Sea ice export through the Fram Strait derived from a combined model and satellite data set

. Sea ice volume export through the Fram Strait plays an important role on the Arctic freshwater and energy redistribution. The combined model and satellite sea ice thickness (CMST) data set assimilates CryoSat-2 and Soil Moisture 15 and Ocean Salinity (SMOS) thickness products together with satellite sea ice concentration. The CMST data set closes the gap of stand-alone satellite-derived sea ice thickness in summer, and therefore allows us to estimate sea ice volume export during the melt season. In this study, we first validate the CMST data set using field observations, and then estimate the continuous seasonal and interannual variations of Arctic sea ice volume flux through the Fram Strait from September 2010 to December 2016. The results show that seasonal and interannual sea ice volume export vary from about -240 (±40) to -970 (±60) km 3 and 20 -1970 (±290) to -2490 (±280) km 3 , respectively. The sea ice volume export reaches its maximum in spring and the mean amount of the melt season ice volume export accounts about one third of the yearly total volume amountexport occurs in the melt season. The minimum monthly sea ice export is -11 km 3 in August 2015 and


Introduction
The sea ice extent and volume in the Arctic region undergo a decline for the past decades and will likely continue to decrease (Comiso and Hall, 2014;Meier et al., 2014;Stroeve and Notz, 2015). The decline of ice extent changes the surface albedo, and as a consequence, the absorption of solar shortwave radiation increases. The variability of ice volume, however, exerts influence on heat, freshwater budget and weather systems in the lower latitudes (Gregory et al., 2002;Tilling et al., 2015). 30 Correspondingly, both the thermodynamic processes and dynamic processes can affect Arctic sea ice mass budget (Ricker et al, 2018). The sea ice outflow driven by atmospheric circulation is an important component of dynamic processes. The Fram Strait serves as the primary outlet of the Arctic sea ice export (Krumpen et al., 2016). Moreover, the ice outflow through the strait into the Nordic Seas covers approximately 25% of the total Arctic freshwater export (Lique et al., 2009;Serreze et al., 2006). 35 Variations of satellite-based Arctic sea ice volume and sea ice export through the Fram Strait have been estimated by numerous studies (Bi et al., 2018;Kwok and Cunningham, 2015;Ricker et al., 2018;Spreen et al., 2009). Nevertheless, with respect toin terms of the volume flux, the primary focus of these studies are the variations during the winterfreezing season (October-April). This is mainly due to the limitations in retrieving sea ice thickness and motion by satellite remote sensing during the melt season (May-September). It is mainly caused by more melt ponds and statured water vapor in the sea ice surface, which 40 restrains satellite-based ice thickness limited to the cold season only (Mu et al., 2018a). The speed-up of sea ice drift usually accompanies with thin summer sea ice, meanwhile the faster sea ice drift the larger retrieving errors there would be (Spreen et al., 2011;Sumata et al., 2014). Melting sea ice with a less scattering surface could significantly suppress the signal-to-noise ratio and obstruct the employment of satellite imagery to retrieve ice drift. For above-mentioned reasons, the spaceborne sea ice drift data usually induce much more uncertainties in the melt season. All these deficiencies make the estimate of the Arctic 45 sea ice thickness and drift variations all year round difficult with only satellite sea ice data.
Sea ice volume flux, compared to area flux, could reflect the sea ice mass balance in a more comprehensive way. However, the amounts of Fram strait sea ice volume export during the winterfreezing season do not demonstrate a conspicuous growth or decline trend (Ricker et al., 2018;Spreen et al., 2009). And the variation of the melt season ice volume flux through the Fram Strait still remains a query owing to the fact that sea ice thickness observations are sparse in the melt season, and so does 50 the yearly total amount of ice volume flux. In terms of sea ice volume flux, Ricker et al. (2018), Bi et al. (2018) and Zamani et al. (2019) point out that the variation of ice drift plays the major role in determining the annual and interannual ice volume export variability. Due to thermodynamic growth and deformation, the sea ice thickness on the other hand drives the increase in the seasonal cycle of the exported volume. For this reason, an accurate data set of sea ice drift and thickness is crucial to better estimate sea ice volume output. However, the limitations of spaceborne sea ice thickness and drift data during the melt 55 season poses a great challenge to derive the sea ice flux.
Employing the benefits of both the CryoSat-2 (CS2) and the Soil Moisture and ocean Salinity satellite (SMOS) sea ice thickness products, the new data set (combined model and satellite thickness, CMST) that assimilates these data together with satellitederived sea ice concentration (Mu et al., 2018a;Mu et al., 2018b) provides the daily sea ice thickness, concentration and drift estimates simultaneously. Moreover, taking advantages of model dynamics and sea ice concentration assimilation, the new sea 60 ice data set extends to cover the melt season when satellite thickness data are limited (Mu et al., 2018a). Previous results reveal that CMST data even have some advantages among the statistically merged satellite data CS2SMOS and Pan-Arctic Ice-Ocean Modelling and Assimilation System (PIOMAS) thickness product when comparing with the in-situ observations (Mu et al., 2018a). Therefore, the CMST sea ice product enables us to examine the all-year-round changes in sea ice volume export through the Fram Strait for 2010-2016, during a time when Arctic sea ice is undergoing dramatic changes. Further, we also 65 calculate the sea ice thickness, concentration and drift frequency distributions along the main sea ice export gate all-yearround.
This paper is organized as follows. Section 2 describes the data used to derive volume flux and validate the CMST data set and the method used to derive the volume flux, including CMST data set, OSISAF, NSIDC and Sentinel-1 SAR sea ice drift, HEM sea ice thickness and ULS thickness. In section 3, firstly, we evaluate the performance of CMST data. Then, we estimate 70 the continuous seasonal and interannual variation of sea ice thickness, concentration and drift in the Fram Strait. Also, the allyear-round variability of sea ice volume export though the Fram Strait is calculated. Uncertainty in our volume flux estimate is discussed in Section 4. Concluding remarks are given in Section 5.

