1. Introduction

The only reliable means for precise and detailed measurement of the draft (and indirectly, thickness) of pack ice is provided by subsea sonar. For more than two decades, data for the scientific study of sea ice have been acquired by sonar mounted on nuclear submarines patrolling the Arctic Ocean (e.g., Williams et al. 1975;Wadhams and Horne 1978; Wadhams 1981; McLaren 1988). In recent years, through improvements in microprocessor and data-storage technologies, self-contained recording sonars have been developed that are capable of long-term moored operation beneath drifting ice (Hudson 1990; Pilkington and Wright 1991; Moritz 1992; Melling and Riedel 1995). A sonar for ice profiling has a narrow, vertically directed beam and operates in a pulsed mode. It is equipped with a pressure sensor, from which its changing depth may be derived, and with pitch and roll sensors to measure the beam orientation. The foremost design objective for an ice-profiling sonar is the realization of a small effective “footprint” on the underside of the ice. This objective, which reflects the small horizontal scale (≈1 m) of appreciable draft variations in ridged ice, dictates that the main beam be narrow, that side lobes be low, and that the sonar be operated as close to the ice as hazard from drifting ridge keels permits. If the sonar beam is too wide, unacceptable biases are introduced into ice-draft statistics (Wadhams 1981). Fortunately, the short-range requirement permits use of high acoustic frequencies (typically greater than 100 kHz), which in turn facilitate the achievement of desirable beam characteristics (main beam width less than 3°) at modest cost.

For the thick ice floes and deep keels that have traditionally been the targets of greatest interest, useful draft observations can be obtained from the travel time of echoes with relative ease. However, useful measurements for thinner ice forms are a challenge because establishing an accurate zero reference for draft in an ever-changing marine environment is difficult (Melling et al. 1995). Ultimately, the time-varying range that is the reference for zero draft must be fine-tuned on the basis of the apparent draft of areas of open water found in the record. How can these be distinguished from areas of thin ice when the exact travel time of echoes from the sea surface is not known? Pattern recognition and Doppler returns can provide some guidance in the identification of ice-free areas (Melling et al. 1995). However, because this guidance is neither clear-cut nor infallible, more information is needed. For example, clouds of air bubbles beneath the surface of wave-agitated leads often complicate the detection of the air–sea interface.

In this study, a sonar with specifications similar to an ice-profiling instrument was used to measure the amplitude of echoes from the underside of drifting arctic pack ice between freeze-up and late winter. The varying strength of these echoes was investigated as a possible indicator of the nature of the surface target.

Echoes are generated through the mechanisms of reflection (coherent return) and scattering (incoherent return). A monostatic sonar, such as used for ice profiling, will receive reflected sound only if the target is smooth and if the axis of the sonar’s beam is close to normally incident upon it. At the high frequencies of interest to ice profiling, Langleben (1970) has determined that the specular echo (actually reflection plus scatter) from the underside of thick first-year sea ice is weak (typically less than 10% of the incident amplitude for sound at near-normal incidence). He attributed the weak reflection to the gradual change in acoustic impedance across the porous skeletal layer forming the bottom of the ice sheet. More comprehensive measurements at normal incidence for four frequencies between 125 and 820 kHz were carried out by Stanton et al. (1986) using sea ice grown in an outdoor pond. They examined the fluctuations in echo amplitude as the beam was moved to sample independent areas of the statistically homogeneous target and showed that the probability densities of observed amplitude could be represented by the Rice function; this is the theoretical form predicted by Rice (1954) for the amplitude PDF of a signal that is composed of a sine wave and additive random noise. In the present context, the coherent reflection from the target is the sine wave and the scattered return is the “noise.” With the 9° beamwidth used for the measurements of Stanton et al. (1986), the relative importance of reflection and backscatter reversed as the frequency was increased from 125 kHz (ice appears smooth) to 820 kHz (ice rough). Mean values of the amplitude reflection coefficient decreased from 0.06 at 125 kHz to 0.04 at the three higher frequencies.

