C-band SAR can operate during both day and night, penetrate clouds, and penetrate thin, dry snow (Bürgmann et al., 2000; Sun et al., 2015). Both InSAR and SAR feature tracking (in original range–azimuth coordinates) can provide measurements of surface motion in the radar line-of-sight (LOS) direction.

InSAR relates the phase offset from successive SAR acquisitions to surface displacement, potentially with mm-level accuracy (Bürgmann et al., 2000; Rosen et al., 2000). InSAR has frequently been applied to measure displacement of ice-rich features, including glaciers and ice sheets (Massonnet and Feigl, 1998; Rosen et al., 2000), rock glaciers (Bertone et al., 2022), and permafrost (Zhang et al., 2022). Recently, InSAR has also been applied to quantify surface movement of glacial lake dams (Scapozza et al., 2019; Yang et al., 2022, 2023; Jiang et al., 2023; Yu et al., 2024).

While InSAR offers unparalleled precision, several factors can reduce measurement accuracy, including atmospheric noise, layover, and radar shadow. InSAR requires (1) coherent surface change with similar scatterer characteristics between radar acquisitions, and (2) sufficiently small phase-change gradients between adjacent pixels to allow reliable phase unwrapping (Itoh, 1982; Handwerger et al., 2015). While errors caused by atmospheric conditions and acquisition geometry can be avoided or corrected, errors caused by rapid surface change may cause underestimation of true LOS surface velocity. InSAR coherence, a unitless measure of the “sameness” of surface scatterers between acquisitions, can be used to discriminate between reliable and unreliable InSAR measurements (e.g., Schmidt and Bürgmann, 2003). InSAR coherence can also be used to identify significant change in surface characteristics, and low coherence has been used to map the extent of desert erosion (e.g., Cabré et al., 2020), landslides (e.g., Ohki et al., 2020; Jacquemart and Tiampo, 2021), flooding (e.g., Chini et al., 2019), and debris-covered glaciers (e.g., Atwood et al., 2010; Frey et al., 2012; Lippl et al., 2018).

Feature tracking (pixel offset) techniques offer an alternative method to retrieve surface displacement measurements from SAR data when InSAR is not possible due to loss of coherence or large displacement gradients between adjacent pixels. Feature tracking involves 2-D cross-correlation of backscatter amplitude values in successive radar images to measure offsets in the range (across-track) and azimuth (along-track) directions. This technique has been used to measure glacier surface velocity (e.g., Fahnestock et al., 1993; Strozzi et al., 2002, 2008; Fahnestock et al., 2016) and fast-moving features surrounding glacial lakes (Scapozza et al., 2019; Yang et al., 2022). While feature-tracking measurements offer lower resolution and precision than InSAR measurements, and measurement quality can be degraded by large surface changes, they are more robust to large surface displacements and rapid surface change (Joughin, 2002; Zheng et al., 2023).

Here, we present a method to create a single cumulative displacement time series from InSAR and feature tracking measurements using a variation of the small baseline subset approach (SBAS; Berardino et al., 2002; Schmidt and Bürgmann, 2003). The SBAS approach uses a network of displacement observations to solve for the displacement of a given pixel between successive acquisitions. It was developed for InSAR interferograms (Berardino et al., 2002) and has subsequently been applied to SAR feature tracking (e.g., Casu et al., 2011; Euillades et al., 2016; Guo et al., 2020; Samsonov et al., 2021) and optical feature tracking offsets (e.g., Bontemps et al., 2018; Altena et al., 2019; Lacroix et al., 2019). The SBAS approach, however, has issues during periods with poor coherence between successive acquisitions, which can introduce errors in the resulting displacement time series. This limitation has previously been addressed by constraining the time series inversion using geophysical constraints parameterized in time (López-Quiroz et al., 2009) and spatial covariance (Jolivet and Simons, 2018). We address this issue by constraining the per-pixel InSAR time series inversion with additional observations from SAR feature tracking, which is more robust to decorrelation than InSAR. Our approach does not require prior assumptions about the displacement patterns of pixels over time.

Previous studies combined InSAR and feature tracking to produce self-consistent surface displacement maps over large ice sheets and ice caps, where surface velocity is often too fast for InSAR alone (e.g., Joughin, 2002; Gray et al., 2005; Liu et al., 2007; Sánchez-Gámez and Navarro, 2017; Joughin et al., 2018). To our knowledge, no studies have combined these techniques to measure year-round surface displacement of ice-cored moraine features, where we expect seasonal variability in surface melt rates and associated debris reworking.

