Introduction
Most of the Antarctic coast is covered by ice shelves comparising about 11% of the total area of Antarctica. In the transitional area between an ice shelf and an ice sheet, changes of ice property are expected to occur in the bottom and internal ice. The grounding line is defined as the boundary at which the ice bottom changes contact from rock to sea water, and it divides the ice shelf from the ice sheet. Changes in the ice-bottom property occur at the grounding line because of the interaction between ice and sea water. Accurate determination of the grounding-line position is necessary not only for predicting likely ic-sheet and ice-shelf respones to changes in climate, but also for understanding internal ice physics in this transitional area. Airborne radar observation, as well as being a useful way to examine the ice-bottom topography, can also be used to diagnose physical properties of the ice sheet. To determine the position of the grounding line, methods using a radio-echo sounder have been used, for example, a hydrostatic-balance equation using surface and bottom topography, amplitude change of the bottom echo (Reference Jacobel, Robinson and BindschadlerJacobel and others, 1994), and measuring the radio scatting strengh at the bottom of the ice (Reference Nishio and UratsukaNishio and Uratsuka, 1991). However, calculation of the sattering strengh is easily affected by other parameters, espacially what values in the ice are used for the attenuation coefficient, and data including many spikes. we previously reported and algorithmfor inferring dependence of scattering at the bottom of the ice on the angle of incidence. Preliminary results of this analysis showed that smooth bottom features were observed in the ice-shelf area far from the grounding line (Reference Uratsuka, Nishio, Olmac and MacUratsuka and others, 1989). This paper shows that the incidence-angle dependence of scattering coefficients at the bottom measured by radio-echo sounding confirms that the position of the grounding line can be determined by detecting different degrees of bottom roughness. This method complements the method of detecting differences in the scattering strengh caused by different underlunig materials.
Some work based on ice-core samples provided valuable information on vertical changes in internal structure such as three sources of the internal mass of the ice shelf: the accumulation of snow in this are, ice from the upsream ice sheet, and frozen sea water (Reference Wakahama and BuddWakahama and Budd, 1976: Reference OerterOerter and others, 1992). A wider survey is neccessary to understand how the internal structure of the ice shelf will be modified and the dynamics at the transitional region near the grounding line. Scattering detected by a radio-echo sounder can be used to examine internal ice structure. In most areas of the ice sheet, internal layer echoes that indicate the internal stratigraphy of the ice sheet are observed by radi-echo sounding. We analyzcd the occurrencc of these internal layer echoes and found that the areas where they are absent are concentrated at or close to the ice shelf.
Radio-Echo-Sounder Observation
The Sør Rondane Mountains are located at a bout 20–30° E, 71–73°S in east Antarctica. There is an ice shelf about 100 km north of the Sør Rondane MOuntain s. Whereas the southern side of the mountains is about 2000 m above sea level; thus the altitude of the mountainous ice shect along a north-south line changes by about 2000 m. Figure 1 is a map of the topography of this area with the flight lines taken for airborne radioecho-sounding measuremet. Observation with a 179 MHz airborne radio-echo sounder was carried out in the austral summer o f 1986 by the 27th Japanese Antarctic Research Expedition (JARE-27). Specifications of the radar are shown in Table 1. The resolution of the radar can be changed by choosing from three different pulse widths, and most of the observations used a 250 ns pulse (21m resolution in ice). The radar was able to measure ice up to 2500m thick. Digital data were accumulated with an on-board 0.25 in (0.63 cm) cassette recorder, along with the aircraft navigation data: Omega and GPS (position), radio and pressure altimeter (altitude) and gyroscope (attitude). A more detailed description of the radars system is given by Reference Uratsuka, Nishio, Olmac and MacUratsuka and others (1989).
Fig. 1. Surface topography and flight lines of radio-echo-sounding observations around the Sor Rondane Mountains.
