3.2. Thickness Distribution
 The thickness distributions P(z) of the 2001, 2004, and 2007 HEM surveys, together with their means, exponential decays, and full width at half maximum (FWHM) values, are shown in Figure 2. FWHM is the width of P(z), where it is at 50% of the maximum. For all four data sets, the distribution was asymmetric, with most of the ice distributed in the thicker part. None of the four distributions showed more than a single maximum, open water, i.e., the maximum at z = 0, not included. Typical sea-ice sections for each data set are shown in Figure 3.
Figure 2. Overall sea-ice thickness distributions including open water. Circles mark the mean ice thickness, and arrows indicate the full width at half maximum (FWHM). Exponential fits for the tails of the distributions are plotted as solid lines.
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Figure 3. 10-km-long sea-ice sections representing typical profiles obtained during each campaign, where Z = 0 marks the sea level. A freeboard to draft ratio of 0.89 was assumed to convert ice thickness into freeboard and draft. Dark sea-ice sections mark level ice as identified with the level-ice filter. Blue bars at the sea-ice surface are melt ponds located by laser dropouts. Most of the larger ridges are melt pond-free. (a) 3 September 2001, 86.5°N/72°E. Level-ice sections at 2 km and 5 km are first-year ice. (b) 3 August 2004, 83.4°N/4.7°W. Melt ponds are present and level-ice thickness ranges from 1–2 m. (c) 3 August 2007, 82.8°N/31°E. Melt ponds are present. (d) 17 September 2007, 82.2°N/109°E. This section was obtained at the marginal sea ice zone.
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 Although 2001 was dominated by MYI and 2007 by FYI, both distribution functions were surprisingly similar in shape, as demonstrated by the similar FWHM (Table 1). This is an indicator for a common dynamic history of both sea-ice regimes, since according to Thorndike et al. , only dynamic components are responsible for a redistribution of thinner ice toward thicker ice and therefore for a broadening of P(z). The larger FWHM of the 2004 data indicates either a larger degree of deformation in the ice cover or the presence of several ice thickness classes with different histories. Both explanations are typical for a MYI cover in the region north of Fram Strait, where sea ice from all over the Arctic Ocean converges, owing to a constriction by the land masses of Greenland and Svalbard. This convergent ice regime includes sea ice from, e.g., North of Greenland which probably remained there for multiple years but also younger MYI which advects from the central Arctic Ocean.
 The most prominent difference between the years was the position of the maxima of P(z), which represents the modal thickness. Modal thickness differed by as much as 1.2 m between the thinner maxima of 0.9 m in 2007 and the thicker ones of 2.0 m and 2.1 m in 2001 and 2004. This reduction was a consequence of the disappearance of MYI from this part of the Arctic Ocean in 2007 [Nghiem et al., 2007]. The mean thickness also decreased from 2.3 m in 2001 to 1.3 m in 2007. The 2004 mean thickness was particularly large, differing from the 2001 mean thickness by 0.35 m, although the modal thickness was similar. This indicates similar thermal but different dynamic histories of the two MYI regimes. The reduction of mean and modal thickness in the central Arctic Ocean within the past 16 years was further studied by Haas  and Haas et al. , who used data ranging back to 1991, including the data presented here. They found a decrease of mean thickness in the central Arctic of 58% between 1991 and 2007.
 As for sea-ice draft distributions from ULS data [Wadhams and Davy, 1986], the tail of the thickness distribution Prdg(z) can be fitted by a negative exponential function (Figure 2)
where zmod is the modal sea-ice thickness, z is the sea-ice thickness, and A and B are two fitting parameters. The curvature B is the inverse of the standard deviation of the mean sea-ice thickness. The lower the curvature of B, the higher the amount of thicker deformed ice. Accordingly, B indicates there was a higher amount of deformed ice in the MYI cover of 2001 than in the FYI cover of 2007, and the degree of deformation of the MYI cover of 2004 was considerably higher than that of both 2001 and 2007. All B values are listed in Table 1. A direct comparison of our curvatures with B values obtained from ULS measurements is difficult, since B is influenced by the different footprint averaging of HEM systems and ULS systems; the HEM method may underestimate the thickness of pressure ridges by up to 50%.
