Control Simulation Experiments of Extreme Events with the Lorenz-96 Model

Sun, Qiwen; Miyoshi, Takemasa; Richard, Serge

doi:https://doi.org/10.5194/npg-2022-12

Preprints

https://doi.org/10.5194/npg-2022-12

Preprints

23 Aug 2022

| 23 Aug 2022

Status: a revised version of this preprint was accepted for the journal NPG and is expected to appear here in due course.

Control Simulation Experiments of Extreme Events with the Lorenz-96 Model

Qiwen Sun, Takemasa Miyoshi, and Serge Richard

Abstract. Control Simulation Experiment (CSE) is a recently developed approach to investigate the controllability of dynamical systems, extending the well-known Observing Systems Simulation Experiment (OSSE) in meteorology. For effective control of chaotic dynamical systems, it is essential to exploit the high sensitivity to initial conditions for dragging a system away from an undesired regime by applying minimal perturbations. In this study, we design a CSE for reducing the number of extreme events in the Lorenz-96 model. The 40 variables of this model represent idealized meteorological quantities evenly distributed on a latitude circle. The reduction of occurrence of extreme events over 100 years runs of the model is discussed as a function of the parameters of the CSE: the ensemble forecast length for detecting extreme events in advance, the magnitude and localization of the perturbations, and the quality and coverage of the observations. The design of the CSE is aimed at reducing weather extremes when applied to more realistic weather prediction models.

Received: 01 Aug 2022 – Discussion started: 23 Aug 2022

Qiwen Sun et al.

Interactive discussion

Status: closed

RC1:
'Comment on npg-2022-12', Anonymous Referee #1, 25 Sep 2022

The manuscript is nicely exploring the possibility to perturb a simulation (that would represent a real system) to reduce the risk of extreme events. This is explored in the context of the Lorenz-96 model, with perturbations built on the difference between members of an ensemble forecast. The authors have carefully design experiments in doing so and they show that a considerable reduction of the occurrence of extremes is notable by using such an approach. They further explore the impact of different parameters like the lead time of the forecast and the amplitude of the perturbations, as well as the possibility to perturb locally the system and the number of observations. This is a well written and very clear thought experiment that is worth publishing in Nonlinear Processes in Geophysics. Here a few points that are worth addressing at the time of revision.

One key aspect of control is the energy to be introduced in the system. The authors have here computed such an energy in the context of the Lorenz system, but it would be important to give a first clue to what quantity of energy would be necessary in a more realistic setting. As the Lorenz-96 model provides a toy model of the large scale variables at a specific latitude, it would be very interesting to convert the energy needed in an energy that the meteorological community could apprehend (power, work…) and discuss that in the conclusions.

When perturbing a system (as done for instance with the increase of CO2), there are extremes that become less frequent like for instance a reduction of cold waves in certain regions with the increase of the global temperature. But this has other effects with an increase of heat waves. If one transposes this to the current setting, some extremes are suppressed, but some others might be arising. Did you see such type of situations in the context of the Lorenz model? In any case it is necessary to elaborate on this somewhere in the manuscript.

In Figure 9, the authors show a saturation of the number of actions as a function of the localization scale. I am wondering whether it is related to the spatial correlation of the perturbations needed. Furthermore I am wondering what is the nature of the global perturbations. Do they look like bred modes? It would be really interesting to elaborate on that aspect.

Minor aspect

- The last paragraph of the introduction should be placed in the conclusions

- Line 126. There is no Appendix in the document

Citation: https://doi.org/10.5194/npg-2022-12-RC1
- AC1:
  'Reply on RC1', Qiwen Sun, 20 Feb 2023
  First of all, let us thank the referees for their careful work on our manuscript. Their remarks allow us to improve the quality of the manuscript, and to clarify some parts of it. We list below the comments, and the corresponding changes in the manuscript.
  One key aspect of control is the energy to be introduced in the system. The authors have here computed such an energy in the context of the Lorenz system, but it would be important to give a first clue to what quantity of energy would be necessary in a more realistic setting. As the Lorenz-96 model provides a toy model of the large scale variables at a specific latitude, it would be very interesting to convert the energy needed in an energy that the meteorological community could apprehend (power, work…) and discuss that in the conclusions.
  
