Radio-echo sounding (RES) is widely used for studying ice sheets, glaciers, and ice caps by sending electromagnetic waves in the radio frequency range into the ice and measuring the strength of the reflected signals as a function of time. An important observation in RES measurements is the azimuthal dependency of the return power, where the strength of the signal varies with the orientation of the polarization. This dependency is influenced by two distinct mechanisms: birefringence and anisotropic scattering . Both mechanisms can be indicative of ice properties critical to palaeoclimate and ice-dynamics research, and, while they may appear independently, they frequently coexist.

Birefringence is directly related to the preferred alignment of ice crystals, commonly known as crystal orientation fabric (COF) or lattice preferred orientation. Individual ice crystals are transversely isotropic about the crystal axis (c axis), with higher dielectric permittivity along the c axis compared to the basal plane. A systematic orientation of ice crystals in the polycrystal results in anisotropic electromagnetic and mechanical properties, along with birefringence. As electromagnetic waves propagate through ice, they decompose into two orthogonal wave components, each polarized with a principal COF axis . For nadir wave propagation (the standard setup in ice-sheet RES), these polarizations lie in the horizontal plane, assuming that one eigenvector is vertical. Horizontal anisotropy causes wave speed differences for these two wave components, which leads to travel-time differences of reflected signals for radar polarization parallel and perpendicular to COF axes . This effect can also manifest as double reflections in radargrams that are misaligned with the COF . Additionally, interference between the two waves leads to power extinction nodes when the phases are shifted by half a wavelength upon reception . In radargrams, these appear with a vertical spacing that depends on the strength of horizontal anisotropy and radar frequency and with an azimuthal periodicity of 90° in both co-polarized (transmit and receive polarizations are parallel) and cross-polarized (transmit and receive polarizations are perpendicular) measurements. In the absence of anisotropic scattering, co-polarized power extinction (CoPE) nodes emerge at an azimuth of 45° from the principal COF axis, while cross-polarized power extinction (XPE) aligns with COF axes see, for example, Fig. 5 infor an illustrative overview. This effect persists with a 90° azimuthal periodicity, even if none of the principal directions of the COF are vertical .

Anisotropic scattering describes the directional dependence of ice's scattering properties, which causes variations in signal intensity based on the orientation of the antenna. Scattering of radio waves in ice sheets arises from two main mechanisms: volume scattering, driven by small-scale inhomogeneities within the ice, and surface scattering, caused by reflections at internal interfaces e.g.. Volume scattering includes contributions from air bubbles, dust, and impurities and shows anisotropic characteristics when these scatterers are rotationally asymmetric, such as elongated air bubbles or small-scale fluctuations in horizontal permittivities related to COF . Surface scattering, on the other hand, takes place at reflection horizons typically linked to volcanic eruptions and climatic transitions ; material boundaries like water, air, or sediment inclusions ; or abrupt changes in COF . Anisotropic reflections may emerge when these interfaces exhibit directional roughness e.g. or involve transitions in COF with horizontal anisotropy . Importantly, anisotropic scattering is distinguishable from birefringence by its azimuthal periodicity of 180° in co-polarized return power, compared to the 90° periodicity associated with birefringence .

An important distinction must be made between horizontally anisotropic COFs causing birefringence and COFs that lead to anisotropic scattering. Horizontally anisotropic COFs are characterized by a large difference in their horizontal eigenvalues, causing strongly birefringent properties, and are typically found in dynamic areas of ice sheets. Examples of COFs with strong horizontal anisotropy include vertical girdles often found in flank flow e.g. or horizontal single maxima which develop in shear zones e.g.. The scattering property, however, seems to arise from variations in the directional relative permittivities (i.e. εx′, εy′) and not from the COF type itself. In other words, it is the noise of the horizontal eigenvalue distribution rather than the COF type that causes anisotropic scattering. For example, a horizontal single maximum could in theory be highly anisotropic without causing anisotropic scattering if it is perfectly constant with depth, while a weak girdle can cause stronger anisotropic scattering when the horizontal eigenvalues fluctuate with depth.

