3.1. Annual Cycles of Multiyear Ice Coverage (2000–2006)
 Here, we provide only a brief description of the procedure used to construct annual cycles of MY sea ice coverage of the Arctic Ocean [Kwok, 2004]. As the MY ice coverage, AMY, is not directly observable in QuikSCAT data in all seasons, the time series shown in Figure 2 is obtained by considering the area balance of MY ice within the Arctic Ocean over annual cycles between October and September. Using the fact that ice export explains a large fraction of the Arctic MY ice coverage, we can write:
The annual cycle begins on October 1 (i.e., t = 0) near the beginning of the growth season. We use the QuikSCAT MY coverage on the first of each calendar year (i.e., AMY(Jan-1)) to provide an area tie-point because the reliability of this estimate is highest in the middle of winter. At the beginning of freeze up, the signatures of MY and FY ice are unstable due to moisture on the surface [Kwok, 2004]. In equation (1), AMY-export(t) is the time-series of cumulative MY ice area export at the Fram Strait and other passages (sign is positive for export). This construction of AMY(t) assumes that MY sea ice does not melt and deforms little. During the winter (Oct–May), these are reasonable statements. Also, we assume that lateral melt of thick MY year ice during the summer is negligible. Even though this could be an issue as the MY ice cover thins, the area balance results provide an upper bound estimate of summer (Jun–Sep) Arctic MY ice coverage. The root-sum-squared of the uncertainties in monthly export (∼7 × 103 km2) and MY coverage from QuikSCAT (∼150 × 103 km2) provide an estimate of the expected uncertainty in the MY coverage time series (error bars in Figure 2).
Figure 2. Seven annual cycles of Arctic Ocean multiyear ice coverage constructed using QuikSCAT data and ice export. The open circles show multiyear (MY) ice coverage on January 1. The dashed lines show the replenishment of the MY ice reservoir by first-year ice that survived the summer. The quantities next to the dashed lines are replenishment areas in 106 km2.
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 The annual cycles of AMY (in Figure 2) show a monotonic decrease in coverage from the beginning of the growth season that is due to ice flux primarily through Fram Strait: ∼10% of the Arctic Ocean ice cover is lost to export every year. Ice export is typically lower during the summer months (Jun–Sep) because of reduced ΔP and lower MY fraction at the flux gate. The step increase in MY ice area at the end of each summer is the FY ice area that survives the summer. These FY ice areas replenish the MY ice reservoir after each year's depletion through export and melt. A balance between export and replenishment is necessary to maintain a stable MY ice cover. For the six summers from 2000 to 2005, these areas are: 1.0, 1.2, 0.4, 0.4, 0.9, and 0.1 × 106 km2. The variability is remarkably high. The near zero replenishment at the end of summer of 2005, at 0.1 × 106 km2, stands out as the smallest of the six summers. Because of this low replenishment, the MY ice coverage in January 2006 is lower by ∼0.6 × 106 km2 when compared to that in January 2005 and is the lowest over the record. The next sections examine this abrupt decline in terms of the anomalies in ice export within the longer-term record of freeze and melt over the Arctic Ocean.
3.2. Large Export During the Summer of 2005
 On an Arctic Ocean scale, these anomalously high gradients are associated with the patterns of sea level pressure (SLP) distributions shown in Figure 3. In the mean August and September SLP fields, the high density of isobars perpendicular to the Fram Strait is evident. These gradients are associated with troughs of low pressure in the Greenland Sea in August and in Barents/Norwegian Seas in September. Since ice motion is largely wind-driven and nearly parallel to the isobars of surface pressure, the result is an increased sea ice outflow. In particular, the arrangement of SLP pattern in September also shows a strong Trans-polar drift stream that favors the Eastern Arctic Ocean as the source region of sea ice exported through Fram Strait. This suggests that the large depletion of the MY ice cover in the Eastern Arctic reported by Nghiem et al.  can in part be explained by the anomalous SLP patterns during the summer. This large expanse of first-year ice in the Eastern Arctic on January 2006 can be seen Figures 1d and 1e.
 The consequence of summer ice export is different from that of the winter. During the winter or growth season, the MY ice depleted by area export is replaced by FY ice. Depending on the winter conditions, these seasonal ice areas have an opportunity to grow and thus a chance to survive the subsequent summer and contribute to the replenishment of the MY ice reservoir. This is not true of ice area exported during the summer; since there is no freezing of the vacated areas, summer export contributes directly to the depletion of the MY ice cover and open water production. Thus, from a replenishment perspective, for a given net annual ice export it would be better to have the higher ice export during the early winter than the summer. For the 2005 summer, ice export is directly responsible for ∼40% of the ∼0.6 × 106 km2 of decrease in MY coverage. The warmer atmosphere and ocean explain the balance of this decrease.
