the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Jul 2024
Convex optimization of initial perturbations toward quantitative weather control
Abstract. This study proposes introducing convex optimization to find initial perturbations of atmospheric models for realizing specified changes in subsequent forecasts. In the proposed method, we formulate and solve an inverse problem to find effective perturbations in atmospheric variables so that controlled variables satisfy specified changes at a specified time. The proposed method first constructs a sensitivity matrix of controlled variables, such as accumulated precipitation, to the initial atmospheric variables, such as temperature and humidity, through sensitivity analysis using numerical weather prediction (NWP) models. The sensitivity matrix is used to solve the inverse problem as convex optimization, in which a global optimal solution can be found computationally efficiently. The proposed method was validated through a benchmark warm bubble experiment using an NWP model. The experiments showed that identified perturbation successfully realized specified spatial distributions of accumulated precipitation. These results demonstrated the possibility of controlling the real atmosphere by solving inverse problems and adding small perturbations to atmospheric states.
This preprint has been withdrawn.
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-1952', Anonymous Referee #1, 14 Aug 2024
Mitigating or controling the impacts of extreme weather events are very important and urgent. This study introduced an optimization method to conduct the quantitative weather control experiments and confirmed that the method has a potential to control the weather (accumulated precipitation). Overall, this manuscript is very interesting and well organized. However, there are several problems in the current version, and I suggest a major revision. My main concerns are listed as follows:
1. In this study, L2 and L1 norms were used. Figures 2 and 3 show that the results are significantly different for these two norms. Then, in the realistic weather control field experiments, which norm should be applied? Besides, why were these two norms used? How to choose a suitable norm?
2. The optimization problem (4) seems to be solvable directly by solving a system of linear equations. If so, the optimization process may not be necessary.
3. In the proposed approach, the linearity assumption was made. The rationality of this assumption should be validated. For example, the results from the nonlinear simulation and linear simulation should be compared.
4. The sensitivity matrix S was obtained using the definition of partial derivative. For a relative simple model this study used, it can be obtained easily. But in a more realistic three-dimensional GCM model, calculating matrix S in this way is very difficult and time-consuming. How to overcome this problem in real application?
5. In the section 3.3, different control variables were examined. Could you please add a discussion about how to choose the control variables for weather control experiments in real application?
6. Sections 3.2 and 3.3: the results of the numerical experiments show that the optimal perturbations can induce the atmosphere state to shift a desired state. But the physical processes about the state shift are unclear. Could you indicate the time development of the optimal perturbation and reveal the related physical processes?
7. Figure 3c displays that for L1 norm, the perturbed case is greater than the upper bound. This means that the perturbation does not statisfy the constraint condition. What is the reason? Does this reflect the important effects of nonlinear physical processes? If so, please make clear.
8. Although optimization requires minimal perturbation, in practical applications, perturbation amplitude may still exceed the controllable range. How should we make decisions to control the weather in this situation?
Citation: https://doi.org/10.5194/egusphere-2024-1952-RC1 -
RC2: 'Comment on egusphere-2024-1952', Anonymous Referee #2, 26 Aug 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-RC2-supplement.pdf
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AC1: 'Comment on egusphere-2024-1952', Toshiyuki Ohtsuka, 15 Oct 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-AC1-supplement.pdf
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EC1: 'Comment on egusphere-2024-1952', Olivier Talagrand, 28 Oct 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-EC1-supplement.pdf
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AC2: 'Reply on EC1', Toshiyuki Ohtsuka, 05 Nov 2024
We appreciate your taking the time to handle our manuscript. We understand your standpoint to give importance to directly handling nonlinear problems without linearization. We also understand you may think that weather control is a remote possibility.
On the other hand, using linearized models is common and often successful in control design, even for nonlinear systems such as drones, automobiles, steel-making processes, and chemical processes. From the viewpoint of control engineering, we should first apply linear control methods and then attempt nonlinear control methods only when the linear control methods fail to meet the design specifications. Although nonlinear control methods may be necessary at a certain stage of progress in weather control, we are confident that our approach will serve as one of the fundamental techniques in the future.
