MIPV-NWP-PINN V1.0: Development of a Multi-scale Photovoltaic Power Forecasting Framework Integrating Numerical Weather Prediction with Physics-Informed Neural Networks

Zhang, Fei; Li, Xingcai; Wang, Zifa; Wen, Yunyun; Zhou, Xuyang; Wu, Zichen; Wang, Zhuoran; Chen, Huansheng; Wang, Zhe; Chen, Xueshun

doi:10.5194/egusphere-2025-4439

Preprints

https://doi.org/10.5194/egusphere-2025-4439

Preprints

28 Oct 2025

| 28 Oct 2025

MIPV-NWP-PINN V1.0: Development of a Multi-scale Photovoltaic Power Forecasting Framework Integrating Numerical Weather Prediction with Physics-Informed Neural Networks

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

Abstract. Photovoltaic (PV) power generation has become a cornerstone of clean energy, for which accurate forecasting is essential to ensure safe and efficient grid integration. However, raw Numerical Weather Prediction (NWP) outputs often fail to provide reliable forecasts because PV power is influenced by multiple coupled factors, including meteorological factors and photovoltaic modules. To address this challenge, this study develops a multi-scale PV power forecasting framework that integrates NWP with deep learning techniques (MIPV-NWP-PINN) and evaluates its performance using PV module monitoring data from a power station in northwestern China. First, a regional high-resolution NWP system based on the Weather Research and Forecasting (WRF) model is established to generate multi-scale meteorological forecasts with lead times of 6 hours, 1 day, 3 days, and 5 days. Next, a novel hybrid correction model that combines Quantile Mapping with a Temporal Pattern Attention-based Long Short-Term Memory (TPA-LSTM) network is proposed to improve the accuracy of Global Horizontal Irradiance (GHI) forecasts. This correction approach reduces the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) by more than 23 % compared to raw NWP outputs. Building on these corrected meteorological forecasts, a Physics-Informed Neural Network (PINN)-iTransformer model is developed for the final prediction of PV power. By incorporating physical constraints directly into its loss function, this model consistently outperforms state-of-the-art alternatives across all forecasting horizons, achieving reductions of 15.5 % in RMSE and 12.4 % in MAE. This physics-constrained framework substantially improves the accuracy and robustness of PV power forecasting across multiple time scales. The enhanced reliability directly supports secure PV grid integration and contributes to the broader transition toward low-carbon energy systems.

Received: 10 Sep 2025 – Discussion started: 28 Oct 2025

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Journal article(s) based on this preprint

12 Jun 2026

MIPV-NWP-PINNs V1.0: development of a multi-scale photovoltaic power forecasting framework integrating numerical weather prediction with physics-informed neural networks

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

Geosci. Model Dev., 19, 4999–5017, https://doi.org/10.5194/gmd-19-4999-2026,https://doi.org/10.5194/gmd-19-4999-2026, 2026

Short summary

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4439', Anonymous Referee #1, 01 Dec 2025
Dear Authors,

I read your manuscript with pleasure and find it interesting. I will provide my initial set of responses in the following text.
Summary: The manuscript argues that better forecasting of solar PV generation at a higher temporal resolution is necessary for solar PV infrastructure analysis. This becomes even more important because large overestimation of solar PV generation is observed in the authoritative datasets. The authors propose to correct for this bias by introducing a Physics informed itransformer model. The authors also take us through the full forecast pipeline all the way from GNI forecasting to comparative PV power forecasting results. The authors claim that their PINN-itransformer model provides higher fidelity and better accuracy in very short term PV power forecasting, but may still lack in relatively long term forecasting tasks.
Reviewer comments:
While the manuscript is surprisingly well written and concise, I do have some general comments to help communicate the manuscript better.
1.) In data and Methods:
A) Why "The initial 12 hours of each simulation run were discarded". Add more context here on why only 12 and what happens when you discard this initial forecast?

B) Clarity is required on what is meant by - itransformer, physics-itransformer, PC-itransformer, PINN-itransformer. These terminologies are used further in the results section. What I find is that the writeup for these models in data and section seems to look OK, but it is confusing due to cross referencing with previous published work. I suggest that more details and fundamental information be added in the 4 models to make it accessible for readers.

