Conditional Nonlinear Optimal Perturbation Research Articles

A paralleled embedding high-dimensional Bayesian optimization with additive Gaussian kernels for solving CNOP

Conditional Nonlinear Optimal Perturbation (CNOP) is widely used in atmospheric and oceanic predictability studies. Solving CNOP is essentially a nonlinear optimization problem with certain constraints. One method to solve CNOP is the intelligent optimization algorithm. But it may not always obtain the satisfactory solution and efficiency because of the local exploitation of individual particles. The Bayesian optimization algorithm can avoid this local stagnation by building a global probability grasp for the optimization space of CNOP. Nonetheless, the limit of approximately 20-dimensional optimization space hampers its application in solving CNOP of high-dimensional numerical models. To overcome this bottleneck, we propose a paralleled embedding high-dimensional Bayesian optimization with additive Gaussian kernels (PEBOA) algorithm, which mainly consists of the feature extraction process and low-dimensional optimization process. In PEBOA, a feature extraction method (deepFE) using the convolutional Autoencoder with residual connections and customized constraint-preserved loss function is designed, which compresses 10 million dimensional data to relatively low-dimensional search spaces, from tens to hundreds of dimensions. Then, we propose the strategy of additive Gaussian kernels, with which the Bayesian optimization algorithm can optimize in relatively low-dimensional search spaces. Concretely, a kernel handles a subspace, and a subspace can handle dimensions approximately not more than 20. Additionally, the modified acquisition function can sample multiple candidates simultaneously with the aim of accelerating the optimization process. We apply PEBOA to solve CNOP of Regional Ocean Modeling System (ROMS) for identifying optimal initial errors of upstream Kuroshio transport variation, which is a 10 million dimensional and time-consuming problem. The computational performance of PEBOA and physical mechanisms of the obtained CNOP are analyzed. Experimental results indicate that deepFE excels Principal Component Analysis (PCA) in terms of relative error ratio, the magnitude of objective function values, and the obtained CNOP pattern. Besides, compared to deepFE-based Particle Swarm Optimization, PEBOA has better solving efficiency with 3.4% larger objective function values and 2.2 times greater likelihood of obtaining the valid CNOP. Furthermore, the modified acquisition function reduces computation time by about 71.0% with four cores. The physical mechanism analysis shows that CNOPs obtained by PEBOA are almost identical to the adjoint method, which can cause an anomalous increase (decrease) in upstream Kuroshio transport and maintain physics consistency.

Optimal Precursors for Central Pacific El Niño Events in GFDL CM2p1

Abstract Compared to the canonical eastern Pacific El Niño, the understanding and ability to predict the central Pacific (CP)-type event still need further improvement. In this study, the principal component analysis–based particle swarm optimization algorithm (PPSO) is applied in Geophysical Fluid Dynamics Laboratory Climate Model version 2p1 (GFDL CM2p1) to obtain the optimal precursors (OPRs) for CP El Niño events, based on the conditional nonlinear optimal perturbation (CNOP) method. For this, three normal years with neither El Niño nor La Niña events, i.e., three cases, are chosen as the reference states. The obtained OPRs for these cases exhibit a consistent positive sea surface temperature (SST) perturbation distribution in the subtropical North Pacific (20°–40°N, 175°E–140°W), which is further proven to be crucial for the evolution of CP El Niño based on the Northern and Southern Hemisphere significance test results. Mechanically, these positive SST perturbations are enhanced and reach the equatorial Pacific via wind–evaporation–SST (WES) feedback to evolve into a CP El Niño at the end of the year. The nonlinear approach is adopted to investigate the predictability of CP El Niño events and can shed some light on future studies.

