The Aquarius FT product was generated using the Aquarius weekly averaged polar gridded L-band TB product distributed on the EASE-Grid 2.0, above the parallel 50∘ N, with a spatial resolution of 36km×36km (Brucker et al., 2014). This formatted TB was specially designed for the study of northern regions. For each Aquarius radiometer, the product average TB values were calculated from every measurement made during a week, combining ascending and descending orbits. The FT classification algorithm is based on a seasonal threshold approach (STA) using a frost factor index (FFrel; Eq. 1), introduced by Rautiainen et al. (2014), where FFNPR is the frost factor based on the normalized polarization ratio between TB at vertical and horizontal polarizations (TBV and TBH; Eq. 2). FFfr and FFth are reference frozen and thawed frost factors obtained for each pixel and each radiometer by averaging, respectively, the five minimum FFNPR found during winter (January and February) and five maximum FFNPR found during summer (July and August) over the three available dataset periods. FFrel=FFNPR-FFfrFFth-FFfrFFNPR=TBV-TBHTBV+TBH A threshold (τ) was determined by optimization to classify the surface as frozen or thawed if the FFrel is lower or higher than the threshold (Eq. 3). IfFFrel<τ→freezeorifFFrel>τ→thaw. The thresholds optimized (Table 1) in Roy et al. (2015) over North America for three basic land covers (tundra, forest, open land) were applied over the Northern Hemisphere using the Land Cover Classifications derived from Boston University MODIS/Terra Land Cover Data (LCCBU; see Sect. 2.4). The optimization method calculates the threshold that gives the best accuracy when the product retrievals are compared to in situ air temperature stations. It was shown that optimized thresholds only slightly improved the accuracies by 1 % to 4 % compared to a fixed threshold of 0.5. For the tundra site, a broad range of threshold values ([0.3–0.7]) caused an insignificant variation of accuracy.

Aquarius operated three non-scanning radiometers at different incidence angles (29.2, 38.4 and 46.3∘) and with different 3 dB footprint sizes (respectively 76 km × 94 km, 84 km × 120 km and 97 km × 156 km). Based on the LCCBU, the thresholds found in Roy et al. (2015) were used to create FT maps for each radiometer. The three FT maps were then blended to create a fourth map, which offers more complete spatial coverage. For every grid cell, radiometer 2 (38.4∘) was prioritized, then radiometer 1 (29.2∘) was used, while radiometer 3 was only used if data from the other radiometers were not available for the given grid cell. This blended algorithm was chosen based on the performance given for each radiometer in Roy et al. (2015) (radiometer 2 gave the best results, while radiometer 3 gave the worst results). Due to the width of Aquarius' swath and its revisit time, 16.5 % of the terrestrial 36 km grid cells have less than 95 % observations over the period and 16 % were not measured at all. Thus, the intercomparison with the FT-ESDR product (Sect. 2.2) was only made when FT-AP data were available for a given date. The time span for this analysis runs from August 2011 with the first Aquarius observations to 31 December 2014 with the latest FT-ESDR data available at the time of our analysis.

The first version of the FT-ESDR product (Kim et al., 2011) was based on an STA similar to the FFrel but applied exclusively to the TBV at 37 GHz instead of the NPR. In the new extended product (Kim et al., 2017b; NSIDC: https://nsidc.org/data/nsidc-0477/versions/4), a modified seasonal threshold algorithm (MSTA) was used to determine thresholds for each grid cell to obtain better accuracy. It consists of a grid-cell-wise weighted empirical linear regression relationship between the 37 GHz TBV measurements and daily surface air temperature (SAT) estimates from the ERA-Interim global reanalysis.

