Introduction

An upsurge of interest two to three decades ago in the distribution, dissolution and physical characteristics of icebergs was prompted primarily by a perceived possibility that Antarctic icebergs might be utilized as a freshwater source suitable to quench the thirst of large cities. Following a series of conferences (Reference HusseinyHusseiny, 1978; Reference RussellRussell, 1979; Annals of Glaciology, vol. 1, 1980), the rise and fall of a small informal but informative journal (Iceberg Research, 1982–91, published by the Scott Polar Research Institute, Cambridge, UK) and several landmark publications (e.g. Reference Weeks and CampbellWeeks and Campbell, 1973; Reference SchwerdtfegerSchwerdtfeger, 1979; Reference Robe and ColbeckRobe, 1980), the consensus was that icebergs might, for a cost comparable with desalination, be diverted as they drifted in the known ocean currents, to a Southern Hemisphere location where they might be utilized. There, the utilization of the icebergs poses problems perhaps greater than the initial harvesting (Reference Lawson and Russell-HeadLawson and Russell-Head, 1983).

In recent years several large icebergs have broken away from the Antarctic continent (e.g. Reference Lazzara, Jezek, Scambos, MacAyeal and van der VeenLazzara and others, 1999). We have seen the partial collapse of the Larsen Ice Shelf (Reference Rott, Skvarca and NaglerRott and others, 1996, Reference Rott, Rack, Nagler and Skvarca1998, Reference Rott, Rack and Skvarca2002), realized that as much as 20–30% of the ice discharge from the Antarctic continent may be in the form of basal meltwater (Reference Jacobs, Hellmer and JenkinsJacobs and others, 1996) and found new evidence of ice-sheet thinning in the Pine Island and Thwaites Glacier drainage basins (Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998; Reference RignotRignot, 2001; Reference ZwallyZwally and others, 2002). Thus, there are now further reasons to examine iceberg distribution and dissolution rates: (1) as an indicator of melt or freeze rates at the underside of the polar ice shelves given a warmer atmosphere and ocean than exists at present, i.e. iceberg studies can be treated as calibration experiments of how ice shelves may react to further climate change, (2) to better understand abrupt climate-change mechanisms (Heinrich events) (Reference HemmingHemming, 2004) in which iceberg calving and associated freshwater flux are essential elements, (3) for comparison with Antarctic mass budget so that estimates might be made of the ratio of iceberg discharge to melt from the continent (e.g. Reference OrheimOrheim, 1985) and (4) as a tool for a better understanding of the freshwater input and physical oceanography of the Southern Ocean (the movement of icebergs is an indicator of ocean currents). One inexpensive method of estimating the iceberg dissolution rate is by statistical analysis of large datasets collected over many years from Antarctic research and station resupply vessels.

Using the Australian Antarctic Program (AAP) iceberg dataset, Hamley and Reference BuddBudd (1986) extended the work of Reference Budd, Jacka and MorganBudd and others (1980). They examined the concentration and size distribution of icebergs in the Australian sector of the Southern Ocean to infer iceberg median life and dissolution rates. Hamley and Budd found a median life for icebergs >1000 m wide, before major breakage, to be about 0.2 years. This estimate, they suggested, applies to icebergs within the Circumpolar Current and may not be applicable to coastal icebergs in cold slow-moving water. They estimated a dissolution rate for a mean water temperature of +1°C, of 0.12 md^–1. Reference Budd, Jacka and MorganBudd and others (1980) had 1 year (1977/78) of rigorously collected data at their disposal. Reference Hamley and BuddHamley and Budd (1986) had 6 years (1978/79–1983/84) of data available. We now have a further 16 years (1984/85–1999/2000) of data. In this paper, we build on the previous work. The paper is modelled on the Hamley and Budd approach (using similar data plots, although we now consider the data in terms of volume as well as concentration), and uses the additional 16 years of data to refine the descriptions of the size distribution, and to re-evaluate the rate of dissolution of icebergs in the Southern Ocean.

Iceberg Data Collection

The AAP has routinely collected iceberg distribution and size data since its first expeditions south in 1948. Observations were often qualitative, however, and in 1977 a more rigorous quantitative data collection routine was initiated. Data collected included (1) iceberg number concentration within a 28 km (15.1 mi (int., naut.)) radius (using ship’s radar), (2) maximum visible horizontal dimension at the waterline, referred to as ‘width’, classed into one of five categories (when possible using sextant and radar), (3) for tabular icebergs, height above the waterline (using sextant and radar), (4) photographs to determine shape, (5) sea-ice concentration, (6) ocean temperature and (7) ship’s latitude and longitude. The five width categories were 10–50, 50–200, 200–500, 500–1000 and >1000 m. Reference Budd, Jacka and MorganBudd and others (1980) carried out the most comprehensive (to that date) examination of iceberg concentration and size distributions, using the 1977/78 data.

The AAP was not alone in routinely collecting ship-based iceberg observations (e.g. Reference OrheimOrheim, 1980). In 1982/83, guidelines established by the Scientific Committee on Antarctic Research (SCAR) Working Group on Glaciology for collecting and archiving these data were adopted. The SCAR iceberg project is coordinated by Norsk Polarinstitutt (Reference OrheimOrheim, 1985; personal communication from O. Orheim, 2003). As of 2003 it had accumulated data on more than 234 000 icebergs, of which 80% have been classified by size. The data are being prepared for presentation on the World Wide Web (at http://www.npolar.no). More recently, the US National Ice Center (NIC) has made available (at http://www.natice.noaa.gov) a collection of observations, commencing in 1979, of icebergs >10 mi (int., naut.) (18.53 km) long (also see Reference Long, Ballantyne and BertoiaLong and others, 2002).

