Articles | Volume 31, issue 1
https://doi.org/10.5194/npg-31-165-2024
© 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-31-165-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
28 Mar 2024
Research article |
| 28 Mar 2024
| 28 Mar 2024
The sampling method for optimal precursors of El Niño–Southern Oscillation events
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Junjie Ma
School of Mathematics, North University of China, Taiyuan 030051, China
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Bin Shi, Dehai Luo, and Wenqi Zhang
EGUsphere, https://doi.org/10.5194/egusphere-2024-2747, https://doi.org/10.5194/egusphere-2024-2747, 2024
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In this paper, our main focus is on studying the optimal disturbances of the initial blocking amplitude and preexisting synoptic-scale eddies, as well as the influence of the westerly wind. This study utilizes the 1-dimensional forced NLS equation that specifically considers the zonal direction.
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023, https://doi.org/10.5194/npg-30-263-2023, 2023
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We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.
Bin Shi, Dehai Luo, and Wenqi Zhang
EGUsphere, https://doi.org/10.5194/egusphere-2024-2747, https://doi.org/10.5194/egusphere-2024-2747, 2024
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In this paper, our main focus is on studying the optimal disturbances of the initial blocking amplitude and preexisting synoptic-scale eddies, as well as the influence of the westerly wind. This study utilizes the 1-dimensional forced NLS equation that specifically considers the zonal direction.
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023, https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary
Short summary
We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Big data and artificial intelligence
Learning extreme vegetation response to climate drivers with recurrent neural networks
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Characterisation of Dansgaard–Oeschger events in palaeoclimate time series using the matrix profile method
Evaluation of forecasts by a global data-driven weather model with and without probabilistic post-processing at Norwegian stations
A comparison of two causal methods in the context of climate analyses
A two-fold deep-learning strategy to correct and downscale winds over mountains
Downscaling of surface wind forecasts using convolutional neural networks
Data-driven methods to estimate the committor function in conceptual ocean models
Exploring meteorological droughts' spatial patterns across Europe through complex network theory
Integrated hydrodynamic and machine learning models for compound flooding prediction in a data-scarce estuarine delta
Predicting sea surface temperatures with coupled reservoir computers
Using neural networks to improve simulations in the gray zone
The blessing of dimensionality for the analysis of climate data
Producing realistic climate data with generative adversarial networks
Identification of droughts and heatwaves in Germany with regional climate networks
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Remember the past: a comparison of time-adaptive training schemes for non-homogeneous regression
Francesco Martinuzzi, Miguel D. Mahecha, Gustau Camps-Valls, David Montero, Tristan Williams, and Karin Mora
Nonlin. Processes Geophys., 31, 535–557, https://doi.org/10.5194/npg-31-535-2024, https://doi.org/10.5194/npg-31-535-2024, 2024
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We investigated how machine learning can forecast extreme vegetation responses to weather. Examining four models, no single one stood out as the best, though "echo state networks" showed minor advantages. Our results indicate that while these tools are able to generally model vegetation states, they face challenges under extreme conditions. This underlines the potential of artificial intelligence in ecosystem modeling, also pinpointing areas that need further research.
Tobias Sebastian Finn, Lucas Disson, Alban Farchi, Marc Bocquet, and Charlotte Durand
Nonlin. Processes Geophys., 31, 409–431, https://doi.org/10.5194/npg-31-409-2024, https://doi.org/10.5194/npg-31-409-2024, 2024
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We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.
Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau
Nonlin. Processes Geophys., 31, 433–447, https://doi.org/10.5194/npg-31-433-2024, https://doi.org/10.5194/npg-31-433-2024, 2024
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The characterisation of abrupt transitions in palaeoclimate records allows understanding of millennial climate variability and potential tipping points in the context of current climate change. In our study an algorithmic method, the matrix profile, is employed to characterise abrupt warmings designated as Dansgaard–Oeschger (DO) events and to identify the most similar transitions in the palaeoclimate time series.
