Review Reports - A New Antenna Pattern Correction Method for a Cross-Track Scanning Microwave Sounder with Full-Circular Sampling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript addresses antenna pattern correction (APC) for cross-track microwave sounders, with particular attention to observations near the Earth scan edge and in spatially heterogeneous scenes. By exploiting the full-circle scanning geometry of CAMS, the authors propose a multi-angle inversion framework that incorporates additional out-of-swath samplings. The study is technically sound, the physical motivation is reasonable, and the simulation results are generally consistent with the stated objectives.

The work represents a useful engineering-oriented extension of existing APC concepts rather than a fundamentally new theoretical framework. With revisions aimed at clarifying the novelty, strengthening its positioning relative to the existing literature, and improving the transparency of the methodological presentation, the manuscript could make a valuable contribution to the Remote Sensing community.

Major Comments

Positioning with respect to existing methods

The manuscript provides an adequate overview of conventional APC practices, but the discussion of related inversion- and deconvolution-based approaches remains limited. Similar ideas, such as multi-angle inversion, footprint deconvolution, and Backus–Gilbert-type reconstruction, have been explored for cross-track microwave sounders (e.g., AMSU-A, ATMS).

The novelty of the present work appears to lie primarily in the exploitation of additional out-of-swath samplings enabled by the full-circle scanning geometry of CAMS, rather than in the inversion formulation itself. This distinction should be stated more explicitly, and the method should be better positioned within the broader literature on antenna pattern inversion and brightness temperature reconstruction.
Comparison with existing operational approaches

Although foreign sensors such as AMSU-A and ATMS are mentioned, the manuscript does not provide a substantive comparison between the proposed method and the strategies these instruments actually use to mitigate scan-edge effects. The “undersampled” approach used as a baseline is useful for isolating the impact of additional sampling, but it does not fully represent real-world APC implementations.

Clarifying how the undersampled baseline relates to existing operational methods and discussing whether and how the proposed approach could be applied to sensors without full-circle scanning would strengthen the manuscript.
Clarity of methodological motivation

Section 4 introduces numerous equations with limited conceptual guidance. While the formulation is mathematically correct, the physical motivation for the inversion strategy is not sufficiently articulated before the formalism is presented.

A short conceptual overview at the beginning of the methodology section explaining why single-angle APC becomes underdetermined at scan edges, and how multi-angle observations improve observability, would substantially improve readability.
Definition of retrieval targets (BT1 vs. BT3)

The distinction between BT1 (3 dB beam-scale brightness temperature) and BT3 (main-beam-scale brightness temperature) is central to interpreting the results, but their physical meanings are not clearly defined when first introduced. It should be explicitly stated that both quantities are derived from the same correction framework, differing only in the definition of effective spatial representativeness.
Validation scope

The validation relies entirely on simulated scenarios. While this is acceptable for a methodological study, the conclusions occasionally read as if the method were directly ready for operational application. Either a limited demonstration using real observations or a clearer discussion of the remaining steps toward operational use would improve the balance of the conclusions.
Minor Comments：
Sensitivity to Real-World Uncertainties: The current validation is primarily conducted under ideal simulated conditions. It is recommended to add a brief discussion (2–3 sentences) addressing the robustness of the inversion algorithm when encountering potential measurement errors in the antenna gain patterns or calibration drifts in the cold-space observations.
Computational Efficiency and Real-time Processing: Given that the method relies on matrix inversion, a brief mention of the algorithm's computational latency is suggested. For operational satellite missions, evaluating whether the processing speed can satisfy real-time data requirements is a critical factor for practical application.

Author Response

Comment 1:

Positioning with respect to existing methods

The manuscript provides an adequate overview of conventional APC practices, but the discussion of related inversion- and deconvolution-based approaches remains limited. Similar ideas, such as multi-angle inversion, footprint deconvolution, and Backus–Gilbert-type reconstruction, have been explored for cross-track microwave sounders (e.g., AMSU-A, ATMS).