 To summarize, we can state that the 2007 FYI and the 2001 MYI distributions are similar in shape but not in mean and modal thickness, for which 2001 showed a higher agreement with the 2004 MYI. The most plausible explanation is that 2001 MYI and 2007 FYI experienced similar dynamic but different thermodynamic histories, namely, different ice-growth periods. The opposite is true for 2001 and 2004 MYI, where similar modal thicknesses were produced thermodynamically, but both regimes were subject to different dynamics in that the 2004 regime was subject to heavier deformation, owing to the location in a convergent drift regime north of Fram Strait.
 As a further conclusion, we hypothesize that the tail of thickness distributions Prdg(z) and the FWHM value do not necessarily increase with age, as shown by the comparison between 2001 MYI and 2007 FYI. The transition into a convergent stage has a stronger effect on both parameters as demonstrated by the 2004 data. However, the connection of curvature B and the amount of deformed ice in 2004 could be biased by the broad FWHM. In other words, we can think of the 2004 P(z) as a superposition of several P(z) from different ice regimes, each with a slightly different mode. Each ice thickness mode has an associated tail due to deformed ice, and therefore modes might be influenced by tails. Moreover, we conclude that in a MYI regime, only the FYI mode would be distinctly separated from the dominant one. A mode related to sea ice older than 2 years simply increases the FWHM, as the 2004 thickness distribution implies. P(0) determines the amount of open water with only 2001 with 4% and 2007b with 5.4% showing a significant amount.
 Compared to earlier ULS measurements of late summer sea-ice thickness between Fram Strait and the North Pole [Wadhams and Davis, 2000b], the 2004 mean sea-ice thickness between 82°N and 85°N is 60% thinner than in 1976 and 22% thinner than in 1996.
3.3. Ridge Distribution
 Even when modal thickness is a good indicator for distinguishing between FYI and MYI, pressure ridge parameters are not. The mean height of pressure ridge sails differed by a maximum of only 0.13 m in all regimes and therefore cannot be taken as a reference, either for the age or for the modal or mean ice thickness of a regime. However, all data are based on summer measurements; in winter, the conditions may be different owing to an absence of surface melting. Nevertheless, pressure ridge sail distributions provide information about the degree of deformation within a sea-ice regime. Intuitively, we expect higher sails, a higher sail density, and a smaller spacing between the sails in a more deformed ice regime, such as in the 2004 survey area north of Fram Strait, where we observed the highest mean sail height and the highest mean sail density or lowest mean sail spacing, respectively. The histograms and the fitted distribution functions of the three sail parameters are shown in Figure 4. Further statistical ridge parameters are listed in Table 2.
Figure 4. (a) Distribution of sail heights fitted with a negative exponential function. No sails lower than the cutoff height of 0.8 m are detected. (b) Histograms of sail spacing plotted with a bin width of 0.4 m together with the lognormal fits. (c) Histograms of sail density in sails per kilometer with a bin size of 1 together with the lognormal fits.
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Table 2. Ridge-Sail Parametersa
|Year||Mean Sail Height (m)||Max Sail Height (m)||Curvature D||Mean Sail Spacing (m)||Min/Max Spacing (m)||Modal Sail Spacing (m)||Mean Sail Density (1/km)||Modal Sail Density (1/km)||Min/Max Density (1/km)|
|2001||1.21 ± 0.40||4.61||2.47||193 ± 254||0.88/2433||11||5.17 ± 3.27||3 and 5||0/16|
|2004||1.27 ± 0.48||4.90||2.15||139 ± 230||0.22/5662||8||7.20 ± 5.10||5||0/40|
|2007a||1.17 ± 0.38||4.36||2.75||233 ± 322||0.72/3686||6||4.28 ± 3.35||2||0/23|
|2007b||1.14 ± 0.36||4.97||2.93||220 ± 353||0.64/5021||6||4.50 ± 3.83||2||0/28|
 Of the three ridge parameters, sail height h differs least between the three different ice regimes. For instance, in the 2001 MYI regime with a modal thickness of 2.0 m, mean sail height was just 0.04 m or 10% higher than in the 2007a FYI regime with a modal thickness of 0.9 m. As for the tail of the thickness distribution, the distribution of sail heights can be described by a negative exponential fit for all data sets (Figure 4a). The fitting function is
where C and D are the fitting parameters and hcut is the cutoff height of 0.8 m. The curvature D of the distribution and mean sail height plus its standard deviation for every year are shown in Table 2. The correlation r between fitted and calculated sail height distributions is higher than 0.99 for all years.