Table I. Specifications of the radio-echo sounder
Bottom Scattering Characteristics
Bottom Scattering Characteristics in the Ice Shelf
The bottom features of ice shelves are very important for understanding the mass balance of ice sheets (Reference ThomasThomas, 1979) because ice and sea water interact at the ice-shelf bottom (Reference MorganMorgan, 1972). In particular, the roughness of the ice-shelf bottom is an indication of the interaction between ice and sea water. Reference NealNeal (1979) ivestigated the smoothness of the bottom of the Ross Ice Shelf using an “ESM recording” of radio-echo sounding. Other research investigating bottom features of ice shelves by radio-echo sounding has also been reported (Reference Shabtaie, Whillans and BentleyShabtaie and others, 1987; Reference Jenkins and DoakeJenkins and Doake, 1991). These reports discuss the reflection coefficient from bootom echoes. Generally, the scattering coefficient, which is defined in radar equations (e.g. Reference Ulaby, Moore, Moore adn and FungUlaby and others, 1982), is used for discussing the properties of the target plane. The scattering coefficient describes the effects of both boundary roughness and difrerences in the medium below the ice, and is dependent on the incidence angle. If the target plane is very smooth comparable to the radar wavelength, the scattering will be specular and the incidence-angle dependence will be restricted in the small incidence-angle range. In the extreme case of a smooth surface, the reflection coefficient calculated in the equation in, for example, Reference Shabtaie, Whillans and BentleyShabtate and others (1987) is approximately the same one defined in plane-wave theory, and independent of the radar pulse width. The Fraunhofer criterion shown below is a more quantitative indicator of speculat scattering (Reference Ulaby, Moore, Moore adn and FungUlaby and others, 1982):
where θ is the incidence λ is the wavelength, and Δh is the root-mean-square height deviation. Assuming a 179 MHz frequency, the mean roughness value of the Fraunhofer criterion is less than about 5 cm in the nadir direction. As a larger deviation of Δh is possipble in the area illuminated by the same pulse-range gate, it is better to use scattering coefficients defined from a radar equation rather than as reflection coefficients.
When the radar system has a wide antenne-beam patten rather than a pulse-illuminated area, the echo shape formed by the scattering signal is strongly dependent on the incidence angle. The incidence angle can be calculated from the delay time, and the scattering coefficient can be inferred using an appropriate radar equation. In the case of an ice sheet, the radar equation should include the effect of refraction at the air/ice interface. Reference Uratsuka, Nishio, Olmac and MacUratsuka and others (1989) proposed a radar equation which satisfies the above conditions, as follows:
Here, σ° is the scsttering coefficient of the incidence angle at the ice-sheet bottom, n is the refractive index, z is the ice thickness, and θ2 is the refractive angle (equal to the incidence angle at the bottom), which through Snell’s law is related to θ1, the angle of incidence on the surface. We define
In addition, these geometrical parameters should be related to the delay time t as follows:
Other parameters are defined as follows: Pr is received power; Pt transmitted power; G is antenna peak gain; f(θ1) is normalized antenna pattern; λ is wavelength (= 1.67 m); τ is pulse width; c is light speed; δ is penetration depth; H is airplane altitude; L is system loss.
Reference Uratsuka, Nishoi, Mae, S, Paren, Sackinger and WadhamsUratsuka and others (1990) reported the incidence-angle dependence of scattering coeffients along a flight line in the ice-shelf area and concluded that specular scattering, inferred by the incidence-angle dependence of the scattering coefficient, increases with distance from the grounding line. Here, we examine differnces in the smoothness of a grounded ice bottom and a floating ice bottom very close to the grounding line.
