Determination of the Backward Predictability Limit and Its Relationship with the Forward Predictability Limit

Li, Xuan; Ding, Ruiqiang; Li, Minglu

doi:10.1007/s00376-019-8205-z

Cited by 8 publications

(3 citation statements)

References 38 publications

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“…In search of the corresponding initial states, the situation that multiple states meet the condition may happen. In this case, we always choose a state that maximizes the prediction lead time of the extreme state, as the corresponding initial state (Li et al, 2019). Therefore, the LPL of the extreme state x(t ex ) can be quantitatively estimated as:…”

Section: The Backward Nonlinear Local Lyapunov Exponent Methodsmentioning

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%

“…The NLLE method cannot estimate the prediction lead time of extreme events. In order to estimate the prediction lead time of extreme events,Li et al (2019) developed the NLLE method and proposed the BNLLE method.…”

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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: The Backward Nonlinear Local Lyapunov Exponent Methodsmentioning

confidence: 99%