Measurements of arctic sea-ice draft have been taken by Navy submarines for nearly five decades. The data are in two inherently different forms, analog paper charts and digitally recorded data. “Raw” analog drafts digitized from paper charts are biased toward thicker ice by over 30 cm compared with the digital drafts. This is due to the coarser temporal resolution of the paper charts compared the digital data. We examine coincident analog and digital data to determine how they can be made equivalent in mean draft and draft distribution (the histogram of draft vs. fractional frequency of observation). Image processing techniques are used to thin vertical features in the scanned chart images; this produces a “final” analog mean draft that is essentially unbiased (2 ± 6 cm) relative to the digital mean and final draft distributions that are in good agreement.
 Since 1957 the U.S. Navy has been sending submarines under the arctic ice pack on a regular basis. The submarines are equipped with an upward looking sonar that continually measures sea-ice draft. The Navy has recently allowed the release of large amounts of these data, much of which is now available from the National Snow and Ice Data Center (NSIDC).
 The ice draft data have been recorded on two different media. Until 1976 all data were recorded only on paper strip charts, hereinafter referred to as analog data. Starting in 1976 data were often recorded both in analog form and digitally. The digitally recorded data, also referred to as DIPS data (for Digital Ice Profiling System), are referred to hereinafter as the digital data. Ice draft data have been used to examine topics such as quantifying the abundance of ice features (ridges and leads), assessing the spatial pattern of the Arctic ice cover [Hibler, 1979; Bourke and Garrett, 1987], testing for climate change signals [McLaren, 1989; McLaren et al., 1994; Shy and Walsh, 1996; Rothrock et al., 1999; Wadhams and Davis, 2000; Tucker et al., 2001] and testing sea ice models [Zhang et al., 2003; Rothrock et al., 2003]. Some investigations have used only analog or only digital data; others have used mixtures of analog and digital data. However the analog and digital data have important differences and the issue of a possible systematic difference between the two has not been addressed in the literature.
 Almost all of the publicly available data come from digital records. The small amount of analog data that has been digitized is not part of the NSIDC archive and is available only as summary statistics [e.g., LeSchack, 1980; McLaren, 1986]. We are currently working with the U.S. Navy Arctic Submarine Laboratory (ASL) to release data from cruises with only an analog record. While there are several types of charts, this paper considers the most prevalent type, curvilinear charts in use from about 1975 to 2001. In this paper we demonstrate just how the analog and digital records differ and what processing steps can be taken to produce data that are equivalent, focussing on the mean ice draft and the draft distribution. Our goals are to produce analog data that are unbiased relative to the digital data and determine confidence levels for the equivalence of the two types of data.
2. Test Data
 To assess the potential bias and develop possible solutions we compare concurrent digital and analog data for 37 samples of draft measurements. For each sample the submarine was travelling at constant speed, depth, and heading. The samples have speeds (3–17 knots) and depths (170–750 ft) that are typical of submarine operations in the Arctic. The data come from one summer and one spring cruise (September 1997 and April 1999). Each sample is 10 km in length except for three samples 4–8 km long.
 Ice draft is measured by an upward looking sonar mounted on the submarine's conning tower. The sonar emits a sound pulse that travels upward, reflects off the overlying ice or sea surface, and is received at the same sonar transducer. Ice draft is calculated from the total travel time of the pulse and the boat's depth using an assumed sound speed. The return pulse is measured as signal strength vs. time. The digital recorder (DIPS) records only the deepest draft for each pulse, defined as the point at which the return signal strength exceeds a set threshold for a set minimum duration. Consecutive returns (about 6 s−1) form a continual record of draft vs. time. This time series of deepest draft, or first return, constitutes the digital record. The entire return pulse is recorded on a paper chart by a stylus sweeping out a trace whose darkness indicates signal strength (Figure 1a). This constitutes the analog record.
 The digital data were obtained from ASL where they had already undergone initial editing to remove noisy data. (In the SCICEX 1999 data, for instance, roughly 5–15% of the data points were culled as bad data.) The data were left as drafts vs. time and not interpolated to 1-m spacing (as unlike the data at the NSIDC). A few stray bad data points that had been edited from the digital data at ASL were edited from the paper charts, affecting less than 0.1% of the data.