Measurements at 120 and 188 kHz (beamwidth ≈ 9°) for a variety of natural and artificial sea ice forms are reported by Jezek et al. (1990). Here again Rice theory was an acceptable model for the probability density of observed echo fluctuations. For very thin growing sea ice, having a dendritic interface with sea water, the mean amplitude reflection coefficient was strongly dependent on thickness, decreasing from values near unity to about 0.1 as ice thickened from 0 to 6 cm. In situations where the dendritic interface of thick sea ice had been thermally altered by immersion in warm sea water, a dramatic increase in the reflection coefficient to about 0.25 was observed. Coefficients as high as 0.4 were obtained for slush layers and lake ice.

Additional measurements on natural sea ice are discussed by Garrison et al. (1991) and Bush et al. (1995). The first paper presents values for the reflection coefficient of thick growing first-year ice, obtained using wide-beam sound sources within the frequency range 15–300 kHz, which are in accord with others cited above. The second discusses observations made with a narrowbeam (2.6°) sonar operating at 300 kHz. These indicate that average values for the amplitude reflection coefficient derived using a narrowbeam sonar are appreciably lower than earlier results (0.011 for 4-cm growing ice, 0.005 for 65-cm growing ice, and 0.013 for 60-cm melting ice) and that the range of variation exceeded the mean. Bush et al. (1995) comment that since the low values obtained are almost certainly indicative of scattered, not reflected, returns, it is appropriate to use the scattering coefficient of the surface (in decibels relative to 1 m² m⁻²) in preference to the reflection coefficient. This is essential when comparing measurements made by different sonars because, if echoes are dominated by scattering, the derived effective reflection coefficient is dependent on the sonar beamwidth.

The field program and sonar calibration are discussed first (sections 2 and 3). Next, the observations are presented (section 4) and an interpretation is provided (section 5). A discussion of the ramifications of this study for ice profiling by sonar (section 6) precedes a concluding summary.

2. Field measurements

This study was conducted using a WASP (water-structure profiler) sonar moored in an arctic sea to observe the widely varying surface conditions encountered between autumnal freeze-up and late winter. The WASP is a low-power digital sonar using a computer hard disk as the data storage medium. The 490-Mb drive in this unit supported the recording of echo profiles at 10-s intervals for almost 6 months. For this work, the WASP was reconfigured with reduced gain, commensurate with interest in surface targets, and with a narrowbeam transducer appropriate for ice profiling. Operating parameters are summarized in Table 1.

The WASP was deployed in early September 1995 in the Beaufort Sea about 100 km north of Tuktoyaktuk, Canada. It was secured on a short taut-line mooring at a depth of 52 m. The mooring design constrained variations in beam direction to within 1° of zenith under typical current conditions. The WASP operated until the end of February 1996, at which time the data-storage capacity was exhausted. It was recovered through the ice at the end of March. A 300-kHz Doppler sonar for the measurement of ice motion and a 200-kHz ice-profiling sonar were moored within 100 m at the same location.

Stormy ice-free conditions prevailed at the site until the first appearance of nilas on 22 October. Thereafter, a wide range of first-year ice forms was observed in a seasonally evolving progression similar to that documented by Melling and Riedel (1996). Unfortunately, data recorded between mid-September and 22 October could not be retrieved because of a malfunction of the WASP firmware. Since storm waves had been suppressed by new ice by the later date, no observations of subsurface bubble clouds were recorded. For the remainder of the deployment, the concentration of ice was close to ten-tenths.

To acquire observations of bubble clouds in relation to sea state, the WASP was later deployed within a few kilometers of a wave-measuring buoy in Georgia Strait on the Pacific coast of Canada. Operating parameters were those of Table 1, except that the depth was shallower (46–50 m, depending on tide) and the bin size smaller (0.12 m). The instrument operated between 21 June and 15 July 1996, observing seas with significant-wave height (SWH) as large as 0.8 m. These observations encompass the range of sea states likely to occur in fetch-limited arctic leads.

3. Calibration

The beam pattern and transmit voltage response of the acoustic transducer at 400 kHz were measured in a tank at a range of 4.25 m using a Reson TC4014 calibration hydrophone. Electronic gain of the WASP was measured using a purely resistive sine-wave source at the same frequency. These calibrations were cross-checked for the sonar as a complete system by measuring the echo from a 40-mm-diameter spherical calibration target (tungsten carbide, target strength −43.7 dB) at a range of 22.5 m. The accuracy of the system gain listed in Table 1 is estimated to be ±1 dB.