Bottom Scattering Characteristics Near the Grounding Line
A tentative grounding line is shown as the dashed line in Figure 1. This line was determined by comparing the ice-bottom topography measured by a sounder and calculated by the hydrostatic equation:
where dis the inferred ice thickness and h is the measured elevation of the ice surface above sea level (Reference Nishio and UratsukaNishio and Uratsuka, 1991). Scattering coefficients that are within 1 km of this tentative grounding line on the inland and ice-shelf sides are plotted in Figure 2. These plots are derived from Equation (2) and (3), using the data from the A–1, −2, −11, −12 and −13 flight lines shown in Figure 1. As Figure 2 shows, the scattering features from the inland-ice side anf from the ice-shelf (floating-ice) side aretypically different. In the incidence-angle range of 10–20°, scattering coefficients of ice from the inland side are 5–10 dB greater than those of floating ice. IN this analysis, we did not calculate the scattering coefficients at incidence angles of less than 10° because then the scattering signals arrived at the receiver simultaneously. The values of the scattering coefficients are sensitive to the attenuation coefficients and these are assumed to be constant in depth. Reference Nishio and UratsukaNishio and Uratsuka (1991) discussed the relationship between the grounding line and the scattering coefficients at the nadir incidence (σ°(0): mean value at incidence angles of 0–10°) of the ice-shelf bottom along a flight line (A-13) using Equations (2) and (3). They showed that σ°(0) of floating ice is about 10–20 dB higher than that of inland ice. This difference may be caused mainly by the differences in media:rock or water. The position of the grounding line determined by Equation 4 agreed with that determined by radar analysis to within a few kilomaters. Based in this, we suggested that scattering coefficients are a good indicator of the position of the grounding line. However, the distribution of scattering coefficients along a flight line includes many spikes, which are caused primarily by error in the inferred attenuation coefficient. Figure 2 confirms that differences in the ice bottom exist not only in terms of the contrasing material but also in terms of roughness. Information from scattering in the nadir direction σ°(0) and the incidence angle dependence σ° (θ) is complementary. Combining this our present results shown in Figure 2 suggests a very steep dependence of the the scattering coefficient on the incidence angle in the range 0–20°. These results suggest that a boundary of strongly specular scattering exists very close to the grounding line.
Fig. 2. Incidence-angle dependencies of scattering coefficients near grounding line determined using Equations (2) and (3). Upper panel (a) summarizes the data from a zone 1 km inland of the grounding line. Lower Panel (b) summarizes the data from a zone 1 km on the ice-shelf side of the grounding line.
Double-Trip Echoes
ON the ice shelf, double-trip scattering echoes were often observed. Double-trip echoes occur when the pulse reflects twice from the ice/water interface and once from the ice/air interface. Double-trip echoes are indicative of relatively low power loss due to attenuation in the ice and/or specular scattering. As shown in Figure 3, doubletrip echoes are observed only on the ice/shelf area, and their appearance begins at the groundind line in some observations. Though the bottom part of the ice shelf consists of saline ice which attenuates radio waves, radar reflections are stronger there. This strong signal appears to be due to specular scattering. These results are consistent with Reference Uratsuka, Nishoi, Mae, S, Paren, Sackinger and WadhamsUratsuka and others (1990) and Reference Nishio and UratsukaNishio and Uratsuka (1991).
Fig. 3. Appearance of double-trip echoes: thick lines indicate occurrence and duration of the double-trip echoes along the flight line.
Occurrence of Internal-Layered Echoes
A differntial filtered Z scope (DFZ) is very useful for studying the layered echoes within internal ice. The DFZ image is produced using the first derivative of the received power against the vertical distance. In about 70% of our observations, internal layers are detected using DFZ images. This filter process clearly shows the peaks of echoes and reduces the wide dynamic range of a radar signal to a limited dynamic range for disply. As such, these filtering effects emphasize the leading edge of echoes, but the strength of an image is no longer proportional to the scattering strength. It is importtant to take these filter effects into account when discussing the occurrence of internal-layer echoes detected by DFZ images. To avoid confusion due to ferminology, we define the “internal layer” as a physical layer of ice, the “internal echo” as the echo signal from internal ice, the “layered echo” and “internal-layered echo” as layered characteristics in the internal echo, and the “DFZ image” as the differential filtered image between the ice-surface echo and the ice-bottom echo. We have to distinguish strictly between the layered echo and the layered pattern which is shown by DFZ, because in some cases the layered pattern shown results from a mixture of internal ice and surface features that originate in the same range gates owing to the wide beam antenna of the ragar system.