The novelty of the present work appears to lie primarily in the exploitation of additional out-of-swath samplings enabled by the full-circle scanning geometry of CAMS, rather than in the inversion formulation itself. This distinction should be stated more explicitly, and the method should be better positioned within the broader literature on antenna pattern inversion and brightness temperature reconstruction.

Response 1:

We thank the Reviewer for the suggestion.

The Reviewer noted that the introduction provides limited discussion on the related inversion methods. This is because our work primarily focuses on antenna pattern correction (APC) during calibration process to derive the coefficients for converting apparent antenna temperature of TA into brightness temperature TB of the scene. While both APC and other reconstruction methods (such as the BG method[23]) are based on the correcting the influences of the antenna pattern to the observations, their principles are different and they are operated at different stages of radiometry data processing. To clarify, APC is the process of deriving pixel-scale (3dB) brightness temperatures TB from the antenna temperatures TA at each raw field of view, whereas methods like Backus–Gilbert reconstruction aims to further enhance resolution based on these pixel-level brightness temperatures TB. Our research and background introduction are centered specifically on studies related to antenna pattern correction (APC) to TA measurements.

According to the reviewer's suggestion on novelty, we have refined the description of our innovations. This work attempts to address the uncertainty in the measurements of scene brightness temperatures introduced by antenna pattern. We developed a matrix inversion-based APC method for a full-circular sampling microwave sounder. For the first time, the actual measurements from the outer Earth scene are utilized to retrieve brightness temperatures for swath-edge pixels. Compared to the traditional methods, the method shows an improved performance especially over heterogeneous scenes with TB dramatic changes. Furthermore, it is also proved from this study that the additional sampling to the outer swath effectively enhances APC accuracies of the pixels nearby the swath edges. This work provides a valuable reference of APC processing for other microwave radiometers, whether on the APC method or the sampling strategy. The revised discussion on novelty can be found in the third paragraph of the Introduction section. To sharpen the focus on the novelty in the paper, we have deleted the correction differences analysis presented in the initial Section 5.3.

Comment 2:

Comparison with existing operational approaches

Although foreign sensors such as AMSU-A and ATMS are mentioned, the manuscript does not provide a substantive comparison between the proposed method and the strategies these instruments actually use to mitigate scan-edge effects. The “undersampled” approach used as a baseline is useful for isolating the impact of additional sampling, but it does not fully represent real-world APC implementations.

Clarifying how the undersampled baseline relates to existing operational methods and discussing whether and how the proposed approach could be applied to sensors without full-circle scanning would strengthen the manuscript.

Response 2:

We agree with the Reviewer's point that the article lacks a clear discussion on the representativeness of the "lack sampling" approach for the real-world APC implementations.

Firstly, regarding the strategies for handling edge effects for instruments like AMSU-A and ATMS, to our knowledge, a common practice is to reduce the observational scan range (as referenced in Banghua Yan, 2020, where AMSU-A adopts a scan range of only about ±48°, discarding observations near the limb to mitigate edge effects. In contrast, CAMS adopts a scan range of about ±62°). Our research in this paper focus on the impact on the additional samplings, rather than the proper scan range. Therefore, for swath edge scenarios, our comparison benchmark is chosen to be APC by matrix inversion but without real outer-swath sampling[19]. In those studies, auxiliary out-of-swath information is employed as boundary conditions to solve the matrix equations at the swath edges. The highest-accuracy auxiliary information available should be selected for comparative evaluation. For CAMS, its data have not been well assimilated and simulating brightness temperatures for its extreme out-of-swath regions at incidence angles over 70 degree would introduce considerable errors. Therefore, at current stage, auxiliary information for these outer edge regions is extrapolated from TA0 within the Earth scan range of CAMS. By comparing different extrapolation strategies including 'linear', 'nearest', 'spline' and 'cubic', it is found that the 'nearest' extrapolation yielded the smallest deviation from real measured TA within the additional sampling region. Consequently, the 'nearest' extrapolation was adopted to generate auxiliary information for the lack-sampling APC, which was then compared against the proposed method utilizing real samplings at the scan edge. We have revised section 5.1 to explicitly clarify the representativeness of the "lack sampling" approach.

