This study uses TB data from the Special Sensor Microwave/Imager (SSM/I, 1987–2008), and the Special Sensor Microwave Imager/Sounder (SSMIS, 2009 to present) re-projected to 25 km equal-area scalable earth-grid (EASE-Grid) available from the National Snow and Ice Data Center in Boulder, Colorado (Armstrong et al., 1994). These sensors provide a continuous time series of TB since 1987 (Table 1). We do not perform sensor cross calibration given that only small differences were found between sensors (Abdalati et al., 1995; Cavalieri et al., 2012; Stroeve et al., 1998). Since our melt detection algorithm (described below) only uses the relative change in the temporal variations in TB, slight offsets in absolute TB between sensors should not affect algorithm performance. The gaps in the data are filled by linear interpolation from adjacent days. Vertically polarized TB from both morning and afternoon overpasses are utilized to increase the likelihood of observing melt events. Due to large temporal gaps in the early SSM/I record, the time series used begin in the fall of 1988 and extend to 2014 (Table 1). Although horizontal polarized measurements are more sensitive to ice lenses within the snowpack (Derksen et al., 2009; Rees et al., 2010), there is not much difference between the two polarizations for melt detection and we use vertically polarized measurements to be consistent with Wang et al. (2013).

As the purpose of this study is to detect winter melt events, the winter period duration (WPD) is defined as occurring between the main snow onset date (MSOD) in the fall (beginning of continuous dry snow cover on the ground) and the main melt onset date (MMOD) in the spring (i.e., the beginning of the period with frequent melt–refreeze diurnal cycles) at each pixel. Figure 1 illustrates the steps involved in detecting melt events for the WPD, based on the temporal variations in the difference of the brightness temperature (TBD) between 19 and 37 GHz and a 37 GHz TB threshold. For dry snow conditions, as snow accumulates TBD increases due to the larger scattering effect of the microwave signal by snow grains at 37 vs. 19 GHz (Chang et al., 1987). Upon the appearance of liquid water in snow, TB increases at both frequencies and results in a sharp drop in TBD to similar magnitudes seen in snow-free conditions, but will quickly revert back to dry snow TBD levels once the snow refreezes, allowing for the detection of melt–refreeze events (Fig. 2).

The purpose of determining MSOD is to capture the earliest start date of the continuous dry snowpack. The MSOD is determined as the first date when (1) TBD ≥ Tsn (a threshold = mean July TBD + 3.5 K) for 7 out of 10 days and (2) TB37v < 253 K for 10 out of 11 days (Fig. 1). The thresholds and conditions were optimized by comparing the PMW determined MSOD to daily snow depth observations from the Global Surface Summary of the Day dataset archived at the National Climate Data Center (http://www.ncdc.noaa.gov). The TB criterion in (2) is applied to exclude periods with TBD fluctuations related to early season freeze/thaw cycles rather than winter melt events (see below for its derivation).

MMOD is determined following Wang et al. (2013). Their algorithm was based on temporal variations in TBD relative to the previous 3-day average TBD (referred to as M hereafter). Melt onset was detected if the difference in M and daily TBD was greater than a threshold (THold = 0.35 ⋅ M) for four or more consecutive days. Based on trial and error, the MMOD detection algorithm in Wang et al (2013) is modified here to detect mid-winter melt events that are typically of shorter duration. Firstly, the threshold is modified slightly from THold = 0.35 ⋅ M to THnew = 0.4 ⋅ M (pixel-dependent) since the goal is to detect melt events with one or more days of duration (instead of four or more days as in the previous study), and secondly, a TB37v threshold condition is added following Semmens et al. (2013) to mitigate false detection due to TBD changes not related to melt (e.g., from noise or artifacts from data gap filling). The resulting expression for winter melt event conditions is (M-TBD) > THnew and TB37v ≥ 253 K for one day (Fig. 1), referred to as the winter TBD algorithm hereafter. The TB37v ≥ 253 K condition was obtained by evaluating a range of TB37v values from 250 to 255 K, at 1 K increments to identify the threshold most sensitive to the presence/absence of liquid water in snow. This was inferred from histograms of daily maximum (Tmax⁡), mean (Tm), and minimum (Tmin⁡) air temperatures for days detected as melting at all available weather stations during 2000–2007 (see locations in Fig. 5b, ∼ 5100 observations in total). The results show that for TB37v = 253 K, Tmax⁡ is ≥ 0 ∘C for nearly 96 % of cases, Tmin⁡ is < 0 ∘C for 94 %, and Tm is ≥ 0 ∘C for 80 %. This suggests that the PMW-detected winter melt events are consistent with diurnal positive air temperature events, while most of the events (80 %) probably last multiple hours, thus corresponding to days with Tm ≥ 0 ∘C. If a melt event is detected within 10 days of the MMOD, then it is not considered a mid-winter melt event but rather a preliminary melt event to the MMOD, and is excluded from the analysis.