C) G_POA is used here, but defined only in the results section. I suggest rewriting the description of models from scratch, do not assume that the readers would have read the referenced work by Fan, Sun et al. etc. before. I would suggest that the authors follow this pattern
§ Describe the model in plain English by adding what the model can do and give an application example

§ Describe the core functioning of the model, its equations and layer description

§ Describe in detail how this model will be used in the subsequent steps/validation studies.

eg. 𝒅𝑷(𝒕)/𝒅𝒕 = −𝒌·(𝑷̂(𝒕)−𝑷𝒆𝒒(𝒕)) this equation just comes from nowhere and we do not get a context on why this is important. The only pointer is that some components eg. equilibrium is defined from Fan et al. paper
2) Data Engineering
A) GHI correction: the 400/100/400 split is counterintuitive, Here you are loosing nearly 50% of your data points. I would suggest using stratified sampling and doing 10 fold cross validation technique to use all data for training and prediction. e.g. in the 10 fold cross validation 90% of the samples are used for training and 10% for validation, this is then used in conjunction with rolling window approach to use all data for training. If this is unsuitable then do 700/100/100 split.

B) Why use only RMSE/MAE as the metric for evaluation, why not other error metics. What I mean is that define the rational for RMSE/MAE.

C) Why is this logical? "the inherent challenge for neural networks to model long-range temporal dependencies". what are the inherent challenges? why not use RNN/LSTM for long term forecast? How long is the long term forecast? I am assuming here that the forecast cycle can have seasonal and repetitive behaviour after 365 days?

D) Please define in detail what the residuals are in different models. I assume that in the physics-itransformer, the physics model is predicting the PV output and you compare that with actual observations to generate the residuals?

3) For figure number 15 comparisons, I think it would be beneficial if the authors can provide the ranking of the different comparative models to understand how accurate the PINN-itransformer is from the current state of art.
4) Code-> I went through the Zenodo repository, here my recommendation would be to revoke hardcoded file paths from the python files. Additionally, please add some user manual here e.g. steps/order in which the files would be run.
5) Limitations -> Add limitations of the model eg. this model is only training on the historical data or very short term real data. Would this model break if we do the forecasting for 1 year/5 year/20 years? What is the result of validation with SolarGIS data at monthly level? What will happen when we forecast for regions that are in gobi desert etc. where there is not much cloud based variability. Have you tested for 2025 time series as the model was trained for 2020 timer series. Add additional limitations that the authors seems necessary

I hope that the suggestions will help you in refining an already b=nice manuscript. All the best with the updates.
Citation: https://doi.org/10.5194/egusphere-2025-4439-RC1
- AC3: 'Reply on RC1', Xueshun Chen, 29 Jan 2026
  
  Thank you for your valuable comments and suggestions, which have greatly helped improve the quality of our manuscript. We have carefully addressed all the issues raised in your review.
  
  Please find our detailed point-by-point responses and the corresponding revisions in the attached document. The main changes in the revised manuscript have been highlighted for your convenience.
  
  We hope that the revisions adequately address your concerns. Should you have any further questions, please do not hesitate to contact us.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC3
CEC1:
'Comment on egusphere-2025-4439 - No compliance with the policy of the journal', Juan Antonio Añel, 08 Dec 2025

Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".

https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
The Zenodo repository that you have provided does not seem to contain the WRF model used for your work. Also, I have not found in it model output files for the simulations that you mention in your manuscript. Therefore, the current situation with your manuscript is irregular. Please, publish your the WRF code and data in one of the appropriate repositories according to our policy and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy.
Also, you must include a modified 'Code and Data Availability' section in a potentially reviewed manuscript, containing the information of the new repositories.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in our journal.
Juan A. Añel

Geosci. Model Dev. Executive Editor

Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC1
- AC1:
  'Reply on CEC1', Xueshun Chen, 09 Dec 2025
  Subject: Response to Code and Data Policy compliance regarding manuscript [https://doi.org/10.5194/egusphere-2025-4439]
  Dear Dr. Juan A. Añel,
  Thank you for your detailed assessment of our manuscript and for bringing the non-compliance with the ‘Code and Data Policy’ to our attention. We sincerely apologize for this oversight in our initial submission. We fully appreciate the critical importance of reproducibility and transparency in Geoscientific Model Development.
  We have taken immediate steps to address your concerns and have significantly updated our repository to ensure full compliance with the journal's policy. Specifically, we have implemented the following updates:
  WRF Model Code and Configuration
  