Since 1982/83 all Australian data have been made available to the Norsk Polarinstitutt collection. This involved a change in the observation radius to 12 mi (int., naut.) (22.2 km). Starting with the 1984/85 austral summer season, the observation radius for the Australian data was further reduced to 6mi (int., naut.) (11.1 km). It was apparent (Reference WadhamsWadhams, 1988; Reference Allison and MusilAllison and Musil, 1989; Musil, 1999) that small icebergs are difficult to measure with any accuracy at long range, the number may have previously been underestimated, and size estimates for icebergs less than 50 m were particularly unreliable. The height of the bridge of the ships used is such that distance to the horizon is a reasonable estimate of 6 mi (int., naut.) (11.1 km). The width categories were also changed (and the number increased) to 25–100, 100–200, 200–400, 400–800, 800–1600, 1600–3200 and >3200 m. Reference Hamley and BuddHamley and Budd (1986) suggested that size groupings that exactly doubled in size with each step would help refine the estimates of iceberg dissolution rates. In hindsight, this change was probably not wise since it rendered the Australian data incompatible for direct comparison with the rest of the data in the Norsk Polarinstitutt collection. Interpolation from one scheme to another, however, is not difficult.

The area covered by the Australian iceberg dataset extends from 50 to 150° E and from the Antarctic coast to as far north as the most northerly sightings. The frequency of observations at any one location within the area is extremely variable and is determined by the logistical priorities each operational season. Figure 1 is a map of the area, showing the distribution of observations for the period 1984/85–1999/2000. A clear feature of the map is the concentration of observations along the broad shipping lane between the three Australian stations, Mawson, Davis and Casey, and from Casey to the northeast, the direction of Hobart. Note the absence of observations in one small coastal area (~112–130° E) where, for operational reasons or because sea ice has prevented it, ships have not visited. There is a concentration of observations in the region north of Mertz Glacier (140–150° E), the location of some major sea-ice and oceanographic research projects. Other than this, the number of observations west of 60° E and east of 130° E is too small for us to draw strong conclusions and we therefore usually restrict the discussion to the area between 60 and 130° E. Within this area, the concentration of observations is sufficient everywhere south of ~60°S to draw some meaningful conclusions.

Fig. 1. Map showing distribution of the total number of iceberg observations from AAP voyages, for the period 1984/85–1999/2000. Locations marked from west to east along the Antarctic coast are E – Enderby Land, Ma – Mawson, A – Amery Ice Shelf, D – Davis, Mi – Mirny, H – Helen Glacier, S – Shackleton Ice Shelf, V – Vanderford Glacier, C – Casey, T – Totten Glacier, Me – Mertz Glacier and N – Ninnis Glacier.

This dataset, consisting of all iceberg data collected on AAP voyages between, and including, the austral summer seasons 1978/79 and 2000/01, is one of the most complete and long-term collections of such data. It is available on the World Wide Web at the Antarctic Climate and Ecosystems CRC site (http://staff.acecrc.org.au/~jacka/ climate).

Data Editing and Quality

We have carried out a detailed scrutiny of the entire Australian iceberg dataset, and it is the corrected dataset that appears on the above website. The records have been logged by a large number of observers on many ships. The observers exhibit varying degrees of training and attention to detail. Errors can be made for many reasons, ranging from simple typographical errors to faulty equipment giving erroneous values.

Checking of data can often be done line by line. Sometimes however, whole sections of data need to be examined to spot ‘the odd one out’. We cannot claim the dataset is now perfect, but we have removed the worst errors and inconsistencies. The accuracy of the observations is spatially and temporally variable, and impossible to determine. Since we are often dealing with relatively low numbers of observations at any particular location, the data are usually co-added over a substantial range of latitude and longitude so any remaining positional errors will be of little significance. We now have a total of 7186 observations of 60 749 icebergs, covering a period of ~20 years, and we can have greater confidence in these results than we did 20 years ago (cf. Reference Hamley and BuddHamley and Budd, 1986). The following data quality categories were checked:

Spatial Distribution

Figure 2 is a map of iceberg concentration (the number of icebergs sighted within 6 mi (int., naut.) (11.1 km) of the ship, divided by the number of observations) for the area covered by the data, over the 16 year period of the study (1984/85–1999/2000). It is evident that higher concentrations of icebergs are found adjacent to coastal locations of high glacial discharge (e.g. the Amery Ice Shelf (70–80° E), Helen Glacier and Shackleton Ice Shelf (90–95° E), Vanderford Glacier (105–110° E) and Ninnis and Mertz Glaciers (140–150° E)). There are also some areas where iceberg concentrations close to the coast are high because they are grounded in areas where the east wind drift forces them into relatively shallow water (e.g. off Enderby Land (50–60° E) and off the Mawson coast (60–70° E)).

Fig. 2. Map showing contours of iceberg concentration (total number of icebergs sighted within 6mi (int., naut.) (11.1 km) radius of the ship, divided by the number of observations) for the period 1984/85–1999/2000. The more northern dashed curve is the northern extent of the mean maximum sea-ice extent (after Reference JackaJacka, 1983). The southern dashed curve is transcribed from Figure 3.

In the deeper water away from the coast, the pattern of iceberg distribution is more interesting and more important for interpretation in terms of dissolution rates. First, note the more northerly dashed curve in Figure 2 indicates the mean (over 10 years) northern edge of the sea ice at maximum extent (Reference JackaJacka, 1983). Maximum sea-ice extent occurs in September to mid-October. This curve closely envelops the northern extent of the higher iceberg concentrations, observed primarily during the austral summer. Higher temperatures and the distribution of ocean currents would seem to be the major controls on the northern extent of both sea ice and icebergs.

