Navy submarines in the Arctic Ocean routinely obtain observations from an upward-looking sonar of the draft of the sea ice cover overhead. Draft data are now publicly available from some 40 cruises from 1975 to 2000 covering over 120 000 km of track in roughly the central half of the Arctic Ocean. To apply these observations to geophysics, error estimates are needed. This paper assesses how well the correction of the data during normal processing accounts for the major sources of error in the draft data from U.S. Navy submarines and what errors remain in the data. The error treated is the error for the average draft over tens of kilometers. The following sources of error are considered: measurement precision error; errors in identifying open water (as ice of zero draft); sound speed error; errors caused by variable sonar footprint size, by uncontrolled gain and thresholds, and by ship’s trim; and differences between data from analog charts and digitally recorded data. The bias with respect to the actual draft is +29 cm and is important both for knowing the actual ice draft and for comparing drafts from submarines with thicknesses in models and with draft, thickness, or freeboard estimated by other vehicles and technologies. The standard deviation is 25 cm. This number estimates the repeatability and comparability of draft measurements by U.S. Navy submarines and is important for examining the submarine data for regional and temporal variation. These errors are tolerable for an operational data source with a signal many meters in amplitude.
Sea ice in the Arctic Ocean appears to be in decline, both in extent and in thickness (Parkinson et al. 1999; Stroeve et al. 2005; Rothrock et al. 1999; Tucker et al. 2001; Wadhams and Davis 2000). Observations of ice draft (about 89% of thickness) are available from upward-looking sonars (ULSs) on naval submarines and on moorings. This paper addresses the measurement accuracy of ice draft observations from U.S. Navy submarines. The U.S. Navy’s Arctic Submarine Laboratory (ASL) had the foresight to save all ice draft data starting with the first cruise in 1958 and continuing until the present. There have been over 70 cruises, roughly one per year, each lasting some 20–40 days and transiting much of the Arctic Ocean, sometimes once, sometimes twice. Many of these draft data have been released for a region covering about half of the Arctic Ocean and are archived for public use at the National Snow and Ice Data Center (NSIDC). They comprise an invaluable resource for climate research (Fig. 1 and Table 1). There is fairly equal coverage of the winter–spring (January–June) maximum or the summer–autumn (July–December) annual minimum draft. Data newly released in 2006 include all the cruises listed in Table 1 as University of Washington analog/scanned and digitized (UW A/S) data and 1999 Scientific Ice Expeditions (SCICEX).
These are operational data, taken during military missions to ensure the safe maneuvering of the submarine, and they were never intended to serve as scientific data much less to acquire uniform spatial and temporal sampling. The data acquisition procedures and instrumentation are typically not well documented, and such information is in hard-to-find data reports or exists only in the memories of naval personnel. The details of editing and processing the data have been modified over time. That said, we find that the data have great value for scientific use and enough accuracy to resolve the large signal in sea ice draft.
There exists no comprehensive study of the errors and uncertainties in the draft data, although the literature contains scattered examinations of some aspects of the errors as sidelights to using the data for sea ice studies. Tucker et al.’s (1992) work particularly contains a comprehensive listing of issues. Melling et al. (1995) wrote a useful paper on measurement errors for moored upward-looking sonars.
The purpose of this paper is to assess how well the correction of the data during normal processing accounts for the major sources of error in the U.S. submarine draft data and to estimate what errors remain in the data. The error we consider is the error introduced by the measurement system into measured mean draft over tens of kilometers, not the error in each sonar return (or “ping”). We regard this as a first-order estimate of measurement error; we do not have experimental validation of all errors, in some cases only rough estimates from experience processing the data. We have simply tried to make good estimates, neither very conservative nor very optimistic, to get a useful overall error budget. Lacking specific data to the contrary, we sometimes assume errors are normally distributed. We do not treat sampling error, which involves how long a draft profile or how large a sample is required to reduce to some desired level the uncertainty in the estimate of some statistic such as mean draft.