To extract surface displacement information from the Sentinel-1 SLC products, we generated both interferograms and feature tracking offsets using the Hybrid Pluggable Processing Pipeline (HyP3) ISCE2 Plugin (Hogenson et al., 2025), which enables batch processing with the Jet Propulsion Laboratory InSAR Scientific Computing Environment, ISCE version 2.6.3 (Rosen et al., 2012; Fig. 2).

We used the insar_tops_burst workflow to process interferograms with five looks (effectively, a spatial averaging factor of five) in the range direction and one look in the azimuth direction, geocoded to 20 m by 20 m pixels (Figs. S2 and S3 in the Supplement). To form redundant networks of ascending and descending interferograms, we created interferograms for each burst acquisition using the three nearest burst acquisitions in time. In total, we processed 636 ascending burst interferograms and 675 descending burst interferograms (Table 1).

We selected a local “reference area” and “stable area” (Fig. 1) as close to the moraine dam as possible, with high mean InSAR coherence for the entire study period. The reference area (∼0.06 km2, ∼144 pixels) was used to remove atmospheric noise, while the stable area (∼0.03 km2, ∼87 pixels) was used to assess derived measurement accuracy and precision.

We co-registered all SLCs and performed feature tracking on the SLC products in radar coordinates at the native resolution using a modified version of the insar_tops_burst workflow and the “dense ampcor” ISCE2 feature tracking routine (Fig. 2). We selected kernel sizes and skip sizes based on the characteristics of the moraine dam and an empirical sensitivity analysis. The moraine dam is roughly square (∼800 m by 900 m) in ground range. To maximize the number of unique feature-tracking measurements over the moraine dam that do not extend beyond its edges, we chose to use kernel sizes and skip sizes that were roughly square in ground range. Kernels that span the moraine dam and the surrounding area are likely to produce poor matches due to intra-kernel variability in the magnitude and direction of surface displacement.

Smaller kernel sizes will result in poor matching, while larger kernel sizes will reduce the spatial resolution of the output feature tracking measurements. We found that a kernel size of 10 pixels in azimuth and 60 pixels in range (141 m by 138 m in ground range) was the smallest possible square kernel size that provided high-quality matches. We used a skip size of 4 pixels in azimuth and 20 pixels in range, or 56 m by 46 m in ground range, to minimize interpolation without increasing processing time. Smaller skip sizes substantially increased processing time with negligible improvement, while larger skip sizes required more interpolation between sparse measurements. The search window size was set to 10 pixels in azimuth and 30 pixels in range, or 141 m by 69 m, which is much larger than the expected cumulative surface displacement of the moraine dam over the study period.

To estimate the accuracy of our feature tracking measurements, we first calculated the ground-range resolution of the slant-range SLCs. Following Notti et al. (2010) we computed the ratio of slant-range resolution to ground-range resolution (R-index) for the SLCs, considering terrain slope, terrain aspect, and the radar LOS vectors. We used this index to calculate the SLC resolution in the ground-range direction (Fig. S4 in the Supplement). Over the moraine dam, the median ground-range resolution was 4.38 m for the ascending SLCs and 3.82 m for the descending SLCs. Assuming perfect SLC co-registration and a conservative feature-tracking precision of 0.2 pixels (Fialko et al., 2001; Strozzi et al., 2002), the theoretical accuracy of our feature tracking measurements is 2.82 m in azimuth, 0.88 m in range for the ascending SLCs, and 0.76 m in range for the descending SLCs. Given the expected mean surface velocity of <1 myr-1 for the moraine dam (Fujita et al., 2009), we generated feature tracking offsets with multi-year temporal baselines to maximize displacement between acquisitions. As longer temporal baselines could result in degraded quality due to significant changes in surface scatterer characteristics, we generated offsets for all possible feature tracking image pairs with temporal baselines of 4, 5, and 6 years (Table 1). In total, we generated 192 ascending and 210 descending feature tracking offset maps with corresponding signal-to-noise ratio (SNR) maps. The expected precision in the range direction for the 4, 5, and 6 year feature tracking offset maps is 0.22, 0.18, and 0.15 myr-1, respectively.

Since both InSAR interferograms and the component of feature-tracking motion in the slant-range direction are measurements of displacement along the radar LOS (Fig. S5 in the Supplement), these measurements can be combined to produce more accurate estimates of LOS surface displacement over time. We used the Miami INsar Time-series software in PYthon (MintPy) package (Yunjun et al., 2019) to prepare cumulative LOS displacement time series from all InSAR and feature tracking observations for each relative orbit.

