Investigation of spatiotemporal variability of melt pond fraction and its relationship with sea ice extent during 2000-2017 using a new data

The accurate knowledge of variations of melt ponds is important for understanding Arctic energy budget due to its albedo-transmittance-melt feedback. In this study, we develop and validate a new method for retrieving melt pond fraction (MPF) from the MODIS surface reflectance. We construct an ensemble-based deep neural network and use in-situ observations 15 of MPF from multi-sources to train the network. The results show that our derived MPF is in good agreement with the observations, and relatively outperforms the MPF retrieved by University of Hamburg. Built on this, we create a new MPF data from 2000 to 2017 (the longest data in our knowledge), and analyze the spatial and temporal variability of MPF. It is found that the MPF has significant increasing trends from late July to early September, which is largely contributed by the MPF over the first-year sea ice. The analysis based on our MPF during 2000-2017 confirms that the integrated MPF to late 20 June does promise to improve the prediction skill of seasonal Arctic sea ice minimum. However, our MPF data shows concentrated significant correlations first appear in a band, extending from the eastern Beaufort Sea, through the central Arctic, to the northern East Siberian and Laptev Seas in early-mid June, and then shifts towards large areas of the Beaufort Sea, Canadian Arctic, the northern Greenland Sea and the central Arctic basin.