The pattern of iceberg distribution suggests that icebergs generated by the Amery Ice Shelf initially drift slightly northeast (compare a transect in Figure 2 along longitude 70° S with another along 80° S). Icebergs generated by the Shackleton Ice Shelf seem to drift due north from the Mirny coast, and icebergs generated by Vanderford Glacier drift northwest. There are low concentrations of icebergs north of Vanderford Glacier;note, however, that the apparently low-concentration area near the coast at ~115–120° E is because there are very few data here. The result of these drift directions from the coast is that there are high iceberg concentrations north of 64° S at longitude 85–95° E. In this area, the icebergs are caught in the west-to-east flowing Circumpolar Current. Thus there are elevated concentrations evident as far north as the maximum sea-ice extent limit, and to the east as far as 140° E.

Earlier work by Reference Tchernia and JeanninTchernia and Jeannin (1984) using satellite tracking techniques and Reference Crepon, Houssais and Saint GuilyCrepon and others (1988) who examined the effect of wind on iceberg drift, along with more recent work using satellite-borne microwave backscatter experiments (Reference YoungYoung, 1998) indicates that the motion of the larger icebergs is determined by the ocean currents. In turn, the ocean currents are influenced by the bathymetry. Figure 3 shows ocean bathymetry (after Reference Row and HastingsRow and Hastings, 1995; Reference Row, Hastings and DunbarRow and others, 1995) in the iceberg observation area. Reference Bindoff, Rosenberg and WarnerBindoff and others (2000) examined water circulation in the area. They noted the latitude, at each of eight north–south transects, at which the ‘westward flow became eastward’. The dashed curve in Figure 3, through the latitudes listed by Reference Bindoff, Rosenberg and WarnerBindoff and others, closely follows the near-shore bathymetry (at ~Ί1000 m depth). In Figure 2 we see that the same curve approximately envelops the southern boundary of the band of higher iceberg concentration between 90 and 150° E. We will see in the next section that the iceberg concentration distribution at these longitudes has two maxima, corresponding with the two currents (the nearcoast, west-flowing east wind drift, and the east-flowing Circumpolar Current).

Fig. 3. Map showing contours of ocean depth (after Reference Row and HastingsRow and Hastings, 1995; Reference Row, Hastings and DunbarRow and others, 1995), along with a schematic diagram of the ocean surface circulation (after Reference Bindoff, Rosenberg and WarnerBindoff and others, 2000). The dashed curve, the slope current (Reference Bindoff, Rosenberg and WarnerBindoff and others, 2000), is effectively the boundary between the west-flowing east wind drift and the east-flowing Circumpolar Current.

Size Distribution

Figure 4a and b show iceberg concentration and iceberg volume, respectively, within 6mi (int., naut.) (11.1 km) radius (total and within different size categories up to >200 m), for the period 1984/85–1999/2000, as a function of latitude for each 10° longitudinal section, 60–70°, 70–80°,. . ., 140–150° E (see later for details of volume calculations). Figure 4a (plotted in reverse order on the longitude axis) can be compared with Hamley and Budd’s (1986) figures 1 and 2, noting that Hamley and Budd’s concentrations were observed over a 12mi (int., naut.) (22.2 km) radius. The general trend of the data is similar to that reported by Hamley and Budd. The ‘total’ plots of Figure 4a and b reflect the picture outlined above.

Fig. 4. Iceberg concentration (a) and total iceberg volume (b) within the observation radius of 6mi (int., naut.) (11.1 km) for the period 1984/85–1999/2000, as a function of latitude for each 108 longitudinal section, 60–70, 70–80, . . . , 140–1508 E. Data are accumulated in 18 latitudinal increments, and are plotted for the total number of icebergs, and for each size category.

Near the coast (i.e. between the dashed curve of Figure 3 and the coast), icebergs tend to move towards the west in the east wind drift. At ~80–90° E, they drift northwards, influenced by the bathymetry in and northeast of Prydz Bay (northeast of the Amery Ice Shelf) as shown in Figure 3 (solid curves, after Reference Bindoff, Rosenberg and WarnerBindoff and others (2000)), until they are caught, and carried towards the east, in the more northerly west-to-east flowing Circumpolar Current. While local eddies may also cause some south-to-north transfer of icebergs across the boundary between the two dominant currents, the north-to-south transfer is likely to be about the same. There is, therefore, an area of lower iceberg concentration between the two major currents. Thus, in Figure 4a and b, at longitudes east of 90° E the curves exhibit two maxima in iceberg concentration and volume at the latitudes of the two currents, and, as noted in the previous section, the latitude of the enclosed minimum agrees well with the current direction change at locations listed by Reference Bindoff, Rosenberg and WarnerBindoff and others (2000). The total number of icebergs reduces (due to dissolution – melting, breakage, etc.) east of 90° E until 120–130° E where the concentration and total ice volume is relatively very low. Finally (from Fig. 4), following the Circumpolar Current, there are peaks in iceberg concentration and volume at 130–140 and 140–150° E due to iceberg production by Ninnis and Mertz Glaciers.

