Fast data assimilation using a nonlinear Kalman filter and a model surrogate: An application to the Columbia River estuary

A fast and adjoint-free nonlinear data assimilation (DA) system was developed to simulate 3D baroclinic circulation in estuaries, leveraging two recently developed technologies: (1) a nonlinear model surrogate that executes forward simulation three orders of magnitude faster than a forward numerical circulation code and (2) a nonlinear extension to the reduced-dimension Kalman filter that estimates the state of the model surrogate. The noise sources in the Kalman filter were calibrated using empirical cross-validation and accounted for errors in model and model forcing.The DA system was applied to assimilate in situ measurements of water levels, salinities, and temperatures in simulations of the Columbia River estuary. To validate the DA results, we used a combination of cross-validation studies, process-oriented studies, and tests of statistical and dynamical consistency. The validation studies showed that DA improved the representation of several important processes in the estuary, including nonlinear tidal propagation, salinity intrusion, estuarine residual circulation, heat balance, and response of the estuary to coastal winds.     

Ensemble-based Kalman filters in strongly nonlinear dynamics

This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, ensemble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.     

Development of an Operational Hybrid Data Assimilation System at KIAPS

This study introduces the operational data assimilation (DA) system at the Korea Institute of Atmospheric Prediction Systems (KIAPS) to the numerical weather prediction community. Its development history and performance are addressed with experimental illustrations and the authors’ previously published studies. Milestones in skill improvements include the initial operational implementation of three-dimensional variational data assimilation (3DVar), the ingestion of additional satellite observations, and changing the DA scheme to a hybrid four-dimensional ensemble-variational DA using forecasts from an ensemble based on the local ensemble transform Kalman filter (LETKF). In the hybrid system, determining the relative contribution of the ensemble-based covariance to the resultant analysis is crucial, particularly for moisture variables including a variety of horizontal scale spectra. Modifications to the humidity control variable, partial rather than full recentering of the ensemble for humidity further improves moisture analysis, and the inclusion of more radiance observations with higher-level peaking channels have significant impacts on stratosphere temperature and wind performance. Recent update of the operational hybrid DA system relative to the previous 3DVar system is described for detailed improvements with interpretation.     

Typhoon Track Forecast with a Hybrid GSI-ETKF Data Assimilation System

A hybrid grid-point statistical interpolation-ensemble transform Kalman filter (GSI-ETKF) data assimilation system for the Weather Research and Forecasting (WRF) model was developed and applied to typhoon track forecast with simulated dropsonde observations. This hybrid system showed significantly improved results with respect to tropical cyclone track forecast compared to the standard GSI system in the case of Muifa in 2011. Further analyses revealed that the flow-dependent ensemble covariance was the major contributor to the better performance of the GSI-ETKF system than the standard GSI system; the GSI-ETKF system was found to be potentially able to adjust the position of the typhoon vortex systematically and better update the environmental field.     

非线性滤波在含“开关”过程的资料同化中的应用研究

利用一个描述实际数值天气预报模式中比湿在单格线上随时间发展的偏微分方程作为控制方程,研究分析了非线性滤波方法在含开关过程的资料同化中的有效性和可行性。首先在贝叶斯理论框架下,讨论了一般情形的非线性滤波方法,然后对基于粒子滤波(PF)和基于集合卡尔曼滤波(EnKF)的两种同化方法进行对比,由于EnKF是通过对集合成员的统计分析得到的误差分布的一阶矩和二阶矩来近似真实误差分布的,所以当用高斯分布近似真实误差分布所产生的误差较大时,基于EnKF的同化方法得到的结果也会有较大的误差。最后分别从观测算子为线性和非线性、观测误差为高斯型和非高斯型4种情形进行数值试验,结果显示当观测误差为高斯型时,无论观测算子为线性还是非线性,基于PF和基于EnKF的同化方法都能克服由开关过程给资料同化带来的困难,给出满意的同化结果;而当观测误差为非高斯型时,EnKF出现滤波不稳定,产生了非理想的同化结果,但PF方法仍然能够有效地发挥作用,给出满意的同化结果。     

