Articles | Volume 31, issue 3
https://doi.org/10.5194/npg-31-319-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-31-319-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
10 Jul 2024
Research article |
| 10 Jul 2024
| 10 Jul 2024
Leading the Lorenz 63 system toward the prescribed regime by model predictive control coupled with data assimilation
Graduate School of Science and Engineering, Chiba University, Chiba, Japan
Shunji Kotsuki
CORRESPONDING AUTHOR
Institute for Advanced Academic Research, Chiba University, Chiba, Japan
Center for Environmental Remote Sensing, Chiba University, Chiba, Japan
Research Institute of Disaster Medicine, Chiba University, Chiba, Japan
Related authors
Kenta Kurosawa, Atsushi Okazaki, Fumitoshi Kawasaki, and Shunji Kotsuki
EGUsphere, https://doi.org/10.5194/egusphere-2025-595, https://doi.org/10.5194/egusphere-2025-595, 2025
This preprint is open for discussion and under review for Nonlinear Processes in Geophysics (NPG).
Short summary
Short summary
We propose Ensemble Model Predictive Control (EnMPC), a novel method that improves control of complex systems like weather by integrating control theory with data assimilation. Unlike traditional methods, which are computationally expensive, EnMPC uses ensemble simulations to efficiently handle uncertainties and optimize solutions. This approach reduces computational cost while maintaining accuracy, making it a promising step toward real-world applications in dynamic system control.
Shunji Kotsuki, Fumitoshi Kawasaki, and Masanao Ohashi
Nonlin. Processes Geophys., 31, 237–245, https://doi.org/10.5194/npg-31-237-2024, https://doi.org/10.5194/npg-31-237-2024, 2024
Short summary
Short summary
In Earth science, data assimilation plays an important role in integrating real-world observations with numerical simulations for improving subsequent predictions. To overcome the time-consuming computations of conventional data assimilation methods, this paper proposes using quantum annealing machines. Using the D-Wave quantum annealer, the proposed method found solutions with comparable accuracy to conventional approaches and significantly reduced computational time.
Kenta Kurosawa, Atsushi Okazaki, Fumitoshi Kawasaki, and Shunji Kotsuki
EGUsphere, https://doi.org/10.5194/egusphere-2025-595, https://doi.org/10.5194/egusphere-2025-595, 2025
This preprint is open for discussion and under review for Nonlinear Processes in Geophysics (NPG).
Short summary
Short summary
We propose Ensemble Model Predictive Control (EnMPC), a novel method that improves control of complex systems like weather by integrating control theory with data assimilation. Unlike traditional methods, which are computationally expensive, EnMPC uses ensemble simulations to efficiently handle uncertainties and optimize solutions. This approach reduces computational cost while maintaining accuracy, making it a promising step toward real-world applications in dynamic system control.
Yuka Muto and Shunji Kotsuki
Hydrol. Earth Syst. Sci., 28, 5401–5417, https://doi.org/10.5194/hess-28-5401-2024, https://doi.org/10.5194/hess-28-5401-2024, 2024
Short summary
Short summary
It is crucial to improve global precipitation estimates to understand water-related disasters and water resources. This study proposes a new methodology to interpolate global precipitation fields from ground rain gauge observations using ensemble data assimilation and the precipitation of a numerical weather prediction model. Our estimates agree better with independent rain gauge observations than existing precipitation estimates, especially in mountainous or rain-gauge-sparse regions.
Rikuto Nagai, Yang Bai, Masaki Ogura, Shunji Kotsuki, and Naoki Wakamiya
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-26, https://doi.org/10.5194/npg-2024-26, 2024
Preprint under review for NPG
Short summary
Short summary
Controlling chaotic systems is a key step toward weather control. The Control Simulation Experiment (CSE) modifies weather systems using small perturbations, as shown in studies with the Lorenz-63 model. However, the effectiveness of CSE compared to other methods is unclear. This study evaluates CSE against Model Predictive Control (MPC). Simulations reveal that MPC achieves higher success rates with less effort under certain conditions, linking control theory and atmospheric science.