CMST sea ice data 75
The CMST sea ice data in addition to ice thickness and concentration also provide the modelled ice drift velocities. They estimation data are generated by an Arctic reginal ice-ocean model accompanying with CS2, SMOS sea ice thickness and SSMIS sea ice concentration assimilationed. This Arctic regional model (Losch et al., 2010;Mu et al., 2017;Nguyen et al., 2011;Yang et al., 2014) is configured on the basis of the Massachusetts Institute of Technology generation circulation model (MITgcm) (Marshall et al., 1997). To reflect the impacts of atmospheric uncertainties on the sea ice data assimilation, the 80 atmospheric ensemble forecasts of the United Kingdom Met Office (UKMO) Ensemble Prediction System (EPS; https://www.ecmwf.int/en/research/projects/tigge http://tigge.ecmwf.int) are used as atmospheric forcing (Mu et al., 2018b;Yang et al., 2015;Yang et al., 2016). The Parallel Data Assimilation Framework (PDAF, Nerger and Hiller, 2013; http://pdaf.awi.de) is applied to assimilate satellite thickness (e.g., SMOS thickness data thinner than 1 m and weekly mean CS2 thickness data) and concentration data (provided by the Integrated Climate Data Center, http://icdc.cen.uni-hamburg.de). 85 More details about this assimilation process can be found in previous studies (Mu et al., 2018a;Mu et al., 2018b). CMST provides grid cell-averaged ice thickness, i.e., the effective ice thickness (Mu et al., 2018a;Schweiger et al., 2011) with a resolution about 18 km. Further taking advantage of model dynamics and ice concentration assimilation, the daily CMST thickness data in summer are also available from OctoberSeptember 2010 to December 2016. Although the time span of CMST data do not contain span the recent two years (i.e., year of 2017 and 2018), it does cover the year of the lowest sea ice extent 90 record at that time (i.e., 2012 and 2016) (Parkinson and Comiso, 2013;Petty et al., 2018).

OSI SAF drift data
As suggested by Sumata et al. (2014), the merged OSI SAF sea ice drift product (OSI-405) reveals a better performance than other low-resolution sea ice drift products in the Fram Strait. Thus, we use it for comparison with CMST drift data when calculating sea ice volume export. The merged drift data can be download from the Ocean and Sea Ice Satellite Application 95 Facility (OSI SAF, http://www.osi-saf.org/?q=content/sea-ice-products). The merged drift products are retrieved from multiple sensors and channels (shown in

NSIDC sea ice drift 100
The latest released Polar Pathfinder Daily 25 km EASE-Grid sea ice drift data from the National Snow and Ice Data Center (NSIDC, https://nsidc.org/data/nsidc-0116/versions/4) are also used to evaluate the CMST drift too. These data cover both the melt season and the freezing season and widely used in the modeling and data assimilation (Miller et al., 2006;Stark et al., 2008). The input sea ice motion data sets are obtained from AVHRR, AMSR-E, SMMR, SSM/I, SSM/I, International Arctic Buoy Program (IABP) buoys and National Center for Environmental Prediction (NCEP) / National Center for Atmospheric 105 Research (NCAR) Reanalysis wind data. More descriptions can be seen in the NSIDC ice motion user guide (https://nsidc.org/data/nsidc-0116/versions/4).