Figure 5a is a plot of iceberg concentration (means across all latitudes) as a function of longitude. The pattern of increasing concentration from the west to 90–100° E in all size classes, and then the decrease in concentration as the icebergs are caught in the Circumpolar Current flowing east from 90–100° E, is evident. Figure 5b, a similar plot but of iceberg volume, reveals that, primarily due to the presence of a few large (>800 m) icebergs in the west of the study area, the total volume decreases from west to east throughout the study region, but with a dip in the 80–90° E sector. In addition, comparison of Figure 5a and b shows that, although the numbers of smaller icebergs are greater, an extremely small percentage of the volume is included in the 25–100 m size category. The bulk of the ice is accounted for within the relatively few icebergs in size categories >400 m. Note for the plots of Figure 4 we found it most convenient to include size categories for the concentration data that included the smaller icebergs, then a ‘>200 m’ category, yet in Figure 4b, only the larger icebergs were included with a ‘<400m’ category.

Fig. 5. Iceberg concentration (a) and volume (b) as a function of longitude, plotted for each size category and for the total number of icebergs.

At 80–90° E, where the iceberg drift direction is primarily towards the north as they transfer from one current to the other, there is a relatively high concentration of icebergs across the full latitude band from the coast to the northern extent. West of 80° E and to the north, iceberg concentrations and volumes are relatively low, since, predominantly, they are drifting to the east. Near the coast the concentration is higher, due to production and grounding along the Mawson coast. Examination of the different size categories west of 80° E (Fig. 4a) reveals curves of similar shape and magnitude within each longitudinal section, i.e. at each longitude the contribution to the total concentration is approximately equal for each of the three size categories 25–100, 100–200 and (less clearly) >200 m. At 80–90° E, there is a decrease in iceberg concentration with increasing size category. From 60 to 62° S there is a greater contribution to the total concentration from the 25–100 m icebergs. Apart from this and a peak in concentration of >200 m icebergs near the coast, the shape of the distribution is similar for each size category. East of 90° E, while there is a decrease in iceberg concentration with increasing size category, most of the variability in the total concentration is due to variability in the 25–100 m category. As described above, this variability characterizes the two major currents in which these icebergs are transported.

In terms of iceberg total volume (Fig. 4b), there is a clear trend at every longitude for decreasing volume with decreasing latitude. Furthermore, while concentrations of the smaller size categories dominate, the trend in volume is controlled by the few large icebergs, especially in the western sectors of the study area where there are some large icebergs near the coast.

Temporal Change

With 16 years of data at our disposal we can examine whether there have been any significant changes with time, in the concentration, volume and distribution of icebergs. Figure 6a and b show the concentration and volume, respectively, of icebergs within 11.1 km (total across all size categories) in each of the 10° longitudinal sectors, averaged over the two 5 year and one 6 year periods, 1984/85 austral summer to 1988/89, 1989/90–1993/94 and 1994/95–1999/ 2000. We have also included the iceberg concentrations and volumes for the period 1978/79–1983/84, i.e. the data examined by Hamley and Budd (1986). Both iceberg concentration and volume in the study area for 1984/85–1988/89 are higher (on average by a factor >2) than in the following two periods. They are also higher than in the earlier 6 year period, but by a lesser amount. A study at the University of Sheffield, UK (personal communication from T. Silva, 2005) which examines the same iceberg dataset on an annual basis has also found a reduction in both the concentration and total volume of icebergs during the 1980s with lower values during the 1990s. Volumes and concentrations were similar, however, in the 120–130° E sector and west of 80° E. That is, the greater volume and concentration during the 1984/85–1988/89 period occurred between 80 and 120° E, the same area as that fed by the gyre operating northeast of Prydz Bay. For the two later periods, they are similar in all longitudinal sectors.

Fig. 6. Iceberg concentration (a) and volume (b) for each of the time periods, 1978/79–1983/84 (the data considered by Reference Hamley and BuddHamley and Budd, 1986), 1984/85–1988/89, 1989/90–1993/94 and 1994/95–1999/2000, as a function of latitude for each 108 longitudinal section, 60–70, 70–80, . . . , 140–150° E. The ‘off-the-scale-value’ in (a) for the 1984/85–1988/89 period at 130–1408 E, is due to a single set of observations of in excess of 300 icebergs in the two smallest size categories.

Data from the SCAR Antarctic iceberg database at Norsk Polarinstitutt (personal communication from O. Orheim, 2003) covering observations around the entire Antarctic continent (more detailed in the Indian and Atlantic Ocean sectors than the Pacific sector) do not indicate significantly higher concentrations of icebergs in the 1984–88 period. This eliminates large continent-wide iceberg production as a cause of the higher concentrations in our study area. Maps of iceberg concentration and iceberg volume within 11.1 km radius for each of the four periods (Fig. 7a and b) show relatively low numbers in coastal areas during the two later periods. During the 1978/79–1983/84 and, especially, the 1984/85–1988/89 periods, however, higher coastal concentrations and volumes are evident, neighbouring the locations of ice shelves and outflow glaciers. Thus, the higher numbers seem to be the result of elevated local iceberg production. These observations demonstrate the episodic nature of iceberg release into the Southern Ocean, due to the episodic nature of the calving of large icebergs, especially from the large ice shelves (e.g. Reference Fricker, Young, Allison and ColemanFricker and others, 2002).

Fig. 7. Maps of iceberg concentration (a) and volume (b) for each of the four periods, (i) 1978/79–1983/84 (data adjusted, since the observation radius was 12 mi (int., naut.) (22.2 km)), (ii) 1984/85–1988/89, (iii) 1989/90–1993/94 and (iv) 1994/95–1999/2000.

Dissolution Rates

Dissolution process

Figure 8 shows the size frequency distribution of icebergs bounded by our northern and southern limit, in 10° longitude steps (cf. Reference Hamley and BuddHamley and Budd, 1986, fig. 6). The similarity of the curves at each of the different longitudes indicates the dissolution process is similar at all longitudes. The shape of the curves, indicating an approximate doubling of frequency with a halving of iceberg size, indicates the dominant dissolution process is breakage (rather than melt) with melting of the smallest category only accounting for final dissolution. There are fewer data for icebergs in the 120–130° E sector, leading to a less smooth curve.