In section 2 we review the basics of the observation and describe the routine data processing. In section 3 the procedure of finding open-water sections and calibrating the draft with an open-water offset is discussed. Beginning with section 4 we discuss errors remaining in the data: sound speed error in section 4, the error due to variable depth and sonar footprint size in section 5, error due to lack of output power and gain control in section 6, error due to trim angle in section 7, and differences between data derived from analog charts and digitally recorded data in section 8. Some special topics and caveats are discussed in section 9. Errors in positions and distance along a draft profile are discussed in section 10. In section 11, all the errors in draft are collected to provide an estimate of the total error: the bias and the standard deviation.
2. The observation and an overview of processing
A submarine upward-looking sonar draft measurement is made by a sonar transducer mounted in the conning tower of the submarine. A highly focused beam of sound is transmitted upward through the water column, reflecting off the bottom of the sea ice and returning to the transducer (Fig. 2). The recording system measures two quantities: the pressure at a sensor located in the submarine’s hull, which is interpreted as keel depth (D̂); and the return signal strength as a function of time. [We use a circumflex (^) to indicate measured quantities.] To convert time to draft requires writing the travel time from the transducer to the overhead target and back again (2τ̂) in terms of measured range
where ĉ is the assumed mean sound speed in the water column, and finally writing the measured ice draft d̂ as
This conversion from time to draft is done within the ship’s ULS recording system. Thus, using (2), the return signal strength received as a function of time is known as a function of draft. For U.S. submarines the height H of the transducer above the keel is 51.5 ft or 15.7 m. The system precision for d̂, measured as the standard deviation in a sequence of pings when the ship is stationary under smooth ice, is ±6 cm (T. Luallin 2001, personal communication).
The output from the sonar system is typically recorded in two formats. An analog or paper strip chart records the entire return signal scaled to read as draft in feet and with the darkness of the trace indicating signal strength (Fig. 3). Beginning in 1976, most submarines were also equipped with a digital recording system [Digital Ice Profiling System (DIPS)] that uses a set of hard-coded thresholds to determine whether the signal has sufficient strength and duration to count as a valid return, in which case the deepest draft of the target is digitally recorded. This recorded signal is called the “first return.” The draft is measured and recorded about 6 times per second; this record is referred to as the raw data. At typical speeds, this provides a spatial profile of draft with a data spacing of about 1 m. DIPS records time, depth, speed, and course once a second. For paper charts, time, depth, speed, and course changes are handwritten on the chart, and location, speed, depth, and course changes are recorded in logs. The data are classified secret by the military and are archived at the Arctic Submarine Laboratory.
The raw draft data from U.S. submarines have been processed into corrected drafts by three groups, following the methodology initiated at ASL. First, Bronson Hills Associates working with the Cold Regions Research and Engineering Laboratory processed most of the DIPS data. Second, some DIPS data and much chart data were processed by us at the Applied Physics Laboratory at the University of Washington. Third, many DIPS cruises were processed by the Environmental Working Group (EWG), a U.S.–Russian collaboration aimed at releasing classified U.S. and Russian data. A fourth group headed by P. Wadhams, formerly of the Scott Polar Research Institute in the United Kingdom, processed data from Royal Navy submarines and from a 1976 cruise; we do not attempt to describe its processing procedures.
Processing includes (i) editing the data to remove spurious points (Fig. 3a), (ii) calibrating the drafts to sea level (section 3), (iii) tying the draft to navigation data, and (iv) stripping out segments during submarine maneuvers. The digital data have all been processed in this way. The trace on the analog chart data must be digitized before these steps can be applied. In some cases (see section 9b), this has been done by running a cursor over the trace by hand on a digitizing tablet (McLaren 1986; LeSchack 1980). For those cruises listed in Table 1 as UW A/S, charts were first scanned to produce bitmap images, and the trace was then digitized using image processing techniques (Wensnahan and Rothrock 2005). These procedures capture the “first return” (deepest draft) on the chart, ignoring return signals from shallower features in the ice cover, and are thus quite comparable to the digitally recorded data.
For the classified data from most cruises to be cleared for public release, times are rounded to the nearest third of a month, positions to the nearest 5′ of latitude and longitude. In the 1990s there were several cruises designated as SCICEX, in which civilian scientists were invited to play a role and for which the time and position data were not rounded. The data are reviewed by ASL and approved for public release as unclassified data. Unfortunately, with few exceptions data have been released only within a region known as the SCICEX Box, which excludes the exclusive economic zones of foreign countries and covers roughly half the Arctic Ocean. Figure 4 shows this box and the cruise tracks where there are publicly available data.