John Bjørnar Bremnes, Thomas N. Nipen, and Ivar A. Seierstad
Nonlin. Processes Geophys., 31, 247–257, https://doi.org/10.5194/npg-31-247-2024, https://doi.org/10.5194/npg-31-247-2024, 2024
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During the last 2 years, tremendous progress has been made in global data-driven weather models trained on reanalysis data. In this study, the Pangu-Weather model is compared to several numerical weather prediction models with and without probabilistic post-processing for temperature and wind speed forecasting. The results confirm that global data-driven models are promising for operational weather forecasting and that post-processing can improve these forecasts considerably.
David Docquier, Giorgia Di Capua, Reik V. Donner, Carlos A. L. Pires, Amélie Simon, and Stéphane Vannitsem
Nonlin. Processes Geophys., 31, 115–136, https://doi.org/10.5194/npg-31-115-2024, https://doi.org/10.5194/npg-31-115-2024, 2024
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Identifying causes of specific processes is crucial in order to better understand our climate system. Traditionally, correlation analyses have been used to identify cause–effect relationships in climate studies. However, correlation does not imply causation, which justifies the need to use causal methods. We compare two independent causal methods and show that these are superior to classical correlation analyses. We also find some interesting differences between the two methods.
Louis Le Toumelin, Isabelle Gouttevin, Clovis Galiez, and Nora Helbig
Nonlin. Processes Geophys., 31, 75–97, https://doi.org/10.5194/npg-31-75-2024, https://doi.org/10.5194/npg-31-75-2024, 2024
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Forecasting wind fields over mountains is of high importance for several applications and particularly for understanding how wind erodes and disperses snow. Forecasters rely on operational wind forecasts over mountains, which are currently only available on kilometric scales. These forecasts can also be affected by errors of diverse origins. Here we introduce a new strategy based on artificial intelligence to correct large-scale wind forecasts in mountains and increase their spatial resolution.
Florian Dupuy, Pierre Durand, and Thierry Hedde
Nonlin. Processes Geophys., 30, 553–570, https://doi.org/10.5194/npg-30-553-2023, https://doi.org/10.5194/npg-30-553-2023, 2023
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Forecasting near-surface winds over complex terrain requires high-resolution numerical weather prediction models, which drastically increase the duration of simulations and hinder them in running on a routine basis. A faster alternative is statistical downscaling. We explore different ways of calculating near-surface wind speed and direction using artificial intelligence algorithms based on various convolutional neural networks in order to find the best approach for wind downscaling.
Valérian Jacques-Dumas, René M. van Westen, Freddy Bouchet, and Henk A. Dijkstra
Nonlin. Processes Geophys., 30, 195–216, https://doi.org/10.5194/npg-30-195-2023, https://doi.org/10.5194/npg-30-195-2023, 2023
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Computing the probability of occurrence of rare events is relevant because of their high impact but also difficult due to the lack of data. Rare event algorithms are designed for that task, but their efficiency relies on a score function that is hard to compute. We compare four methods that compute this function from data and measure their performance to assess which one would be best suited to be applied to a climate model. We find neural networks to be most robust and flexible for this task.
Domenico Giaquinto, Warner Marzocchi, and Jürgen Kurths
Nonlin. Processes Geophys., 30, 167–181, https://doi.org/10.5194/npg-30-167-2023, https://doi.org/10.5194/npg-30-167-2023, 2023
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Joko Sampurno, Valentin Vallaeys, Randy Ardianto, and Emmanuel Hanert
Nonlin. Processes Geophys., 29, 301–315, https://doi.org/10.5194/npg-29-301-2022, https://doi.org/10.5194/npg-29-301-2022, 2022
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Benjamin Walleshauser and Erik Bollt
Nonlin. Processes Geophys., 29, 255–264, https://doi.org/10.5194/npg-29-255-2022, https://doi.org/10.5194/npg-29-255-2022, 2022
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Raphael Kriegmair, Yvonne Ruckstuhl, Stephan Rasp, and George Craig
Nonlin. Processes Geophys., 29, 171–181, https://doi.org/10.5194/npg-29-171-2022, https://doi.org/10.5194/npg-29-171-2022, 2022
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Our regional numerical weather prediction models run at kilometer-scale resolutions. Processes that occur at smaller scales not yet resolved contribute significantly to the atmospheric flow. We use a neural network (NN) to represent the unresolved part of physical process such as cumulus clouds. We test this approach on a simplified, yet representative, 1D model and find that the NN corrections vastly improve the model forecast up to a couple of days.
