Utilization of a Lightweight 3D U-Net Model for Reducing Execution Time of Numerical Weather Prediction Models
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article is considered not adequately associated with Atmospheric Sciences per se and can be hardly recommended for experts in the field. No concrete results are presented and relatively few references are addressed directly associated with the Atmospheric Sciences’.
The article practically used numerical weather prediction to support an elaborate computational application related to the utilization of several techniques associated with Artificial Intelligence and/or Deep learning algorithms, as well as high performance computation in general. From these perspectives, it could be readdressed to a Journal associated with the Computational Sciences.
Some more specific comments within the context of the article are as follows:
General comment:
The authors are selectively explaining the acronyms, more specifically,
line 3:
It should be stated that GloSea6 stands for Met Office Global Seasonal Forecasting System version 6.
line 12:
It should be stated that the initials BiCGStab, most probably, stand for Biconjugate gradient stabilized method.
line 13:
The initials CH-UNet should be explained. In general, the authors assume that the reader should be accustomed with several acronyms associated with computer sciences, which is not the case especially for this Journal.
line 98:
Please explain the acronym SwinRNN (may be Swin Recurrent Neural Network, what Swin stands for ?)
line 107:
Please explain the acronym: SwinRDM
line 133:
Please explain LDAPS (may be local data assimilation and prediction system).
Additional comments:
line 23:
Please replace "human life" with "public safety in general"
line 44:
Why the model is computationally demanding? Apparently the number of grid points is 50x85x38, which is quite small. What is the geographical domain?
line 91:
Please correct "Kwon" to "Kwok"
line 150:
Please, replace "inconveniencing meteorological" to "inconveniences to".
lines 236, 272 and other places,
The references are cited without their leading authors.
lines 339-340: What is the physical meaning of the variables. For which physical variables explicitly, is there any improvement? From this perspective, the statistics are rather vague.
line 399:
Please, place some relevant references.
------ End of comments -----
Author Response
The article is considered not adequately associated with Atmospheric Sciences per se and can be hardly recommended for experts in the field. No concrete results are presented and relatively few references are addressed directly associated with the Atmospheric Sciences’.
The article practically used numerical weather prediction to support an elaborate computational application related to the utilization of several techniques associated with Artificial Intelligence and/or Deep learning algorithms, as well as high performance computation in general. From these perspectives, it could be readdressed to a Journal associated with the Computational Sciences.
Thank you for your thoughtful feedback on this paper. We propose a method and a framework for integrating deep learning models into NWP models, enabling weather modeling with fewer resources. We believe this approach can significantly benefit the field of weather modeling, allowing efficient research even on small to medium-scale servers and providing valuable tools for broader weather applications.
The authors are selectively explaining the acronyms, more specifically,
General comment:
Comments 1: line 3: It should be stated that GloSea6 stands for Met Office Global Seasonal Forecasting System version 6.
Response 1: Thank you for your valuable suggestion. We have carefully reviewed the relevant section and have explicitly clarified in LINE 3 that GloSea6 refers to the Met Office Global Seasonal Forecasting System version 6.
“The Korea Meteorological Administration (KMA) adopted the Met Office Global Seasonal Forecasting System version 6 (GloSea6) NWP model from the UK and runs it on a supercomputer.”
Comments 2: line 12: It should be stated that the initials BiCGStab, most probably, stand for Biconjugate gradient stabilized method.
Response 2: Thank you for your valuable suggestion. We have carefully examined the relevant section and explicitly clarified in LINE 13 that BiCGStab refers to the Biconjugate Gradient Stabilized Method.
“The profiling identified "tri_sor.F90" as the main CPU time hotspot. By combining the Biconjugate gradient stabilized (BiCGStab) method , used for solving the Helmholtz problem, with a deep learning model, we reduced unnecessary hotspot calls, shortening execution time.”
Comments 3: line 13: The initials CH-UNet should be explained. In general, the authors assume that the reader should be accustomed with several acronyms associated with computer sciences, which is not the case especially for this Journal.
