Introduction

The world’s ice sheets and glaciers play an important role in the global climatic system. Not only the large ice sheets of Greenland and Antarctica and the sea-ice cover, but also small glaciers may contribute significantly to sea-level changes in the event of a change in temperature (Reference MeierMeier, 1984). The polar ice caps and the Greenlandic inland ice shield are very sensitive to changes in temperature.

In principle, there are two processes that may cause mass loss in the large ice sheets: (1) break-up (dynamic process), and (2) ablation (climatically induced process); the two may interact. Fast-moving glaciers and ice streams present weakness points in the stability of an ice sheet, and locations where break-up is expected to start. Scenarios for dynamic instabilities have been discussed in Reference HughesHughes (1973), Reference Clarke, Nitsan and PatersonClarke and others (1977), Reference Schubert and YuenSchubert and Yuen (1981), Reference Alley and WhillansAlley and Whillans (1991) and Reference HuybrechtsHuybrechts (1993), among others.

Since the Greenland ice sheet is located in a relatively warm climate, it is particularly sensitive to changes in temperature. Data collected under the Program for Arctic Regional Climate Assessment (PARCA) indicate an increase in temperature of 2°C on the central Greenland Inland Ice from the standard decade 1951–60 to 1995–99 (Reference Steffen and BoxSteffen and Box, 2001). A surface lowering in some of the marginal areas of the Greenland ice sheet has been observed from airborne laser altimeter data (Reference KrabillKrabill and others, 1999). Changes in the extent and surface structure of the ablation area of the Greenland ice sheet are indicators of the response of the ice sheet to temperature change, but little is known about regional variability. Large-scale approaches to monitor elevation changes from satellite radar altimetry have been published by Reference Zwally, Brenner, Major, Bindschadler and J. G.Zwally and others (1989) for the entire Greenland ice sheet, by Reference HerzfeldHerzfeld and others (1997) for the Lambert Glacier/Amery Ice Shelf region of Antarctica, and by Reference BindschadlerBindschadler (1984) for the Jakobshavn Isbræ area. In this paper we take a different approach to the study of changes in ice sheets and their possible dependence on climatic change, which (a) utilizes the variable ice surface roughness rather than absolute elevation, and (b) studies the ice sheet in a sensitive area, a part of the ablation area, and (c) at high resolution. The Glacier Roughness Sensor (GRS) is used to measure surface roughness directly on the ice, to provide subscale information for satellite data and to study micromorphologic processes on the ice surface.

Ice surface roughness is an important parameter in the study of ablation processes and their changes, as the energy available for melting varies by a factor of 2 with surface roughness changes (Reference Herzfeld, Box, Steffen, Mayer, Caine and LoslebenHerzfeld and others, in press). Here, we describe measurements and analyses of surface roughness in the ablation area of Jakobshavn Isbræ drainage basin, in a seasonal comparison of the spring and summer ice surface.

Study Area

Jakobshavn Isbræ and its drainage basin is an ideal location for the study of both dynamically and climatically induced changes in the Greenland ice sheet. Jakobshavn Isbræ is the world’s fastest-moving ice stream; it starts on the Greenland Inland Ice and accelerates to 7 kma^–1 (19md^–1; Reference Echelmeyer, Clarke and HarrisonEchelmeyer and others, 1991) or 20.6 md^–1 (7.519kma^–1; Reference Pelto, Hughes and BrecherPelto and others, 1989) at the calving front. Faster-moving ice can be traced for 80 km up the ice sheet for the longer, wavy southern branch (south ice stream), which joins the shorter north ice stream along a feature called “the zipper” because of the pattern of merging crevasses (Reference Echelmeyer, Clarke and HarrisonEchelmeyer and others, 1991). Surface velocity in the flow direction is about 1000 m a^–1 50 km upstream of the calving front (Reference Iken, Echelmeyer, Harrison and FunkIken and others, 1993). Ice thickness at the calving front is about 800 m, as can be told from floating icebergs that have turned to the side. The ice stream follows a geological trough that continues in the ice fjord. The adjacent slower-moving ice (we measured a maximum directional velocity of approximately 0.3 m d^–1) has a surface morphology that is dominated by wind, snowfall and ablation processes. In the slow-moving part south of the south ice stream, measurements of surface roughness were carried out during expeditions MICROTOP97 and MICROTOP99 as part of a larger project to study ice-surface properties from satellite and with field data (for MICROTOP97 see, e.g., Reference Herzfeld, Mayer, Feller and MimlerHerzfeld and others, 2000a,Reference Herzfeld, Stauber and Stahlb).

Morphologic properties at any scale are not captured by absolute elevation (above an imaginary zero reference, such as sea level) but rather by changes of elevation in space, in mathematical terms dh/dx, where h is elevation and x location. At larger scale this is topographic relief, at small scale roughness. So, ice surface roughness is a morphologic characteristic of ice surfaces.

