please see the attached file

The study provides valuable insights into firn properties using altimetry data from CryoSat-2 (CS2) and ICESat-2 (IS2), but there are several areas that need clarification and refinement to validate the conclusions. Before any major insight or conclusion can be drawn I find that there are several aspect of the methodology that needs more validation or attention to ensure the accuracy of the results. Except that I find that its a very interesting approach that can yield some good scientific insight into this area.

Below are detailed comments and suggestions to help improve the study with a focus on the main methodology for the altimetry components and firn models.

General Comments

LeW Computation:

In Figure 1 (related to L87), it is clear that using thresholds at 0.01 and 0.99 may result in unrealistic LeW values unrelated to the volume/surface scattering ratio. How exactly is LeW computed? Is a peak finder algorithm employed? I strongly suggest either smoothing the waveform for better LeW extraction or using the Offset Center of Gravity (OCOG) method to compute the width after identifying the leading edge. Alternatively, the overall OCOG amplitude could serve as the max. The critical objective is to minimize jitter in the LeW estimation. A specific example is pixel C, where the algorithm identifies a maximum beyond the true leading edge, likely near bin 40–45, which aligns with observations for pixel A.

DEM (Section 2.3)

The REMA description should be moved to the beginning of the data description section. Introducing it first provides essential context, as the DEM is referenced throughout both the CS2 and IS2 sections.

FDM (Section 2.4)

Given the availability of multiple firn models such as GSFC and GEMB, have you compared their results against the IMAU-FDM model? Previous analyses have shown substantial spatial and temporal differences among these models, which I think is crucial when evaluating penetration depth from laser and radar measurements. At a minimum, a discussion on the potential impact of model differences is necessary to gauge the validity of the results.

Furthermore, models like GSFC and GEMB have been updated to include data through the end of 2024, which presents a valuable opportunity to extend your CS2 and IS2 time series analysis. Incorporating these more recent datasets will enhance the robustness of your study and help provide more insight into how melt events affect the LeW and elevation relationships.

Resolution (Sections 3.1, 3.2, and 3.3):

The current 50x50 km binning resolution seems excessively coarse and likely introduces decorrelation, especially for the "dz" variable but also to elevation as you are mixing a lot of different elevations regions. Increasing the spatial resolution would likely improve both spatial and temporal patterns and correlations. 

Correlation (Section 4.3):

The low correlation values (~0.3) are surprising, especially when using a 50% threshold, which should generally yield higher correlations due to its more sensitive to volume change. I remember seeing much larger correlations in both Antarctica and Greenland using the same methodology you have provided. A few factors may contribute to this, including the coarse resolution and the LEPTA slope correction method. LEPTA may inadvertently remove signal by basing its correction on leading-edge range information that varies over time. Testing a more traditional slope correction method, as suggested you explained in Li et al. (2022), would help to better understand this. Additionally, localized analyses are likely to reveal higher correlations, as elevation usually de-correlates a lot more over larger distance while LeW might have larger spatial cohesion.

Specific Comments

L54: The Nilsson et al. (2015) study was not limited to NEEM; it covered the entire LRM region, although the time series presented was from NEEM.

L59: Provide a theoretical penetration depth for Ku-band frequencies. For Ku-band over the Greenland Ice Sheet (GrIS), penetration depth is typically 1-2 meters. Additionally, mention that the bias is retracker-dependent.

L85: Consider updating to Baseline-E, as it includes significant improvements in waveform processing compared to Baseline-D.

L87: The 0.01 threshold for LeW seems too low; most studies use thresholds between 0.05 and 0.15 to account for noise. What is the impact of changing these values to 0.05 and 0.95? A more robust approach would be to compute LeW using OCOG parameters, which are less sensitive to noise.

L91: The 50% threshold is appropriate for focusing on volume scattering rather than surface scattering. However, the LeW extraction algorithm needs to be redefined or better explained. OCOG-based methods would offer greater robustness.

L98: Include a map figure or inset to indicate pixel locations, as their current placement is unclear to the reader.

L103: Justify the use of a 50x50 km binning resolution, as it appears excessively coarse. Correlation length analysis could support this choice, or consider aligning the resolution with firn models, which typically have a 10 km resolution. If empty pixels result from a 10 km grid, they can be filled using gentle interpolation.

L117: The DEM resolution (100 m) and search radius (50 m) may not be optimal. Wouldn't this setup yield identical DEM values for adjacent locations? A higher-resolution DEM (e.g., 10 m from REMA) would likely provide more accurate results, particularly in areas with complex topography.