An example of the performance of the winter TBD algorithm is shown in Fig. 2 for a case at Pudasjarvi, Finland (65.4∘ N, 26.97∘ E), during the 2013–2014 winter. At Pudasjarvi station, the snow depth first became greater than 0 cm on day of year (DOY) 291 of 2013. The snow depth was mostly less than 10 cm for days 291 to 332, with two periods of no snow on the ground while Tmax⁡ fluctuated around 0 ∘C. The PMW detected MSOD was on DOY332, corresponding within one week of the date of continuous snow cover above 10 cm observed at the station (Fig. 2b). MMOD was detected on DOY64 of 2014; however, there was still snow on the ground until DOY108, typical of high-latitude snow cover where melt onset is followed by the spring thaw, which is a sustained period with high diurnal air temperature variation where the snowpack is melting during the day and refreezing at night. At the end of this melt–refreeze period, the snowpack may be actively melting both day and night until snow disappearance, which can take several weeks (Semmens et al., 2013). During winter 2013–2014, 20 melt days in total were detected at Pudasjarvi, all corresponding to days with Tmax⁡ ≥ 0 ∘C. However, not all days with Tmax⁡ ≥ 0 ∘C are detected by PMW as melting, for example DOY351–352, for reasons which will be explained further in the validation section.

The winter TBD algorithm is applied to time series of TB for each winter over the period 1988–2013. Melt events may last from one to several days and in some cases the algorithm may split events. For this reason we use the annual number of melt days (rather than number of events) in presenting and analyzing the results. The WPD varies at each pixel and is determined by MSOD and MMOD as described above. This approach is referred to as “PMW-varying” in the following analysis. Since we focus on melt events during the winter period, the TBD algorithm is only applied to pixels with MSOD detected before the end of December and with MMOD later than 1 March, i.e., with WPD > 60 days. The PMW-varying approach is internally consistent in that it takes account of annual variations in winter temperature and snow cover. This is not the case for analysis using a fixed “winter” window where spurious trends can be created from changing seasonality (i.e., earlier snow melt). To highlight this, a fixed window approach is also applied (“PMW-fixed”) where the TBD algorithm is applied to time series of TB from November to April. The results presented in the following sections are from the PMW-varying method unless explicitly indicated otherwise. Since the microwave response of melt on permanent snow and ice is different from seasonal terrestrial snow cover, we mask out the Greenland ice sheet and glaciers in our analyses.

Winter melt event information from the 0.75∘ × 0.75∘ latitude/longitude European Centre for Medium-Range Weather Forecasts Re-Analysis Interim (ERA-I) (Dee et al., 2011) and the 1/2∘ latitude by 2/3∘ longitude Modern Era-Retrospective Analysis for Research and Applications (MERRA) (Rienecker et al., 2011) reanalyses were used to evaluate the melt event climatology generated by the PMW method. Melt events in the reanalyses are inferred from 6-hourly air temperatures over the same period as the satellite data. For the comparison, a winter thaw event is defined as a period of above-freezing daily mean air temperature occurring during the winter period dominated by below-freezing air temperatures. Here the winter period is defined by 0 ∘C crossing dates (between fall and spring) obtained with a centered 30-day moving average of daily mean air temperature, which is analogous to the “PMW-varying” method described above. An additional condition is imposed of a surface snow cover of at least 10 cm depth for ERA-I and 4 mm SWE (snow water equivalent) for MERRA to obtain results comparable to the PMW method of detection over snow-covered ground. The mean daily air temperature is the average of the 00:00, 06:00, 12:00 and 18:00 UTC values. Snow depths for ERA-I are taken from the daily snow depth reconstruction described in Brown and Derksen (2013) to avoid various inconsistencies with the snow depths in the reanalysis.

