Roughness variance

Roughness of the ice surface can be quantified by the roughness variance, (Reference Andreas, Lange, Ackley and WadhamsAndreas and others, 1993). The roughness variance defined for an elevation variable, h_xn (where "x" can be replaced by "s" to denote snow surface, "t" for ice top surface or "b" for ice bottom surface) is defined as

where is the mean elevation (distance from sea level) of surface x, n is the number of points on the transect and σ_× is the root-mean-square (rms) elevation roughness.

Data reduction

Ridges on each floe were distinguished from unridged ice (Fig. 2) using methods similar to those applied to submarine sonar profiles under Arctic ice (Reference Wadhams and HomeWadhams and Home, 1980). Modifications were made for the NBP Ross Sea datasets as they were shorter in length, contained thinner ice and contained more high-frequency fluctuations. A ridge was defined by the presence of a ridge keel underwater (Fig. 2). The Rayleigh criterion defines a pressure ridge keel as one where the draft minima (troughs) on either side of the focal maximum (crest) descend at least halfway toward the local level ice. In the present analysis, overlapping keels were considered as part of the same ridge. Local level horizon was defined using the D2 definition (Reference Wadhams and HomeWadhams and Home, 1980). A level ice point is one whose draft differs by < 0.25 m from every point within 10 m on either side. A ridge keel must also be deeper than a minimum draft, called the cutoff value; 5 and 9 m cut-offs were frequently used for the Arctic sonar profiles. These values were inappropriate for the NBP Ross Sea dataset, since the maximum draft measured was only 2.5 m and the mean draft was 0.80 m. The size difference between Arctic and Antarctic ridges was also noted by Reference Worby, Jeffries, Weeks, Morris and JañaWorby and others (1996), who reduced the cut-off heights for ridge sails to 0.5 m from the usual values of 0.75−1 m to allow for the smaller ridges in the Amundsen and Bellingshausen Seas. We tested the NBP Ross Sea dataset with cut-off values of 1, 0.75 and 0.5 m for ridge keels. We found that cut-off values of 0.75 and lm missed a significant portion of ridges (72% and 55%, respectively), while a cut-off value of 0.5 m captured 80% of the ridges. Hence, we adopted the definition that a ridge keel is an underwater feature which satisfies the Rayleigh criterion and is at least 0.5 m deep.

Each identified ridge is represented as an individual data point in the following analysis. Once the ridges were removed, each one of the remaining regions is classified as unridged ice (Fig. 2) and is represented as an individual data point.

Mean thickness and roughness

The mean thickness and roughness values were reasonably similar for the two autumn cruises (NBP 95−3 and NBP 98−3), and these cruises were dissimilar to the summer cruise (NBP 99−1) (Table 2). Summer ice was thicker and had a deeper snow cover. As a result of the heavy snow load, the summer snow/ice interface was often submerged below sea level, and mean summer freeboard was −0.04 m. The roughness of the summer ice and snow surfaces was around twice as great as that of autumn ice. For the autumn cruises, there was slightly thicker ice, thinner snow and rougher surfaces in 1998 than in 1995.

Table 2.

Mean values of snow and ice thickness and roughness of ice floes for each ross sea dataset

Ridges contained thicker ice, deeper snow and rougher ice bottom surfaces than unridged regions (Table 2). At the ice bottom surface, ridges were nearly four times as rough as unridged regions, but ice top surface and snow surface were similar in roughness. Mean freeboards of both ridges and unridged regions were at or close to zero.

Linear regressions

Linear regressions were performed between mean snow elevation, h_s, and mean ice thickness, z-_× (Fig. 3a-f); snow surface roughness, σ_s, and mean ice thickness, z-_× (Fig. 4a-f); snow surface roughness, σ_S, and ice bottom roughness, σ_h (Fig. 5a-f); and snow surface roughness, a_s, and ice top surface roughness, σ_t (Fig. 6a-c). The majority of correlations are significant at the 99% confidence level.

Fig. 3.