Fig. 8. The size frequency (concentration as per cent of total concentration within each size category) distribution, of icebergs bound by the northern and southern limits described in Figure 2, in 10° longitudinal sectors as indicated.

Iceberg area and volume calculations

For calculations of iceberg area, A, i.e. the area of the top (or bottom) surface, we assume the observed linear dimension, d, is (on average) the diagonal of a rectangular iceberg with length to breadth ratio, r, so that

where

From a photographic survey of 525 icebergs, Reference DmitrashDmitrash (1971) concluded r was in the range 1.5–1.6. From satellite observations, Reference Young, Turner, Hyland and WilliamsYoung and others (1998) found mean r values for over 1000 icebergs near the coast within our study area to be in the range 1.3–1.5, over all size classes. The large icebergs calving from ice shelves are observed generally, however, to have r values closer to 3. Using Hamley and Budd (1986) as a guide, we have assumed r = 1.5 (R = 0.46) for icebergs <400m in observed linear dimension, r = 2 (R = 0.40) for icebergs 400–800m and r = 3 (R = 0.30) for icebergs >800 m.

The iceberg volume, V, is

where h is the iceberg height above the waterline (freeboard height) and s is the ratio of height to total thickness.

For examination of factors controlling dissolution rate, it is also informative to investigate the total iceberg surface area below the ocean surface, A _w, i.e. the area of iceberg in contact with the water,

where

i.e.

Iceberg thickness

Most of the large icebergs (>400 m) have calved from ice shelves, and the major Antarctic ice shelves have a freeboard height of ~30–40m at the front. The Amery Ice Shelf, the probable primary source of the largest icebergs within our study area, is ~40m high at the front. Analysis of 215 observations, from the current dataset, of iceberg height to length ratio gives a mean ratio of 0.092, with standard deviation 0.046; i.e. for a 400m iceberg, a height of 37 m. A height to thickness ratio, s, of 1 : 7 is expected (Reference Shabtaie and BentleyShabtaie and Bentley, 1982), and we assign these icebergs an average thickness of 250 m. Note that Hamley and Budd (1986) indicate tabular icebergs >60m high (with a smooth curve in their figure 9, at ~60m height). While we concede many of the observed data indicate heights in excess of 60m for large tabular icebergs, we believe these are due to overenthusiastic observers.

Fig. 9. Iceberg concentration (a) and volume (b) plotted as a function of width, within each 108 longitudinal section of our dissolution study area.

The irregularly shaped (non-tabular) icebergs (which, for area and volume calculations, we continue to assume to be rectangular) and tabular icebergs that have calved from the fast-flowing coastal outflow glaciers (e.g. Ninnis, Mertz, Totten and Vanderford Glaciers) are often observed to be ≥50 m high and occasionally up to 60m high. We assign a height of 50m (and an average thickness of 300 m; i.e. s is 1 : 6) to the size categories 100–200 and 200–400 m. Icebergs with linear dimension <100m are in the range 10–30m high. They also repeatedly roll, so little snow cover is present and they are near-solid ice with negligible snow. An average thickness of 90m is assigned to these smaller icebergs, i.e. s = 1: 9.

Concentration change

Figure 9a (cf. Reference Hamley and BuddHamley and Budd, 1986, fig. 8) shows plots of iceberg concentration as a function of width for the longitudinal sections we wish to examine east of 90–1008 E. The figure indicates similar features to those of Figure 8. The data of Figure 9a are also shown in Table 1, with calculations aimed at estimating dissolution rate. Table 1 is divided into four sections, (a) 90–100° E, (b) 100–110° E, (c) 110–120° E and (d) 120–130° E, and three dissolution rates (averages across all size categories) are calculated between these sections.

Table 1. Details of area and volume calculations, in 10° longitudinal sectors and different size categories, for icebergs moving towards the east in the Antarctic Circumpolar Current. Concentration, surface area, water contact area and volume are average quantities within the observation circle, of radius 6 mi (int., naut.) (11.1 km)

Current speeds, residence times and dissolution rates

To calculate dissolution rates, we require drift rates and, from these, mean residence times of icebergs in each of the 10° longitudinal sectors of the study area. The earliest measurements in this regard are from the First GARP Global Experiment (FGGE) (Reference HofmannHofmann, 1985) which included only a very few drifting buoys south of 60° S. The iceberg-tracking project of Reference Tchernia and JeanninTchernia and Jeannin (1984), which included several icebergs tracked by the AAP within the study area, provides some additional data. Reference BuddBudd (1986) summarized the data available at that time, giving a mean west to east drift component at 55–60° S, between 90 and 120° E, of 0.11 ms^–1 (9.50kmd^–1) and between 120 and 150° E of 0.21 ms^–1 (18.14 km d^–1).

From buoys placed within the sea-ice zone such that they freeze into the sea ice, Reference Heil and AllisonHeil and Allison (1999) examined mean daily sea-ice drift velocities. Most of their study is in the east wind drift, but a few measurements are north of the Antarctic Divergence, where they provide a mean sea-ice drift velocity between 80 and 97.5° E of 0.13 ms”¹ (11.23 km d^–1) and between 97.5 and 100° E of 0.23 ms^–1 (19.87 km d^–1). These speeds are similar to Budd’s (1986) mean west to east drift components quoted above. Reference Bindoff, Rosenberg and WarnerBindoff and others (2000) provide updated modelled current speeds, again predominantly south of the Antarctic Divergence, but with a few measurements further north. New data (Table 2) from N. Bindoff and C. Domingues (personal communication, 2003) indicate current speeds less than one-third of the above values for the east-flowing water north of the Antarctic Divergence. The mean speed across the longitudinal span from 95 to 135° E in the 60–62° S band is 3.0kmd^–1. Note the low speeds in the intermediate band, and the higher east to west speeds south of the Divergence. Bindoff and Domingues’ calculations are, however, based on geostrophic considerations, i.e. neglecting wind effects, and may underestimate current speeds by as much as 50%.