3. Processing Analog Data
 Obtaining digital information from the analog record involves a number of steps. First, the paper charts were scanned to produce a digital bitmap or image of the chart. A scanner, computers, and disc writers were integrated and installed at ASL to accomplish the large task of scanning more than 3000 existing paper charts (each over 20 m long). Next, image processing software was used to extract the data trace from the chart image by applying a simple threshold to the pixel data, defining how dark a mark must be to count as data. Much as the digitally recorded data rely on a fixed threshold, the extraction of the trace from the scanned chart relies on defining a threshold. Threshold selection is affected by the darkness of the trace on the chart, the darkness of the paper background, and the brightness of the scanned chart image. Fortunately, the submariners are trained to adjust the sonar in order to produce a clear, distinct, and dark trace on the paper chart.
 Setting a threshold is a balancing act. The carbon used by the recording stylus can “bleed”, blurring fine-scale details. Keels are generally less heavily written than areas of relatively flat ice. The threshold must therefore be set low enough to pick out the fainter keels without being so low that it washes out the details in the blurred areas. Our experience is that the threshold is fairly constant for most cruises, with occasional adjustments for individual cruises or sections of charts. Each pixel in the trace in Figure 1a thus translates into one of the gray points in Figure 1b.
 The recording stylus rotates, resulting in a curved trace (Figure 1a) which must be transformed to a rectilinear coordinate system and scaled for time and depth as in Figure 1b. As a final processing step, the charts were examined to identify areas of open water, and all drafts were offset so that open water areas have a draft of 0 m. (This same procedure was used to assign an open water offset to the digitally recorded data.) This process produces analog and digital drafts calibrated to within approximately ±5 cm.
 The most obvious way to derive an ice draft time series from the gray cloud in Figure 1b is to take the first return or deepest draft at each time, to mimic the digitally recorded data. The blue time series in Figure 1b is the first return from the raw pixel data. The red time series is the coincident digitally recorded first return.
4. The Bias and Its Elimination
 It is apparent that the two time series in Figure 1b are not equivalent. The raw analog data are less variable and often miss shallow drafts that appear in the digital signal up inside the gray cloud. Analog keels are generally wider. The mean drafts for the raw analog and the digitally recorded data for each of the 37 test samples are shown in Figure 2 (solid dots). The analog mean draft is greater than the equivalent digital mean by an average of 34 ± 15 cm.
 To compare the draft distributions from the 37 samples we first produce histograms of draft vs. fractional frequency of observation using 30 cm bins for both the analog and digital data. We then normalize the bin drafts for both the analog and digital distribution using the mode of the analog distribution for each sample. For example, if the analog histogram has a mode of 2 m, the draft associated with each bin in the histogram is divided by 2 m such that the bin containing the mode has a non-dimensional value of 1. This process allows an intercomparison of histograms for all 37 samples. The average of all of the normalized draft distributions for the 37 samples is shown in Figure 3a. We also calculated the difference between the digital and analog distributions for each sample (Figure 3b).
 The differences between the analog and digital records are primarily due to a single issue: the analog data lack the temporal resolution of the digital data. The sonar acquires approximately six data points per second, and both the digital and analog data are recorded at that rate. The analog chart was scanned at a resolution of 200 pixels/inch or about 1/3 s at a typical chart feed rate of 1 in/min or 0.42 mm/s. However, the resolution of the analog chart is inherently limited by the width of the mark made by the stylus which is approximately 0.5 mm or 1 s. The lower temporal resolution of the paper record means that keels appear wider and narrow shallow features are filled in. Consequently analog ice drafts are consistently biased toward thicker ice relative to the digital data.