Instrumentation and Survey Set-Up

Surface roughness data were collected with the GRS, an instrument designed specifically for the survey of microtopography/roughness of snow and ice surfaces at cm to 100m scales. The GRS is a towed instrument that surveys surface roughness in swath mode with 0.1m along-track spacing, 0.2m across-track spacing and sub-centimeter accuracy. The GRS works mechanically with electronic registration. The instrument consists of a 2m by 2m large sled frame supporting eight survey arms (eight channels) that are hinged on a main crossbar and touch the ground. As the sled is pulled across the ice, the survey arms move freely over the surface, with their ends following the ups and downs of microtopography. Angular motion of each arm is registered digitally with a frequency of 10Hz. If the sled is pulled at 1ms^–1 velocity, this translates into 0.1m along-track spacing of observations.

Differential global positioning system (GPS) data, obtained by an antenna and receiver integrated in the GRS and co-registered during survey, provide locational reference, and clinometer data are available for correction for instrument motion if necessary. The instrument itself, repeatability of measurements, accuracy, error levels and the influence of new snow are described and analyzed in Reference Herzfeld, Mayer, Feller and MimlerHerzfeld andothers (1999).

During MICROTOP97 and MICROTOP99 expeditions, GRS surveys were carried out in survey grids of 175 m by multiples of 25 m, which were staked out using classic surveying methods (Fig. 1). The size of the survey areas was determined under the constraints that (1) they are large enough to contain sufficiently many repetitions of characteristic morphologic features, (2) small enough to be morphologically homogeneous, (3) large enough to encompass several synthetic aperture radar (SAR) data pixels which may show some variability, and (4) small enough to be covered by a man-hauled instrument in a reasonable time. Surveying approximately normal to the general strike of the dominant morphologic structures allows a saving in width of the area and thus in total survey time. Correlation lengths/spatial frequencies can then easily be determined from vario functions of track data. Spatial covariation is higher in all other directions, and highest in the across-track direction. Time data (times of network marker passes of the GRS) are also recorded manually and provide a back-up for locational correction. The vario functions analyzed here are processed from time-data-corrected files.

Fig. 1. GPS networks of MICROTOP97 and MICROTOP99 experiments, Jakobshavn Isbræ drainage basin, West Greenland. data collected in tracks in the survey areas shown. 1997 GPS base station is in ICECAMP97;1999 base station is in ICECAMP99.

Analysis Method: Geostatistical Surface Classification

The analysis method utilized to obtain ice-surface-morphologic characteristics is geostatistical surface classification (Reference Herzfeld, Stauber and StahlHerzfeld and others, 2000a). In investigations of surface roughness, we study properties of the spatial derivative of surface elevation, or (micro)topography. In the same way that topographic relief and landforms (rather than elevation) are the objective of morphology at a large scale, surface roughness is the variable that captures micromorphologic processes.

The analytically defined spatial derivative needs to be calculated numerically from a dataset. One way to do this is by building differences of elevation values over given distances. Forming the (mathematical) limit of such expressions, for distance increments approaching zero, yields the value of the surface slope in a given location:

(1)

This approach gives a local slope value, the slope at point x₀. If we are interested in characteristics of the surface (in a given area (e.g. the study area)) then the actual slope value at each location is not relevant. Parameters that describe the morphology a bit more generally and are valid for the whole study area are more valuable. Therefore, we form differences of elevation values again, but average over all points that have the same common distance (or distance and direction), according to:

(2)

for pairs of points (x _i, z(x _i)), (x _i + h, z(x _i + h)) ϵ D, where V is a region in R2 (case of survey profiles) or R₃ (case of survey areas) and n is the number of pairs separated by a distance, or lag, h (€: element of; R₂,R₃: two-and three-dimensional space of real numbers (coordinates), respectively). The function v1(h) is called the first-order vario function . If we let the values of the first-order vario function take the place of the data in Equation (2), we can calculate the second-order vario function v₂. This may be repeated to obtain vario functions of higher order (Reference HerzfeldHerzfeld, 2002; Reference Herzfeld, Mayer, Vaine, Losleben and ErbrechtHerzfeld and others, 2003), which are particularly useful in snow and ice surface analysis. Note that formally, but not mathematically, v₁ corresponds to the sample variogram, but for the variogram generalization is not possible.

