Articles | Volume 30, issue 2
https://doi.org/10.5194/npg-30-129-2023
© Author(s) 2023. 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-30-129-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
09 Jun 2023
Research article |
| 09 Jun 2023
| 09 Jun 2023
Data-driven reconstruction of partially observed dynamical systems
Pierre Tandeo
CORRESPONDING AUTHOR
IMT Atlantique, Lab-STICC, UMR CNRS 6285, 29238, Brest, France
Odyssey, Inria/IMT/CNRS, Rennes, France
RIKEN Center for Computational Science, Kobe, 650-0047, Japan
Pierre Ailliot
Laboratoire de Mathematiques de Bretagne Atlantique, Univ Brest, UMR CNRS 6205, Brest, France
Florian Sévellec
Laboratoire d’Océanographie Physique et Spatiale, Univ Brest CNRS IRD Ifremer, Brest, France
Odyssey, Inria/IMT/CNRS, Rennes, France
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Paul Platzer, Pierre Tandeo, Pierre Ailliot, and Bertrand Chapron
EGUsphere, https://doi.org/10.5194/egusphere-2023-2997, https://doi.org/10.5194/egusphere-2023-2997, 2024
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Old observations are necessary to understand the atmosphere. When direct observations are not available, one can use indirect observations such as tide gauges, which measure the sea-level in portal cities. The sea level rises when local air pressure decreases, and when wind pushes water towards the coast. Several centuries-long tide gauge records are available. We show that these can be complementary to direct pressure observations for studying storms and anticyclones in the 19th century.
Pierre Le Bras, Florian Sévellec, Pierre Tandeo, Juan Ruiz, and Pierre Ailliot
EGUsphere, https://doi.org/10.5194/egusphere-2023-2649, https://doi.org/10.5194/egusphere-2023-2649, 2023
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The goal of this paper is to weight several dynamic models in order to improve the representativeness of a system. It is illustrated using a set of versions of an idealized model describing the Atlantic Meridional Overturning Circulation. The low-cost method is based on data-driven forecasts. It enables model performance to be evaluated on their dynamics. Taking into account both model performance and codependency, the derived weights outperform benchmarks in reconstructing a model distribution.
Robin Marcille, Maxime Thiébaut, Pierre Tandeo, and Jean-François Filipot
Wind Energ. Sci., 8, 771–786, https://doi.org/10.5194/wes-8-771-2023, https://doi.org/10.5194/wes-8-771-2023, 2023
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A novel data-driven method is proposed to design an optimal sensor network for the reconstruction of offshore wind resources. Based on unsupervised learning of numerical weather prediction wind data, it provides a simple yet efficient method for the siting of sensors, outperforming state-of-the-art methods for this application. It is applied in the main French offshore wind energy development areas to provide guidelines for the deployment of floating lidars for wind resource assessment.
Juan Ruiz, Pierre Ailliot, Thi Tuyet Trang Chau, Pierre Le Bras, Valérie Monbet, Florian Sévellec, and Pierre Tandeo
Geosci. Model Dev., 15, 7203–7220, https://doi.org/10.5194/gmd-15-7203-2022, https://doi.org/10.5194/gmd-15-7203-2022, 2022
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We present a new approach to validate numerical simulations of the current climate. The method can take advantage of existing climate simulations produced by different centers combining an analog forecasting approach with data assimilation to quantify how well a particular model reproduces a sequence of observed values. The method can be applied with different observations types and is implemented locally in space and time significantly reducing the associated computational cost.
Etienne Pauthenet, Loïc Bachelot, Kevin Balem, Guillaume Maze, Anne-Marie Tréguier, Fabien Roquet, Ronan Fablet, and Pierre Tandeo
Ocean Sci., 18, 1221–1244, https://doi.org/10.5194/os-18-1221-2022, https://doi.org/10.5194/os-18-1221-2022, 2022
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Temperature and salinity profiles are essential for studying the ocean’s stratification, but there are not enough of these data. Satellites are able to measure daily maps of the surface ocean. We train a machine to learn the link between the satellite data and the profiles in the Gulf Stream region. We can then use this link to predict profiles at the high resolution of the satellite maps. Our prediction is fast to compute and allows us to get profiles at any locations only from surface data.
Paul Platzer, Pierre Tandeo, Pierre Ailliot, and Bertrand Chapron
EGUsphere, https://doi.org/10.5194/egusphere-2023-2997, https://doi.org/10.5194/egusphere-2023-2997, 2024
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Old observations are necessary to understand the atmosphere. When direct observations are not available, one can use indirect observations such as tide gauges, which measure the sea-level in portal cities. The sea level rises when local air pressure decreases, and when wind pushes water towards the coast. Several centuries-long tide gauge records are available. We show that these can be complementary to direct pressure observations for studying storms and anticyclones in the 19th century.
