For the most part, the ice station drifts followed one of two distinct trajectories through the summer analysis period. During the analysis period, the 2002, 2003, and 2006 stations drifted across the long axis of the Amundsen Basin, over the Gakkel Ridge, and into the Nansen Basin (Figure 1). The latitude of these stations at the end of the summer period ranged from 84.4° to 85.3° N, 515 to 612 km from the North Pole (Table 1). The 2006 station was deployed on the western slope of the Lomonosov Ridge, the only one deployed to the west of the Lomonosov Ridge. The 2005, 2007, 2008, 2009 and 2010 stations followed a trajectory along the axis of the Amundsen Basin (approximately the Prime Meridian), directly toward the entrance to Fram Strait. These stations drifted relatively far south over the summer period, to the range 84.5° to 81.9°N latitude, 608 to 885 km from the North Pole. The 2007 station nearly reached the entrance to Fram Strait by day 275, the most southerly displacement any of the stations during the summer period. The trajectory of the 2004 station was anomalous. Ice motion in the Transpolar Drift was very slow during the 2004 summer, with the result that this station remained above 88°N, within the central part of the Nansen Basin throughout the summer season. By a wide margin, the 2004 station remained closest to the Pole (Table 1).
 In the remainder of this section, we describe the variability of the ocean-to-ice heat fluxF0 and the shortwave flux entering the upper ocean Frwfor the 2002–2010 NPEO drift stations and make a comparison between the amount of heat entering the upper ocean from the shortwave flux and the amount of heat transported to the ice cover by the ocean-to ice heat flux. Owing to storage of incoming radiation in the upper ocean,F0 is not expected to equal Frw instantaneously. Given that the analysis period spans the times of significantly nonzero Frw and F0, as described above, averages of these fluxes over the analysis period should be nearly equal, if insolation is the dominant heat source supporting the ocean to ice heat flux. If the summer average of F0 were greater than Frw, it would imply that heat sources in addition to the shortwave flux entering the ocean were significant. To quantify the observed inter-annual variability and to make a meaningful comparison betweenF0 and Frw, we introduce two averaging procedures. Temporal averages over individual summer analysis periods are denoted using an overline notation, e.g., refers to the summer average (over days 122–275) of the ocean-to-ice heat flux. Ensemble averages over the nine realizations of the repeated drifts are denoted using an angle-bracket notation, e.g., 〈F0(t)〉 refers to the nine-year ensemble average of summer-averaged ocean-to-ice heat flux as a function of year day. It is also possible to combine the two averages to produce an ensemble summer average of the flux, . Summer averages and ensemble summer averages are listed in Table 2.
3.1. Ocean-to-Ice Heat Flux
 Records of temperature, salinity, and ice velocity from the AOFBs provide highly resolved time series estimates of δT and u*0 from 2002 to 2010 (Figure 3). These time series document the intra and inter-annual evolution of near-surface heat content and surface mechanical forcing over this period.
Figure 3. Summer heating season departure from freezing δT (gray) and interface friction speed u*0 (eddy correlation, red, and Rossby similarity model, blue) for the 2002–2010 drift stations. Ensemble averaged quantities, 〈δT(t)〉 and 〈u*0(t)〉, are in the tenth panel.
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 The ensemble-averaged time series ofδT (Figure 3, tenth panel) provides a view of the typical intra-annual evolution of upper ocean heat content. At the start of the analysis period on 01 May,δTwas close to zero. Through mid-June (about year day 165),δTincreased slowly to a value of about 15 mK. This period of slow heating was followed by more rapid heating through early August (about year day 216), at which point the ensemble-averaged time series reached a maximum value of 128 mK. For the remainder of August and through September,δT decreased back toward zero. The ensemble summer average was = 45 mK (Table 2).
