*4.2. Comparison with Model-Based Studies*

Based on the agreement among observation-based studies, snow albedo feedbacks of our work are compared with those from the 25 models that participated in CMIP5 (Qu and Hall [56], Table 1 of their paper).

Snow albedo feedback over the NEL estimated from the 25 models ranges from 0.18 to 0.78 W·m−2·K<sup>−</sup>1, with the ensemble mean of 0.42 ± 0.15 W·m−2·K<sup>−</sup>1. Our result is 0.18 ± 0.08 W·m−2·K<sup>−</sup>1. The global snow albedo feedback of the 25 models ranges from 0.03 to 0.16 W·m−2·K<sup>−</sup>1, with ensemble mean of 0.08 ± 0.03 W·m−2·K−1, and, in our case, it is 0.04 ± 0.02 W·m−2·K−1. In general, results of our work fall near the lower bound of the 25 models. The ensemble means of both hemispheric and global snow albedo feedbacks estimated by Qu and Hall [56] are larger than our results and the other partially observation-based results mentioned above. This might indicate an overall overestimation of snow albedo feedback by most of the 25 models. For the purpose of offering detailed information for model optimism, the possible source of discrepancies between this study and the 25 models is discussed below.

According to Qu and Hall, snow albedo feedback is mainly determined by two terms: one represents the variations in planetary albedo with surface albedo ( *∂α<sup>P</sup> ∂α<sup>S</sup>* ), and the other is the change in surface albedo associated with a 1 ◦C increase in *Ts* ( *αS TS* ) [56]. The spread of *∂α<sup>P</sup> ∂α<sup>S</sup>* is mainly determined by the surface albedo kernel, because this term is calculated as the ratio of surface albedo kernel to the TOA shortwave radiation. As the kernels used in models are also used in this study, we consider this coefficient is of little contribution to the difference. As a result, the major source of the discrepancy would be originated from *<sup>α</sup><sup>S</sup> TS* . Specifically, increase in the area-averaged surface air temperature (*Ts*) is relatively consistent both among the models and between model simulations and observations, thus surface albedo change (*αS*) could be the largest source of discrepancy between our work and the 25 models. Surface albedo change, which is mainly determined by albedo contrast between snow-covered and snow-free surface, is also considered to be most uncertain (threefold spread in CMIP3 and persists to be large in CMIP5) among models. However, as the spread of surface albedo change between snow-covered and snow-free surface is not directly analyzed in Qu and Hall's work [56], further investigations are still required.

Despite the fact that there are other factors contributing to the discrepancies, surface albedo change is considered as the predominate difference and possibly being overestimated by most of the 25 models. Therefore, model parameterization should specifically focus on this factor.

Moreover, according to Hall and Qu, the surface albedo decrease associated with loss of snow cover, rather than the reduction in snow albedo due to snow metamorphosis is more important in the determination of snow albedo feedback [41]. Thus, in turn, the significance of albedo constraint by snow cover data of high spatial and temporal resolutions in this study is strengthened. The information of snow cover change, as well as the constrained albedo data, can be guidance for the model parameterizations.
