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.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

A comparison of the strength and position variability of the Kuroshio Extension SST front

This study compares the seasonal and interannual-to-decadal variability in the strength and position of the Kuroshio Extension front(KEF)using high-resolution satellite-derived sea surface temperature(SST)and sea surface height(SSH)data.Results show that the KEF strength has an obvious seasonal variation that is similar at different longitudes,with a stronger(weaker)KEF during the cold(warm)season.However,the seasonal variation in the KEF position is relatively weak and varies with longitude.In contrast,the low-frequency variation of the KEF position is more distinct than that of the KEF strength even though they are well correlated.On both seasonal and interannual-to-decadal time scales,the western part of the KEF(142°–144°E)has the greatest variability in strength,while the eastern part of the KEF(149°–155°E)has the greatest variability in position.In addition,the relationships between wind-forced Rossby waves and the low-frequency variability in the KEF strength and position are also discussed by using the statistical analysis methods and a wind-driven hindcast model.A positive(negative)North Pacific Oscillation(NPO)-like atmospheric forcing generates positive(negative)SSH anomalies over the central North Pacific.These oceanic signals then propagate westward as Rossby waves,reaching the KE region about three years later,favoring a strengthened(weakened)and northward(southward)-moving KEF.

Estimating the Predictability Limit of Tropical Cyclone Tracks over the Western North Pacific Using Observational Data

In this study,the nonlinear local Lyapunov exponent(NLLE)approach was used to quantitatively determine the predictability limit of tropical cyclone(TC)tracks based on observed TC track data obtained from the Joint Typhoon Warning Center.The results show that the predictability limit of all TC tracks over the whole western North Pacific(WNP)basin is about 102 h,and the average lifetime of all TC tracks is about 174 h.The predictability limits of the TC tracks for short-,medium-,and long-lived TCs are approximately 72 h,120 h,and 132 h,respectively.The predictability limit of the TC tracks depends on the TC genesis location,lifetime,and intensity,and further analysis indicated that these three metrics are closely related.The more intense and longer-lived TCs tend to be generated on the eastern side of the WNP(EWNP),whereas the weaker and shorter-lived TCs tend to form in the west of the WNP(WWNP)and the South China Sea(SCS).The relatively stronger and longer-lived TCs,which are generated mainly in the EWNP,have a longer travel time before they curve northeastwards and hence tend to be more predictable than the relatively weaker and shorter-lived TCs that form in the WWNP region and SCS.Furthermore,the results show that the predictability limit of the TC tracks obtained from the best-track data may be underestimated due to the relatively short observational records currently available.Further work is needed,employing a numerical model to assess the predictability of TC tracks.

Predictability of the 7·20 extreme rainstorm in Zhengzhou in stochastic kinetic-energy backscatter ensembles

The scale-dependent predictability of the devastating 7·20 extreme rainstorm in Zhengzhou,China in 2021 was investigated via ensemble experiments,which were perturbed on different scales using the stochastic kinetic-energy backscatter(SKEB)scheme in the WRF model,with the innermost domain having a 3-km grid spacing.The daily rainfall(RAIN24h)and the cloudburst during 1600-1700 LST(RAIN1h)were considered.Results demonstrated that with larger perturbation scales,the ensemble spread for the rainfall maximum widens and rainfall forecasts become closer to the observations.In ensembles with mesoscale or convective-scale perturbations,RAIN1h loses predictability at scales smaller than 20 km and RAIN24h is predictable for all scales.Whereas in ensembles with synoptic-scale perturbations,the largest scale of predictability loss extends to 60 km for both RAIN1h and RAIN24h.Moreover,the average positional error in forecasting the heaviest rainfall for RAIN24h(RAIN1h)was 400 km(50-60)km.The southerly low-level jet near Zhengzhou was assumed to be directly responsible for the forecast uncertainty of RAIN1h.The rapid intensification in low-level cyclonic vorticity,mid-level divergence,and upward motion concomitant with the jet dynamically facilitated the cloudburst.Further analysis of the divergent,rotational and vertical kinetic spectra and the corresponding error spectra showed that the error kinetic energy at smaller scales grows faster than that at larger scales and saturates more quickly in all experiments.Larger-scale perturbations not only boost larger-scale error growth but are also conducive to error growth at all scales through a downscale cascade,which indicates that improving the accuracy of larger-scale flow forecast may discernibly contributes to the forecast of cloudburst intensity and position.