Extent of the Impact of Arctic Atmospheric Uncertainty on Extended‐Range Forecasting of Cold Events in East Asia

AbstractThe extended‐range predictability of three simulated extreme cold events in East Asia in the Community Atmosphere Model (version 4) control experiment, whose atmospheric circulation backgrounds are similar to two recent observational cases, is investigated. The results show that they have a predictability of four pentads. Then, we evaluate the extent of the forecast uncertainty in the 4th pentad caused by the initial atmospheric uncertainties in the Arctic, which are large due to sparse instrumental observations. The initial uncertainty leading to the largest forecast uncertainty is obtained by the conditional nonlinear optimal perturbation method, and referred to as the CNOP‐type initial uncertainty. The forecast of the cold surge in the 4th pentad fails after adding the CNOP‐type initial uncertainty at day 0. In comparison, the forecast uncertainties are much weaker when the initial conditions are perturbed by noises, and the weaker influence may be due to the noises' lack of spatial structure. In terms of how the CNOP‐type initial uncertainty develops, a baroclinic structure is seen in the uncertainties on the first 2 days, followed by a propagating Rossby wave feature from the 2nd pentad to the 4th pentad. Meanwhile, synoptic transient eddy feedback also plays an essential role. The results suggest that the CNOP‐type initial uncertainty has potential to identify sensitive areas for targeted observations; plus, it could serve as a member of ensemble initial perturbations, since it indicates the largest uncertainty growth.

Dimension shifting based intelligent algorithm framework to solve conditional nonlinear optimal perturbation

Conditional Nonlinear Optimal Perturbation (CNOP) method is an effective way to study the predictability of oceanic and climatic events. A framework combining the Feature Extraction method and Intelligent Algorithm (FEIA) is frequently used to solve CNOP because it is gradient-free and scalable at high-dimensional scales. However, the fixed latent subspace of FEIA framework makes it challenging to achieve both the quality of solutions and the solving efficiency. To overcome this bottleneck, this paper proposes Dimension Shifting based Intelligent Algorithm (DSIA) framework to solve CNOP in the large-scale model. DSIA framework adopts the dimension shifting strategy, which dynamically shifts search particles in different low-dimensional spaces. To verify the feasibility of DISA framework, we take a Regional Ocean Modeling System (ROMS) model of double-gyre variation as an experimental case. In experiments, we figure out that the selection of feature extraction method and the shifting dimension set are two influential factors for the performance of DSIA framework. Besides, in comparative experiments, DSIA framework yields better objective function values and more valid CNOP than FEIA framework. Moreover, convergence experiments demonstrate DSIA framework can solve CNOP with an appropriate number of function evaluations and has better convergence performance. In conclusion, experimental results prove that DSIA improves both quality of CNOP and solving efficiency.

Error Evolutions and Analyses on Joint Effects of SST and SL via Intermediate Coupled Models and Conditional Nonlinear Optimal Perturbation Method

A seasonal predictability barrier has long been noticed in ENSO forecasting with numerical models. Previous studies explored the impact of seasonal optimal initial perturbation evolutions in sea surface temperature anomalies (SSTA) on ENSO forecasting using the intermediate coupled model (ICM) via the conditional nonlinear optimal perturbation (CNOP) method. In this paper, we investigate the joint effects of SSTA and sea level anomalies (SLA) from the perspective of the optimal growth initial error (OGE). After determining the four seasonal OGEs about SSTA and SLA (i.e., SSTA-OGE, SLA-OGE and Joint-OGE), we first demonstrate the patterns, evolutions and the resulting spring predictability barrier (SPB) of the above OGEs. Then, we analyze the mechanism of OGE evolutions and SPB. Finally, we conduct observing system simulation experiments to determine the best (economic) observation network. Our experimental results indicate that the ENSO evolution error induced by SSTA-OGE and Joint-OGE presents season dependency, but SLA-OGE has no impact on ENSO evolution. Moreover, Joint-OGEs induce error evolutions and the SPB with more significant intensity than SSTA-OGEs and SLA-OGEs. From mechanism analyses, the evolutions of SSTA-OGEs are mainly dominated by Bjerknes feedback. Further, the evolution dynamics of Joint-OGEs primarily contain the continuous heating between the upper ocean combined with Bjerknes feedback and thermal diffusion in response to the discharge process. In addition, comprehensive and economical sensitive areas are identified through Joint-OGE, including the central-eastern equatorial Pacific and the western and north-eastern tropical Pacific boundary, which contribute to the ENSO prediction benefits reaching 58.31% on average.