3. Open-water offset, identification, and correction
The raw draft measurement is made as in Eq. (2). Generally, all raw drafts are greater than zero; even open water has a raw value that is positive by up to 1.5 m. This is due to an adjustment made by the crew to ensure that the raw data signal is definitely on the paper chart. We refer to this positive value for open water as the “open-water offset” or “open-water correction”:
The corrected draft dc is then defined as the raw draft less the open-water correction:
which then by definition is zero for open water. Aside from the removal of spurious points that bear no relation to neighboring data points, and the removal of data taken during ship maneuvers, this open-water correction is the only correction applied to the data. This corrected draft dc is the value released for public archival.
Open water must be identified by an analyst, and this task is tedious and somewhat subjective. Typical open- water selections are shown in Fig. 3b. Comiso et al. (1991) reports that open water has a “characteristic ‘grassy’ echo due to high return signal strength.” Melling et al. (1995) states that in draft data from moored ULS, open water can be distinguished from thin ice by its longer return pulse. Our experience is that neither of these features can be relied on. The open-water return sometimes has a fuzzier appearance on the analog charts that leads to a longer return pulse, but this occurs in the chart data infrequently and primarily when the power and gain settings of the sonar system are set relatively high. For all U.S. Navy data, open water is taken to be the minimum draft within a window of between 5 and 25 km (as discussed further later in this section) without requiring any unusual appearance of the return signal. Comparisons of open-water offsets selected by two independent analysts show a standard deviation of ±8 cm in their different selections of Δ with no significant bias attributable to the analyst. These two analysts are the person who processed nearly all the digitally recorded data and the person who processed all the (UW) analog chart data. In fact, it should be emphasized that this procedure of selecting open-water offsets was used both for (UW) analog chart analysis and for all analysis of digitally recorded data.
Thin ice is prevalent in arctic leads, particularly in winter, and is easily mistaken for open water leading to a negative bias. It is our experience in working with the analog data that ice up to roughly 30 cm thick can be wrongly identified as open water. This estimate comes from comparing tentatively selected open water with thinner “open water” areas identified subsequently in the search for a “good” patch of open water. Such tentative and false open-water patches are seldom more than 30 cm deeper than a good patch. So we estimate the bias due to open-water selection to fall in a range of 0 to −30 cm, which we write as −15 ± 8 cm, the standard deviation being taken as a quarter of the range. Such a bias is less likely in summer months (July and August) when open water is more prevalent and young ice less so.
The open-water correction varies along the profile. The fundamental unit for reporting profile data is a “segment,” defined as a portion of the cruise when the ship was running at one nominal depth and speed and on a straight course (within a few degrees). Data in the archive are grouped into segments of lengths of several kilometers to 50 km. During open-water identification, these segments are subdivided into “sections,” in which the open-water offset appears to be constant. The offset is reset whenever the submarine changes depth or speed, when the crew “vents” the depth detector to maintain its accuracy, or when the offset appears to have changed for no obvious reason. During such a cruise “event,” when the submarine changes depth or speed or the depth detector is recalibrated, the change from old to new open-water offset Δ may be as large as 60 cm.
A single open-water correction is applied to each section of data. This single correction method accounts for specific events that would cause the calibration to change. It is our experience that Δ exhibits little or no drift and that specific events (venting, or changes in speed or depth) account for almost all shifts in Δ. In short sections of data with few open-water patches we are less confident in the open-water identification. Generally, sections longer than 5 km are sufficient for selecting open water. If no open-water patch appears within 25 km, the data were usually discarded, unless the open-water patches on either side of a “blank” section have very similar open-water offsets. The analog data are further checked for consistency in mean draft and in the spatial profile from segment to segment to weed out obviously poor open-water identification. This type of final check was not done for the digitally recorded data.