The extended FT-ESDR product used in this study is derived from the SSM/I 37 GHz brightness temperatures (footprint of 38 km × 30 km) and resampled at a grid cell resolution of 25 km on the global Ease-Grid v1.0. The observations were recorded twice per day, which gives the possibility of attributing discrete frozen or thawed states for morning and afternoon. The final classification offers four discrete surface states: “frozen all day”, “thawed all day”, “frozen in AM and thawed in PM” (transitional) and “thawed in AM and frozen in PM” (inverse-transitional). In this study, the latter two classes were combined into a single transitional class. In order to compare the two products, the FT-ESDR was first spatially resampled to the EASE-Grid 2.0 with the nearest neighbor method choosing the smallest distance between pixel centers. Then, FT-ESDR was temporally resampled for the same weekly calendar as the FT-AP. The temporal FT-ESDR sampling procedure was based on the rule that the most frequently occurring class over the 7 days of a week is adopted as the value for the entire week. In cases where the frozen and thawed classes occurred with equal frequency during a single week (e.g., 2 days frozen, 2 days thawed and 3 days transitional), the transitional class was attributed. This latter class occurs mainly during the transition seasons of spring and fall. Thus, we assigned the transitional class to the thawed class during spring and summer since it indicates the beginning of the thawing process and we assigned the transitional class to the frozen class during fall and winter since it indicates the beginning of the freezing process. This FT-ESDR resampling procedure ensured that the two products were at the same temporal and spatial resolutions with only the frozen and thawed categories, making the comparison possible.

The land cover information (Fig. 1) comes from the EASE-Grid 2.0 LCCBU (Brodzik and Knowles, 2011; NSIDC: nsidc.org/data/nsidc-0610/versions/1), using the same grid as the FT-AP product. The 17 land cover classes were grouped to obtain four classes: tundra, forest, open land (savanna, cropland and grassland) and water (see Roy et al., 2015). Each grid cell was assigned its single most prominent class of land cover which is used for the selection of its thresholds (Table 1). All grid cells with more than 20 % of water and ice indicated by the LCCBU were masked.

Six weather stations (Table 2) were selected for validation from the National Climatic Data Center (NCDC) Climate Data Online website (CDO; https://www.ncdc.noaa.gov/cdo-web/datasets). Two tundra, two forest and two open land sites were chosen for a comparison between the product classifications and the in situ SAT. All of the sites are more than 200 km from a coast, except the Kamchatka site; its distance of about 85 km from the sea may have an influence on the large L-band field of view. The average SAT for each day (TAVGday) was used to create a time series for each site. For statistical purposes, the weekly resampling method used on the FT-ESDR product was also applied to the SAT daily values, using 0 ∘C as the threshold between frozen and thawed states (TAVGweek; see Roy and al., 2015).

Ruggedness values from a 30 arcsec resolution elevation map (Gruber, 2012; University of Zurich: http://www.geo.uzh.ch/microsite/cryodata/pf_global/) were resampled to the EASE-Grid 2.0 with the drop in the bucket approach. In order to represent a ruggedness value at the Aquarius footprint scale, the mean value of a 3×3 grid cell window centered on each weather station pixel was calculated (Rug_mean). To each value a class was attributed according to the Gruber (2012) classification.

Figure 2a shows the percentage of concordant classifications between the two products for the 3.7-year overlapping period. Overall, the results show that there is good agreement between the two products. In general, forest areas have a better percentage of concordance than other land covers. However, some regions show important discrepancies, especially along coastal margins and in mountainous and open areas (such as in northern Europe, Kazakhstan (and surroundings) and the Canadian Prairies). Those lower percentages correspond to regions where lower accuracies to detect the FT were already noted in Roy et al. (2015) and Kim et al. (2017a) (see Sect. 4). Figure 2b shows that 77.1 % of the common grid cells have more than 80 % agreement. More specifically, 41.6 % of the grid cells have more than 90 % agreement over 3.7 years, with 10.0 % of them having more than 95 %. About 35.5 % of the grid cells have an agreement between 80 % and 90 %; only 22.8 % of the cells have an agreement lower than 80 %.

An analysis was made to identify similarities and differences between the two products used for retrieving surface FT state during the freezing (fall) and thawing (spring) periods. For each land cover type, Fig. 3 shows the time series of the fraction of land frozen (for all land at latitudes greater than 50∘ N). To reduce the effect of obvious false frozen retrievals in summer (discussed below) on the analysis and to focus on the differences primarily related to the physics of the measurements (i.e., L band vs. Ka band), only grid cells with an agreement percentage between FT-AP and FT-ESDR higher than 80 % (from Fig. 2a) were considered. Light blue zones indicate periods for which the FT-ESDR transitional class is set to the frozen class (see Sect. 2.2).

