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\bibcite{cmip5_ice_sensitivity}{{54}{2015}{{Stroeve and Notz}}{{Stroeve, and Notz}}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Comparison of the atmospheric opacity parameters that result from the application of the isotropic model to the Arctic summertime (MJJA) mean state radiative fields in the different climate models and observations. (Top Row) All-sky RS repeated from Fig. 1. (Second Row) Cloud reflectivity defined as the isotropic reflectivity applied to the all-sky radiative fields minus that defined from the clear-sky fields with the latter shown in the third row. (Bottom row) All-sky absorptivity. The (full Arctic) domain average is shown in the upper right of each panel. The four models for which kernels are available are shown to the left columns and the observational calculation from CERES data is shown to the right.\relax }}{50}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Estimates of global (and annual) SIAF from climate models and observations using the radiative sensitivity (RS) from the isotropic model applied to the climatology and the change in surface albedo under external forcing normalized by the global mean temperature change. (Upper left) Arctic sea ice changes over the historical (2007 to 2016 minus 1982 to 1991 averages). The black bars show the CMIP5 model distribution using the climate model specific radiative sensitivity and ice changes, the blue bars show the distribution using the model specific sea ice changes and observational RS and the red bars show the distribution using the observational sea ice change and model specific radiative sensitivity. Solid vertical lines show the model mean of each distribution. The dashed vertical line shows the observational estimate. The overlayed dark and thinner distribution shows the histogram of observational estimates of ice albedo feedback calculated from a Monte Carlo re-sampling of subsets of the ice albedo data and radiative data; the black distribution shows the impact of uncertainties in the observational RS and IS combined, the blue distribution shows the impact of the IS uncertainty only and the red shows the impact of the RS uncertainty only. (Lower Left) As in the above panel except using the modeled changes in the 4XCO$_{2}$ simulations. (Lower Right) Distribution of surface albedo feedback in the Southern Ocean diagnosed from 4XCO$_{2}$ normalized sea ice changes. Because the observational estimate of sea ice changes over the historical simulation is not statistically significant, the red distribution is calculated from the model specific radiative sensitivity and the model mean normalized sea ice change.\relax }}{54}}
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\@writefile{lof}{\contentsline {figure}{\numberline {A2}{\ignorespaces (Top panel) Scatter plot of MJJA radiative sensitivity calculated by (ordinate) radiative kernels and (abscissa) the isotropic model from the mean state in the same climate model. All four climate models and Arctic gridpoints considered collectively. (Bottom panel) Scatter plot of MJJA radiative sensitivity calculated from radiative kernels in one model versus the radiative sensitivity calculated from radiative kernels in a different model (selected at random). The dashed black line shows the 1:1 line.}}{57}}
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\@writefile{lof}{\contentsline {figure}{\numberline {A3}{\ignorespaces (Top panel) Scatter plot of NDJFM radiative sensitivity calculated by (ordinate) radiative kernels and (abscissa) the isotropic model from the mean state in the same climate model. All four climate models and Southern Ocean gridpoints considered collectively. (Bottom panel) Scatter plot of NDJF radiative sensitivity calculated from radiative kernels in one model versus the radiative sensitivity calculated from radiative kernels in a different model (selected at random). The dashed black line shows the 1:1 line.}}{58}}
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