A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution （DE） algorithm to calculate a conditional nonlinear optimal perturbation （CNOP）. The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming （SQP） algorithm and the spectral projected gradients （SPG2） algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.     

Three-Dimensional Structure of Optimal Nonlinear Excitation for Decadal Variability of the Thermohaline Circulation

The decadal variability of the North Atlantic thermohaline circulation（THC） is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures： the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.     

Can Adaptive Observations Improve Tropical Cyclone Intensity Forecasts?简

In order to investigate whether adaptive observations can improve tropical cyclone （TC） intensity forecasts,observing system simulation experiments （OSSEs） were conducted for 20 TC cases originating in the western North Pacific during the 2010 season according to the conditional nonlinear optimal perturbation （CNOP） sensitivity,using the fifth version of the PSU/NCAR mesoscale model （MM5） and its 3DVAR assimilation system.A new intensity index was defined as the sum of the number of grid points within an allocated square centered at the corresponding forecast TC central position,that satisfy constraints associated with the Sea Level Pressure （SLP）,near-surface horizontal wind speed,and accumulated convective precipitation.The higher the index value is,the more intense the TC is.The impacts of the CNOP sensitivity on the intensity forecast were then estimated.The OSSE results showed that for 15 of the 20 cases there were improvements,with reductions of forecast errors in the range of 0.12％-8.59％,which were much less than in track forecasts.The indication,therefore,is that the CNOP sensitivity has a generally positive effect on TC intensity forecasts,but only to a certain degree.We conclude that factors such as the use of a coupled model,or better initialization of the TC vortex,are more important for an accurate TC intensity forecast.     

A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations简

A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared.     

几种约束优化算法求解含“开关”过程的条件非线性最优扰动的比较

求解条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)属约束最优化问题,一般采用基于伴随模式提供梯度信息的约束优化算法(简称ADJ)进行求解。当优化问题涉及不连续的\"开关\"过程时,传统优化算法的寻优能力会受到较大的影响。近年来遗传算法(Genetic Algorithm,GA)因其在非光滑优化问题中的鲁棒性备受关注,但GA的性能不仅与优化问题有关,还取决于遗传算子的配置。本文将一种新的约束GA(GA1)用于求解CNOP,并对GA1,ADJ及具有不同遗传算子配置的约束GA(GA2)求解含\"开关\"过程的CNOP时的性能进行了比较。数值试验结果显示,GA1和GA2的全局寻优能力明显优于ADJ,后者易于陷入局部最优;对于不同的初猜值(不同的初始种群),GA1求解的CNOP能够保持一个较为一致的空间结构,ADJ求解的CNOP呈现了明显的两种结构,一种代表的是全局CNOP,一种是局部CNOP。通过验证不同遗传策略对优化结果的影响发现,对不同的优化问题,采用合适的遗传策略以及合适的参数设置是获取更好优化结果的一种有效途径。     

权重平衡有向网络下分布式约束优化的连续时间算法设计

本文研究权重平衡有向网络下分布式约束优化问题的求解,其中网络的全局目标函数是由每个智能体的局部目标函数的和构成,全局的约束是由每个智能体的局部约束的交构成.为了分布式求解该问题的最优解,首先引入智能体的局部共轭函数将其转换为Fenchel对偶问题.其次,从Fenchel对偶问题出发,提出一类基于奇异摄动系统的分布式连续时间算法.在局部目标函数和其梯度分别满足强凸和Lipschitz（李普希兹）连续的情况下,结合凸分析方法和Lyapunov（李雅普诺夫）稳定性理论,结果表明所提算法能够获得原问题和对偶问题的最优值.最后,数值仿真进一步验证了所提算法的有效性.     

The Sensitive Regions Identified by CNOPs of Three Typhoon Events

In this paper, several sets of observing system simulation experiments (OSSEs) were designed for three typhoon cases to determine whether or not the additional observation data in the sensitive regions identified by conditional nonlinear optimal perturbations (CNOPs) could improve the short-range forecast of typhoons. The results show that the CNOPs capture the sensitive regions for typhoon forecasts, which implies that conducting additional observation in these specific regions and eliminating initial errors could reduce forecast errors. It is inferred from the results that dropping sondes in the CNOP sensitive regions could lead to improvements in typhoon forecasts.     

On the Application of a Genetic Algorithm to the Predictability Problems Involving \"On-Off\" Switches

The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on-off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on-off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on-off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.     

Impact of Different Guidances on Sensitive Areas of Targeting Observations Based on the CNOP Method

The conditional nonlinear optimal perturbations(CNOPs) obtained by a fast algorithm are applied to determining the sensitive area for the targeting observation of Typhoon Matsa in 2005 using an operational regional prediction model-the Global/Regional Assimilation and PrEdiction System(GRAPES).Through a series of sensitivity experiments,several issues on targeting strategy design are discussed,including the effectivity of different guidances to determine the sensitive area(or targeting area) and the impa...     

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION ON-OFF SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the on-off switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedur...