Thank you for your feedback. I have attached a document containing detailed responses addressing each of the raised issues individually.

On behalf of myself and my co-authors, I would like to express our gratitude for your insightful and constructive comments on our manuscript. We appreciate the time and effort you dedicated to reviewing our work and providing valuable feedback.

Your comments have been instrumental in helping us improve the quality of our manuscript. We particularly appreciate your suggestions regarding comparison with the DPR product. We have incorporated your suggestions into the manuscript, and we believe that the revisions have significantly enhanced the overall quality of our work. Please see below for the point-to-point responses. We used italic fonts to differentiate from your comments.

Major comments:

The OE method is well described, but it is difficult for the audience who are not familiar with GPM DPR algorithms to understand the novelty of this work. Since this work is expected to ‘improve’ GPM retrievals, the GPM algorithm should be well presented. In particular, the authors should discuss the aspects that this algorithm are different from GPM.

We have provided a more detailed description of the algorithm. In addition, we added a subsection that summarizes main differences and similarities between the algorithms:

In Section 3 we added:



The DPR retrieval algorithm utilizes measured radar reflectivity, total path integrated attenuation estimates corrected for non-precipitating particles, the relationship between precipitation rate and mass-weighted mean diameter (PR − D_m), and phase information based on the melting layer detection. It generates profiles of precipitation rate and drop size distribution parameters (D_m, N_w). Additionally, profiles of effective reflectivity and specific attenuation coefficients are provided. The algorithm employs the PR − Dm relationship with an adjustment parameter, ε, aiming to reconcile discrepancies between the surface reference technique PIA and the one simulated from hydrometeor profiles. Version 06 had a single ε value along the profile, while Version 07 introduces varying ε in the column.

The PR-Dm relation, replaces the traditionally used relation involving specific attenuation (k) and effective radar reflectivity factor (Z_e). While using the k-Z_e relation with the Hitschfeld-Bordan attenuation correction method (Hitschfeld and Bordan, 1954) enables the derivation of a Z_e profile from the Z_m profile without the need for scattering tables, this relation is not applicable at the Ka-band due to the weaker correlation between involved parameters. This limitation arises from rain extinction being strongly affected by absorption rather than being dominated by scattering. Consequently, the Hitschfeld-Bordan method leads to inconsistencies in attenuation correction at two frequencies.

The algorithm follows a logical sequence: assuming a gamma DSD with a fixed shape parameter, a relationship between PR and D_m imposes a unique solution for a given effective reflectivity. Consequently, the corresponding values for N_w is found and by using the scattering tables the specific attenuation coefficient k is obtained. The process begins at the top, where the measured reflectivity is assumed to be unaffected by attenuation and is iteratively corrected using the estimated k. This procedure is applied throughout the column, resulting in the unattenuation profile. The process is iterated with different values of ε to minimize the difference between the simulated PIA at the SRT-estimate.

For more details about the changes introduced in version 6 of the GPM-DPR algorithm, refer to the Algorithm Theoretical Basis Document (Iguchi et al., 2018) or to the algorithm description provided by SETO et al. (2021). Additionally, the study conducted by Chase et al. (2020) provides a thorough evaluation of the PR-D_m relation in both rain and snow using disdrometer measurements. They conclude that the PR-D_m retrieval may not be optimal in snow due to the variability of snowflake mass, suggesting the exploration of alternative techniques.

In section 4 we added subsection 4.4. Similarities and differences with the DPR product.

Despite the distinct mechanics employed by our algorithm, specifically our reliance on the optimal estimation framework, and the iterative nature of the DPR product, which primarily aims at fitting the measurements, there exist notable similarities between these two approaches. For instance, the utilization of principal components in our method shares an underlying idea with the PR-D_m relationship. The principal components determine orthogonal directions within the space of microphysical parameters while providing insights into which component is most likely to change. The first principal component, for instance, represents the direction that undergoes the most significant changes as it is characterized by the largest variance, by definition. Variations along this principal component can be likened to imposing the PR-D_m relationship, a step analogous to the approach adopted in the DPR product. A noteworthy similarity arises when altering the second principal component; this modification influences the PR-D_m relationship, akin to the e-adjustment implemented in the DPR product. Despite these similarities, our approach offers a distinct advantage – a priori knowledge regarding the natural variability of these relationships, quantified by their respective standard deviations. This insight allows for a more nuanced understanding of how these relationships may vary in real-world scenarios.