Sentinel-1 SAR sea ice drift
To further validate the CMST sea ice drift in the Fram Strait, the sea ice drift data retrieved from Sentinel-1 Synthetic Aperture Radar (SAR) images are used as the reference products (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5999601/). Based on 110 the different polarization channels, thousands of HH and HV polarization images are calculated as monthly mean sea ice drift at 79°N along the gate from 15°W to 5°E (Muckenhuber et al., 2018). These SAR drift data are derived by an open-source feature-tracking algorithm (Muckenhuber et al., 2016). Owing to the better performance of the HV polarization channel (Muckenhuber et al., 2016), we only use the southward velocity component of HV polarization for the validation. More information about the Sentinel-1 SAR sea ice drift can be obtained in the previous studies (Muckenhuber et al., 2016;115 Muckenhuber et al., 2018).

HEM sea ice thickness
For the purpose of evaluating the performance of CMST sea ice thickness, the helicopter-borne electromagnetic induction sounding (HEM) sea ice thickness (https://data.npolar.no/dataset/1ed8c57e-8041-42fd-95bb-cfe4e181e9b8) is utilized for intercomparision. This HEM measurement campaigns consist of 9 separate flights implemented in the Fram Strait from August 120 to September, 2014. The helicopter-measured sea ice thickness is named as "total thickness" including snow layer. Thus, following Krumpen et al. (2016), we assume the thickness of snow or weathered ice is 0.1 m, i.e., we subtract the 0.1 m snow thickness from the "total thickness" in the later calculation. Sea ice concentration is low in the operational areas during this period and the data have not been adjusted with sea ice concentration. Because the CMST model thickness are effective thickness (e.g.i.e., mean thickness over one the model grid), for easy comparison, and as recommended by the data providers 125 (https://data.npolar.no/dataset/1ed8c57e-8041-42fd-95bb-cfe4e181e9b8), we adjust this data with the CMST ice concentration to obtain daily mean ice floe thickness.

ULS sea ice thickness
The upward looking sonars (ULS) measurement (moored at 79°N, 5°W) in the Fram Strait is deployed and maintained by the Norwegian Polar Institute. Since ULS measures sea ice draft, the derived sea ice thickness is less affected by uncertainties in 130 the snow layer depth and ice density. Moreover, the ULS provides year-round measurements and are therefore used to validate the CMST thickness. More details about the ULS data can be found in previous work (Hansen et al., 2013). In this study, we use a 1-year data set of monthly mean sea ice thickness from September, 2010 to August, 2011.

Retrieving methods in sea ice volume export
The sea ice thickness, concentration and drift in CMST data set are provided on the a cube-spherical sphere Arakawa C grid 135 with a resolution of 18 km. Both sea ice variables in CMST and the OSI-405 merged data are projected to the geographic coordinates at first. Following Krumpen et al. (2016) and Ricker et al. (2018), we define the Fram Strait export gate with zonal and meridional components as shown in Figure 1. The zonal gate is situated at 82°N between 12°W and 20°E, and the meridional gate is located at 20°E between 80.5°N and 82°N. The chosen gates are dedicated to decrease errors and bias in low resolution drift data and thickness data from satellite (Krumpen et al., 2016;Ricker et al., 2018). Secondly, we use linear 140 interpolation method to interpolate the CMST data and OSI SAF data onto the zonal gate with a spatial resolution of 1° and onto the meridional gate with a spatial resolution of 0.15°, which is of the purpose to better match the model grids with the interpolated grids.
Following Ricker et al. (2018), we also define the negative values represent ice volume loss from the Arctic Basin through the outlet and the sea ice volume flux can be estimated as following formulas: 145 where Lx is the size of zonal interpolated grid while and Ly is the size of meridional interpolated grid. Hx and v are the interpolated effective ice thickness and meridional velocity at the zonal gate. Hy and u are the interpolated effective ice thickness and zonal velocity at the meridional gate. Note that ice concentration information is not involved in equations (1)  150 and (2) because the calculation process of CMST model effective ice thickness has already taken ice concentration information into account.
The total sea ice volume export (QEX) through the Fram Strait is obtained by adding the zonal ice volume flux (Qx) and meridional ice flux (Qy) together: Uncertainties of sea ice volume export (δ Q x ) are evaluated as: This strategy is used to estimate the expected uncertainties of volume flux via the zonal gate. δv and δH represent ice drift uncertainty and ice thickness uncertainties, respectively. Expected sea ice volume flux uncertainties along the meridional gate can be determined by the similar method of (4). 160 Detailed sSea ice volume export derived from CMST thickness and drift areis represented by M2 in detail in Table 2 (Section 3.2). The results derived from CS2 thickness and OSI SAF drift for Ricker et al. (2018) are represented by R. To investigate the flux biases (R vs M1) due to the existing deviations between the CMST and the CS2 thickness data, ice thickness from CMST thickness and ice drift from OSI SAF drift are also used to calculate the flux that is shown by M1.