This constant open-water correction accounts for a number of sources of error in the draft d̂ calculated by Eq. (2), including open-water identification issues discussed above; issues involving sound speed, discussed in section 4; and error in the ship’s depth D̂ because of the spatial gradient of surface pressure, which is discussed here. The ship’s measurement of depth is measured relative to sea level pressure, which changes with distance. This change could cause an error in the open-water correction to grow as the submarine moves away from an open-water patch. Generally, the distance between open-water patches is between 5 and 25 km, so consider a distance L = 25 km and take a typical sea level pressure gradient dp/dx to be 25 mbar (1000 km)−1. The error in depth D, and therefore from (2), in draft d that accumulates over a distance L is (1/ρg)(dp/dx)L, or about 0.7 cm, which is negligible. (The water density ρ is ∼103 kg m−3 and the acceleration of gravity g is ∼10 m s−2.) Variable surface pressure is a greater issue for moored sonars for which temporal pressure changes can be much larger and no open-water correction is made; see Melling et al. (1995) for more details.
In summary the raw draft data are corrected by an open-water offset Δ that is a constant over substantial sections of profile. The error in the open-water correction and therefore in the corrected draft dc, from above, is a positive bias in draft of 15 ± 8 cm plus a random “operator error” (repeatability) of ±8 cm.
4. Sound speed errors
We consider sound speed error in three manifestations. First, the possible change in sound speed within the top 20 m of the water column where ice draft is sensed; second, the large-scale basinwide gradients of vertically integrated sound speed; and third, the smaller-scale variability of the same quantity. All three of these turn out to be either negligible or accounted for by the open-water correction.
The ULS recording system scales all drafts using an assumed sound speed. The additive open-water correction properly accounts for uncertainty in the sound speed for open water (dc = 0), but not for drafts other than zero. We can compute the sound speed error by considering the time it takes for the sound wave to move from the depth of some draft dc to open water (Δτ = τow − τd) in two ways: as correctly computed with a real sound profile from the surface to the actual draft d, and as approximately computed above in section 2 with the open-water corrected draft dc and an assumed sound speed:
The sonar system on U.S. submarines is almost always set to ĉ = 1436.2 m s−1. Figure 5a shows summer and winter sound speed profiles c(z) for three locations within the SCICEX Box chosen for their wide range of temperature and salinity. The sound speed is calculated using the equations from Leroy (1969) using the climatological data of Steele et al. (2001). Within the top 25 m (the depth of the deepest ice) the sound speed ranges from 1435 to 1442 m s−1. The right-hand equality in (5) allows the computation of corresponding values of actual draft d and corrected draft dc, using the sound profiles in the figure. The sound speed error dc − d is plotted in Fig. 5b. For ice of 3-m draft, the error is a fraction of a centimeter. For deep keels, the error can reach between +1 and −5 cm. This error is much less than the error that would be obtained in computing the entire range from the transducer to the ice cover if there were no open-water correction; it involves the sound speed profile only in a water layer as thick as the ice. We regard this source of sound speed error as negligible.
To evaluate the other two sources of sound speed error, we need to know sound speed from near the surface to the depth of the transducer. Depths have not been put in the public archive for much of the ice draft data (see section 10), but they were included for data processed from analog charts at the University of Washington, roughly 40 000 km of data (see Table 1). Figure 6 shows a histogram of the fraction of track length at various depths for these cruises. The bulk of the data is taken at a keel depth of about 400 ft (121.9 m) or a transducer depth of about 110 m, and a second group at a transducer depth of about 170 m. For sound speed data we examined expendable CTD casts from the SCICEX 1997 and 1998 submarine cruises. The casts were made every 40–50 km along the cruise track over depths from 20 to 1000 m at 1-m intervals. We calculated the mean sound speed from 20 to 110 m and from 20 to 170 m for each cast from temperature, salinity, and depth using equations from Leroy (1969). Figure 7a shows the cast locations for the 1997 cruise, and Fig. 7b shows typical mean sound speeds. Large-scale gradients of mean sound speed for both cruises over both depth ranges are no more than 0.003 m s−1 km−1. Over a 25-km section this yields a change in sound speed of no more than 0.075 m s−1. Assuming a nominal sound speed of 1440 m s−1, the draft error due to large-scale gradients weighted by the frequency of submarine depths in Fig. 6 is no more than 0.6 cm, negligible for our purposes.
