The backward nonlinear local Lyapunov exponent and its application to quantifying the local predictability of extreme high-temperature events

The backward nonlinear local Lyapunov exponent (BNLLE) was developed based on the NLLE method to quantitatively investigate the local predictability of extreme events. By studying the dynamical characteristics of error growth preceding extreme events, the local predictability limits of these events can be determined. In this study, the BNLLE method is used to quantify the local predictability limits of two extreme high-temperature events (EHTEs) that occurred in Europe during the summer of 2019. The results show that the error dynamics are dependent on the geographical location. During the early forecast period, positive error-growth rates are mainly located in southern regions, whereas negative error-growth rates are mainly located in northern regions. However, the variations in the error growth rates exhibit regional differences with the forecast time. As such, the relative growth of initial errors (RGIEs) also depends on the geographical location. From the RGIEs, the local predictability limits of the two EHTEs are determined to be 11 and 9 days, respectively. By measuring the forecast skill, the local predictability limits (11 and 9 days) are verified to be reasonable and realistic. Therefore, the BNLLE method can quantify the local predictability of EHTEs, and is an effective technique for studying the predictability of future extreme weather and climate events.