data density of SIV for the 79°N flux gate in this paper.

For the missing ice area flux dates because of the missing SIV estimates, we will use atmospheric parameter-estimate ice area flux instead. Following the linear relationship 4 reported in (Vinje, 2001), the missing daily area fluxes are interpolated by using a simple relationship based on the difference of sea level pressure between Svalbard and Greenland.

(4)

This relationship does not include any sea ice area related variability but the pressure difference is an often-used proxy for SIV variability in the Fram Strait (e.g., Smedsrud et al., 2017). We only use it to produce a gapless ice area flux time series. In most months more than 90% of the days are covered by satellite data (Figure 9) and the approximation by atmospheric parameters is not dominating our results.

Here, we compare our area flux with that derived from NSIDC-A. Due to its frequent missing values in the Fram Strait by NSIDC-A SIV data set, the daily area flux of NSIDC-A is lower than that of our new results in general (Figure 10). The correlation coefficient between the two is 0.20 in general. The correlation coefficient of our improved daily sea ice area flux (Equation 3) and the sea level pressure derived sea ice area flux (Equation 4) is 0.57, higher than that of NSIDC-A of 0.30. The average daily sea ice area flux derived from our improved SIV (1.23 × 10⁸ km²/d) is 59% higher than that from NSIDC-A (0.77 × 10⁸ km²/d) (Figure 10). The result means that the improved SIV present higher southward ice motion than NSIDC-A and thus a larger ice area flux out of the Arctic with the same used sea ice concentration.

Figure 10

Daily sea ice area flux across the 79°N transect of the Fram Strait derived from NSIDC-A (blue) and improved SIV in this paper, respectively. Data is available from October to April; gaps occur during summer.

Due to the sparse data density of NSIDC-A, it's hard to acquire reliable monthly sea ice area flux estimates. Here, we use NSIDC-M that has better spatial coverage than NSIDC-A for comparison on monthly basis. In addition, we also compare with the data derived from SAR SIV. This SAR area flux is based on the 3-day ice motion and corresponding sea ice concentration from 2004 to 2014 (Smedsrud et al., 2017).

The results (Figure 11a) show that the area flux derived from the new SIV retrieval method has a similar annual variation with SAR-derived area flux from 2002 to 2014, and the correlation coefficient between them is 0.85. For the same winter period, the correlation between NSIDC-M and SAR-derived area flux is 0.72 and increase to 0.85 when including the summer periods. The area flux derived from NSIDC-M SIV (61 ± 23 × 10³ km²) tends to be underestimated and is almost half of SAR-derived sea-ice area flux (104 ± 31 × 10³ km²). This underestimation of NSIDC data sets is consistent with its underestimation in southward SIV discussed above. All the three have the maximum ice area flux occurring in March and minimum occurring in the February (Figure 11b). The SAR SIV based and our new SIV based ice area flux show a similar intensity of seasonal cycle with the SD of 9.61 × 10³ and 10.24 × 10³ km², while the NSIDC-M based seasonal cycle is much weaker with the SD of 6.74 × 10³ km². Referring to the method used by Ricker et al. (2018) on calculating the uncertainty of sea ice volume flux, we estimate the uncertainty of sea ice area flux according to the equation as follows:

(5)

Figure 11

(a) Monthly sea ice area flux through 79°N transect through the Fram Strait from 2002 to 2017. The winter means (squares) are linked by dashed lines. (b) Seasonal cycle of sea ice area flux through 79°N transect.

The L means the width of the grid. The V and SIC mean the meridional ice velocity and sea ice concentration, respectively. In this paper, the σ_SIC is set to 10% and the σ_V are acquired from the retrieval procedure in Section 4.1. In general, the magnitude of uncertainty is close to half of the sea ice area and does not exhibit significant intraseasonal variation from October to April (Figure 11b).

6 Conclusions

In this paper, we improve the PM-based MCC SIV retrieval algorithm for the Fram Strait region by following three aspects: (a) We adjust the size of the template window to 14 × 14 based on comparison to higher resolution SAR SIV vectors; (b) We add the bilinear interpolation process on the candidate Tb fields before MCC calculation; (c) The spatial variable SIV uncertainties are estimated by MCC values. The improved algorithm is applied to the SIV retrieval based on 89 GHz Tb fields from October 2002 to December 2011 (AMSR-E); and October 2012 to December 2018 (AMSR2). The ice velocity with a 1 day time-span present faster ice motion than that with a 2 day time-span and can grasp the fast ice motion and fast variation of ice motion in low latitudes south of 80°N effectively. The new data set can capture higher ice velocities better and, thus also show the higher southward ice velocity through the Fram Strait. Most PM-based SIV tend to underestimate SIV in high ice velocity regions like the Fram Strait (Spreen et al., 2020; Sumata et al., 2014). Our SIV data is now not only comparable to SAR-based SIV estimates but also can cover a much longer time period and larger area.

The inter-comparison between four SIV data sets indicates that our improved data set can reproduce the fast ice motion and the center of high ice motion speed during winter. The SIV error of the improved ice velocity is similar to that of Ifremer-A but 17% lower than that of OSISAF-A data. Besides, its data density is 34% and 10% larger than of Ifremer-A and OSISAF-A, respectively, mainly due to its larger width of template window.

We also use the improved sea ice velocities to estimate sea-ice area flux through the 79°N transect. Our results are consistent with that derived from SAR-based SIV and is significantly higher than that from NSIDC SIV data sets. Hence, the improved SIV data set is confirmed to effectively improve the sea ice area flux estimates through the Fram Strait.

Acknowledgments

This work was supported by the National Natural Science Foundation of China [No. 41922044]; the National Key Research and Development Program of China [No. 2018YFA0605903]; the Guangdong Basic and Applied Basic Research Foundation [No. 2020B1515020025]; the Guangdong Basic and Applied Basic Research Foundation [No. 2019A1515110295]; and the Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) [No. 311021008]. Gunnar Spreen was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Transregional Collaborative Research Centre TRR-172 “ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)3” (grant 268020496).

Open Research

Data Availability Statement

Gridded brightness temperature used in this paper are achieved in the University of Bremen (https://seaice.uni-bremen.de/data). Sea ice concentration used in this paper are achieved at PANGAEA (https://doi.org/10.1594/PANGAEA.898399 & https://doi.pangaea.de/10.1594/PANGAEA.919777). The low-resolution sea ice drift from Ifremer are available at ftp://ftp.ifremer.fr/ifremer/cersat/products/gridded/psi-drift/quicklooks/arctic/amsre-merged/. The low-resolution sea ice drift from OSISAF are available at ftp://osisaf.met.no/archive/ice/drift_lr. The Sentinel-1 SAR sea ice drift data sets are achieved at CMS (https://resources.marine.copernicus.eu/product-detail/SEAICE_GLO_SEAICE_L4_NRT_OBSERVATIONS_011_006/INFORMATION). The IABP buoy data sets are achieved at ftp://iabp.apl.washington.edu/pub/IABP/. The Sentinel-1 SAR derived sea ice area flux produced by Smedsrud et al. (2017) are available at https://doi.org/10.1594/PANGAEA.868944. The improved sea ice velocity data sets in the Fram Strait, as well as the sea ice area flux estimates through the Fram Strait that produced in this paper are available at https://zenodo.org/record/5760228#.Ya2qfbgzbD4.