*4.1. Comparison with Partially Observation-Based Studies*

There are extremely limited observation-based snow albedo feedback studies, so only three of the compatible ones (with similar study area of the North Hemisphere) are chosen for further comparison: snow and ice albedo radiative forcing estimation by Flanner et al. for 1979–2008 [33], both snow albedo radiative forcing and feedback estimations by Chen et al. for 1982–2013 [57] and snow albedo feedback estimation by Peng et al. for 1980–2006 [58]. It should be noted that, although feedback was also quantified in Flanner and coworkers' study, the regional mean value of the combining snow and ice albedo feedback makes it incomparable with our snow albedo feedback results.

The magnitude of snow albedo feedback is examined first. By using a linear fit between snow albedo radiative forcing change and temperature increase during the study period, Chen et al. calculated snow albedo feedback over the North Hemisphere to be 0.17 ± 0.008 W·m−2·K−<sup>1</sup> [57]. By multiplying the sensitivity of end date of snow cover to temperature by difference in black surface albedo before and after snowmelt, the result is 0.19 ± 0.17 W·m−2·K−1, according to Peng et al. [58]. With the method of block bootstrap test, snow albedo feedback of this study is 0.18 ± 0.08 W·m−2· ◦C<sup>−</sup>1. Despite the different methods and datasets applied in each work, results of the three studies agree well.

Snow albedo radiative forcing is also compared, as it's a key parameter of feedback and offers valuable spatial information. Both Flanner and coworkers' work and our work show similar snow albedo radiative forcing pattern in terms of spatial distribution and temporal variation [33]. Large snow albedo radiative forcing is found in the northern part of Eurasia, the mid-high latitude of North America and the Tibetan Plateau in both works, though the Tibetan Plateau exhibits even larger values in our work. In addition, seasonal cycle of snow albedo radiative forcing in both works show a single peak (peaks in April), with the largest value in spring months. Chen and coworkers' work, however, shows a relatively weaker consistency with us [57]: smaller value in the Tibetan Plateau as compared with Flanner et al. and our work, and a clear tendency of snow albedo radiative forcing with latitude, i.e., the higher latitudes exhibit larger radiative forcing.

While different surface albedo kernels used in these studies have proven to vary only a little [33,56], differences among the results of snow albedo radiative forcing are considered mainly due to albedo change caused by snow cover change ( *∂α <sup>∂</sup><sup>S</sup>* (*t*,*r*)). In Chen and coworkers' work, surface albedo instead of snow albedo data was used, thus the influence of vegetation change was imported to snow albedo change [57]. In addition, according to the conclusions of Singh et al., the coarse resolution of snow data (1◦ and monthly [33]) is likely to result in an overestimate of snow albedo radiative forcing [53].