The satellite-based winter TBD algorithm is validated with surface-based PMW radiometer measurements and near-surface air/snow temperature observations recorded on 12–13 April 2010 during a field campaign near Churchill, Manitoba, Canada (Derksen et al., 2012). A modified version of the winter TBD algorithm is applied to the surface-based radiometer measurements due to the continuous nature of the data. We simply used the average TB values from the stable pre-melt period as our reference frozen TBD value instead of a previous 3-day average.

Furthermore, we try to characterize winter melt events detectable by the winter TBD algorithm using snow pit surveys recorded during multiple PMW snow measurement campaigns conducted between 2005 and 2010 in both the boreal forest and tundra environments of Canada (Table 2). The number of satellite-detected melt events for the specific EASE-Grid pixels surrounding the snow pit locations are compared to the number of melt forms/ice formations identified within the snowpack. A melt feature identified lower (closer to the ground) is consider an early winter event, while those melt features identified closer to the surface of the snow are considered more recent events. An example of the coincident satellite, air temperature and snow pit information for a survey site near Thompson, Manitoba, is shown in Fig. 3. Hourly air temperatures from weather stations in the vicinity of the snow pits (within 70 km) are examined to identify if and when a melt event occurred in the region; how long the melt event lasted; what the average temperature was for the duration of the event and what the minimum, maximum and average 36 h air temperatures were preceding the melt event. Results of the field evaluation are presented in Sect. 3.1

Gridded (5∘ × 5∘) monthly surface air temperature over land areas during the study period are obtained from the Climatic Research Unit (University of East Anglia) CRUTem4 dataset (Jones et al., 2012). Seasonal air temperature trends for the fall (September–November), winter (December–February) and spring (March–May) periods are computed to assist the interpretation of trends in winter melt events. The Mann–Kendall method is used for trend analysis taking into account serial correlation following Zhang et al. (2000). Trends are only computed at grid cells with melt events detected in at least 12 winters, and grid cells with trends statistically significant at 90 % level are shown. Correlations between the winter melt-related variables are computed using the Pearson correlation method with significance levels determined from the two-tailed Student's t test.

Figure 4 illustrates the time series of the surface-based radiometer TB and air/snow temperature measurements recorded during the 12–13 April melt event near Churchill. The area shaded in green highlights the period for which the modified TBD algorithm identified the melt event. As the near-surface air temperatures approached 0 ∘C, TB increased rapidly at both 19 and 37 GHz. The detected melt onset occurred ∼ 40 min after the 11 cm and 7 cm air temperatures crossed the 0 ∘C threshold and 25 min before the 2 m air temperature exceeded 0 ∘C, likely due to radiant heating from the sun to the snow surface and the boundary layer air temperature probe. The -1 cm snow temperature did not reach 0 ∘C until 3 h after the detected melt onset, suggesting that the rapid increases in TB here were responses to the appearance of liquid water in the snow surface. The influence of radiant heating is evident during the late afternoon/early evening as the incoming solar radiation lessens as the sun begins to set (∼ 19:00 LT), at which point the snowpack and boundary layer air temperatures all drop below 0 ∘C, coinciding with a decrease in TB even while the 2 m air temperatures are still positive. Compared to the rapid increase in TB during the melt onset, the more gradual decrease in TB is likely due to the mixed effects of uneven refreezing of the snow surface and delayed freezing of subsurface liquid water.

The validation results from the seven snow pit survey sites and 12 melt events are summarized in Table 2. The performance of the winter TBD algorithm is highlighted in bold for a successful melt detection and in italic for a failed detection. The results suggest that a successful detection is likely when the melt duration lasts for periods longer than 6 h and/or the melt event has been preceded by warm air temperatures that have warmed the snowpack to near melting conditions (previous day's Tmax⁡ > -3 ∘C). In these situations, it is common for melt features to form within the snowpack. The algorithm does not reliably identify short duration melt events or events that occur immediately after extremely cold air/snowpack temperatures (previous 36 h minimum air temperature < -13 ∘C). In these instances, the snowpack likely has enough thermal inertia to remain within a frozen state for the whole duration of the melt event, or very quickly return to a frozen state and thus liquid water is not detectable with satellite TB. Out of all 12 melt events investigated, 6 events coincided with observed ROS. Of the six ROS events, half were associated with successful satellite melt detection. Those ROS events that were successfully detected were followed by a continued warming of air temperatures that likely delayed the refreezing of the liquid water in the snow. Those ROS events that were not detected fall under the category of a short-duration melt event as described above.