Pierre Le Bras, Florian Sévellec, Pierre Tandeo, Juan Ruiz, and Pierre Ailliot
EGUsphere, https://doi.org/10.5194/egusphere-2023-2649, https://doi.org/10.5194/egusphere-2023-2649, 2023
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The goal of this paper is to weight several dynamic models in order to improve the representativeness of a system. It is illustrated using a set of versions of an idealized model describing the Atlantic Meridional Overturning Circulation. The low-cost method is based on data-driven forecasts. It enables model performance to be evaluated on their dynamics. Taking into account both model performance and codependency, the derived weights outperform benchmarks in reconstructing a model distribution.
Said Obakrim, Pierre Ailliot, Valérie Monbet, and Nicolas Raillard
Adv. Stat. Clim. Meteorol. Oceanogr., 9, 67–81, https://doi.org/10.5194/ascmo-9-67-2023, https://doi.org/10.5194/ascmo-9-67-2023, 2023
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Ocean wave climate has a significant impact on human activities, and its understanding is of socioeconomic and environmental importance. In this study, we propose a statistical model that predicts wave heights in a location in the Bay of Biscay. The proposed method allows us to understand the spatiotemporal relationship between wind and waves and predicts well both wind seas and swells.
Robin Marcille, Maxime Thiébaut, Pierre Tandeo, and Jean-François Filipot
Wind Energ. Sci., 8, 771–786, https://doi.org/10.5194/wes-8-771-2023, https://doi.org/10.5194/wes-8-771-2023, 2023
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A novel data-driven method is proposed to design an optimal sensor network for the reconstruction of offshore wind resources. Based on unsupervised learning of numerical weather prediction wind data, it provides a simple yet efficient method for the siting of sensors, outperforming state-of-the-art methods for this application. It is applied in the main French offshore wind energy development areas to provide guidelines for the deployment of floating lidars for wind resource assessment.
Juan Ruiz, Pierre Ailliot, Thi Tuyet Trang Chau, Pierre Le Bras, Valérie Monbet, Florian Sévellec, and Pierre Tandeo
Geosci. Model Dev., 15, 7203–7220, https://doi.org/10.5194/gmd-15-7203-2022, https://doi.org/10.5194/gmd-15-7203-2022, 2022
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We present a new approach to validate numerical simulations of the current climate. The method can take advantage of existing climate simulations produced by different centers combining an analog forecasting approach with data assimilation to quantify how well a particular model reproduces a sequence of observed values. The method can be applied with different observations types and is implemented locally in space and time significantly reducing the associated computational cost.
Etienne Pauthenet, Loïc Bachelot, Kevin Balem, Guillaume Maze, Anne-Marie Tréguier, Fabien Roquet, Ronan Fablet, and Pierre Tandeo
Ocean Sci., 18, 1221–1244, https://doi.org/10.5194/os-18-1221-2022, https://doi.org/10.5194/os-18-1221-2022, 2022
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Temperature and salinity profiles are essential for studying the ocean’s stratification, but there are not enough of these data. Satellites are able to measure daily maps of the surface ocean. We train a machine to learn the link between the satellite data and the profiles in the Gulf Stream region. We can then use this link to predict profiles at the high resolution of the satellite maps. Our prediction is fast to compute and allows us to get profiles at any locations only from surface data.
Marceau Michel, Said Obakrim, Nicolas Raillard, Pierre Ailliot, and Valérie Monbet
Adv. Stat. Clim. Meteorol. Oceanogr., 8, 83–95, https://doi.org/10.5194/ascmo-8-83-2022, https://doi.org/10.5194/ascmo-8-83-2022, 2022
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In this study, we introduce a deep learning algorithm to establish the relationship between wind and waves in order to predict the latter. The performance of the proposed method has been evaluated both on the output of numerical wave models and on in situ data and compared to other statistical methods developed by our research team. The results obtained confirm the interest of deep learning methods for forecasting ocean data.
Dafydd Stephenson, Simon A. Müller, and Florian Sévellec
Geosci. Model Dev., 13, 2031–2050, https://doi.org/10.5194/gmd-13-2031-2020, https://doi.org/10.5194/gmd-13-2031-2020, 2020
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Different water types are created at the sea surface with a signature based on the local conditions of the atmosphere. They then take these conditions with them into the deeper ocean, and so their journey is an important climate process to understand. In this study, we modify and repurpose a specialised model which simulates the ocean forward and backward in time to determine where new ocean water goes, where at the surface existing water comes from, and how old it is, by tracking it as a dye.