  This remark about energy is indeed a very important issue, and probably the next step in the elaboration of realistic CSEs. For our investigations, we have defined a notion of “energy” in order to quantify and compare the role of various parameters. However, due to the simplicity of the model, it is not clear if any valuable information can be extracted from this quantity. We looked at the literature if a proper notion of energy was elaborated and discussed for the Lorenz-96 model, but we could not find any reasonable one. As a consequence, we decided not to interpret our notion of energy, and to keep such a quantitative analysis for a more realistic model. Nevertheless, a comment about the notion of energy has been added in the conclusion.
  When perturbing a system (as done for instance with the increase of CO2), there are extremes that become less frequent like for instance a reduction of cold waves in certain regions with the increase of the global temperature. But this has other effects with an increase of heat waves. If one transposes this to the current setting, some extremes are suppressed, but some others might be arising. Did you see such type of situations in the context of the Lorenz model? In any case it is necessary to elaborate on this somewhere in the manuscript.
  
  This remark is interesting, and one related comment has been added in the conclusion of the manuscript. The Lorenz-96 model is probably too simple to clearly observe any side effects of reducing the positive extreme values. However, we thought about this and checked this effect with the following procedure. At the beginning of the investigations, it was decided to concentrate on the positive extreme values, disregarding the negative extreme values. Once the CSEs were performed, we checked if the statistics of the extreme negative values had changed, since this could have been a negative side effect of our control. It turns out that avoiding positive extreme values had statistically no impact on the negative ones. In fact, Figure 5 seems to indicate a small reduction of the negative extreme values, but similar figures for different parameters α and T did not show any significant changes. For that reason, we had decided not to report on this issue. With a more elaborate model, it is certainly an effect which should be carefully appraised.
  In Figure 9, the authors show a saturation of the number of actions as a function of the localization scale. I am wondering whether it is related to the spatial correlation of the perturbations needed. Furthermore I am wondering what is the nature of the global perturbations. Do they look like bred modes? It would be really interesting to elaborate on that aspect.
  
  Yes, in Figure 9(a), the saturation of the dashed line (neighbor sites) clearly indicates that perturbing additional sites which are far away from the site of interest does not lead to any benefit. This fact is indeed related to spatial correlations, since perturbations performed at random sites do not show such a saturation. This localization effect and this saturation are interesting for future applications: It shows that a local control is sufficient, with a corresponding reduction of the energy provided to the system, as illustrated in Figure 9(b).
  About bred vectors, let us recall that the perturbation we identify is the difference between the EnKF ensemble state evolving to the extreme and the EnKF ensemble state evolving to the most non-extreme. The EnKF ensemble perturbations are considered as an extension of bred vectors. Therefore, the difference between the two ensemble states is somewhat related to the bred vectors. However, in our investigations, we did not elaborate further on bred vectors, but indeed in future studies we should look more carefully in this direction. In terms of effectiveness, working with bred vectors would allow us to provide the smallest perturbation to the system for the biggest impact.
  The last paragraph of the introduction should be placed in the conclusion.
  
  This paragraph has been removed and integrated in the conclusion.
  Line 126. There is no Appendix in the document.
  
  This sentence has been removed.
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC1
RC2:
'Review of npg-2022-12: Control Simulation Experiments of Extreme Events with the Lorenz-96 Model by Sun et al.', Anonymous Referee #2, 13 Jan 2023

The authors propose a method (Control Simulation Experiment) to control the number of extreme events in the Lorenz-96 model. The sensitivity of this technique to the choice of various parameters, such as the forecast lead time in which extreme events are detected or the amplitude of the perturbations. The authors find that the method is effective to reduce extremes and the sensitivity tests show how the perturbations can be tuned in order to reduce the high number of extreme events with a minimized action over the system.

General comment:

The manuscript is clear, the technical details of the experiments performed are well described. The authors provide several references to contextualize their research. This manuscript can be of interest for NPG readers, however my main concern is about the implications of this study in a more realistic context. The Control Simulation Experiment is aimed at reducing the extremes, but the challenge is that the models are able to simulate these extremes and in case of ensemble forecasting how the ensemble should be designed to include extremes. Therefore, I do not see the benefit of reducing the extremes in a simulation, when those states actually take place in the system that the model represents. I suggest including some clarifications in the introduction in this regard as well as in the conclusions to better express the general objective of this research.