We thank the reviewer for highlighting this important point regarding the applicability of our method to instruments without full-circular sampling. We acknowledge that our original discussion on this aspect was insufficient. In fact, for most microwave sounders, adding a few sampling points beyond the nominal Earth-view swath does not pose a hardware barrier and may require only minor software modifications. A key objective of this work is to advocate for the adoption of this enhanced sampling scheme in microwave sounders. We have revised subsection 4.4.2 to investigate the number of additional samplings required, and it is found that utilizing merely 3 samplings out of Earth swath would be highly effective. Also, the full-circle sampling mode may help in detecting calibration error in cold space and hot targets.

Comment 3:

Clarity of methodological motivation

Section 4 introduces numerous equations with limited conceptual guidance. While the formulation is mathematically correct, the physical motivation for the inversion strategy is not sufficiently articulated before the formalism is presented.

A short conceptual overview at the beginning of the methodology section explaining why single-angle APC becomes underdetermined at scan edges, and how multi-angle observations improve observability, would substantially improve readability.

Response 3:

This is indeed a very valuable suggestion. Emphasizing the methodological innovation in Section 4 is crucial.

The uncertainty introduced by antenna observations stems from the unknown brightness temperature distribution of the observed scene. This is a dilemma!

Compared to traditional APC, the advantage of APC by matrix inversion lies in its ability to leverage neighboring sampling, thus providing a more accurate estimate of the scene's brightness temperature distribution during antenna correction. We have enhanced the methodological motivation in Section 4 accordingly. Additionally, we have included brief overviews in relevant subsections and further highlighted the innovative aspects of the method in Section 4.2(line 275-281).

Comment 4:

Definition of retrieval targets (BT1 vs. BT3)

The distinction between BT1 (3 dB beam-scale brightness temperature) and BT3 (main-beam-scale brightness temperature) is central to interpreting the results, but their physical meanings are not clearly defined when first introduced. It should be explicitly stated that both quantities are derived from the same correction framework, differing only in the definition of effective spatial representativeness.

Response 4:

We thank the reviewer for this suggestion. In the original manuscript, to highlight the performance of different brightness temperature resolutions in heterogeneous scenes, we employed the same correction framework to derive BT1 and BT3(now revised as BT2). Considering the need for a more representative baseline, we have now modified the comparison to use the traditional APC method from a different framework(which relies on beam efficiencies), making the comparative results more significant and convincing. The change can be found in Section 5.1, line 519-530.

Comment 5:

Validation scope

The validation relies entirely on simulated scenarios. While this is acceptable for a methodological study, the conclusions occasionally read as if the method were directly ready for operational application. Either a limited demonstration using real observations or a clearer discussion of the remaining steps toward operational use would improve the balance of the conclusions.

Response 5:

We thank the Reviewer's suggestion. The focus of this paper is on highlighting the effectiveness of APC in specific scenarios, which is why the study is centered around simulation work.

Following the Reviewer's suggestion, we have revised the Discussion section to clearly reflect the remaining steps toward operational use in the real-world: Regarding the limitation of noise amplification in the deconvolution process, we are currently developing targeted APC schemes aimed at suppressing noise in the corrected brightness temperatures and improving algorithm efficiency. In future work, we will address systematic errors caused by non-ideal antenna reflection and transmission characteristics, and validate the overall correction performance using independent references. These efforts are intended to advance the method toward operational use in the calibration for space-borne microwave radiometers.

Comment 6:

Sensitivity to Real-World Uncertainties: The current validation is primarily conducted under ideal simulated conditions. It is recommended to add a brief discussion (2–3 sentences) addressing the robustness of the inversion algorithm when encountering potential measurement errors in the antenna gain patterns or calibration drifts in the cold-space observations.

Response 6:

The Reviewer's suggestion is valuable. Sensitivity analysis is indeed a crucial component of APC algorithm research. We have restructured Section 4.4 and rearranged 4.4.1 for error analysis. This analysis examines the algorithm's sensitivity to errors in 3dB beam efficiency and antenna temperature(direct result of cold space calibration drifts). We also discusses the decay pattern of single-point error, which provides a basis for the settings of boundary conditions and the additional samplings.

Comment 7:

Computational Efficiency and Real-time Processing: Given that the method relies on matrix inversion, a brief mention of the algorithm's computational latency is suggested. For operational satellite missions, evaluating whether the processing speed can satisfy real-time data requirements is a critical factor for practical application.

Response 7:

We thank the reviewer for raising this important point regarding computational cost, which is indeed a critical consideration for practical applications. In response to this comment, we have revised subsection 4.4.3 to discuss the algorithm time cost and feasibility of operation use. The algorithm of APC aims to produce coefficients which converts antenna temperature to brightness temperature of observed pixels. The coefficients producing process can be carried out before the operation stage. For a full orbit of CAMS scanning containing about 2000 scan lines, producing APC coefficients takes about 8 hours per channel on a ordinary computer. Once the APC coefficients are derived, the correction process of matrix multiplication can be completed instantly for operation use.

Reviewer 2 Report

Comments and Suggestions for Authors

A New Antenna Pattern Correction method for a Cross-track Scanning Microwave Sounder with Full-circular Sampling

The paper proposed a new antenna pattern correction algorithm for CAMS which show effective enhancement of the accuracy by comparative analysis at Earth scan edges.

There are two major concerns for me in this paper. First of all, the novelty of the correction method is not clearly introduced in this paper. In section 3 and 4, I only recognized a common matrix inversion method, although in section 5 authors mentioned about “additional samplings” and “lacking samplings”. But they are not correlated with the method introduced in section 3 and 4. The other issues is that the results comparison are not good. The so called “lack samplings”method is not referred to any specific studies. To show the improvements, authors should apply the most common or most updated matrix inversion methods in the community and give credits to those inventors.

Major comments:

In the introduction, line 68-72, could you express explicitly what kinds of methods in this paper to overcome the limitation (1) and (2) listed previously?
In Figure 1, it is better to apply polar coordinates to show the radiation pattern.
I think section 3 and 4 should be merged together to be a methodology section. The most important is that I did not find any innovations. I only find a traditional matrix inversion method is introduced. Authors should point out the novelties in this paper (as the indicated in the title and abstract). Which part of the method are used common methods or past studies? Which part of the method is new improvement distinguished with other studies? How do the method overcome limitation (1) and (2) (mentioned in introduction)? Those are key points for the paper.
Otherwise, Problem 3 is not solved. This paper is using traditional method and applied to new instruments.
Give clear definitions of the boundary region, is it out of the earth scene? Or could be any scan lines out of 10 selected scan lines?
Does the solving region means the 10 selected scan lines?
Fig 7 is hard to understand. I think authors need to revise and make it to be correlated with the description in 4.4.1.
Line 319, any reason for selecting 10 scan lines?
Section 4.2 considering [80, 160] for the earth scene. But in equations in 4.4.1 are different. Why do not considering the whole 230 pixels in the beginnings?
I do not understand the index of j in Eq (38) and (39). Why m and n have different index? Why j is not j1-10,…,j1-1,j2+1,..,j2+10 but j=0,…,19
Using equation to express boundary condition (a) and (b). The description is not clear for me.
Line 381-385, what does additional samplings mean? Boundary conditions or samplings beyond the Earth scene? The term of “lack sampling” is confusing.
I think the paper does not do good result comparisons. The “lack sampling” method is not scientifical. Authors should give the most common used or most updated matrix inversion algorithms in the community and give references in the paper. Mark this algorithm by the name of inventors.
To be consistent for the result legends for all the figures (from Fig. 9 to the end). It is better to define all the legends at beginning. “BT1” has different meaning for Fig 10 and Fig 12. I think both “BT1” and “BT3” are proposed by this paper. BT0 is a new term in Fig 13. All those are making readers confusing.

Minor comments:

1. Multiple typos in the paper, “swarth” should be “swath”

Author Response

Response:

We thank the reviewer for the insightful comments. The novelty of our method primarily lies in its implementation of matrix inversion for cross-track scanning microwave sounders by utilizing outer swath samplings. Section 3 presents the fundamental theory of matrix inversion, which does not contain novel contributions. The innovation is introduced in Section 4, where we introduce outer swath samplings into APC for pixels near swath edges—an approach not previously explored. Section 4 details our proposed methodology. Specifically, Section 4.2 explains how directional vectors for outer-swath pixels are computed, which are then employed in the antenna pattern grid matching in Section 4.3. we have strengthened the text in beginning of Section 4, paragraph after equation (21) in 4.2, and paragraph after Fig.6 in 4.3, to explicitly highlight the novel aspects of our method and how it addresses the limitations discussed in the introduction.

Regarding the comparative analysis, the reviewer's point is well taken. However, we want to clarify that our focus is on the APC by matrix inversion in the calibration procedure, not all matrix inversion methods. Under this condition, the "lack sampling" method indeed represents the performance of common matrix inversion APC method without additional samplings outer the swath(like CIMR case[19], where the impact of out-of-the-swath knowledge on the APC performance is analyzed.). For CAMS, the method proposed in this paper is a common matrix inversion APC in addition to the innovation of incorporating outer swath samplings. Therefore, the comparison between "additional samplings" and "lacking samplings" is valid in proving the novel aspects of our work compared to the common APC method by matrix inversion. We have added citation to show this point in the revised Section 5.1.

Major comments:

Comment 1: In the introduction, line 68-72, could you express explicitly what kinds of methods in this paper to overcome the limitation (1) and (2) listed previously?

Response 1: First, the proposed approach mitigates the limitations of the traditional APC over inhomogeneous scenes by employing 3-dB beam-scale matrix inversion. Second, the utilization of outer swath samplings effectively reduces the uncertainty in APC for swath-edge pixels. The revision can be found in the third paragraph of Section 1.

Comment 2: In Figure 1, it is better to apply polar coordinates to show the radiation pattern.

Response 2: The Cartesian coordinate representation is a format commonly used in antenna test reports and related studies; therefore, we have chosen to retain the format of Figure 1. We have normalized the antenna gain to better reflect the radiation pattern..

Comment 3: I think section 3 and 4 should be merged together to be a methodology section. The most important is that I did not find any innovations. I only find a traditional matrix inversion method is introduced. Authors should point out the novelties in this paper (as the indicated in the title and abstract). Which part of the method are used common methods or past studies? Which part of the method is new improvement distinguished with other studies? How do the method overcome limitation (1) and (2) (mentioned in introduction)? Those are key points for the paper.

Response 3: The separation between Sections 3 and 4 in our outline reflects their distinct roles. Section 3 presents the fundamental theory of matrix inversion for APC, which is not novel and forms the common foundation for all matrix-inversion-based APC methods. Section 4, however, details the implementation of this theory specifically for the CAMS scan geometry, thereby embodying the methodological innovations of our work. Presenting the foundational theory separately in Section 3 serves to provide readers unfamiliar with this field with a clear understanding of the logical framework and implementation principles of APC by matrix inversion, thereby enhancing the readability and accessibility of Section 4. We acknowledge the reviewer's important point regarding the clarity of innovation, which was also raised by other reviewers. In response, we have strengthened the text in beginning of Section 4, paragraph after equation (21) in 4.2, and paragraph after Fig.6 in 4.3, to explicitly highlight the novel aspects of our method and how it addresses the limitations discussed in the introduction.

Comment 4: Otherwise, Problem 3 is not solved. This paper is using traditional method and applied to new instruments.

