4.1. Impact of Clear-Sky Radiative Fluxes
 The impact of anomalous thermodynamics, clear-sky fraction and surface albedo on the radiative fluxes at the surface during the anomalous 2007 sea ice minimum year within the box region are examined in this section.Figure 6ashows the monthly (solid) and climatology (dashed) evolution of MODIS cloud fraction (black) and ERA-Interim surface albedo (blue). In general, cloud fraction was anomalously high, by as much as 20% during late autumn, in agreement withSchweiger et al.  and Graversen et al. . Surface albedo decreased from climatology during July and was anomalously low for the remainder of the year. Net surface clear-sky LW (blue), SW (red) and total flux (black) are shown inFigure 6b. Clear-sky SWN is calculated using the monthly averaged SZA and albedo for the region, neglecting contributions from aerosol forcing. Without clouds to reflect SW to space, climatological SWN (red dashed) increases rapidly after the end of the polar night and peaks in July near 230 W m−2, before declining to zero as both SZA and surface albedo increase. The reduction in surface albedo during 2007 resulted in an anomalous increase of SWN ranging between +20–40 W m−2. Net LW (LWN) during clear-skies (blue) is always negative due to the lack of cloud greenhouse trapping surface emission to space [e.g.,Stramler et al., 2011]. The deficit in LWN during 2007 was slightly greater than climatology during all months except during midsummer. However, the total clear-sky net radiation (black) during the melt period is strongly controlled by the annual cycle in SW. Both climatology and 2007 averages indicate that a clear-sky surplus of energy is available at the surface from May through August, peaking between 150 and 180 W m−2 in July.
Figure 6. The monthly (solid lines) evolution of 2007 and the monthly climatology of 2003–2010 (dashed lines) of (a) MODIS cloud fraction (black) and ERA-Interim surface albedo fraction (blue); (b) clear-sky net shortwave (red), net longwave (blue) and total net (black) radiation at the surface (W m−2); (c) net radiative anomalies (black) relative to climatology, including the net radiative anomalies estimated using the climatological upwelling surface longwave radiation (green); all in W m−2; (d) surface temperature (K); (e) monthly ice melt (positive) or freeze (negative) thickness (black) (m) due to the net clear-sky surface radiative flux estimated usingequations (2)–(3); the green line is the monthly clear-sky melt/freeze thickness estimated using the climatological upwelling surface longwave radiation.
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 Total clear-sky net radiative anomalies for 2007 are shown in black inFigure 6c, where an additional 20 and 40 W m−2is available to melt ice during July and August, respectively, in strong agreement with all-sky model estimates reported inJ. Zhang et al. . During summer, more energy is absorbed and melting is enhanced via the ice-albedo feedback [e.g.,Sellers, 1969], causing the surface temperature (Figure 6d, black) to increase above the melting temperature of saline water. Surface temperatures remain above climatology into autumn and winter via the anomalous heat absorption in the open ocean during the melt season. Perovich et al.  have shown the ocean absorption can enhance ice melt from the bottom up on the order of 500% over the Beaufort Sea region. Even with an albedo 20% lower than climatology in September, the increased SZA and a LWN deficit of 15 W m−2 more than climatology (Figure 6b) prevented the total net flux anomaly from being positive, marking the end of the radiative melt season.
 To emphasize the surface temperature impact on clear-sky LW anomalies, included inFigure 6cis the monthly net clear-sky radiative anomalies (green line) calculated using climatological LWU; these calculations are not biased by large surface temperature changes observed during 2007 (Figure 6d). The results indicate: (1) an increase in net radiative anomalies of 10 to 20 W m−2relative to the observed evolution (black line); (2) a clear signature of the thermodynamic anomalies on the LWD through April; and (3) positive radiative anomalies through years end from a combination of positive LWD anomalies and a reduction in LWU based on cooler surface temperatures. Anomaly calculations including LWU climatology are shown to highlight the importance of thermodynamic anomalies on total net radiation and to remove the positive surface temperature feedback on LWN. The actual radiative anomalies available for surface-melt or temperature modification will lie between the two curves inFigure 6c.
 Clear-sky ice melt associated with the monthly radiative fluxes are estimated following:
where M is total melt (m), Fcsis net clear-sky radiative flux (W m−2), Ls is latent heat of fusion (3.34 × 105 J kg−1), ρi is density of pure ice (917 kg m−3), and fis monthly clear-sky fraction (converted to total seconds of month with clear-sky conditions). Net clear-sky fluxes (W m−2) are calculated from
indicating the dependence on surface albedo (αs), SZA (included in SWD) and thermodynamic anomalies on the LWN; the impact of water-vapor anomalies on monthly averaged SWD was found to be small (order of 2 W m−2) relative to the downwelling radiance and is thus ignored, although recently Di Biagio et al. have shown that SW water-vapor forcing can be exceptionally large (−20 to −80 W m−2). Figure 6eshows monthly clear-sky ice melt (positive thickness, (m)) and freeze (negative thickness) for 2007 (black line) and climatology (black dashed). According to climatology, total ice thickness continually increases during the polar night and stops increasing with decreasing SZA between March and April. The onset of melt begins in May and continues through August. The annual cycle of ice thickness for 2007 follows that of climatology, however absolute values differ. Enhanced clear-sky LWD during the 1st four months inhibits the total ice growth, even with larger MODIS cloud fractions (reduced clear-sky fraction) during these months. Surface temperature and LWD anomalies for 2007 are shown together inFigure 7. They exhibit a distinct positive correlation with a high correlation coefficient (R = 0.92). The change in LWD flux required for a certain temperature change can be estimated by ∂LW/∂T = 4σT3. Between January and May, the anomalous clear-sky LWD is large enough to account for more than 80% of the observed surface temperature changes, highlighting the rapid adjustment of the surface to radiative forcing.Table 1shows cumulative ice-thickness anomalies split into seasons and for the full year. For January to April, large LWD anomalies resulted in a reduction of ice growth of just over 6 cm.