Optimal Arctic sea ice concentration perturbation in triggering Ural blocking formation

Utilizing the Community Atmospheric Model version 4, the role of Arctic sea ice concentration (SIC) in triggering the Ural Blocking (UB) event formation on subseasonal timescale is investigated. Taking eight zonal flows as the reference states, the optimal Arctic SIC perturbations that trigger zonal flows into UB events on subseasonal timescale are obtained with the conditional nonlinear optimal perturbation approach. The numerical results show that the Arctic SIC decline in the Greenland, Barents and Okhotsk Seas can trigger zonal flows into UB events on a timescale of four pentads (20 days). Further diagnosis shows that the SIC decline in these regions locally warms the low troposphere via diabatic processes in the first pentad. Then, dynamic processes, such as temperature advection, modulate the temperature in the middle troposphere and weaken the meridional temperature gradient between the Arctic and mid-latitudes upstream of the Ural sector. The weakened meridional temperature gradient further decelerates the background zonal flow near the Ural sector and triggers UB formation in four pentads. This investigation highlights the role of Arctic SIC in the Greenland, Barents and Okhotsk Seas in triggering the formation of UB events on subseasonal timescale. The spatial characteristics of the optimal SIC perturbations may provide scientific support for SIC target observations in capturing the precursor of UB formation and improving UB prediction skills on subseasonal timescale.

Applications of CNOP-P Method to Predictability Studies of Terrestrial Ecosystems

In this paper, recent research on terrestrial ecosystem predictability using the conditional nonlinear optimal parameter perturbation (CNOP-P) method is summarized. The main findings include the impacts of uncertainties in climate change on uncertainties in simulated terrestrial ecosystems, the identification of key physical parameters that lead to large uncertainties in terrestrial ecosystem modeling and prediction, and the evaluation of the simulation ability and prediction skill of terrestrial ecosystems by reducing key physical parameter errors. The study areas included the Inner Mongolia region, north–south transect of eastern China, and Qinghai–Tibet Plateau region. The periods of the studies were from 1961 to 1970 for the impacts of uncertainties in climate change on uncertainties in simulated terrestrial ecosystems, and from 1951 to 2000 for the identification of the most sensitive combinations of physical parameters. Climatic Research Unit (CRU) data were employed. The numerical results indicate the important role of nonlinear changes in climate variability due to the occurrences of extreme events characterized by CNOP-P in the abrupt grassland ecosystem equilibrium state and formation of carbon sinks in China. Second, the most sensitive combinations of physical parameters to the uncertainties in simulations and predictions of terrestrial ecosystems identified by the CNOP-P method were more sensitive than those obtained by traditional methods (e.g., one-at-a-time (OAT) and stochastic methods). Furthermore, the improvement extent of the simulation ability and prediction skill of terrestrial ecosystems by reducing the errors of the sensitive physical parameter combinations identified by the CNOP-P method was higher than that by the traditional methods.

Application of the CNOP‐P Ensemble Prediction (CNOP‐PEP) Method in Evapotranspiration Forecasting Over the Tibetan Plateau to Model Parameter Uncertainties

AbstractModel parameter errors are one of the sources of uncertainty when simulating or predicting evapotranspiration (ET) over the Tibetan Plateau (TP). To enhance the ET simulation ability and prediction skill over the TP, the conditional nonlinear optimal parameter perturbation (CNOP‐P) method is used to establish an ensemble prediction method (called the CNOP‐PEP method) to represent uncertainties arising due to the model parameters to implement ensemble prediction experiments. The one‐at‐a‐time (OAT) method and the traditional stochastically perturbed parametrization (SPP) scheme are also employed to implement ensemble prediction experiments for comparison with the CNOP‐PEP method. The numerical results show that all ensemble prediction experiments conducted with the three methods exhibit improved prediction skills compared to the reference ET over the TP. Furthermore, the prediction skill by employing the CNOP‐PEP method is more excellent than those of the OAT and SPP methods when predicting ET over the TP. The physical mechanism analysis shows that the improved evaporation characterization obtained with the ensemble prediction experiments plays a key role in reducing uncertainties when simulating and predicting ET over the TP. The above results indicate that ensemble prediction methods are a helpful tool to improve the simulation ability and prediction skill of the ET over the TP for analyzing model parameters. In addition, the CNOP‐PEP method can supply prime ensemble members to represent uncertainties in model parameters.