To avoid cumulative displacement errors caused by poor feature tracking matches, we aggregated the available feature tracking offset products over time and prepared a single median velocity product for each relative orbit. These median velocity products were then used to constrain the cumulative displacement solution from the network of InSAR interferograms from the same relative orbit (Fig. 2).

Several preprocessing steps were required to produce the median feature tracking velocity products for each relative orbit. We first converted all feature tracking offsets in range from pixels to C-band phase in radians, the same unit as our interferograms. We then masked all pixels with signal-to-noise ratio lower than 8 to remove unreliable measurements (Casu et al., 2011). This threshold was set to minimize the resulting magnitude of noise in the stable area. Next, we calculated the median surface displacement in range observed in the reference area and subtracted it from each offset map to mitigate potential co-registration bias. At this point we divided each feature tracking offset map in range by its temporal baseline and computed a per-pixel median rate for the entire time series stack, resulting in a single median velocity product for each relative orbit. We masked any pixels with less than 10 feature-tracking observations or a mean InSAR coherence greater than 0.85 during late summer (day of year 220–280, the lowest coherence period), as the InSAR measurements alone should provide accurate displacement time series for those pixels. We also computed the per-pixel standard deviation of the feature tracking offset maps to assess variability due to real changes and measurement error.

Prior to time series inversion, we removed interferograms with mean coherence less than 0.6 over the moraine dam, unless they were required to form a continuous network. This filter effectively removed interferograms impacted by intermittent snow accumulation, larger (>200 m) perpendicular baselines, or large surface change over the temporal baseline. To convert our per-pixel median feature tracking velocity (displacement rate) products into a cumulative displacement product analogous to an interferogram for the full 2017 to 2024 study period, we multiplied by the appropriate temporal baseline for the ascending (7.29 years) and descending (7.36 years) time series. The cumulative feature tracking displacement product was assigned a uniform coherence of 0.6, which is the minimum allowable mean coherence for the moraine dam area. The network of per-pixel displacement measurements, including the interferograms and the ∼7 year cumulative feature tracking displacement product, was then inverted using phase variance, a measure of expected phase noise calculated using coherence (Tough et al., 1995; Hanssen, 2001), as a weight (Yunjun et al., 2019). As coherence is used to calculate phase variance, the cumulative feature tracking displacement product is weighted lower than interferograms where coherence is greater than 0.6.

Following the time series inversion, we computed and removed the median apparent displacement over the reference area from the LOS displacement estimate at each time step to mitigate atmospheric noise. The standard deviation of the median apparent displacement values over the reference area was 3.1 cm for the ascending data (n=214) and 0.5 cm for the descending data (n=227). The moraine dam is approximately 900 by 800 m and the reference area is only 250 m northwest of the moraine dam. Given the expected correlation length scales of several km for atmospheric noise in mountains (e.g., Bekaert et al., 2015), the apparent displacement in the reference area should be similar to the atmospheric noise over the moraine dam. To evaluate remaining measurement uncertainty, we first computed the mean apparent displacement in the stable area at each time step, then computed the standard deviation of this spatial mean over all time steps to characterize the magnitude of remaining atmospheric noise. The standard deviation was 0.2 cm for the ascending orbit and 0.4 cm for the descending orbit. Finally, we delineated a “moving area” polygon over the moraine dam including pixels with mean velocity of ∼1 cmyr-1 above the background noise level in the ascending and descending cumulative displacement time series.

Given two cumulative displacement measurements over the moraine dam, each with a different LOS from different relative orbits, we can solve for two components of the 3D surface displacement vector (Wright et al., 2004; Fuhrmann and Garthwaite, 2019). Since the mean LOS incidence angle at the site is 35.8° for the ascending burst and 37.8° for the descending burst, and the mean LOS azimuth (defined clockwise from north) is 79.3° for the ascending burst and 280.5° for the descending burst, we chose to solve for the vertical (up/down) and horizontal (east/west) surface displacement components. We assume that any north/south displacement would be negligible when projected into the available LOS vectors.

The LOS unit vector (l^) of each pixel can be defined as: 1l^=cos⁡(γ)sin⁡(θ)n^+sin⁡(γ)sin⁡(θ)e^-cos⁡(θ)z^, for ascending (l^asc) and descending (l^des) geometry, where γ is the LOS azimuth angle, θ is the LOS incidence angle defined relative to surface-normal direction, and n^, e^ and z^ represent the north, east, and up axes, respectively, which define the up/down (l^ud=0n^+0e^+1z^) and east/west (l^ew=0n^+1e^+0z^) unit vectors.