Figure 7. Monthly clear-sky surface temperature anomalies (K, black line) and clear-sky downwelling longwave radiation anomalies (W m−2, blue line) for 2007. The anomalies are positively correlated with an R-value of 0.92.
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Table 1. Cumulative Seasonal and Annual Anomalies in 2007 Ice Thickness Relative to Climatological Ice Thicknessa
| ||Ice Thickness Δz (m)|
|2007 LWU CLIM||0.105||0.044||0.321||0.470|
 Total clear-sky ice melt for May to August for 2007 was 0.713 m, compared to a climatological melt amount of 0.706 m (+0.7 cm anomalous melt,Table 1). Using submarine and satellite measurements of ice thickness from 1955 to 2008, Kwok and Rothrock report the mean thickness for this region to be between 1 and 2 m in early spring, and 0.5 and 1 m by the end of the melt season. Thus, climatological clear-sky ice melt of 0.7 m represents a substantial fraction of the total ice thickness of the region. Of the melting months, June is the only month during 2007 where melt was larger than climatology despite the relatively large radiative flux anomalies during July and August (Figure 6c). During these months, surface albedo was significantly lower due to increased open-water fraction, but the MODIS effective clear-sky fraction for these months was only 15 and 10%, respectively. Had all the clear-sky anomalous energy for July and August (Figure 6c) been consumed in melting ice, over 1 m of anomalous melt would have occurred. This anomaly agrees with the estimate made by Graversen et al. , where there it was attributed mainly to increased LWD from enhanced cloudiness [see also Schweiger et al., 2008].
 Despite the lack of anomalous contribution to melt during summer, positive thermodynamic anomalies during autumn and early winter inhibited the growth of first-year ice (Figure 6e), cumulatively by as much as 21 cm (Table 1). This clear-sky contribution to ice-growth retardation occurs even as the clear-sky fractions are anomalously low during this time of year (Figure 6a). Such a reduction on ice growth is considered important for the total melt amount of the following year, however such an examination is beyond the scope of this paper. Nevertheless, quantitatively we do note that the ice area for 2008 for the box region was the second lowest of the 8 years examined (Figure 1). Summing the clear-sky contributions for 2007, we find the yearly cumulative ice thickness to be nearly 0.3 m less than climatology (Table 1), a reduction that is approximately 15–30% of the annual climatological ice thickness of this region [Kwok and Rothrock, 2009]. Using the climatological value of LWU (Figure 6e, green line), thickness changes are even larger for the majority of months, and the total cumulative contribution to ice thickness is nearly 0.5 m less than climatology (Table 1).
4.2. Clear-Sky Melt Sensitivity
 Monthly clear-sky ice melt is highly sensitive to the cloud fraction and surface albedo as shown above, and here we develop a metric to quantify potential ice melt with the competing factors. The temporal evolution of anomalous ice melt associated with anomalies in radiatively important variables is shown inFigure 8(climatological mean values are given in the bottom left of each panel). Contours of anomalous clear-sky ice-melt (m) are shown for an anomalous LWD of 9 W m−2(the average LWD anomaly for June–August 2007). Additionally, solid lines represent the sensitivity of the zero-line contour (no change from climatology) for LWD anomalies of −20 (blue), 0 (black) and +20 (red) W m−2.
Figure 8. Temporal evolution of the monthly clear-sky sea-ice melt (positive contours) and freeze (negative contours) anomalies (m) for hypothetical cloud fraction (ordinate) and surface albedo (abscissa) anomalies for (a) June, (b) July, and (c) August. The melt (freeze) anomalies are calculated for a clear-sky LWD anomaly of +9 W m−2, the average clear-sky LWD anomaly for these three months during 2007. Cloud fraction and albedo anomalies are applied relative to the monthly climatological mean values provided in the bottom left of each panel. Solid lines indicate the cloud fraction and surface albedo anomaly combinations where there is no change in ice melt (freeze) relative to climatology for LWD anomalies of −20 (blue), 0 (black) and +20 W m−2.
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 Clearly, the largest clear-sky melt anomalies occur when both albedo and cloud fraction are anomalously low, and there is a distinct nonlinearlity to the anomalies especially during June and July (Figures 8a and 8b). During August, nonlinearity decreases as mean values restrict the permitted anomalies of cloud fraction and albedo and as SZAs increase. For example, a decrease in both mean cloud fraction and albedo by 10% results in an increased melt of 0.39, 0.40, and 0.28 m for June, July, and August, respectively. However, this increased melt occurs when both cloud fraction and albedo decrease together, a covariability that was not observed from 2003 to 2010, suggesting a potential feedback between cloud fraction and diminishing sea ice [Kay and Gettelman, 2009; Vavrus et al., 2011]. However, as shown in Figure 8, increased melt can occur for increased cloud fraction (decrease in clear-sky frequency) if albedo decreases sufficiently; this is what occurred during June 2007. For July and August 2007, the cloud fraction increases were slightly too large for the observed surface albedo decreases, and thus the climatological melt could not be exceeded regardless of the magnitude of LWD flux anomaly; the zero-line contours for the LWD anomaly ranges tested nearly collapse onto each other (Figure 8). The temporal evolutions of enhanced melt anomalies shown in Figure 8 can be applied anywhere in the high latitudes where similar SZA and surface albedo conditions are encountered. Simple adjustments must be made for the mean cloud fraction and albedo values (baseline anomaly adjustments), as well as applying the appropriate LWN fluxes based on surface temperature changes and changes to LWD.