基于遗传算法的四维变分资料同化技术的研究

将遗传算法应用于四维变分资料同化问题,提供一种新的较为有效的数值预报初始场优化方法,给出了相应的理论依据和详细算法,并结合变分问题本身的特点,设计合理的遗传编码、遗传操作和遗传参数.同时,以二维的浅水方程模式为例建立基于遗传算法的变分同化模型,并从多方面与伴随模式变分同化方案进行分析比较.数值试验结果表明,基于遗传算法的变分同化方案取得了比较满意的同化效果.     

Variational Data Assimilation for a Lorenz Model Usinga Non-Standard Genetic Algorithm

Summary  Data assimilation in meteorology and oceanography for strongly nonlinear dynamical systems is challenging. The dynamical system studied here is the classical three-variable Lorenz model. In this context data assimilation with weak-constraint variational methods performs better than other methods like strong-constraint variational methods or Kalman filters. The difficulty in tracking the chaotic Lorenz orbit by assimilation of noisy observations results from the inherent instability in the system. In variational methods a cost function has to be minimized. It is known, that in the Lorenz case the structure of the cost function becomes more and more complex with increasing length of the assimilation time interval and with reduction of the observational data quality. This paper proposes a non-standard implementation of a genetic algorithm for searching the global minimum in case of a weak-constraint formulation. The good performance of this non-local search is shown, but the algorithm is computationally demanding due to a very large number of control parameters within the weak-constraint formulation and, thus, the algorithm is applicable for simple systems only. Received December 12, 1998 Revised May 11, 1999     

具约束条件的四维变分资料同化问题

考察了具约束条件的四维变分资料同化问题，首先引入解决该类问题的一般理论与方法，然后用有限元浅水模式对具高频重力波约束条件的四维变分同化问题进行数值试验。采用伴随技术方法和约束最优化的罚函数法和增广拉格朗日方法，使定义的约束目标函数达到最小，而得到最优解。数值试验结果表明：以控制重力波增长为约束条件的四维变分资料同化，能够更有效的滤除扰动分量，得到最优初始场。由此也表明了对数值天气预报中的这类问题是可以用具约束条件的四维变分资料同化来处理。     

用遗传算法重构副热带高压特征指数的非线性动力模型

用遗传算法从离散时间序列资料中反演重构了非线性动力模型。首先, 用Lorenz系统的时间积分数据进行模型重构试验,随后,对十年平均的副热带高压形态指数时间序列进行动力模型参数反演和仿真预报试验。结果表明,遗传算法具有的全局搜索和并行计算优势能够较为准确地描述和刻画副热带高压活动,能对副高活动进行较为准确的描述与建模,是诊断和预测副热带高压等复杂天气系统活动的一条有效途径。     

线性化物理过程对GRAPES 4DVAR同化的影响

线性化物理过程能够改善四维变分同化中极小化收敛的稳定性和增加极小化过程中对大气物理过程和动力更加精确的描述,它是四维变分同化中非常重要的一部分。通过在GRAPES全球模式中研究线性化物理过程,尤其是两个湿线性化物理过程,改善切线性模式预报精度,来提高GRAPES全球四维变分同化的分析和预报效果。线性化物理过程的开发首先需要简化原非线性化物理过程中的强非线性项,然后对线性化物理过程进行规约化,以抑制切线性扰动的异常增长。目前GRAEPS全球模式中的线性化物理过程主要包括次网格尺度地形参数化、垂直扩散、积云深对流和大尺度凝结。线性化物理过程预报精度的检验方法是通过选择合适大小的初始扰动（同化分析增量）,来比较非线性模式和切线性模式中的扰动演化的纬向平均误差。然后以绝热版本的切线性模式为基础,通过冬、夏两个个例试验来分别检验4个线性化物理过程的12 h预报效果。试验结果表明,通过添加次网格地形参数化和垂直扩散两个干线性化物理过程方案,可以有效抑制住绝热版本切线性模式低层扰动的异常增长,大幅度改善切线性模式预报效果。通过添加积云深对流和大尺度凝结两个湿线性化物理过程,可以在热带区域和中、高纬度地区提高切线性模式中湿变量和温度变量的近似精度,提高GRAPES全球四维变分同化的分析和预报效果。      

Improving the extreme rainfall forecast of Typhoon Morakot (2009) by assimilating radar data from Taiwan Island and mainland China