The local variation is calculated as the standard deviation of the difference between the sound speed along the cruise track and a second-order polynomial fit of those data (Fig. 7b) and is ±0.5 m s−1 on average for both the 20–110 and 20–170 depth ranges in both 1997 and 1998. Again we use Fig. 6 to obtain a depth weighted average draft error and obtain ±4 cm. This effect and the one above from large-scale sound speed variation would appear as changes in open-water offset Δ and so are included in the open-water correction error found in section 3.
5. Ship depth and sonar footprint
The signal “seen” by the sonar is complicated by many issues: “the value of draft attributed to ice at the beam axis will be an overestimate, and sloping features will thereby be broadened. The magnitude of this error depends not only on the beam pattern of the sonar, but also on the gain of the receiver, the sensitivity of its threshold detector, and the properties of the ice target (geometry, reflection coefficient, and range)” (Melling et al. 1995). By using data from Vinje et al. (1998), in this section we take into account some of the geometric issues. The following section (section 6) deals in a very empirical way with gain issues and indirectly with variability of the ice reflectivity as discussed by Melling (1998).
Because the sonar beam is not infinitesimally narrow, the sonar insonifies a finite area of the underice surface, the “footprint.” A finite footprint diameter causes the first return to be biased toward deeper draft compared to the mean draft within the footprint or the draft exactly in the center of the footprint. The amount of bias varies with the nominal footprint diameter or width WFP, which in turn is proportional to the beamwidth and to the transducer depth DT. The deeper the submarine, the broader the footprint, and the larger the bias. The transducer and therefore the beamwidth has been the same for all U.S. submarines since 1960 and has been reported as 2° for the full (−3 dB) beamwidth (McLaren 1986; McLaren et al. 1994). We have no more detailed information on how this beamwidth is defined. We have, then,
The most direct investigation to quantify the bias was reported by Vinje et al. (1998) who used high-resolution two-dimensional maps of ice draft measured in situ in the Greenland and Barents Seas to estimate footprint error EFP defined as the difference between the draft of the deepest draft (dc) within the footprint and the mean draft (dmean) within the footprint. By forming averages over various footprint sizes, Vinje et al. derived relationships between footprint error and the footprint width (Fig. 8), which we characterize as
our evaluation of coefficients a and b is given in Table 2. For U.S. submarines the transducer depth is 51.5′ or 15.7 m less than the submarine (keel) depth; as seen in Table 2 the footprint diameter ranges from 2.6 up to 6 m.
The conclusion from Vinje’s work is that footprint error (a positive bias in draft) increases with increasing footprint diameter and depends on the roughness of the ice. From Table 2 we see that when evaluated for the U.S. submarine data, this bias varies 28–54 cm in winter to 15–30 cm in summer.
To use Vinje’s results to estimate submarine drafts for footprint error requires that we again use the depth histogram in Fig. 6. Assuming that roughly half the cruise track is under multiyear summer ice and half is under multiyear winter ice, we obtain a histogram of the footprint error with a mean of +44 cm and a standard deviation of 9 cm. [We neglect first-year ice because (a) its coverage is order 10% in the perennial ice cover where the draft data are taken, (b) we do not have data from Vinje on it in summer, and (c) it has the same footprint error as multiyear ice in winter.] This is our best estimate of the footprint error remaining in the archived data.
This estimate of error applies only in some mean sense, which we take to be the mean draft over segment lengths on the order of tens of kilometers. It is not the error of any single sonar return, the error for which could be much larger, for example, for shoulders of ridges, or much smaller, for example, for level ice. A higher-level error treatment would take account of ice roughness in assessing footprint error.
6. Uncontrolled output power and gain versus thresholds
The above estimates of footprint diameter are idealized by the assumption that the return power is roughly constant. In reality, though, the effective beamwidth depends on the sonar’s output power and the gain applied to the return signal, both of which are set by the crew but are not recorded. For some cruises power and gain adjustments were made regularly when the submarine changed depth resulting in analog charts where the draft trace is dark, clear, and distinct at all submarine depths, but for other cruises power and gain settings were changed only sporadically, and the trace intensity varies substantially when the submarine changes depth. For the digitally recorded data this is a distinct problem since a fixed threshold is applied to determine the first return no matter what the power and gain settings. The problem is mitigated somewhat during processing (of both digital and analog data) when sections with very low power or gain settings are simply deleted as unusable. The analog data produced by our group (UW A/S in Table 1) have the advantage of a user-defined threshold to partially counteract intensity variations.