Shunji Kotsuki, Kenta Shiraishi, and Atsushi Okazaki
EGUsphere, https://doi.org/10.48550/arXiv.2407.17781, https://doi.org/10.48550/arXiv.2407.17781, 2024
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Artificial intelligence (AI) is playing a bigger role in weather forecasting, often competing with physical models. However, combining AI models with data assimilation, a process that improves weather forecasts by incorporating observation data, is still relatively unexplored. This study explored coupling ensemble data assimilation with an AI weather prediction model ClimaX, succeeded in employing weather forecasts stably by applying techniques conventionally used for physical models.
Toshiyuki Ohtsuka, Atsushi Okazaki, Masaki Ogura, and Shunji Kotsuki
EGUsphere, https://doi.org/10.48550/arXiv.2405.19546, https://doi.org/10.48550/arXiv.2405.19546, 2024
Preprint withdrawn
Short summary
Short summary
We utilize weather forecasts in the reverse direction and determine how much we should change the temperature or humidity of the atmosphere at a certain time to change the future rainfall as desired. Even though a weather phenomenon is complicated, we can superimpose the effects of small changes in the atmosphere and find suitable small changes to realize desirable rainfall by solving an optimization problem. We examine this idea on a realistic weather simulator and show it is promising.
Shunji Kotsuki, Fumitoshi Kawasaki, and Masanao Ohashi
Nonlin. Processes Geophys., 31, 237–245, https://doi.org/10.5194/npg-31-237-2024, https://doi.org/10.5194/npg-31-237-2024, 2024
Short summary
Short summary
In Earth science, data assimilation plays an important role in integrating real-world observations with numerical simulations for improving subsequent predictions. To overcome the time-consuming computations of conventional data assimilation methods, this paper proposes using quantum annealing machines. Using the D-Wave quantum annealer, the proposed method found solutions with comparable accuracy to conventional approaches and significantly reduced computational time.
Kenta Kurosawa, Shunji Kotsuki, and Takemasa Miyoshi
Nonlin. Processes Geophys., 30, 457–479, https://doi.org/10.5194/npg-30-457-2023, https://doi.org/10.5194/npg-30-457-2023, 2023
Short summary
Short summary
This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.
Mao Ouyang, Keita Tokuda, and Shunji Kotsuki
Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, https://doi.org/10.5194/npg-30-183-2023, 2023
Short summary
Short summary
This research found that weather control would change the chaotic behavior of an atmospheric model. We proposed to introduce chaos theory in the weather control. Experimental results demonstrated that the proposed approach reduced the manipulations, including the control times and magnitudes, which throw light on the weather control in a real atmospheric model.
Shunji Kotsuki, Takemasa Miyoshi, Keiichi Kondo, and Roland Potthast
Geosci. Model Dev., 15, 8325–8348, https://doi.org/10.5194/gmd-15-8325-2022, https://doi.org/10.5194/gmd-15-8325-2022, 2022
Short summary
Short summary
Data assimilation plays an important part in numerical weather prediction (NWP) in terms of combining forecasted states and observations. While data assimilation methods in NWP usually assume the Gaussian error distribution, some variables in the atmosphere, such as precipitation, are known to have non-Gaussian error statistics. This study extended a widely used ensemble data assimilation algorithm to enable the assimilation of more non-Gaussian observations.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Simulation
A comparison of two nonlinear data assimilation methods
Quantum data assimilation: a new approach to solving data assimilation on quantum annealers
Comparative study of strongly and weakly coupled data assimilation with a global land–atmosphere coupled model
Reducing manipulations in a control simulation experiment based on instability vectors with the Lorenz-63 model
Control simulation experiments of extreme events with the Lorenz-96 model
A range of outcomes: the combined effects of internal variability and anthropogenic forcing on regional climate trends over Europe
Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis
Control simulation experiment with Lorenz's butterfly attractor
Reduced non-Gaussianity by 30 s rapid update in convective-scale numerical weather prediction
A study of capturing Atlantic meridional overturning circulation (AMOC) regime transition through observation-constrained model parameters
Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation
Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales
Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty
Generalization properties of feed-forward neural networks trained on Lorenz systems
Vivian A. Montiforte, Hans E. Ngodock, and Innocent Souopgui
Nonlin. Processes Geophys., 31, 463–476, https://doi.org/10.5194/npg-31-463-2024, https://doi.org/10.5194/npg-31-463-2024, 2024
Short summary
Short summary
Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, diffusive back-and-forth nudging and concave–convex nonlinearity, which account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impact which method is better suited for a problem.