This study examined the impact of an improved initial field through assimilating ground-based radar data from mainland China and Taiwan Island to simulate the long-lasting and extreme rainfall caused by Morakot (2009). The vortex location and the subsequent track analyzed through the radial velocity data assimilation (VDA) are generally consistent with the best track. The initial humidity within the radar detecting region and Morakot’s northward translation speed can be significantly improved by the radar reflectivity data assimilation (ZDA). As a result, the heavy rainfall on both sides of Taiwan Strait can be reproduced with the joint application of VDA and ZDA. Based on sensitivity experiments, it was found that, without ZDA, the simulated storm underwent an unrealistic inward contraction after 12-h integration, due to underestimation of humidity in the global reanalysis, leading to underestimation of rainfall amount and coverage. Without the vortex relocation via VDA, the moister (drier) initial field with (without) ZDA will produce a more southward (northward) track, so that the rainfall location on both sides of Taiwan Strait will be affected. It was further found that the improvement in the humidity field of Morakot is mainly due to assimilation of high-value reflectivity (strong convection) observed by the radars in Taiwan Island, especially at Kenting station. By analysis of parcel trajectories and calculation of water vapor flux divergence, it was also found that the improved typhoon circulation through assimilating radar data can draw more water vapor from the environment during the subsequent simulation, eventually contributing to the extreme rainfall on both sides of Taiwan Strait.     

Improving the Extreme Rainfall Forecast of Typhoon Morakot(2009) by Assimilating Radar Data from Taiwan Island and China's mainland

This study examined the impact of an improved initial field through assimilating ground-based radar data from China's mainland and Taiwan Island to simulate the long-lasting and extreme rainfall caused by Morakot(2009). The vortex location and the subsequent track analyzed through the radial velocity data assimilation(VDA) are generally consistent with the best track. The initial humidity within the radar detecting region and Morakot's northward translation speed can be significantly improved by the radar reflectivity data assimilation(ZDA). As a result, the heavy rainfall on both sides of Taiwan Strait can be reproduced with the joint application of VDA and ZDA. Based on sensitivity experiments, it was found that, without ZDA, the simulated storm underwent an unrealistic inward contraction after 12-h integration, due to underestimation of humidity in the global reanalysis, leading to underestimation of rainfall amount and coverage. Without the vortex relocation via VDA, the moister(drier) initial field with(without) ZDA will produce a more southward(northward) track, so that the rainfall location on both sides of Taiwan Strait will be affected. It was further found that the improvement in the humidity field of Morakot is mainly due to assimilation of high-value reflectivity(strong convection) observed by the radars in Taiwan Island, especially at Kenting station. By analysis of parcel trajectories and calculation of water vapor flux divergence, it was also found that the improved typhoon circulation through assimilating radar data can draw more water vapor from the environment during the subsequent simulation, eventually contributing to the extreme rainfall on both sides of Taiwan Strait.     

数值模式初值的敏感性程度对四维同化的影响

用著名的Ｌｏｒｅｎｚ系统作了共轭变分同化的数值试验。发现随着模式对初值敏感性程度的增加，用这种方法得到和模式相协调的初始场愈来愈困难，直到某些情况下的完全失败。这表明四维同化和可预报期限是联系在一起的。另一方面，随着方程不精确程度的增加，变分同化的效果愈来愈差，直到所做的预报无任何意义可言。如果在做变分同化的同时对模式参数也进行反演，就可使得基于Ｌｏｒｅｎｚ系统所做的预报效果大大提高。     

FOUR-DIMENSIONAL DATA QUALITY CONTROL THROUGH THE ADJOINT APPROACH*

Using the variational four-dimensional (4-D) data assimilation technique (the adjoint method), we defined the error/mean-error ratios (EMER) of observational data. The plausibility of marking the gross error using the EMER is investigated theoretically under some assumptions.Idealized numerical experiments are carried out using the simple Lorenz model to test the quality control scheme.     

IMPACT OF DIABATIC PROCESSES IN AGCM ON 4-DIMENSIONAL VARIATIONAL DATA ASSIMILATION*

The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manually.A cost function measuring spectral errors of 6-hour forecasts to "observation" (the NCEP reanalysis data) was minimized using the L-BFGS (the limited memory quasi-Newton algorithm developed by Broyden,Fletcher,Goldfard and Shanno) for optimizing parameters and initial conditions.Minimization of the cost function constrained by an adiabatic version of the NCEP global model converged to a minimum with a significant amount of decrease in the value of the cost function.Minimization of the cost function using the diabatic model, however,failed after a few iterations due to discontinuities introduced by physical parameterizations.Examination of the convergence of the cost function in different spectral domains reveals that the large-scale flow is adjusted during the first 10 iterations,in which discontinuous diabatic parameterizations play very little role.The adjustment produced by the minimization gradually moves to relatively smaller scales between 10-20th iterations.During this transition period,discontinuities in the cost function produced by "on-off" switches in the physical parameterizations caused the cost function to stay in a shallow local minimum instead of continuously decreasing toward a deeper minimum. Next,a mixed 4D-Var scheme is tested in which large-scale flows are first adiabatically adjusted to a sufficient level,followed by a diabatic adjustment introduced after 10 to 20 iterations. The mixed 4D-Var produced a closer fit of analysis to observations,with 38% and 41% more decrease in the values of the cost function and the norm of gradient,respectively,than the standard diabatic 4D-Var,while the CPU time is reduced by 21%.The resulting optimal initial conditions improve the short-range forecast skills of 48-hour statistics.The detrimental effect of parameterization discontinuities on minimization was also reduced.     

