Using Conditional Nonlinear Optimal Perturbation to Generate Initial Perturbations in ENSO Ensemble Forecasts

Using the latest operational version of the ENSO forecast system from the National Marine Environmental Forecasting Center (NMEFC) of China, ensemble forecasting experiments are performed for El Niño-Southern Oscillation (ENSO) events that occurred from 1997 to 2017 by generating initial perturbations of the conditional nonlinear optimal perturbation (CNOP) and Climatically relevant Singular Vector (CSV) structures. It is shown that when the initial perturbation of the leading CSV structure in the ensemble forecast of the CSVs-scheme is replaced by those of the CNOP structure, the resulted ensemble ENSO forecasts of the CNOP+CSVs-scheme tend to possess a larger spread than the forecasts obtained with the CSVs-scheme alone, leading to a better match between the root mean square error and the ensemble spread, a more reasonable Talagrand diagram and an improved Brier skill score (BSS). All these results indicate that the ensemble forecasts generated by the CNOP+CSVs-scheme can improve both the accuracy of ENSO forecasting and the reliability of the ensemble forecasting system. Therefore, ENSO ensemble forecasting should consider the effect of nonlinearity on the ensemble initial perturbations to achieve a much higher skill. It is expected that fully nonlinear ensemble initial perturbations can be sufficiently yielded to produce ensemble forecasts for ENSO, finally improving the ENSO forecast skill to the greatest possible extent. The CNOP will be a useful method to yield fully nonlinear optimal initial perturbations for ensemble forecasting.

Target observation of mesoscale eddies in the ocean

<p>Previous studies show that the kinetic energy of mesoscale eddies (MEs) accounts for more than 80% of the global ocean energy. The theoretical study and numerical simulation of MEs will enable us to better understand the dynamics of ocean circulation. Weiss and Grooms (2017) found that assimilating uniform observations taken over MEs is much better than assimilating a subset of observations on a regular grid for improving prediction skill of SSH associated with ocean state. In the present study, we use a conditional nonlinear optimal perturbation (CNOP) approach to investigate the sensitivity of the ocean state sea surface height (SSH) predictions on MEs with a two-layer quasi-geostrophic model and show the optimal assimilating scheme. In the study, the CNOPs of SSH predictions are first computed. It is found that, if one regards the regions covered by the grid points with large values of CNOPs as sensitive area of SSH predictions, the sensitive areas are mainly located on MEs. Furthermore, the stronger the MEs, the more the MEs grid points covered by the sensitive area. Especially, these grid points associated with sensitive areas are not uniformly distributed over the MEs. It is obvious that the predictions of SSH are quite sensitive to the initialization of MEs (especially that of the particular region of large values of CNOPs for strong MEs, rather than of the uniformly distributed grid points over MEs). Therefore, an appropriate initialization of MEs is much helpful for improving the prediction accuracy of SSH. And the CNOPs of SSH prediction here may provide useful information on how to improve initialization of MEs.</p>

Nonlinear character analysis for bistability in virus–immune dynamics

Structured abstract Aim: The nonlinear characters of two linearly stable equilibrium states (virus and immune) for a theoretical virus-immune model are analyzed. Methods: Conditional nonlinear optimal perturbation (CNOP), Lyapunov method and linear singular vector method. Results & conclusion: Two linearly stable equilibrium states (immune-free and immune) with linear methods are nonlinearly unstable using the CNOP method. When the CNOP-type of initial perturbation is used in the model, the immune-free (immune) equilibrium state will be made into the immune (immune-free) equilibrium state. Through computing the variations of nonlinear terms of the model, the nonlinear effect of immune proliferation plays an important role in abrupt changes of the immune-free equilibrium state compared with the linear term. For the immune equilibrium state, the nonlinear effect of viral replication is also an important factor.

A Parallel Hybrid Intelligence Algorithm for Solving Conditional Nonlinear Optimal Perturbation to Identify Optimal Precursors of North Atlantic Oscillation

The North Atlantic Oscillation (NAO) is the most prominent atmospheric seesaw phenomenon in North Atlantic Ocean. It has a profound influence on the strength of westerly winds as well as the storm tracks in North Atlantic, thus affecting winter climate in Northern Hemisphere. Therefore, it is necessary to investigate the mechanism related with the NAO events. In this paper, conditional nonlinear optimal perturbation (CNOP), which has been widely used in research on the optimal precursor (OPR) of climatic event, is adopted to investigate which kind of initial perturbation is most likely to trigger the NAO anomaly pattern with the Community Earth System Model (CESM). Since CESM does not have an adjoint model, we propose an adjoint-free parallel principal component analysis (PCA) based genetic algorithm (GA) and particle swarm optimization (PSO) hybrid algorithm (PGAPSO) to solve CNOP in such a high dimensional numerical model. The results demonstrate that the OPRs obtained by CNOP trigger the reference flow into typical NAO mode, which provide the theoretical underpinning in observation and prediction. Furthermore, the hybrid algorithm can accelerate convergence and avoid falling into a local optimum. After parallelization with Message Passing Interface (MPI) and Compute Unified Device Architecture (CUDA), the PGAPSO algorithm achieves a speed-up of 40× compared with its serial version. The results as mentioned above indicate that the proposed algorithm can efficiently and effectively acquire CNOP and can also be generalized to other complex numerical models.

A Novel Approach for Solving CNOP and its Application in Identifying Sensitive Regions of Tropical Cyclone Adaptive Observations

In this paper, a novel approach is proposed for solving conditional nonlinear optimal perturbation (CNOP), named it adaptive cooperation co-evolution of parallel particle swarm optimization and wolf search algorithm (ACPW) based on principal component analysis. Taking Fitow (2013) and Matmo (2014) as two tropical cyclone (TC) cases, CNOP solved by ACPW is used to investigate the sensitive regions identification of TC adaptive observations with the fifth-generation mesoscale model (MM5). Meanwhile, the 60 km and 120 km resolutions are adopted. The adjoint-based method (short for the ADJ-method) is also applied to solve CNOP, and the result is used as a benchmark. To validate the validity of ACPW, the CNOPs obtained from the different methods are compared in terms of the patterns, energies, similarities and simulated TC tracks with perturbations. (1) The ACPW can capture similar CNOP patterns with the ADJ-method, and the patterns of TC Fitow are more similar than TC Matmo. (2) When using the 120 km resolution, similarities between CNOPs of the ADJ-method and ACPW are higher than those using the 60 km. (3) Compared to the ADJ-method, although the CNOPs of ACPW produce lower energies, they can obtain better benefits gained from the reduction of CNOPs, not only in the entire domain but also in the sensitive regions identified. (4) The sensitive regions identified by CNOPs-ACPW has the same influence on the improvements of the TC tracks forecast skills with those identified by CNOPs-ADJ-method. (5) The ACPW has a higher efficiency than the ADJ-method. All conclusions prove that ACPW is a meaningful and effective method for solving CNOP and can be used to identify sensitive regions of TC adaptive observations.