 In terms of inter-annual variability, summer-averaged departure from freezing, , was relatively large in 2002 and 2008, moderate in 2003, 2007, 2009 and 2010, and relatively small is 2004, 2005, and 2006 (Table 2). That is, summertime upper ocean heat content passed through a minimum during the period 2002–2010. Most of this variability is associated with the magnitude of δTduring the upper ocean heat content peak of mid-summer rather than the timing of the onset or cessation of elevatedδT at the beginning and end of summer (Figure 3). Or, in other words, most of the inter-annual variability can be explained by modulating the magnitude of the typical heat content time series as represented by the ensemble average time series. There are several exceptions to this general statement, though. The 2007 drift time series has a large maximal value ofδT but only an average value of , because of a relatively late onset of warming. The upper ocean started to warm relatively early during the 2006 drift, but small values of δT through the remainder of summer caused the 2006 drift to have the smallest value of , 29 mK, of the observational period. The large of the 2002 drift was sustained in part by a persistence of elevated temperatures later in the season than was typical. The 2008 drift contained an anomalous period of elevated temperature early in the summer season.
 Within the summer analysis period, variability in u*0 arises as a result of the passage of atmospheric storm systems at a multiday, synoptic time scale (Figure 3). Large storms forced peak u*0 in excess of 1 cm s−1. The ensemble-averagedu*0 time series (Figure 3, tenth panel) indicates that surface forcing tended to increase moderately during August and September (yeardays 215–275) in comparison to June and July. Typical values of were about 0.8 cm s−1 (Table 2). There is good correlation between the eddy-correlation and Rossby-similarity model versions ofu*0. The magnitudes of the eddy-correlation estimates are about 80% of the Rossby similarity estimates. Summer surface forcing was relatively weak in 2004 ( = 0.58 cm s−1) and was relatively strong in 2008 and 2010 ( = 0.86 and 0.87 cm s−1, respectively). A cumulative distribution of u*0 over each summer time series (Figure 4) shows the dominance of low wind, low surface stress conditions for 2004, in contrast to the dominance of higher surface stress for years 2008 and 2010. Through most of the summers, u*0 was greater than 1 cm s−120–30% of the time, but for 2004 this occurred less than 5% of the time. Thus, the summer of 2004 was characterized by weak synoptic-scale surface forcing in addition to slow, season-scale drift. The 2002, 2003 and 2008 drifts had largeu*0 values during June (year days 153 to 182). The average June values of u*0 were 0.9, 0.7 and 1.0 cm s−1 for 2002, 2003, and 2008, respectively. The average June values for the other years were less than 0.6 cm s−1.
Figure 4. A cumulative sum of friction velocity u*0 for each summer time series for 2002 to 2010. This summarizes the distribution of stress values during each summer.
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 The typical summertime evolution of F0is illustrated with the ensemble-averaged time series (Figure 5, tenth panel). Significant heat transports to the base of the ice began in early June (close to year day 160) at about the same time that the rate of increase of δT accelerated (Figure 3, tenth panel). Over the time span of these observations, then, both IOBL warming and ocean-to-ice flux typically began in early June. The two versions of theF0 estimates compare well, the significant differences result only from the u*0 differences described above. Because of the lack of eddy correlation estimates for the 2002 and 2003 drifts, quantitative descriptions of F0will be made using the version based on Rossby-similarityu*0.
Figure 5. Ocean-to-ice heat fluxF0 for the 2002–2010 drift stations. Ensemble average in the tenth panel. Heat fluxes calculated with Rossby similarity based friction velocities are plotted in blue, and heat fluxes calculated with eddy correlation based friction velocities are plotted in red.