Evaluation of the sensitivity on mesoscale eddy associated with the sea surface height anomaly forecasting in the Kuroshio Extension

The sensitivity of the sea surface height anomaly (SSHA) forecasting on the accuracy of mesoscale eddies over the Kuroshio Extension region, which was determined by the conditional non-linear optimal perturbation (CNOP) method using a two-layer quasigeostrophic model, is evaluated by adopting multiply realistic marine datasets through an advanced particle filter assimilation method. It is shown that, if additional observations are preferentially assimilated to the sensitive area of mesoscale eddies identified by the CNOP, where the eddies present a clear high- to low-velocity gradient along the eddy rotation, the forecasting skill of the SSHA can be more significantly improved. It is also demonstrated that the forecasts of the SSHA in the region where the large-scale mean flow possesses much stronger barotropic and/or baroclinic instability tend to exhibit stronger sensitivity to the accuracy of the initial field in the sensitive area of mesoscale eddies. Therefore, more attention should be preferentially paid to the assimilation of the additional observations of the mesoscale eddies for the SSHA forecast in the region with a strong velocity shear of ocean circulation. The present study verifies the sensitivity on mesoscale eddies of SSHA forecasts derived by the two-layer quasigeostrophic model using multiply sets of realistic oceanic data, especially including observation and reanalysis data, which further additionally demonstrates the importance of targeted observations of mesoscale eddies to the SSHA forecast in the regions of strong velocity shear of ocean circulation and provides a more credible scientific basis for the field campaign of the targeted observations for mesoscale eddies associated with the SSHA forecasting.

A New Sensitivity Analysis Approach Using Conditional Nonlinear Optimal Perturbations and Its Preliminary Application

A New Sensitivity Analysis Approach Using Conditional Nonlinear Optimal Perturbations and Its Preliminary Application

A Biological‐Parameter‐Optimized Modeling Study of Physical Drivers Controlling Seasonal Chlorophyll Blooms off the Southern Coast of Java Island

AbstractA physical‐biogeochemical model consists of many key parameters; theoretically, 10,000 or more numerical experiments are required to obtain a set of optimal biological parameters. The corresponding computing resources are too expensive when running a three‐dimensional and high‐resolution physical‐biogeochemical model. In this study, we improve the performance of a three‐dimensional physical‐biogeochemical model via the conditional nonlinear optimal perturbation method for southern Java Island, where chlorophyll blooms occur seasonally. Based on the improved model results, we calculated the mixed‐layer nutrient budget, thereby characterizing how each physical process transports nutrients into the surface oligotrophic layer and then stimulates the chlorophyll blooms during the southeast monsoon season. Nutrients that upwell along the submarine slope are found in narrow regions along the coast and spread into most of the study area by local wind‐induced offshore transport. The contribution of nonlinearity (advection) is essential to modulating the upslope movement of nutrients off the coast. If local winds are neglected in the model, onshore transport induced by the pressure gradient force in the zonal direction (alongshore) and subsequent downwelling would be dominant, and chlorophyll blooms would diminish in most regions. The role of the South Java Coastal Current varies under the joint influence of remote and local wind forcings. The Indonesian Throughflow from the Lombok Strait also contributes to surface phytoplankton growth along its path off the south of Java Island.

Recent Progress in Applications of the Conditional Nonlinear Optimal Perturbation Approach to Atmosphere-Ocean Sciences

Recent Progress in Applications of the Conditional Nonlinear Optimal Perturbation Approach to Atmosphere-Ocean Sciences

An Ensemble Forecasting Method for Dealing with the Combined Effects of the Initial and Model Errors and a Potential Deep Learning Implementation