However, given the significant difference in opinions, we have decided to withdraw our manuscript, as you suggest. Thank you again for your consideration.
Citation: https://doi.org/10.5194/egusphere-2024-1952-AC2
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AC2: 'Reply on EC1', Toshiyuki Ohtsuka, 05 Nov 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-1952', Anonymous Referee #1, 14 Aug 2024
Mitigating or controling the impacts of extreme weather events are very important and urgent. This study introduced an optimization method to conduct the quantitative weather control experiments and confirmed that the method has a potential to control the weather (accumulated precipitation). Overall, this manuscript is very interesting and well organized. However, there are several problems in the current version, and I suggest a major revision. My main concerns are listed as follows:
1. In this study, L2 and L1 norms were used. Figures 2 and 3 show that the results are significantly different for these two norms. Then, in the realistic weather control field experiments, which norm should be applied? Besides, why were these two norms used? How to choose a suitable norm?
2. The optimization problem (4) seems to be solvable directly by solving a system of linear equations. If so, the optimization process may not be necessary.
3. In the proposed approach, the linearity assumption was made. The rationality of this assumption should be validated. For example, the results from the nonlinear simulation and linear simulation should be compared.
4. The sensitivity matrix S was obtained using the definition of partial derivative. For a relative simple model this study used, it can be obtained easily. But in a more realistic three-dimensional GCM model, calculating matrix S in this way is very difficult and time-consuming. How to overcome this problem in real application?
5. In the section 3.3, different control variables were examined. Could you please add a discussion about how to choose the control variables for weather control experiments in real application?
6. Sections 3.2 and 3.3: the results of the numerical experiments show that the optimal perturbations can induce the atmosphere state to shift a desired state. But the physical processes about the state shift are unclear. Could you indicate the time development of the optimal perturbation and reveal the related physical processes?
7. Figure 3c displays that for L1 norm, the perturbed case is greater than the upper bound. This means that the perturbation does not statisfy the constraint condition. What is the reason? Does this reflect the important effects of nonlinear physical processes? If so, please make clear.
8. Although optimization requires minimal perturbation, in practical applications, perturbation amplitude may still exceed the controllable range. How should we make decisions to control the weather in this situation?
Citation: https://doi.org/10.5194/egusphere-2024-1952-RC1 -
RC2: 'Comment on egusphere-2024-1952', Anonymous Referee #2, 26 Aug 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-RC2-supplement.pdf
-
AC1: 'Comment on egusphere-2024-1952', Toshiyuki Ohtsuka, 15 Oct 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-AC1-supplement.pdf
-
EC1: 'Comment on egusphere-2024-1952', Olivier Talagrand, 28 Oct 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1952/egusphere-2024-1952-EC1-supplement.pdf
-
AC2: 'Reply on EC1', Toshiyuki Ohtsuka, 05 Nov 2024
We appreciate your taking the time to handle our manuscript. We understand your standpoint to give importance to directly handling nonlinear problems without linearization. We also understand you may think that weather control is a remote possibility.
On the other hand, using linearized models is common and often successful in control design, even for nonlinear systems such as drones, automobiles, steel-making processes, and chemical processes. From the viewpoint of control engineering, we should first apply linear control methods and then attempt nonlinear control methods only when the linear control methods fail to meet the design specifications. Although nonlinear control methods may be necessary at a certain stage of progress in weather control, we are confident that our approach will serve as one of the fundamental techniques in the future.
However, given the significant difference in opinions, we have decided to withdraw our manuscript, as you suggest. Thank you again for your consideration.
Citation: https://doi.org/10.5194/egusphere-2024-1952-AC2
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AC2: 'Reply on EC1', Toshiyuki Ohtsuka, 05 Nov 2024
Model code and software
SCALE-RM Team SCALE, RIKEN https://scale.riken.jp/
Weather-Control-by-InitCond Toshiyuki Ohtsuka https://github.com/ohtsukalab/Weather-Control-by-InitCond
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