Shunji Kotsuki, Fumitoshi Kawasaki, and Masanao Ohashi
Nonlin. Processes Geophys., 31, 237–245, https://doi.org/10.5194/npg-31-237-2024, https://doi.org/10.5194/npg-31-237-2024, 2024
Short summary
Short summary
In Earth science, data assimilation plays an important role in integrating real-world observations with numerical simulations for improving subsequent predictions. To overcome the time-consuming computations of conventional data assimilation methods, this paper proposes using quantum annealing machines. Using the D-Wave quantum annealer, the proposed method found solutions with comparable accuracy to conventional approaches and significantly reduced computational time.
Kenta Kurosawa, Shunji Kotsuki, and Takemasa Miyoshi
Nonlin. Processes Geophys., 30, 457–479, https://doi.org/10.5194/npg-30-457-2023, https://doi.org/10.5194/npg-30-457-2023, 2023
Short summary
Short summary
This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.
Mao Ouyang, Keita Tokuda, and Shunji Kotsuki
Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, https://doi.org/10.5194/npg-30-183-2023, 2023
Short summary
Short summary
This research found that weather control would change the chaotic behavior of an atmospheric model. We proposed to introduce chaos theory in the weather control. Experimental results demonstrated that the proposed approach reduced the manipulations, including the control times and magnitudes, which throw light on the weather control in a real atmospheric model.
Qiwen Sun, Takemasa Miyoshi, and Serge Richard
Nonlin. Processes Geophys., 30, 117–128, https://doi.org/10.5194/npg-30-117-2023, https://doi.org/10.5194/npg-30-117-2023, 2023
Short summary
Short summary
This paper is a follow-up of a work by Miyoshi and Sun which was published in 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.
Clara Deser and Adam S. Phillips
Nonlin. Processes Geophys., 30, 63–84, https://doi.org/10.5194/npg-30-63-2023, https://doi.org/10.5194/npg-30-63-2023, 2023
Short summary
Short summary
Past and future climate change at regional scales is a result of both human influences and natural (internal) variability. Here, we provide an overview of recent advances in climate modeling and physical understanding that has led to new insights into their respective roles, illustrated with original results for the European climate. Our findings highlight the confounding role of internal variability in attribution, climate model evaluation, and accuracy of future projections.
Dikraa Khedhaouiria, Stéphane Bélair, Vincent Fortin, Guy Roy, and Franck Lespinas
Nonlin. Processes Geophys., 29, 329–344, https://doi.org/10.5194/npg-29-329-2022, https://doi.org/10.5194/npg-29-329-2022, 2022
Short summary
Short summary
This study introduces a well-known use of hybrid methods in data assimilation (DA) algorithms that has not yet been explored for precipitation analyses. Our approach combined an ensemble-based DA approach with an existing deterministically based DA. Both DA scheme families have desirable aspects that can be leveraged if combined. The DA hybrid method showed better precipitation analyses in regions with a low rate of assimilated surface observations, which is typically the case in winter.