ponds were estimated during the expedition. The MPFs from HOTRAX used in the network training were measured at 77°-79°N and 84°-87°N on 13, 21, 29 August and 6 September 2005. The coverage of each MPF measurement is about 57 m×70 m. The obtained measurement from HOTRAX is the MPF relative to the grid (the coverage of each observation). The data can be found at http://psc.apl.uw.edu/data/.
• DLUT: MPFs were collected during two Chinese Arctic Research Expeditions by the Dalian University of Technology (DLUT, Lu et al., 2010;Huang et al., 2016). The first survey of DLUT was conducted from July to September 2008 during the third Chinese Arctic Research Expedition. During the cruise, eight helicopter flights were conducted and more than 9000 aerial images were obtained in the Pacific sector of the Arctic. The MPF was estimated from the digital image with a camera resolution of 3264×2248 pixels. The flight altitude generally varied around 100 m according to weather conditions. At this height, each snapshot covers an area of approximately 98 m×67 m (Lu et al., 2010). The second survey of DLUT was conducted from July to September 2010. The underway ship-and helicopterbased ice observations were primarily in the Chukchi Sea, Beaufort Sea, Canada Basin and Central Arctic Ocean. The images were classified into three distinct surface categories (sea ice/snow, water and melt ponds). The areal fraction of each category is determined by a camera resolution of 3264×2248 pixels. The flight altitude varied between 150 m to 500 m. Each image covers an area between 147 m×100 m and 490 m×335 m (Huang et al., 2016). The images from the two cruises are spaced without overlapping, and each image represents an independent scene. The DLUT MPF used in the network training was measured at 84°N and 86°N on 20 August 2008 and 13 August 2010. The coverage of each MPF estimated from the airborne image is about 98 m×67 m (first survey), 147 m×100 m and 490 m×335 m (second survey). The obtained measurement from DLUT is the MPF relative to the grid (image area).
• TransArc: MPFs were collected from the ice breaker RV Polarstern during the Germany Trans-Polar cruise ARKXXVI/3 (Nicolaus et al., 2012, hereafter referred to as TransArc). The TransArc conducted from August to October 2011. Visual observations of sea ice conditions were performed hourly from the bridge of Polarster. Sea ice type and thickness, snow depth, pond coverage, and surface scattering layer depth were recorded during the cruise. The observations followed the ASPeCT protocol with additional observations on melt ponds. It should be noted that the TransArc MPF was recorded on multiyear and first-year ice respectively for some cases, the MPF was estimated by using the linear mix of these values. The recording visibility in TransArc ranges between 50 m to 10 km based on ASPeCT (https://epic.awi.de/id/eprint/31658/14/ASPeCt_metcodes.pdf). The TransArc MPF used in the network training was measured at 84°-87°N on 13, 29 August and 6 September 2011 and the visibility of the records ranges from 500 m to 1000 m. The obtained measurement from TransArc is the MPF relative to sea ice cover. The data can be found at https://doi.pangaea.de/10.1594/PANGAEA.803312.
• PRIC-Lei: MPFs were collected during the Arctic Research Expeditions by the Polar Research Institute of China in summer from 2010 to 2016 (Lei et al., 2017, hereafter referred to as PRIC- Lei). Half-hourly Arctic Shipborne Sea Ice Standardization Tool (ASSIST) observations were conducted at the bridge of the R/V Xuelong to document sea ice concentration, sea ice and snow thickness, fractions of melt ponds (the area ratio relative to sea ice cover), dirty ice (with severe impurity depositions) and ridging, and floe size. Sea ice concentration was only assessed for a local area with a diameter of 2 km, which was reduced to 1 km on foggy days and melt pond fraction was estimated around the ship within 1 km.  (Fetterer et al., 2008). Development of this data set was based on experience gained using reconnaissance imagery during the Surface Heat Budget of the Arctic Ocean (SHEBA) and earlier summer ice monitoring experiments (NSIDC 2000, Fetterer andUntersteiner 1998). Visible band imagery from high-resolution satellites were acquired over the Beaufort Sea, the Canadian Arctic, the Fram Strait, and the East Siberian Sea during summer of 1999, 2000 and 2001. Imagery was analyzed using supervised maximum likelihood classification to derive either two (water and ice) or three (pond, open water, and ice) surface classes. The estimated pond coverage was under 500 m square cells within 10 km square images (image resolution is 1 m). The NSIDC MPF used in the network training was estimated from June to August in 2000 and 2001. The coverage of each MPF estimation is 500 m×500 m. The measurement from NSIDC is the MPF relative to grid (the coverage of each observation). The data can be found at https://nsidc.org/data/G02159/versions/1.