Abstract In this paper, a new nonlinear forcing singular vector (NFSV) approach is proposed to provide mutually independent optimally combined modes of initial perturbations and model perturbations (C-NFSVs) in ensemble forecasts. The C-NFSVs are a group of optimally growing structures that take into account the impact of the interaction between the initial errors and the model errors effectively, generalizing the original NFSV for simulations of the impact of the model errors. The C-NFSVs method is tested in the context of the Lorenz-96 model to demonstrate its potential to improve ensemble forecast skills. This method is compared with the orthogonal conditional nonlinear optimal perturbations (O-CNOPs) method for estimating only the initial uncertainties and the orthogonal NFSVs (O-NFSVs) for estimating only the model uncertainties. The results demonstrate that when both the initial perturbations and model perturbations are introduced in the forecasting system, the C-NFSVs are much more capable of achieving higher ensemble forecasting skills. The use of a deep learning approach as a remedy for the expensive computational costs of the C-NFSVs is evaluated. The results show that learning the impact of the C-NFSVs on the ensemble provides a useful and efficient alternative for the operational implementation of C-NFSVs in forecasting suites dealing with the combined effects of the initial errors and the model errors. Significance Statement A new ensemble forecasting method for dealing with combined effects of initial errors and model errors, i.e., the C-NFSVs, is proposed, which is an extension of the NFSV approach for simulating the model error effects in ensemble forecasts. The C-NFSVs provide mutually independent optimally combined modes of initial perturbations and model perturbations. This new method is tested for generating ensemble forecasts in the context of the Lorenz-96 model, and there are indications that the optimally growing structures may provide reliable ensemble forecasts. Furthermore, it is found that a hybrid dynamical–deep learning approach could be a potential avenue for real-time ensemble forecasting systems when perturbations combine the impact of the initial and the model errors.

Toward targeted observations of the meteorological initial state for improving the PM2.5forecast of a heavy haze event that occurred in the Beijing–Tianjin–Hebei region

Abstract. An advanced approach of conditional non-linear optimal perturbation (CNOP) was adopted to identify the sensitive area for targeted observations of meteorological fields associated with PM2.5 concentration forecasts of a heavy haze event that occurred in the Beijing–Tianjin–Hebei (BTH) region, China, from 30 November to 4 December 2017. The results show that a few specific regions in the southern and northwestern directions close to the BTH region represent the sensitive areas. Numerically, when predetermined artificial observing arrays (i.e. possible “targeted observations”) in the sensitive areas were assimilated, the forecast errors of PM2.5 during the accumulation and dissipation processes were aggressively reduced; specifically, these assimilations, compared with those in other areas that have been thought of as being important for the PM2.5 forecasts in the BTH region in previous studies, exhibited a more obvious decrease in the forecast errors of PM2.5. Physically, the reason why these possible targeted observations can significantly improve the forecasting skill of PM2.5 was interpreted by comparing relevant meteorological fields before and after assimilation. Therefore, we conclude that preferentially deploying additional observations in the sensitive areas identified by the CNOP approach can greatly improve the forecasting skill of PM2.5, which provides, beyond all doubt, theoretical guidance for practical field observations of meteorological fields associated with PM2.5 forecasts.

Impact of Optimally Growing Initial Errors on the Mesoscale Predictability of Heavy Precipitation Events along the Mei-Yu Front in China

Abstract Based on the conditional nonlinear optimal perturbation (CNOP) approach, the impact of the optimally growing initial errors on the mesoscale predictability of typical mei-yu front heavy precipitation events over eastern China was explored. First, based on a nonlinear optimization system built using the high-resolution Weather Research and Forecasting Model and particle swarm optimization algorithm, the CNOPs for three heavy precipitation cases were obtained. The CNOPs as the optimally growing initial errors caused the largest forecast errors and made the 24-h accumulated precipitation stronger than any other kind of initial errors. Moreover, the CNOPs showed faster growth and saturation than the random errors in space, highlighting the importance of the initial error with specific spatial structure in the meso- and convective-scale processes. Despite different CNOPs having particular spatial structures, the large amplitudes of the CNOPs at lower levels were mainly located in the rainband along the mei-yu front. Although the spectral energies of the CNOPs increased with increasing scales, the forecast error growth for the CNOPs generally followed the well-known three-stage conceptual model. Moreover, the large-scale and large-amplitude initial errors in the CNOPs were the most influential in terms of the forecast quality. This suggests that reducing large-scale initial errors can potentially improve the forecast accuracy. However, the mesoscale predictability of the mei-yu front heavy precipitation events is inherently limited, for which the moist convection was found to be the main reason.