Specific comments:

L11: “of the first two authors” can be removed.

L34-35: In line with my general comment, what is the benefit of reducing simulated weather extremes that occur in reality?

L149: (j,j) -> (i,j)

L170: Why only the maximum value is used to define extremes and not the minimum?

L199: When the procedure to generate the perturbation vectors is described and the selection of the ensemble member B is explained, the alternative computation in case an ensemble member B is not found (L208-209) should be indicated here.

L281: It is more correct saying similar or approximately equal instead of equal.

L292-293: The meaning of this sentence is not clear.

Fig.10: Please, indicate the meaning of the triangle in the caption.

Citation: https://doi.org/10.5194/npg-2022-12-RC2
- AC2:
  'Reply on RC2', Qiwen Sun, 20 Feb 2023
  First of all, let us thank the referees for their careful work on our manuscript. Their remarks allow us to improve the quality of the manuscript, and to clarify some parts of it. We list below the comments, and the corresponding changes in the manuscript.
  The manuscript is clear, the technical details of the experiments performed are well described. The authors provide several references to contextualize their research. This manuscript can be of interest for NPG readers, however my main concern is about the implications of this study in a more realistic context. The Control Simulation Experiment is aimed at reducing the extremes, but the challenge is that the models are able to simulate these extremes and in case of ensemble forecasting how the ensemble should be designed to include extremes. Therefore, I do not see the benefit of reducing the extremes in a simulation, when those states actually take place in the system that the model represents. I suggest including some clarifications in the introduction in this regard as well as in the conclusions to better express the general objective of this research.
  
  We agree that if the model can not predict extremes, our approach can not work. For this reason, our CSE is based on perfect-model assumption. The EnKF OSSE is designed that way, and the CSE is also designed with this assumption. Let us emphasize that current ensemble prediction systems tend to predict extreme events although not perfect yet. So, if we have good ensemble prediction systems in the future, and at least one ensemble member showing the occurrence of extremes, we could potentially apply our CSE. Note that this underlying assumption has been added in the conclusion of our manuscript.
  L11: “of the first two authors” can be removed.
  
  This has been corrected.
  L34-35: In line with my general comment, what is the benefit of reducing simulated weather extremes that occur in reality?
  
  This has been discussed above.
  L149: (j,j) -> (i,j)
  
  This has been corrected.
  L170: Why only the maximum value is used to define extremes and not the minimum?
  
  At the beginning of the investigations, this had been an arbitrary choice. Later on, it has been used to check if avoiding maximum values would generate the negative impact of having more negative values. As mentioned in a previous response, the number of extreme negative values has not changed statistically. In future investigations, avoiding both extreme values could be implemented.
  L199: When the procedure to generate the perturbation vectors is described and the selection of the ensemble member B is explained, the alternative computation in case an ensemble member B is not found (L208-209) should be indicated here.
  
  The alternative process has been moved to L199.
  L281: It is more correct saying similar or approximately equal instead of equal.
  
  This has been corrected.
  L292-293: The meaning of this sentence is not clear.
  
  The sentence has been moved to the subsequent paragraph, with additional explanation. In L291, the sentence has also been modified as: ….introduced in Sect. 2.3, need to be adapted for achieving the smallest RMSE.
  The following sentence will be added at the end of the subsequent paragraph:
  
  In Figure 10, the triangle indicates which combination of values for L and ρ leads to the smallest RMSE. This information is also reported in the second figure. By looking at the position of the two triangles, we observe that the RMSE and the average spread take approximatively the same value (about 0.31). Since the spread is computed as the RMSE but with the truth replaced by the mean value of the ensemble members, this concurrence means that the ensemble members spread sufficiently to cover the unknown truth of the model.
  Fig.10: Please, indicate the meaning of the triangle in the caption.
  