Response 3: Thank you for your insightful suggestion. We agree that abbreviations like CH-UNet may lack clarity for readers. To address this, we have revised LINE 15 as follows:
“We also propose Convolutional block attention module based Half-UNet (CH-UNet) , a lightweight 3D-based U-Net architecture, for faster deep-learning computations.”
Comments 4: line 98: Please explain the acronym SwinRNN (may be Swin Recurrent Neural Network, what Swin stands for ?)
Response 4: Thank you for your thoughtful feedback. Based on your suggestion, we have included the abbreviation for SwinRNN and provided additional explanations about Swin in LINES 100 and 104.
“SwinRNN is structured to utilize atmospheric variables arranged in a grid and extract multi-scale features through cube embedding and the Shifted Window (Swin) Transformer, which shifts the grid by half the window size during the encoding process”
Comments 5: line 107: Please explain the acronym: SwinRDM
Response 5: Thank you for your valuable feedback. In LINE 110, we have thoughtfully incorporated additional details regarding the abbreviation SwinRDM to enhance clarity.
“SwinRNN with Diffusion Model (SwinRDM)”
Comments 6: line 133: Please explain LDAPS (may be local data assimilation and prediction system).
Response 6: Thank you for your insightful feedback. In LINE 136, we have included the long form of LDAPS, “Local Data Assimilation and Prediction System (LDAPS),” to provide greater clarity and improve understanding.
Additional comments:
Comments 7: line 23: Please replace "human life" with "public safety in general"
Response 7: Thank you for your valuable feedback. We have updated LINE 25 to read as “public safety in general.”
“Weather forecasting is crucial to modern society, including its impact on industry, agriculture, and public safety in general.”
Comments 8: line 44: Why the model is computationally demanding? Apparently the number of grid points is 50x85x38, which is quite small. What is the geographical domain?
Response 8: Thank you for your valuable guidance. The grid size of 50x38x85 presented in the text refers to the grid assigned to a single process, not the entire model. The full grid is 200x152x85, and, similar to GloSea6, the geographical domain covers the entire globe. To provide clearer information to readers, we have revised LINE 359 as follows.
“The total grid size used in Low GloSea6 is 200 (width) × 152 (height) × 85 (depth). We divided the entire grid equally in the vertical direction and assigned it to 16 cores for parallel processing. As a result, the grid allocated to each core’s process is a 3D grid with a size of 50 (width) × 38 (height) × 85 (depth), containing a total of 161,500 cells per process.”
Comments 9: line 91: Please correct "Kwon" to "Kwok"
Response 9: Thank you for your valuable feedback. We have revised the cited author information in LINE 93 accordingly.
“For example, Kwok et al. [2] achieved third place in the core and transfer learning challenges of the Weather4cast 2021 competition using a U-Net neural network architecture with a Variational Autoencoder-style bottleneck structure.”
Comments 10: line 150: Please, replace "inconveniencing meteorological" to "inconveniences to".
Response 10: Thank you for your valuable feedback. We have revised the phrase you mentioned in LINE 155 accordingly.
“This method aims to avoid inconveniences to researchers who use traditional NWP models.”
Comments 11: lines 236, 272 and other places, The references are cited without their leading authors.
Response 11: Thank you for your thoughtful suggestion. To maintain consistency throughout the manuscript, we have revised the references as follows:
In LINE 241, "Previous studies by Tae [13], Mittal [14], and Allaviranloo [15]";
in LINE 278, "Numerous previous studies by Vorst [16], Wang et al. [17], Long et al. [18], and Havdiak et al. [19]";
and in LINE 371, "Fully Convolutional Network (FCN), as proposed by Long et al. [24]."
Comments 12: lines 339-340: What is the physical meaning of the variables. For which physical variables explicitly, is there any improvement? From this perspective, the statistics are rather vague.