Bo Christiansen
Nonlin. Processes Geophys., 28, 409–422, https://doi.org/10.5194/npg-28-409-2021, https://doi.org/10.5194/npg-28-409-2021, 2021
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In geophysics we often need to analyse large samples of high-dimensional fields. Fortunately but counterintuitively, such high dimensionality can be a blessing, and we demonstrate how this allows simple analytical results to be derived. These results include estimates of correlations between sample members and how the sample mean depends on the sample size. We show that the properties of high dimensionality with success can be applied to climate fields, such as those from ensemble modelling.
Camille Besombes, Olivier Pannekoucke, Corentin Lapeyre, Benjamin Sanderson, and Olivier Thual
Nonlin. Processes Geophys., 28, 347–370, https://doi.org/10.5194/npg-28-347-2021, https://doi.org/10.5194/npg-28-347-2021, 2021
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This paper investigates the potential of a type of deep generative neural network to produce realistic weather situations when trained from the climate of a general circulation model. The generator represents the climate in a compact latent space. It is able to reproduce many aspects of the targeted multivariate distribution. Some properties of our method open new perspectives such as the exploration of the extremes close to a given state or how to connect two realistic weather states.
Gerd Schädler and Marcus Breil
Nonlin. Processes Geophys., 28, 231–245, https://doi.org/10.5194/npg-28-231-2021, https://doi.org/10.5194/npg-28-231-2021, 2021
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We used regional climate networks (RCNs) to identify past heatwaves and droughts in Germany. RCNs provide information for whole areas and can provide many details of extreme events. The RCNs were constructed on the grid of the E-OBS data set. Time series correlation was used to construct the networks. Network metrics were compared to standard extreme indices and differed considerably between normal and extreme years. The results show that RCNs can identify severe and moderate extremes.
Jonathan M. Lilly and Paula Pérez-Brunius
Nonlin. Processes Geophys., 28, 181–212, https://doi.org/10.5194/npg-28-181-2021, https://doi.org/10.5194/npg-28-181-2021, 2021
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Long-lived eddies are an important part of the ocean circulation. Here a dataset for studying eddies in the Gulf of Mexico is created through the analysis of trajectories of drifting instruments. The method involves the identification of quasi-periodic signals, characteristic of particles trapped in eddies, from the displacement records, followed by the creation of a measure of statistical significance. It is expected that this dataset will be of use to other authors studying this region.
Cristian Lussana, Thomas N. Nipen, Ivar A. Seierstad, and Christoffer A. Elo
Nonlin. Processes Geophys., 28, 61–91, https://doi.org/10.5194/npg-28-61-2021, https://doi.org/10.5194/npg-28-61-2021, 2021
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An unprecedented amount of rainfall data is available nowadays, such as ensemble model output, weather radar estimates, and in situ observations from networks of both traditional and opportunistic sensors. Nevertheless, the exact amount of precipitation, to some extent, eludes our knowledge. The objective of our study is precipitation reconstruction through the combination of numerical model outputs with observations from multiple data sources.