Table 2. Modelled oceanographic data for the study area (personal communication from N. Bindoff and C. Domingues, 2003), providing a 10 year mean picture. Depth integration of the data is a linear interpolation using data at 10, 32, 62, 104, 161 and 238 m depth. Longitude and latitude provide the position of the midpoints of data bins of 28 latitude × 10° longitude (i.e. data in the first row pertain to the area 60–62 8S, 95.0–105.0 °E)

Hamley and Budd (1986) assumed an average iceberg speed through their study area of 5.0kmd^–1, equating to a residence time of 107 days per 10° longitudinal sector (532.6 km at 61.5° S), i.e. a total residence time across three sectors, T _R = 321 days. They noted that one iceberg had moved through the study area at 7.94 km d ^–1 but considered this to be the maximum likely speed because icebergs were frequently caught in large-scale eddies, so that the residence time in the area is increased. We assume (1) the same residence time as Hamley and Budd for each of the 10° sectors and (2) a residence time of 177 days per 10° longitude, corresponding to an iceberg drift speed of 3.0kmd^–1, i.e. T _R = 531 days, to estimate half-lives, T _1/2, for each size range:

where V _i is initial (i.e. within the 90–100° E sector) total iceberg volume within the size range, and Vf is the final (i.e. within the 120–130° E sector) total iceberg volume within the same size range. Table 3 shows calculated halflives for each size category. The mean half-life across all sizes is 191 days with standard deviation 38 days assuming an iceberg drift speed of 5km d^–1, and 318 days with standard deviation 63 days for an iceberg drift speed of 3 km d^–1. The half-life calculated for the total of all icebergs is 186 days (for drift speed 5 km d^–1) or 310 days (drift speed 3kmd^–1). Hamley and Budd (1986) estimated a half-life of 0.2 years (~73 days), pointing out that this was about the same across all size categories.

Table 3. Half-life calculations for each size category, and for the total iceberg volume. The calculations shown are across the full study area,* 90–130° E. It is assumed that the total residence time is (a) 3 × 107 days and (b) 3 × 177 days

Assuming the dissolution of the smallest iceberg category is due entirely to melt, we can use the half-life to estimate a linear melt rate. The shape of the iceberg must also be assumed, and a cube with longest linear dimension (the diagonal) 62.5 m (i.e. the mean dimension of the smallest category) has sides of 44.2 m, and volume 86 351 m³. In one half-life the volume is reduced to 43 175 m³, i.e. a cube with sides of 35.1 m. The linear melt rate for the smallest category is then (44.2 – 35.1)/187 = 0.049 md^–1 (assuming from Table 3 a half-life of 187days at drift speed 5km d^–1) or (44.2 – 35.1)/311 = 0.029 md^–1 (assuming a half-life of 311 days at drift speed 3 km d^–1). Some previous studies (e.g. Reference Budd, Jacka and MorganBudd and others, 1980; Reference Neshyba and JosbergerNeshyba and Josberger, 1980; Reference Russell-HeadRussell-Head, 1980) have estimated melt rates in the temperature range 0–2°C to be ~0.1 m d^–1. Hamley and Budd (1986) estimated a melt rate of 0.12 m d^–1, but it is unclear how their estimate was made. While we suggest here that iceberg melt rates may be half to a quarter of those estimated in previous work, it needs to be recognized that information concerning drift speeds is most wanting.

An alternative approach to the problem of estimating dissolution rates is to assume the volume loss as icebergs move from one 10° sector to the next is related to the iceberg area exposed to ocean water, A _w, i.e. to the total iceberg surface area below the water surface. This quantity is tabulated for each iceberg size category in each 10° longitude sector in Table 1. Table 4 and Figure 10 show volume loss (calculated by subtracting the total ice volume per 11.1 km observation area in each 10° sector from the volume in the 10° sector immediately to the west) as a function of A _w. Values used in Table 4 and Figure 10 are means across each interval pair. There are thus three points for each size category.

Fig. 10. Iceberg total volume loss (per 6mi (int., naut.) (11.1 km) observation radius) across 108 longitude sectors, plotted as a function of total iceberg surface area below the ocean surface, A _w, i.e. in contact with ocean water (in the same observation area). Full circles are the three points (i.e. across 3 × 10° sectors) pertaining to the iceberg size range, 25–100 m; full triangles are points for the 100–200 and 200–400m size ranges. Squares (full and open) are for the 400–800, 800–1600 and 1600–3200m size ranges. Straight lines are regression fits through the data represented by full squares (r ² = 0.94) and full triangles plus one open square (r ² = 0.68).