Response 12: Thank you for your thorough review. The variables we presented, such as “cr,” "r," "v," "t," "x1," "b1," "p1," "x2," "b2," and "p2," follow the variable naming conventions used in the BiCGStab process implemented within GloSea6. As BiCGStab is a method used for numerical operations among various meteorological variables, its variables do not represent specific meteorological parameters. Descriptions of these variables in the context of the BiCGStab process are provided in Table 4. To enhance clarity, we have added the explanation to LINES 344 and 349 as follows.
“shows the correlation heatmap among the variables directly used in the BiCGStab process”,
“The variables used in the analysis do not represent specific meteorological variables, as they were utilized in the BiCGStab computational process for numerical operations on various variables. This indicates that the methodology can be applied to all processes and meteorological variables where the BiCGStab method is employed, such as pressure increment calculations in GloSea6”.
Additionally, thank you for your valuable suggestions. Our study is not aimed at improving specific physical variables but rather focuses on approximating the variable “x,” calculated in BiCGStab, by employing a deep learning model. This approach aims to reduce computational costs while maintaining results similar to those of the traditional BiCGStab method. To achieve this, we conducted a correlation analysis among variables to reduce the number of features used in the deep learning model, enabling computation with lower processing demands.
Comments 13: line 399: Please, place some relevant references.
Response 13: In response to your feedback, we have included references to related studies that utilized the U-Net architecture for meteorological forecasting in LINE 415.
“such as those by Kim [26] and Fernandez [27],”
We sincerely appreciate your insightful review of our manuscript. As our article is intended for submission to the Atmosphere journal’s special issue, “Deep Learning Algorithms for Weather Forecasting and Climate Prediction,” We aimed to apply our machine learning approach to enhance numerical weather forecasting models. Through this approach, our study demonstrates its applicability not only to improving the accuracy of specific meteorological variable predictions or enhancing the performance of specific weather models but also to providing a universally applicable methodology for studies involving numerical weather prediction. Consequently, our research offers meteorological researchers a practical solution for running weather models efficiently without being constrained by limited computational resources.
In universities and research institutions, the inability to access supercomputers often necessitates running weather models on small to medium-scale servers, which can be inconvenient. To address this, we propose a method to integrate deep learning models into existing Numerical Weather Prediction (NWP) models, enabling seamless meteorological research even on servers with relatively limited computational resources. Additionally, we suggest a restricted application approach to avoid increasing the difficulty of interpreting the physical aspects of existing NWP models. Furthermore, we propose a lightweight U-Net architecture to achieve even faster model execution times.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper proposes a method to reduce the execution time of numerical weather prediction (NWP) models by integrating a lightweight 3D U-Net model, which is a significant contribution for research institutions with limited computational resources.
The authors have validated the effectiveness of the CH-UNet model in reducing computational resource requirements while maintaining or improving predictive accuracy through detailed experiments. The paper is well-structured, logically rigorous, comprehensively designed in terms of experiments, and the results are convincing.
Author Response
Comments 1: This paper proposes a method to reduce the execution time of numerical weather prediction (NWP) models by integrating a lightweight 3D U-Net model, which is a significant contribution for research institutions with limited computational resources.
The authors have validated the effectiveness of the CH-UNet model in reducing computational resource requirements while maintaining or improving predictive accuracy through detailed experiments. The paper is well-structured, logically rigorous, comprehensively designed in terms of experiments, and the results are convincing.
Response 1: Thank you for reviewing our manuscript and providing your evaluation. We are committed to addressing this revision carefully to ensure that our machine-learning approach can be effectively applied to the field of meteorological research.
Thank you for your insightful feedback on this manuscript. We proposed a framework that integrates existing Numerical Weather Prediction (NWP) models with deep learning models to enable efficient execution of weather models even with limited computational resources. Our approach demonstrated a 2.6% reduction in execution time compared to traditional NWP models.