To estimate the amount of error attributable to variations in power and gain settings, we simulated different intensities in the analog charts by selecting a chart with a relatively dark trace and applying two extreme thresholds, thus producing two possible chart images with two different apparent intensities (Fig. 9). The two simulated charts with two different intensities were then processed, giving two extreme estimates of mean draft. Assigning the 69-cm range between the means in Figs. 9b and 9c to be the 95% range of a normal distribution, then the standard deviation is about a quarter of that or ±17 cm. We take this value as the uncertainty caused by variations in return signal strength. Several similar tests on charts under less rough ice gave a smaller range.
The effective beamwidth is potentially modified by variations in the reflectivity of the ice. Measurements by Melling (1998) show that the scattering coefficient is −7 dB for open water and rapidly decreases as ice forms and thickens to 1 m. Beyond 1 m both deformed and undeformed ice have a fairly constant coefficient of around −30 dB independent of thickness though the coefficient is highly variable over short length scales in a seemingly random manner with a range of around ±5 dB. The potential exists that target identification based on thresholding will on occasion identify strong scattering targets at the edge of the beam as being the first return. However, there will also be times when weak targets will not trigger the threshold. Ultimately, the impact of this effect on the mean draft is not known, though it may add to the bias and uncertainty. We feel the test described in the preceding paragraph deals with these issues as well as possible.
7. Ship’s trim angle
The schematic in Fig. 2 assumes zero trim angle, that is, a ship running precisely level. In reality, the trim angle can vary: in the Arctic Ocean during “level” flight, the trim angle α is maintained within ±0.25°. The most obvious place for this to cause error is in the range to the ice, which is no longer r̂ but is instead r̂/cosα, giving an error of r̂(−1 + 1/cosα). Even at 190 m, the maximum depth in Fig. 6, this error is less than a centimeter, and we neglect it. A more sizeable error arises from the fact that the pressure port and the transducer measuring r̂ are separated horizontally by x = 18.8 m (61.7 ft). The ship’s depth used in the draft calculation can differ from the depth at the transducer by ±x tanα or ±8 cm. Assuming the ship spent much of the time at the extremes of this trim window, we regard the trim error as having zero mean and a standard deviation of 8 cm.
8. Analog charts compared to digitally recorded data
The sonar signal returning to the submarine from the ice may be a single distinct pulse, multiple distinct pulses, or multiple pulses that blend together to make longer pulses. The chart retains this information (Figs. 3 and 9). The digital recording system, however, records only the first return signal that meets specified signal strength and minimum duration criteria. To maintain continuity with the digital data, the analog data available at NSIDC are also based on only the first return (Wensnahan and Rothrock 2005). Hence both datasets report only the deepest ice within the footprint of the instrument. The open-water offset is identified and selected by exactly the same procedure in the processing of chart data and of digitally recorded data. The error in the comparability of analog data with digitally recorded data is ±6 cm in mean draft (Wensnahan and Rothrock 2005). We assume that this error is mostly due to the finite chart pen width and relatively slow paper feed rate.
9. Special cases and problems
a. In-water targets and instrument interference
An early step in processing is removing spurious data (Fig. 3a). Interference from other instruments on board affects the data to a greater or lesser degree depending on the cruise. For example, during SCICEX cruises submarines carried additional acoustical instrumentation producing especially noisy data (particularly 1996 SCICEX). Editing removes much of the noise. Targets in the water column (such as fish) are seen only rarely in the data and are fairly easy to identify and exclude. This is a complicated issue requiring subjective choices in processing data, but we see no way to assign a value to any resulting error.
b. Hand-digitized paper charts
Until recently the process of scanning the paper charts to produce a digital image was not feasible. The procedures of digitizing the charts on a digitizing tablet following the trace by hand or with a mechanical line-following arm have received considerable use (McLaren 1986; LeSchack et al. 1971; Wadhams 1984). We caution that drafts from hand-digitized charts appear to miss some shallow portions of draft in between deeper features and are likely biased toward deeper drafts by an unknown amount (Wadhams 1984). Their comparability with digitally recorded data has not to our knowledge been examined. This would call into question any comparison of DIPS and A/S data (Table 1) with hand-digitized (A/H) data.