Response 4: The primary innovation of our method lies in the application of outer swath sampling within a cross-track scanning framework, representing an integration of the algorithmic approach with specific instrument characteristics. The exploitation of these instrumental characteristics constitutes a significant aspect of this work's originality.

Comment 5: Give clear definitions of the boundary region, is it out of the earth scene? Or could be any scan lines out of 10 selected scan lines?

Response 5: We have revised Section 4.4.2 to explicitly define the boundary region as sufficient area covering the effective reception range of pixels at edges of solving region( including both scanline and scan position directions). Boundary region contain pixels out of the earth scene due to the novelty of our method, see the revised Fig. 8. Based on the calculation results, the boundary region may contain at least 7 scan lines. We round up and set j_boundary=10. We revised the paragraph after Fig. 8 to reflect this change.

Comment 6: Does the solving region means the 10 selected scan lines?

Response 6: The solving region is the area selected for performing APC. Refer to equation(38) and Fig.8, it is bounded by j=[j1,j2] and i=[80-i_extra,160+i_extra].

Comment 7: Fig 7 is hard to understand. I think authors need to revise and make it to be correlated with the description in 4.4.1.

Response 7: We have revised Figure 7 (now Figure 8) to achieve better correlation with the textual description. The updated figure explicitly highlights the definitions of the solving region, the boundary region and the additional sampling region, and visually clarifies the required range of the boundary region.

Comment 8: Line 319, any reason for selecting 10 scan lines?

Response 8: As stated in response 5, the number 10 was chosen because it is sufficient to fully cover the effective reception range (the circle in Fig. 8) of the edge pixels in the solving region, preventing the introduction of more unknowns.

Comment 9: Section 4.2 considering [80, 160] for the earth scene. But in equations in 4.4.1 are different. Why do not considering the whole 230 pixels in the beginnings?

Response 9: We thank the reviewer for highlighting this potentially confusing point. The Earth-scene scanning positions are consistently fixed within [80, 160]. There is no need to include all 230 pixels to perform APC to Earth swath due to the limited impact of error introduced by boundary conditions. Therefore, we redefined the solving region(comment 6) and revised equations(38)(39) and the corresponding text.

Comment 10: I do not understand the index of j in Eq (38) and (39). Why m and n have different index? Why j is not j1-10,…,j1-1,j2+1,..,j2+10 but j=0,…,19

Response 10: The discrepancy between indices m and n arises because, before incorporating the boundary conditions, the number of knowns(m) and unknowns(n) are unequal. We thank the reviewer for identifying the issue with the scan line indexing and have revised the relevant descriptions of equation(38)(39).

Comment 11: Using equation to express boundary condition (a) and (b). The description is not clear for me.

Response 11: Following the reviewer's suggestion, we have represented the two boundary setting conditions using equations (41)(42) .

Comment 12: Line 381-385, what does additional samplings mean? Boundary conditions or samplings beyond the Earth scene? The term of “lack sampling” is confusing.

Response 12: In this text, "additional samplings" specifically refer to the measurements acquired by CAMS from beyond the Earth swath, e.g., at scan positions 79 and 161. "Lack of sampling" denotes the scenario in common matrix inversion APC methods where such data are unavailable. We have revised Fig.8 to show the difference between additional samplings region and boundary, the additional samplings region still belongs to the solving region and serves to improve the APC performance for swath edge pixels. We have revised Section 5 to elaborate on the setup of the comparison framework. The use of "lack sampling" is indeed confusing and is thus prevented.

Comment 13: I think the paper does not do good result comparisons. The “lack sampling” method is not scientifical. Authors should give the most common used or most updated matrix inversion algorithms in the community and give references in the paper. Mark this algorithm by the name of inventors.