Furthermore, while the integration of existing NWP models with deep learning models has often posed challenges for meteorological researchers in terms of physical interpretation, our study proposes a method that is effectively applied. This approach not only reduces the execution time of weather models but also facilitates ease of interpretation from a physical perspective.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis is a very interesting research work. Initially, I thought it should submitted to the IT journal.
After checking it, I recommend this manuscript for publication. It would help readers understand how to apply ML methods to the NWP model.
Author Response
Comments 1: This is a very interesting research work. Initially, I thought it should submitted to the IT journal.
After checking it, I recommend this manuscript for publication. It would help readers understand how to apply ML methods to the NWP model.
Response 1: Thank you for your evaluation of our manuscript. Our study aims to support meteorological researchers who lack access to supercomputers or face computational resource constraints, enabling them to conduct research more efficiently. We sincerely appreciate your insightful review.
This manuscript was prepared for submission to the special issue of the Atmosphere journal, titled “Deep Learning Algorithms for Weather Forecasting and Climate Prediction.” It explores methods for integrating deep learning and machine learning techniques into conventional numerical weather prediction models. We sincerely thank you for your efforts in reviewing our work, enabling further improvements to our manuscript.
Thank you for your feedback and evaluation. We proposed a method that integrates deep learning approaches into existing Numerical Weather Prediction (NWP) models to enable seamless meteorological research on small to medium-scale servers in universities and research institutions without access to supercomputers. This approach resulted in a 2.6% reduction in execution time compared to traditional methods, demonstrating that weather model simulations can be performed with lower computational resources. To address the challenge of physical interpretability that arose in previous studies when integrating NWP models with deep learning models, we propose an effective application of deep learning to the BiCGStab solver, identified as the hotspot consuming the most CPU time. By doing so, we present a deep learning integration framework that enables meteorological researchers to conduct seamless and efficient weather research.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsReview of the Manuscript: “Utilization of a Lightweight 3D U-Net Model for Reducing
Execution Time of Numerical Weather Prediction Models” by Hyesung Park and Sungwook Chung
Overview:
In this paper,the author elaborated a way in detail,which integrated deep learning technology CH-Unet with Low GloSea6 without altering the original configuration of Low GloSea6 or complicating physical Interpretation.The way can reduce execution time and improve meteorological research efficiency.This research is very necessary and important.The paper is well written, However, there are still some problems needed to be properly addressed. Detailed comments are listed below.
Major Comments:
1. As a suggestion,try to make the source of concluding statements in the paper as clear as possible, e.g., Line 138,”the application of deep learning technology has been limited to specific weather variables”,what is the scientific basis for such a write-up?
2. Please pay attention to the logical relationship between statements and other details, such as Line 285, is it reasonable to use two “therefore”？Line 492, Chapter 4.A is not found in the paper . Line 566, 582 and 588, please write the specific chapter number clearly .
3. By the way,Is there any target value or ideal value for the reduction of CH-UNet execution time? Are there the corresponding solutions?
4. Please accept after modification .
Comments for author File: Comments.pdf
The paper is well written
Author Response
In this paper,the author elaborated a way in detail, which integrated deep learning technology CH-Unet with Low GloSea6 without altering the original configuration of Low GloSea6 or complicating physical Interpretation.The way can reduce execution time and improve meteorological research efficiency.This research is very necessary and important.The paper is well written, However, there are still some problems needed to be properly addressed. Detailed comments are listed below.
Thank you for showing deep interest in our manuscript and providing insightful feedback. We will carefully incorporate your suggestions to ensure that the paper becomes more technically robust.
Comments 1: As a suggestion,try to make the source of concluding statements in the paper as clear as possible, e.g., Line 138,”the application of deep learning technology has been limited to specific weather variables”,what is the scientific basis for such a write-up?
Response 1: Thank you for your valuable feedback. We have highlighted that certain prior studies adopt a post-processing approach to predict specific meteorological variables using deep learning, while others propose entirely new models for predicting all meteorological variables, significantly diverging from conventional numerical weather modeling frameworks. These methods often pose interpretative challenges for meteorological researchers due to the unique characteristics of deep learning architectures. To make this point clearer, we have added citations to related studies for each case in LINE 142.