 The spacing s and density d of pressure ridges can be approximated by a lognormal distribution [Wadhams and Davy, 1986]
where μ, σ, and θ are the fitting parameters and x represents s or d, respectively. The maximum of P(x) is at
and the mean is at
The fitting parameters for P(s) and P(d) are listed in Tables 3 and 4. Mean spacing and density are directly related, whereas the modes differed significantly. Modal spacing in relation to mean spacing was 6 to 11 m, almost equal for all data sets, but differences in modal density were 2 to 5 sails per kilometer in the same order of magnitude as differences in mean density. This is evidence that ridge sails tend to emerge in clusters, with a preferential spacing between 6 and 11 m within the cluster. Those clusters are probably associated with a single deformation zone in which the number of keels is not necessarily equal to the number of sails. Larger sail spacing in the distribution function can be assigned to level-ice areas which separate two deformation zones from each other. The correlations r between the true distributions of s and d and the lognormal fits are higher than 0.9 and 0.99, respectively, for all data except 2001, where they are 0.69 and 0.95, respectively. The lower correlation for 2001 most probably results from the smaller number of samples and the consequently coarser distribution histogram, and not from the fact that the 2001 sail distribution follows a different functionality, which would be in contrast to previous publications [e.g., Davis and Wadhams, 1996; Wadhams, 2000a].
Table 3. The Three Lognormal Fit Parameters for Sail Spacing, the Mean and Modal Sail Spacing, and the Correlation r Between Fit and Measurements
|Year||σ||μ||θ||smean (m)||smax (m)||r|
Table 4. The Three Lognormal Fit Parameters for Sail Density, the Mean and Modal Sail Density, and the Correlation r Between Fit and Measurements
|Year||σ||μ||θ||dmean (m)||dmax (m)||r|
3.4. Standard Errors
 To quantify how representative the obtained results are, we calculate the standard error of the modal and mean thickness as well as of the means of the examined ridge parameters [Wadhams, 1997]. The standard error ɛ is given by
where is the mean or mode of the complete data set, Zi is the mean or mode of the ith subsection of the data set, n is the number of subsections, and l is the length of the particular subsection. Thus the standard error is the standard deviation of an ensemble of subsection means or modes where all subsections concatenate to form the complete data set. The standard error ɛ is a function of the subsection length l, but also of the degree of homogeneity of the ice regime, expressed by, e.g., multiple modes in the distribution function or a large FWHM. As a consequence, different ice regimes require different section lengths to determine the overall mean or the overall mode with a certain statistical reliability. For the determination of ɛ, we subdivided the flights into smaller sections ranging from 50 m to the maximum flight length and even longer sections by concatenating all flights in a particular year. Results of all standard error determinations are shown in Figure 5.
Figure 5. Standard error ɛ versus profile length. (a) Absolute value of ɛ of mean thickness (left) and modal thickness (right). The red line denotes the threshold for reliability of 0.2 m. (b) ɛ in percent of the mean thickness (left) or modal thickness (right). (c) Circles are mean thickness (left) and modal thickness (right) and error bars indicate ɛ. (d) ɛ of mean ridge-sail heights as percentage of the mean. (e) ɛ of mean ridge spacing as percentage of the mean. (f) ɛ of mean ridge density in percentage of the mean. Except in Figure 5a, the red dotted line marks a 12.75% threshold. This threshold is aligned with the threshold for reliable mean thickness measurements of Wadhams .