• NPI: The MPFs were collected by the Norwegian Polar Institute (NPI) during the field campaign on Arctic sea ice north of Svalbard in summer 2012 (Divine et al., 2015;Divine et al., 2016). The data set presents regional scale of about 150 km morphological properties of a relatively thin, 70-90 cm modal thickness, first-year Arctic sea ice pack in an advanced stage of melt. The data comprises fractions of three surface types (bare ice, melt ponds, and open water) along the flight tracks calculated from images acquired by a helicopter-borne camera system during icesurvey flights from late July to early August 2012. For a typical flight altitude of about 35 m over sea ice, the camera lenses used in the setup provide a footprint of about 60 by 40 m. For typical helicopter roll (pitch) angles of about −2° (1°), the distortion of the image plane from an ideal rectangular one and the associated uncertainty in the image area of less than 1% is considered insignificant. Therefore no correction for pitch and roll was applied to the images (Divine et al., 2015). The NPI MPF used in the network training was measured at 80-82°N on 3 August 2012. The coverage (footprint) of each MPF record is about 60 m×40 m. The obtained measurement from NPI is the MPF relative to sea ice. The data can be found at https://data.npolar.no/dataset/5de6b1e4-b62f-4bd4-889c-8eb7bb862d3b.
Figures 1 to 6 show the observed MPF (used as target data in the network training) in the original resolution from above six sources overlaid on the NASA Team sea ice concentration (SIC). The MPF here is the fraction relative to the grid area. It appears that most of the MPF observations are in the grid with SIC above 40%.      3) We provided information from two additional in-situ observations, which are used as the completely independent validation data in this study (note: we add observations from JOIS as another completely independent validation dataset in this revision).
• Webster: The MPFs were retrieved by the Polar Science Center, University of Washington based on the classified high-resolution visible band satellite images following Webster et al. (2015). The image data source has been referred to as Global Fiducial Imagery, Literal Image Derived Products, National Technical Means images, and MEDEA Measurements of Earth Data for Environmental Analysis. The MPFs were measured at 69-86.5°N over the Beaufort Sea, Chukchi Sea, the Canadian Arctic, the Fram Strait, and the East Siberian Sea from May to August for the period of 1999-2014. The scene size (square grid) of the MPFs ranges from 5 to 25 km. The obtained measurement from Webster is the MPF relative to sea ice cover. In validation, the MPF has been transferred to the fraction relative to the grid (image area) using the measured SIC from Webster. The data and detailed description can be found at http://psc.apl.uw.edu/melt-pond-data/.
• JOIS: The MPFs were collected from the ship-based observations by Joint Ocean Ice Study (JOIS). The JOIS was conducted during 2003-2014 on the Canadian Coast Guard Ship Louis S. St-Laurent (Tanaka et al., 2016). The forward-looking camera imagery were gathered by two types of devices, a KADEC-EYE in 2005 and a Netcam-XL during 2008-2014. The cameras were mounted with a view of the horizon and ice pack in front of the ship. The images were classified into five types (water only; ice only; water and ice; pond and ice; water, pond and ice). Due to the camera malfunction and other bad ice conditions, information was missing in some years (Tanaka et al., 2016). The MPFs used here were obtained during the JOIS2011, measured at 68.5-88.5°N from 19 July to 11 September. The image in 1024×768 pixel was taken every 1-10 minute by Netcam-XL and the ice areas sampled per image range from 1453 to 2397 m 2 . The total amount of the images is 34233. The obtained measurement from JOIS is the MPF relative to the grid (image area). Figure 7 shows the observed MPF in the original resolution from JOIS overlaid on NASA Team SIC. Since the MPF from Webster is a single value on each observation date, we show the SIC of the observed MPF using scatter plot ( Figure 8). Here the MPF is the fraction relative to the grid. The results show that most of the observations from JOIS are within the grids with SIC above 40%. The MPF from Webster are mainly measured at SIC above 60%.