Validation of CMST data
Firstly, the field and satellite-based observations are used to evaluate the performance of CMST sea ice data in the Fram Strait.
The mean sea ice drift and thickness of nearly 6 years' CMST data are shown in Figure 1a. The mean sea ice thickness is distributed as expected (Tilling et al., 2015;Kwok et al., 2018), i.e.e.g., the relatively thicker ice, which is more than 2.5 m, mainly distributes in the north of Greenland and the Canadian Arctic Archipelago and the sea ice becomes thinner towards the 170 Eurasia coasts (Figure 1a). We then compare the mean difference between the CMST drift and the latest released sea ice drift data (V4) from the NSIDC. The circulation patterns (the Transport Drift and the Beaufort Gyre) and magnitudes distributions of the two sea ice drift data (CMST vs. NSIDC) are quite similar (Figure not shown). The relatively larger differences of sea ice drift speed are found in the southwestern Greenland Sea along the coast of Greenland and ice edge, which is shown in Figure 1b. It is noticeable that the mean sea ice drift speed of CMST is larger than the NSIDC in most areas. This may suggest 175 that the CMST sea ice drift performs better than NSIDC drift data in the Fram Strait for that NSIDC drift data usually exist underestimations in sea ice velocity (Sumata et al., 2015;Sumata et al., 2014). For further validation of CMST sea ice velocity, we compare the CMST southward velocities that affect sea ice volume flux most with high-resolution Sentinel-1 SAR sea ice drift data. Results (Figure 1c and 1d) show that both CMST drift and NSIDC drift generally overestimate the southward velocities near the Greenland but underestimate the velocity far away from the Greenland. Although biases are found with 180 respect to SAR drift dataNevertheless, monthly mean CMST drift data show a better performance than NSIDC drift data especially near the Greenland.
Further assessments of CMST thickness and drift data are shown in Figure 2. The geography map (Figure 2a) shows the trajectories of HEM measurement campaigns and the site of ULS. Helicopter-borne daily mean sea-ice thickness is first used to evaluate the CMST thickness data in the Fram Strait in this study. Monthly CMST sea ice thickness is also compared with 185 the thickness derived from the ULS data (shown in Figure 2c). Note that the comparison period for CMST thickness and ULS thickness is from September 2010 to August 2011, since the ULS data afterwards have not been available for this study.
Monthly mean CMST sea ice drift over the entire Fram Strait gate is evaluated with OSI SAF drift used in Ricker et al. (2018) within the same period from September 2010 to December 2016 and the same domain defined before. For quantitative metrics, The correlation coefficient (CC), the relative bias (RB) and the root-mean-squared error (RMSE) are explored to quantify the 190 comparison. These statistic metrics are calculated as follows (Chen et al., 2013;Zhang et al., 2019): where "Cov()" represents the covariance operator, "σ" is the standard deviation, and the sizenumber of the "OBS" denotes the observations (OBS) is indicated by Nand "N" denotes the number of samples, respectively.
Statistical analysis between CMST and HEM sea ice thickness shows that the CC, RB and RMSE are 0.59, 15.13% and 0.66 200 m, respectively. Furthermore, statistics indicate that the CMST data is comparable to ULS measurements with a CC of 0.68, a low RB (1.74%) and RMSE (0.328 m). Note that the CMST thickness has been already quantitatively evaluated with more observation records by a previous study (Mu et al., 2018a) and exhibits some advantages over the widely used CS2SMOS and PIOMAS thickness data. The CC between CMST drift and OSI SAF drift shows a high correlation of 0.93 (Figure 2d) in the freezing season (October-April). The RB (-6.05%) and RMSE (0.985 km d -1 ) are also relatively quite low. These statistical 205 metrics suggest a good performance of CMST over the Fram Strait outlet in simulating reproducing the real sea ice drift and thickness.