If we assume that the observed cumulative ascending (dasc(t)) and descending (ddes(t)) displacement at time t is only sensitive to the up/down (dud(t)) and east/west (dew(t)) surface displacement components, we obtain the following equations: 2dasc(t)=dud(t)l^asc⋅l^ud+dew(t)l^asc⋅l^ew,3ddes(t)=dud(t)l^des⋅l^ud+dew(t)l^des⋅l^ew, We can then rearrange these equations to solve for the up/down and east/west displacement components: 4dud(t)=ddes(t)l^asc⋅l^ew-dasc(t)l^des⋅l^ew(l^asc⋅l^ew)(l^des⋅l^ud)-(l^des⋅l^ew)(l^asc⋅l^ud),5dew(t)=dud(t)l^asc⋅l^ud-dasc(t)l^asc⋅l^ew, To accomplish this, we interpolated the descending orbit cumulative displacement time series to match the acquisition dates of the ascending orbit time series, and then solved for the vertical and east/west displacement at every pixel at each ascending acquisition time.

To compute the vertical and east/west surface velocity, we divided the observed cumulative displacement by the time between acquisition dates. We aggregated these velocity component time series to compute the per-pixel monthly median values over the entire study period.

To identify and map areas of buried ice, we calculated a winter coherence map using the per-pixel median coherence for all 12 d temporal baseline observations from winter to early spring (day of year 0–100), and a summer coherence map using the per-pixel median coherence for observations in late summer (day of year 220–280). We attribute large observed seasonal decreases in InSAR coherence to surface changes caused by melting of buried ice during warm months.

We identified and processed two Maxar WorldView-3 in-track stereo image pairs spanning the 2017–2024 study period, including the 11 February 2016 WorldView-3 stereo pair (catalog IDs 104001001854B000, 10400100175C2D00) used by Haritashya et al. (2018), and a new in-track stereo pair acquired on 30 January 2025 (10400100A0D45D00, 10400100A193EE00). We used the latest version (3.5.0-alpha) of the Ames Stereo Pipeline (Shean et al., 2016; Beyer et al., 2018) and the processing settings outlined by Bhushan and Shean (2021) and Bhushan et al. (2024) to prepare the corresponding DEMs with 1 m posting.

We co-registered the 30 January 2025 DEM to the 11 February 2016 DEM using the demcoreg (Shean et al., 2023) implementation of the Nuth and Kääb (2011) algorithm (Fig. S6 in the Supplement). We then corrected residual in-track “jitter” and cross-track “CCD array geometry” artifacts (see Shean et al., 2016) by fitting a Savitzky-Golay filter (window of 101 px, 2nd-order polynomial basis function) to the median of elevation difference residuals over static surfaces for each row and column (Fig. S7 in the Supplement).

We prepared final cumulative elevation change and elevation change rate maps for the ∼9 year period (Fig. 3C). The final elevation difference residuals over all exposed static control surfaces used during co-registration had a median of 0.00 m and normalized median absolute deviation (NMAD) of 0.14 m (<0.5 px) for the ∼9 year period (Fig. S8 in the Supplement), corresponding to a 1-sigma uncertainty of ∼1.6 cmyr-1. The elevation difference residuals over the stable area used for calibration of the InSAR and feature-tracking results (see Fig. 1 for context) had a mean bias of -0.54 cm and a standard deviation of 7.77 cm, corresponding to apparent vertical displacement rates of -0.06 and 0.87 cmyr-1, respectively.

Following co-registration, we created shaded relief maps for the two DEMs using the “combined” hillshade option in the gdaldem utility (Rouault et al., 2024). We digitized the lake and pond shoreline using the 30 January 2025 orthoimages and shaded relief map, and masked the hillshade products over water. We then used the Ames Stereo Pipeline correlator to prepare dense horizontal sub-pixel displacement maps tracking surface motion between the hillshade products (disp_mgm_corr.py utility of Bhushan and Shean, 2025), following the methods outlined in Bhushan et al. (2024). The final horizontal velocity (myr-1) components (Fig. 3A and B) were calculated based on the 1 m DEM pixel size and the ∼9 year time period. To assess the uncertainty of the validation data, we computed the mean and standard deviation of the observed east/west (-1.5 cmyr-1, 2.3 cmyr-1, respectively) and north/south (-2.0 cmyr-1, 1.9 cmyr-1, respectively) velocity components over the stable area.