Dylan Harries and Terence J. O'Kane
Nonlin. Processes Geophys., 27, 453–471, https://doi.org/10.5194/npg-27-453-2020, https://doi.org/10.5194/npg-27-453-2020, 2020
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Different dimension reduction methods may produce profoundly different low-dimensional representations of multiscale systems. We perform a set of case studies to investigate these differences. When a clear scale separation is present, similar bases are obtained using all methods, but when this is not the case some methods may produce representations that are poorly suited for describing features of interest, highlighting the importance of a careful choice of method when designing analyses.
Jaqueline Lekscha and Reik V. Donner
Nonlin. Processes Geophys., 27, 261–275, https://doi.org/10.5194/npg-27-261-2020, https://doi.org/10.5194/npg-27-261-2020, 2020
Moritz N. Lang, Sebastian Lerch, Georg J. Mayr, Thorsten Simon, Reto Stauffer, and Achim Zeileis
Nonlin. Processes Geophys., 27, 23–34, https://doi.org/10.5194/npg-27-23-2020, https://doi.org/10.5194/npg-27-23-2020, 2020
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Statistical post-processing aims to increase the predictive skill of probabilistic ensemble weather forecasts by learning the statistical relation between historical pairs of observations and ensemble forecasts within a given training data set. This study compares four different training schemes and shows that including multiple years of data in the training set typically yields a more stable post-processing while it loses the ability to quickly adjust to temporal changes in the underlying data.
Cited articles
Barclay, A., Gill, P. E., and Ben Rosen, J.: SQP methods and their application to numerical optimal control, in: Variational Calculus, Optimal Control and Applications: International Conference in Honour of L. Bittner and R. Klötzler, Trassenheide, Germany, 23–27 September 1996, 207–222, Springer, https://doi.org/10.1007/978-3-0348-8802-8_21, 1998. a
Battisti, D. S. and Hirst, A. C.: Interannual variability in a tropical atmosphere-ocean model: Influence of the basic state, ocean geometry and nonlinearity, J. Atmos. Sci., 46, 1687–1712, 1989. a
Bjerknes, J.: Atmospheric teleconnections from the equatorial Pacific, Mon. Weather Rev., 97, 163–172, 1969. a
Boucharel, J., Almar, R., Kestenare, E., and Jin, F.-F.: On the influence of ENSO complexity on Pan-Pacific coastal wave extremes, P. Natl. Acad. Sci. USA, 118, e2115599118, https://doi.org/10.1073/pnas.2115599118, 2021. a
Cane, M. A.: Modeling sea level during El Niño, J. Phys. Oceanogr., 14, 1864–1874, 1984. a
Cashin, P., Mohaddes, K., and Raissi, M.: Fair weather or foul? The macroeconomic effects of El Niño, J. Int. Econ., 106, 37–54, 2017. a
Chen, D., Zebiak, S. E., Busalacchi, A. J., and Cane, M. A.: An improved procedure for El Niño forecasting: Implications for predictability, Science, 269, 1699–1702, 1995. a
Chen, D., Cane, M. A., Zebiak, S. E., and Kaplan, A.: The impact of sea level data assimilation on the Lamont model prediction of the 1997/98 El Niño, Geophys. Res. Lett., 25, 2837–2840, 1998. a
Chen, D., Cane, M. A., Kaplan, A., Zebiak, S. E., and Huang, D.: Predictability of El Niño over the past 148 years, Nature, 428, 733–736, 2004. a
Cherubini, S. and De Palma, P.: Nonlinear optimal perturbations in a Couette flow: bursting and transition, J. Fluid Mech., 716, 251–279, 2013. a
