**3. Methods**

The melt season parameters were determined by fitting sigmoids to CLARA-A2 SAL pentad (5 day) mean albedo values using non-linear regression [48]. For each grid cell and year the 5-day mean albedo values from the end of January until the end of August were used for the sigmoid fitting. Figure 2 shows two examples of sigmoid fitting. To include all changes in albedo during the melt season, the dates of snow melt at the onset was taken to be the date at which the sigmoid reached 99% of its variation range (i.e., a change of 1% (relative) from the pre-melt albedo level). Likewise the end of the snow melt season was defined to be the date at which the sigmoid reached 1% of its variation range. These thresholds were chosen in order to include the whole dynamic change in surface albedo during melt season. The length of the melt season was then the difference between the start and end date of melt. The albedo values corresponding to the dates of the onset and end of melt were used as the representative albedo values preceding and following the melt season.

**Figure 2.** Sigmoid fitting for 5-day mean albedo data for (**a**) location 55.375◦N, 47.625◦E for year 2006 and (**b**) location 68.125◦N, 120.125◦E for the year 2007. The growth of vegetation after snow melt is manifested in (**b**) where the albedo values after melt season increase slightly as the vegetation starts to produce leaves.

In some cases the snow melt onset could not be determined, because the melt had already started before the first cloud-free albedo pentad of the year was available for the grid cell in question. The final analyses included only the grid cells for which (1) both the snow melt onset and end days were retrieved successfully; (2) the albedo difference between the start and end date of melt was larger than 5% absolute albedo units; and (3) data meeting these two criteria were available for at least 10 years. The mean values of *R*<sup>2</sup> and RMSE of the final sigmoid regressions were 0.989 and 5.55 (albedo

percentage), respectively. The corresponding median values were 0.993 and 4.75. In the analyses only the grid cells for which *R*<sup>2</sup> > 0.95 and RMSE < 20 (for the sigmoid fitting) were included. This lead to discarding about 2% of the data. The final dataset consisted of 2.46 million grid cell level melt seasons. Figure 3 shows the number of years with successful melt season retrievals per resolution unit.

**Figure 3.** Number of successful retrievals of melt season per resolution unit during the 34 years.

The effect of random error in the albedo data on the derivation of the melt season timing was estimated by using 6 different sigmoids with different levels of albedo prior to melt. After constructing artificial data around these sigmoids, the data was modified by introducing relative random error of +12.5% to −12.5% to it. This error is larger than the level of typical variation of albedo values. These data with random error were then used to produce sigmoids and to extract the melt season parameters. The analysis was repeated for 100 different cases for each of the six chosen pre-melt levels with random error. The effect of relative random error in the albedo data on the start date of melt was 1.3 days (standard deviation) and 1.1 days for the end dates of melt.

The trends for the melt season parameters (start and end times of melt, the length of the melt season and albedo levels before and after the melt season) for each grid cell over the 34 years were detected using linear regression. The trends were determined using rolling 5-year means. Only 5-year means with data from at least 3 years were included in the trend fitting, and the fitting was carried out only for grid cells that had at least 20 mean values during the 34 years. This gave 72092 grid cell level estimates of trends in pre melt season albedo. From these 30% had *R*<sup>2</sup> larger than 0.5.

The climatic dependencies of the melt season parameters were studied using ERA-Interim re-analysis data [46] for air temperature at 2 m, precipitation and wind speed prior to melt. The time interval used in the analysis was 14 days prior to melt. Correlation analysis between ERA-Interim climate data and surface albedo or day of onset of melt were carried out only for the grid cells for which data were available for at least 20 years. The analysis was performed by looking at the linear correlation coefficient between the melt season parameter in question and the climatic parameters.

The GlobCover2009 land-use data set (Figure 1) was coarsened to the same resolution as the melt season data (CLARA-A2 resolution of 0.25◦). The area of the boreal forest was determined by looking at GlobCover classes 70, 90 and 100. The tundra areas were determined as the grid cells with land-use class 140, 150 and 200 that are north of 55◦N in North America and 65◦N in Europe.
