Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method

Li, Xuan; Ding, Ruiqiang; Li, Minglu

doi:10.1007/s00376-020-2100-5

Cited by 8 publications

(4 citation statements)

References 40 publications

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“…The spatial distribution of the LPLs has a layered structure, whereby the LPLs of events on an individual orbit around the center of either regime are broadly the same, whereas the LPLs are not the same for events on different orbits. Li et al (2020a) noted that the events on an individual orbit around the center of either regime may have similar dynamical properties, which leads to similar LPLs. Different LPLs characterize events on different orbits due to the variable dynamical properties of the different orbits.…”

Section: Discussionmentioning

confidence: 99%

“…For both the warm and cold regimes, the LPLs of the events on different orbits of a dynamical trajectory are different, whereas they are similar for the same orbit of a dynamical trajectory (i.e., the LPLs exhibit an obvious layered structure). Li et al (2020a) noted that this phenomenon is determined by the specific structure of the Lorenz attractor. The events on an individual orbit around the center of either regime may have similar dynamical properties, which leads to similar LPLs.…”

Section: Local Predictability Of Extreme Eventsmentioning

confidence: 99%

“…As such, the FTLE method may not be suitable for studying the predictability of extreme events. Based on the nonlinear local Lyapunov exponent (NLLE, e.g., Ding and Li, 2007;Ding et al, 2008;Li et al, 2020b)method (e.g., Ding and Li, 2007;Ding et al, 2008;Li et al, 2020a), we recently developed a new method, which is the backward nonlinear local Lyapunov exponent (BNLLE) method (Li et al, 2019;Li et al, 2020a;Li et al, 2021). The BNLLE method takes into account nonlinearity, and can be used to study the predictability of given states and, in particular, extreme states.…”

Section: Introductionmentioning

confidence: 99%

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A New Technique to Quantify the Local Predictability of Extreme Events: The Backward Nonlinear Local Lyapunov Exponent Method

Ding

2022

Front. Environ. Sci.

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Extreme weather events have a large impact on society, but are challenging to forecast accurately. In this study, we carried out a theoretical investigation of the local predictability of extreme weather events using the Lorenz model. We introduce a new method using the backward nonlinear local Lyapunov exponent to quantitatively estimate the local predictability limits of extreme events. The local predictability limits of extreme events on an individual orbit of a dynamical trajectory are broadly the same, whereas this is not the case if they are on different orbits. The specific structure of the Lorenz attractor is responsible for this phenomenon. Our results show that the local predictability limits of extreme events do not decrease or increase monotonically as the events increase in magnitude. This indicates that the magnitude of extreme events is not the only factor that affects the local predictability. The dynamical flow, initial error size, and structure of an attractor may also affect the local predictability. We also quantitatively compared the local predictability of extreme warm and cold events. This showed that the local predictability limits of extreme warm events are higher than extreme cold events at the same probability. A statistical analysis (i.e., the minimum, first quartile, median, third quartile, and maximum) also suggests that the extreme warm events have higher local predictability limits. In general, extreme warm events are more predictable than extreme cold events.

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Section: Discussionmentioning

confidence: 99%

Section: Local Predictability Of Extreme Eventsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Technique to Quantify the Local Predictability of Extreme Events: The Backward Nonlinear Local Lyapunov Exponent Method

Ding

2022

Front. Environ. Sci.

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“…The LDA was previously used to estimate the upper prediction limit of the analog-based predictions for a nonlinear system (e.g. Ding and Li 2007, Astudillo et al 2017, Li et al 2020. Here the LDA prediction horizon as a reference can help to indicate how well the RC prediction performance has been reached, and this will also present the comparison between the RC and a traditional analog-based prediction method for the first time.…”

Section: Introductionmentioning

confidence: 99%

Estimating prediction horizon of reservoir computer on L63 system when observed variables are incomplete

Huang

2023

J. Phys. Complex.

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Reservoir computer (RC) is an attractive neural computing framework that can well predict the dynamics of chaotic systems. Previous knowledge of the RC performance is established on the case that all variables in a chaotic system are completely observed. However, in practical circumstances the observed variables from a dynamical system are usually incomplete, among which there is a lack of understanding of the RC performance. Here we utilize mean error growth curve to estimate the RC prediction horizon on the Lorenz63 system (L63), and particularly we investigate the scenario of univariate time series. Our results demonstrate that the prediction horizon of RC outperforms that of local dynamical analogs (LDAs) of L63, and the state-space embedding technique can improve the RC prediction in case of incomplete observations. We then test the conclusion on the more complicated systems, and extend the method to estimate the intraseasonal predictability of atmospheric circulation indices. These results could provide indications for the future developments and applications of RC.

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Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability

Feng

Ding

et al. 2021

Adv. Atmos. Sci.

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Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method

Cited by 8 publications

References 40 publications

A New Technique to Quantify the Local Predictability of Extreme Events: The Backward Nonlinear Local Lyapunov Exponent Method

A New Technique to Quantify the Local Predictability of Extreme Events: The Backward Nonlinear Local Lyapunov Exponent Method

Estimating prediction horizon of reservoir computer on L63 system when observed variables are incomplete

Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability

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