In view of the limited dynamic range of the receiver (48 dB), selection of an appropriate operating gain for the WASP in this application was critical. Existing data on surface reflection coefficients (see introduction) were judged to be of little value in this decision since a specular return from a surface target would rarely be picked up by the very narrow beam of the WASP. To acquire some pertinent data prior to the arctic deployment, the WASP was used to observe echoes from a calm sea surface (lightly roughened by capillary waves) in waters adjacent to the Institute of Ocean Sciences. The instrument setup for this purpose was that detailed in Table 1, except that smaller values were used for gain (49.5 dB), minimum range (0 m), and pulse interval (1 s).

The WASP was deployed briefly at each of four depths between 31 and 77 m. The maximum amplitude received from each ping was noted as the surface echo. Figure 1a illustrates that the measurements of the surface echo were consistent with return from an infinite planar target having an average reflection coefficient for amplitude of 0.028. However, the variation about this average was large (about 6 dB for ±1 standard deviation). From Fig. 1b, it is clear that the probability density of echo amplitude does not have the symmetrical Gaussian form expected for a coherent return. It is also not possible to match simultaneously the position and magnitude of the observed probability peak using the single-parameter Rayleigh function representative of single scattering. A lognormal form provides a closer representation of the observed probability density. The amplitude reflection, calculated for an infinite planar target, was not perfect (value of 1), as normally assumed for a water–air interface; rather, the 5th, 50th, and 95th percentile points of the probability density of reflection coefficient were 0.0085, 0.026, and 0.055, respectively.

For the arctic deployment, the gain of the WASP was adjusted such that all but the weakest 5% of the echoes from a calm sea surface would saturate the receiver at the planned deployment depth of 55 m. Implicit in this decision was the assumption that the target strength of sea ice would always be weaker than that of an ice-free sea surface.

4. Observations

More than 1.1 million echoes were recorded during the arctic deployment. Figure 2 presents a 1800-ping sample of the data acquired over a 5-h period in December 1995. The range and maximum amplitude of the surface echo are shown. The range plot is a typical topographic section for first-year pack ice, where level floes of about 1-m draft are separated by ice keels extending as deep as 14 m. Most obvious in the amplitude plot are the dramatic fluctuations from ping to ping. There is little indication of any correlation between echo amplitude and target type (e.g., level versus ridged ice).

Very slow ice drift in late January 1996 permitted repeated examination of a single level first-year floe that was presumably homogeneous in surface properties. Figure 3 is a probability density compiled from the almost 64 000 echoes received from this target. The clear asymmetry of the empirical probability density precludes a Gaussian fit, which would indicate a coherent return from the sea ice. However, neither do the Rice and Rayleigh forms predicted for incoherent returns by Stanton et al. (1986) provide suitable fits. A single-parameter Rayleigh function, which peaks at the same value of echo amplitude, as the data is plotted in Fig. 3, where its serious overestimate of the probability density at low amplitude is clear. The lognormal curve is the subjectively best representation of the skewed distribution of the observations.

Under similar conditions of drift in mid-February, the WASP observed low rubble on the shoulder of a ridge keel. Again, the curve providing the best subjective fit to the observations (Fig. 4) is a lognormal function. The observed probability is clearly not Rayleigh distributed (dashed curve), nor could Rice or Gaussian functions provide an appropriate representation. In average amplitude the echo from the ice rubble is close to that from thick level ice (Fig. 3), but its fluctuations are appreciably smaller.

To examine statistical behavior over the entire dataset, amplitude probability densities were calculated for surface echoes grouped according to range. In Fig. 5, results are presented in terms of the 5th, 50th, and 95th percentile points of the probability density plotted against the approximate value of ice draft. At deep draft, a larger number of bins have been grouped to compensate for the smaller number of targets detected. The observed amplitudes have been calibrated to yield the surface backscattering coefficient S, in decibels relative to 1 m² m⁻², using a sound attenuation of 0.102 dB m⁻¹ appropriate to winter hydrographic conditions in this area (Francois and Garrison 1982). The lower axis in Fig. 5 is the equivalent amplitude reflection coefficient, K, for a planar target. If the return is incoherent, as appears to be the case for these data, K is dependent not only on the properties of the surface but also on the solid angle of the sonar beam, Ψ, according to S = 10 log[K²/(4Ψ)]. Reflection coefficients are provided here for continuity with earlier published results, but use of the backscattering coefficient is preferred.