  The following sentence has been added in the caption of Figure 10:
  
  The triangles indicate which combination of values for L and ρ leads to the smallest RMSE. This information is also reported in the second figure.
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC2
EC1:
'Comment on npg-2022-12', Natale Alberto Carrassi, 17 Jan 2023

Dear Authors
we have now received two very useful and positive reports about your works. I think they both address aspects of your work that can be improved, particularly in relation to the applicabilty.
I encourage you to take them into account while preparing the revised manuscript.
Please send first detailed responses to the Reviewers' quests.
Best Regards

Citation: https://doi.org/10.5194/npg-2022-12-EC1
- AC3: 'Reply on EC1', Qiwen Sun, 20 Feb 2023
  
  Dear Professor Carrassi,
  Thank you for your comments.
  We have replied the referee comments and revised the manuscript.
  Best regards,
  Qiwen
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC3

Interactive discussion

Status: closed

RC1:
'Comment on npg-2022-12', Anonymous Referee #1, 25 Sep 2022

The manuscript is nicely exploring the possibility to perturb a simulation (that would represent a real system) to reduce the risk of extreme events. This is explored in the context of the Lorenz-96 model, with perturbations built on the difference between members of an ensemble forecast. The authors have carefully design experiments in doing so and they show that a considerable reduction of the occurrence of extremes is notable by using such an approach. They further explore the impact of different parameters like the lead time of the forecast and the amplitude of the perturbations, as well as the possibility to perturb locally the system and the number of observations. This is a well written and very clear thought experiment that is worth publishing in Nonlinear Processes in Geophysics. Here a few points that are worth addressing at the time of revision.

One key aspect of control is the energy to be introduced in the system. The authors have here computed such an energy in the context of the Lorenz system, but it would be important to give a first clue to what quantity of energy would be necessary in a more realistic setting. As the Lorenz-96 model provides a toy model of the large scale variables at a specific latitude, it would be very interesting to convert the energy needed in an energy that the meteorological community could apprehend (power, work…) and discuss that in the conclusions.

When perturbing a system (as done for instance with the increase of CO2), there are extremes that become less frequent like for instance a reduction of cold waves in certain regions with the increase of the global temperature. But this has other effects with an increase of heat waves. If one transposes this to the current setting, some extremes are suppressed, but some others might be arising. Did you see such type of situations in the context of the Lorenz model? In any case it is necessary to elaborate on this somewhere in the manuscript.

In Figure 9, the authors show a saturation of the number of actions as a function of the localization scale. I am wondering whether it is related to the spatial correlation of the perturbations needed. Furthermore I am wondering what is the nature of the global perturbations. Do they look like bred modes? It would be really interesting to elaborate on that aspect.

Minor aspect

- The last paragraph of the introduction should be placed in the conclusions

- Line 126. There is no Appendix in the document

Citation: https://doi.org/10.5194/npg-2022-12-RC1
- AC1:
  'Reply on RC1', Qiwen Sun, 20 Feb 2023
  First of all, let us thank the referees for their careful work on our manuscript. Their remarks allow us to improve the quality of the manuscript, and to clarify some parts of it. We list below the comments, and the corresponding changes in the manuscript.
  One key aspect of control is the energy to be introduced in the system. The authors have here computed such an energy in the context of the Lorenz system, but it would be important to give a first clue to what quantity of energy would be necessary in a more realistic setting. As the Lorenz-96 model provides a toy model of the large scale variables at a specific latitude, it would be very interesting to convert the energy needed in an energy that the meteorological community could apprehend (power, work…) and discuss that in the conclusions.
  
  This remark about energy is indeed a very important issue, and probably the next step in the elaboration of realistic CSEs. For our investigations, we have defined a notion of “energy” in order to quantify and compare the role of various parameters. However, due to the simplicity of the model, it is not clear if any valuable information can be extracted from this quantity. We looked at the literature if a proper notion of energy was elaborated and discussed for the Lorenz-96 model, but we could not find any reasonable one. As a consequence, we decided not to interpret our notion of energy, and to keep such a quantitative analysis for a more realistic model. Nevertheless, a comment about the notion of energy has been added in the conclusion.
  When perturbing a system (as done for instance with the increase of CO2), there are extremes that become less frequent like for instance a reduction of cold waves in certain regions with the increase of the global temperature. But this has other effects with an increase of heat waves. If one transposes this to the current setting, some extremes are suppressed, but some others might be arising. Did you see such type of situations in the context of the Lorenz model? In any case it is necessary to elaborate on this somewhere in the manuscript.
  
