Unusual Radar Echoes from the Greenland Ice Sheet

Airborne radar images of part of the Greenland ice sheet reveal icy terrain whose radar properties are unique among radar-studied terrestrial surfaces but resemble those of Jupiter's icy Galilean satellites. The 5.6- and 24-centimeter-wavelength echoes from the Greenland percolation zone, like the 3.5- and 13-centimeter-wavelength echoes from the icy satellites, are extremely intense and have anomalous circular and linear polarization ratios. However, the detailed subsurface configurations of the Galilean satellite regoliths, where heterogeneities are the product of prolonged meteoroid bombardment, are unlikely to resemble that within the Greenland percolation zone, where heterogeneities are the product of seasonal melting and refreezing.

benzene was fixed at its 6-31 G**fl6-31 G** geometry, and the M+4**benzene intermolecular separation was optimized in C6, symmetry. For both models used in the calculations of the 2:1 complexes, the cation was sandwiched between two staggered, face-to-face benzene molecules (each fixed at the 6-31G**//6-31G** monomer geometry) along the vector connecting the centroids of the rings. Model maintained D6d symmetry constraints, whereas in model 11, C6, symmetry was maintained. These calculated gasphase structures were then used in the solution studies. 15. All solution studies were performed at constant temperature (298 K) and pressure (1 atm) with the use of statistical perturbation theory (25) and the program BOSS (26). The complexes were treated as a single solute and placed at the center of a box 20 A on a side containing 260 TIP3P water (27) molecules. Periodic boundary conditions were applied, and an 8.5 A cutoff was used. A series of four simulations with double-wide sampling were performed for each system with 9 x 105 steps of equilibration, followed by averaging over 2 x 106 configurations. The OPLS parameters for benzene were optimized previously for benzene-water simulations (28), and parameters for the cations M+ had been optimized to repro-duce relative hydration energies (29). The high quality of these parameters is seen in a comparison of the calculated and experimental relative aqueous solvation energies (respectively, in kilocalories per mole): Li+/Na+, 24.5 versus 23.9; NaC/KC, 17.0 versus 17.6; and KC/Rb+, 5.6 versus 5.1. However, when used to calculate gasphase M+4**benzene binding energies, the OPLS parameters give poor quantitative agreement with the ab initio results. As such, we felt it would be inappropriate to relax the M+.-benzene distance during the aqueous simulations because the OPLS parameters may lead to incorrect energies or geometries. Thus, we adopted a combined approach (Fig. 1) in which the binding energies were taken from the gas-phase calculations, and statistical perturbation theory was used to determine the relative solvation energies of the various species with fixed geometries. Relative free energies of hydration were determined through stepwise perturbation of one alkali metal complex into another. Because the overall perturbations were relatively small, a fairly large step size (X = 0. 125) was used. Perturbations in the 1:1 complexes involved the mutation of Na+ to Li+ and K+ to Na+ Unusual Radar Echoes from the Greenland Ice Sheet E. J. Rignot, S. J. Ostro, J. J. van Zyl, K. C. Jezek Airborne radar images of part of the Greenland ice sheet reveal icy terrain whose radar properties are unique among radar-studied terrestrial surfaces but resemble those of Jupiter's icy Galilean satellites. The 5.6-and 24-centimeter-wavelength echoes from the Greenland percolation zone, like the 3.5-and 13-centimeter-wavelength echoes from the icy satellites, are extremely intense and have anomalous circular and linear polarization ratios. However, the detailed subsurface configurations of the Galilean satellite regoliths, where heterogeneities are the product of prolonged meteoroid bombardment, are unlikely to resemble that within the Greenland percolation zone, where heterogeneities are the product of seasonal melting and refreezing.
It has been known since the 1970s that radar echoes from the icy Galilean satellites are extraordinary (1). The radar reflectivities (2) of Europa, Ganymede, and Callisto are several orders of magnitude greater than those recorded for comets, the moon, the inner planets, and nonmetallic asteroids, and they show little dependence on the radar wavelength. In addition, the circular polarization ratios juc of the icy satellites E. J. Rignot, S. J. Ostro, J. J. van  Propulsion Laboratory airborne syntheticaperture radar (AIRSAR) instrument above a vast portion of the Greenland ice sheet called the percolation zone ( Fig. 1), where summer melting generates water that percolates down through the cold, porous, dry snow and then refreezes in place to form massive layers and pipes of solid ice (8). The radar observations were collected simultaneously at 5.6-, 24-, and 68-cm wavelengths, and the complete scattering matrix (9) of each resolution element was measured at each radar wavelength. At the time of the radar flight, ground teams recorded the snow and firn (old snow) stratigraphy, grain size, density, and temperature (10) at ice camps in three of the four snow zones identified by glaciologists to characterize four different degrees of summer melting (8). Figure 2 shows average values of the radar reflectivity o0RL (2), loc, and FL obtained from AIRSAR measurements at the Crawford Point site in the percolation zone.