To enable direct comparison of our time series results with the DEM-derived validation data, we first masked pixels with a cold-season coherence of <0.7 (Fig. 4). These areas contain rapid winter displacement caused by backwasting of ice cliffs, which have large signals in the DEM difference products that we do not expect to capture with Sentinel-1 SAR observations. We next resampled the 1 m DEM-derived products to match the 20 m grid of the Sentinel-1 SAR observations using median resampling, then smoothed the DEM-derived products to match the SAR feature tracking resolution using a 7 px by 7 px (∼140m×140m) Gaussian kernel. We computed zonal statistics (mean, standard deviation) for each velocity component (up/down, east/west) over the moraine dam. We also computed R2 values between the InSAR/SAR velocity component and the corresponding DEM-derived validation velocity component. Finally, we used the north/south component of DEM-derived velocity to assess expected bias caused by our up/down and east/west decomposition (See “LOS Decomposition bias” section in the Supplement for additional details).

We prepared two additional time series from the same Sentinel-1 SLC products: a standard InSAR-only SBAS time series and a SAR-feature-tracking-only SBAS time series. The InSAR-only SBAS time series used the same processing parameters as described for our combined approach, but did not include the scaled median velocity product from feature tracking for the inversion (blue row in Fig. 2 system of equations). The SAR-feature-tracking-only SBAS time series included the same set of 4, 5, and 6 year temporal baseline pairs from our combined approach (192 ascending and 210 descending), as well as all possible image pairs with a 3 year temporal baseline (182 ascending and 132 descending), to ensure that the system was overdetermined (total ascending n=374, descending n=342). As with the DEM-derived validation, we computed zonal statistics (mean, standard deviation) for each velocity component (up/down, east/west) for the InSAR-only and SAR-feature-tracking-only SBAS time series over the moraine dam.

We examined the mean InSAR coherence from all pairs on both the ascending and descending orbits over the Imja Lake moraine dam during the full 2017–2024 study period (Fig. 4). The pair temporal baseline strongly controlled InSAR coherence over the moraine dam moving area (Fig. 4C and G), with shorter temporal baselines (i.e., 12 d) offering higher mean coherence than longer temporal baselines (i.e., 36–60 d). Over the stable area, we observed no obvious relationship between temporal baseline and coherence (Fig. 4D and H). Descending orbit coherence was on average slightly higher (mean 0.80) than ascending orbit coherence (0.74) over the moraine dam moving area for 12 d temporal baseline interferograms.

We observed a systematic seasonal cycle in InSAR coherence values over the moraine dam moving area. Coherence remained largely stable from the beginning of the year until early June. For 12 d temporal baseline interferograms, mean coherence decreased by approximately 0.3 from June through mid-September. Coherence then increased from mid-September through mid-November. This seasonal decrease in coherence lags about 60 d behind the timing of positive mean daily maximum temperatures at the nearby Pyramid Station (Fig. 4C and G). No significant seasonal coherence change was observed over the stable area (Fig. 4D and H).

The decrease in coherence is spatially constrained. Visual inspection of mean coherence maps from the annual high-coherence period (December–May) and low-coherence period (June–November) revealed that coherence decreased over almost all of the moraine dam moving area (Fig. 4A–D). Several areas of low coherence in December–May expanded and displayed a further decrease in coherence during June–November. Areas of high-coherence in December–May also displayed a decrease in coherence during June–November. Low-coherence areas were mostly consistent between ascending and descending orbits, with minor discrepancies potentially explained by differences in the LOS and acquisition time (18:00 LT for ascending, 06:00 LT for descending) of the two relative orbits.

Applying our technique to identify and map areas of buried ice, we observed a substantial decrease (0.34) in median coherence over the moraine dam moving area between the winter–early spring (0.92) and late summer (0.58) (Fig. 5). There was no measurable decrease over the stable area.