  This remark is interesting, and one related comment has been added in the conclusion of the manuscript. The Lorenz-96 model is probably too simple to clearly observe any side effects of reducing the positive extreme values. However, we thought about this and checked this effect with the following procedure. At the beginning of the investigations, it was decided to concentrate on the positive extreme values, disregarding the negative extreme values. Once the CSEs were performed, we checked if the statistics of the extreme negative values had changed, since this could have been a negative side effect of our control. It turns out that avoiding positive extreme values had statistically no impact on the negative ones. In fact, Figure 5 seems to indicate a small reduction of the negative extreme values, but similar figures for different parameters α and T did not show any significant changes. For that reason, we had decided not to report on this issue. With a more elaborate model, it is certainly an effect which should be carefully appraised.
  In Figure 9, the authors show a saturation of the number of actions as a function of the localization scale. I am wondering whether it is related to the spatial correlation of the perturbations needed. Furthermore I am wondering what is the nature of the global perturbations. Do they look like bred modes? It would be really interesting to elaborate on that aspect.
  
  Yes, in Figure 9(a), the saturation of the dashed line (neighbor sites) clearly indicates that perturbing additional sites which are far away from the site of interest does not lead to any benefit. This fact is indeed related to spatial correlations, since perturbations performed at random sites do not show such a saturation. This localization effect and this saturation are interesting for future applications: It shows that a local control is sufficient, with a corresponding reduction of the energy provided to the system, as illustrated in Figure 9(b).
  About bred vectors, let us recall that the perturbation we identify is the difference between the EnKF ensemble state evolving to the extreme and the EnKF ensemble state evolving to the most non-extreme. The EnKF ensemble perturbations are considered as an extension of bred vectors. Therefore, the difference between the two ensemble states is somewhat related to the bred vectors. However, in our investigations, we did not elaborate further on bred vectors, but indeed in future studies we should look more carefully in this direction. In terms of effectiveness, working with bred vectors would allow us to provide the smallest perturbation to the system for the biggest impact.
  The last paragraph of the introduction should be placed in the conclusion.
  
  This paragraph has been removed and integrated in the conclusion.
  Line 126. There is no Appendix in the document.
  
  This sentence has been removed.
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC1
RC2:
'Review of npg-2022-12: Control Simulation Experiments of Extreme Events with the Lorenz-96 Model by Sun et al.', Anonymous Referee #2, 13 Jan 2023

The authors propose a method (Control Simulation Experiment) to control the number of extreme events in the Lorenz-96 model. The sensitivity of this technique to the choice of various parameters, such as the forecast lead time in which extreme events are detected or the amplitude of the perturbations. The authors find that the method is effective to reduce extremes and the sensitivity tests show how the perturbations can be tuned in order to reduce the high number of extreme events with a minimized action over the system.

General comment:

The manuscript is clear, the technical details of the experiments performed are well described. The authors provide several references to contextualize their research. This manuscript can be of interest for NPG readers, however my main concern is about the implications of this study in a more realistic context. The Control Simulation Experiment is aimed at reducing the extremes, but the challenge is that the models are able to simulate these extremes and in case of ensemble forecasting how the ensemble should be designed to include extremes. Therefore, I do not see the benefit of reducing the extremes in a simulation, when those states actually take place in the system that the model represents. I suggest including some clarifications in the introduction in this regard as well as in the conclusions to better express the general objective of this research.

Specific comments:

L11: “of the first two authors” can be removed.

L34-35: In line with my general comment, what is the benefit of reducing simulated weather extremes that occur in reality?

L149: (j,j) -> (i,j)

L170: Why only the maximum value is used to define extremes and not the minimum?

L199: When the procedure to generate the perturbation vectors is described and the selection of the ensemble member B is explained, the alternative computation in case an ensemble member B is not found (L208-209) should be indicated here.

L281: It is more correct saying similar or approximately equal instead of equal.

L292-293: The meaning of this sentence is not clear.

Fig.10: Please, indicate the meaning of the triangle in the caption.