Takemasa Miyoshi and Qiwen Sun
Nonlin. Processes Geophys., 29, 133–139, https://doi.org/10.5194/npg-29-133-2022, https://doi.org/10.5194/npg-29-133-2022, 2022
Short summary
Short summary
The weather is chaotic and hard to predict, but the chaos implies an effective control where a small control signal grows rapidly to make a big difference. This study proposes a control simulation experiment where we apply a small signal to control
naturein a computational simulation. Idealized experiments with a low-order chaotic system show successful results by small control signals of only 3 % of the observation error. This is the first step toward realistic weather simulations.
Juan Ruiz, Guo-Yuan Lien, Keiichi Kondo, Shigenori Otsuka, and Takemasa Miyoshi
Nonlin. Processes Geophys., 28, 615–626, https://doi.org/10.5194/npg-28-615-2021, https://doi.org/10.5194/npg-28-615-2021, 2021
Short summary
Short summary
Effective use of observations with numerical weather prediction models, also known as data assimilation, is a key part of weather forecasting systems. For precise prediction at the scales of thunderstorms, fast nonlinear processes pose a grand challenge because most data assimilation systems are based on linear processes and normal distribution errors. We investigate how, every 30 s, weather radar observations can help reduce the effect of nonlinear processes and nonnormal distributions.
Zhao Liu, Shaoqing Zhang, Yang Shen, Yuping Guan, and Xiong Deng
Nonlin. Processes Geophys., 28, 481–500, https://doi.org/10.5194/npg-28-481-2021, https://doi.org/10.5194/npg-28-481-2021, 2021
Short summary
Short summary
A general methodology is introduced to capture regime transitions of the Atlantic meridional overturning circulation (AMOC). The assimilation models with different parameters simulate different paths for the AMOC to switch between equilibrium states. Constraining model parameters with observations can significantly mitigate the model deviations, thus capturing AMOC regime transitions. This simple model study serves as a guideline for improving coupled general circulation models.
Sangeetika Ruchi, Svetlana Dubinkina, and Jana de Wiljes
Nonlin. Processes Geophys., 28, 23–41, https://doi.org/10.5194/npg-28-23-2021, https://doi.org/10.5194/npg-28-23-2021, 2021
Short summary
Short summary
To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data are sparse and the model can be non-linear. We propose a novel approach to address these challenges.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207, https://doi.org/10.5194/npg-27-187-2020, https://doi.org/10.5194/npg-27-187-2020, 2020
Short summary
Short summary
A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.
Valentin Resseguier, Wei Pan, and Baylor Fox-Kemper
Nonlin. Processes Geophys., 27, 209–234, https://doi.org/10.5194/npg-27-209-2020, https://doi.org/10.5194/npg-27-209-2020, 2020
Short summary
Short summary
Geophysical flows span a broader range of temporal and spatial scales than can be resolved numerically. One way to alleviate the ensuing numerical errors is to combine simulations with measurements, taking account of the accuracies of these two sources of information. Here we quantify the distribution of numerical simulation errors without relying on high-resolution numerical simulations. Specifically, small-scale random vortices are added to simulations while conserving energy or circulation.
Sebastian Scher and Gabriele Messori
Nonlin. Processes Geophys., 26, 381–399, https://doi.org/10.5194/npg-26-381-2019, https://doi.org/10.5194/npg-26-381-2019, 2019
Short summary
Short summary
Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – it is
trained– and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate- and weather-related applications.
Cited articles
Burgers, G., van Leeuwen, P. J., and Evensen, G.: Analysis Scheme in the Ensemble Kalman Filter, Mon. Weather Rev., 126, 1719–1724, https://doi.org/10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2, 1998.
Chen, C. C. and Shaw, L.: On receding horizon feedback control, Automatica, 18, 349–352, https://doi.org/10.1016/0005-1098(82)90096-6, 1982.
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res.-Oceans, 99, 10143–10162, https://doi.org/10.1029/94JC00572, 1994.
Henderson, J. M., Hoffman, R. N., Leidner, S. M., Nehrkorn, T., and Grassotti, C.: A 4D-Var study on the potential of weather control and exigent weather forecasting, Q. J. Roy. Meteor. Soc., 131, 3037–3051, https://doi.org/10.1256/qj.05.72, 2005.