Sea ice thickness, concentration and drift variation
In this study, the spring, summer, autumn and winter span from March to May, June to August, September to November and December to February, respectively. For convenience, so we define the spring (March-May), summer (June-August), autumn 210 (September-November) and winter (December-February) periods, respectively. The continuous and all-year-round covered seasonal variation of Arctic sea ice thickness and concentration are shown in Figures 3 and 4. During the study period, both the Arctic sea ice thickness and concentration show a significant seasonal variation, e.g., the sea ice thickness reach its maximum in spring (except for 2013), while the sea ice concentration has a peak value in spring/winter. Figure 3, the distribution of sea ice thickness along the Fram Strait zonal gate features thicker sea ice in the east 215 of Greenland than that in the west of Svalbard, showing a gradually thinning trend from west to east. And along with the meridional gate, sea ice is thickening from the northern Svalbard to the central Arctic Ocean, which is in line with other studies (Hansen et al., 2013;Kwok et al., 2004;Krumpen et al., 2016;Vinje et al., 1998). Note that the sea ice thickness hits its minimum in the autumn of 2011, and such anomaly is also found in previous studies based on sea ice satellite data (Kwok and Cunningham, 2015;Tilling et al., 2015). Also, it is notable that the mean thickness of the winter 2013 arises a significant 220 thickening comparing with other winters. This remarkable thickening may be linked to the anomalously cooling in 2013 which enhances the thermodynamic ice growth (Tilling et al., 2015). respectively. We also compare these sea ice variables with Ricker at al. (2018). The results show that the CMST ice thickness and drift are smaller than that of CS2 and OSI SAF, while the CMST ice concentration is a little larger than OSI SAF ice concentration. The Such underestimation ofthinner CMST sea ice thickness found in the Fram Strait is discussed to be 235 reasonable ( Figure 6 in Mu et al., (2018b) because of the assimilation of SMOS thickness data. The previous study shows that the mean Arctic-wide OSI SAF drift is slightly larger than IABP/D buoy ice drift (Sumata et al., 2014), which suggests the slight underestimation of CMST drift seems also tenable. Further validation with more ice drift data over the Arctic basin (e.g., buoy drift data) is needed; however, it is beyond the scope of this work. In terms of variation trend, they are in good agreement with those of Ricker at al. (2018). As shown in Figures 5 and 7, the averaged sea ice thickness and drift reveal a significant 240 seasonal cycle. That is, the variations of sea ice thickness and motion always accompany with spring augment increase and autumn decrease. The analysis of ice concentration shows a steadily low values in the melt season. And the 6-year mean sea ice thickness, concentration and drift averaged over the entire Fram Strait gate are about 1.7 m, 85% and 5 km d -1 .

As shown in
Following Ricker et al. (2018), the relative standard deviation (RSD=SD/mean) is used to measure the effects of different sea ice variables on the variability of the ice volume output. Variables with a lager RSD contributes to a greater impact on the 245 volume variation. As shown in Figures 5, 6 and 7, the RSD of ice thickness is 0.30 which is about twice of ice concentration (0.14). The RSD of ice drift is 0.50 which is the largest contributor with an RSD of 0.50. It is shown that the ice drift with maximal RSD is more likely to affect variations in sea ice volume flux, which is corresponding to the previous findings in where n represents the number of the grid cells accounted by in the different thickness bins, and N grids is the sum of n over all 255 the bins. As suggested by Figure 8, the thickness along the zonal gate is much thicker than the meridional gate. Thin ice is more observed in Autumnautumn and winter over the zonal gate according to the RF distribution in Figure 98. Although the maximum thickness over the entire Fram Strait occurs in May and June (Figure 5), higher RF in thick ice bins are found in summer (June, July and August in our definition) over zonal gate. Over the meridional gate, the ice thickness in summer and spring is almost uniformly distributed, while in Augustautumn and Winterwinter, high RFs are more found in thin ice bins. In 260 statistics, the seasonal mean sea ice thickness thicknesses are 2.06 m for spring, 2.11 m for summer, 1.32 m for autumn and 1.43 m for winter over the entire outlet, respectively. Nevertheless, the mean relative frequency of sea ice drift distribution ( Figure 9) shows that the ratio of summer sea ice drift lower than 6 km d -1 is in the majority (more than 90% of zonal gate) indicating that the sea ice drift is much slower than other seasons. Also, the ice drift along the zonal gate is usually faster than the meridional gate and the meridional sea ice velocities are slower than 6 km d -1 during summer. The seasonal mean sea ice 265 velocity over the entire gate is larger than 5 km d -1 except that is 3 km d -1 in summer. And it can be found that the spring and winter ice concentration along the zonal gate is larger than that of summer and autumn.