Julie Bessac, Pierre Ailliot, Julien Cattiaux, and Valerie Monbet
Adv. Stat. Clim. Meteorol. Oceanogr., 2, 1–16, https://doi.org/10.5194/ascmo-2-1-2016, https://doi.org/10.5194/ascmo-2-1-2016, 2016
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Several multi-site stochastic generators of zonal and meridional components of wind are proposed in this paper. Various questions are explored, such as the modeling of the regime in a multi-site context, the extraction of relevant clusterings from extra variables or from the local wind data, and the link between weather types extracted from wind data and large-scale weather regimes. We also discuss the relative advantages of hidden and observed regime-switching models.
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Annika Vogel and Richard Ménard
Nonlin. Processes Geophys., 30, 375–398, https://doi.org/10.5194/npg-30-375-2023, https://doi.org/10.5194/npg-30-375-2023, 2023
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Yung-Yun Cheng, Shu-Chih Yang, Zhe-Hui Lin, and Yung-An Lee
Nonlin. Processes Geophys., 30, 289–297, https://doi.org/10.5194/npg-30-289-2023, https://doi.org/10.5194/npg-30-289-2023, 2023
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In the ensemble Kalman filter, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the accuracy of analysis and prediction. This study proposes a new algorithm to use cost-free pseudomembers to expand the ensemble space effectively and improve analysis accuracy during the analysis step, without increasing the ensemble size during forecasting.
Eugenia Kalnay, Travis Sluka, Takuma Yoshida, Cheng Da, and Safa Mote
Nonlin. Processes Geophys., 30, 217–236, https://doi.org/10.5194/npg-30-217-2023, https://doi.org/10.5194/npg-30-217-2023, 2023
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Antoine Perrot, Olivier Pannekoucke, and Vincent Guidard
Nonlin. Processes Geophys., 30, 139–166, https://doi.org/10.5194/npg-30-139-2023, https://doi.org/10.5194/npg-30-139-2023, 2023
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This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test bed is introduced that shows the ability of our equations to reproduce the statistics estimated from an ensemble of forecasts. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.
Elia Gorokhovsky and Jeffrey L. Anderson
Nonlin. Processes Geophys., 30, 37–47, https://doi.org/10.5194/npg-30-37-2023, https://doi.org/10.5194/npg-30-37-2023, 2023
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Older observations of the Earth system sometimes lack information about the time they were taken, posing problems for analyses of past climate. To begin to ameliorate this problem, we propose new methods of varying complexity, including methods to estimate the distribution of the offsets between true and reported observation times. The most successful method accounts for the nonlinearity in the system, but even the less expensive ones can improve data assimilation in the presence of time error.
Chu-Chun Chang and Eugenia Kalnay
Nonlin. Processes Geophys., 29, 317–327, https://doi.org/10.5194/npg-29-317-2022, https://doi.org/10.5194/npg-29-317-2022, 2022
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Andrey A. Popov, Amit N. Subrahmanya, and Adrian Sandu
Nonlin. Processes Geophys., 29, 241–253, https://doi.org/10.5194/npg-29-241-2022, https://doi.org/10.5194/npg-29-241-2022, 2022
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Numerical weather prediction requires the melding of both computational model and data obtained from sensors such as satellites. We focus on one algorithm to accomplish this. We aim to aid its use by additionally supplying it with data obtained from separate models that describe the average behavior of the computational model at any given time. We show that our approach outperforms the standard approaches to this problem.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter Jan van Leeuwen, Gilad Lerman, and Efi Foufoula-Georgiou
Nonlin. Processes Geophys., 29, 77–92, https://doi.org/10.5194/npg-29-77-2022, https://doi.org/10.5194/npg-29-77-2022, 2022
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The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
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Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Zofia Stanley, Ian Grooms, and William Kleiber
Nonlin. Processes Geophys., 28, 565–583, https://doi.org/10.5194/npg-28-565-2021, https://doi.org/10.5194/npg-28-565-2021, 2021
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In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.
Stephen Jewson, Giuliana Barbato, Paola Mercogliano, Jaroslav Mysiak, and Maximiliano Sassi
Nonlin. Processes Geophys., 28, 329–346, https://doi.org/10.5194/npg-28-329-2021, https://doi.org/10.5194/npg-28-329-2021, 2021
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Climate model simulations are uncertain. In some cases this makes it difficult to know how to use them. Significance testing is often used to deal with this issue but has various shortcomings. We describe two alternative ways to manage uncertainty in climate model simulations that avoid these shortcomings. We test them on simulations of future rainfall over Europe and show they produce more accurate projections than either using unadjusted climate model output or statistical testing.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, https://doi.org/10.5194/npg-28-295-2021, 2021
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Data assimilation aims to improve hydrologic and weather forecasts by combining available information from Earth system models and observations. The classical approaches to data assimilation usually proceed with some preconceived assumptions about the shape of their probability distributions. As a result, when such assumptions are invalid, the forecast accuracy suffers. In the proposed methodology, we relax such assumptions and demonstrate improved performance.