  As requested, we have archived the exact source code of the WRF model used in our study. To further ensure the reproducibility of our operational forecasting workflow, we have also included:
  
  (a) The forecasting scripts (namelist.wps and namelist.input).
  (b) FNL reanalysis data used for initial and boundary conditions.
  Model Output Data
  
  We have uploaded the specific model output files required to reproduce the results presented in the manuscript. This includes:
  
  (a) The output data following GHI correction.
  (b) The PV power output comparison data across different prediction scales.
  Enhanced Documentation
  
  To assist users, we have added detailed README files for the datasets and code components. These documents provide comprehensive data descriptions and step-by-step workflow instructions.
  
  New Repository and DOI
  
  All updated code, scripts, and data are now available on Zenodo under the following permanent identifier: DOI: https://doi.org/10.5281/zenodo.17850993
  
  We confirm that the ‘Code and Data Availability’ section in the revised manuscript will be updated to cite this new DOI and describe the available resources.
  We believe these additions satisfy the GMD Code and Data Policy. We remain committed to open science and hope these materials will be valuable to the community.
  Thank you again for your guidance.
  Sincerely,
  
  Xueshun Chen
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC1
  - CEC2: 'Reply on AC1', Juan Antonio Añel, 10 Dec 2025
    
    Dear authors,
    Many thanks for addressing this issue so quickly. I have checked the repository and we can consider now the current version of your manuscript in compliance with the code policy of the journal.
    Juan A. Añel
    Geosci. Model Dev. Executive Editor
    
    Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC2
  - CEC3: 'Reply on AC1', Juan Antonio Añel, 10 Dec 2025
    
    Dear authors,
    Many thanks for addressing this issue so quickly. I have checked the repository and we can consider now the current version of your manuscript in compliance with the code policy of the journal.
    Juan A. Añel
    Geosci. Model Dev. Executive Editor
    
    Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC3
RC2:
'Comment on egusphere-2025-4439', Anonymous Referee #2, 19 Dec 2025
Reviewer Comments
This manuscript presents a multi-scale photovoltaic (PV) power forecasting framework (MIPV-NWP-PINN) integrating WRF-based numerical weather prediction, a hybrid GHI bias correction model (QM-TPA-LSTM), and a physics-informed deep learning architecture (PINN-iTransformer). The topic is timely and relevant, and the proposed framework is technically sound. The combination of NWP, statistical correction, and PINN-based forecasting represents a novel and valuable contribution to PV power prediction. Nevertheless, several issues related to clarity, methodological justification, generalizability, and interpretability should be addressed.
Major Comments
In the abstract, the statement “raw Numerical Weather Prediction (NWP) outputs often fail to provide reliable forecasts because PV power is influenced by multiple coupled factors, including meteorological factors and photovoltaic modules” may be misleading. As currently written in the abstract, it may give the impression that PV power is directly predicted from NWP outputs. The authors are encouraged to clarify that NWP provides meteorological inputs, and that uncertainties arise from both atmospheric forecast errors and the subsequent PV power conversion process.

The literature review presented in the Introduction is relatively lengthy and could be streamlined. In Section 1, it is suggested to reorganize this part around the core research problems by clearly summarizing: (1) the limited accuracy of NWP-derived GHI; (2) the “black-box” nature and lack of physical consistency in many PV power forecasting models; and (3) the potential of Physics-Informed Neural Networks (PINNs) to embed physical laws into the loss function and improve physical consistency. A more concise, problem-oriented review would improve readability and strengthen the overall motivation.

While multi-site validation is conducted for GHI correction, the PV power forecasting results presented in Section 4 (e.g., the multi-horizon comparisons in Figures 12–15) are mainly based on a single station. The applicability of the proposed PINN-iTransformer to other regions, climatic conditions, and PV configurations should therefore be discussed more explicitly, or additional validation should be provided.