Classification of DFZ Images
To avoid being misled by instrumental disturbances, filtering effects or confusing surface echoes, we classified the DFZ images into four categories according to their layered pattern, echo strength and other characteristics. Type A is assigned when tupical layer echoes exist. As shown in Figure 4a, the layer pattern is contininous and the echoes occurat regular intervals. Type B is assigned in a less typical case, though internal echoes can be distinguished from other echoes as shown in Figure 4b. This case includes echoes which are not always multiple-layered or stratified, but obviously have internal caused. An example of type C is shown in Figure 4c where it is difficult to distinguish the echoes caused by various factors such as surface topography or rocks on the surface. Images affected by instrumental problems for any reason are classified in type D. Instrumental problems occurred when the ice sheet was too shallow to distinguish the surface echo, when the image was obtained with a 60 ns pulse width which too short to digitize, when the aircraft was changing direction, or when the aircraft altitude suddenly changed. Finally, we define images where the pattern is random and no apparent layering exists as type E (see Fig. 4d).
Fig. 4. Examples of DFZ images: (a) Typical case of layered echoes (type A); (b) Example of type B: only one obvious stratified echo is found: (c) Multiple echoes appear to have an internal origin, but may be caused by a surface feature (type C): (d) No layered structure was found (type E). Every horizontal distance in these figures is 14.0 km. Sampled points are shown in Figure 5.
Fig. 5. Map of layered echoes:
After rough surveying using the image pattern, we examined differences except type D. We found, for example, that strong surface echoes sometimes exceed the internal-layered signal level and prevent the internal layering from appearing in the DFZ image. This kind of DFZ image was reclassified as type D. The change from type A or B to type E is very sudden and the signal level becomes weaker. After detailed examination of the echo strength of type E, however, this does not mean that no scattering existed in the internal ice, but only that any layered or structured patterns were not observed. It may be possible to detect layered echoes with different instruments that use different radio frequencies or a finer resolution. The results from along the flight lines are plotted according to the above classification on the topogralhic map shown in Figure 5.
Occurrence of Layered Echo
From Figure 5, we can see that except for the areas where there was an instrumental (type D) or surface-feature disturbance (type C) problem, internal echoes are continuously observed in most of the area. However, no layered echoes are observed at or near the ice shelf. Reference HarrisonHarrison (1973) reported that the appearance of internal-layered echoes was very rare in the Ross Ice Shelf region, but he concluded that this was due to a radar problem. However, no serious instrumental problem occurred during our observation of the ice shelf. The transition from the presence of internal layers to their obsence is very clear along a topographic contour line of about 600 m, which is about 20–30 km inland from the grounding line.
Internal echoes also failed to appear where flight lines were perpendicular to the inferred flowline, for example, around 21°E, 71°40′S (site (e), Fig. 5) and around 22° E, 72°25′S (site (f), Fig. 5). Antennas of the radar system were installed under the wings of the airplane, and the electric-field direction was along the direction of the airplane heading. That is, the antenna polarization of the radar was in the same direction as the flight line.
Discussion
The boundary between the appearance and the absence of layered echoes is about 20 –30 km inland from the grounding line. Clearly the absence of internal layers is not caused by the influence of sea water, and we have elimination the possibility of an onsatumental problem.
It is interesting that layers at all depths disappear at the same point. If separation of the internal layers is smaller than the radar resolution, which depends on the pulse and beam widths, neighboring peaks will be fused. This is plausible if a tendency towards narrower separation is observed. However, we did not find such a tendency. Observation using differnt radio freauencies may show a different boundary, but the internal ice change which causes the absence of layered echoes may occur at a point in the inland ice sheet far from the grounding line. Reference Fujita and MaeFujita and Mae (1994) proposed that the internal layered echoes are caused by a vertical change in the fabric pattern or acidity. They estimate that scattering due to fabric-pattern change is larger than that due to acidity change at a frequency of 179 MHz. The internal-layer echoes seem likely to disappear near the grounding line due to deformation of the fabric. Deformation of the fabric can also occur inland from the grounding line due to other strong forces such as tides.