4)
Here we describe the way of the network training using the 8-day composite of MODIS surface reflectance and a specific day in-situ MPF measurement. For example, corresponding to a MPF observation from NSIDC on 4 July 2000 used as the training (target) data in the network, the surface reflectance from MOD09A1 (8-day composite) used as the input data in the network was obtained from the data file named "2000.07.03" (https://e4ftl01.cr.usgs.gov/MOLT/MOD09A1.006/). That means the date spanning of this MOD09A1 file is 3 July 2000 and 10 July 2000, which covers the MPF observation date. This is also applied to the validation.
For each 8-day composite of MOD09A1, we have 40 tiles (h09v02-h26v02, see https://modis-land.gsfc.nasa.gov/MODLAND_grid.html for details) in total to cover the entire Arctic. We mosaiced all the tiles into one *.hdf file using the MODIS Reprojection Tool (MRT) and then reprojected the mosaic to a GeoTIFF on the 500 m polar stereographic grid using ArcGIS. Each band (band 1, 2, 3 and 5) of the MOD09A1 was stored as a separate GeoTIFF file. For the network training, the input is the surface reflectance from the GeoTIFF files of the four bands on the 500 m polar stereographic grid.
For the observed MPFs from each source, we use the corresponding latitude and longitude to determine which gird cell (500 m polar stereographic grid) the observation falls in. If more than one observation from one source on a specific day fall in the same 500 m polar stereographic grid, the average of those observations is used as the training (target) data in the network. Note: the observed MPF relative to sea ice area has been transformed to the MPF relative to the grid (image area or coverage of each observation) based on the observed SIC in the network training.
In this study, we construct an ensemble-based deep neural network (hereafter referred to as DNN). The input of the network training is the four bands (band 1, 2, 3 and 5) of MOD09A1 on the 500 m polar stereographic grid. The training (target) data is the observed MPF relative to the grid (image area or coverage of each observation) from six sources (HOTRAX, DLUT, TransArc, PRIC-Lei, NSIDC, NPI). We choose the MOD09A1 from the file which covers the observation date as described above. It should be noted that in the network training, we only consider the grids that meet the following conditions: i) the values of MOD09A1 band 1, 2, 3, 5 are all within the valid range (MODIS Surface reflectance User guide collection 6, https://lpdaac.usgs.gov/documents/306/MOD09_User_Guide_V6.pdf); ii) the observed MPF is above 0 and below 100%; iii) the observed SIC (with MPF considered) relative to the gird is larger than the MPF relative to the grid.
For the final MPF data retrieval, the aforementioned GeoTIFF files were resampled from the 500 m to 12.5 km polar stereographic grid using the mean in a 25×25 window size by considering the valid data range of MOD09A1. We then apply the obtained DNN as mentioned above to derive the MPF dataset on the 12.5 km polar stereographic grid. The input for retrieving the MPF dataset are the four bands of MOD09A1 on the 12.5 km polar stereographic grid. The output is the MPF relative to the grid on the 12.5 km polar stereographic grid. For validation with the retrieved MPF on the 12.5 km polar stereographic grid, the average of the corresponding observations is calculated within the 12.5 km grid cell.
To further address the concern, we also trained the networks using the daily MODIS surface reflectance from MOD09GA (https://lpdaac.usgs.gov/products/mod09gav006/, Vermote and Wolfe, 2015), instead of the 8-day composite MOD09A1, on the 500 m polar stereographic grid and in-situ observations. The results are shown in section 6).
"2) Your evaluation and presentation of the results appears to be very global. The only "true" kind of evaluation figure is Figure 4 and if I am not mistaken then there aren't any figures showing inter-comparisons of the actual melt-pond fraction for single 8day periods with independent data. Wouldn't it therefore be a good idea to i) include mapbased inter-comparisons between, e.g. the Istomina et al. data Fig. 10 and Fig. 11. One could doubt that your results are independent of the actual sea-ice concentration due to the dominating impact of any open water on the brightness temperatures used for the sea-ice concentration data set you used as seaice mask (which was one of the things avoided by Rösel et al.