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 In the following, we denote ɛ of the mean and the modal thickness by ɛmean and ɛmod. For thickness determination, the error is limited to the maximum accuracy of the HEM bird of ±0.1 m, which represents a 0.2 m thickness interval. Therefore, we consider a measurement of mean or modal thickness as representative for a particular ice regime if ɛ is equal to or below the interval of 0.2 m. Previous thickness studies suggested an ɛmean as a percentage of the overall mean thickness of 12.75% as the threshold for representativeness [Wadhams, 1997]. We tested for both criteria to evaluate our results. ɛmean decreases steadily as l increases and reaches the accuracy of 0.2 m at a length of 10 km in 2001, at 100 km in 2004, and at 15 km in 2007 (Figure 5a, left). All data sets fulfill the Wadhams  requirement for representativeness at profile lengths of 5 km for 2001, 30 km for 2004, and 100 km for 2007 (Figure 5b, left). However, we prefer the absolute standard error, since an error of, for instance, 0.2 m should have the same weight in thicker and thinner ice regimes. Furthermore, the comparison of absolute standard errors obtained in different thickness regimes is justified owing to the nondependency of the standard error on mean thickness [Wadhams, 1997; Percival et al., 2008]. All ɛmean values are shown on the left side of Figures 5a–5c. The decrease of ɛmean with profile length is a measure for the wavelength of thickness variations within the data set, with space and time information mixed. In ɛmean(50 m), for example, all wavelengths greater than 50 m are included. A comparison of the two less-deformed ice regimes (2001, 2007) shows that for short profile lengths, ɛmean2001 was higher than ɛmean2007 and vice versa for longer profile lengths (Figure 5a, left). This indicates that spatial variability in the 2001 data set occurred on shorter-length scales than in the 2007 data set. In other words, on length scales longer than 10 km, the MYI cover in 2001 was even more homogeneous than the FYI cover in 2007. But 2007 covered a much larger area and a much longer time span, i.e., larger variations can naturally be expected. So, this conclusion is only valid for the data sets themselves and cannot be taken as a statement for the complete ice-thickness distribution of the TPD in the particular year. Haas et al.  highlighted the remarkable self-similarity of all 2007 profiles. ɛmean can be taken as a quantification of this similarity. In the area covered in 2007, on 100 km sections over a time span of 1.5 months, the deviation of the section means to the overall mean was not greater than 0.15 m, which is indeed remarkably low. For 2001, the same applies to profile lengths of even 15 km, but here a time span of only 1 month is covered and a shorter total profile length is found. In 2004, a higher ɛmean suggests a lower self-similarity of the obtained thickness profiles, and this even with a smaller extent of the survey area than in 2007.
 In 2001 and 2007, ɛmod reached 0.2 m for a subsection length of 50 km. In 2004, the minimum value of ɛmod was still as high as 0.6 m for a section length of 100 km. The dependence of ɛmod on the subsection length l showed a different behavior than for ɛmean. The modal standard error ɛmod was characterized by more abrupt changes (Figure 5a, right), which are based on the fact that the modal thickness reflects just a single thickness out of the distribution, namely, the maximum, whereas all others are neglected and it means that there are other frequent thickness classes which differ significantly from the dominant one. The profile length for which ɛmod starts to decrease for the first time is probably correlated to the length of deformed sea-ice sections, since modes of level-ice sections must dominate those of deformed sections. Positions where a steeper decline of ɛmod starts probably mark the minimum length for which the main ice class becomes dominant. The magnitude of the decline reflects the ice-thickness difference between the dominant and the second-most-frequent thickness class. This is the difference of the MYI and FYI modes in the 2001 data (see section 3.6), but also the occurrence of thin ice sections with a mode of 0.1 m are a reason for abrupt declines in ɛmod. In the MYI regime of 2004, the jump of ɛmod occurs at a larger length than in 2001 and 2007 because thickness classes are present which differ significantly from each other but are more equally frequent than in the MYI regime of 2001. This is also indicated by the larger FWHM (Table 1) of the 2004 data. In the more homogeneous FYI regime of 2007, ɛmod is generally smaller and shows no abrupt declines because the different dominant thickness classes are similar in thickness (smaller FWHM). Strictly speaking, with an ɛmod of more than 0.2 m, like in the 2004 data, the assignment of just a single modal thickness to the study region is not warranted.
 Since the mean and mode of a thickness distribution are not equal, modes of short profiles more likely reflect the overall mean thickness than the overall modal thickness (Figure 5c, right). This is easier to understand if we imagine a section length of only one sample. Then the mean of all modes of these one-sample sections is naturally equal to the overall mean thickness. Beyond a certain section length, the mean modal thickness decreases until it is equal to the overall modal thickness. In the less deformed FYI regime of 2007 from 30 km length onward, the true modal thickness was achieved; in the 2001 MYI regime from 50 km length onward and in the heterogeneous and more deformed 2004 MYI regime, not even at 100 km length.