Abd AlRahman AlMomani and Erik Bollt
Nonlin. Processes Geophys., 28, 153–166, https://doi.org/10.5194/npg-28-153-2021, https://doi.org/10.5194/npg-28-153-2021, 2021
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This paper introduces a tool for data-driven discovery of early warning signs of critical transitions in ice shelves from remote sensing data. Our directed spectral clustering method considers an asymmetric affinity matrix along with the associated directed graph Laplacian. We applied our approach to reprocessing the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.
Shin'ya Nakano
Nonlin. Processes Geophys., 28, 93–109, https://doi.org/10.5194/npg-28-93-2021, https://doi.org/10.5194/npg-28-93-2021, 2021
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The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, and Matthieu Plu
Nonlin. Processes Geophys., 28, 1–22, https://doi.org/10.5194/npg-28-1-2021, https://doi.org/10.5194/npg-28-1-2021, 2021
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Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Pengcheng Yan, Guolin Feng, Wei Hou, and Ping Yang
Nonlin. Processes Geophys., 27, 489–500, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
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A system transiting from one stable state to another has to experience a period. Can we predict the end moment (state) if the process has not been completed? This paper presents a method to solve this problem. This method is based on the quantitative relationship among the parameters, which is used to describe the transition process of the abrupt change. By using the historical data, we extract some parameters for predicting the uncompleted climate transition process.
Reinhold Hess
Nonlin. Processes Geophys., 27, 473–487, https://doi.org/10.5194/npg-27-473-2020, https://doi.org/10.5194/npg-27-473-2020, 2020
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Forecasts of ensemble systems are statistically aligned to synoptic observations at DWD in order to provide support for warning decision management. Motivation and design consequences for extreme and rare meteorological events are presented. Especially for probabilities of severe wind gusts global logistic parameterisations are developed that generate robust statistical forecasts for extreme events, while local characteristics are preserved.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 27, 307–327, https://doi.org/10.5194/npg-27-307-2020, https://doi.org/10.5194/npg-27-307-2020, 2020
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Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.
Carlos Osácar, Manuel Membrado, and Amalio Fernández-Pacheco
Nonlin. Processes Geophys., 27, 235–237, https://doi.org/10.5194/npg-27-235-2020, https://doi.org/10.5194/npg-27-235-2020, 2020
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We deduce that after a global thermal perturbation, the Earth's
atmosphere would need about a couple of months to come back to equilibrium.
André Düsterhus
Nonlin. Processes Geophys., 27, 121–131, https://doi.org/10.5194/npg-27-121-2020, https://doi.org/10.5194/npg-27-121-2020, 2020
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Seasonal prediction of the of the North Atlantic Oscillation (NAO) has been improved in recent years by improving dynamical models and ensemble predictions. One step therein was the so-called sub-sampling, which combines statistical and dynamical predictions. This study generalises this approach and makes it much more accessible. Furthermore, it presents a new verification approach for such predictions.
Courtney Quinn, Terence J. O'Kane, and Vassili Kitsios
Nonlin. Processes Geophys., 27, 51–74, https://doi.org/10.5194/npg-27-51-2020, https://doi.org/10.5194/npg-27-51-2020, 2020
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This study presents a novel method for reduced-rank data assimilation of multiscale highly nonlinear systems. Time-varying dynamical properties are used to determine the rank and projection of the system onto a reduced subspace. The variable reduced-rank method is shown to succeed over other fixed-rank methods. This work provides implications for performing strongly coupled data assimilation with a limited number of ensemble members on high-dimensional coupled climate models.
Nina Schuhen
Nonlin. Processes Geophys., 27, 35–49, https://doi.org/10.5194/npg-27-35-2020, https://doi.org/10.5194/npg-27-35-2020, 2020
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We present a new way to adaptively improve weather forecasts by incorporating last-minute observation information. The recently measured error, together with a statistical model, gives us an indication of the expected future error of wind speed forecasts, which are then adjusted accordingly. This new technique can be especially beneficial for customers in the wind energy industry, where it is important to have reliable short-term forecasts, as well as providers of extreme weather warnings.
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Short summary
The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system without knowing the model equations. It is illustrated using the three-dimensional Lorenz system, where only two components are observed. The proposed data-driven procedure is low-cost, is easy to implement, uses linear and Gaussian assumptions and requires only a small amount of data. It is based on an iterative linear Kalman smoother with a state augmentation.
The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical...