c. Surface waves in open water
Surface waves, likely remnant ocean swell, are occasionally present in open-water sections (Fig. 3c) near the ice margins. This effect is infrequent since the data primarily come from the central Arctic where the ice pack dampens the waves, and where there are few areas with sufficient fetch for wave generation. When seen, typical wave amplitudes are around ±15 cm, and wavelengths are hundreds of meters. Such long wave swell is not uncommon in the Arctic Ocean (Johannessen et al. 1999). In our processing of UW analog data, the open-water calibration in these sections is set to the middle of the wave to eliminate bias in the draft. Negative drafts of up to 20 cm are converted to a draft of 0 cm. An exception was made for the 2000 cruise where significant wave action is seen well into the pack as the result of Hurricane Michael. In this case, the draft data include both negative and positive values of draft, which could usefully be interpreted as wave amplitude. For the digitally recorded data, the open-water offset has been set at the top of the wave to exclude any negative values of draft, a procedure that biases the draft by up to about +15 or +20 cm. Because of the small amount of data affected, we regard error due to surface waves as negligible.
d. EWG interpolation
In most respects, the procedures and errors discussed above apply to processing by the Environmental Working Group. However, there is one significant difference: in the EWG procedure, sections of profile with data gaps were filled with values interpolated between the nearest data point on either end of the hiatus, over lengths up to more than 10 km. These interpolated data were then used in the computation of statistics for the segment. We advise that these statistics are tainted by the interpolation and that they should be further inspected; it seems likely the statistics should be recomputed omitting the interpolated data. We also find a lack of correspondence between the number of files of statistics and of profiles.
e. Stuck depth detector
The depth of the submarine is continually changing by small amounts as the submarine “porpoises” as it attempts to maintain a given depth. On two cruises the depth detector became stuck and changed in large jumps rather than smoothly. On the 1995 SCICEX cruise the problem could not be corrected. Fortuitously, the 1998 SCICEX cruise had an independent depth detector on board, and this could be used to correct the draft record; there is a probable positive bias in draft after correction of about 8 cm [due to an uncertainty in a clock adjustment of about ±3 s (Dickinson et al. 2002, their Fig. 7)].
f. No useable data
There were a number of cruises for which no useable data could be obtained. Reasons include no useable draft data, no navigation data, no releasable data within the SCICEX Box, and bad pressure data. We believe nearly all useable data from 1975 through 2000 are now available at NSIDC.
g. 1976 data
There are now two versions of data from the 1976 cruise of the USS Gurnard at NSIDC (Table 1): 1976-UK-DIPS and 1976-UW-A/S. The latter version contains nearly 4 times as much data as the U.K. version. Furthermore, where the two versions overlap, we find that the 1976-UK version is considerably smoother than the 1976-UW-A/S version, reads on average some tens of centimeters greater, and appears to have had no open-water correction applied. Our recommendation is that the 1976-UW-A/S data be used.
10. Navigation errors and interpolation of distance
The released data are reported as profiles of draft as a function of distance along the path of the submarine. The distance is itself subject to errors that would affect any spatial statistics such as autocorrelation or keel spacing. Error can arise from a number of sources including the inertial navigation system, inaccurate ship speed, and additionally for charts only, misrecorded ship speed, and interpolation of navigation data when the ship did not maintain constant speed. The distance is calculated either from the submarine speed (as done by our UW group for the analog data) or from latitude and longitude as measured by the inertial navigation system of the submarine (as done for the digital data). We find from chart analyses that the discrepancy between the two methods ranges over ±10%, suggesting a standard deviation of about ±5%.
11. Summary and discussion
Over 120 000 km of profiles of ice draft data spanning the years 1975–2000 and covering about the central half of the Arctic Ocean are now publicly archived. These data provide a valuable long-term record of ice draft in the central half of the Arctic Ocean. Putting them to good use requires an assessment of their quality. We summarize the errors discussed in this paper as being of two types: first, a bias with respect to the actual draft, and second, a standard deviation about that bias that estimates the repeatability and comparability of draft measurements by U.S. Navy submarines. These two measures of accuracy are summarized in Table 3.