ENSO机理及其预测研究

资料分析研究表明ENSO(El Ni?o和La Ni?a)实际上是热带太平洋次表层海温距平的循环,而次表层海温距平的循环是赤道西太平洋异常纬向风所驱动的,赤道西太平洋的异常纬向风又主要由异常东亚冬季风所激发。因此可以将ENSO的机理视为主要是由东亚季风异常造成的赤道西太平洋异常纬向风所驱动的热带太平洋次表层海温距平的循环。同时分析还表明,热带西太平洋大气季节内振荡(ISO)的明显年际变化,作为一种外部强迫,对ENSO循环起着十分重要的作用;El Ni?o的发生同大气ISO的明显系统性东传有关。资料分析也表明,El Ni?o持续时间的长短与大气环流异常有密切关系。 用非线性最优化方法研究El Ni?o－南方涛动(ENSO)事件的可预报性问题,揭示了最容易发展成ENSO事件的初始距平模态,即条件非线性最优扰动(CNOP)型初始距平;找出能够导致显著春季可预报性障碍(SPB),且对ENSO预报结果有最大影响的一类初始误差——CNOP型初始误差,进而探讨耦合过程的非线性在SPB研究中的重要作用,提出了关于ENSO事件发生SPB的一种可能机制;用CNOP方法揭示了ENSO强度的不对称现象,探讨ENSO不对称性的年代际变化问题,提出ENSO不对称性年代际变化的一种机制;建立了关于ENSO可预报性的最大可预报时间下界、最大预报误差上界和最大允许初始误差下界的三类可预报性问题,分别从三个方面揭示ENSO事件的春季可预报性障碍现象,比较有效地量化了模式ENSO事件的可预报性。 利用中国科学院大气物理研究所地球流体力学数值模拟国家重点实验室的ENSO预测系统,研究了海洋资料同化在ENSO预测中的应用,该系统可以同时对温、盐剖面资料和卫星高度计资料进行同化。并且在模式中采用次表层上卷海温的非局地参数化方法,可有效地改进ENSO模拟水平。采用集合卡曼滤波(Ensemble Kalman Filter,EnKF)同化方法以及在集合资料同化中“平衡的”多变量模式误差扰动方法为集合预报提供更加精确和协调的初始场,ENSO预报技巧得到提高。     

Atmospheric data assimilation on the equatorial beta plane

Abstract

Kalman filter theory shows great promise when applied to the assimilation of atmospheric observations. Previous work has concentrated on extratropical dynamics, and tropical aspects have not yet been seriously tackled. In this article, a Kalman filter is applied to the linearized shallow water equations on an equatorial beta plane. The system or model error is constructed from the slow eigenmodes of the model and is based on an expansion in parabolic cylinder functions. The resulting second‐moment statistics are discussed in some detail. The Kalman filter is applied to a special observation network that allows the diagonalization of the system. Following Daley and Ménard (1993), it is then possible to obtain the complete space and time solution for the second‐moment forecast and analysis error statistics. The slow (low‐frequency) and fast (high‐frequency) error statistics are examined separately for both the optimal and suboptimal cases.     

The Impact of Satellite Radiance Data Assimilation within a Frequently Updated Regional Forecast System Using a GSI-based Ensemble Kalman Filter

A regional ensemble Kalman filter (EnKF) data assimilation (DA) and forecast system was recently established based on the Gridpoint Statistical Interpolation (GSI) analysis system. The EnKF DA system was tested with continuous threehourly updated cycles followed by 18-h deterministic forecasts from every three-hourly ensemble mean analysis. Initial tests showed negative to neutral impacts of assimilating satellite radiance data due to the improper bias correction procedure. In this study, two bias correction schemes within the established EnKF DA system are investigated and the impact of assimilating additional polar-orbiting satellite radiance is also investigated. Two group experiments are conducted. The purpose of the first group is to evaluate the bias correction procedure. Two online bias correction methods based on GSI 3DVar and EnKF algorithms are used to assimilate AMSU-A radiance data. Results show that both variational and EnKF-based bias correction procedures effectively reduce the observation and background radiance differences, achieving positive impacts on forecasts. With proper bias correction, we assimilate full radiance observations including AMSU-A, AMSU-B, AIRS, HIRS3/4, and MHS in the second group. The relative percentage improvements(RPIs) for all forecast variables compared to those without radiance data assimilation are mostly positive, with the RPI of upper-air relative humidity being the largest. Additionally, precipitation forecasts on a downscaled 13-km grid from 40-km EnKF analyses are also improved by radiance assimilation for almost all forecast hours.     