Response 13:

We understand the reviewer's concern. We would like to clarify that the focus of the paper is specifically on Antenna Pattern Correction (APC) algorithms for radiometer calibration, rather than on more general matrix inversion algorithms. An APC algorithm is essentially the implementation of antenna temperature inversion based on a specific instrument's scan geometry. Applying a most updated APC algorithm (e.g., one developed for a large mesh antenna like CIMR[19]) to the CAMS case would essentially yield what we describe in Section 5.1 as the method without outer-swath sampling. The method proposed in this paper utilizes a fundamental framework for APC in cross-track scanning geometry, in addition to the innovation of incorporating outer swath samplings. Consequently, by controlling whether real outer swath samplings or auxiliary out-of-swath information are used, we can effectively compare the APC performance at the swath edges, thereby highlighting the significance of the proposed method and the introducing of additional samplings.

Comment 14: To be consistent for the result legends for all the figures (from Fig. 9 to the end). It is better to define all the legends at beginning. “BT1” has different meaning for Fig 10 and Fig 12. I think both “BT1” and “BT3” are proposed by this paper. BT0 is a new term in Fig 13. All those are making readers confusing.

Response 14: We thank the reviewer for pointing this out. We have now defined all legends at beginning within Section 5.1.

Reviewer 3 Report

Comments and Suggestions for Authors

Summary

The manuscript proposes a novel Antenna Pattern Correction (APC) method for the Compact Atmospheric Microwave Sounder (CAMS). The authors leverage the instrument's full-circular scanning capability to utilize sampling data outside the Earth swath as boundary conditions for a matrix inversion approach. The study claims that this method improves correction accuracy at the scan edges and enhances the detection of brightness temperature gradients in heterogeneous scenes (e.g., coastlines) by retrieving temperatures at the 3dB beamwidth scale rather than the main beam scale.

The topic is relevant to the remote sensing community, specifically for small satellite microwave sounders. The mathematical derivation is generally clear. However, there are concerns regarding the validation methodology, the handling of noise amplification, et al. These issues need to be addressed before publication.

Major Comments

1.Section 5 (Result), Page 15, Lines 368-378

The validation strategy involves using CAMS raw antenna temperatures (TA) to interpolate a "reference brightness temperature (TB)" field, convolving it back to simulate TA, and then applying the correction. While this checks the mathematical self-consistency of the inversion algorithm, it is a circular logic that does not validate the method against "true" geophysical biases or calibration errors.

The authors should validate the method against independent data. For example, comparing the corrected TBs against simulated TBs derived from Numerical Weather Prediction (NWP) models (e.g., ECMWF or GFS) coupled with a radiative transfer model. Alternatively, a cross-calibration comparison with a mature instrument (like ATMS or AMSU-A) would provide stronger evidence of the method's effectiveness in real-world scenarios.

2. Section 4.4.1, Page 13, Lines 319-322

The authors state: "Select 10 scan lines at both ends of the solving region... to set constraint equations". The choice of "10 scan lines" appears arbitrary.

Please provide a theoretical or empirical justification for this number. Is the performance sensitive to this parameter? Would 5 lines be insufficient, or would 20 lines improve accuracy further? A brief sensitivity test regarding the size of the boundary region would strengthen the methodology.

Minor Comments

Page 1, Abstract, Line 18 ; Page 2, Line 80 ; Page 16, Line 382 ; Page 21, Line 519 …

The word "swarth" is consistently misspelled. It should be "swath" (e.g., "outside the swath"). Please correct this throughout the manuscript.

Author Response

Thank you for your comments. Please check our reply in the attachment!

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript presents a novel APC method tailored for cross-track scanning microwave sounders, particularly focusing on the CAMS. However, probably there are some suggestions to be considered:

Most of the references cited are published before even 2000. Please include more recent published papers related;
Why is the frequency point chosen in Fig. 1(a) 87.2 GHz, instead of the 89 GHz or 89.2 GHz mentioned in Line 84 and 92?
Is the "outside the swarth" in Line 12 the same meaning with the "out-of-swath" in Line 49? So the "swarth" in Abstract should be corrected to "swath"?
There is no finding about the novelty of the proposed APC method in Introduction and the Section 3&4;
The manuscript is more like a review rather than a frontier research paper.