Several patterns are clear in Fig. 5. At draft values indicative of ridge keels (>2 m), the percentile points for backscattering coefficient are approximately independent of draft, and 90% of values fall within a domain about 10 dB in width. In early winter, curves do not extend to large draft since deep ridge keels have not yet developed. No seasonal variation in the backscattering from keels is apparent, and echoes were seldom saturated except in late winter, when keels of deep draft (13–17 m) were observed at shorter range. At drafts less than 2 m, the 5th percentile decreases, and the 95th percentile increases to the saturation level of the receiver, as draft decreases. Although the truncation of the echo at the saturation level precludes calculation of the spacing of the 5th and 95th percentiles, an increase to about 20 dB is suggested by subjective extrapolation of tendencies observed in Fig. 5. The depth at which the probability density widens migrates downward as the ice season progresses. This downward migration tracks the thickening of undeformed seasonal ice by freezing (Melling and Riedel 1996) and indicates that the echoes from level ice fluctuate more widely than those from deformed ice. Associated with the broadening of the probability density at small ice draft is an increase in the 50th percentile to the saturation level of the receiver. At the shallowest values of draft (<0.4 m) the shift in the average backscatter to higher values is sufficient to reverse the decreasing trend in the 5th percentile.

For ridge keels, the median value of the backscattering coefficient is about −30 dB. For level ice, the median increases from about −30 dB for ice of 1–2-m draft to a value greater than the receiver saturation level (−22 dB) for targets of draft less than 0.4 m. For a calm ice-free sea surface, observed at reduce gain in Patricia Bay (see Fig. 1), the 5th, 50th, and 95th percentiles of backscattering coefficient were −16.5, −6.8, and −0.2 dB, respectively (5th and 50th percentiles are plotted in Fig. 5). Because trends to larger backscatter are seen in the percentile curves for sea ice at draft as large as 0.4 m, it appears that the surface scattering coefficient does not change abruptly with the first appearance of sea ice at the surface but decreases gradually from open-water values as the ice thickens to at least 0.2 m. In the context of equivalent reflection coefficients, values for level ice increase from about 0.0018, a value 20 times lower than that for coherent returns from similar ice (Langleben 1970; Jezek et al. 1990; Garrison et al. 1991), to greater than 0.0044.

The probability density of echo amplitude is plotted in Fig. 6 for three regimes segregated by range. The approximate corresponding values of draft are indicated (±0.2 m). For the domain containing young and thin level ice (top frame), which includes open water, more than two-thirds of echoes are saturated. Unfortunately, the integration interval for echo amplitude (determined by bin size) was chosen as too large a fraction of the pulse length for these observations, so that the high incidence of saturation for young and thin ice targets had a significant effect on the occurrence frequency of amplitude values greater than 200. The useful part of the probability density (amplitude less than 200) for this ice population is broad and flat. Although the empirical probability densities are similar in shape to the lognormal curve plotted, their amplitudes are too low. The reason is inhomogeneity in the backscattering coefficient of the targets grouped into the shallow-draft category for the preparation of Figs. 5 and 6. The range in the draft of targets in this category is quite broad because the resolution is two bin lengths (0.34 m), and the uncertainty in the position of the surface introduced by tides is ±0.16 m. In addition, the backscattering coefficient increases sharply with decreasing draft below 1 m (Fig. 5). Thus, surfaces having quite different average target strength were grouped for analysis at shallow draft, and the individual lognormal distributions that presumably characterized each homogeneous target were obscured. Much better fits are possible using linear combinations of two or more lognormal functions with different means.

For level ice in the medium/thick category (Fig. 6, middle frame) the fraction of saturated echoes decreases from 32% at 0.8-m draft to only 5% at 1.8 m. The observed probability densities compare favorably with the plotted lognormal curves over much of the amplitude range. The positive departure of data from the curves at large amplitudes is a consequence of the saturation effect noted above. With decreasing draft, the observed mode of probability remains the same, but the width of the distribution increases.

For ridged ice (Fig. 6, bottom frame) the fraction of saturated echoes is very small. The observed probability densities in three different ranges of draft are well represented by lognormal functions. The observed increase in modal echo amplitude with draft is a consequence of the smaller sound transmission losses for targets of greater draft.