Linear regression between mean snow elevation (h_s) and mean ice thickness (z-j. (a-c) roughnesses averaged over each entire profile for individual cruises; (d) linear regression of all cruise data combined; (e,f) roughnesses over individual unridged regions and ridges, respectively. the correlation coefficient (r), the significance level ( % sig) and the standard error (se) of the slope of the regression are given in each graph. plus/minus 2se corresponds to 95% confidence interval of the regression.

Fig. 4.

Linear regression between snow surface roughness (a_s) and mean ice thickness ( zi). (a-c) roughnesses averaged over each entire profile for individual cruises; (d) linear regression of all cruise data combined; (e,f) roughnesses over individual unridged regions and ridges, respectively.

Fig. 5.

Linear regression between snow surface roughness (a_s) and ice bottom roughness (a_h). (a-c) roughnesses averaged over each entire profile for individual cruises; (d) linear regression of all cruise data combined; (e,f) roughnesses over individual unridged regions and ridges, respectively.

Fig. 6.

Linear regression between snow surface roughness (a_s) and ice top surface roughness (<r_t). (a) linear regression of all cruise data combined; (b, c) roughnesses over individual unridged regions and ridges, respectively.

Cruises varied in the strength of correlation between each pair of variables. For example, correlation between h_s and z; was considerably stronger in NBP 99−1 than in NBP 95−3 or NBP 98−3 (Fig. 3a-c); correlation between a_s and z, was stronger in NBP 95−3 and NBP 98−3 than in NBP 99−1 (Fig. 4a-c); and scatter between a_s and a_h was considerable on all three cruises (Fig. 5a-c). However, for each pair of variables, the data points from all three cruises converge relatively well along a linear trend (Figs 3d, 4d and 5d). The strongest correlation was between h_s and zi (R ∼ 0.85; Fig. 3d), while the correlations between a_s and z_i (Fig. 4d) and between a_s and a_h (Fig. 5d) were slightly weaker and similar in strength (R ∼ 0.71). Despite the similarity in correlation coefficients, scatter between a_s and a_h was considerably greater than between a_s and zi.

Regressions for ridges and unridged regions differed among the variable pairs. There was stronger correlation between h_s and zi for both ridges and unridged regions (Fig. 3e and f). Weaker correlation and large data scatter were found for both ridges and unridged regions between <r_s and z_h σ_s and σ_b, σ_s and σ_t (Figs 4e and f, 5e and f and 6b and c), with the correlation being considerably stronger for ridges than for unridged regions.

Mean thickness and roughness

Interseasonal, regional and interannual variations were observed in the thickness and roughness of Ross Sea ice. Ice and snow were thicker and surfaces were rougher in NBP 991 than in NBP 95−3 and NBP 98−3. The autumn ice in NBP 953 and NBP 98−3 contained a higher fraction of thin, new ice than the summer ice in NBP 99−1. By the summer, the ice cover had had time to thicken both dynamically and thermodynamically, and to accumulate snow. NBP 99−1 took place in the eastern Ross Sea where winds are more variable and ice export is less effective than in the western Ross Sea (Reference Marshall and TurnerMarshall and Turner, 1997), where katabatic winds of high directional constancy and the cyclonic circulation of the Ross Sea maintain efficient ice export Reference Jacobs and ComisoJacobs and Comiso, 1989). Consistently high concentrations of sea ice (Reference Sturman and AndersonSturman and Anderson, 1986) and variable winds (Reference Marshall and TurnerMarshall and Turner, 1997) in the eastern Ross Sea promote dynamic thickening and roughening of ice surfaces. The snow surface in this region could also roughen as a result of variable winds, floe rotation (Reference Massom, Drinkwater and HaasMassom and others, 1997) and increased ice deformation. Interannual variability was observed between NBP 95−3 and NBP 98−3, which took place in the same season and similar geographical locations, with 1998 being a year of less snow accumulation and greater ice thickness and roughness.