 We summarize that for a clear characterization of a sea-ice regime with respect to its mean thickness, survey lengths of 10 to 15 km may be necessary in relatively homogeneous MYI or FYI regimes such as 2001 and 2007. In heterogeneous and deformed MYI regimes like 2004, a minimum of 100 km can be required. For a representative modal thickness profile, lengths of 50 km are necessary in homogeneous MYI and FYI regimes, and at least 500 km may be necessary in heterogeneous MYI regimes, where an assignment of a dominant modal thickness can even be questionable at all.
 The standard error ε in dependence of section length l for sail height, spacing, and density is shown in Figures 5d, 5e, and 5f in terms of percentage of the mean. Likewise, regarding the standard error of the mean and modal thickness, a value of 12.75% of the mean was taken as a threshold for representative results. For a section length of 100 km, mean sail spacing could be obtained with the lowest standard error, followed by mean sail height and mean sail density, which has the highest error. The small standard error for spacing accounts for the clustering of sail heights with a preferred spacing of between 6 to 11 m within each cluster. In other words, only short profile lengths are necessary to obtain typical spacing of sail heights within deformation zones. A better quantity to describe the distribution of deformation zones as a whole is the sail density. Since the pattern in which deformation zones appear is less regular than sail spacing within a deformation zone, the standard error of sail density is higher. For sail density, the length of the data set correlates with the standard error. Hence, 2001 shows the lowest standard errors, and the longest data set of 2007b shows the largest ones. This result indicates that compared to sea-ice thickness, the distribution of deformation zones cannot be associated with huge homogeneous regimes of FYI or MYI as is possible with thickness.
3.5. Melt Ponds
 Melt ponds were detected with the method described in section 2.3, which is applicable for open melt ponds only. Open melt ponds were present during the 2004 and 2007a surveys, whereas almost all of the melt ponds were refrozen during 2001 and 2007b. Henceforth, only the 2004 and 2007a data were taken for melt pond coverage determination. In Figure 3, positions having melt ponds, which are defined as laser data dropouts over ice thicker than 0.1 m, are marked with light blue bars. Mean melt pond concentrations amounted to 15 ± 14% for 2004 and 15 ± 11% for 2007a, where the errors are standard errors for profile lengths of 35 km. These results can be compared with visual observations of melt pond concentrations during each expedition, for which the 2001 melt pond concentration varied between 10% and 30% (all refrozen) [Haas and Lieser, 2003], 2004 between 30% and 40% (during the last two flights partially refrozen) [Lieser, 2005], and 2007 melt pond concentration between 20% and up to 50% (2007b all refrozen or transformed to thaw holes) [Schauer, 2008]. The difference between laser-derived melt pond concentration and visual observations or aerial photography (Figure 6) suggests that the laser provides an underestimation of the true concentration. In Figure 7, the effect of open melt ponds on the overall thickness distributions of 2004 and 2007a is shown. It can be seen that ponded ice is on average thinner than pond-free ice even with the water column of the melt pond included in the ice thickness value, since the HEM instrument measures the distance from the surface of melt ponds to the ice-ocean interface. Furthermore, Figure 7 shows that melt ponds preferably form on ice with a thickness less than or equal to the modal ice thickness, which was 1 m thicker in 2004 than in 2007. Additional information about the brightness and the color of melt ponds is known from visual observations. The 2007 melt ponds were on average darker than those during 2001 and 2004 (Figure 6), which accounts for thinner or no ice below the melt pond.
Figure 6. Aerial photographs of typical sea-ice conditions for all four data sets. (a) Mid-August melt pond concentration is lowest of the four data sets and all ponds are refrozen. (b) End of July melt ponds are open. (c) Beginning of August melt ponds are open and mostly dark colored. (d) Mid-September melt ponds are refrozen. The red arrow points to a refrozen melt pond, and the green arrow points to a thaw hole.
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Figure 7. P(z) − P(z)noponds is the difference between sea-ice thickness distributions including ponded ice and excluding ponded ice. Above zero refers to ice-thickness ranges which are overrepresented in ponded ice, and below zero refers to an underrepresentation in ponded ice.