At 5.6 and 24 cm, Jr was higher than unity at an incidence angle 0 of 180, decreased toward higher incidence angles, and showed few spatial features. At 68 cm, CORLwas 1/10 as large but showed kilometerscale spatial variations. At 5.6 and 24 cm, 1C was larger than unity for incidence angles larger than 300 and 450, respectively, increasing to 1.6 and 1.4 at 660. At 68 cm, gc was everywhere less than 0.8 and dropped as low as 0.1 in some places, with kilometer-scale spatial variations negatively correlated with those observed in the radar reflectivity images. At 5.6 cm FL was as large as 0.46 and at 24 cm it was 0.22, but it remained less than 0.1 at 68 cm.
In the AIRSAR scenes of the Swiss  cm, and pc was < 1 at 68 cm, indicating a change in the scattering process at the longer wavelengths, whereas 70-cm estimates of p.c for the icy satellites apparently exceeded unity (12). Also, p.c for the percolation zone decreased significantly at incidence angles from 660 to 180, whereas no such difference has been noticed for the icy satellites (see the caption for Fig. 3); and JpLis a much stronger function of the incidence angle for the percolation zone than in the case of the icy satellites (1). Several years ago, Zwally (13) suggested that ice inclusions could be responsible for the low emissivities measured for the percolation zone by spaceborne microwave radiometers. Since then, surface-based radio sounding experiments, and airborne active and passive microwave measurements (14), have supported the hypothesis that volume scattering from subsurface ice layers and ice pipes is the major influence on the radar returns. Recent surface-based radar observations conducted at Crawford Point (10) at 5.4 and 2.2 cm further indicate that, at incidence angles between 100 and 700, most of the scattering takes place in the most recent annual layer of buried ice bodies. Figure 4 shows a representative example of firn stratigraphy in the percolation zone in early summer. Ice bodies generated from a previous summer melt are found 1.8 m below the surface. Ice layers, a millimeter to a few centimeters thick, extend at least several tens of centimeters in diameter, parallel to the firn strata (8). Ice pipes, several centimeters thick and several tens of centimeters long, are vertically extended masses reminiscent of the percolation channels that conduct meltwater down through The fact that radar returns measured at 68 cm are significantly weaker and have lower polarization ratios than those at 5.6 and 24 cm suggests that the discrete scatterers responsible for the radar echoes are typically less than a few tens of centimeters thick, similar to the scales of the solid-ice inclusions. The 68-cm echoes probably are dominated by single reflections from deeply buried layers of denser firn or concentrated ice bodies, whereas the 5.6-and 24-cm echoes probably are dominated by multiple scattering from the ice layers and pipes in the most recent annual layer. The relatively sharp decrease in pc and FL for 0 < 400 perhaps reveals the presence of a strong, specular reflection from the ice layers at small incidence angles, which is also suggested by the strong dependence of radar reflectivity on incidence angle. Ice layers and pipes also form in the soaked zone, but the snow there is so saturated with liquid water that the radar signals are strongly attenuated, cannot interact with the buried ice formations, and hence yield echoes with low reflectivities and polarization ratios. In the dry-snow zone, the snow is cold, porous, clean, and therefore very transparent at microwave frequencies but does not contain solid-ice scatterers that could interact with the radar signals.
For the icy satellites, no in situ measurements exist or are planned, but theoretical interpretations favor subsurface volume scattering as the source of the radar signatures. Hapke (15) suggested that the mechanism responsible for the satellites' radar behavior is the coherent backscatter effect, also known as weak localization (16), which has been observed in laboratory-> I 8  figure 10 of (1)1. Disk-resolved echo spectra, which are equivalent to brightness scans through a slit parallel to the projected spin vector, show hardly any variation in lc across the satellite disks [figures 2 and 3 of (1)]. For Greenland, points (squares) are averages of measurements that span incidence angles 0 from 180 to 66°. Of the projected area, 10% is at 0 < 180 and 17% is at 0 > 660.