“Additionally, in several studies such as those by Kwok et al. [2], Frnda et al. [4], and Cho et al. [5], the application of deep learning technology has been limited to specific weather variables. Although some studies, including Chen et al. [3] and Lam et al. [6], have attempted to predict overall weather variables, their structures differ significantly from existing NWP models, potentially causing inconvenience for meteorological researchers.”
Comments 2: Please pay attention to the logical relationship between statements and other details, such as Line 285, is it reasonable to use two “therefore”？Line 492, Chapter 4.A is not found in the paper . Line 566, 582 and 588, please write the specific chapter number clearly .
Response 2: Thank you for your thoughtful suggestions. We agree that the use of two "therefore" statements in close proximity could create logical ambiguity. Accordingly, we revised LINE 292 as follows:
“As a result, iterative methods must be employed. As illustrated in Figure 4, Low GloSea6 employs the BiCGStab method to solve large-scale three-dimensional linear systems, calling it a total of four times within the dual loop structure of ENDGame in atm_step_4A.”
In addition, we corrected the reference in LINE 507 to “Chapter 4.1” to ensure accuracy. Furthermore, we explicitly specified the chapter numbers in LINE 581, 597, and 603 for greater clarity.
Comments 3: By the way,Is there any target value or ideal value for the reduction of CH-UNet execution time? Are there the corresponding solutions?
Response 3: Thank you for your valuable feedback. In general, when applying machine learning models, there is no predefined or estimated target or ideal value in advance. In our study, the CH-UNet does not have a predefined target or ideal value for execution time reduction. Our primary objective is to integrate deep learning models like CH-UNet into numerical weather models such as GloSea6 to find out whether our proposed solution is feasible and how much it can reduce the execution time. This approach aims to provide a viable solution for researchers who face challenges conducting meteorological studies due to the lack of access to supercomputers or limited computational resources.
By applying the proposed CH-UNet, we demonstrated a 2.6% reduction in execution time compared to the traditional numerical calculations of Low GloSea6. This result highlights the potential for conducting weather model simulations at a lower cost, making meteorological research more accessible and feasible.
Comments 4: Please accept after modification .
Response 4: We have reviewed your feedback and incorporated the suggested revisions to enhance the clarity of the results presented in this manuscript.
Thank you for your thoughtful feedback on our study. We have carefully reviewed your suggestions and incorporated revisions to improve the manuscript. By integrating the existing NWP model, Low GloSea6, with the deep learning model, CH-UNet, we achieved a 2.6% reduction in execution time compared to the traditional NWP model. Additionally, we propose a framework that maintains the structure of existing NWP models to ensure ease of use in meteorological research while minimizing challenges related to physical interpretability by applying deep learning effectively to specific hotspots. Furthermore, the results of this study demonstrate that weather model simulations can be effectively performed even with limited computational resources.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsReviewer's comments on revision 2.
---------------------------------------
The authors replied to the reviewer's comments associated the clarifications to the text. The reviewer acknowledges their effort positively.
They also mention that this work is addressed to an Atmosphere journal’s special issue, “Deep Learning Algorithms for Weather Forecasting and Climate Prediction”.
However, this statement is not considered by itself sufficient by the reviewer to place his acceptance.
The reviewer should consider upon a positive decision, the following, major revisions:
1. The structuring of the article is in vague accordance to the one recommended by the template of Atmosphere, (i.e. Introduction, Materials and Methods, Results). It should be clear with the Journal Editors if such a structuring is acceptable. In the reviewer's opinion, it is not difficult for the authors to reform the article accordingly. The reviewer will consider his decision only if he is assured of the appropriate structuring.
2. Of particular importance is their reply to comment 9, i.e.
Comment 9: lines 339-340: What is the physical meaning of the variables. For which physical variables explicitly, is there any improvement? From this perspective, the statistics are rather vague.