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 The equal amount of melt pond concentration in 2004 and 2007a suggests that overall surface melting was not stronger in either of the 2 years. However, since the ice was thinner in 2007, the same amount of melt ponds triggered different processes. Not only are melt ponds on thinner ice more easily transformed into thaw holes, but their darker surface also amplifies the albedo feedback. In 2007b, many thaw holes emerged (Figure 6d) which reduced the ice concentration at some locations, e.g., at the Pacific-Siberian ice edge (Figure 1d), significantly. Once melt ponds are transformed into thaw holes and the sea ice concentration is lowered, the thinning of ice is even accelerated as described in section 3.7. The question why the ice concentration was lower close to the ice edge but not over widespread areas of the 2007 FYI cover is discussed in section 3.8.
 Furthermore, we should note that large amounts of thaw holes probably reduce the mechanical strength of the sea-ice cover. Together with the 2007 persistent southerly winds over the Pacific sector of the Arctic Ocean [Maslanik et al., 2007b], the thaw hole-related fragmentation of the sea ice cover may be a further reason for the increased drift velocity in 2007, as a fragmented sea ice cover is easier to move [Rampal et al., 2009].
3.6. Level Ice
 Level ice was identified using two criteria. First, the numerical differentiation of sea-ice thickness along the profile using a three-point Lagrangian interpolator must be <0.04, and second, level-ice sections must extend at least 100 m in length, which is approximately two times the footprint of the HEM Bird. Such identified level-ice sections are marked black in Figure 3. Compared to the level-ice definition of former studies [e.g., Wadhams and Horne, 1980], which defined a measurement point as level if either of the two points 10 m left or right of it did not differ more than 0.25 m in draft, our criterion is more strict and the amount of level ice identified (see Table 1) is lower than visual observations of the sea-ice cover imply. However, a definition of level ice is always to a certain degree arbitrary, and for our purpose, which is to extract the thermally grown ice thicknesses, we want to minimize the amount of deformed ice passing the level-ice filter as much as possible. With all the deformed sea ice removed, P(z) becomes normally distributed (Figure 8) and mean and modal thickness agree to within ±0.1 m. The 2004 and 2007b data sets have a second mode at 0.1 m, representing thin ice on refrozen leads. Of particular interest is the second mode in the 2001 data of 1.1 m, representing sporadically occurring first-year ice. It is sporadic because the FYI mode ±0.2 m sums up to not more than 6% of the level ice, which is 0.96% of the total data set. For 2001 and 2004, level ice of even 3 m and thicker occurred, which is most probably deformed ice which accidentally fulfilled the level-ice criterion. The shift of the modal thicknesses in the 2001 and 2007b data from 2.0 m and 0.9 m in the complete thickness distribution to 1.8 m and 0.8 m in the level-ice distribution (Tables 1 and 5) can be explained with the strict criterion and the consequence is that not 100% of the level ice is identified. Another explanation could be the uncertain relation between modal and level-ice thickness. The mean length of level-ice areas is longest for 2001, a little bit shorter for 2007, and shortest in the 2004 data (Table 5).
Figure 8. Level-ice thickness distributions. Circles mark mean sea-ice thicknesses, and error bars indicate their standard deviations.
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Table 5. Mean and Modal Thickness of Level Ice and the Mean and Maximum Length of Continuous Level-Ice Sections
|Year||Mean Thickness (m)||Modal Thickness (m)||Mean Length (m)||Max Length (m)|
|2001||1.89 ± 0.37||1.8||160 ± 77||552|
| || ||1.1|| || |
| || ||0.1|| || |
|2004||1.96 ± 0.72||2.1||148 ± 54||426|
| || ||0.1|| || |
|2007a||0.97 ± 0.31||0.9||158 ± 69||680|
|2007b||0.84 ± 0.31||0.8||154 ± 66||888|
| || ||0.1|| || |
 When we interpret the second mode at 1.1 m in the 2001 level-ice histograms as a FYI mode (Figure 8), the level-ice thickness of 2007a and 2007b was only 0.2 m and 0.3 m thinner than level FYI in 2001. Compared to previous studies, this lies within the interannual variation of melting and freezing rates. Haas and Eicken , for instance, observed changes of level ice thickness within a summer FYI cover in the Laptev Sea of 0.3 m between 1995 and 1996, and Perovich et al.  showed yearly melting rates at the North Pole between 0.4 m and 0.7 m. Therefore, 2007 was not exceptional with regard to melting rates, at least not within the pack. This result is also supported by Kwok et al. , who found a considerably thinner Arctic MYI cover in 2007 but a negligible trend toward thinner FYI.