controlled experiments of scattering of light from weakly absorbing, disordered random media. Coherent backscattering can theoretically produce strong echoes with gc > 1 (the helicity of the incident polarization is preserved through multiple forward scattering) and FL 0.5, provided that (i) the scattering heterogeneities are comparable to or larger than the wavelength (17), and (ii) the relative refractive index of the discrete, wavelength-sized scatterers is smaller than 1.6 [ figure 9 of (18)1. As noted by Ostro and Shoemaker (19), prolonged impact cratering of the satellites probably has led to the development of regoliths similar in structure and particle-size distribution to the lunar regolith, but the high radar transparency of ice compared with that of silicates permits longer photon path lengths and higher order scattering. Hence, coherent backscatter can dominate the echoes from Europa, Ganymede, and Callisto but contributes negligibly to lunar echoes. Similarly, the upper few meters of the Greenland percolation zone are relatively transparent (unlike the soaked zone) and, unlike the dry-snow zone, contain an abundance of solid-ice scatterers at least as large as the radar wavelength, with a relative refractive index of -1.3, so coherent backscatter also can dominate the echoes Width (cm) Fig. 4. Snow stratigraphy at Crawford Point on the day of the AIRSAR observations. Snow grain diameters are less than 1 mm in finegrained snow and more than 1 mm in coarsegrained snow. The average snow density is 0.2 g/cm3 in the top 40 cm and 0.4 g/cm3 between 40 and 200 cm. Wind crusts are paper-thin layers of firmly bonded, fine-grained snow. Depth hoar consists of large, skeletal crystals formed in snow strata by crystallization directly from water vapor when a temperature gradient exists in the snow.
there. However, it seems unlikely that the detailed subsurface configurations of the satellite regoliths, where heterogeneities result from meteoroid bombardment, would resemble that within the Greenland percolation zone, where heterogeneities are the product of seasonal melting and freezing.
We conclude that a variety of natural subsurface configurations can yield exotic radar properties. Given the increasing number of solar system surfaces (5-7) characterized by high radar reflectivities and polarization ratios, it is desirable to define as accurately as possible the physical constraints provided by the radar measurements. The Greenland percolation zone constitutes a uniquely accessible, natural laboratory for studying exotic radar scattering processes in a geological setting. Direct sampling and high-resolution, multiwavelength radar imaging of that terrain could reveal the detailed relation between radar signature and subsurface configuration, thereby furnishing a modicum of ground truth for interpreting echoes from extraterrestrial surfaces.  (6) is conceptually similar to the UKT14 instrument but offers the advantage of seven spatial elements arranged in a six-element daisy pattern around the central channel. Each beam has an HPBW of 12 arc sec at 1300 pLm. At IRAM, the sky-chopping secondary was set to an east-west throw of 45 arc sec at a frequency of 2.0 Hz.
Accurate pointing for each observation was determined by offsetting to the calculated PCS position (7) after the use of a Gaussian fit routine to center on bright, nearby millimeter point sources. The telescope pointing errors derived from pointing checks on these nearby sources were 1 to 2 arc sec root mean square; these are small compared to the telescope beam size.
Uranus was used to calibrate the measured flux density for the 1991 JCMT and 1993 IRAM observations. Jupiter was used to calibrate the 1993 JCMT observations. We used the standard submillimeter telescope correction algorithm to compensate for finite-size effects of Uranus and Jupiter in the telescope beam. We adopted brightness temperatures for Uranus of 92.5 and 97.5 K at 1100 and 1300 pm, respectively. For Jupiter we adopted brightness temperatures of 148.5, 162.5, 170, and 170 K at 450, 800, 1100, and 1300 pLm, respectively. We (8). At IRAM, telescope elevation scans called sky dips were routinely made to characterize the telluric opacity. The 1300-pm zenith opacities for our observing sessions are given in Table 1. The maximum angular separation between Pluto and Charon is only 0.9 arc sec; hence our measurements represent the combined flux density from both Pluto and Charon (Table 1). Figure 1A depicts this set of measurements, along with Altenhoff and colleagues' 1300-1Lm grand average of 15 + 1.4 mjy made in 1986. The January and February 1993 observations were of the same hemisphere of Pluto. The combination of our multiple observations gives an error-weighted detection of 10.5 ± 5.1 mJy at 1300 pLm. At 800 pum we detected 33 ± 7 mjy from the PCS.
To invert our measurements and derive a temperature solution for Pluto, we first write the total flux density from Pluto and Charon as the superposition of the flux from their two gray-body Planck functions