3.3. Relationship to the Record of Freezing and Melting
 In this section, we examine the relationship between the record of Ar and the seasonal records of freezing and melting. The measures used here are the freezing degree-days (FDD) between October and May and melting degree-days (MDD) between June and September: FDD is the cumulative sum of the daily mean temperatures below −1.8°C; and, MDD is the cumulative sum of the daily mean temperatures above 0°C. Replenishment of MY ice at the end of each summer is clearly dependent on the MDD of that summer but it also depends on the FDD of the preceding winter as higher FDDs indicate more growth, and thus a thicker ice cover that could survive the summer. Of course, the dependence on longer-term records of FDD and MDD is also important but their impact is more difficult to quantify and isolate because of the integrative nature of ice growth and melt.
 The first two columns of Figure 1 show the spatial fields of FDD and MDD anomalies of the seven years leading up to the summer of 2005 as well as that of the following winter and summer. The color scale is chosen such that cumulative temperatures indicating warmer seasons are in red, i.e., higher MDD or reduced FDD, and cooler seasons are in blue. On a broad Arctic Ocean scale, there is a negative trend in FDD (less freezing) and a positive one in the MDD anomalies (more melting temperatures). In fact, the winters and summers preceding the fall of 2005 have been anomalously warm – this is true even in the longer records of these parameters shown in Figure 4 (discussed below). Thus, the near zero replenishment of MY ice during the 2005 summer is potentially a cumulative effect of the persistent trends in FDD and MDD over this short record.
Figure 4. Time-series of spatially averaged FDD and MDD from 1958–2006. The spatial averages are taken over that area of the Arctic Ocean bounded by the passageways into the Pacific, and the Greenland and Barents Seas. For the FDD time-series, the squared correlation increases from 0.64 to 0.76 from the linear to cubic fits (shown here). Similarly, for the MDD the squared correlation increases from 0.26 to 0.32.
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 One question that could be answered is whether there is any relationship between replenishment area, Ãr (‘∼’ for anomalies), and the anomalies of the previous year's spatially averaged FDD and the MDD of the current summer (i.e., DD, DD). The spatial averages are taken over that area of the Arctic Ocean bounded by the passageways into the Pacific, and the Greenland and Barents Seas. To do this, we explore possible correlation between Ãr and the following variables: DD, DD, αDD + βDD, and the correlation of the detrended Ãr with the same detrended variables. The sum of αDD + βDD is chosen to test whether the combination of variables better explains the variance. The results are: ρ(Ãr, DD) = 0.78, 0.56; ρ(Ãr, DD) = −0.62, −0.01; and, ρ(Ãr, αDD + βDD) = 0.79, 0.62. The first quantity is the correlation of the anomalies while the second is the correlation of the detrended anomalies. Because there are strong trends in each variable, the correlations are reduced after their removal. The previous winter's DD explains more of the variance in Ãr than the detrended DD. This suggests, not surprisingly, that the replenishment area is dependent on the state (thickness and seasonal growth) of the ice cover entering the melt season. Similarly the summer's DD explains more of the variance than the detrended DD. In fact, ρ(Ãr, DD) is almost zero if DD is detrended; this is most likely due to the fact that DD is a much noisier variable since the air temperature is constrained to be near melting (i.e., ice bath) over most of ice cover during the summer. The much narrower range of variability of DD compared to DD can be seen in the degree-day scales in Figure 1. The linear combination of αDD + βDD explains ∼63% and ∼40% of the variance before and after detrending, and as expected is higher than those with the individual variables. With the caveat that only a short time-series is considered here, the results indicate that Ãr is correlated to the behavior of MDD of the summer but more so to the FDD of the preceding winter.
 It is also interesting to note that there seems to be little correlation between the spatial patterns of FDD or MDD anomalies (Figures 1a and 1b) and MY coverage of the following winter (Figure 1d). We expect that the changes in MY ice coverage associated with warming, unlike that of ice export which is immediate, to be a slower multi-year response and may not be attributable directly to the spatial warming effects of only the preceding summer and/or winter. This is in contrast to that of the behavior of the replenishment area.
 To place these eight recent years of FDD and MDD anomalies within the context of a longer-term multi-decadal record, we examine their spatially averaged behavior since 1958 (Figure 4). Again, the spatial averages are taken over that area of the Arctic Ocean bounded by the passageways into the Pacific, and the Greenland and Barents Seas. The gray region represents the extent of the short 8-year record shown in Figure 1. Linear and cubic polynomials are fitted to both time series (only cubic fits are shown in Figure 4). The FDD time series shows clearly the accelerated warming since the mid-1980s; 80% of the net decrease in FDD occurred after the mid-1980s. The positive trend in the MDD is also clear, although the increasing slope in the cubic fit seems to be biased by the much higher MDD of the last three years of the record. Nevertheless, both point to warmer winters and summers associated with what seems to be accelerating trends of warming over the Arctic Ocean during the past 20 years, and potentially lower average replenishment areas.