3.7. Dependence of Thickness on Sea-Ice Concentration
 Accounting for the lower albedo of an open ocean, a decreasing sea-ice concentration causes additional heat gain of the ocean via short-wave insolation and therefore causes additional melting. Hence, it is of interest to analyze the relation between level sea-ice thickness and open-water content for all three data sets. According to the instrument accuracy of ±0.1 m, our definition of open-water content is the fraction of the thickness distribution function where ice thickness is lower than 0.1 m.
 For the analysis of the dependence of level-ice thickness on ice concentration, we picked all modal thicknesses emerging for each flight. This time not only the overall maximum in the distribution was picked, but every local maximum as well. This highlights the distribution of larger areas with the same level-ice thickness within each flight. Plots of open water fraction versus thickness modes are shown in Figure 9. In 2001, the majority of level-ice modes fell within a range between 1.6 and 2.0 m, independent of sea-ice concentration, although a maximum open-water content of 15% could be observed (Figure 9a). The profiles with an open-water content of >10% were obtained in the region of the North Pole. Two modes are distinctly thinner and had a thickness of 1.0 and 1.1 m, representing first-year ice. The 2004 data showed a much larger scattering of modal thicknesses, ranging from 0.1 m to 3.6 m, where the majority of the modes lay within 1.5 and 2.0 m (Figure 9b). Owing to the low fraction of open water (6%), the variability in sea-ice concentration was too low for the identification of a significant relationship between ice concentration and level-ice thickness. The same applied for 2007a, where no significant amount of open water was present in the data (Figure 9c). Here the modes were much less scattered, and the majority of the modal thicknesses were between 0.6 and 1.0 m. The only significant dependence on open water could be observed in the 2007b data, where modal thickness decreased gradually with an increasing amount of open water (Figure 9d). For profiles with open-water content of below 10%, the modes were concentrated between 0.6 and 1.0 m, as for 2007a. Ignoring the modes of thin ice, which represent young ice formed in September 2007, this decreasing behavior can be described by a linear relationship:
where W is the open-water content and Z is the level-ice thickness. There are several explanations for the absence of a thickness dependence on open water content in 2001. First, the maximum open water fraction was only 15%; second, open water spots occurred in huge open leads and not in the form of a fragmented ice cover as in 2007; and third, heat gain of the ocean and downwelling short-wave radiation were not as high as in 2007 [Kay et al., 2008; Perovich et al., 2008]. The gradient of increasing open water content in 2007b was directed toward the Pacific sea-ice margin of the 2007 sea-ice cover. Therefore, we continue the discussion of the thin 2007b sea ice in section 3.8.
Figure 9. Modes of level-ice thickness of individual 35 km sections (18.5 km in 2001) plotted versus open water fraction. All modes, not only the dominant modes, of all individual sections are plotted. The circle size denotes the point density, i.e., the number of modes plotted on the same position. The dashed line in Figure 9d is a linear fit to level-ice modes thicker than 0.1 m and with an open water content of >10%.
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3.8. Thickness Gradients Toward the Ice Edge
 The 2004, 2007a, and 2007b data sets allow the study of thickness gradients from the sea-ice edge into the closed ice pack. In Figure 1, the different distributions of sea-ice concentration along the three ice edges are visible. The 2004 sea-ice edge north of Fram Strait was exceptionally far north and showed a sharp transition from open water to high ice concentrations (Figure 1b). Of similar sharp appearance was the sea-ice margin north of the Barents Sea in the 2007a data (Figure 1c). Moreover, the location of the edge remained stable during the time of rapid sea-ice decline in August and September 2007. The 2007 sea-ice decline was rather pronounced at the Pacific-Siberian ice margin, where a widespread decrease in ice concentration was visible already in August (Figure 1c and Figure 1d).