Table 4. Iceberg surface area in contact with ocean water (mean across each pair of 108 sectors), along with iceberg volume loss and mass of freshwater input to the ocean, for each size category, as icebergs move (three steps) from one 10° longitudinal to the next

From Figure 10 we see that the data fall into three distinct groups: the largest icebergs (all those >800 m, and two of the three points for the 400–800 m category), the mid-sized icebergs (all the icebergs in the size range 100–400 m and the one datum from the 400–800 m range in the longitudinal sector 90–100° E to 100–110° E) and the smallest icebergs (all those <100m). For the largest icebergs, Figure 10 indicates a straight line relationship (r ² = 0:94) between surface area below water and volume loss, with slope 47.5 m. This quantity, 47.5 m per 10° of longitude, can be regarded as a linear dissolution rate. Note, however, that this applies to five surfaces (four sides and the base) of the iceberg, and it therefore might be expected to be a factor of up to five greater than the linear dissolution rate estimated above (i.e. ~9.5 m per 10° of longitude, or 0.089 m d^–1 for a residence time of 107 days or 0.054 md^–1 for a residence time of 177 days).

There is also a linear relation (although not as strong as for the larger icebergs; r ² = 0.68) between the surface area below water and volume loss for the mid-sized icebergs. Note also in this set of data, one point indicating a volume gain. This, of course, can happen because the study is statistical in nature, and a large number of breakages of larger icebergs in the sector to the west can result in an increase in icebergs of one particular size to the east, although the total iceberg volume is decreased. The data indicate that these mid-sized icebergs have in total (noting there are many more icebergs in this size category) a greater surface area under water than the larger icebergs (thus the shift on the area scale by about 20 × 10⁴ m²). The dissolution rate (the slope of the straight line) for these data is 59.8 m per 10° longitude and, again, this is expected to be primarily due to breakage into smaller size categories.

The three points for the smallest size category indicate low surface area and low volume loss. No strong relationship is evident between volume loss and area exposed to water, and dissolution of these icebergs is almost entirely due to melt.

Temperature

Water temperatures, integrated over depths of 10, 32, 62, 104, 161 and 238 m, are included in Table 2 (personal communication from N. Bindoff and C. Domingues, 2003). The mean temperature across the study area between 60 and 62° S is 1.15°C, and between 62 and 64° S is 0.82°C. Thus an estimate of 1 °C for the mean temperature within the study area seems reasonable. Note that the mean temperature south of the Antarctic Divergence (in the 64–66° S bin) is 2° lower than north of the Divergence.

Freshwater Input to the Ocean

From the ice volume loss as the icebergs move through the study area, we can estimate the mass of freshwater input to the ocean. We need to assume mean iceberg density values for the different size categories;these are implied by the discussion above, of iceberg height to thickness ratio. For icebergs in the size category >400 m, we assume a height to thickness ratio (in sea water with density taken as 1030 kg m^–3) of 1 : 7 (i.e. a mean iceberg density, ρ = (6/7) × 1030 = 883 kg m^–3). For icebergs in the 100–400m size categories, we assume a height to thickness ratio of 1:6 (ρ = (5/6) × 1030 = 858 kg m^–3) and for the smallest category, <100m, a ratio of 1:9 (p = (8/9) × 1030 = 915 kg m^–3).

In Table 4, the mass of freshwater input to the ocean per 11.1 km observation radius area is provided by multiplying the iceberg volume loss by the relevant mean iceberg density. Values in Table 4 are the freshwater input implied by the dataset, for each size category (and total across all size categories) per 10° of longitude. The total freshwater contribution from iceberg dissolution as the icebergs traverse from 90–100 to 100–110° E is 23.8 Mt (2.38 × 10¹⁰kg) per 11.1 km observation radius (i.e. per 387 km²). The area of our study region between 90 and 100° E is ~2.8 × 10⁵ km², and between 100 and 110° E is ~2.4 × 10⁵km². Since we are considering icebergs travelling from the first of these sectors to the second, we have assumed an ocean area of 2.6 × 10⁵ km² to estimate the total mass discharge, M _T, within our latitudinal bands, per 10° longitudinal sector as a result of iceberg dissolution to be

Similarly, for icebergs moving from 100–110 to 110–120° E (mean 10° sector area: 2.3 × 10⁵ km²)

and for icebergs moving from 110–120 to 120–130° E (mean area: 1.7 × 10⁵ km²)

To calculate the freshwater input on a time basis, we again need the estimates of drift rate (or residence time within each 10° sector). The total freshwater contribution from iceberg dissolution between 90–100 and 100–110° E is 2.38 × 10¹⁰kg per 11.1km observation radius (387km²). That is 61.5 kg m^–2 or, assuming a residence time of 107 days for each 10° longitude, 210 kg m^–2 a^–1 (equivalent to precipi-tation of 21.0 cm a^–1). Between 100–110 and 110–120° E, the freshwater contribution is 176kgm^–2a^–1 (equivalent to precipitation of 17.6 cm a^–1), and between 110–120 and 120–130° E it is 78 kg m^–2 a^–1 (equivalent to precipitation of 7.8cm a^–1). Details for each size category are shown in Table 4. The above quantities are of the same order as those of Reference Silva, Bigg and NichollsSilva and others (2006) who estimate iceberg freshwater input around the whole continent, based on the NIC large iceberg dataset.

Comparison with Antarctic Ice Sheet Outflow

The amount of ice crossing the grounding zone of the Antarctic ice sheet amounts to ~411 km³ a^–1 for East Antarctica and ~429 km³ a^–1 for West Antarctica (Reference Rignot and ThomasRignot and Thomas, 2002). Much of the snow accumulated on the continent, however, is deposited in the coastal area, downstream of the grounding zone including of course, the ice shelves. The Intergovernmental Panel on Climate Change (IPCC) estimate (Reference Church and HoughtonChurch and Gregory, 2001) of total accumulation (i.e. P – E, where P is precipitation and E is evaporation) over the Antarctic ice sheet is 2246 ± 86 Gt a^–1. Of this, the IPCC estimates ~2072 ± 304 Gt a^–1 output by iceberg production. However, it has been realized since the IPCC report that as much as a third of the ice-sheet output may be accounted for by basal melt (Reference Jacobs, Hellmer and JenkinsJacobs and others, 1996). Thus, we might expect ~1500 Gt a^–1 of the output to be from calving of icebergs.