The winter TBD algorithm is very sensitive to liquid water within the snow, but does not necessarily capture all events that can create melt features within the snowpack, largely due to the fact that liquid water from both melt and ROS events tends to re-freeze quickly during the winter months. Unless these events occur very close to the timing of the satellite overpass (ascending ∼ 18:30 LT and descending 06:30 LT), they may remain undetected. In addition, widespread, spatially expansive melt or ROS events are rare (Bartsch, 2010; Cohen et al., 2015), and as such may be missed by the coarse-resolution (25 km) PMW data. These limitations are common to other melt detection techniques that utilize current spaceborne passive microwave sensors.

Figure 5 shows the PMW-derived MSOD, MMOD and WPD during the 1988–2013 period. On average, continuous snow cover starts in the Canadian Arctic islands and high-elevation regions of the Arctic in September and progresses to the open tundra in October (Fig. 5a). By November, most of the areas north of 50∘ N are covered by snow except for some temperate maritime and lower-latitude regions where continuous snow cover sets in December. The spring main melt onset starts at lower latitudes in March, progresses to the boreal forests and tundra in April/May, and reaches the high Arctic in June (Fig. 5b), giving rise to spatial variability in the duration of the winter period from one to seven months on average (Fig. 5c). A pixel-wise definition of winter period for melt detection is required to account for this spatial variability as well as the temporal variability from year-to-year fluctuations in snow cover.

During the 26 winters covered by this study, melt occurred at least once everywhere north of 50∘ N using the PMW-varying window method (Fig. 6a). However, the average cumulative number of melt days is less than one week per winter for most areas, with more melt days (around two weeks per winter) occurring in areas with a relatively long snow season and more temperate winter climates (e.g., central Québec and Labrador, southern Alaska and Scandinavia). The spatial distribution patterns of NMD (number of melt days) from ERA-I (Fig. 6c) and MERRA (Fig. 6d) generally agree with that from PMW. However, ERA-I detects about one week more melt days on average in most areas, while MERRA detects fewer melt days in Québec and central Canada relative to PMW. Both ERA-I and MERRA detect more melt days in southern Alaska and western North America (NA). These are relatively deep snowpack regions where melt may not occur in short periods of freezing air temperatures due to the thermal inertia of the snowpack. Compared to the PMW-varying window method (Fig. 6a), there are many more melt days detected using the PMW-fixed window method (Fig. 6b), especially in the relatively temperate climate regions (e.g., northern Europe and lower latitudes of NA and Russia) where the WPD is relatively short and thus limits the possible number of melt days to be detected.

Figure 7 shows the monthly mean NMD from October to June during the period 1988–2013. Winter melt events mainly occur in the fall (October–November) and spring (April–June) months at high latitudes (> 60∘ N) where continuous snow starts early and melts late (Fig. 5). During November to March for the period 1988–2013, no winter melt events are detected across large areas of Siberia and the Canadian and Alaskan tundra where the monthly surface air temperature is usually lower than -20 ∘C (not shown). On average, April has the maximum extent and duration of winter melt events (Fig. 7).

The PMW-derived estimates of changes in snow cover (MSOD, MMOD and WPD) over the 1983–2013 period are shown in Fig. 8. Large regions of the Arctic exhibit trends toward later snow onset, particularly over northern Scandinavia, western Russia, Alaska and Québec (Fig. 8a, d). The timing of the spring main melt onset date exhibits trends to earlier melt over most of the Arctic except for northern Europe and western NA (Fig. 8b, e). The net effect is significant negative trends in winter duration period that exceed -10 days decade-1 over large regions of the Arctic (Fig. 8c, f).

Over the study period, there are few significant trends in NMD over the Arctic (Fig. 9a, c), and where there are significant trends, these are dominated by decreases over northern Europe. The spatial distribution patterns of NMD trends contrast markedly between the PMW-varying and the PMW-fixed results (Fig. 9b, d). Trends from PMW-fixed are dominated by increasing trends in NMD over most of the Arctic except for northern Europe. Corresponding trends from the reanalyses are not shown because the annual winter thaw frequency series from ERA-I and MERRA are not always consistent over the 1988–2013 period in some regions. For example over northern Québec (not shown) the two series are well correlated over the period from 1980 to 2001 (r = 0.75, p < 0.001) but diverge markedly after 2001, when numerous changes in data assimilation streams occurred in both reanalysis datasets (Rapaic et al., 2015). This underscores the advantage of the PMW melt detection approach, which is based on a consistent TB time series.