FOUR-DIMENSIONAL DATA QUALITY CONTROL THROUGH THE ADJOINT APPROACH

Using the variational four-dimensional (4-D) data assimilation technique (the adjointmethod), we defined the error/mean-error ratios (EMER) of observational data. The plausibilityof marking the gross error using the EMER is investigated theoretically under some assumptions.Idealized numerical experiments are carried out using the simple Lorenz model to test the qualitycontrol scheme.     

遗传算法求解最大预报误差的可行性研究

利用条件非线性最优扰动（conditional nonlinear optimal perturbation,CNOP）可以实现最大预报误差的上界估计。CNOP通常由基于梯度信息的约束优化算法进行求解,且其中的梯度信息由伴随模式提供。然而当非线性模式中含不连续＂开关＂时,传统伴随方法不能为优化过程提供正确的梯度方向,从而导致优化失败。为此,采用自适应变异和混合交叉的遗传算法,联赛选择机制和小生境技术的约束处理方法来求解最大预报误差上界。为检验新方法的有效性,以修改的Lorenz模型作为预报模式,对3个初始态分别用新方法和传统伴随方法进行比较,数值试验结果显示新方法求解出的最大预报误差的上界更加精确。     

GRAPES全球切线性和伴随模式的调优

伴随技术是四维变分同化（4DVar）系统中计算代价函数梯度的最佳办法,切线性和伴随模式的效果和效率直接影响着4DVar系统的发展。基于GRAPES（Global and Regional Assimilation PrEdiction System）全球切线性和伴随模式1.0版本,利用GRAPES全球模式2.0版本在并行框架和性能等方面的改善,重新优化和设计了GRAPES全球切线性伴随模式2.0版本,提高了GRAPES全球切线性和伴随模式的效果和效率,优化了切线性模式程序结构,使其计算时间最优可控制在非线性模式的1.2倍以内;采用在切线性模式中保存基态的方法,重构了伴随模式的程序结构,使其计算时间最优控制在非线性模式的1.5倍以内;在GRAPES全球切线性物理过程的设计中,将线性物理过程的轨迹基态计算和切线性扰动计算解耦,提高了GRAPES全球切线性和伴随模式的计算效果和效率。     

GPS折射角资料的变分同化试验

越来越多的新型观测资料为数值天气预报水平的进一步提高提供了许多新的机会。在各种新型的观测资料中,GPS(全球定位卫星系统)折射角资料无疑是非常重要的。GPS折射角资料具有分辨率高、全天候探测、覆盖全球等优点,实现对GPS折射角资料的变分同化,将具有非常重要的意义。文中介绍了如何获得及同化GPS折射角资料的原理。对GPS折射角资料的变分同化可以分为两种:间接同化和直接同化,文中对这两种方法都作了具体介绍。在变分同化的最小化过程中,计算效率无疑是最重要的,而优化步长的计算又直接关系到算法效率的成败。根据最小化算法的特点,通过数学推导,得出一种适合于各种最小化算法的计算优化步长的自适应方法。最后,还利用1995年10月11日的GPS折射角资料进行了数值试验,结果表明了变分同化方法和计算优化步长方法的有效性。     

Evaluating the Tree Population Density and Its Impacts in CLM-DGVM

Vegetation population dynamics play an essential role in shaping the structure and function of terrestrial ecosystems.However,large uncertainties remain in the parameterizations of population dynamics in current Dynamic Global Vegetation Models(DGVMs).In this study,the global distribution and probability density functions of tree population densities in the revised Community Land Model-Dynamic Global Vegetation Model(CLM-DGVM) were evaluated,and the impacts of population densities on ecosystem characteristics were investigated.The results showed that the model predicted unrealistically high population density with small individual size of tree PFTs(Plant Functional Types) in boreal forests,as well as peripheral areas of tropical and temperate forests.Such biases then led to the underestimation of forest carbon storage and incorrect carbon allocation among plant leaves,stems and root pools,and hence predicted shorter time scales for the building/recovering of mature forests.These results imply that further improvements in the parameterizations of population dynamics in the model are needed in order for the model to correctly represent the response of ecosystems to climate change.     