Response 9: Thank you for your thorough review. The variables we presented, such as “cr,” "r," "v," "t," "x1," "b1," "p1," "x2," "b2," and "p2," follow the variable naming conventions used in the BiCGStab process implemented within GloSea6. As BiCGStab is a method used for numerical operations among various meteorological variables, its variables do not represent specific meteorological parameters. Descriptions of these variables in the context of the BiCGStab process are provided in Table 4. To enhance clarity, we have added the explanation to LINES 344 and 349 as follows.
“shows the correlation heatmap among the variables directly used in the BiCGStab process”,
“The variables used in the analysis do not represent specific meteorological variables, as they were utilized in the BiCGStab computational process for numerical operations on various variables. This indicates that the methodology can be applied to all processes and meteorological variables where the BiCGStab method is employed, such as pressure increment calculations in GloSea6”.
The authors should demonstrate the explicit relations of the considered variables with concrete atmospheric parameters in detail to be comprehensible by the community of atmospheric sciences. If this cannot be done or explained, the reviewer should be expected to retain his reservation upon any positive consideration regarding the publication.
End of Reviewer's comments on revision 2.
-----------------------------------------------
Author Response
The authors replied to the reviewer's comments associated the clarifications to the text. The reviewer acknowledges their effort positively.
They also mention that this work is addressed to an Atmosphere journal’s special issue, “Deep Learning Algorithms for Weather Forecasting and Climate Prediction”.
However, this statement is not considered by itself sufficient by the reviewer to place his acceptance.
The reviewer should consider upon a positive decision, the following, major revisions:
Comments 1: The structuring of the article is in vague accordance to the one recommended by the template of Atmosphere, (i.e. Introduction, Materials and Methods, Results). It should be clear with the Journal Editors if such a structuring is acceptable. In the reviewer's opinion, it is not difficult for the authors to reform the article accordingly. The reviewer will consider his decision only if he is assured of the appropriate structuring.
Response 1: We sincerely appreciate your thoughtful advice. Following your suggestion, we have restructured the paper to adhere to the template of Atmosphere with the sections organized as “Introduction, Materials and Methods, Experiments, and Conclusion.” These changes, which are highlighted on PAGE 2 to 16, were made to align the manuscript with the journal's format. Your guidance has significantly contributed to strengthening our work, and we thank you once again for your valuable suggestions.
Comments 2: Of particular importance is their reply to comment 9, i.e.
Comment 9: lines 339-340: What is the physical meaning of the variables. For which physical variables explicitly, is there any improvement? From this perspective, the statistics are rather vague.
Response 9: Thank you for your thorough review. The variables we presented, such as “cr,” "r," "v," "t," "x1," "b1," "p1," "x2," "b2," and "p2," follow the variable naming conventions used in the BiCGStab process implemented within GloSea6. As BiCGStab is a method used for numerical operations among various meteorological variables, its variables do not represent specific meteorological parameters. Descriptions of these variables in the context of the BiCGStab process are provided in Table 4. To enhance clarity, we have added the explanation to LINES 344 and 349 as follows.
“shows the correlation heatmap among the variables directly used in the BiCGStab process”,
“The variables used in the analysis do not represent specific meteorological variables, as they were utilized in the BiCGStab computational process for numerical operations on various variables. This indicates that the methodology can be applied to all processes and meteorological variables where the BiCGStab method is employed, such as pressure increment calculations in GloSea6”.
The authors should demonstrate the explicit relations of the considered variables with concrete atmospheric parameters in detail to be comprehensible by the community of atmospheric sciences. If this cannot be done or explained, the reviewer should be expected to retain his reservation upon any positive consideration regarding the publication.
Response 2: Thank you for your insightful suggestions. Based on your recommendations, we have aimed to explain the meteorological significance of the BiCGStab variables used in the feature correlation analysis for deep learning, as they pertain to Low GloSea6. The relevant details can be found in the manuscript on LINES 283–309 and 356–396.