Citation: https://doi.org/10.5194/npg-2022-12-RC2
- AC2:
  'Reply on RC2', Qiwen Sun, 20 Feb 2023
  First of all, let us thank the referees for their careful work on our manuscript. Their remarks allow us to improve the quality of the manuscript, and to clarify some parts of it. We list below the comments, and the corresponding changes in the manuscript.
  The manuscript is clear, the technical details of the experiments performed are well described. The authors provide several references to contextualize their research. This manuscript can be of interest for NPG readers, however my main concern is about the implications of this study in a more realistic context. The Control Simulation Experiment is aimed at reducing the extremes, but the challenge is that the models are able to simulate these extremes and in case of ensemble forecasting how the ensemble should be designed to include extremes. Therefore, I do not see the benefit of reducing the extremes in a simulation, when those states actually take place in the system that the model represents. I suggest including some clarifications in the introduction in this regard as well as in the conclusions to better express the general objective of this research.
  
  We agree that if the model can not predict extremes, our approach can not work. For this reason, our CSE is based on perfect-model assumption. The EnKF OSSE is designed that way, and the CSE is also designed with this assumption. Let us emphasize that current ensemble prediction systems tend to predict extreme events although not perfect yet. So, if we have good ensemble prediction systems in the future, and at least one ensemble member showing the occurrence of extremes, we could potentially apply our CSE. Note that this underlying assumption has been added in the conclusion of our manuscript.
  L11: “of the first two authors” can be removed.
  
  This has been corrected.
  L34-35: In line with my general comment, what is the benefit of reducing simulated weather extremes that occur in reality?
  
  This has been discussed above.
  L149: (j,j) -> (i,j)
  
  This has been corrected.
  L170: Why only the maximum value is used to define extremes and not the minimum?
  
  At the beginning of the investigations, this had been an arbitrary choice. Later on, it has been used to check if avoiding maximum values would generate the negative impact of having more negative values. As mentioned in a previous response, the number of extreme negative values has not changed statistically. In future investigations, avoiding both extreme values could be implemented.
  L199: When the procedure to generate the perturbation vectors is described and the selection of the ensemble member B is explained, the alternative computation in case an ensemble member B is not found (L208-209) should be indicated here.
  
  The alternative process has been moved to L199.
  L281: It is more correct saying similar or approximately equal instead of equal.
  
  This has been corrected.
  L292-293: The meaning of this sentence is not clear.
  
  The sentence has been moved to the subsequent paragraph, with additional explanation. In L291, the sentence has also been modified as: ….introduced in Sect. 2.3, need to be adapted for achieving the smallest RMSE.
  The following sentence will be added at the end of the subsequent paragraph:
  
  In Figure 10, the triangle indicates which combination of values for L and ρ leads to the smallest RMSE. This information is also reported in the second figure. By looking at the position of the two triangles, we observe that the RMSE and the average spread take approximatively the same value (about 0.31). Since the spread is computed as the RMSE but with the truth replaced by the mean value of the ensemble members, this concurrence means that the ensemble members spread sufficiently to cover the unknown truth of the model.
  Fig.10: Please, indicate the meaning of the triangle in the caption.
  
  The following sentence has been added in the caption of Figure 10:
  
  The triangles indicate which combination of values for L and ρ leads to the smallest RMSE. This information is also reported in the second figure.
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC2
EC1:
'Comment on npg-2022-12', Natale Alberto Carrassi, 17 Jan 2023

Dear Authors
we have now received two very useful and positive reports about your works. I think they both address aspects of your work that can be improved, particularly in relation to the applicabilty.
I encourage you to take them into account while preparing the revised manuscript.
Please send first detailed responses to the Reviewers' quests.
Best Regards

Citation: https://doi.org/10.5194/npg-2022-12-EC1
- AC3: 'Reply on EC1', Qiwen Sun, 20 Feb 2023
  
  Dear Professor Carrassi,
  Thank you for your comments.
  We have replied the referee comments and revised the manuscript.
  Best regards,
  Qiwen
  
  Citation: https://doi.org/10.5194/npg-2022-12-AC3

Qiwen Sun et al.

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Short summary

This paper is a follow up of a work by T. Miyoshi and Q. Sun which was published as NPG letters in 2022. The Control Simulation Experiment is applied to the Lorenz 96 model for avoiding extreme events. The results show that extreme events of this partially and imperfectly observed chaotic system can be avoided by applying pre-designed small perturbations. These investigations may be extended to more realistic numerical weather prediction models.


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