Ridges and unridged regions exhibited different characteristics, with ridges having a rougher ice bottom, greater ice thickness and accumulating more snow. Despite the differences in snow loading and ice stresses, isostatic balance was maintained across both ridges and unridged regions, as reflected by their mean freeboards of zero.

Comparison of surface roughness with other Antarctic regions

Sea-ice roughness values from various studies were compared according to geographical location, season and ice type (Table 3). Roughness values fell into two categories according to the age of ice floes. Early season (autumn to spring) first-year ice was low in roughness (Table 3). Late season (summer) first-year ice was similar to multi-year ice (Table 3) where roughness was up to three times that of early season first-year ice. From NBP 95−3, NBP 98−3 and NBP 99−1, we observed interannual, regional and interseasonal variability in sea-ice roughness (Table 2). When the comparison was expanded to include eight other cruises from previous studies in other parts of Antarctica, we found that interseasonal variations stood out over interannual and regional variability for first-year ice (Table 3). For the multi-year ice in the western Weddell Sea, roughness values were consistent among measurements made in different years and seasons (Table 3). This suggests that processes which create sea-ice roughness are independent of year and location, and that ice-floe age and deformation history are the most important factors in determining roughness.

Table 3.

Comparison of rms snow and sea-ice roughness values (m) in antarctica

Linear regression

In the linear regressions between h_s and zi; σ_s and zi; and σ_s and σb, we observed variations between cruises and over ridges and unridged regions (Figs 3a-f, 4a-f and 5a-f). Despite the differences in data scatter and linear regression, a good linear trend emerged for each pair of variables when all profiles from the cruises were combined. This suggests that processes maintaining the relationships between snow elevation and ice thickness; snow surface roughness and ice thickness; and snow surface roughness and ice bottom roughness, are independent of season, year, location and deformation history of the ice floes.

Correlation between h_s and z_i over ridges and unridged regions (Fig. 3e-f) was stronger than correlations between <r_s and _zi (Fig. 4e and f), and <r_s and a_h (Fig. 5e and f). This difference is primarily due to the different mechanisms that determine h_s and a_s.

Mean snow elevation, h_s

The stronger correlation between h_s and z_× in NBP 99−1 than in NBP 95−3 and NBP 98−3 can be attributed to the presence of slush. Slush is the layer of saturated snow between the snow/ice interface and the sea level on a flooded ice floe, where z_f < 0. As explained below, slush enhances the capability of predicting z_i from h_s by separating h_s from z_i, and by making little contribution to buoyancy.

The isostatic balance of a non-flooded ice floe (z_f ≥ 0) is as follows:

where ρ_s is the density of snow, _pi is the density of sea ice (assumed to be 900 kg m⁻³; Massom and others, 1998) and _pw is the density of sea water (1024 kg m⁻³). Mean ρ_s values for NBP 95−3, NBP 98−3 and NBP 99−1 were 340, 320 and 520 kg m⁻³, respectively (Reference Sturm, Morris, Massom and JeffriesSturm and others, 1998; Reference Morris and JeffriesMorris and Jeffries, 2001). Isostatic balance in a non-flooded ice floe is maintained between h_s(= z_s + z_f), which contains snow and some ice, and z_d. Translation between z_d and z_i also depends on the isostatic balance, and the multiple dependencies make the relationship between h_s and z_i complex and scattered.

The isostatic balance of a flooded ice floe (z_f < 0) is as follows:

where z_f indicates the thickness of the slush layer and ρ_s] is density of slush, which is estimated to be close to that of sea water (0.96 kg m⁻³) (Reference AdolphsAdolphs, 1998), although field measurements arrive at lower values (0.70 kg m⁻³) (Reference AdolphsAdolphs, 1998) as sea water is invariably lost during the measurement procedure. The small difference between ρ_s] and ρ_w means that the effect of slush on buoyancy is small. As a result, the isostatic balance is maintained between h_s and z_i, allowing z_i to be predicted effectively from h_s.

