**1. Introduction**

The globally averaged surface temperature has increased by 0.85 ◦C over the period of 1880–2012 [1], with particularly strong warming signals appearing at high northern latitudes [2–4]. This is known as the Arctic amplification [5–7]. One of the main contributions to the amplified warming is perhaps the positive surface albedo feedback [8–10], primarily snow and ice albedo feedback. The ice,

specifically, refers to bare ice, melting ice (mainly includes sea ice, glaciers and ice caps), snow-covered ice, open water, etc. [1]. In the warming climate, the decreasing snow cover (ice) extent and snow (ice) depth are leading to a less reflective planet that absorbs more solar radiation, and thus warming the earth further [11,12].

Climate feedback variables are valuable indicators of climate change due to their sensitivity to temperature. Specifically, a central task of climate change research is to quantify the Equilibrium Climate Sensitivity (ECS, [13–15]), which refers to the equilibrium change in annual mean surface temperature with a doubling of the atmospheric equivalent carbon dioxide concentration [16–18]. However, no agreement has been reached on the magnitude of the ECS [19], and the large uncertainty in the ECS is primarily attributed to the inaccurate estimation of individual feedbacks [20–22].

Models are useful tools for climate feedback study for their capability of long-term simulation. Energy balance models were first used mainly for the recognition of feedback mechanisms and dynamic processes [23–25]. Later on, General Circulation Models (GCMs) were widely used to investigate whether variables act as positive or negative feedbacks and the magnitude of each feedback [26–28]. In recent development, the Atmosphere–Ocean General Circulation Models (AOGCMs) make it possible for more detailed and comprehensive estimation of individual feedbacks [17,29,30]. However, feedback estimations from model simulations are still associated with large uncertainties, i.e., fivefold intermodel difference on surface albedo feedback was reported in the Fourth Assessment Report (AR4) of Intergovernmental Panel on Climate Change (IPCC) models [31]. Such uncertainty remains in IPCC AR5 [1,32].

Observation-based research has also made its contribution to feedback assessment, with more realistic representation of the climate from observations. For example, Flanner et al. found that the Coupled Model Intercomparison Project Phase 3 (CMIP3) models underestimated the snow and ice albedo feedback in Northern Hemisphere, as compared with results based on satellite observations of the Extended Advanced Very High Resolution Radiometer Polar Pathfinder (APP) product and Moderate Resolution Imaging Spectroradiometer (MODIS) data [33]. Fletcher et al. showed that the modeled average snow albedo feedback in the CMIP3 models was slightly larger than satellite observations [34]. Dessler reported an agreement on both global average and spatial pattern between model results and individual feedbacks that were calculated based on reanalysis data of ERA-Interim [35] and Modern-Era Retrospective Analysis for Research and Applications (MERRA, [36]) [37]. However, problems also exist in observation-based results. For example, the coarse resolution of observational data would either temporally or spatially smooth the feedbacks, especially in snowmelt seasons [38,39].

Due to the fact that large differences and uncertainties remain in snow albedo feedback assessments, an effective way to improve its accuracy is to use observation-based results to constrain model assessments [1]. Nonetheless, most snow albedo feedback studies were based on model simulations, and only few on observations [40–42]. Moreover, most of these studies calculate the combining effects of snow albedo feedback and ice albedo feedback, namely surface albedo feedback [13,37,43]. As a result, it is impossible to separate the contribution of snow or ice albedo feedback, as well as their uncertainties.

Being motivated by these scientific findings and limitations, this study specifically focuses on the quantification of snow albedo feedback by remotely sensed snow cover products of MODIS (MOD10C1 and MYD10C1), atmospheric reanalysis data and radiative kernel data. The purpose is to examine the source of the differences between our result and partially observation-based results, as well as Coupled Model Intercomparison Project Phase 5 (CMIP5) model-based results, and to provide precise information of snow cover change and snow albedo radiative forcing for model parameterization.

Data and method are described in Section 2. Spatial and temporal variability of snow cover, snow albedo radiative forcing and its feedback are calculated and analyzed in Section 3. Comparison and discrepancy analysis with both partially observational-based and model-based studies, strengths and uncertainties of this work are discussed in Section 4. Conclusion follows in Section 5.