The feature-tracking offset maps showed coherent motion of the moraine dam surface. The spatial mean of the per-pixel median LOS velocity over the moving area was +13.6 cmyr-1 for the ascending orbit and +7.8 cmyr-1 for the descending orbit, with a maximum per-pixel median LOS velocity of +46.1 cmyr-1 for the ascending orbit and +29.3 cmyr-1 for the descending orbit (Fig. 6A and B). For both orbits, higher velocity was observed on the eastern side of the moving area near the lake shoreline. The mean SNR of the feature tracking products over the moraine dam moving area was 11.4 for the ascending orbit and 14.0 for the descending orbit (Fig. 6C and D). The spatial mean of the per-pixel standard deviation of LOS velocity was 13.7 cmyr-1 for the ascending orbit and 25.9 cmyr-1 for the descending orbit (Fig. 6E and F). The spatial mean of per-pixel median LOS velocity over the stable area was 0.7 cmyr-1 for the ascending track and -0.3 cmyr-1 for the descending track, though the feature tracking velocity values were ultimately masked in these areas with high InSAR coherence prior to inversion (Sect. 4.2). Positive LOS velocities are also observed over the Lhotse Glacier northwest of the moraine dam (Fig. 6A and B).

Most pixels in the moving area showed positive range change (i.e., movement away from the satellite) over the course of the study period for both ascending and descending orbits (Fig. 7A and B). The mean total LOS displacement of the moraine dam moving area over the 7 year study period was 97.7 cm for the ascending orbit and 50.5 cm for the descending orbit, with a maximum LOS displacement of 338.6 cm for the ascending orbit and 207.4 cm for the descending orbit. The largest displacements were observed on the east side of the moving area near the lake shore, while limited displacement was observed on the northern, southern, and western margins of the moving area. While many pixels displayed constant LOS velocities over time, others showed apparent seasonal fluctuations (Fig. 7E and F). To assess error caused by atmospheric noise, we first computed the mean apparent displacement in the stable area at each time step, then computed the standard deviation over all time steps. These values were 0.2 cmyr-1 for the ascending orbit and 0.3 cmyr-1 for the descending orbit, indicating that our approach for atmospheric noise removal was effective.

After decomposing the LOS displacements into vertical and east/west displacements, we found that the observed LOS displacement of the moraine dam is consistent with downward and eastward motion (Figs. 7 and 8). The mean total vertical displacement of the moraine dam moving area over the study period was -93.4 cm, with a maximum total vertical displacement of -337.0 cm. The mean total eastward displacement was 38.3 cm, with a maximum displacement of 174.1 cm. Over the stable area, the mean total vertical and horizontal displacements were 0.7 and 0.8 cm, respectively. While some pixels showed constant velocity over time, the pixels with the highest velocity displayed more seasonal variability, with increased velocity during the warmer months (Fig. 7G and H).

The monthly median velocity maps show year-round movement of the moraine dam with a clear seasonal cycle. Vertical velocity was lowest (between -8.6 and -10.1 cmyr-1) between January and April (Fig. 8A and B). The moraine dam moving area vertical velocity increased from May to October, when the mean vertical velocity reached -21.7 cmyr-1 (Fig. 8A and B). The vertical velocity over the moraine dam moving area decreased in November and December (Fig. 8A).

From December to May, the mean horizontal velocity of the moraine dam moving area was 6.0 to 8.3 cmyr-1 to the east, with limited pixel-to-pixel variability (Fig. 8A and C). Between June and September, some pixels began to move westward, and pixel-to-pixel variability increased (Fig. 8A and C). The mean east/west velocity in the moving area decreased from June through September (Fig. 8A and C).

Our analysis shows that both the magnitude and direction of the combined InSAR and feature tracking velocity time series are consistent with the corresponding DEM-derived validation components (Fig. 9; Table 2). The mean vertical velocity in the moving area from DEM differencing was -15.0 cmyr-1. The mean vertical velocity from our combined InSAR and feature-tracking time series approach was -13.0 cmyr-1. The InSAR-only SBAS underestimates both vertical and horizontal velocity (Fig. 9). The feature-tracking-only SBAS captures velocity magnitude, but fails to capture short-term variability and contains large errors.

We interpret the observed seasonal decrease in coherence to be caused by melting of buried ice and associated debris reworking. The lag between the onset of air temperatures above freezing and melt onset (Fig. 4) is likely related to debris cover insulation. Both the melting of buried ice and debris reworking will change the moraine surface geometry, altering the scattering characteristics of the surface and decreasing coherence.