From section 2 the measurement precision is ±6 cm. In section 3 we concluded that the bias due to selecting the open-water offset is likely in the range 0–30 cm, which we enter in Table 3 as −15 ± 8 cm. In addition there is “operator error” of ±8 cm. In section 4 we estimated that the sound speed error not accounted for by the open-water correction is quite small and contains no bias. In section 5 we concluded that the likely overall effect of variations in depth and footprint size has a bias of +44 cm, and a standard deviation of 9 cm. In section 6 we estimated that lack of control of the power and gain contributes zero bias and a standard deviation of about 17 cm. In section 7 the error due to trim angle variation was found to have zero mean and a standard deviation of 8 cm. In section 8 we quoted the rms error of 6 cm for the comparison between data from analog charts and digitally recorded data.
We compute the combined bias in Table 3 by adding the biases to obtain a combined bias of +29 cm. That is, the measured drafts are probably on average about 29 cm too large. This bias is important for knowing the actual draft of the ice cover and for comparing draft from U.S. submarines both with thicknesses in models and with draft, thickness, or freeboard estimated by other methods and technologies. The standard deviation of measurements from U.S. submarines is computed by adding the variances in column 4. It is applicable when studying regional and temporal variation within the submarine data themselves. The value of 25 cm is a surprisingly low number and shows that with drafts ranging over many meters, there is a large signal compared to this measurement “noise.” We reiterate that these values represent the measurement errors of draft in some average sense, say, over tens of kilometers and not for each sonar ping. We have not treated here but intend to treat in future the topic of sampling error dealing with questions such as how large a sample is required to reduce the uncertainty in mean draft to a desired level, and how does sampling uncertainty in mean draft decrease as the sampling size or profile length is increased.
How serious are the errors summarized in Table 3 compared to the signal—the draft measurements themselves? Figure 10 shows the summer and winter distributions of mean draft averaged over 30–60 km. The error of ±25 cm that we have estimated applies to each of these average values. All the structure seen in these histograms—the overall range of more than 5 m and the large differences between summer and winter—represents signal that is well resolved by these measurements.
These errors each have different and unknown spatial scales. An error in the open-water offset would pertain over one section of many kilometers. If the sound speed error were more significant it might be considered as a function of season and region. The error due to gain is likely constant over each segment of constant depth. To try to consider the autocorrelations of each of these, much less cross correlations between them, to say how they might “average out” would seem to reach beyond our understanding of the errors.
The one error that should be dealt with in the future is the quite significant 44-cm bias from varying footprint size. The ship depths are known for all cruises but archived only for the UW analog data (∼40 000 km of data). It would be a modest undertaking to add depths to the archive for the digitally recorded data (∼80 000 km of data). This largest source of bias could then be treated systematically.
There are more data from earlier cruises whose charts have less contrast than the charts already processed (six cruises before 1971 with about 1500 km of winter data and 4200 km of summer data). We believe that with more sophisticated techniques many of these charts could be analyzed and would extend the useful record of ice draft back another 15 yr to 1960.
We are greatly indebted to the present and past staff of the Arctic Submarine Laboratory, to J. Gossett, T. Luallin, B. Markham, and especially to D. Bentley, for their continual instruction, guidance, and collaboration in our processing of data, but more than that, for their stewardship of the large volume of data in charts. Two individuals performed a great deal of the most tedious work in our processing of data from charts: L. Wise digitized all the charts on a large-format scanner and burned CDs of the chart images, and P. Hezel did most of the processing from chart images to corrected data. We thank D. Farmer who transcribed logs of navigation data into digital data and processed the 1999 SCICEX data. We are grateful for the constructive suggestions from several reviewers. This material is based upon work supported by the National Science Foundation under Grant 9910331 and Grant 0453825, and we gratefully acknowledge the generous support of M. Ledbetter and N. Swanberg of the Office of Polar Programs at the National Science Foundation.
Corresponding author address: D. A. Rothrock, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105. Email: firstname.lastname@example.org