Another notable similarity between our algorithm and the DPR product lies in the approach to assimilating the measured reflectivity. Traditionally, the measured reflectivity is corrected for attenuation prior to microphysical retrievals (e.g. Vulpiani et al., 2006). Both our and the DPR algorithm adopt this step solely to obtain the initial guess. Subsequently, an iterative procedure is initiated, and the distribution of microphysical parameters within the column is modified to align with the measured reflectivity. Both algorithms employ a top-down approach, estimating attenuation caused by various hydrometeors from scattering tables. The attenuation accumulates along the propagation path until reaching the surface. The total PIA estimate serves as a crucial constraint for both algorithms, ensuring the stability of the iterative process. The difference lies in the modelling of the melting layer. In our approach, we solely estimate the attenuation caused by melting particles using the parametrization of Matrosov (2008). In contrast, the DPR product simulates the melting particles and their associated scattering properties within the melting zone. This simulation yields reflectivity and hydrometeor properties profiles within the melting zone. In our case, hydrometeor properties are obtained solely through continuity, and no measurements are simulated within the melting zone.

It is essential to highlight a nuanced difference in our algorithm compared to the DPR product. Our algorithm is designed to simultaneously fit the measured reflectivity at Ku and Ka bands, alongside the differential PIA estimate. Conversely, the DPR product appears to prioritize fitting the Ku-band reflectivity. This prioritization is justified due to challenges in simultaneously fitting both channels under non-uniform conditions (Mroz et al.,2018). Notably, our algorithm is tailored for stratiform rain scenarios, where such conditions are minimized, while the official DPR product is designed to be a versatile one-for-all approach.

The primary distinction between the two algorithms centers on how ice is modeled. Our approach employs the simulation of realistic ice hydrometeors, complemented by discrete dipole simulations of scattering properties. In contrast, the DPR product adopts "soft-spheres" simulations, representing ice particles as a uniform mixture of air and ice. In this case, scattering simulations can be approximated using Mie theory. However, it's essential to emphasize that the primary difference in our approaches is not the shape of the particles or the scattering simulation methodology.

What sets our algorithm apart is the capacity of the OE algorithm to accommodate changes in the density of ice particles, while the DPR product maintains a fixed density of spherical air-ice mixtures at 0.1g/cm³. This unique flexibility allows the OE algorithm to search for solutions that ensure continuity in the water mass flux through the melting zone. Importantly, this coherence in the fluxes is achieved without sacrificing the continuity of the melted equivalent size, and it is obtained with the radar measurements matching. The ability to adjust ice particle density provides a crucial advantage, enabling our algorithm to navigate to physically consistent solution more effectively.

The manuscript is poor in organization. Section 2 is DPR measurements; Section 3 is DPR retrieval, and 4 for OE. I understand that we usually inference the reason from results. However, it is better to analyze the issues in DPR retrieval and then show the issues in observations in a scientific paper.

We chose to adopt this structure to establish a logical flow, beginning with the presentation of DPR measurements, as they form the foundation of our retrievals. Subsequently, we introduce the official retrieval framework to highlight the issues impacting the precipitation product. The OE algorithm, presented later in the manuscript, is then proposed as a solution to address these identified issues. It's important to note that our intention is not to delve into issues related to the observations. Instead, we adhere to the conventional structure found in AMT articles, where the methodology section logically follows the presentation of data.

Validation should be made in ice. The current ‘validation’ is sanity check, not validation, since the validation was not in ice. The validation should be made against in-situ measurement of ice. There are several aircraft campaigns designed for GPM validation, and the in-situ observations can be used for quantitative validation.