基于非线性滤波的风廓线雷达数据处理

针对实际工程中风廓线雷达风向、风速随高度分布取值的非线性特性以及非气象干扰因素,基于非线性化方法——扩展卡尔曼滤波法,对风廓线雷达探测数据进行滤波处理.先利用泰勒展开式的一次项对非线性方程作线性化处理,再结合经典的卡尔曼滤波进行滤波估计,将非线性滤波问题转化为一个近似的线性滤波问题.仿真实验结果表明,该方法可以有效去除风场数据中掺杂的噪声干扰,很好地发挥了其非线性特性,滤波效果优于传统的卡尔曼滤波,具有一定的工程应用前景.     

基于RFID和自适应卡尔曼滤波的室内移动目标定位方法

本文研究了UHF-RFID（超高频-射频识别）环境下的移动目标定位问题,提出了一种结合自适应卡尔曼滤波和BVIRE（边界虚拟参考标签）的移动机器人定位方法,即B-AKF（Boundary-Adaptive Kalman Filter）定位方法.首先,利用UHF-RFID系统对移动机器人进行初始定位,其次,考虑模型和噪声统计特性不确定性,采用自适应卡尔曼滤波方法对机器人的运动状态进行预测和更新,并引入自适应因子补偿噪声方差不确定性问题.最后,搭建了基于UHF-RFID的定位实验平台,并通过实验研究表明,相比于传统的线性BVIRE和线性卡尔曼滤波方法,所提出的自适应卡尔曼滤波方法具有更高的定位精度和更强的鲁棒性能.     

风暴尺度天气下利用集合卡尔曼滤波模拟多普勒雷达资料同化试验I.不考虑模式误差的情形

本文在假定模式无偏差的情况下, 利用一次风暴过程的模拟多普勒雷达资料进行一系列风暴天气尺度的集合卡尔曼滤波资料同化试验, 检验集合卡尔曼滤波在风暴天气尺度资料同化方面的效果, 并验证各集合卡尔曼滤波参数对同化效果的影响。试验结果表明, 集合卡尔曼滤波能有效地应用于风暴尺度的资料同化; 40个集合成员以及6 km的局地化尺度能较好地滤除采样误差造成的虚假相关, 同时可以将观测信息传递到无观测的模式格点; 利用背景场加上空间平滑的高斯型随机扰动生成初始成员的方式较未经过平滑的方式有更好的分析效果; 背景场扰动方法能够提高样本的离散度; 只同化反射率的同化试验表明, 反射率的同化效果较明显, 也证明了集合卡尔曼滤波在非常规资料同化中的作用; 增加径向风资料同化的效果优于只进行反射率同化的结果。     

基于集合卡尔曼滤波的土壤水分同化试验

集合卡尔曼滤波是由大气数据同化发展的新的顺序同化算法,它利用蒙特卡罗方法计算背景场的误差协方差矩阵,克服了卡尔曼滤波需要线性化的模型算子和观测算子的难点。我们发展了一个基于集合卡尔曼滤波和简单生物圈模型(SiB2,Simple Biosphere Model)的单点陆面数据同化方案。利用1998年7月6日至8月9日青藏高原GAME-Tibet实验区MS3608站点的观测数据进行了同化试验。结果表明,利用集合卡尔曼滤波的数据同化方法可以明显地提高表层、根区、深层土壤水分的估算精度。     

Impact of Coastal Radar Observability on the Forecast of the Track and Rainfall of Typhoon Morakot(2009)Using WRF-based Ensemble Kalman Filter Data Assimilation

This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot(2009)using a WRF-based ensemble Kalman filter(EnKF)data assimilation(DA)system.The results showed that the performance of radar EnKF DA was quite sensitive to the number of radars being assimilated and the DA timing relative to the landfall of the tropical cyclone(TC).It was found that assimilating radial velocity(Vr)data from all the four operational radars during the 6 h immediately before TC landfall was quite important for the track and rainfall forecasts after the TC made landfall.The TC track forecast error could be decreased by about 43% and the 24-h rainfall forecast skill could be almost tripled.Assimilating Vr data from a single radar outperformed the experiment without DA, though with less improvement compared to the multiple-radar DA experiment.Different forecast performances were obtained by assimilating different radars, which was closely related to the first-time wind analysis increment, the location of moisture transport, the quasi-stationary rainband, and the local convergence line.However, only assimilating Vr data when the TC was farther away from making landfall might worsen TC track and rainfall forecasts.Besides, this work also demonstrated that Vr data from multiple radars, instead of a single radar, should be used for verification to obtain a more reliable assessment of the EnKF performance.     