Where the magnitude of the seasonal change in coherence is large (Fig. 5), we assume that buried ice is present. We find evidence for buried ice over most of the moraine dam, including areas displaying near-zero surface displacement. This is consistent with previous geophysical survey results. Hambrey et al. (2008) used both GPR and ERT to document buried glacier ice tens of meters thick (over 40 m in places) overlain by up to 20 m of debris along the eastern portion of the moraine. Somos-Valenzuela et al. (2012) found consistent evidence for buried ice throughout 13 GPR transects across the moraine dam, ranging in bottom depth from 0–65 m. The deepest ice bottom depths (40–60 m) were documented on the northeast moraine dam, while shallower ice bottom depths (20–40 m) were documented around the southwest margin of the moraine dam, near the outlet. Dahal et al. (2018) conducted a dense ERT survey of the area surrounding the moraine dam outlet to the southwest, finding evidence for discontinuous blocks of glacier ice at depths varying from 0–20 m. Note that Hambrey et al. (2008) and Dahal et al. (2018) estimated debris thickness but were not able to locate the bottom of the debris-covered ice, and thus presented only a lower bound on ice thickness. Meanwhile Somos-Valenzuela et al. (2012) presented an ice-bottom depth, but did not estimate debris thickness, resulting in only an upper bound on ice thickness. We observe a smaller seasonal change in coherence over the southwest corner of the dam near the outlet (Fig. 5), which is consistent with the isolated ice deposits mapped by Dahal et al. (2018). The magnitude of observed seasonal coherence change is likely also related to overlying debris thickness, as thicker debris (1) provides more insulation, suppressing melt, and (2) experiences less surface change per volume of ice melt at depth.

While other processes could also contribute to decreased coherence during warmer months, we did not observe loss of coherence over the stable area during the warmer months (Fig. 4D and H). This suggests that seasonal melt of massive, buried ice is primarily responsible for the observed coherence loss over the moraine dam.

The observed spatial variability in seasonal coherence change may be explained by debris thickness and proximity to the lake and surface ponds, which can enhance downwasting and backwasting (Johnson, 1971; Driscoll, 1980; Watanabe et al., 1995). Low coherence during colder months was observed in some locations, especially bordering the lake and surface ponds (Fig. 4A and C). These areas tend to coincide with areas experiencing rapid subsidence in our DEM-derived validation data (Fig. 3). When air temperatures are below freezing, these locations potentially experience additional ice degradation and associated debris reworking due to melt caused by contact with water and by calving.

Overall, our measured vertical velocity values (Figs. 7 and 8; Table 2) are lower than those documented by earlier studies. Watanabe et al. (1995) measured the position of five painted boulders in November 1989 and October 1994 and documented cumulative vertical displacements of -0.3 to -13.5 m with a mean of -4.8 m over the 5 year period (corresponding to vertical velocity range of -0.06 to -2.70 myr-1 and mean of -1.0 myr-1). Fujita et al. (2009) performed topographic surveys using a theodolite in November 2001 and GPS receivers in April 2002 and October 2007. They created digital elevation models (DEMs) with 1 m posting for each survey and differenced to estimate cumulative vertical surface displacement. They report cumulative vertical displacement values for the “left bank” and “right bank” of -1.63 ± 1.71 m and -1.97 ± 1.67 m (mean ±1-sigma), respectively, with a total range of vertical velocity values over the moraine dam of -0.06 to -1.03 myr-1 for the 6 year period from 2001 to 2007. Haritashya et al. (2018) measured mean vertical velocity over the moraine dam between February 2000 and February 2016 of less than -0.5 myr-1, with a maximum of -1.9 myr-1, and uncertainty of 0.7 myr-1. The disagreement with our measured vertical velocity values likely results from some combination of inaccurate and/or incomplete sampling of the moraine dam surface in previous work, and/or a real decrease in the moraine dam vertical velocity over time.

During the warmer months, we observed a clear increase in downward vertical velocity over much of the moraine dam (Fig. 8A and B), likely associated with melting of buried ice. The highest downward velocity over the moving area was observed in October with mean velocity of -21 cmyr-1. Seasonal increases in velocity were first observed over the northern margin of the lake and surface ponds, suggesting earlier seasonal melt in these locations. Small areas of apparent upward displacement at the southern margin of the lake (Fig. 8B) are likely caused by consistent unwrapping errors due to low coherence (Fig. 4B and D). East-west displacement during the warmer months was variable, with some areas mostly moving east and some areas mostly moving west (Fig. 8C). This variability in horizontal displacement direction could be caused by the variable topography of the moraine dam, as the apparent direction of displacement caused by melt of sloped ice surfaces depends on the surface aspect.

If we extrapolate the observed mean subsidence rates for the 2017 to 2024 period forward in time and consider the current moraine dam topography (Figs. 1 and S1), we find that the northeast area of the moraine dam bordering the lake edge is most vulnerable to subsidence below the current lake level. This topographic evolution would result in westward expansion of Imja Lake, decreasing the width of the moraine dam.