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 From mid-July to near the end of August (yeardays 185 to 230),F0 reached a plateau value of about 15 W m−2. The summer average of the ensemble-averaged time series was 7.6 W m−2 (Table 2). There was significant inter-annual variability inF0 (Figure 5). As expected, was correlated with (Table 2). was large in 2002, 2008 and 2010 (9.7, 10.5 and 10.5 W m−2, respectively), moderate in 2003, 2007 and 2009 (7.6, 8.0 and 7.6 W m−2, respectively), and small in 2004, 2005, and 2006 (4.6, 5.4, and 4.8 W m−2, respectively). The onset of F0 was earlier for 2002 and 2008 than for other years, which is at least partially attributable to the strong June surface forcing of those two years that was noted above. The largest heat flux events, with instantaneous F0 > 60 W m−2, occurred during the two, large, mid-summer storms of the 2008 drift and a storm near the end of August during the 2010 drift.
 In an idealized, one-dimensional scenario, the IOBL heat budget represents a balance between tendency of heat content, incoming solar radiation, ocean-to-ice heat flux, and heat flux entering the IOBL from below. TheδT, u*0, and F0 time series (Figures 2 and 4) reveal aspects of this simple budget: near-surface temperature tends to increase during lulls in surface forcing and tends to decrease when the forcing is strong. Examples of a warming upper ocean during calm conditions include the periods 2005 year day 209–229 and 2007 year day 207–215. During these periods, apparently, the incoming radiative flux exceededF0, and hence the IOBL warmed. There are numerous examples of the opposite case in each of the years. The two most dramatic examples occurred in 2008, when large storms beginning on year days 191 and 217 led to large decreases in δT. During these periods, apparently, F0 was greater than the incoming radiative flux, and the IOBL cooled, releasing the stored heat to ice melting.
 As a quantification of the relative roles of δT and u*0in producing inter-annual variability of , we introduce two perturbation quantities using the temporal and ensemble averaging procedures introduced above. With u*0 as an example, we define
where the prime and double prime notations denote inter- and intra-annual perturbations, respectively. The prime variables have a value for each year, while the double prime variables have values for each day of the summer. Introducing this notation intoequation (1), the summer averaged heat flux may be expressed as
 Within this framework, then, inter-annual variability of the summer average heat flux, , arises from inter-annual, first-order perturbations/variability inδT (second term on right hand side) and in u*0(third term), inter-annual, second-order combined perturbations ofδT and u*0(fourth term), and intra-annual correlation ofδT and u*0 perturbations (fifth term). The values of these terms for each of the drifts are listed in Table 2.
 As expected, the intra-annual correlation ofδT and u*0was always negative, because the surface layer tends to cool during strong surface forcing events. Interestingly, there was not very much inter-annual variation in this term, indicating thatF0could have been reasonably well estimated using only season-averaged quantities and the ensemble-averaged value for the term .
3.2. Penetrating Radiation
Figure 6. Summer heating season surface shortwave radiation Fr(gray) and open water fraction 1 -C(red lines are SSMI-based estimates and green lines are divergence-based estimates) for the 2002–2010 drift stations. Ensemble averages in the tenth panel.
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 The two instantaneous estimates of open water fraction (SSMI, and IABP) do not agree very well (Figure 6). The SSMI open water fraction estimates vary between 0 and 0.2 over the summer seasons. The divergent opening IABP estimates have magnitudes comparable to the SSMI estimates, but correlate poorly with the passive microwave estimates. An exception is the open water estimates obtained for the 2010 drift. During summer 2010, the SSMI and divergent-opening estimates are consistent, with both dominated by a low-concentration event during August and September associated with a persistent low pressure system over the gyre [Kawaguchi et al., 2012].
 Although the two instantaneous open water fraction estimates do not provide a consistent view of the conditions along the individual drift station trajectories, the ensemble-average SSMI and IABP estimates are reasonably consistent (Figure 6, tenth panel). In the ensemble mean, both time series start the summer season at near-zero open water fraction. The May averages of the SSMI and IABP open water fraction estimates are 0.02 and 0.01 respectively. Both of these open water fraction estimates increase through the summer analysis period, reaching September–averaged values of 0.16.