In the description of the PINN-iTransformer framework, particularly in the subsection introducing the physics-informed loss and the first-order relaxation ODE, the physical meaning of the relaxation coefficient k is not sufficiently explained. In addition, the role of the physics-informed loss weight (λ) is introduced without further discussion. Clarifying whether k is constant or learnable, and providing a brief sensitivity or ablation analysis for λ, would strengthen the physical interpretability and robustness of the proposed approach.

Minor Comments
Although the manuscript emphasizes the importance of aerosol and cloud effects on GHI in the Introduction, the QM-TPA-LSTM model described in the GHI correction section remains purely statistical. This limitation should be more clearly acknowledged and discussed, particularly in relation to physical interpretability.

While improved PV power forecasting accuracy is demonstrated in the results section, the manuscript does not discuss how these forecasts could be used in downstream applications such as grid operation or energy management. A brief discussion in the concluding section would enhance the applied value of the study.

In the PV power forecasting analysis, additional investigation of prediction errors—such as SHAP analysis or other interpretability methods—would be beneficial for understanding the sources of model error and the relative importance of input variables.

Throughout the manuscript, please ensure consistent terminology, particularly for forecasting horizons (e.g., “6 h” vs. “6-hour” vs. “6 hours”) and model names (e.g., PINN-iTransformer vs. PINN–iTransformer).

In the methodological sections and equations, several symbols (e.g., k, λ, and variables related to PV power and irradiance) are introduced without being clearly defined at first occurrence. Providing clearer definitions or a concise summary of symbols would improve readability.

In the multi-panel figures presenting PV forecasting results, some fonts and legends are relatively small. Improving font size and legend placement would enhance clarity.

Please ensure that physical units (e.g., W m⁻², kW, MW) are consistently formatted throughout the manuscript and that spacing between numbers and units follows journal conventions.
Citation: https://doi.org/10.5194/egusphere-2025-4439-RC2
- AC2: 'Reply on RC2', Xueshun Chen, 29 Jan 2026
  
  Thank you for your valuable comments and suggestions, which have greatly helped improve the quality of our manuscript. We have carefully addressed all the issues raised in your review.
  
  Please find our detailed point-by-point responses and the corresponding revisions in the attached document. The main changes in the revised manuscript have been highlighted for your convenience.
  
  We hope that the revisions adequately address your concerns. Should you have any further questions, please do not hesitate to contact us.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4439', Anonymous Referee #1, 01 Dec 2025
Dear Authors,

I read your manuscript with pleasure and find it interesting. I will provide my initial set of responses in the following text.
Summary: The manuscript argues that better forecasting of solar PV generation at a higher temporal resolution is necessary for solar PV infrastructure analysis. This becomes even more important because large overestimation of solar PV generation is observed in the authoritative datasets. The authors propose to correct for this bias by introducing a Physics informed itransformer model. The authors also take us through the full forecast pipeline all the way from GNI forecasting to comparative PV power forecasting results. The authors claim that their PINN-itransformer model provides higher fidelity and better accuracy in very short term PV power forecasting, but may still lack in relatively long term forecasting tasks.
Reviewer comments:
While the manuscript is surprisingly well written and concise, I do have some general comments to help communicate the manuscript better.
1.) In data and Methods:
A) Why "The initial 12 hours of each simulation run were discarded". Add more context here on why only 12 and what happens when you discard this initial forecast?

B) Clarity is required on what is meant by - itransformer, physics-itransformer, PC-itransformer, PINN-itransformer. These terminologies are used further in the results section. What I find is that the writeup for these models in data and section seems to look OK, but it is confusing due to cross referencing with previous published work. I suggest that more details and fundamental information be added in the 4 models to make it accessible for readers.

C) G_POA is used here, but defined only in the results section. I suggest rewriting the description of models from scratch, do not assume that the readers would have read the referenced work by Fan, Sun et al. etc. before. I would suggest that the authors follow this pattern
§ Describe the model in plain English by adding what the model can do and give an application example

§ Describe the core functioning of the model, its equations and layer description

§ Describe in detail how this model will be used in the subsequent steps/validation studies.

eg. 𝒅𝑷(𝒕)/𝒅𝒕 = −𝒌·(𝑷̂(𝒕)−𝑷𝒆𝒒(𝒕)) this equation just comes from nowhere and we do not get a context on why this is important. The only pointer is that some components eg. equilibrium is defined from Fan et al. paper
2) Data Engineering
A) GHI correction: the 400/100/400 split is counterintuitive, Here you are loosing nearly 50% of your data points. I would suggest using stratified sampling and doing 10 fold cross validation technique to use all data for training and prediction. e.g. in the 10 fold cross validation 90% of the samples are used for training and 10% for validation, this is then used in conjunction with rolling window approach to use all data for training. If this is unsuitable then do 700/100/100 split.