for good reason). It is also not clear to me (and seems not to be described in the methods section overwhelmingly detailed) how the reflectances of open water and melt ponds are unmixed efficiently enough to identify open water as open water and to not identify an actual melt pond as a certain fraction of open water as well."
Response:

5)
We provided the map-based comparisons between our MPF data (hereafter referred to as DNN_MPF) and the MPF from Rösel et al. (2015) (https://icdc.cen.unihamburg.de/1/daten/cryosphere/arctic-meltponds.html, hereafter referred to as UH_MPFv2). The DNN_MPF is retrieved from DNN_MPF+NASASIC (see details in section 12)). Note: Both the DNN_MPF and UH_MPFv2 are retrieved from the 8-day composite of MODIS, but different version of MODIS (DNN_MPF from version 6 and UH_MPFv2 from version 5). Here we included one more MPF product. That is the MPF from Istomina et al.
(https://seaice.unibremen.de/databrowser/#p=MERIS_fraction, hereafter referred to as UB_MPF). The UB_MPF consists of daily averages of the MPF retrieved from MERIS (Medium Resolution Imaging Spectrometer) swath Level 1b data using the MPD (Melt Pond Dector) retrieval (Zege et al., 2015). To compare with DNN_MPF and UH_MPFv2, we calculated the 8-day averages of the UB_MPF corresponding to the date ranges of the MODIS 8-day composite. All the MPFs are the fraction relative to the 12.5 km polar stereographic grid. Here we only consider the grids with SIC above 30% (Note: the DNN_MPF is restricted using NASA Team SIC and the UH_MPFv2, UB_MPF are restricted using the SIC by 100 minus the open water fraction in UH_MPFv2 dataset). In general, the climatology of the three MPFs are within 40%. In May, the DNN_MPF and UH_MPFv2 have similar pattern in much of the Arctic Ocean, although the DNN_MPF is relatively larger in the sea ice edge zone. The UB_MPF is generally larger than the other two data in the central Arctic. In June, the three data have comparable MPF in the ice edges (around 20-25%), especially in the Baffin Bay, Greenland Sea and Kara Sea. In the Arctic Basin, the DNN_MPF tends to evolve early in the eastern Arctic dominated by the first-year ice, while the UH_MPFv2 and UB_MPF seem to evolve early in the western Arctic. The MPF of all three data increases quickly in the bands of the Beaufort, Chukchi and East Siberian Seas. In July, higher fractions (above 25%) gradually extend to the central Arctic for the three data. The DNN_MPF and UB_MPF have higher fractions in the eastern and western Arctic basin, respectively, while the UH_MPFv2 has similar amount of MPF in the two regions. In August, the MPF of the three data gradually decreases. The UH_MPFv2 is generally higher than the other two data. The UH_MPFv2 and UB_MPF have the slowest and fastest decrease rate, respectively, while the decrease rate of the DNN_MPF is in between. The DNN_MPF and UH_MPFv2 have longer durations of high fractions than UB_MPF in the ice edges, especially for UH_MPFv2 with fraction above 25% for most areas until late August. By the end of August, the DNN_MPF and UB_MPF are less than 20% in the Arctic basin, while the UH_MPFv2 still maintains high fraction. . Same as figure 9, except for the UB_MPF Figure 12 shows the time series of the three MPFs relative to sea ice (note: we only consider the grids with SIC above 30% during 2003-2011). The DNN_MPF was transformed from the fraction relative to grid to sea ice using NASA Team SIC; the UH_MPFv2 and UB_MPF were transformed from the fraction relative to grid to sea ice using the UH_MPFv2 SIC (100 minus open water fraction in UH_MPFv2). The three datasets have similar pond fraction in early May (8.5%, 9.7 and 10.7% for DNN_MPF, UH_MPFv2 and UB_MPF). The MPFs of DNN_MPF and UB_MPF grow relatively quicker and are relatively larger than that of UH_MPFv2 until the end of June. From early July, the UH_MPFv2 always have higher MPF than that of the other two data. The DNN_MPF, UH_MPFv2 and UB_MPF reach the largest MPF ~27%, ~28% and ~27% in late July, the end of July, and early July, respectively. The MPF of UB_MPF decreases about two weeks earlier than that of the other two data. In August, the MPF of DNN_MPF and UB_MPF decrease relative faster than that of the UH_MPFv2. The UH_MPFv2 maintains high values (above 25%) for a longer duration than that of the other two data. The standard deviations of the three data are larger in August.