Following machine learning and deep learning approaches, we integrated the role of BiCGStab—adjusting the Exner perturbation computed in the pressure field to satisfy the current physical constraint state, precomputed in the previous step—into the deep learning model. This integration enables the prediction of the final converged result without repeating the iterative convergence process. The deep learning model functions equivalently to a mathematical formula, performing the same role as BiCGStab. By utilizing numerous perceptrons capable of capturing latent information within extensive training datasets, the model can infer the final corrected Exner perturbation without iterative numerical computations.
Additionally, it is worth noting that the meteorological variables involved in the Helmholtz problem [24] and the variables analyzed for correlation and used as features [23] in this study may not perfectly align in their semantic meanings. In other words, in the context of our machine learning approach, the variables represent values tailored for training or prediction in a machine learning or deep learning model. While they are related to specific meteorological variables, our primary focus was on replicating the role of BiCGStab as closely as possible. To achieve this, we utilized the variables directly involved in the computational process of BiCGStab, ensuring consistency with its operations and emphasizing the prediction of these variables in their computational context.
Moreover, to provide the atmospheric science community with a clearer connection to meteorological parameters, we have elaborated on the relationship between the initial input variables of BiCGStab, such as "x" and "b", and atmospheric parameters as much as possible. While other variables are not directly associated with meteorological parameters, we have included detailed explanations regarding their roles within BiCGStab, such as temporary storage latent variables or variables indicating the direction of convergence. These additional details aim to enhance the understanding of meteorological researchers, making the paper more accessible and comprehensible to the community.
LINES 283–309:
“As shown in Figure 2, Low GloSea6 performs computations for the vertical and horizontal wind components in the outer loop of the double-loop structure of ENDGame. During this process, the Helmholtz procedure calculates the pressure increments using the BiCGStab method, which is invoked a total of four times to accelerate the computation of the Helmholtz problem. Numerically, BiCGStab is a solver that resolves "Ax=b" iteratively to converge and determine the pressure increments. A detailed explanation of the variables within BiCGStab for solving the Helmholtz problem in Low GloSea6 used in this study is provided in the discussion below.
The input variables for BiCGStab are "x" and "b". The variable "x" represents the deviation of the Exner function value at the next time step relative to the reference Exner field, precomputed in the previous step. The use of the Exner function is motivated by the need for computational acceleration in BiCGStab, as it reduces the computational cost by converting the pressure field into a dimensionless variable and simplifying the governing equations through non-dimensionalization. The variable "b" corresponds to the right-hand side of the linear equation "Ax=b". It is precomputed by combining wind, density, potential temperature, and pressure as inputs. Other variables are computed internally within BiCGStab to ensure convergence and are iteratively updated during each step. Among these, the residual variable "r" measures how well the current estimate "x" satisfies the right-hand side "b". The variable "p" represents the optimal direction to reduce the residual "r" and is computed using a preconditioner in Low GloSea6. The preconditioner employed here is the "tri_sor" module, identified as a hotspot through prior profiling. Additionally, there are correction-related variables such as "v", "s", and "t", which are used to update the residual during the iterative process. In this study, we aim to analyze the correlations between the input variables "x" and "b" and the internally computed variables within BiCGStab. These correlations will be utilized for deep learning training. The detailed methodology for this analysis is presented in Chapter 2.2.”