B) Why use only RMSE/MAE as the metric for evaluation, why not other error metics. What I mean is that define the rational for RMSE/MAE.

C) Why is this logical? "the inherent challenge for neural networks to model long-range temporal dependencies". what are the inherent challenges? why not use RNN/LSTM for long term forecast? How long is the long term forecast? I am assuming here that the forecast cycle can have seasonal and repetitive behaviour after 365 days?

D) Please define in detail what the residuals are in different models. I assume that in the physics-itransformer, the physics model is predicting the PV output and you compare that with actual observations to generate the residuals?

3) For figure number 15 comparisons, I think it would be beneficial if the authors can provide the ranking of the different comparative models to understand how accurate the PINN-itransformer is from the current state of art.
4) Code-> I went through the Zenodo repository, here my recommendation would be to revoke hardcoded file paths from the python files. Additionally, please add some user manual here e.g. steps/order in which the files would be run.
5) Limitations -> Add limitations of the model eg. this model is only training on the historical data or very short term real data. Would this model break if we do the forecasting for 1 year/5 year/20 years? What is the result of validation with SolarGIS data at monthly level? What will happen when we forecast for regions that are in gobi desert etc. where there is not much cloud based variability. Have you tested for 2025 time series as the model was trained for 2020 timer series. Add additional limitations that the authors seems necessary

I hope that the suggestions will help you in refining an already b=nice manuscript. All the best with the updates.
Citation: https://doi.org/10.5194/egusphere-2025-4439-RC1
- AC3: 'Reply on RC1', Xueshun Chen, 29 Jan 2026
  
  Thank you for your valuable comments and suggestions, which have greatly helped improve the quality of our manuscript. We have carefully addressed all the issues raised in your review.
  
  Please find our detailed point-by-point responses and the corresponding revisions in the attached document. The main changes in the revised manuscript have been highlighted for your convenience.
  
  We hope that the revisions adequately address your concerns. Should you have any further questions, please do not hesitate to contact us.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC3
CEC1:
'Comment on egusphere-2025-4439 - No compliance with the policy of the journal', Juan Antonio Añel, 08 Dec 2025

Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".

https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
The Zenodo repository that you have provided does not seem to contain the WRF model used for your work. Also, I have not found in it model output files for the simulations that you mention in your manuscript. Therefore, the current situation with your manuscript is irregular. Please, publish your the WRF code and data in one of the appropriate repositories according to our policy and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy.
Also, you must include a modified 'Code and Data Availability' section in a potentially reviewed manuscript, containing the information of the new repositories.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in our journal.
Juan A. Añel

Geosci. Model Dev. Executive Editor

Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC1
- AC1:
  'Reply on CEC1', Xueshun Chen, 09 Dec 2025
  Subject: Response to Code and Data Policy compliance regarding manuscript [https://doi.org/10.5194/egusphere-2025-4439]
  Dear Dr. Juan A. Añel,
  Thank you for your detailed assessment of our manuscript and for bringing the non-compliance with the ‘Code and Data Policy’ to our attention. We sincerely apologize for this oversight in our initial submission. We fully appreciate the critical importance of reproducibility and transparency in Geoscientific Model Development.
  We have taken immediate steps to address your concerns and have significantly updated our repository to ensure full compliance with the journal's policy. Specifically, we have implemented the following updates:
  WRF Model Code and Configuration
  
  As requested, we have archived the exact source code of the WRF model used in our study. To further ensure the reproducibility of our operational forecasting workflow, we have also included:
  
  (a) The forecasting scripts (namelist.wps and namelist.input).
  (b) FNL reanalysis data used for initial and boundary conditions.
  Model Output Data
  
  We have uploaded the specific model output files required to reproduce the results presented in the manuscript. This includes:
  
  (a) The output data following GHI correction.
  (b) The PV power output comparison data across different prediction scales.
  Enhanced Documentation
  
  To assist users, we have added detailed README files for the datasets and code components. These documents provide comprehensive data descriptions and step-by-step workflow instructions.
  