Sea ice volume export through the Fram Strait
In this section, sea ice volume export over all seasons is investigated. Firstly, the examination of monthly Arctic sea ice volume export through the Fram Strait is demonstrated shown in Table 2. Both our results and Ricker et al. (2018) find that the 270 maximum monthly sea ice export takes place in March 2011. The maximum of CMST data is -442 km 3 that is less than that (-540 km 3 ) of Ricker et al. (2018). Consistently, the lowest sea ice output for each study occurs in February 2011 when excluding the melt season (May-September). The minimum of the results shown in Ricker et al. (2018) is -21 km 3 while that is -34 km 3 in CMST data. Although there are some differences in flux calculated based on CMST data and CryoSat-2 thickness and OSISAF drift data, both the estimations show a similar trend in annual cycle. Furthermore, the CMST data can provide sea ice 275 variables (e.g., sea ice thickness, concentration and drift) in the melt season that remote sensing retrieval data cannot cover.
Taking advantage of CMST data, this study is trying to fill the research gap in the summer sea ice volume export. It is found that another minimum of ice export occurs in August 2015 because of the rather slow mean sea ice velocity (shown in Figure   11) during the study period. The minimum value for CMST is -11 km 3 that is 10 km 3 less than -21 km 3 (R) in February 2011 and 23 km 3 less than that for M2. 280 Moreover, the seasonal variation of sea ice export though Fram Strait is shown in Figure 10. The ice volume output shows a significant seasonal variation. The seasonal maximums are found in spring of all years (2011-2016) and the low values usually occur in summer and autumn. The maximum seasonal ice export of -970 (±60) km 3 (sea ice volume export has been rounded off to significant figures in seasonal and interannual time scales) takes place in the spring of 2012 owing to both simultaneously faster ice drift and thicker ice thickness, while the minimum flux of -240 (±40) km 3 occurs in autumn of 2016 caused by 285 simultaneously rather slower ice motion and thinner ice thickness. Unlike in other autumns ice export, the ice volume export of autumn 2013 abnormally increases and reaches -620 (±60) km 3 . This abnormal increase can be also explained by the faster ice drift (shown in Figure 9).
Furthermore, we standardize the sea ice volume export, ice drift and thickness and then calculate the correlations of determination (R 2 ) between monthly sea ice volume export and thickness, and also for sea ice drift (shown in Figure 11). R 2 290 between For monthly mean sea ice flux and drift drift, R 2 is 0.77, which is much higher than that against thickness R 2 (QEX, thickness) =( 0.16). This result shows that the sea ice drift variation contributes more to sea ice flux variation on its monthly variability. However, when averaged over seasonal time scale, both the sea ice drift and thickness become significant factors for their close R 2 within the range of 0.36-0.46. Analogously, this conclusion was pointed out by Ricker et al., (2018) and Haibo Bi et al., (2016). In addition, the Arctic Oscillation (AO) and North Atlantic Oscillation (NAO) index are used to analyze 295 the possible links between atmospheric circulation and sea ice volume flux through the Fram Strait ( Figure 12). The AO and NAO indexes index are both downloaded obtained from National Oceanic and Atmospheric Administration (NOAA). We calculate the seasonal mean AO and NAO index and find that the correlation of ice volume flux against AO index (0.55) is higher than that against NAO index (0.34). Both of our study and Ricker et al. (2018) find that the AO may influence the sea ice export (2011-2016) more directly. 300 The CMST-based sea ice volume during both the melt season and the freezing season are is first reported in this study. The estimations show that the mean ice volume export during the melt season is -750 (±120) km 3 which is about half of that during the freezing season (-1500±160 km 3 ). Annually, sea ice volume export ( Figure 13) is also calculated-2250 km 3 and varies from -1970 (±290) to -2490 (±280) km 3 . It is verified again that the annual sea ice volume export through the Fram Strait does not show a significant growth or decline trend (Ricker et al., 2018;Spreen et al., 2009). And the minimummaximum yearly ice 305 volume export occurs in the year of 2013 2012 while the ice volume export reaches its maximumminimum in 20132012. This decline in ice volume export derives from the decreases of both mean thickness and drift speed drop though the Fram Strait.