On this basis, 2% of the total Antarctic iceberg dissolution is accounted for within our 30° longitude study sector. The Amery Ice Shelf (which drains ~Ί2% of East Antarctica) and the Shackleton Ice Shelf are the primary sources of icebergs into our study area. While 2% (distributed over 8% of the latitudinal extent of the coastline) is a smaller than expected fraction of the total (perhaps our observations and calculations have underestimated the total fraction), it needs to be noted that the Ross and Ronne–Filchner Ice Shelves discharge the greater proportion of the Antarctic ice into the Ross and Amundsen Seas and consequently around the Antarctic Peninsula into the Weddell Gyre, and the Weddell Sea area, on the opposite side of the Antarctic continent.

Conclusions

Several findings emerge from this study, concerning the distribution, movement, melt rates and freshwater input of icebergs in the Southern Ocean.

• 1. In the near-coastal regions, the distribution of icebergs is determined by the locations of the major ice outflow regions from the Antarctic ice sheet, and by the nearcoastal bathymetry, which causes icebergs to become grounded in shallow water.

• 2. In the deeper water away from the coast, the northern extent of Antarctic icebergs is remarkably similar to the northern extent of the maximum sea-ice extent, both being influenced by ocean temperature and current patterns in the area. The east–west distribution of icebergs is determined by the currents which are, in turn, influenced by the deep ocean bathymetry, and by the iceberg dissolution itself.

• 3. In the Circumpolar Current east of 90° E, there is a decrease in iceberg concentration with increasing size category. Almost all the variability in the concentration is due to variability in the concentration of smaller icebergs.

• 4. Total iceberg volume is dominated by the larger icebergs. The effect on total iceberg volume of concentrations of icebergs <200 m in linear dimension is very small, and it is the disintegration of the larger icebergs, primarily by breakage and subsequent melting as they drift towards the east, that accounts for most of the volume loss.

• 5. The concentration and total volume of icebergs in our study area in 1984/85–1988/89 were higher (on average by a factor >2) than in the following two 5 year periods and (by a lesser amount) in the previous 6 year period. Volumes and concentrations were similar, however, in the 120–130° E sector and west of 80° E. That is, the greater volume and concentration during the 1984/85–1988/89 period occurred between 80 and 120° E, the same area fed by the gyre operating northeast of Prydz Bay. These changes in concentration are not noted elsewhere around the Antarctic continent, and demonstrate the episodic nature of iceberg calving within local regions.

• 6. At temperatures ~1°C, iceberg dissolution rates, ~0.03–0.05 md^–1, are more than a factor of two lower than previously estimated; however, these calculations are highly dependent upon assumed drift speeds, which have the largest uncertainty.

• 7. The total mass contribution of fresh water to the ocean due to iceberg dissolution as they traverse the 30° longitudinal sector studied is ~32Gt. This amounts to a contribution equivalent to precipitation of ~Ί5.5cma¯¹. This total mass of ice melted within the 30° sector study area accounts for ~2% of the iceberg total discharged from the Antarctic ice sheet.

Future Work

The collection and statistical analysis of datasets as described here will continue to provide useful estimates of iceberg distributions and dissolution rates cheaply and conveniently. Programs such as the SCAR iceberg program are particularly valuable now that there is near-universal access to the data through the World Wide Web.

For a more accurate assessment of iceberg dissolution rates, however, and to better understand the processes of iceberg dissolution, we require studies that include repeat measurements on selected large icebergs. These projects need to be carried out over 1–5 years. Measurements are required of thickness (using ice thickness radar from the surface and, perhaps, upward-looking sonar from below), underwater side shape, i.e. depth profiles (using sidescanning sonar from ships), and width and length (using satellite remote-sensing techniques). That is, a full description of iceberg size is required. Recent techniques have been developed by US scientists (personal communication from T. Scambos, 2007) for measuring iceberg dissolution rates, by establishing self-reading ice radars on large icebergs. These radars are set up to measure the ice thickness once a day, and to transmit real-time data back to the laboratory. First fieldwork with this instrumentation was carried out during the 2006/07 austral summer Antarctic field season. Snow accumulation rate, ice temperature and horizontal ice strain rate on the iceberg surface, along with movement rate and meteorological (requiring placement of automatic weather stations (AWS) on the icebergs) and oceanographic data, will provide an indication of the iceberg dissolution rates and the dependence on weather and sea conditions.

Several icebergs should be examined, including a selection in the coastal region (i.e. in the east wind drift regime with low in situ water temperature) and a selection of more northerly icebergs (that have moved into the Circumpolar Current with relatively higher water temperatures). For each iceberg, a sequence of at least two (and preferably three to five) sets of measurements over the 5 year period of the project should be made. A project such as outlined above has been proposed for the AAP, and some preliminary work, including placement of an AWS, has been carried out on the B9B iceberg in East Antarctica. It is expected that further fieldwork will be carried out within the next few years.

For the longer term, however, more accurate satellite-based sensing of icebergs from the current and future generation of remote-sensing instrumentation (e.g. Reference Scambos, Sergienko, Sargent, MacAyeal and FastookScambos and others, 2005) will provide the best estimates of iceberg dissolution rates. Even these measurements, though, need high-quality ‘ground-truth’ measurements, such as provided by the ship-based observations.