Azimuthal power fluctuations have been observed in previous airborne and ground-based polarimetric experiments, defined here as RES measurements including multiple polarization directions. Most of these studies have focused on identifying the horizontal component and orientation of electromagnetic anisotropy, typically associated with COF, and therefore relevant for ice-flow mechanics . This can be analysed using methods like CoPE and XPE node analysis , coherence phase analysis , or travel-time differences . CoPE nodes, in particular, can be valuable for estimating horizontal COF anisotropy over large areas, as they can also be observed in single-polarized radar measurements , the most common type used for large-scale airborne ice-sheet surveys. However, the presence of anisotropic scattering complicates these analyses by influencing the vertical elongation and azimuthal spacing of CoPE nodes, as well as the angular width of dipole nodes in coherence phase data . Therefore, understanding the role of anisotropic scattering is crucial for accurately interpreting COF anisotropy and birefringence signatures in radargrams.

In this study, we use ground-based quad-polarized (transmit and receive polarizations are sequentially rotated by 90°, resulting in two co-polarized and two cross-polarized modes) ultra-wideband RES data to quantify the relative importance of anisotropic scattering and birefringence effects in a dynamic region of the Greenland Ice Sheet (GrIS). Our study site (see Fig. ) is located in the onset region of the Northeast Greenland Ice Stream (NEGIS), near the East Greenland Ice-core Project (EastGRIP) drill site. The NEGIS region is of particular interest due to relatively fast ice flow reaching 55 ma-1 at the drill site; where deformation-induced anisotropic scattering mechanisms can be expected, and the COF is known to be highly anisotropic in the ice-stream centre . We synthesize the full azimuthal response from quad-polarized measurements, and then we use curve-fitting methods to determine the amplitude and orientation of 90 and 180° periodic co-polarized power fluctuations at different depths, with a spacing of 5 km along the radar lines. Our results show that anisotropic scattering dominates most of the survey area, especially within the ice stream and in ice from the Wisconsin period. Additionally, the strength and orientation of anisotropic scattering correlate with ice-sheet stratigraphy, with a sharp reversal in directionality at the 11.4 ka isochrone, marking the transition from Holocene to Wisconsin ice, at a depth of approximately 1300 m outside the shear margins. We propose that small-scale vertical variations in the COF are the most probable cause of the observed anisotropic scattering patterns, making the scattering orientation a direct indicator of COF orientation.

The RES data used in this study were recorded in June/July 2022 with a quad-polarized ground-based system. The radar operated at a centre frequency of 330 MHz with 300 MHz bandwidth and a chirp length of 10 µs. Eight channels from the digital system were divided into 10 amplifiers with peak transmit power of 150–250 W per amplifier, feeding a 10×10 element array. This setup formed a 2.7m×2.7m antenna resting on a balloon and was dragged over the snow surface at an average speed of ∼3 ms-1. A high-power switch coordinated the polarization of transmit and receive channels for quad-polarized recording (HH, HV, VV, and VH, where V denotes along-track polarization). The receivers were blocked during the 10 µs transmit time, corresponding to an approximate depth of 630 m for the first recorded returns. A detailed description of the radar system can be found in .

The radar survey was conducted along the lines shown in Fig. , which are mostly aligned parallel/perpendicular to the general southwest to northeast surface ice-flow direction and cover a distance of approximately 450 km, spanning the entire width of the ice stream. Figure  shows an example radargram (profile A in Fig. ) in the four polarization modes HH, HV, VV, and VH. Additionally, a circular radargram (turning circle) with an approximate radius of 50 m was recorded near the EastGRIP camp for testing purposes (Fig. c). Data processing followed a standard procedure including coherent integration, pulse compression, incoherent integration, channel integration, and interpolation to a consistent grid . While synthetic aperture radar (SAR) focusing of the RES data could improve some radargram sections, challenges related to irregular tracks and high bandwidth complicated motion compensation, limiting overall improvement. Consequently, SAR focusing was not employed. The final trace spacing after processing is approximately 25–30 m on average, while it is approximately 0.7 m in the turning circle.