Variability in the ratio z_i : h_s can be explained by the differences in the relative densities and proportions of ice and snow above sea level. We observed a higher z_i : h_s ratio in NBP 99−1 (4:1) than in NBP 98−3 (3:1), which was, in turn, higher than in NBP 95−3 (2:1) (Fig. 3a-c). Snow density in NBP 99−1 was highest, being 1.5 times greater than in NBP 95−3 and NBP 98−3. For the same h_s, the heavier load in NBP 99−1 required a greater buoyancy force created by a larger ice volume below the sea level. Hence the ratio of _zi:h_s was greatest in NBP 99−1. Between NBP 95−3 and NBP 98−3, there was only 6% difference in ρ_s, and h_s was the same for both years. However, there was 0.02 m more ice freeboard in NBP 98−3 than in NBP 95−3, and since the ice was three times more dense than snow, the load for the same h_s increased. An increased load required a larger ice volume to provide the buoyancy force, and hence the z_i : h_s ratio was greater in NBP 98−3 than in NBP 95−3.

Snow surface roughness, σ_s

Snow surface roughness is primarily determined by ice top surface topography and wind redistribution. Snow preferentially collects in depressions. Winds at speeds of > 6−8 m s"¹ are able to redistribute the snow (Reference Andreas and ClaffeyAndreas and Claffey, 1995), building it up in the lee of sails, filling in between sails and keeping the tops of sails bare (Reference Lange and EickenLange and Eicken, 1991). A snow surface with a hard crust would require higher winds to initiate redistribution (Reference Andreas and ClaffeyAndreas and Claffey, 1995). Snowdrifts on ice floes are often omnidirectional because of floe rotation and changes in prevailing wind direction (Reference Massom, Drinkwater and HaasMassom and others, 1997). The snow surface amplifies the roughness of the ice top surface, and the amplification is stronger in unridged regions than in ridges (Fig. 6a-c). Analysis of the frequency of snow surface roughness reveals that, although the magnitude of ice roughness has been amplified, the frequency of roughness features has been decreased, resulting in a smoothing effect over the ice top surface (Reference Andreas and ClaffeyAndreas and Claffey, 1995; Reference Massom, Drinkwater and HaasMassom and others, 1997).

The poor correlation between a_s and z_i and σb over unridged regions (Figs 4e and 5e) can be attributed to the large discrepancy between σ_s and σ_t decoupling the snow surface from the processes determining z_i and a_h. Why does a large discrepancy between σ_s and σ_t exist in the unridged regions and not in ridges (Fig. 6b and c)? We suggest that the modification of ice top surface roughness, effects of nearby ridges and nucleation of roughness features on the snow surface are possible reasons. After the snow cover has been laid down, ice top surface can be smoothed by formation of snow ice. Snow ice is formed by the freezing of snow and floodwater at the interface between snow and ice, and this new ice layer smooths out small perturbations on the ice top surface, thereby reducing a_t. Hence, <r_t that is measured subsequent to snow-ice formation has a lower value than when the snow cover was first laid down (Reference Worby, Jeffries, Weeks, Morris and JañaWorby and others, 1996). In ridges, a_t is dominated by the crest of the keel or sail, with its large deviation from the mean surface. Flooding and subsequent smoothing of troughs by the growth of snow ice has a relatively small effect on the <r_t over the entire ridge.

Wind redistributes snow so that it builds up in the lee of ridge sails, and snowdrifts have been observed up to 10 m away from a ridge (Reference Sturm, Morris, Massom and JeffriesSturm and others, 1998). The roughness of this wind-drifted snow is independent of the ice top surface roughness. As a result, <r_s and <r_t are decoupled close to ridges, and unridged regions can have a disproportionately large <r_s. On flat level ice surface, <r_s can also be decoupled from <r_t, as small icy nodules with sub-centimeter diameters can act as the foci for the formation of extensive dune features which can be up to lm high and 35 m long (Reference Massom, Drinkwater and HaasMassom and others, 1997; Reference Sturm, Morris, Massom and JeffriesSturm and others, 1998).