  New Repository and DOI
  
  All updated code, scripts, and data are now available on Zenodo under the following permanent identifier: DOI: https://doi.org/10.5281/zenodo.17850993
  
  We confirm that the ‘Code and Data Availability’ section in the revised manuscript will be updated to cite this new DOI and describe the available resources.
  We believe these additions satisfy the GMD Code and Data Policy. We remain committed to open science and hope these materials will be valuable to the community.
  Thank you again for your guidance.
  Sincerely,
  
  Xueshun Chen
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC1
  - CEC2: 'Reply on AC1', Juan Antonio Añel, 10 Dec 2025
    
    Dear authors,
    Many thanks for addressing this issue so quickly. I have checked the repository and we can consider now the current version of your manuscript in compliance with the code policy of the journal.
    Juan A. Añel
    Geosci. Model Dev. Executive Editor
    
    Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC2
  - CEC3: 'Reply on AC1', Juan Antonio Añel, 10 Dec 2025
    
    Dear authors,
    Many thanks for addressing this issue so quickly. I have checked the repository and we can consider now the current version of your manuscript in compliance with the code policy of the journal.
    Juan A. Añel
    Geosci. Model Dev. Executive Editor
    
    Citation: https://doi.org/10.5194/egusphere-2025-4439-CEC3
RC2:
'Comment on egusphere-2025-4439', Anonymous Referee #2, 19 Dec 2025
Reviewer Comments
This manuscript presents a multi-scale photovoltaic (PV) power forecasting framework (MIPV-NWP-PINN) integrating WRF-based numerical weather prediction, a hybrid GHI bias correction model (QM-TPA-LSTM), and a physics-informed deep learning architecture (PINN-iTransformer). The topic is timely and relevant, and the proposed framework is technically sound. The combination of NWP, statistical correction, and PINN-based forecasting represents a novel and valuable contribution to PV power prediction. Nevertheless, several issues related to clarity, methodological justification, generalizability, and interpretability should be addressed.
Major Comments
In the abstract, the statement “raw Numerical Weather Prediction (NWP) outputs often fail to provide reliable forecasts because PV power is influenced by multiple coupled factors, including meteorological factors and photovoltaic modules” may be misleading. As currently written in the abstract, it may give the impression that PV power is directly predicted from NWP outputs. The authors are encouraged to clarify that NWP provides meteorological inputs, and that uncertainties arise from both atmospheric forecast errors and the subsequent PV power conversion process.

The literature review presented in the Introduction is relatively lengthy and could be streamlined. In Section 1, it is suggested to reorganize this part around the core research problems by clearly summarizing: (1) the limited accuracy of NWP-derived GHI; (2) the “black-box” nature and lack of physical consistency in many PV power forecasting models; and (3) the potential of Physics-Informed Neural Networks (PINNs) to embed physical laws into the loss function and improve physical consistency. A more concise, problem-oriented review would improve readability and strengthen the overall motivation.

While multi-site validation is conducted for GHI correction, the PV power forecasting results presented in Section 4 (e.g., the multi-horizon comparisons in Figures 12–15) are mainly based on a single station. The applicability of the proposed PINN-iTransformer to other regions, climatic conditions, and PV configurations should therefore be discussed more explicitly, or additional validation should be provided.

In the description of the PINN-iTransformer framework, particularly in the subsection introducing the physics-informed loss and the first-order relaxation ODE, the physical meaning of the relaxation coefficient k is not sufficiently explained. In addition, the role of the physics-informed loss weight (λ) is introduced without further discussion. Clarifying whether k is constant or learnable, and providing a brief sensitivity or ablation analysis for λ, would strengthen the physical interpretability and robustness of the proposed approach.

Minor Comments
Although the manuscript emphasizes the importance of aerosol and cloud effects on GHI in the Introduction, the QM-TPA-LSTM model described in the GHI correction section remains purely statistical. This limitation should be more clearly acknowledged and discussed, particularly in relation to physical interpretability.