Improving typhoon predictions by assimilating the retrieval of atmospheric temperature profiles from the FengYun-4A's Geostationary Interferometric Infrared Sounder (GIIRS)

The Geostationary Interferometric Infrared Sounder (GIIRS) onboard China's FengYun-4A geostationary satellite provides an unprecedented opportunity to observe the three-dimensional thermodynamic structure of typhoons in the western North Pacific Ocean with high spatiotemporal resolutions. Field campaigns of targeting observation based on the conditional nonlinear optimal perturbation (CNOP) sensitivity were carried out utilizing the GIIRS on FY-4A for five typhoons: Chan-hom, Maysak, and Higos in 2020 and typhoons Chanthu and Conson in 2021 and collected temporally continuous observations for the thermodynamic structure of typhoons and their environments.This study investigated the impact of atmospheric temperature profile retrieved from the collected GIIRS radiance on typhoon analysis and prediction in a regional Hurricane WRF (HWRF) model using the ensemble-variational data assimilation scheme. Despite the case dependence, the assimilation of the additional satellite retrieval generally improves the typhoon track forecasts relative to those with simply the operational observations assimilated. The improvement mainly occurs beyond two days and the average reduction of track errors reaches up to 100 km at about day 3. Diagnostics show that the improvement of initial temperature condition influences the geopotential height and wind fields roughly through the hydrostatic relationship. The assimilation of temperature retrieval also shows some potential in improving wind forecasts in the near-coast areas at upper and lower levels and the precipitation forecasts on land.

Optimal Precursor Triggering Kuroshio Large Meander Decay Obtained in a Regional Ocean Model

AbstractThis study investigates the optimal precursor (OPR) triggering Kuroshio large meander (LM) decay using a conditional nonlinear optimal perturbation (CNOP) approach and a regional ocean modeling system (ROMS). The results show that the large amplitudes of the OPR are mainly concentrated at 1,000–2,500 m in the LM upstream region (west of 137°E), and their propagation downstream along the Kuroshio axis contributes to triggering the transition from the LM path to the nonlarge meander (NLM) path. Using the growth of the OPR, it is found that baroclinic instability contributes to the fast vertical development of the perturbations in the early stage of the LM decay, while barotropic processes play a leading role during the cyclonic ring shedding of the LM decay. In particular, the LM decay process is evaluated by the depth‐integrated vorticity equation, implying that the advection term dominates over the beta effect in the LM decay. Furthermore, the vorticity balance associated with the cyclonic eddy indicates that the advection and divergence terms represent a main balance in the spin‐down process of the cyclonic eddy. Under the effects of both, high potential vorticity water flows out from the LM meander tip and then the amplitude of the LM experiences a remarkable decrease. With the detachment of a cyclonic ring, a transition from the LM path to the NLM path occurs. This study further deepens our understanding of the LM decay and provides us some useful hints about designing the observation system of the LM.

Role of hydrological parameters in the uncertainty in modeled soil organic carbon using a coupled water-carbon cycle model

Soil organic carbon is the largest carbon pool in the terrestrial biosphere. Large uncertainties exist in the numerical simulations of soil organic carbon due to inaccuracies in their mathematical descriptions of hydrological processes. In this study, the upper limit of uncertainty in modeled soil organic carbon that is induced by hydrological parameter errors, which may stem from measurement or experiential errors, is estimated in China under four different arid and humid conditions. The study was conducted using a conditional nonlinear optimal perturbation related to parameters (CNOP-P) approach and a model of the coupled water-carbon cycle (the Lund-Potsdam-Jena Wetland Hydrology and Methane Dynamic Global Vegetation Model, LPJ-WHyMe). Uncertainties in hydrological processes resulted in the largest error (2.73 kg C m−2 yr−1, 20.2%) in the modeled soil organic carbon in the arid and semiarid regions of northern China, with errors of 1.20 kg C m−2 yr−1 (6.1%) in northeastern China, 0.45 kg C m−2 yr−1 (3.3%) in southern China, and -1.71 kg C m−2 yr−1 (13.7%) in the semihumid region of northern China. By analyzing the three components of soil organic carbon, the fast soil carbon pool was found to be the main cause of the uncertainties in modeled soil organic carbon in the four regions of China. Moreover, belowground litter was another cause of the uncertainties in the modeled soil organic carbon in northeastern China and in the semihumid region of northern China. Additional results indicated that the simulation and prediction abilities of soil organic carbon could be improved by reducing parameter errors in hydrological processes through observations or targeted observations. The parameter sensitivity test showed that the benefits to modeling soil organic carbon were similar when reducing the errors in the sensitive hydrological parameter subset, compared to the benefits of reducing the errors in all the hydrological parameters.