Inoue, D. and Yoshida, H.: Model Predictive Control for Finite Input Systems using the D-Wave Quantum Annealer, Sci. Rep.-UK, 10, 1591, https://doi.org/10.1038/s41598-020-58081-9, 2020.
Kalnay, E., Li, H., Miyoshi, T., Yang, S.-C., and Ballabrera-Poy, J.: 4-D-Var or ensemble Kalman filter?, Tellus A, 59, 758–773, https://doi.org/10.1111/j.1600-0870.2007.00261.x, 2007.
Keerthi, S. S. and Gilbert, E. G.: Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations, J. Optim. Theor. Appl., 57, 265–293, https://doi.org/10.1007/BF00938540, 1988.
Lawson, W. G. and Hansen, J. A.: Implications of Stochastic and Deterministic Filters as Ensemble-Based Data Assimilation Methods in Varying Regimes of Error Growth, Mon. Weather Rev., 132, 1966–1981, https://doi.org/10.1175/1520-0493(2004)132<1966:IOSADF>2.0.CO;2, 2004.
Lorenz, E. N.: Deterministic Nonperiodic Flow, J. Atmos. Sci., 20, 130–141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2, 1963.
Lorenz, E. N.: Predictability – A problem partly solved. Proc, Seminar on Predictability, Seminar on Predictability, Reading, 4–8 September 1995, ECMWF, 1–18, https://www.ecmwf.int/en/elibrary/75462-predictability-problem-partly-solved (last access: 23 January 2024), 1996.
Mayne, D. Q. and Michalska, H.: Receding horizon control of nonlinear systems, IEEE T. Automat. Contr., 35, 814–824, https://doi.org/10.1109/9.57020, 1990.
Mayne, D. Q., Rawlings, J. B., Rao, C. V., and Scokaert, P. O. M.: Constrained model predictive control: Stability and optimality, Automatica, 36, 789–814, https://doi.org/10.1016/S0005-1098(99)00214-9, 2000.
Miyoshi, T. and Sun, Q.: Control simulation experiment with Lorenz's butterfly attractor, Nonlin. Processes Geophys., 29, 133–139, https://doi.org/10.5194/npg-29-133-2022, 2022.
Ohtsuka, T.: A continuation/GMRES method for fast computation of nonlinear receding horizon control, Automatica, 40, 563–574, https://doi.org/10.1016/j.automatica.2003.11.005, 2004.
Ouyang, M., Tokuda, K., and Kotsuki, S.: Reducing manipulations in a control simulation experiment based on instability vectors with the Lorenz-63 model, Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, 2023.
Schwenzer, M., Ay, M., Bergs, T., and Abel, D.: Review on model predictive control: an engineering perspective, Int. J. Adv. Manuf. Technol., 117, 1327–1349, https://doi.org/10.1007/s00170-021-07682-3, 2021.
Sun, Q., Miyoshi, T., and Richard, S.: Control simulation experiments of extreme events with the Lorenz-96 model, Nonlin. Processes Geophys., 30, 117–128, https://doi.org/10.5194/npg-30-117-2023, 2023.
Yang, S.-C., Kalnay, E., and Hunt, B.: Handling Nonlinearity in an Ensemble Kalman Filter: Experiments with the Three-Variable Lorenz Model, Mon. Weather Rev., 140, 2628–2646, https://doi.org/10.1175/MWR-D-11-00313.1, 2012.
Short summary
Recently, scientists have been looking into ways to control the weather to lead to a desirable direction for mitigating weather-induced disasters caused by torrential rainfall and typhoons. This study proposes using the model predictive control (MPC), an advanced control method, to control a chaotic system. Through numerical experiments using a low-dimensional chaotic system, we demonstrate that the system can be successfully controlled with shorter forecasts compared to previous studies.
Recently, scientists have been looking into ways to control the weather to lead to a desirable...