Discussions
The ensemble standard deviation (SD) map of CMST ice concentration, thickness and drift shows that uncertainties are larger downstream the east of Greenland (Figure 14). SoTherefore, following Krumpen et al. (2016) and Ricker et al. (2018), a 310 different gateway over the Fram Strait that consists of a zonal gate and a meridional gate located at a slightly higher latitude comparing to previous studies is chosen Kwok and Rothrock, 1999;Spreen et al., 2009). Alternatively, the choice of lower latitude gate at 79°N (e.g., the ULS moored sites) is suggested to utilize the ULS thickness for rough volume flux calculation when ice thickness data is unavailable. It should be noted that the studies at different locations of Fram Strait gates and study over different periods will introduce deviations on the final ice volume estimation (Krumpen et al., 2016;315 Kwok et al., 2004;Kwok and Rothrock, 1999;Ricker et al., 2018;Spreen et al., 2009). For example, Ricker et al. (2018) investigated the sea ice flux in the Fram Strait and pointed out that the maximum (-540 km  We investigate the similar period with Ricker et al. (2018), but further extend the sea ice volume flux estimation to include the summermelt seasons. Also, the CMST sea ice thickness data used in this study are evaluated to be reasonable when compared with in-situ observations (Mu et al., 2018a). The other important driver (sea ice drift) of ice volume export has also been compared with OSI SAF drift used in former estimations (Ricker et al., 2018) and Sentinel-1 SAR sea ice drift. The monthly mean CMST ice drift of CMST data show a better performance than NSIDC drift data (Figure 1), and meanwhile, a good 325 consistency is found between CMST drift and OSI SAF (Figure 2d and Figure 7) drift.The monthly mean ice drift of CMST and OSI SAF shows a good consistency (Figure 2d and Figure 7). Furthermore, the CMST ice drift can provide the absent values where remote sensing data cannot detect. TOverall, the estimation of volume export in this study reveals a reasonable sea ice volume export all year round.
The nearly 6 years' ice volume export through the Fram Strait is calculated and shown in Table 2. Besides the ice volume 330 export (R) of Ricker et al. (2018), we also calculate the export using OSI SAF drift and CMST thickness (M1), and also using CMST thickness and drift (M2), respectively. It can be concluded that R is larger than M1 and M2 because R is derived from thicker CS2 thickness ( Figure 5) and relatively faster OSI SAF drift (Figure 7). In addition, M1 is generally larger than M2 also due to the faster OSI SAF ice motion for most periods. There are also cases that M2 is sometimes larger than M1 owing to the largerwhen CMST CMST has higher ice motion than that of OSI SAF,. Ffor example, in March, April and November 335 there are five months of M2 in the freezing season ofof 2014 that. Ricker et al. (2018) gave their multi-year averaged volume export of -1711 km 3 in the freezing season. Our average estimate (M2) based on the CMST ice thickness and drift is -1580 km 3 while the volume flux (M1) derived from CMST thickness and OSI SAF drift is -1600 km 3 in the freezing season. The similar results between M1 and M2 are because that the CMST drift deviates minorly to OSI SAF drift in the cold seasons.
But more reliable validations of CMST ice drift need more in-situ records and more systematic evaluations. are larger than 340 M1. One reason is that both M1 and M2 are based on the same CMST thickness but the CMST sea ice drift is faster than OSI SAF in the months of March, April and November.
We have calculated the ice export in the zonal gate and the meridional gate covering both the melt season and the freezing season, respectively. The ice volume export through the meridional outlet shows a more robust increase from autumn to spring while the annual mean meridional ice export is only 8% of zonal gate (shown in Figure 10). To further validate the sea ice 345 volume export in the melt season, we compare our CMST-based volume flux (e.g., M2) with the relative short-term summer ice volume flux that Krumpen et al. (2016) derived from airborne ice thickness and NSIDC ice drift data on the same export gates. The intercomparison shows that the sea ice volume export in August 2011 and July 2012 estimated by Krumpen et al. (2016) are smaller than this study. The underestimation of summer sea ice volume may deduce from a general underestimation of NSIDC drift during the melt season (Krumpen et al., 2016;Sumata et al., 2015;Sumata et al., 2014). 350 Through the Fram Strait gate located at ~79°N, Additionally, Kwok et al. (1999 and2004) investigated the summer sea ice export by using ULS thickness and area flux in the freezing season. The average annual ice volume flux is -2218 km 3 yr -1 from 1991 to 1998 while the mean sea ice volume export from 1990 to 1995 is -2366 km 3 yr -1 Kwok and Rothrock, 1999). The annual average volume flux in this study is -2250 km 3 yr -1 that is similar to the volume flux from 1991 to 1998  and a little smaller than the period of 1990-1995(Kwok and Rothrock, 1999. To compare with 355 previous studies Kwok and Rothrock, 1999;Vinje et al., 1998), we also calculate the sea ice volume flux through the Fram Straitsame gate located at 79°N, which completely follows previous work Kwok and Rothrock, 1999;Vinje et al., 1998). Results (Figure 15) show that our annual mean sea ice volume export (-1352 km -3 ) is smaller than previous these studies (Vinje et al. 1998, which is expected because of the decline of sea ice thickness in recent decades. All these works show consistent seasonality with maximum export in March 360 and minimum export in August. In a recent study (Wei et al., 2019), Wei et al. (2019) calculateds the annual mean sea ice volume export (-3216 km 3 yr -1 ) through the Fram Strait using MITgcm-ECCO2 from their simulation during 1979 to 2012.
Their estimations give a long period of sea ice volume export through the Fram Strait which can serve as an important reference when focusing on the long-term trend and the variations of the volume flux. However, this estimation derived from MITgcm-ECCO2 seems to overestimate the volume flux owing to the overestimations of sea ice drift and thickness (Wei et al., 2019). 365 Therefore, the CMST data which assimilates CS2 and SMOS sea ice thickness and SSMIS sea ice concentration simultaneously have more advantages in calculating sea ice volume and extent export. Ricker et al. (2018) and Bi et al. (2018), gave their averaged freezing season volume export that are of -1711 km 3 and -1463 km 3 , respectively, based on the CS2 thickness data and different ice drift data over a similar period and outflow gates. Our average estimate of QEX,CMST,CMST (e.g., M2) based on the CMST ice thickness and drift is -1580 km 3 while the QEX, CMST, OSISAF (e.g., M1) derived from CMST thickness and OSI 370 SAF drift is -1600 km 3 in the freezing season. The similar results between M1 and M2 are because that the CMST drift are comparable with OSI SAF drift in the cold seasons. But more reliable validations of CMST ice drift need more in-situ records and more systematic evaluations.