Influence of Arctic Sea Ice Concentration on Extended‐Range Prediction of Strong and Long‐Lasting Ural Blocking Events in Winter

AbstractIt is traditionally considered that the predictability of atmosphere reaches approximately 2 weeks due to its chaotic features. Considering boundary conditions, the lead prediction time can exceed 2 weeks in certain cases. We find that the Arctic sea ice concentration (SIC) is crucial for extended‐range prediction of strong and long‐lasting Ural blocking (UB) formation. By applying the rotated empirical orthogonal function‐based particle swarm optimization algorithm, the conditional nonlinear optimal perturbation is calculated with the Community Atmosphere Model, version 4, to identify the optimally growing boundary errors in extended‐range prediction of strong and long‐lasting UB formation. It is found that SIC perturbations in the Greenland Sea (GS), Barents Sea (BS), and Okhotsk Sea (OKS) are important for strong and long‐lasting UB formation prediction in four pentads. Further analysis reveals that the SIC perturbations in these areas first influence the local temperature field through the diabatic heating process and further affect the temperature field in the Ural sector mainly by advection and convection processes. Moreover, the zonal winds in the Ural sector are adjusted by the thermal wind balance, thus affecting UB formation. The local characteristics of the SIC perturbations indicate that the GS, BS, and OKS may be sensitive areas in regard to extended‐range prediction of strong and long‐lasting UB formation, which can provide scientific support for the SIC target observations in the future.

A New Scheme for Capturing Global Conditional Nonlinear Optimal Perturbation

Conditional nonlinear optimal perturbation (CNOP) represents the initial perturbation that satisfies a certain physical constraint condition, and leads to a maximum prediction error at the moment of prediction. The CNOP method is a useful tool in studying atmosphere and ocean predictability problems. Generally, the optimization algorithm based on the gradient of the cost function to compute CNOP requires an initial guess. The traditional scheme randomly chooses the initial guess of CNOP within the constraint range and therefore this scheme is called RIG-CNOP. However, the RIG-CNOP scheme reduces the probability of capturing the global CNOP in many cases, such as the prediction model is strongly nonlinear or long-term prediction is performed, or multiple extreme values existed in the cost function. Considering the limitations of the RIG-CNOP scheme, we propose a new initial guess selection scheme. In this scheme, we first pre-analyze a series of random initial guesses, and then, an optimal initial guess is selected. The above process replaces the initial guess selection scheme in the traditional scheme, which is called PAIG-CNOP. Numerical experiments are conducted utilizing the Lorenz-63 model. Also, to compare the performance of the PAIG-CNOP method with the RIG-CNOP method in capturing global CNOP, the CNOP and the maximum cost function value (MCFV) obtained by the filtering method (FM) are used as benchmarks (this value is called FMMCFV in brief). The experimental results show that even the prediction model is strongly nonlinear or the prediction time is long, or the cost function has multiple extreme values, the PAIG-CNOP method can capture the global CNOP with a high probability. The results show that the PAIG-CNOP method has a higher probability of capturing the global CNOP than the RIG-CNOP method. In addition, we use an ensemble-based technique in the computation of gradients, thus avoiding the use of adjoint techniques in the maximization process. Due to the attractive features of the new method, the PAIG-CNOP method is an efficient and useful method for solving CNOP, it can be more easily applied to obtain the global CNOP of operational prediction models.