\begin{sidewaysfigure}
\label{arc_kernel}
\centering
\includegraphics[width=50pc]{F1.pdf}
\caption{Arctic summertime (MJJA) surface albedo radiative sensitivity (RS) calculated from radiative kernels (upper panels) and estimated from the climatological radiative fields using the idealized isotropic radiation model (lower panels) in the same models. The squared spatial correlation coefficient between the kernel isotropic methods in the same model are provided in the middle and the Arctic domain averaged values are shown in the upper right of each panel.Note that there is no RS calculation from the GFDL model because mean state fields from this simulation were not saved.} Observational estimates from CERES EBAF satellite data and the isotropic model are shown to the right.
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{so_kernel}
\centering
\includegraphics[width=50pc]{F2.pdf}
\caption{As in Fig. 1 but for the NDJF RS in the Southern Ocean. Domain averaged surface albedo feedbacks exclude the Antarctic continent. Note that the figures are ordered by domain average RS over the Southern Ocean and this order differs from Fig. 1.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{cartoon}
\centering
\includegraphics[width=50pc]{F3.pdf}
\caption{Schematic of the single layer isotropic model modified from T07.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{arc_kernel_cs}
\centering
\includegraphics[width=50pc]{F4.pdf}
\caption{Comparison of Arctic Summertime (MJJA) full sky and clear sky surface albedo kernels.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{arc_kernel_param}
\centering
\includegraphics[width=40pc]{F5.pdf}
\caption{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.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{arctic_iso}
\centering
\includegraphics[width=50pc]{F6.pdf}
\caption{Arctic summertime (MJJA) radiative sensitivity estimated using the isotropic model and the climatological radiation fields for CMIP5 historical simulations. Models are ordered as in reading a book (left to right then down) according to the domain average albedo feedback. Asterisks denote the models for which radiative kernel calculations are available that have been repeated from Fig. 1. The dark purple line shows the sea ice edge designated by the MJJA 50 $\%$ sea ice concentration contour. The full domain spatial average is shown in the upper left corner of each panel in black, the Arctic ocean average is shown in the lower right corner in blue and, the spatial average over the sea ice is shown in the lower left corner in purple. Observational estimates from CERES satellite data are shown in the bottom right panel.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{sidewaysfigure}
\label{so_iso}
\centering
\includegraphics[width=50pc]{F7.pdf}
\caption{As in Fig. 6 but for the NDJF Southern Ocean RS. Domain averaged surface albedo feedbacks exclude the Antarctic continent. The dark purple line shows the sea ice edge designated by the NDJF 50 $\%$ sea ice concentration contour. Note that models are ordered by Southern Ocean domain averaged RS and this order differs from that in Fig. 6. Asterisks denote the models for which radiative kernel calculations are available that have been repeated from Fig. 2.}
\end{sidewaysfigure}
\efloatseparator
 
\begin{figure}\label{obs_maps}
\centering
\includegraphics[width=24pc]{F8.pdf}
\caption{Spatial maps of observational estimates of summertime (MJJA) radiative sensitivity(RS, top), ice sensitivity (IS, middle) and the radiative impact of surface albedo change ( $RI_{TOA,\alpha}$, bottom). The RS is calculated from the isotropic shortwave model applied to the CERES data. The IS is calculated from Observational Best Estimate (OBE) surface albedo change between 1982 and 2016 divided by the global mean surface temperature change.  The left panels show the central estimates of each quantity and the right panels show the uncertainty (2 standard deviations, $\sigma$) calculated from a Monte Carlo bootstrapping re-sampling with replacement as described in the Appendix.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{feedback_spread}
\centering
\includegraphics[width=37pc]{F9.pdf}
\caption{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.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{soden_iaf}
\centering
\includegraphics[width=37pc]{F10.pdf}
\caption{Comparison of ice albedo feedback calculated from CMIP5 4XCO$_{2}$ using (ordinate) the method of \citet{soden_kernel} with RS in all models set to the GFDL surface albedo kernel versus (abscissa) the method introduced here with RS calculated from the model specific climatological radiative fluxes via the isotropic model. The blue markers show the contribution of the ocean domain only and the red markers show the full domain. All values shown are the contribution to the global mean. Dots show individual models and filled squares show the ensemble average with bars showing one standard deviation of the mean. The upper left shows the NH, the upper right the SH and the bottom the global mean. The black line is the 1:1 line.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{arc_kernel_donohoe}
\centering
\includegraphics[width=37pc]{AP1.pdf}
\appendcaption{A1}{Arctic summertime (MJJA) surface albedo radiative sensitivity (RS) calculated from radiative kernels (upper panels) and estimated from the climatological radiative fields using the idealized isotropic radiation model of T07 (middle panels) and \citep{donohoe_battisti_11a} in the same models (bottom panels). The squared spatial correlation coefficient between the kernel isotropic methods in the same model are provided in the middle and the Arctic domain averaged values are shown in the upper right of each panel.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{ker_iso_scatter}
\centering
\includegraphics[width=32pc]{AP2.pdf}
\appendcaption{A2}{(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.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{ker_iso_scatter_SO}
\centering
\includegraphics[width=32pc]{AP3.pdf}
\appendcaption{A3}{(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.}
\end{figure}
\efloatseparator
 
\begin{figure}\label{comp_delta_alb}
\centering
\includegraphics[width=32pc]{AP4.pdf}
\appendcaption{A4}{Comparison of the (MJJA) surface albedo changes (1982-2016) calculated from the NSIDC sea ice concentration data (left) and the APP-x surface albedo data (right).}
\end{figure}
\efloatseparator