During the colder months, we observed widespread downward and eastward displacement of the moraine dam surface, with a mean velocity within the moving area of -10.5 and 7.3 cmyr-1, respectively (Fig. 8). The high coherence values over the moraine dam during colder months (Fig. 4) provide high confidence in these measurements. Assuming that air temperatures during the colder months were mostly below freezing (Fig. 4C and G), we do not attribute this displacement to melt of buried ice. While debris settling and frost creep could potentially explain some component of downward and horizontal motion, they are not expected to cause displacement of this magnitude on these time scales (Colman and Pierce, 1986; Bursik, 1991; Hallet and Putkonen, 1994) and we do not observe similar motion over debris outside the moraine dam. We instead attribute this motion primarily to flow of the thick, massive ice within the moraine dam.

Downward and eastward movement is consistent with along-slope flow for the broad moraine dam surface slopes (Fig. S1). The mean surface slope of the moving area is 9.5°. Somos-Valenzuela et al. (2012) found evidence for ice bottom depths between 30 and 60 m over much of the moraine dam. Assuming debris thickness of less than 1–20 m (Hambrey et al., 2008), buried ice in the moraine dam should have thickness of 10 to 60 m. We generally observe higher east/west and vertical surface velocity during colder months over areas with deeper ice bottom depths documented by earlier studies. Near-zero velocity was observed over the southwest portion of the moraine dam, where Dahal et al. (2018) observed discontinuous blocks of buried ice. The observed mean winter velocity magnitude (combining the vertical and east/west components) of 12.8 cmyr-1 over the moving area of the moraine dam is consistent with expected surface velocity values for a simple ice flow model and the range of measured ice thickness (See Sect. S1 in the Supplement, Fig. S9).

Previous surface displacement measurements also provide evidence for flow of buried ice within the moraine dam. Watanabe et al. (1995) described westward movement of several boulders along the outlet channel of -0.96 myr-1. Fujita et al. (2009) described horizontal flow rates of less than 0.17 myr-1 in an unspecified direction. These results potentially suggest that at some point before our study period, the flow direction of the moraine dam evolved from original westward, downvalley flow (the original flow direction of Imja Glacier) to the eastward, upvalley flow (toward Imja Lake) observed during our 2017–2024 study period.

The observed change in flow direction is likely related to evolving thickness of lower Imja Glacier through differential ablation both above and below the lake surface (Kjær and Krüger, 2001), changing longitudinal stresses associated with decoupling from the active flowing glacier during retreat, and interaction with the expanding lake. We observed a concave-upward transverse profile (bottom-right panel of Fig. S10 in the Supplement) for the Imja Lake moraine dam during our study period. A similar configuration, where the glacier surface slopes downward from the lateral and terminal moraines toward the centerline, is observed for many debris-covered glaciers in the Everest region (e.g., Nuptse Glacier, Fig. S11 in the Supplement). This scenario introduces driving stress toward the glacier centerline (downslope), which is consistent with the observed direction of motion in our horizontal surface velocity maps. Our detailed displacement time series can potentially be used to constrain ice and debris evolution models, which are needed to better understand the evolution of the Imja Lake moraine dam and implications for changing structural stability.

While our InSAR and feature tracking results improve our understanding of the processes responsible for moraine dam degradation, it is important to discuss some limitations. Underestimation of rapid, localized surface displacement can partly explain why our maximum vertical velocity over the moraine dam surface was only -0.47 myr-1 compared to -1.9 myr-1 from Haritashya et al. (2018). We also see evidence of localized backwasting in our DEM-derived validation dataset (Fig. 3) that is not captured in our InSAR and feature-tracking displacement time series (Figs. 7 and 8).

We also acknowledge limitations of the Sentinel-1 acquisition geometry, with only ∼10 % of any real north/south displacement mapped into LOS measurements for this location. We combined data from ascending and descending passes to calculate vertical and east/west displacement components, assuming that north/south displacement does not substantially contribute to the displacement observations. In fact, some small contribution from north/south displacement is expected, which potentially introduces a source of error in our measurements of surface velocity (Brouwer and Hanssen, 2021). Based on the north/south displacement from the DEM-derived validation dataset, we expect that our LOS decomposition could introduce a bias of less than ∼4 % in mean vertical velocity over the moraine dam moving area and less than ∼3 % in mean east/west velocity over the moraine dam moving area (Sect. S2 in the Supplement, Figs. S12 and S13).