During the deployment of the WASP in the ice-free waters of Georgia Strait, the majority of surface echoes were saturated. However, there was a clear trend in these observations toward a lower incidence of saturated echoes from sea surface as the wave height (or equivalently wind speed) increased (Fig. 7). This result is consistent with observations at 50 kHz (Nützel and Herwig 1995). Their data at normal incidence indicate a decrease in backscatter by approximately 13 dB as wind increased from 3 to 9 m s⁻¹. Note that under calm conditions in Patricia Bay (Fig. 1), no values of scattering coefficient less than −19.5 dB were measured.

Only weak echoes from subsurface clouds of air bubbles were observed in Georgia Strait. These rarely exceeded eight counts in amplitude even at the higher wind and sea conditions encountered. Occasionally, however, strong bubble-associated echoes were received. From one such event, the backscattering cross section of the bubble cloud was calculated to be −29 dB (relative to 1 m² m⁻³) just below the surface and decreased exponentially with depth to −53 dB at 3-m depth (e-folding scale, 1 m). The echo from this cloud was comparable in strength to that from typical sea-ice targets (e.g., Fig. 3).

5. Discussion

These observations demonstrate that fluctuations in the amplitude of echoes from various ice and ice-free surfaces are not distributed according to the Rice or Gaussian forms expected if the coherent component is large (Stanton et al. 1986). The reason is undoubtedly that the precise alignment of beam and target necessary to receive a specular return is a rare occurrence with a narrowbeam sonar such as the WASP. However, the fluctuations also fail to match the Rayleigh function predicted, subject to certain simplifying assumptions, for incoherent scatter, and observed in a number of earlier studies (Stanton et al. 1986; Jezek et al. 1990; Garrison et al. 1991). This observation throws into question the general validity of the assumptions made by Stanton et al. (1986) in their derivation of the probability function of echo fluctuations. Those of questionable applicability to the present data are 1) the echo originates at the water–ice interface only; 2) the surface roughness is small [i.e., (4πσ)² ≪ λ², where σ is the root-mean-square surface roughness and λ is the acoustic wavelength]; and 3) multiple scattering is not a factor.

Stanton et al. (1986) measured a 70-dB attenuation of 420-kHz sound on passing through 0.18 m of sea ice. At a uniform rate of attenuation, a 3-dB decrease in intensity would occur over 7.7 mm of travel (two wavelengths; λ = 3.6 mm at 400 kHz). Thus, 400-kHz sound scattered after penetrating a half-wavelength into the ice could emerge to interfere destructively with sound scattered at the surface. The first assumption is therefore not robust.

An estimate of the root-mean-square scale of surface roughness on the bottom of growing sea ice is 0.3 mm, derived from sound scattering data at 188 kHz (Stanton et al. 1986). This scale is associated with the spacing of ice crystals forming the dendritic water–ice interface of a growing columnar ice zone. For this estimate of roughness, (4πσ)² ∼ 14.2 mm². Since λ² ∼ 13.0 mm² at 400 kHz, the second assumption is invalid.

The apparent universality of the lognormal distribution in these observations is a strong indication that multiple scattering is occurring. The lognormal distribution develops through the law of proportionate effect (Crow and Shimizu 1988), as follows. Following each interaction with the target, the amplitude of the scattered wave is a random fraction of that incident. If successive interactions are independent, then the logarithm of the amplitude of the echo is the sum of logarithms of these independent random fractions. By the central limit theorem, the probability density of the logarithm of amplitude converges to a Gaussian function as the number of interactions increases. In the open, chaotic structure of first-year ice ridges (see, e.g., Melling et al. 1993), the “depth” of the target is several meters and the potential for multiple scattering is quite obvious. The lognormality of the ridge echoes is very clear. The depth of open-water and level-ice targets is less obvious. However, the weakness of the first two assumptions implies that their depth is still large relative to the acoustic wavelength, and multiple scattering can occur.