6)
We provided the scatter plots with retrieved and observed MPF. To check the difference of the retrieved MPF from the network trained by 8-day composite of MODIS (hereafter referred to as DNN_8dayMODIS) and daily MODIS (hereafter referred to as DNN_dailyMODIS) surface reflectance. We further trained the network using the daily MODIS surface reflectance from MOD09GA. We compared the results with the MPF retrieved by DNN_8dayMODIS on the 500 m polar stereographic grid ( Fig. 13 and 14).    Figure 15 shows the scatter plot of the MPF from DNN_MPF+NASASIC and the MPF version2 from University of Hamburg (https://icdc.cen.unihamburg.de/1/daten/cryosphere/arctic-meltponds.html, hereafter referred to as UH_MPFv2) against the observations on 12.5 km polar stereographic grid. We only use the observations where DNN_MPF and UH_MPFv2 are both within valid ranges. The DNN_MPF and DNN_MPFdailyMODIS on 12.5 km polar stereographic grid are both retrieved from the 8-day composite of MODIS (MOD09A1). Note: the DNN_MPF and DNN_MPFdailyMODIS are retrieved using the above-mentioned networks of DNN_8dayMODIS and DNN_dailyMODIS, respectively. The MPF from UH_MPFv2 is missing in validation with NSIDC and NPI (note: the correlation coefficients 0.53 and RMSE 0.107 of UH_MPF with NSIDC in Fig.4 TCD manuscript used the values in Rösel et al. (2012). The UH_MPF in Rösel et al. (2012) is version 1). The results show that the DNN_MPF has better agreement with the observations than DNN_MPFdailyMODIS. The completely independent validation with the observations from Webster (r = 0.63 and r = 0.51 for DNN_MPF and DNN_MPFdailyMODIS) and JOIS (r = 0.50 and r = 0.44 for DNN_ MPF and DNN_ MPFdailyMODIS) shows that the network trained using 8-day composite of MODIS is more robust. This further suggests that our MPF retrieval is reliable.

7)
We provided case studies of the observed MPF overlaid on the daily MODIS (MOD09GA) image with the original resolution ( Fig.16-18). The MODIS images are generated using bands 1 (red), 4 (green) and 3 (blue). Note: we already provided the observed MPF overlaid on the NASA Team SIC in Fig.1-7.
We provided case studies of the observed MPF (original resolution) overlaid on the retrieved MPF of 12.5 km polar stereographic grid (Fig.19-24). The results show that the retrieved MPF generally agrees with the average of the observations in the same grid.

8)
We provided the melt progress of the retrieved MPFs (DNN_MPF, UH_MPFv2 and UB_MPF) and the observed MPFs (Fig. 25). Note: the MPFs here are the fraction relative to grid. We use the average of the observations from HOTRAX, DLUT, TransArc, PRIC-Lei, NSIDC and NPI to represent for the observed MPF on the specific date range. We generally divide the melt progress every five days or more and estimate the average of the observed MPF and the corresponding retrieved MPFs within the days. Note: if the corresponding retrieved MPFs was missing, we use the average of the retrieved MPFs during 2003-2011 within the days. The results show that the DNN_MPF and the UH_MPFv2 are closer to the observed MPFs in May during the early melting season. Then the DNN_MPF shows better agreements with the observed MPFs during early to mid-June. The three retrieved MPFs in July are close and show good agreements with the observed MPFs. In later melting season, the UH_MPFv2 and UB_MPF are respectively larger and smaller than the observed MPFs. The DNN_MPF in later melting season is generally within the range of the UH_MPFv2 and UB_MPF and is closer to the observed MPFs. Figure 25. Evolution of the MPF relative to grid from the retrieved and observed MPF. The x-axis is the melt progress divided by around every five days or more in the period of May to September (i.e., 6.01-6.05 is the period of 1-5 June).