Author Response

Comment 1:

Most of the references cited are published before even 2000. Please include more recent published papers related.

Response 1:

The theory and methodology of antenna deconvolution were established in the last century, which explains our numerous citations to works before 2000. Following the reviewer's suggestion, we have included more recent references in the paper[2][3][12][13][14][15][22].

Comment 2:

Why is the frequency point chosen in Fig. 1(a) 87.2 GHz, instead of the 89 GHz or 89.2 GHz mentioned in Line 84 and 92?

Response 2:

We thank the reviewer for pointing this out. The frequency point chosen in Fig. 1(a) should be 89.2GHz. The error in Fig. 1 has been corrected.

Comment 3:

Is the "outside the swarth" in Line 12 the same meaning with the "out-of-swath" in Line 49? So the "swarth" in Abstract should be corrected to "swath"?

Response 3:

Thank you for pointing this out. The term "swarth" has been corrected to "swath" throughout the manuscript.

Comment 4:

There is no finding about the novelty of the proposed APC method in Introduction and the Section 3&4;

Response 4:

The reviewer's point is important and aligns with concerns raised by other reviewers.

The novelty of our method primarily lies in its utilization of outer swath samplings in the implementation of matrix inversion APC for microwave sounders. We have emphasized this aspect in the Introduction, 3^rd paragraph.

Section 3 presents the principle of matrix inversion, which does not contain novel contributions. In the revised paper, the innovation is emphasized in the beginning of Section 4. The methodological novelty lies in the first-time utilization of sampling from the outer Earth swath to assist in the matrix inversion for pixels near the swath edges. Section 4 details our proposed methodology. Specifically, Section 4.2 explains how directional vectors for outer-swath pixels are computed, which are then employed in the antenna pattern grid matching in Section 4.3. To reflect this, we have strengthened the description of methodological novelty in paragraphs after equation (21) and after Fig. 6.

Comment 5:

The manuscript is more like a review rather than a frontier research paper.

Response 5:

We understand the reviewer's perspective. It is true that research on antenna pattern correction (APC) may not present fundamental breakthroughs in principle, as it essentially involves deconvolving antenna temperature based on a given instrument's scanning geometry. Our study primarily addresses the limitations of conventional APC methods for existing microwave sounders. By integrating the matrix inversion method tailored for cross-track scan geometry with the unique additional sampling capability of CAMS, we have conducted a frontier research withs respect to APC and sampling strategies for spaceborne microwave sounders.

The novelty of our work is two-fold. First, for microwave sounders, it demonstrates improved performance over traditional methods in heterogeneous scenes. Since real-world observations are invariably non-uniform, this improvement carries significant practical meaning and application value. Second, by leveraging outer swath sampling of CAMS, we effectively reduce the uncertainty in corrected brightness temperatures at scan edges. We systematically analyze the precision enhancement contributed by these additional samples across CAMS channels, providing valuable insights for both APC implementation and sampling strategy design in other microwave radiometers.

We further emphasized these points in the introduction and discussion sections. If the reviewer has more specific comments or suggestions regarding the novelty of our method, we would greatly appreciate your feedback.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have comprehensively addressed all the concerns raised in my previous review. I am satisfied with the current version and recommend its acceptance for publication.

Author Response

We are grateful for your invaluable constructive feedback, which has significantly enhanced the quality of this paper.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

There are still two tips for considerations:

Depending on the novelty of the proposed APC method in Introduction and the Section 3&4, I insist on the pointing out the advantage of utilization of sampling from the outer Earth swath to assist in the matrix inversion for pixels near the swath edges. Please list the comparison table to highlight the effectiveness of the proposed APC method, so as to demonstrate improved performance over traditional methods in heterogeneous scenes.
Please try to shrink or compress the content of the fundamental description in Section 3&4, thus making the manuscript more like a frontier research paper.

Author Response

Please see the attachment.

Author Response File: Author Response.docx