The present observation of rather weak surface echoes when using narrowbeam sonar reinforces the deduction that coherent reflections were rarely detected. Representative values of the backscattering coefficient calculated from these data (Fig. 5) are −30 dB for thick (∼1.5 m) growing ice, −25 dB for medium (∼0.6 m) ice, and greater than −22 dB for thin ice (<0.3 m). Values for medium and thin ice measured by Bush et al. (1995) at 300 kHz with a 2.6° beam (−24 dB and −16 dB) compare favorably with the present values at 400 kHz. In contrast, the results of Jezek et al. (1990) and Garrison et al. (1991), who used wider sonar beams capable of picking up the coherent returns from the surface, were very much larger, approximately −17 dB for thick (1.36 m) growing ice and −9 dB for thin (0.1 m) growing ice.

Stanton et al. (1986) use a parameter, γ, defined as

View Expanded

In the far field of the source, γ is related to the characteristics of the sonar and of the reflecting surface by the equation γ = 2π/(k⁴χ²σ²I_c), where k is the acoustic wavenumber, χ is the full beamwidth between the −8.7 dB points for two-way transmission, and σ²I_c is the three-dimensional measure of the roughness of the surface. This equation was derived subject to assumptions that k²χ²l² ≪ 8, where l is the correlation distance across the rough target and that 4k²σ² ≪ 1. Using σ ∼ 0.0003 m and l ∼ 0.01 m from Stanton et al. (1986), the first assumption is easily satisfied in this study, but the second is of marginal validity. With their estimate of σ²I_c (70 × 10⁻¹² m⁴) for growing sea ice and our sonar parameters, we calculate γ ∼ 10, so that the coherent return should be about 10 dB stronger than the scattered return. This is approximately the magnitude of the discrepancy between narrowbeam and wide-beam results noted above.

For the sonar characteristics and environmental conditions of the present study (wind speed < 10 m s⁻¹, SWH < 0.8 m), echoes from subsurface clouds of air bubbles generated by breaking waves would not contribute to a serious incidence of bubble targets misidentified as ice. However, the backscattering cross section of bubble clouds increases very dramatically with wind speed; Dahl and Jessup (1995) suggest an approximate seventh-power dependence, corresponding to a 22-dB increase with a doubling of wind speed. There is a corresponding decrease in the scatter from the sea surface (Fig. 7) to the point that the surface echo may ultimately be weaker than that from subsurface clouds of bubbles (Nützel and Herwig 1995). Where a threshold detector is used for target identification, an increase in wind speed will therefore cause increases in the occurrence and apparent draft of “ice” in open areas between floes.

The intensity of backscatter from bubble clouds is proportional to the product of the bubble backscattering cross section and the number density of bubbles integrated over all sizes. For an individual bubble, there is general increase in cross section as radius squared, but the cross section is dominated by a resonance peak at a radius dependent on acoustic frequency. The resonance frequency, inversely proportional to bubble size, is about 200 kHz for a bubble of 20-μm radius at shallow depth (Clay and Medwin 1977). Measurements of the number-density spectrum of bubbles (Trevorrow 1996) have been used to calculate the scattering cross section of bubble clouds as a function of frequency (Fig. 8). Near the surface, the cross section is largest for a frequency of 120 kHz. It decreases by 8 dB to 400 kHz, and above 500 kHz, where the off-resonance contribution to scattering dominates the return, it is approximately constant.

6. Implications for ice profiling

The very narrow beam of ice-profiling sonar precludes reliable reception of the relatively strong specular reflection from sea ice. The sonar must therefore operate using the incoherent return, which is weak because sea ice is relatively smooth on the scale of the acoustic wavelength. Although ice scatters sound more effectively at higher frequency, because it appears rougher to the sonar, any increase in scattered signal would likely be neutralized by the corresponding increase in sound attenuation with frequency (at 800-kHz attenuation is 26 dB per 100 m higher than at 400 kHz; Francois and Garrison 1982). Ice-profiling sonar must operate to a range of at least 40 m to minimize risk from moving ice (and to much greater range in iceberg-prone seas). Therefore, 400 kHz may be close to the practical upper bound to operating frequency for this instrument.

Can echoes detected by ice-profiling sonar be exploited to discriminate between thin level ice and open water? It is clear that the median scattering coefficient of level ice increases as draft decreases (Fig. 5). However, the data suggest that the transition to values representative of open water is gradual, not abrupt. Because the change is gradual and the average backscatter from the sea surface varies widely with sea state, any target classification algorithm based on echo strength is unlikely to provide unambiguous decisions.