Cherubini, S., De Palma, P., Robinet, J.-C., and Bottaro, A.: Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow, Phys. Rev. E, 82, 066302, https://doi.org/10.1103/PhysRevE.82.066302, 2010. a, b
Duan, W., Mu, M., and Wang, B.: Conditional nonlinear optimal perturbations as the optimal precursors for El Niño–Southern Oscillation events, J. Geophys. Res.-Atmos., 109, https://doi.org/10.1029/2005JC003458, 2004. a
Duan, W., Xu, H., and Mu, M.: Decisive role of nonlinear temperature advection in El Niño and La Niña amplitude asymmetry, J. Geophys. Res.-Oceans, 113, https://doi.org/10.1029/2006JC003974, 2008. a, b
Duan, W., Tian, B., and Xu, H.: Simulations of two types of El Niño events by an optimal forcing vector approach, Clim. Dynam., 43, 1677–1692, 2014. a
Gill, A. E.: Some simple solutions for heat-induced tropical circulation, Q. J. Roy. Meteor. Soc., 106, 447–462, 1980. a
Jin, F.-F.: An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model, J. Atmos. Sci., 54, 811–829, 1997a. a
Jin, F.-F.: An equatorial ocean recharge paradigm for ENSO. Part II: A stripped-down coupled model, J. Atmos. Sci., 54, 830–847, 1997b. a
Kalnay, E.: Atmospheric modeling, data assimilation and predictability, Cambridge University Press, https://doi.org/10.1017/CBO9780511802270, 2003. a, b
Kerswell, R., Pringle, C. C., and Willis, A.: An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar, Rep. Prog. Phys., 77, 085901, https://doi.org/10.1088/0034-4885/77/8/085901, 2014. a
Liu, D. C. and Nocedal, J.: On the limited memory BFGS method for large scale optimization, Math. Program., 45, 503–528, 1989. a
McPhaden, M. J., Zebiak, S. E., and Glantz, M. H.: ENSO as an integrating concept in earth science, Science, 314, 1740–1745, 2006. a
Monokrousos, A., Bottaro, A., Brandt, L., Di Vita, A., and Henningson, D. S.: Nonequilibrium thermodynamics and the optimal path to turbulence in shear flows, Phys. Rev. Lett., 106, 134502, https://doi.org/10.1103/PhysRevLett.106.134502, 2011. a, b
Mu, M. and Qiang, W.: Applications of nonlinear optimization approach to atmospheric and oceanic sciences (in Chinese), Sci. China Math., 10, 1207–1222, https://doi.org/10.1360/N012016-00200, 2017. a
Mu, M., Duan, W. S., and Wang, B.: Conditional nonlinear optimal perturbation and its applications, Nonlin. Processes Geophys., 10, 493–501, https://doi.org/10.5194/npg-10-493-2003, 2003. a
Mu, M., Xu, H., and Duan, W.: A kind of initial errors related to “spring predictability barrier” for El Niño events in Zebiak-Cane model, Geophys. Res. Lett., 34, https://doi.org/10.1029/2006GL027412, 2007. a, b, c
Mu, M., Yu, Y., Xu, H., and Gong, T.: Similarities between optimal precursors for ENSO events and optimally growing initial errors in El Niño predictions, Theor. Appl. Climatol., 115, 461–469, 2014. a
Nocedal, J. and Wright, S. J.: Numerical optimization, Springer, https://doi.org/10.1007/978-0-387-40065-5, 1999. a
Passaggia, P.-Y. and Ehrenstein, U.: Adjoint based optimization and control of a separated boundary-layer flow, Eur. J. Mech. B-Fluid., 41, 169–177, 2013. a
Philander, S. G.: El Niño, La Niña, and the southern oscillation, International Geophysics Series, 46, X–289, 1989. a
Pringle, C. C. T. and Kerswell, R. R.: Using nonlinear transient growth to construct the minimal seed for shear flow turbulence, Phys. Rev. Lett., 105, 154502, https://doi.org/10.1103/PhysRevLett.105.154502, 2010. a, b