Internal ice change also causes a polarization effect, as discussed in detail in the next sub-section. Reference Woodruff and DoakeWoodruff and Doak (1979) showed that the polarization of radio echoes from the ice-shelf bottom changed between inland and floating ice because of a different propagation effect. They suggest that this difference was caused by the effect of tidal strain on crystal orientation. However, the ice thickness at the grounding line is less than 1000 m in our case, much smaller than the distance from the grounding line to the boundary line where the echoes stop appearing. Therefore, the difference is difficult to explain by tidal force.
It should be noted that other radar observations of a lower frequency in the ice shelf reported the existence of internal layers (Reference Jacobel and BindschadlerJacobel and Bindschadler, 1993). Also, it is difficult to explain the isolated layer at about 22°E, 75°S in our data (site (g), Fig. 5).
Polarization Problem
The region along the line from 26°E, 71°20′S to 28°E, 70°50′S (around mark (d), Fig. 5) may also be explained by the polarization effect.
We already suggested in the last paragrph of the previous section that the internal-layer disappearance relates to the angle between the ice-flow direction and polarization of the radar antenna. Reference Fujita and MaeFujita and Mae (1993) reported that the internal signal strength depended on the antenna orientation, when using a 179 MHz ground-based radio-echo sounder. Further analysis by Reference Maeno, Fujita, Kamiyama, Motoyama, Furukawa and UratsukaMaeno and others (in press) found that the attenuation in ice depended on the antenna direction, and the antenna direction of maximum attenuation was along the flow direction. The above two results were obtained by experiments in which co-polarized antennas were rotated at the same spot. In our case, the tendency of the echo strength is similar to the above results, but is not as clear, since we did not control the antenna orientation at the same point. Controlled experiments are necessary of confirm the relationship between the appearance of layered structure in the radar signal and antenna direction. A theoretical approach may provide useful ideas. Some models are proposed to investigate depolarization by internal ice layers (Reference Woodruff and DoakeWoodruff and Doak, 1979; Reference Liu, Bentley and LordLiu and others, 1994). Howevber, they have no results on the internal layer’s appearance.
Conclusion
We examined the basal characteristics near the grounding line using radio-echo-sounding data. The scattering coefficients of the nadir direction changed when very close to the grounding line, the position of which we had previously determined by hydrostatic balance. The difference in scattering strengh was due to the different material below the ice and changes in the bottom reoughness. In this paper, a clear difference in the smooth-bottom features was detected a few kilometers from the grounding line using radio-echo-sounding data to analyze the incidence-angle dependence of the scattering coefficient. This smoothness that begains at the grounding line seems to be caused by the effect of sea water unde5r the ice sheet. The appearance of double-trip echoes supports this belief. Detecting differences in bottom roughness complements detecting differences in the scattering strengh due to different underlying materials. To date, a combination of these methods allows us to determine the position of the grounding line to within a few kilometers. On the other hand, the absences of the internal layer were found in the ice shelf about 20–30 km inland from the grounding line through the classification of the DFZ image according to the appearance characteristics of the internal layer and echo strengh. This fact suggests the internal change forward ice shelf occur at this point. Another disappearance to the ice-flow direction. This polarization problem should be theorectically and experimentally examined in detail.
Further investigation is necessary to explain the above results and the mechnanism of the internal layer.
Acknowledgements
We thank Professor Y. Naito of the National Institute of Polar Research, Tokyo, who was the leader of JARE-27. We also thank Dr K. Okamoto, Director of the Global Environment Division at the Communications Research Laboratory, Tokyo, for his encouragement, and Dr S. Fujita of Hokkaido University for many stimulating discussions.