Vario functions are calculated from GRS data, separately for each of the eight GRS survey channels and jointly for all channels (see Fig. 2). (In a joint vario function, pairs as in Equation (2) are drawn from data of all channels.) Parameters characteristic of surface features are calculated from the vario functions (see the following definitions and equations), and a feature vector is composed of the parameters. Discrimination algorithms are applied to extract and combine features and associate them to an ice-surface class; the algorithms may be deterministic (e.g. Reference Herzfeld and HigginsonHerzfeld and Higginson, 1996) or follow the connectionist association of neural networks (Reference Herzfeld and ZahnerHerzfeld and Zahner, 2001). Surface characterization, classification or segmentation may be performed. Characterization results in a unique description of each surface class. Classification is the assignment of objects (which may be previously unknown to the system) to a surface class, based on the characterization of surface classes. Segmentation of an entire region may be obtained by application of the classification as a moving-window operator to a large spatial dataset.

Fig. 2. Seasonal comparison of GRS data over ice surfaces and corresponding vario functions for simple ice-surface types. Area“RIDGES”, characterized by large meltwater ridge-and-valley systems, Jakobshavn Isbræ drainage basin. (a, b) Spring (May) 1997, dataset area4q.track04 (a4q04), simple morphology of ablation ridges with old snow. (c, d) Summer (July) 1999, dataset area4p.track01 (a4p01.99), simple morphology of molten-out ablation ridges. For location, see survey grids in Figure 1. Left panels: GRS surface roughness profiles (typical section): relative elevation corrected for along-track position, plotted with offset 0.2 m. Right panels: vario functions calculated from GRS data in corresponding left panels. Notice units on vario-function axis in both plots, which indicate that summer surface is rougher than spring surface.

The mainstay of this paper is the application of these methods to derive characteristics of seasonal changes in the ice surface morphology of the Jakobshavn Isbræ ablation area from MICROTOP97 expedition (spring) data and new previously unpublished MICROTOP99 expedition (summer) data. The parameters that are most useful in the seasonal comparison are:

The pond parameter

Parameter-type-1 (pt1) parameters (slope parameters)

Parameter-type-2 (pt2) parameters (relative significance parameters).

(3)

Maximum vario-function value (pond parameter) is the simplest parameter; it is used to distinguish flat areas from areas with morphologic (micro) relief. For instance, the vario function of an evenly spaced hill-and-valley profile in topography is a sinusoidal wave. Then the lag to the first minimum min1 (after the first maximum max1) in the sine curve is the characteristic spacing of hills and valleys in the topographic relief. To distinguish pure hill–valley sequences from overprinted ones and to characterize more complex morphologic structures, significance parameters are introduced (Fig. 3):

Fig. 3. Sketch of geostatistical classification parameters.

Parameter-type-2 (pt2) parameters are relative significance parameters; in this paper, we use:

and p3 = pt2(max1; min₂) , p4 = pt2(max₂; min₂), p5 = pt2 (max_s,min2), p10 = pt2(max₁,min3), where maxi,minj denote local maxima and minima in the vario function (here: v1) for i ≤ j, h_x is the lag, and γ_x the vario-function value for h_x (x stands for any subscript); max_s is the greater of max1 and max₂.

Parameter-type-1 (pt1) parameters are slope parameters; here, we use:

(4)

as well as p8 = pt1 (max_s min₂) and p14 = pt1 (max1,min3). To avoid catching noise rather than features, vario functions may be filtered, depending on application and scale, prior to automated feature detection (Reference Herzfeld and HigginsonHerzfeld and Higginson, 1996).

Expedition MICROTOP97 and MICROTOP99

During expedition MICROTOP97 (May, June 1997), GRS

surveys were carried out in the Jakobshavn Isbræ drainage basin in the ablation area, south of the south ice stream. Survey areas area3, area4 and area5 are located in the vicinity of IceCAMP97 (68°58.712’N, 49°30.280’W; 864ma.s.l.). Camp was set up just outside of the heavily crevassed area, south of the marginal area of the south ice stream, as determined by reconnaissance and video-survey flights in 1996. A shallow crevassed ridge in the ice separates the camp from the heavily crevassed areas to the north, but thin and closed crevasses continue in the ice in survey areas area4 and area5. The camp lies in a shallow depression between a ridge in the north and higher areas in the south. Ice-CAMP99 was located south of the higher and somewhat crevassed area south of IceCAMP97 The location of Ice-CAMP99 was at 68°57.979’N, 49°30.519’W (about 1.5 km south of IceCAMP97; see Fig. 1). Areas area3 and area4 are the same in both expeditions (see Fig. 1) and so are suitable for a seasonal comparison.