9)
We provided the detailed data processing in section 4). For each 8-day composite of MOD09A1, we have 40 tiles (h09v02-h26v02, see https://modisland.gsfc.nasa.gov/MODLAND_grid.html for details) in total to cover the entire Arctic. We mosaiced all the tiles into one *.hdf file using the MODIS Reprojection Tool (MRT) and then reprojected the mosaic to a GeoTIFF on the 500 m polar stereographic grid using ArcGIS. Each band (band 1, 2, 3 and 5) of the MOD09A1 was stored as a separate GeoTIFF file. For the network training, the input is the surface reflectance from the GeoTIFF files of the four bands on the 500 m polar stereographic grid.
For the observed MPFs from each source, we use the corresponding latitude and longitude to determine which gird cell (500 m polar stereographic grid) the observation falls in. If more than one observation from one source on a specific day fall in the same 500 m polar stereographic grid, the average of those observations is used as the training (target) data in the network. Note: the observed MPF relative to sea ice area has been transformed to the MPF relative to the grid (image area or coverage of each observation) based on the observed SIC in the network training.

10)
We provided the accuracy of our dataset using the uncertainties of the MPF (DNN_MPF) and SIC (DNN_SIC) retrieved from DNN_MPF+NASASIC (see section 12) for details). Note: in this revision, we only consider the girds with SIC above 30%. The uncertainties are estimated by the standard deviations among the outputs of networks within 10-90 percentile of the 100 networks (described in line 172-173 in TCD manuscript). Table 1 shows the average standard deviations of the DNN_MPF and DNN_SIC for the period of May to August during 2000-2017. The results show that the magnitude of the uncertainty of our MPF retrieval varies slightly from May to August, with an average of 3.1%. The uncertainty of SIC is relatively larger than that of the MPF, within 4-5% before August and then increases by 1-2% in August and September. Figure 26 shows the spatial distribution of the standard deviations of DNN_MPF averaged for the period of May to September during 2000-2017. The uncertainties of MPF are generally within 4% in much of the Arctic, except for the Canadian Arctic in mid-June (~7%). The MPF in the ice edges does not show large uncertainties. This suggests our MPF retrieval is reliable.

12)
To further address the concern, here we added observed SIC as the target data in the network training, and also retrieved SIC as the second output. We used the observed SIC from three independent sources as the target and trained the network separately.
(note: the first output is MPF, the same as described in section 2 of TCD manuscript). Table 2 provides the detailed information.  in section 2)). The DNN_MPF (no SIC) does not include SIC as the target in the network training.
• DNN_MPF+NASASIC is the network trained by adding the NASA Team SIC (Cavalieri et al., 1996) as the second target. The NASA Team SIC is derived from Nimbus-7 SMMR and DMSP SSM/I-SSMIS Passive Microwave Data using a revised NASA Team algorithm (https://nsidc.org/data/nsidc-0051). In the network training, the NASA Team SIC was resampled from 25 km to the 500 m polar stereographic grid to match the resolution of the MODIS surface reflectance.
• DNN_MPF+FieldSIC is the network trained by adding the observed SIC from multi-sources (HOTRAX, DLUT, TransArc, PRIC-Lei, NSIDC and NPI) as the second target. The observed SIC is obtained from the same sources as the observed MPF. In the network training, the observed SIC was resampled from its original resolution (coverage) to the 500 m polar stereographic grid to match the resolution of MODIS surface reflectance (note: we use the average of the observed SIC from each source located in the same grid as the resampled SIC).
• DNN_MPF+AMSRSIC is the network trained by adding the SIC derived from Advanced Microwave Scanning Radiometer-Earth Observing System and Advanced Microwave Scanning Radiometer 2 (hereafter referred to as AMSR SIC, Spreen et al., 2008) as the second target. The AMSR SIC is developed by the University of Bremen using the ARTIST Sea Ice (ASI) algorithm (https://seaice.uni-bremen.de/sea-iceconcentration). In the network training, the AMSR SIC was resampled from 6.25 km to the 500 m polar stereographic grid to match the resolution of MODIS surface reflectance.
For the final MPF and SIC data retrieval, the data on the 12.5 km polar stereographic grid were used in the ensemble-based network (note: MOD09A1 on the 12.5 km polar stereographic grid was used as the input). The only difference between DNN_MPF (no SIC) and the other three networks (DNN_MPF+NASASIC, DNN_MPF+FieldSIC and DNN_MPF+AMSRSIC) is that the three networks contain SIC as the second target in network training. Therefore, the final dataset from DNN_MPF (no SIC) only contains MPF on the 12.5 km polar stereographic grid and the final dataset from the other three networks contains MPF and SIC on the 12.5 km polar stereographic grid. Figure 31 shows the correlation coefficients and the RMSE of MPF from the above four network training. It appears that the correlation coefficients of the four networks with independent SIC are comparable. This is also true for the RMSE. This suggests that the influence of the ice concentration on the retrieved MPF is minor. This further increases the reliability of our MPF retrieval. We check the spatial correlation coefficients and RMSE of the MPF from three re-trained networks with the MPF from DNN_MPF (no SIC) in each year during 2000-2017. The results show that the average spatial correlation coefficient is ~0.99 and the RMSE is ~0.012. This suggests that the MPF from the re-trained networks are generally consistent with that from DNN_MPF (no SIC). For further comparison, we show the MPF (relative to grid) in 2017 from DNN_MPF (no SIC) and the three re-trained networks (DNN_MPF+NASASIC, DNN_MPF+FieldSIC and DNN_MPF+AMSRSIC). The results show that the spatial MPF during May to September in 2017 from DNN_MPF (no SIC) (Fig.32) are almost the same with that from the three networks added SIC (Fig.33 to 35). This further suggests that the SIC only has very limited effect on the MPF retrieval in our method.     Table 3 shows the percentage of grid cell with MPF greater than SIC (regarded as bad retrieval). The MPF (relative to grid) and SIC used here are both from the three retrained networks (DNN_MPF+NASASIC, DNN_MPF+FieldSIC and DNN_MPF+AMSRSIC). The results show that 0.84-1.31% of the grid cells have bad MPF retrieval when considering grid cell with SIC>15%. It can be reduced to 0.05-0.19% of the grid cells when considering SIC>30%. The bad retrieval (MPF larger than SIC) has been removed in the analyses. Compared to Table 1 in the preliminary response to the review#1, the percentage of the grid with MPF larger than SIC does not change much whether the MPF is from DNN_MPF (no SIC) or the three re-trained networks (note: 1.97% and 0.09% of the grid cells have bad MPF retrieval when considering grid cell with SIC>15% and SIC>30% in DNN_MPF (no SIC)). This suggests that the SIC has very limited effect on the MPF retrieval in our method, which further increases the reliability of our method.
In order to minimize the bad MPF retrievals that are primarily located in the sea ice edge area with small concentration. In this revision, we only consider the grid cell with sea ice concentration greater than 30%, instead of 15%. The original MPF from DNN_MPF (no SIC) has been replaced by the retrieval from DNN_MPF+NASASIC. Response:

13)
In the revision, we provided the explanation why we added band 5 in this study. According to Barber et al., 1992, "Spectral albedos collected over snow surfaces during SIMS '90 indicate minimal variation in reflectance throughout the visible portion of the electromagnetic spectrum. Reflectance decreased within the near-infrared, illustrating the wavelength dependence and sensitivity of snow reflectance to phase changes within the snow cover. A temperature increase of 5.5C° promoted a phase change within the snow pack from ice to liquid and vapour, which caused the associated changes in grain size (increase) and structure (rounding). Spectral albedo in the near-infrared region is most sensitive to these changes". Thus, we added one more near-infrared band (band5) in the MPF retrieval that may detect the changes in the stage of snow melting.
In this revision, we estimated the contribution of the four MODIS bands to the MPF and SIC retrieval in the network training (Fig. 36). The contribution was estimated based on "Connection weights" following Olden and Jackson (2002). The "Connection weights" calculates the product of the raw input-hidden and hidden-output connection weights between each input neuron and output neuron and sums the products across all hidden neurons. The results show that the band 5 accounts for ~20% of the retrieval of MPF and SIC, although its contribution is relatively less than the other three bands. This further suggests that adding band 5 benefits the retrieval.

14)
We provided the explanation of the two improvements in this study. i) We added one near-infrared band (band 5) in the study to extend the bandwidth over 1000 nm. Figure 36 shows the band 5 accounts for about 20% contribution to the retrieval of MPF, which means adding this band benefits the retrieval. The previous research also showed that spectral albedo in the near-infrared region is more sensitive in the changes within the snow pack from ice to liquid and vapour. ii) Compared to the UH_MPFv2, we did not use the fixed spectral reflectance of each surface type (i.e., bare ice, snow covered ice, melt pond and open water) to build the relationship. Instead, we used the observed MPF from multi-sources to directly train the deep neural network. The advantage of our method is that it avoids large uncertainties of spatially and temporally varying reflectance associated with different surface species, which can result in large uncertainties for the retrieval of type fraction.
More recently, Wright and Polashenski (2020) compared the MPF retrieval using the "spectral unmixing" method in Rösel et al. (2015) and a random forest machine learning model which does not rely on the constant spectral reflectance of each surface type. Their results suggested that "it is not possible to consistently derive component surface fractions of sea ice from low resolution imagery using spectral unmixing techniques at an accuracy suitable for validating melt pond models or establishing unambiguous long term trends." Moreover, the "spectral unmixing" is "highly sensitive to error in the input surface reflectance data". Their tests show "the accuracy of the machine learning method to be better than regionally tuning spectral unmixing and it is significantly more feasible to implement.". The RMS error in melt pond determination could be improved from 0.18 they found in spectral unmixing techniques to 0.07 using machine learning. This further suggests that our method based on network training to retrieve the MPF is feasible.
"Lines 120-122: You use a standard sea-ice concentration product as a sea-ice mask. While this is fine, several questions immediately pop up: i) what is meant by "revised NASA Team algorithm (Cavalieri et al., 1996)"? The year of the reference makes clear that it cannot be the enhanced NASA Team algorithm". ii) what are the specifications of this data set in terms of spatial and temporal resolution and how did you pre-process the data to match with the MODIS data? iii) passive microwave concentration have biases during summer as has been discussed, e.g., in Comiso and Kwok in 1996: "Surface and radiative characteristics of the summer Arctic sea ice cover from multisensory satellite observations" and in Kern et al. in 2016: "The impact of melt ponds on summertime microwave brightness temperatures and sea-ice concentrations". Doesn't using such sea-ice concentration data sets as sea-ice mask therefore require a more indepth description of how you used the data and how the expected bias in sea-ice concentration influences your melt-pond retrieval?" Response:

15)
We provided the explanation about the "revised NASA Team algorithm". In the section of "User Guide" at https://nsidc.org/data/nsidc-0051, it says "Sea ice concentrations for this data set were produced using a revised NASA Team algorithm that uses a different set of tie points and weather filters than the original NASA Team algorithm. The NASA Technical Memorandum 104647 (Cavalieri et al., 1997) includes information about differences, such as tie points, between the original algorithm and the revised NASA Team algorithm." In the section of "Citing These Data", it says that we should cite the data as "Cavalieri, D. J., C. L. Parkinson, P. Gloersen, and H. J. Zwally. 1996, updated yearly. Sea Ice Concentrations from Nimbus-7 SMMR and DMSP SSM/I-SSMIS Passive Microwave Data, Version 1. [Indicate subset used]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center. doi: https://doi.org/10.5067/8GQ8LZQVL0VL." Since our final MPF dataset retrieved from DNN is the fraction relative to grid on 12.5 km polar stereographic grid, the NASA Team SIC is also resampled from 25 km (original resolution) to 12.5 km polar stereographic grid to match the grid size of the MPF.

16)
According to section 12), the MPFs retrieved from the networks that included or excluded the SIC as the target data in training are very close. This suggests that sea ice concentration has minor effect on the retrieval of MPF in this study. To further check the uncertainty due to the low ice concentration in the ice edges, we provided the comparison of the MPF relative to sea ice by using a) the NASA Team SIC and b) adjusted NASA Team SIC based on Kern. et al. (2016). According to the Table 12 in Kern. et al. (2016), the SIC retrieved from NASA Team algorithm in CaseA60 and CaseA80 (Cases A60 and A80 denote 100% sea-ice concentration with 40 and 20% (apparent) open-water fraction due to melt ponds) are underestimated by 22.6 and 0% SIC, respectively. We add 22% and 10% SIC to the NASA Team SIC (hereafter referred to as adjusted SIC), where the MPF is above 40% and 30%. We only consider the grids with SIC above 30% during 2000-2017. Figure 37 shows the evolution of the MPF relative to sea ice and adjusted sea ice (note: the MPF is from the DNN_MPF+NASASIC). The results show that the underestimation of SIC in the ice edges due to the presence of melt ponds has minor effect on the evolution of MPF to ice-covered area. This could be explained by the limited percentage ~0.1% and ~2.65% of the grids (SIC above 30%) with MPF (relative to grid) above 40% and 30% shown in Table 4. This suggests that the potentially affected grids only have small amounts in our study, and those grids will not change the major results.  "It appears to me that you did not yet adequately cite the MODIS melt-pond fraction data set of Rösel et al. (2012) which you are using in your overall comparison (e.g. Figure 4). Would you mind to check which version of this data set you used and provide the doi and version of it in your reference list? I guess this would help other potential users to locate the correct data set." "Lines 148-153: I checked the Webster et al. [2015] paper. I have serious doubts that this is the correct reference. I found that this paper basically compares a new method to derive melt-pond fraction based on APLIS campaign data and compared the results with SHEBA data. I did not find the mentioned 2000-2014 MPF data set. Here you would appreciate a hint about where to find this potentially very valuable data set."