基于卡尔曼滤波的中国区域气温和降水的多模式集成预报

利用TIGGE资料集下欧洲中期天气预报中心(ECMWF)、日本气象厅(JMA)、美国国家环境预报中心(NCEP)、中国气象局(CMA)和英国气象局(UKMO)5个模式预报的结果,对基于卡尔曼滤波的气温和降水的多模式集成预报进行研究。结果表明,卡尔曼滤波方法的预报效果优于消除偏差集合平均(BREM)和单模式的预报,但是对于地面气温和降水,其预报效果也存在一定的差异。在中国区域2 m气温的预报中,卡尔曼滤波的预报结果最优。而对于24 h累积降水预报,尽管卡尔曼滤波在所有量级下的TS评分均优于BREM,但随着预报时效增加,其在大雨及以上量级的TS评分跟最佳单模式UKMO预报相当,改进效果不明显。卡尔曼滤波在地面气温和24 h累积降水每个预报时效下的均方根误差均最优,预报效果更佳且稳定。     

Nonlinear measurement function in the ensemble Kalman filter

ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.     

Coupled atmosphere–ocean data assimilation experiments with a low-order climate model

A simple idealized atmosphere–ocean climate model and an ensemble Kalman filter are used to explore different coupled ensemble data assimilation strategies. The model is a low-dimensional analogue of the North Atlantic climate system, involving interactions between large-scale atmospheric circulation and ocean states driven by the variability of the Atlantic meridional overturning circulation (MOC). Initialization of the MOC is assessed in a range of experiments, from the simplest configuration consisting of forcing the ocean with a known atmosphere to performing fully coupled ensemble data assimilation. “Daily” assimilation (that is, at the temporal frequency of the atmospheric observations) is contrasted with less frequent assimilation of time-averaged observations. Performance is also evaluated under scenarios in which ocean observations are limited to the upper ocean or are non-existent. Results show that forcing the idealized ocean model with atmospheric analyses is inefficient at recovering the slowly evolving MOC. On the other hand, daily assimilation rapidly leads to accurate MOC analyses, provided a comprehensive set of oceanic observations is available for assimilation. In the absence of sufficient observations in the ocean, the assimilation of time-averaged atmospheric observations proves to be more effective for MOC initialization, including the case where only atmospheric observations are available.     

Kalman滤波技术在台风路径动力-统计预报中的应用

本文从台风移动的动力学模式出发,讨论了目前台风路径动力—统计预报中所存在的问题,提出了改进的措施,探讨了kalman滤波器的实现方案,并分析了在采用kalman最佳线性递推滤波方法作实际预报时对误差计算的处理方法,从而对台风路径的动力—统计预报作了改进。通过较多独立样本的检验,表明了台风路径动力—统计预报的kalman滤波方法,能够修正台风路径预报的速度和方向,因此具有实际的应用价值。     

Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation

This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.     

GRAPES全球模式的模式误差估计

现代数值天气模式考虑的物理过程和边界条件越来越复杂, 但是它描述的大气状态和真实的大气流体运动轨迹还有一定的差距, 存在模式误差。在以往的研究中, 模式误差往往被忽略, 在集合卡尔曼滤波同化系统中, 如果忽略模式误差会导致滤波发散现象。本文用不同分辨率的模式预报差异估计了GRAPES全球模式的模式误差, 研究发现模式误差随着分辨率降低而线性增加, 而且模式误差随着预报时效的增加呈现线性增长的趋势。     

非绝热加热对赤道地区平均纬向环流的作用——非线性响应

本文设计了一个两层非线性原始方程模式,做低谱展开,求出非线性方程组的解;讨论了在外参数变化情况下解及其相应环流的演变;并与线性响应作了对比。此外,还讨论了定常解的稳定性。 主要结论是:(1)非绝热加热各分量在非线性响应中能强迫出更为接近实际的赤道地区平均纬圈环流圈。(2)在非线性响应中,潜热加热对纬圈环流的作用是最主要的。随着外参数——湿度的变化,解出现突变现象,其对应的赤道地区平均纬圈环流从一个定常态变到另一个定常态;其中对流潜热的作用最为明显,感热加热的作用是次要的。(3)在非线性响应和线性响应中,辐射加热对环流的作用不同;潜热加热对环流的作用相似,但在前者中它要强得多。