Isochrones were traced manually for profiles A and B (Fig. ) and dated following . In doing so, the travel times were converted to depth using a velocity profile inferred from the relative dielectric permittivity obtained from dielectric profiling (DEP) of the EastGRIP core . The DEP complex-valued, ordinary relative dielectric permittivity, ε, was measured at 250 kHz at a resolution of 5 mm, starting at a depth of 13.7 m. We used a smoothed version of the real part of the dielectric record, ε′(z), to estimate the velocity profile in the upper 183 m by extrapolating to a surface value of εs′=1.55. Below the transition into pure ice at a depth of 183 m, we assume a constant relative permittivity in ice of εi′=3.15. The velocity profile is then obtained with 1c(z)=c0ε′(z), where ε′(z) is the relative dielectric permittivity and c0 is the speed of light. The age uncertainties generally increase with depth due to the timescale maximum counting error and because the existing timescale does not extend to the deepest layer traced here seefor discussion of uncertainties. The deepest traced isochrone (74.7 ka; see Fig. ) has an additional uncertainty from the layer tracing across the shear margin in profile B, particularly since the bottom part from 20 km and onward is heavily folded, causing ambiguity in matching the deepest isochrone inside and outside the shear margin.

The effects of anisotropic scattering and birefringence can be distinguished by their periodicity of co-polarized power anomalies, dPHH for definition, see Sect. S1 in the Supplement or. These patterns differ because the two mechanisms are governed by distinct symmetries.

Amplitude variations due to anisotropic scattering originate from variations in scattering properties within the ice that have a two-fold symmetry. This means that the returned signal is strongest in two opposite directions, resulting in a 180° periodicity when co-polarized antennas are rotated.

In contrast, birefringence splits the transmitted radar wave into two orthogonal components that travel at different speeds through anisotropic ice. The relative amplitude of these two wave components depends on the orientation of the antennas relative to the COF axes, while the phase difference depends solely on the degree of anisotropy but is independent of the antenna orientation. Interference between the two wave components modulates the return power. A 90° rotation of co-polarized antennas flips the amplitudes of the two components, but the interference pattern remains unchanged. Therefore, birefringence creates a 90° periodicity in the co-polarized signal .

Both mechanisms exhibit 90° periodicity in cross-polarized anomalies, dPHV, because the transformation of the polarization state, whether through scattering or birefringent phase shifts, inherently alternates every quarter-wave (90°), driven by the geometry of the polarization ellipse.

The full co- and cross-polarized angular response was measured by the radar in a turning circle with approximate diameter of 50 m in the vicinity of EastGRIP (Fig. c). Alternatively, this response can be synthesized from a single quad-polarization measurement using the method described in Eq. (11) of , which shows good agreement with the turning circle measurements (details in Sect. S2 in the Supplement). To assess the relationship between COF, birefringence, and anisotropic scattering, we compared power anomalies from a wave-propagation model , which uses the COF record from the nearby EastGRIP ice core, with both the turning circle data and the synthesized azimuthal response from a single quad-polarized measurement near the turning circle. In the model, we assumed that anisotropic scattering arises solely from vertical fluctuations in horizontal eigenvalues, and birefringence is defined by the observed eigenvalue differences (Sect. S1).

To quantitatively estimate the relative importance of anisotropic scattering (180° dPHH periodicity) and birefringence (90° dPHH periodicity), we then fit the sum of 90°- and 180°-periodic sinusoidal signals to dPHH as a function of azimuth θ: 2f(θ)=A180sin⁡(2θ+φ180)+A90sin⁡(4θ+φ90).

Figure  shows the average azimuthal co-polarized power fluctuations with the fitted function and the contributions of each component at five depth intervals. The relative importance of anisotropic scattering and birefringence is given by the fitted amplitudes A180 and A90, respectively, which are displayed on top of each panel in Fig. , and scattering direction is given by the fitted phases φ180 and φ90. For all three datasets, anisotropic scattering becomes increasingly important relative to birefringence with increasing depth, as the A180A90 ratio increases for all depth increments except between panels (g) and (j). Birefringence is only dominant in shallow depths, notably in the 0–500 m interval of the model output (panel a) and the 500–1000 m interval of the turning circle (panel b). Amplitudes of anisotropic scattering are generally higher in the model compared to radar observations, possibly because the relatively low sampling rate of COF measurements with depth may fail to capture a smoother, more continuous COF-depth function as it may occur in reality.