Rabin, S., Caulfield, C., and Kerswell, R.: Designing a more nonlinearly stable laminar flow via boundary manipulation, J. Fluid Mech., 738, R1, https://doi.org/10.1017/jfm.2013.601, 2014. a
Reddy, S. C. and Henningson, D. S.: Energy growth in viscous channel flows, J. Fluid Mech., 252, 209–238, 1993. a
Sarachik, E. S. and Cane, M. A.: The El Niño-southern oscillation phenomenon, Cambridge University Press, https://doi.org/10.1017/CBO9780511817496, 2010. a
Suarez, M. J. and Schopf, P. S.: A delayed action oscillator for ENSO, J. Atmos. Sci., 45, 3283–3287, 1988. a
Tao, L., Duan, W., and Vannitsem, S.: Improving forecasts of El Niño diversity: a nonlinear forcing singular vector approach, Clim. Dynam., 55, 739–754, 2020. a
Timmermann, A., An, S.-I., Kug, J.-S., Jin, F.-F., Cai, W., Capotondi, A., Cobb, K. M., Lengaigne, M., McPhaden, M. J., Stuecker, M. F., Stein, K., Wittenberg, A. T., Yun, K.-S., Bayr, T., Chen, H.-C., Chikamoto, Y., Dewitte, B., Dommenget, D., Grothe, P., Guilyardi, E,, Ham, Y.-G., Hayashi, M., Ineson, S., Kang, D., Kim, S., Kim, W., Lee, J.-Y., Li, T., Luo, J.-J., McGregor, S., Planton, Y., Power, S., Rashid, H., Ren, H.-L., Santoso, A., Takahashi, K., Todd, A., Wang, G., Wang, G., Xie, R., Yang, W.-H., Yeh, S.-W., Yoon, J., Zeller, E., and Zhang, X.: El Niño–southern oscillation complexity, Nature, 559, 535–545, 2018. a
Wang, B. and Fang, Z.: Chaotic oscillations of tropical climate: A dynamic system theory for ENSO, J. Atmos. Sci., 53, 2786–2802, 1996. a
Wu, B., Zhou, T., and Zheng, F.: EnOI-IAU initialization scheme designed for decadal climate prediction system IAP-DecPreS, J. Adv. Model. Earth Sy., 10, 342–356, 2018. a
Xu, H. and Mu, M.: Software for the Double Precision Zebiak-Cane Model and its tangent linear and adjoint models V1.0, National Copyright Administration of China, 2015SR063121, 2015 (in Chinese). a
Xu, H., Mu, M., and Duan, W.: Optimizing System for ENSO Predictability Research using Conditional Nonlinear Optimal Perturbation (CNOP) V1.0, National Copyright Administration of China, 2015SR063119, 2015 (in Chinese). a
Yu, Y., Duan, W., Xu, H., and Mu, M.: Dynamics of nonlinear error growth and season-dependent predictability of El Niño events in the Zebiak–Cane model, Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, Applied Meteorology and Physical Oceanography, 135, 2146–2160, 2009. a, b, c
Zebiak, S. E.: A simple atmospheric model of relevance to El Niño, J. Atmos. Sci., 39, 2017–2027, 1982. a
Zebiak, S. E.: Atmospheric convergence feedback in a simple model for El Niño, Mon. Weather Rev., 114, 1263–1271, 1986. a
Zheng, Y., Duan, W., Tao, L., and Ma, J.: Using an ensemble nonlinear forcing singular vector data assimilation approach to address the ENSO forecast uncertainties caused by the “spring predictability barrier” and El Niño diversity, Clim. Dynam., 61, 4971–4989, https://doi.org/10.1007/s00382-023-06834-3, 2023. a
Short summary
Different from traditional deterministic optimization algorithms, we implement the sampling method to compute the conditional nonlinear optimal perturbations (CNOPs) in the realistic and predictive coupled ocean–atmosphere model, which reduces the first-order information to the zeroth-order one, avoiding the high-cost computation of the gradient. The numerical performance highlights the importance of stochastic optimization algorithms to compute CNOPs and capture initial optimal precursors.
Different from traditional deterministic optimization algorithms, we implement the sampling...