THE SENSITIVITY INFLUENCE OF NUMERICAL MODEL INITIAL VALUES ON FOUR-DIMENSIONAL ASSIMILATION—STUDY BASED ON LORENZ SYSTEM

Numerical experiments of adjoint variational assimilation have been performed using the knownLorenz system.With the increase of sensitivity of model's initial values,it is more and more difficultto use the adjoint method to get the initial values which are consistent with the dynamics of the fore-cast model.Under some circumstances the algorithm completely fails.This shows that four-dimen-sional assimilation is related to the limit of predictability.On the other hand.with the increase ofmodel equation's error,the result of variational assimilation may become worse and worse so that theprediction has no meaning.But if the model parameters are corrected when variational assimilation ismade,the forecast results can be greatly improved based on Lorenz model.     

THE SENSITIVITY INFLUENCE OF NUMERICAL MODEL INITIAL VALUES ON FOUR-DIMENSIONAL ASSIMILATION-STUDY BASED ON LORENZ SYSTEM*

Numerical experiments of adjoint variational assimilation have been performed using the known Lorenz system.With the increase of sensitivity of model's initial values,it is more and more difficult to use the adjoint method to get the initial values which are consistent with the dynamics of the forecast model.Under some circumstances the algorithm completely fails.This shows that four-dimensional assimilation is related to the limit of predictability.On the other hand.with the increase of model equation's error,the result of variational assimilation may become worse and worse so that the prediction has no meaning.But if the model parameters are corrected when variational assimilation is made,the forecast results can be greatly improved based on Lorenz model.     

副热带高压强度变化的模糊聚类诊断预测

采用模糊C均值聚类 (FCM)、遗传算法 (GA) 和模糊减法聚类 (FSC) 交叉融合、优势互补思想进行副热带高压影响因子的综合聚类分析和副热带高压指数的诊断预测。在统计分析的基础上, 通过选择若干与副热带高压指数关系密切的影响因子构成了高维特征空间, 进行了综合聚类分析, 实现了副热带高压指数的聚类判别和诊断预测。该文提出的综合聚类方法既可克服FCM/GA算法全局/局部寻优的不足, 又可客观确定聚类数目。试验结果表明, 该方法具有良好的分类效果, 判别结果与实况基本相符。     

Rapid scale-up of negative emissions technologies: social barriers and social implications

We describe a new approach that allows for systematic causal attribution of weather and climate-related events, in near-real time. The method is designed so as to facilitate its implementation at meteorological centers by relying on data and methods that are routinely available when numerically forecasting the weather. We thus show that causal attribution can be obtained as a by-product of data assimilation procedures run on a daily basis to update numerical weather prediction (NWP) models with new atmospheric observations; hence, the proposed methodology can take advantage of the powerful computational and observational capacity of weather forecasting centers. We explain the theoretical rationale of this approach and sketch the most prominent features of a “data assimilation–based detection and attribution” (DADA) procedure. The proposal is illustrated in the context of the classical three-variable Lorenz model with additional forcing. The paper concludes by raising several theoretical and practical questions that need to be addressed to make the proposal operational within NWP centers.     

IMPROVEMENT OF OCEAN DATA ASSIMILATION SYSTEM AND CLIMATE PREDICTION BY ASSIMILATING ARGO DATA

The Argo(Array for Real-time Geostrophic Oceanography) data from 1998 to 2003 were used in the Beijing Climate Center-Global Ocean Data Assimilation System(BCC-GODAS). The results show that the utilization of Argo global ocean data in BCC-GODAS brings about remarkable improvements in assimilation effects. The assimilated sea surface temperature(SST) of BCC-GODAS can well represent the climatological states of observational data. Comparison experiments based on a global coupled atmosphere-ocean general circulation model(AOCGM) were conducted for exploring the roles of ocean data assimilation system with or without Argo data in improving the climate predictability of rainfall in boreal summer. Firstly, the global ocean data assimilation system BCC-GODAS was used to obtain ocean assimilation data under the conditions with or without Argo data. Then, the global coupled atmosphere-ocean general circulation model(AOCGM) was utilized to do hindcast experiments with the two sets of the assimilation data as initial oceanic fields. The simulated results demonstrate that the seasonal predictability of rainfall in boreal summer, particularly in China, increases greatly when initial oceanic conditions with Argo data are utilized. The distribution of summer rainfall in China hindcast by the AOGCM under the condition when Argo data are used is more in accordance with observation than that when no Agro data are used. The area of positive correlation between hindcast and observation enlarges and the hindcast skill of rainfall over China in summer improves significantly when Argo data are used.