We now investigate the strength and orientation of anisotropic scattering on larger spatial scales by calculating the synthesized co- and cross-polarized power anomalies and coherence phase difference at intervals of 5 km along the remaining radargrams. We use the same curve-fitting procedure as in Fig.  to determine the orientation and strength of anisotropic scattering and birefringence effects for different depths. The synthesized response is calculated from an average over ∼100 m distance to improve signal-to-noise level, since the driving direction at the analysis points is reasonably constant and the subsurface properties are not expected to change significantly over the corresponding distance. The curve fitting was done at every 20 m depth on the synthesized angular response averaged over a 0.2 µs interval or ∼16 m depth. Figures  and show the co- and cross-polarized power anomalies and coherence phase, as well as the 90 and 180° amplitude–depth profile at every other analysis point (10 km spacing) for two example lines corresponding to profiles A and B in Fig. , respectively. The 90°- and 180°-periodic signal components of the fitted curves are displayed at 800, 1000, 1500, and 2000 m depth in the dPHH panels. Isochrone depths, corresponding to those traced in Fig. , are indicated in blue in the other panels.

The periodicity in the CoPE indicates whether anisotropic scattering or birefringence is dominating the radar response. Among all analysed points and depths, 80 % are dominated by anisotropic scattering, and at 57 % of these points, the 180° periodicity is twice as strong as the 90° periodicity. The lowest scattering dominance is found close to the shear margins and at intermediate depths (∼630–1500 m), where 59 % of the analyses within less than 3 km from the shear margins are dominated by a 180° periodicity. However, deriving strength and orientation of anisotropic scattering and birefringence in the vicinity of the shear margins is particularly difficult due to the overall decreased radar return power related to strongly folded layers. Abrupt changes in the scattering amplitudes often, but not always, coincide with the 11.4 ka isochrone depth indicating the Wisconsin–Holocene transition that is , for example, visible in the amplitude–depth profiles in Figs. a and f–i and d–h.

The orientation of the XPE in the cross-polarized power anomalies can indicate COF rotations . A notable azimuth rotation occurs at a depth of 1200–1400 m between 55 and 75 km in profile A (Fig. f and h), where the XPE is rotated by up to 45°. XPE azimuth rotations also appear particularly pronounced in profile B at 35 km and 55–65 km at depths between 1000 and 1300 m, possibly indicating a COF rotation (Fig. d, f, and g). Notably, the depths where these XPE rotations occur coincide with the depth of the 11.4 ka isochrone for all these examples, and in profile B they go along with an additional change in scattering orientation at the Wisconsin–Holocene transition.

The coherence phase reveals 90°-periodic dipole nodes, which, unlike CoPE nodes in dPHH, remain distinguishable as individual features even in the presence of anisotropic scattering. Anisotropic scattering primarily reduces the angular width of these nodes, providing an alternative indication of scatter strength . Anisotropic scattering appears, for instance, particularly strong at 5–55 km, 95 km in profile A (Fig. a–f and j), and 35–55 km in profile B (Fig. d–f). The vertical spacing between coherence phase nodes further visually indicates the degree of horizontal COF anisotropy in the survey area, corresponding to differences in horizontal eigenvalues. The integrated phase difference can in theory be used to derive horizontal eigenvalue differences, a method which works reliably in low-anisotropy areas e.g.. However, for strong COF anisotropy the depth differences between reflections of opposite polarization directions exceed the radar's range resolution, leading to loss of coherence . Although the phase coherence method could not be applied successfully to our dataset for deriving COF eigenvalues, reprocessing the data to reduce radar bandwidth might improve its applicability in future efforts, albeit at the cost of signal strength .

Figure  shows the orientation of the 180° periodic signal at depths of 800, 1000, 1500, and 2000 m, along with the apparent horizontal eigenvalue difference. The eigenvalue difference was determined using an automated process that measures the travel-time difference between the HH and VV traces. Specifically, the cross-correlation of each trace pair was calculated within a 20 m sliding window to estimate the time delay between signals. Linear regression was then applied to correlated reflections to obtain the depth-averaged apparent eigenvalue difference for method details, see. The uncertainty of this method increases when only shallow reflections are available or when the number of reflections is low. To ensure reliability, we only included results where at least 10 internal reflections could be correlated with a correlation coefficient above 0.6 and where at least one reflection lies below 1200 m depth. Results were discarded where these criteria were not met, particularly in areas with steeply dipping internal layers near shear margins.

The scattering direction in the ice-stream centre is oriented between 95 and 105° clockwise from the surface flow direction at depths of 1000–1500 m where scattering is strongest. Near the shear margins, scattering becomes less dominant and the orientation rotates, which is particularly visible in profile A, following close to the southwestern shear margin in Fig. . This rotation of scattering direction coincides with and explains the apparent reduction in horizontal anisotropy derived from travel-time differences, as HH and VV wave speed differences are maximized when aligned with the COF and minimized when misaligned. Outside the shear margins, the scattering orientation is close to flow-parallel at shallow depths (Fig. a) but rotates by approximately 90° for larger depths (Fig. b and c), notably in profile B in the northwestern corner of Figs.  and  at 35–75 km.