A more severe impediment to the classification of targets using echo amplitude is the wide range of amplitude fluctuations. For level ice, the difference between the 95th and 5th percentiles of scattering coefficient approaches 20 dB. This range is comparable to the difference in the median scattering coefficient between calm open water and thick ice in these observations. Thus, a single amplitude measurement has little value for target identification. If, however, the uncertainty in scattering coefficient could be reduced to less than 3 dB, some useful skill in target identification might result. An average of approximately 45 independent determinations of the scattering coefficient would have a sampling uncertainty of about this magnitude.

The interval between independent values can be determined from the autocorrelation function. Examples calculated from the amplitude time series of echoes from uniform targets are plotted in Fig. 9. The inverse relationship between decorrelation time and the speed of ice drift evident in this figure indicates that the decorrelation of echoes is related to the overlap of target areas on the ice. From the data at the two higher speeds, the dimension of the target area for the WASP is estimated to be 1.0 ± 0.2 m, comparable to the −3 dB width of the beam (two way) at 52-m range. In the zero-speed case of Fig. 9, the finite decorrelation time (∼3600 s) may well be a consequence of ice growth. At a typical growth rate of 1.5 cm day⁻¹, the freezing interface advances by twice the estimated scale of surface roughness (σ ∼ 0.0003 m) during this time.

For an ice-profiling sonar of 2° beam at 50-m depth, 45 independent determinations of the scattering coefficient could be acquired with an ice displacement of about 45 m, provided that a sufficiently short pulse interval is used (1 s if drift speed is 1 m s⁻¹). Thus, some capability to identify the type of target from average scattering coefficient could be achieved at a spatial resolution of 45 m. At lower rates of sampling or faster drift, the spatial resolution would be correspondingly degraded. Unfortunately, level areas in pack ice are typically of small horizontal extent. Figure 10, based on observations discussed by Melling and Riedel (1996), shows that even in first-year pack, where level ice is relatively common, almost three-quarters of the level sections (that have to exceed 10 m to be so classified) are shorter than 45 m in length. Thus, averaging the scattering coefficient would provide little assistance in the identification of most potential open-water targets. Moreover, since the averaging must be carried out in a spatial reference frame, it would be difficult to implement in “real time” within the surface-detection algorithm of the ice-profiling sonar. A solution to this dilemma might lie in the development of a multibeam sonar to obtain additional independent scattering data for the target at off-zenith angles.

From the viewpoint of target identification, the receiver gain used for these arctic observations was too high. Echoes from level targets of small draft were often saturated, while the 5th percentile value was typically more than 25 dB above the minimum detectable signal. Had the gain been lower by 20 dB, the median amplitude typical of ice targets would have been 12, and the majority of echoes would have fallen within the 8-bit dynamic range of the receiver (the observed separation of the 5th percentile for level ice and the 95th percentile for calm water was 40 dB).

However, a reduction in gain would have a detrimental effect on the accuracy of the range measurement, which is derived by timing the sharp rise at the leading edge of the echo (Melling et al. 1995). Since the maximum amplitude of half of all ice echoes would fall below 12, the leading edge of the pulse would be poorly defined at the coarse resolution available, and the selection of a suitable detection threshold would be problematic. These factors imply that if echo amplitude is to be used for target identification in conjunction with ice profiling, the resolution of an 8-bit analog–digital converter is probably inadequate. Ten or more bits, for at least the 60-dB dynamic range, are recommended.

If target identification using echo amplitude is not of interest, then 8-bit analog–digital conversion presents no difficulties, provided that the gain is adequate to boost the majority of echoes at least to the midrange of the analog–digital converter. Assuming that a loss of the weakest 5% of returns from level ice is acceptable, then a gain increase of about 20 dB beyond that used by the WASP is needed. This is the operating premise that has been used (but not without target ambiguity) by ice-profiling sonar for many years (Melling et al. 1995).

The widely varying amplitude of ice echoes has significance for the maximum sidelobe sensitivity tolerable in an ice-profiling sonar. Suppose that the scattering coefficient of a portion of a ridge keel viewed by the sonar through a sidelobe is −25 dB, whereas that of level ice viewed through the main lobe at greater range is −40 dB (cf. Fig. 5). Then a sidelobe attenuation of perhaps 25 dB (two way) is desirable if the range to the ice at the zenith is to be determined correctly. If the echo received via the main lobe is clipped (as is likely at the high gain preferred in this application), or if the area contributing backscatter to the sidelobe exceeds that in the main lobe (as is likely with a narrowbeam sonar), then much greater sidelobe suppression is desirable.