 The finite stylus width can be compensated for by thinning the vertical edges of features using selective application of the image processing technique of “erosion” [Russ, 2002]. Using scaled pixel data (e.g., gray points in Figure 1b), we first eroded the image horizontally (in the time dimension), eliminating any pixels in a given row that have data on only one side of it, so that features are thinned along their left and right edges. However we did not eliminate a pixel if the feature (in that row) would be eliminated completely. Thus a feature only one pixel wide was preserved unchanged, a feature two pixels wide was thinned to only the leftmost single pixel, and a feature three pixels wide was reduced to its centermost pixel. The processes of thresholding, rectilinear correction, and erosion often leads to ragged edges along the sides of keels. A better match between analog and digital data is achieved when as a final step the image is cleaned up in the vertical (draft) dimension, by examining columns of pixels and eliminating isolated clusters of one or two pixels from the column. The pixel data produced by eroding the raw pixel data horizontally and vertically are referred to as the finalpixel data.
 The example in Figure 4 shows that substantial thinning occurs along the sides of vertical features. The analog time series based on the final pixel data is a much better match to the digital data. The digital data still contain a number of narrow features of thin ice absent from the analog data while the analog data have a slight tendency to produce features that are too thin.
 The bias present in the raw analog data all but disappears in the final analog data (open circles in Figure 2). The difference between mean drafts of the final analog and digital samples is 2 ± 6 cm. The same is true for the standard deviations of draft. The raw analog data produce a standard deviation on average 28 cm greater than the digital data, whereas the final analog data overestimate the digital standard deviation by only 1 ± 7 cm. Similar improvement occurs in the draft distribution (Figure 5).
 Submarine upward looking sonar data recorded on paper charts are inherently different from digitally recorded data. The difference is due to the poorer temporal resolution of the analog data and the finite width of the stylus that writes the analog trace. Raw pixel data resulting from simple thresholding of the scanned analog chart produce ice drafts with a substantial bias averaging 34 cm thicker than the digital data. We have developed a technique that thins vertical features in the analog image, resulting in analog draft data largely unbiased compared with existing digital records for three basic statistics: mean draft, standard deviation, and the draft distribution.
 The digital data currently in the NSIDC archive are reported as variable length segments for which the submarine maintained constant speed, depth, and course. Drafts are given along the submarine track and a variety of statistics are derived for each segment. We will soon be providing the NSIDC with analog draft data derived from final pixel data. The analog data will include draft as a function of distance along the submarine track as well as the mean draft, standard deviation, and draft distribution.
 A number of statistics in the digital archive characterize ice features (leads and ridges) and the spatial autocorrelation structure of the draft series (or profile). Because the final analog draft series still differs from the digital series on a point-by-point basis (Figure 4), we will not include these statistics in the analog archive, but, for anyone interested in producing comparable statistics from the analog data, the analog and digital data from the 37 samples used in this study will be available from the NSIDC.
 Finally, a fair amount of analog data was digitized by hand in the 1970s and 1980s [LeSchack, 1980; McLaren, 1986]. It is reported that a manual digitizing tablet was used and produced a data point as often as every 0.05 mm giving a potential temporal resolution of about 0.1 s. It seems unlikely however that this resolution could have been achieved by hand. Moreover, the issue of low temporal resolution due to chart feed rate and stylus width was not addressed in these studies. It is apparent from our work that the draft is highly sensitive to the temporal resolution of the paper record. For example, if the analog first return draft is sampled over one second intervals, the analog mean is over 60 cm greater than the digital mean. It would be enlightening to compare the present technique for digitizing charts with manual methods available twenty or thirty years ago, but we have been unable to locate the manually digitized times series data. We feel that comparisons of digitally recorded data and manually digitized analog data should therefore be made with caution.
 We are indebted to the Arctic Submarine Laboratory for their unwavering cooperation in the processing and release of these invaluable ice draft data, in particular, to the Director of ASL, Capt. Stephen Z. Kelety, to past Directors Capt. Thomas A. Hawkins, and Capt. Jeffrey A. Fischbeck, and to Petty Officer Lee Wise. We thank Terry Luallin for valuable insights into submarine ice draft measurements. We especially wish to thank Dr. Diane Bentley who has been key to the success of this project. This work was generously supported by the National Science Foundation under Grant OPP-9910331.