Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data, the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent (CNLLE) method. The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent (NLLE) and signal-to-noise ratio methods using a coupled Lorenz model. The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings, therefore, it can quantify the predictability limit induced by the external forcings. On this basis, a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields. The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method. This similarity supports ENSO as the major predictable signal for weather and climate prediction. In addition, a ratio of predictability limit (RPL) calculated by the CNLLE method to that calculated by the NLLE method was proposed. The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit. For instance, ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months, as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean. Moreover, the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.