Seasonal Comparison and Results on Ice-Surface-Morphogenetic Processes

MICROTOP97 took place in May and early June, with late-spring conditions on the Inland Ice in the ablation area of Jakobshavn Isbræ. During MICROTOP99, parts of area3 and area4 were resurveyed in summer conditions in the second half of July. In late spring, the ice surface is still covered by compacted, wet and refrozen snow, and occasionally by fresh snow. Fortunately, during MICROTOP97 a storm with heavy snowfall occurred after part of the surveying had been completed, so by resurveying after the snowfall we were able to investigate the effect of fresh snow on the GRS data and the vario-function parameters (Reference Herzfeld, Mayer, Feller and MimlerHerzfeld and others, 1999). Repeat studies on the reproducibility of surveys of the same area were carried out during MICROTOP97; if surveys are undertaken under the same conditions, the results (and ensuing vario-function parameters) are almost the same (Reference Herzfeld, Mayer, Feller and MimlerHerzfeld and others, 1999). Consequently, it is justified to attribute differences between spring and summer surface variograms to seasonal changes in the surface morphology.

In summer (July 1999) the ice surface was completely bare of snow, molten out and saturated with water almost to the surface level. The ice surface was much rougher than in May 1997. In the variogram of area4q (RIDGES) (Fig. 2d), this is reflected in the overall higher variogram values (note that the maximal variogram value is ≈14 in Figure 2b and ≈ 6 0 in Figure 2d; the maximal value on the 7 axis is 120 in Figure 2b and 320 in Figure 2d) and steeper slopes. The pond parameter reflects the difference between spring and summer surfaces: the overall roughness across the surveyed scales is highest in area4 in summer (pond is 90 compared to 14 in spring), and also much higher for area3 (pond = 55 in summer compared to 9.3 in spring). Of the significance parameters, the slope parameter p1 = pt1 (max1, min1) captures the difference between spring and summer surfaces best: for area3, p1 = 0.75 in spring and p1 = 7 in summer; for area4, p1 = 2 in spring and p1 =12.5 in summer; this clear difference is a result of the increased roughness relative to the spacing of the characteristic surface features.

In area3, a complex morphology of ridges and valleys, similar to that in area4, but of smaller relief, interspersed with flat areas, is observed. In May 1997, small sastrugi had formed in the low spots. In spring, the complexity of the surface in area3 shows in the fact that the most significant max–min sequence is max₁ to min₃ , because the subordinate surface features cause the intermediate minima (min₁,min₂) of lower significance; the values related to max1 and min₃ are: p10 = pt2(max1, min₃) = 0:309 and p14 = pt1(max1,min₃) = 2:833 (see Fig. 4; Table 1).

Fig. 4. Seasonal comparison of GRS data and corresponding vario functions for a complex ice surface type. Area3 “ABOVE Ice-CAMP’,’ Jakobshavn Isbræ drainage basin. For location, see survey grids in Figure 1. (a, b) Spring (May) 1997, dataset area3k.track07 (a3k07): ice surface with ridges and ridge segments generated by melting and refreezing with sastrugi in valleys inside segments (complex morphology). (c, d) Summer (July) 1999, dataset area3m.track01 (a3m01.99) (complex morphology with ablation structures of different sizes, overall higher roughness of molten-out surface). Left panels: GRS surface roughness profiles (typical section): relative elevation corrected for along-track position, plotted with offset 0.2 m. Right panels: vario functions calculated from GRS data in corresponding left panels. Notice units on vario-function axis in both plots, which indicate that summer surface is rougher than spring surface.

Table 1. Geostatistical parameters calculated from GRS data of West Greenland ice surfaces

In summer 1999, the larger features are still present (characterized in the vario function by a subordinate minimum followed by a significant minimum), whereas the increased small-scale roughness causes increased overall vario-function values (Fig. 4b). The vario function of the summer surface in area3 has one subordinate minimum less than the vario function of the spring surface (Fig. 4d and b), because the sastrugi in the valleys between the ridges have disappeared; the most significant max-min sequence is max₁ -min ₂ with pt2(max1, min₂) = p3 = p5 = 0.345 (Fig. 4d). In a comparison across seasons, we compare the largest pt2 values, so the summer value is slightly higher than the spring value (0.345 compared to 0.309).

In area4, in spring the ice surface was characterized by very evenly spaced and sized ridges and valleys (Fig. 2). Here, melting led to an increased complexity of surface forms (p2 = 0.222 in summer compared to 0.286 in spring); the large ridges are still the dominant features in this area (p2 = pt2 (max1,min1) is the largest pt2 value, and the associated spacing is approximately the same (3.6 m in summer compared to 4.2 m in spring)). The location of tracks is not exactly the same in both surveys. This means that the large ridge–valley system exists throughout several seasons (for at least 2 years). In conclusion, the ice surface in the ablation area undergoes seasonal changes that show in particular in the smaller-scale features, whereas the large (4 m spaced, up to 2 m high) features remain throughout several years. From comparison with analysis of area3 data, it follows that melting is a more dominant ice-surface-morphogenetic process than wind, as small sastrugi are at times observed between ridges, but disappear later in the year. The relief of the ridge-and-valley systems may increase as the result of a self-enhancing process, in an interplay of snowfall, wind and melting, with a dominance of surficial melting.