LINES 356–396:
“Furthermore, as described in Chapter 2.1.3, we analyzed the correlations among the variables used during the BiCGStab convergence process, beyond the input variables "x" and "b", to identify an additional feature for the deep learning model. As a result, we selected one more input feature, bringing the total number of features used for model training to three. Besides, we confirmed that each variable updates iteratively during the BiCGStab convergence process as their values gradually approach convergence with each iteration. Based on this observation, we selected six features used during the initial 1–2 iterations as the input for the deep learning model. Here, the term "feature," following Brownlee [23], refers to the variables used during model training in machine learning approaches. It may not directly correspond to meteorological variables [24] but rather represents the input or output variables of a machine learning or deep learning model, which could differ slightly in interpretation. Figure 3 illustrates the correlation heatmap among the variables directly used in the BiCGStab process. The detailed procedure for the correlation analysis based on the heatmap is as follows. Among the variables from the first two iterations of BiCGStab, more than half showed near-zero correlations with the output variable. Additionally, variables such as "cr", "r", "v", and "t" exhibited no changes during the first iteration as they were not utilized at this stage. Consequently, we selected variables with a correlation of 0.05 or higher, which displayed very weak correlations, as input features for deep learning training. These variables include "x1", "b1", "p1", "x2", "b2", and "p2".
The variables used in the analysis and for training the deep learning model differ from the initial input variables of BiCGStab. These variables are either updated iteratively in a converging direction or utilized in the correction and numerical computation processes during convergence. They are latent or temporary storage variables and, therefore, do not have direct associations with specific meteorological variables. By leveraging the high potential of artificial neural network structures under machine learning and deep learning approaches, we aimed to capture subtle changes during the initial convergence iterations of BiCGStab. This allows the deep learning model to predict results similar to the actual final convergence output without completing the entire iterative process. Specifically, instead of resolving the Exner perturbation "x" in the initial pressure field to satisfy the current physical constraint state "b" (precomputed using wind, density, and temperature fields), the deep learning model functions as a surrogate correction mechanism to perform the Exner perturbation adjustment directly. Another goal of this study is to integrate the deep learning model into the NWP framework without increasing the difficulty of physical interpretation. To achieve this, we focused on replacing computationally expensive hotspots, such as BiCGStab, which are not directly related to meteorological variables but consume significant execution time during NWP operations. To ensure the selected variables are distinguishable based on BiCGStab iterations, we redefined the variable names. Table 6 provides a detailed explanation of these redefined variables. Here, "x" represents the Exner value after BiCGStab convergence, which is the target predicted by the deep learning model.”
Thank you once again for your thoughtful feedback. Following your suggestions, we revised the manuscript to strengthen its structure and better reflect the connection between the variables considered in the machine learning approach and the meteorological parameters within BiCGStab.
By integrating our proposed deep learning model, CH-UNet, into the conventional NWP model, we achieved a 2.6% reduction in execution time compared to the traditional NWP model. This improvement minimizes unnecessary computational operations during weather model execution, thereby reducing the required computing resources.
In Addition, CH-UNet was designed to achieve superior prediction accuracy with a reasonably low computational cost. This balance allows CH-UNet to accelerate the convergence iterations of BiCGStab when executed subsequently, leading to a notable reduction in overall execution time compared to other deep learning integrations.
We hope that our research can serve as a valuable contribution to the meteorological science community by enabling smoother weather research with fewer computational resources through the integration of deep learning models into conventional NWP frameworks. We aspire for this approach to facilitate more efficient and accessible advancements in meteorological studies.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe author had carefully revised the manuscript according to the previous review comments, please accept the paper.
Author Response
Comments 1: The author had carefully revised the manuscript according to the previous review comments, please accept the paper.
Response 1: Thank you for your valuable advice and suggestions. We have sincerely taken the reviewers' recommendations into account and have made efforts to revise and incorporate them to ensure that this manuscript becomes more technically robust.
Thank you once again for your feedback and evaluation. In this study, we proposed a framework that integrates a deep learning model into the conventional NWP model, Low-GloSea6, achieving an average reduction of 2.6% in overall execution time compared to the traditional approach. This improvement was made possible by reducing the excessive convergence iterations of computationally expensive hotspots, enabling the model to run with fewer computing resources.
This advancement allows the framework to operate efficiently even on small- to medium-scale servers, making it accessible for broader use. As a result, meteorological researchers can perform weather modeling more smoothly, contributing to the meteorological science community and supporting further research endeavors.
Author Response File: Author Response.pdf