Figure 3 gives information on temporal differences between the products. The difference between FT-AP and FT-ESDR in terms of the percentage of frozen grid cells for a given day (Δ%frozen) is greatest during the falls in tundra, at 10 %–27 %. In forest, Δ %frozen is much lower than in tundra, with differences of 0 %–12 %. For these two land covers (tundra and forest), the agreement between the products varies by year. In fall, the horizontal shift between the curves indicates time delays (Δtime) for the two products to reach the same percentage of frozen grid cells. In tundra, Δtime ranges from 1 to 3 weeks. In forest, Δtime is always less than 1 week. This result demonstrates an excellent overall consistency between the products. However, FT-AP shows the percentage of frozen land increasing every summer to a peak that is not perceived with FT-ESDR. In tundra, those maximum values vary between 17 % (2014) and 28 % (2013) and are lower in forest at 7 % (2013) and 10 % (2012). Even if some of those detections represent the real state of the surface, the FT-AP peaks may be mainly caused by false frozen detections, which were noticed in the SMAP product (Derksen et al., 2017). False frozen detections are identified in our analysis using observations from the weather stations (Fig. 6, Sect. 3.3). In open land, FT-AP retrievals tend to vary frequently by showing noticeable unexpected frozen retrievals in summer and thawed retrievals in winter (blue lines in Fig. 3). FT-ESDR shows almost no frozen regions in summer, but unfrozen regions in winter, evidence that the open land regions are at the southern limits of the freeze regions. This in turn makes retrieval more difficult due to the higher temporal variability in FT events in winter.

To spatially represent the information provided by Δtime, maps in Fig. 4 indicate the week of the year of the freeze onset for each product (top and middle maps). The freeze onset is defined as the first week of the year when the state changed from thawed to frozen and stayed frozen for two more consecutive weeks. This variable can only be identified for grid cells that contain observations over several weeks in a row and have good agreement (>80 %) according to Fig. 2a. Figure 4 also shows the difference in freeze onset between the two products (bottom maps), defined as FT-AP minus FT-ESDR. A negative value means that FT-AP detects the freeze onset earlier than FT-ESDR (represented by cold colors) and inversely for a positive value (represented by warm colors).

Comparing FT-AP and FT-ESDR maps shows a global tendency of FT-AP to reach the freeze onset 2–5 weeks earlier than FT-ESDR in the tundra regions (blue zones in Fig. 4). In 2013 and 2014 (Fig. 4c, d), this tendency is stronger, with more regions experiencing an earlier freeze onset by 3–5 weeks according to FT-AP. While these differences are less noticeable in the forest, some local discrepancies are observable with noticeable interannual variabilities.

Table 3 gives freeze onset means (μ) and standard deviations (σ) in weeks of the year for each land cover and year. Over tundra, it shows the greatest freeze onset mean difference (Δμ=μFT-AP minus μFT-ESDR) between the two products in 2013, with Δμ=2.4 weeks, and the smallest difference in 2011, with Δμ=1.3 weeks. Over forest, the differences are much smaller; the greatest occurs in 2011, with Δμ=0.7 weeks, and the smallest in 2012, with Δμ=0.0 weeks. As noted for Fig. 4, FT-AP tends to detect freeze onset earlier than FT-ESDR. These freeze onset differences suggest that there is a divergence in the FT signal at L and Ka bands, and that there might be complementary information in the two signals (this is further addressed in the discussion).

For the thawing period, differences between the products according to Fig. 3 and Table 4 are small for all land covers, meaning that globally the two products respond similarly to landscape thaw. This result is consistent across land covers and for the three spring seasons available for this analysis with a stronger variability for open lands. The sensitivity of passive microwave frequencies to the water present in the snow at the beginning of the thaw explains the similarity between the products in spring (Roy et al., 2017a; Hallikainen et al., 1986). Thaw onset maps created from the difference of thaw onset between the products (bottom maps), defined as FT-AP minus FT-ESDR, illustrate the consistency between products, but highlight some local differences (Fig. 5).