Conclusions
The daily CMST data over all seasons are first used to estimate ice volume export through the Fram Strait. Also, benefitting 375 from the advantage of CMST data, the melt season (e.g. summer season and autumn season) ice volume export can be derived to fill the satellite data gap over such periods. The entire seasonal and interannual variations of Arctic sea ice volume are helpful for communities that focus on climate teleconnection between Polar regions and low latitudes, Arctic freshwater transport and ocean circulation. Conclusions of this study can be drawn as follows: occur in spring and the Arctic sea ice volume hits its minimum in autumn 2011 during the study period.
(2) Along the entire Fram Strait gate, the relative standard deviation (RSD) of ice drift (0.50) is greater higher than the RSD of ice thickness (0.30) and concentration (0.14), demonstrating that ice drift is a main driver of ice volume export through the Fram Strait. The correlations of determination (R 2 ) also show that sea ice drift is a much more important contributor for sea ice volume export on its monthly variabilityscale. 385 (3) The mean sea ice volume export during the melt season is around -750 (±120) km 3 which is about 50% of that during the freezing season (-1500±160 km 3 ). The lowest and largest annual sea ice volume export occur in 2013 and 2012, respectively.
Seasonal sea ice volume export varies from -240 (±40) to -970 (±60) km 3 , while the monthly sea ice export varies between -11 km 3 (August of 2015) and -442 km 3 (March of 2011) during this study period. The abnormal ice volume export increase in autumn 2013 is primarily associated with the faster ice motion. 390 (4) Seasonal variations of The relative frequency (RF) of seasonal variation of CMST sea ice thickness shows that the mean fraction of spring and summer sea ice that is thicker than 2 m in spring and summer is larger more than that in other seasons.
The mean ratio of summer seasonsummer mean ice drift that is lower than 6 km d -1 is in the majority in each year.
The long-term series of sea ice volume export are more important for ocean-climate analysis. An updated and improved CMST V2 sea ice data will be developed in the near future, so to obtain that a longer ice volume exported estimations can be expecteda 395 long-term record for climate research.     -150 -267 -287 -289 -196 -194 -113 -198 -75 -97 -72 -222 525