 The gradients of thickness and open-water fraction P(0) along the ice edge are shown in Figure 10. On average, each sample represents a 35-km-long flight track. They are displayed as a function of latitude, since transects perpendicular to the three ice edges are basically south-north oriented. As we are interested in thickness changes due to melting and freezing, we only considered level-ice thickness. The thickness surveys were performed in time periods of 18 days (2004), 8 days (2007a), and 22 days (2007b), which are time spans where melting and freezing can proceed substantially. To account for temporal changes during the time period of the survey, thickness and open-water samples in Figure 10 are color-coded according to the time progressed. Surface melting could be observed during the first 15 days of 2004 and during 2007a by the presence of open melt ponds. During the last 3 days of the 2004 surveys and during 2007b, thin ice emerged on the melt ponds as an indicator of a decline in surface melting. However, whether these are signs for a thinning or thickening within the survey period cannot easily be answered here, since the amount of bottom melt can be significant even when surface melting comes to a halt [Perovich et al., 2003].
Figure 10. Mean level-ice thickness (circles) of individual 35 km sections and open water fraction (squares) plotted versus latitude. Shaded areas indicate the day within the measurement period, where black is the first day and white the last. A circle and square of the same color correspond to one individual section. Dashed lines are linear fits of the level-ice thickness. Dotted line (only in Figure 10c) is a linear fit to the open water fraction.
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 In 2004, a decrease of mean level-ice thickness from 2.25 m to 1.75 m could be observed toward higher latitudes between 82°N and 85°N. Open-water content remained lower than 8% and showed no significant gradient but a slightly higher concentration of open leads (8%) around 82.8°N and 84.5°N (Figure 10a). The 2007a data showed no trend from the margin at 82°N up to 85.5°N either in mean level-ice thickness or in open-water content, which remained lower than 3% (Figure 10b). In comparison, 2007b showed significant changes in mean level-ice thickness from values of 0.35 m at the margin at 83°N to values of 0.75 m at 85.5°N, whereas north of 85.5°N, level-ice thickness remained constantly scattered around a mean of 0.9 m. The same was true for the open water content, which decreased from a maximum of 40% at the ice margin to a mean of 3% at 85.5°N. Farther north, the maximum open water content was lower than 8% (Figure 10c). These results show that, similarly to the Beaufort Sea [Perovich et al., 2008], melting rates in the central Arctic in 2007 close to the Pacific sea-ice edge were increased, but not within the pack. The thickness gradients in 2004 and 2007b from the edge toward the north can be described by the following linear fits:
where Z is the mean level-ice thickness, L is the latitude, and r is the correlation coefficient. The evolution of ice thickness in time showed no significant correlation in 2004 and 2007a. In 2007b, a thinning of ice during the time period of the survey was implied, but this can be explained by a thinning with increasing open water content as well.
 Compared to previous studies on meridional sea-ice thickness gradients in the region of the Fram Strait and north of it [Wadhams and Davis, 2000b], where the thickness gradient was positive toward the north, the 2004 negative gradient of mean level-ice thickness from 82°N to 85°N (Figure 10a) is somewhat surprising. It can be interpreted as a situation where older ice was situated in the south and younger ice was situated north of it. Probably the older ice was advected from north of Greenland, whereas the younger ice was advected from the Eurasian side of the TPD.
 The reason for the presence of a thickness and concentration gradient at the 2007b ice edge is more difficult to find. Interestingly, the 2007a ice edge did not show such a gradient. Therefore, we pose the question why sea-ice concentration and thickness decreased gradually at the Pacific side but abruptly at the Atlantic side of the 2007 sea-ice cover. An obvious difference between both margins is that the Atlantic margin was stationary, whereas the Pacific margin retreated toward the North Pole during August and September (compare Figures 1c and 1d). This was a consequence of the general drift pattern of the TPD in June–October 2007 parallel to the Atlantic sea-ice boundary caused by an anticyclonic surface wind anomaly [Ogi et al., 2008]. Considering this wind anomaly, which caused on-ice winds at the 2007 Pacific sea-ice margin, it is contrary to previous studies by Wadhams [2000a] that the Pacific sea-ice edge was diffuse instead of compact and abrupt. Another difference between both sea-ice edges was exceptional heat gain of the surface layer of the Arctic Ocean on the Pacific side which could not be observed on the Atlantic side of the ice cover [Steele et al., 2008; Perovich et al., 2008]. Considering both the heat gain and the wind direction, a plausible explanation could be the transport of warmer air masses from the open ocean beyond the Pacific sea-ice margin into the pack. This caused additional surface melting whereby melt ponds were transformed into thaw holes, which amplified the albedo feedback. Further within the ice pack, the warmer air masses cooled down and melting rates were reduced.