This reversal of scattering direction is also visible in the HH–VV power difference of the radargrams, demonstrated for profiles A and B in Fig. , which shows that the power difference clearly follows the ice-sheet stratigraphy. Positive (blue) values indicate increasing return power perpendicular to the driving direction, while negative (red) values indicate increased power parallel to the driving direction. For along-flow profile sections inside the ice stream (e.g. A1–A2, B1–B2, B4–B5), power differences tend to be positive in most parts of the ice column, indicating that the power return approximately perpendicular to ice flow (HH) is up to 10 dB stronger. Profile parts that were recorded perpendicular to ice flow (e.g. A2–A3, B2–shear-margin, B7–B1) show a negative power difference, confirming that more energy is scattered in the direction perpendicular to the flow (in this case VV). A notable change occurs at the 11.4 ka isochrone, marking the Wisconsin–Holocene climatic transition. Inside the ice stream (e.g. the 0–40 km section of profile A and the 0–10 km section of profile B), this transition is marked by an increasing HH–VV power difference, while outside the shear margins (20–70 km of profile B) the sign of the power difference is reversed. In this same section of profile B, a folded unit between the 65.8 and 74.7 ka isochrones is also characterized by different scattering properties and a reversed scattering direction compared to the overlying ice layers. Sections A3–A4, B2–B3, and B5–B6 show alternating signatures of positive and negative power difference, particularly pronounced in Holocene ice, which is a result of birefringence-induced beat signatures: birefringence causes a rotation of the polarization ellipsoid in and out of the profile plane, so the power alternates between being higher parallel (VV) and perpendicular (HH) to the profile direction. These birefringence-induced beat signatures are indicative of the misalignment of radar antennas and COF principal axes. The fact that strong beat signatures are mostly visible at shallow depths might be due to the loss of coherence at larger depths. In both profiles there is an approximately 200 m thick basal echo-free zone.

We observe the presence of both anisotropic scattering and birefringence effects at EastGRIP and in radar lines recorded within a radius of 50 km from the EastGRIP drill site, extending over the entire ice-stream width and beyond the shear margins. Notably, birefringence is most pronounced near the shear margins and at shallow depths but is often superimposed by anisotropic scattering which clearly dominates the azimuthal response in the ice-stream interior and exterior, particularly in ice units dating back to the Wisconsin period. In the following, we first discuss the origin of anisotropic scattering, then examine the relationship between observed backscatter properties and climate-induced ice characteristics, and finally explore the implications of our findings for inferring COF type and orientation.

We used curve-fitting methods to analyse the relative importance of anisotropic scattering and birefringence on the azimuthal power response in ground-based quad-polarized RES data collected in the NEGIS onset region. We found that the 180° periodic effect of anisotropic scattering dominates the co-polarized power anomaly in 80 % of the analysed locations and depths, while the 90° periodic signal of birefringence tends to be only dominant at depths of less than 1000 m and near the shear margins. We conclude that small-scale COF fluctuations, i.e. its variance or noise, with depth is the most likely cause of anisotropic scattering and that the scattering direction is likely aligned with one horizontal eigenvector. Scattering properties strongly follow the ice-sheet stratigraphy, indicating the potential to use quad-polarized measurements to identify ice units with different scattering properties, e.g. basal zones or ice from cold/warm climatic periods.

Our results are in agreement with previous studies which found anisotropic scattering being dominant over birefringence in highly dynamic areas, while the opposite is observed in slow-moving locations of ice sheets. This leads to challenges in deciphering the COF strength and direction from co- and cross-polarized extinction, and we leave a full inversion of quad-polarimetric data as proposed by for future work. While we are confident that anisotropic scattering is mostly related to COF here, it remains unclear how other physical parameters like impurity content and crystal size affect these scattering mechanisms in different ice units and different areas of ice sheets. Continuous high-resolution COF measurements of ice cores as well as larger-scale airborne polarimetric RES surveys would be beneficial for understanding the scattering properties of climatic transitions and mapping their distribution in ice sheets.