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

Abstract

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.