In Sect. 3.1, it was shown that there were some regions where both products show significant discrepancies. In order to better assess the observed variabilities, we looked at six different sites (Fig. 1) to evaluate the temporal evolution of both FT products and compared them to SAT measurements. The objective was to identify any difficulties the products may have monitoring FT in particular conditions. SAT was chosen as the in situ reference since Roy et al. (2015) showed that SAT was the best proxy to validate satellite FT products. Table 5 shows the percentages of agreement of weekly FT detection over the entire period between FT-AP, FT-ESDR and TAVGweek (Fig. 6a–f). The mean agreement between the satellite products and in situ measurement is 81.6 % for FT-AP and 92.0 % for FT-ESDR. Discontinuities in the series (Fig. 6a–f) are caused by the absence of Aquarius observations in a given week.

At the Kamchatka site (Fig. 6a, Table 5), FT-AP has a low agreement with TAVGweek at 67.9 %. The error mostly occurs in summers with obvious false frozen misclassifications, since SAT is over 0 ∘C during that period. In contrast, there is a strong agreement of 94.3 % between FT-ESDR and TAVGweek, with differences occurring in the transitional period with no specific pattern between the years. The difficulty in the retrieval could be due to the fact that the Kamchatka site's grid cell has a very low difference between the minimum and maximum NPR values (ΔNPR) used to create FFfr and FFth, with ΔNPR=0.015 and ΔNPR=0.021 for radiometers 2 and 3, respectively. This low difference may lead to a lower sensitivity to FT. Moreover, there is a change of ruggedness classification (Table 2) from the one grid cell ruggedness (SSM/I footprint scale) to the Rug_mean (Aquarius footprint scale) from undulating to mountainous. With a coastline at about 85 km, a major difference of spatial variability exists between SSM/I and Aquarius measurements over the Kamchatka site.

The Quebec site (Fig. 6b), also over tundra land cover, has better product agreements with TAVGweek than the Kamchatka site, with percentages around 90 %. FT-AP generally has a better agreement with TAVGweek during the fall freezing periods. There are only minor exceptions due to a few false frozen retrievals in summer. These exceptions show a typical situation in which FT-AP detects the freeze onset earlier than FT-ESDR, as mentioned in Sect. 3.2. The relatively high ΔNPR (ΔNPR=0.024 and 0.032 for radiometers 1 and 2, respectively) could be a factor generating fewer false flag retrievals than in the Kamchatka site grid cell.

For forest sites (Fig. 6c–d), both products have good agreement with TAVGweek. The statistics for the Siberia site highlight the highest agreement: 97.7 % for FT-AP and 97.1 % for FT-ESDR. Interestingly, the forest sites have ΔNPR values comparable to those of the tundra sites, with ΔNPR=0.022 and 0.029 for radiometers 2 and 3, respectively, in Siberia, and a unique ΔNPR=0.010 for radiometer 1 in Alaska. The latter value is the lowest of all the sites in this study. Since Alaska has relatively good FT-AP agreements (87.7 % with TAVGweek and 88.9 % with FT-ESDR), clearly small differences between FFfr and FFth alone cannot explain the false frozen retrieval problem at the L band.

At the open land sites, the low agreement (Fig. 6e–f) between FT-AP and TAVGweek (70.9 % in Kazakhstan and 73.3 % in Saskatchewan) is mainly due to the false frozen retrieval in summer. During the transitional period, the FT-AP is in good agreement with TAVGweek, sometimes better than FT-ESDR, especially in the fall of 2012, 2013 and 2014 in Kazakhstan. Nevertheless, FT-ESDR agrees relatively well, with 92.0 % in Kazakhstan and 84.6 % in Saskatchewan. The winter of 2011 in Saskatchewan was particularly warm, and the products reacted differently to a succession of events over 0 ∘C, which affected the overall agreement percentage. The ΔNPR values of the open land sites are 0.088 for radiometer 2 in Kazakhstan and 0.029 and 0.095 for radiometers 1 and 3 in Saskatchewan. Consequently, since these are the highest values of all sites, in this case, the false frozen retrievals cannot be explained by a small value of ΔNPR.

Comparing both products to SAT at different sites shows that FT-AP tends to identify false frozen retrieval in summer periods. It is beyond the scope of this paper to explain why these misclassifications occur, but some hypotheses will be given in Sect. 4.