Concerning the validation of our product in rain, we decided to perform it this way due to the limited number of validation under-flights in the ice phase during stratiform precipitation events. As far as our knowledge extends, only one flight was conducted throughout the entire OLYMPEX campaign, and this event was utilized in the study by Chase et al. (2021). In this study, only a qualitative assessment of their product was performed, refrained from direct comparisons due to disparities in sampling time during in-situ flights and significant differences in sampling volume. The dime difference is caused by the high ground track speed of the satellite. For instance, an in-situ aircraft traveling at 600 km/h intersects only two DPR pixels in one minute. Within a 10-minute window, approximately 20 validation points are collected. This prompts a crucial question regarding the representativeness of the sample and the robustness of potential statistical comparisons. Moreover, in-situ sampling is potentially insufficient to adequately represent the entire radar volume, given their proximity to a one-dimensional cut through a 5x5x0.25 km³ volume. The impact of this sampling volume difference could potentially be mitigated with the collection of large statistics, as discrepancies in the sampling volumes would result in random noise only. However, that would require a lot of flights. Chase et al. (2021) utilized airborne radar data at finer horizontal and vertical resolution for more robust statistics. While we acknowledge their efforts, it's crucial to note that airborne data differ significantly from spaceborne measurements. Airborne data exhibit superior sensitivity, resolution, and reduced signal fluctuations. Additionally, they are less affected by non-uniform beam filling effects compared to satellite measurements.

As you rightly noted, the validation section in our study primarily served as a sanity check. It showcased that a more physically consistent retrieval could be attained without compromising the integrity of the rainfall product. Although our proposal for a more extensive in-situ validation study of DPR products was not secured, this article stands as a proof of concept. The retrieval algorithm is publicly available under the MIT license, welcoming exploration by everyone, including the GPM algorithm team.

To address your comment, we have renamed this section to "Performance Assessment in Rain." Additionally, we have included the following discussion at the beginning of the section:

“The validation of the OE algorithm was exclusively conducted within the rainy portion of the radar profiles. This might appear surprising, given the anticipated improvement in algorithm quality compared to the DPR product above the freezing level. However, this approach is expedient due to the limited availability of DPR under-flights within snow during stratiform precipitation events. To the best of our knowledge, only one flight was conducted throughout the entire OLYMPEX campaign, and this singular event was utilized in the study by Chase et al. (2021). In their study, only a qualitative assessment of the product was conducted, refraining from direct comparisons due to disparities in sampling time during in-situ flights and significant differences in sampling volume. The discrepancy in sampling time arises from the high ground track speed of the satellite (7 km s⁻¹) compared to approximately 600 km h⁻¹ of an in-situ aircraft. Consequently, within a 10-minute window, only 20 validation points are collected.This raises a critical question about the representativeness of the sample and the robustness of potential statistical comparisons. Moreover, in-situ sampling may be inadequate to sufficiently represent the entire radar volume, given its proximity to a one-dimensional cut through a 5×5×0.25 km³ volume. The impact of this difference in sampling volume could potentially be mitigated with the collection of large statistics, as discrepancies in the sampling volumes would result in random noise only.However, as pointed out earlier, collecting these statistics is impractical due to the limited number of validation points per flight, making such an effort very expensive. Chase et al. (2021) overcame this issue by utilizing airborne radar data at finer horizontal and vertical resolutions for more robust statistics. While we acknowledge their efforts, it's crucial to note that airborne data differ significantly from spaceborne measurements. Airborne data exhibit superior sensitivity, resolution, and reduced signal fluctuations. Additionally, they are less affected by non-uniform beam filling effects compared to satellite measurements.The validation presented here served as a sanity check, aiming to assess whether a physically consistent retrieval could be achieved without compromising the integrity of the DPR rainfall product.”

Technical comments (in order of their appearance in manuscript): 

Eq. 11-15: How did you get these parameterizations?

We derived them from derived from the polarimetric radar retrieval. We have made it clear in the text now.

Eq. 20: Where is this equation from?

This is a change of coordinates formula demonstrating how to convert a vector from the space of principal components into a Cartesian coordinate system. In addition to the standard conversion, there is also a normalization step. We included this formula for a more technical audience actively involved in the development of these algorithms.

Line 366: in precipitation properties and and evaluating the accuracy. Extra 'and'

Repetition was removed.

Figure 8 is presented in a single-row, side-by-side arrangement, yet the caption indicating 'Top Panel' and 'Bottom Panel. This discrepancy may be attributed to formatting issues, and it warrants verification.

It was due to formatting, thank you for pointing it out.

Line 413: A similar, case study analysis - A similar case study analysis

The comma was removed.

Line 475: rater than – rather than

It’s corrected now.