 As noted above, the divergent opening estimate assumes that the there is no open water at the beginning of the analysis period. For the most part, the passive microwave data confirm that this is a reasonable assumption. Except for 2004 and, to a lesser extent 2008, the passive microwave estimates indicate that there was little open water at the start of the summer analysis period. The reasonable agreement between the ensemble average SSMI and IABP open water fraction time series suggests that, at least typically, open water in the Transpolar Drift is formed primarily by divergence of ice motion rather than by thermodynamic processes such as lateral melting.
 Ensemble average time series of the shortwave radiation entering the upper ocean, surface shortwave radiation modulated by open water fraction (equation (2)), illustrate the typical seasonal evolution of Frw (Figure 7, tenth panel). Multiplication of Frby open water fraction produces near-zero values ofFrw at the beginning and end of the analysis period. Early in the period, although there was abundant surface flux, there was little open water through which it could enter the ocean. Late in the period, although there was ample open water, the surface flux had decreased with the angle of the sun. Maximum values of Frwtypically occur between early to mid-July (between approximately year days 190 to 200). The peak, ensemble averaged SSMIFrw estimates are nearly 25 W m−2, and the corresponding IABP estimates are about 20 W m−2. The July peak in Frwled the late-July/August plateau inF0 by a few weeks, consistent with the idea from the simple IOBL heat budget that heat from incoming radiation is temporarily stored in the upper ocean and then transported to the bottom of the ice cover.
Figure 7. Estimates of shortwave flux entering the ocean Frw = Fr (1−αw) (1−C) for the 2002–2010 drift stations (red lines are SSMI-based estimates and green lines are divergence-based estimates). Ensemble averages in the tenth panel.
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 Comparison between SSMI and IABP Frw is favorable only when ensemble averaged (Figure 7, tenth panel). Poor intra-annual agreement between SSMI and IABP open water fraction estimates is evident in the twoFrw time series estimates from each year's drift (Figure 7), while the nine year ensemble average shows close agreement through the summer season (Figure 7, tenth panel). Examples include the first half of the 2008 summer during which the SSMI open water fraction was much larger than the IABP fraction, and the beginning and end of the 2005 summer during which the IABP open water fraction was much larger than the SSMI fraction.
3.3. Comparison of F0 and Frw
 We begin by comparing the ensemble-averaged summer averages. The ensemble average over all of the drifts of the ocean-to-ice heat flux was = 7.6 W m−2. This value compares reasonably well to SSMI- and IABP-based , which equals 8.1 and 8.0 W m−2, respectively. These results indicate that, averaged over multiple summer seasons, about 95% of the solar radiation entering the upper ocean was used to melt the bottom of the ice, while the remaining 5% was used for lateral melting or was stored in the upper ocean, and possibly transported to the ice cover after the summer analysis period.
 Although the ensemble-averaged results present a consistent picture of ‘typical’ radiative heat input to the upper ocean, storage in the IOBL, and transport to the ice, neither of the two sets ofFrwestimates explains the inter-annual variability observed in theF0 records (Table 2 and Figure 8), specifically the passage through a clear minima (summer of 2004–2006) over the years of observation. Although the SSMI and IABP estimates are generally greater than or equal to , as would be expected if F0 were primarily supported by Fr, the summer-averaged values are not significantly correlated over the years 2002–2010. For the SSMI estimates, exceeds for all of the drifts except 2002, was 3.2 W m−2, smaller than the for the 2002 summer. For the IABP estimates, is smaller than for the first three years of the record and larger than for the last four years of the record. The IABP Frwrecord is unusually large in 2005. There was only one IABP triangle available this year for the divergent opening estimate, and the apparent over-estimation of open water fraction is probably due to the area of the single triangle providing a poor representation of ice deformation in the immediate neighborhood of the NPEO station. In summary, the summer-averagedFrwestimates are not consistent with each other or with summer-averagedF0; only when ensemble-averaged over the nine summer realizations is a consistent picture formed.