While improved PV power forecasting accuracy is demonstrated in the results section, the manuscript does not discuss how these forecasts could be used in downstream applications such as grid operation or energy management. A brief discussion in the concluding section would enhance the applied value of the study.

In the PV power forecasting analysis, additional investigation of prediction errors—such as SHAP analysis or other interpretability methods—would be beneficial for understanding the sources of model error and the relative importance of input variables.

Throughout the manuscript, please ensure consistent terminology, particularly for forecasting horizons (e.g., “6 h” vs. “6-hour” vs. “6 hours”) and model names (e.g., PINN-iTransformer vs. PINN–iTransformer).

In the methodological sections and equations, several symbols (e.g., k, λ, and variables related to PV power and irradiance) are introduced without being clearly defined at first occurrence. Providing clearer definitions or a concise summary of symbols would improve readability.

In the multi-panel figures presenting PV forecasting results, some fonts and legends are relatively small. Improving font size and legend placement would enhance clarity.

Please ensure that physical units (e.g., W m⁻², kW, MW) are consistently formatted throughout the manuscript and that spacing between numbers and units follows journal conventions.
Citation: https://doi.org/10.5194/egusphere-2025-4439-RC2
- AC2: 'Reply on RC2', Xueshun Chen, 29 Jan 2026
  
  Thank you for your valuable comments and suggestions, which have greatly helped improve the quality of our manuscript. We have carefully addressed all the issues raised in your review.
  
  Please find our detailed point-by-point responses and the corresponding revisions in the attached document. The main changes in the revised manuscript have been highlighted for your convenience.
  
  We hope that the revisions adequately address your concerns. Should you have any further questions, please do not hesitate to contact us.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4439-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by Xueshun Chen on behalf of the Authors (29 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (17 Feb 2026) by Gunnar Luderer

RR by Anonymous Referee #1 (14 Mar 2026)

RR by Anonymous Referee #2 (20 Mar 2026)

ED: Publish subject to minor revisions (review by editor) (12 Apr 2026) by Gunnar Luderer

AR by Xueshun Chen on behalf of the Authors (16 Apr 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (29 May 2026) by Gunnar Luderer

AR by Xueshun Chen on behalf of the Authors (01 Jun 2026)

Journal article(s) based on this preprint

12 Jun 2026

MIPV-NWP-PINNs V1.0: development of a multi-scale photovoltaic power forecasting framework integrating numerical weather prediction with physics-informed neural networks

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

Geosci. Model Dev., 19, 4999–5017, https://doi.org/10.5194/gmd-19-4999-2026,https://doi.org/10.5194/gmd-19-4999-2026, 2026

Short summary

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

Supplement

https://doi.org/10.5194/egusphere-2025-4439-supplement

Data sets

Development of a Multi-scale Photovoltaic Power Forecasting Framework Integrating Numerical Weather Prediction with Physics-Informed Neural Networks Fei Zhang, Xueshun Chen, Xingcai Li https://zenodo.org/records/17086317

Model code and software

Fei Zhang, Xingcai Li, Zifa Wang, Yunyun Wen, Xuyang Zhou, Zichen Wu, Zhuoran Wang, Huansheng Chen, Zhe Wang, and Xueshun Chen

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Month	HTML	PDF	XML	Total
Oct 2025	705	45	25	775
Nov 2025	565	305	40	910
Dec 2025	864	563	109	1,536
Jan 2026	973	644	55	1,672
Feb 2026	723	382	21	1,126
Mar 2026	894	481	22	1,397
Apr 2026	311	95	8	414
May 2026	144	58	4	206
Jun 2026	25	12	0	37

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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Short summary

Solar power generation depends on weather conditions and photovoltaic modules, making accurate forecasts crucial for reliable grid operation. We combined weather prediction and artificial intelligence to improve the solar power prediction at different time scales for a plant. By improving sunlight predictions and incorporating physical constraints into the model, our approach reduced errors significantly. This can help integrate clean energy into power grids safely and efficiently.


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MIPV-NWP-PINN V1.0: Development of a Multi-scale Photovoltaic Power Forecasting Framework Integrating Numerical Weather Prediction with Physics-Informed Neural Networks

Journal article(s) based on this preprint

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Interactive discussion

Peer review completion

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Journal article(s) based on this preprint

Supplement

Data sets

Model code and software

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