Errors associated with the identification of subsurface bubble clouds under open leads as ice can be reduced through the judicious choice of sonar operating parameters. First, since the backscatter from bubble clouds decreases sharply between 150 and 500 kHz (Fig. 8), an operating frequency near the high end of this range is preferred. Second, the echo from a bubble cloud is proportional to the volume that contributes to the echo at any one time. This in turn is proportional to the product of the solid angle of the sonar beam and the length of the sound pulse. The minimum practical beamwidth is the best for ice profiling, as already discussed. Since this also minimizes sensitivity to clouds of bubbles, there is no conflicting requirement here. Shortening the pulse will reduce the strength of bubble-cloud echoes and have little effect on the efficacy of ice profiling since the intended targets are scattering surfaces not volumes. However, a practical lower limit to pulse length is imposed by system bandwidth, which in turn is determined largely by the required signal-to-noise level in the receiver.

Were the gain of the sonar to be increased, as is desirable for reliable ice detection (see above), bubble clouds would cause more frequent errors in ice identification than encountered here. Some dramatic examples are shown by Melling et al. (1995).

7. Conclusions

The distinguishing characteristic of ice-profiling sonar used to measure the draft and underside topography of pack ice is a very narrow (⩽3°) acoustic beam. This narrow beam has a strong effect on the properties of echoes received from the surface.

The echoes received by narrowbeam sonar from a variety of surface targets in ice-covered seas are incoherent. Although sea ice is sufficiently smooth that the coherent reflection is much stronger than the scattered return, the reflection is rarely received through the narrow beam for reasons of geometric misalignment.

The amplitude of incoherent returns fluctuates over a wide range. For all surface targets, the fluctuations have a lognormal probability distribution, indicative of multiple scatter at the target. The separation of the 5th and 95th percentiles of the amplitude distribution for level-ice and open-water targets is equivalent to a difference of 20 dB in the scattering coefficient. For ridge keels, the spread between the reference percentiles is less, about 10 dB.

Median values of the backscattering coefficient at the 400-kHz range from −6.8 dB for calm water to −30 dB for thick level ice and ridge keels. These values, which are much lower than published data for coherent reflections, indicate that these surfaces appear very smooth to sonar at this frequency. The backscattering coefficient of the water–air interface decreases with increasing sea state.

Incoherent echoes from sea ice remain correlated, while target areas overlap. The decorrelation distance is related to the beamwidth (∼1 m for a sonar of 2° beam at 50-m depth). Thus, the decorrelation time is strongly dependent on drift speed.

The change in average scattering coefficient when ice forms at the surface is not abrupt. This fact, coupled with the strong stochastic fluctuations in scattering coefficient, hinders the use of echo amplitude in target identification. Although some skill may accrue if echoes are averaged, the necessary averaging distance exceeds the length of a large proportion of the uniform targets in pack ice.

Ice-profiling sonars recording amplitude require a minimum dynamic range of 60 dB to provide adequate resolution at low amplitudes and to accommodate the very wide range in scattering coefficient (>40 dB) likely to be encountered. For range detection only, a smaller dynamic range suffices, but higher gain is required to boost all but the lowest echoes to the detection threshold.

Increasing the acoustic frequency of ice-profiling sonar much beyond 400 kHz is unlikely to improve performance. Although a frequency increase would provide an increase in the scattering coefficient of targets and reduce sensitivity to bubble clouds, gains here would be neutralized by the increase in round-trip attenuation over the necessary operating range of 40 m or more.

In the absence of ice, echoes from subsurface bubble clouds, generated by breaking waves in windy conditions, are a source of error in ice-draft measurement. The incidence of such errors can be reduced by maximizing the operating frequency and minimizing the beamwidth and pulse length, subject to other constraints, but it cannot be completely eliminated because of the very strong dependence of bubble scattering on wind speed.

Finally, since the amplitude of echoes cannot provide reliable guidance in the discrimination of thin ice from open water, this topic remains an important practical concern in time-varying calibration of the ice-profiling sonar for zero draft and in its use in climate-related studies of sea ice.