An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.     

Data assimilation technique based on the ensemble π-algorithm

A practical realization of the data assimilation algorithm based on the Kalman filter in its non-simplified form is impossible for modern forecast models because of the high dimension of the associated sets of equations and nonlinearity of predicted processes. The main direction in the Kalman filter realization is an ensemble approach. Under the assumption of ergodicity of random forecast errors, a so-called π-algorithm can be considered, which is alternative to the ensemble Kalman filter and where probabilistic averaging is replaced by averaging over time. In the present paper, we suggest a generalization of the π-algorithm based on the ensemble approach. The algorithm is easy to implement; however, its applicability to the data assimilation problems, convergence, and relation to the Kalman filter are still to be studied. The applicability of the ensemble π-algorithm to the data assimilation problem is considered by an example of a simple one-dimensional advection equation. The use of such a simple equation allows us to compare the classical Kalman filter algorithm with various practical approaches to its realization.     

动态时变参数方法在云量精细化预报中的应用研究

利用2008年1月—2013年12月以及2017年1—11月全球天气预报系统（GFS）预报场资料,采用自适应线性最小二乘回归（LS）和自适应递推卡尔曼（Kalman）滤波两种动态时变参数方法,建立了河套周边地区0~168 h预报时效的总云量精细化预报,并与GFS模式直接输出的总云量、线性预报模型逐步回归预报方法得到的总云量以及非线性预报模型BP神经网络和最小二乘支持向量机回归方法（LSSVM）得到的总云量进行了对比,结果如下:（1）相比GFS模式直接输出的总云量,LS、BP神经网络、LSSVM得到的总云量与实况值的平均绝对误差均明显减小。LS方法误差最小,LS方法的年MAE均在20%~25%,且随着预报时效的延长,改进效果越大。LS方法、多元逐步回归方法、BP神经网络、LSSVM四种方法在6—8月的改进效果最大。（2）LS方法预报的总云量与实况云量的相关性最好,即使168 h预报时效的相关系数依然在0.64以上,远高于其他几种模型的预报结果。（3）LS方法能够明显地提高少云和多云天空状况下预报的击中率,且最优（少云击中率平均提高24 %,多云击中率平均提高34 %）。（4）自适应递推Kalman滤波方法存在预报滞后现象,改进效果不明显。      

雷达定量降水估算在水文模式汛期洪水预报中的应用试验

通过雷达测雨技术获得高时空分辨率的降雨信息,作为水文模型的输入,用以提高水文预报的精度。文章以湖北省白莲河流域为例,利用分组Z-I关系转化雷达反射率为雨强,运用地面雨量站网实测雨量对其进行校准,将不同方法估算得到的雨量结果输入新安江模型进行洪水预报测试,结果表明未校准雷达估算降雨量直接输入水文模型,其结果是不理想的;利用校准后的雷达估算降雨量进行洪水预报,精度得到了很大提高。     

A data assimilation technique based on the π-algorithm

A practical implementation of the data assimilation algorithm based on the Kalman filter in its complete formulation is impossible due to high dimension of the associated equation sets and to nonlinearity of the predicted processes. The main direction in the implementation of the Kalman filter is an ensemble approach. Under the assumption of ergodicity of random forecast errors, an alternative algorithm with respect to the ensemble Kalman filter can be considered, in which probability averaging is replaced by time averaging. The proposes algorithm is based this assumption. The algorithm is easy to implement; however, its convergence, applicability to the data assimilation problems, and connection to the Kalman filter have not been studied. In the paper, applicability of the π-algorithm to data assimilation is considered on an example of a simple one-dimensional advection equation. Use of this simple equation allows comparing the classical Kalman filter algorithm with various practical approaches to its implementation.     

业务模式晴雨预报能力分析及其改进方法研究

以欧洲中心全球预报模式和中国华南区域中尺度模式(GZ 3 km)为例分析了2019年中国南方逐日晴雨预报的情况,并讨论模式晴雨预报的性能。借助TS检验评估方法,在与简单外推预报等的比较中,发现模式雨量预报特点及模式晴雨预报的统计规律,如两个模式同时预报晴天,或者模式预报有雨且降水量大于某阈值等情况,其预报准确率非常高;而对于两个模式预报不一致,或模式预报有雨且雨量较小等情况,则存在较大不确定性。基于上述研究,提出利用模式预报改进观测外推和利用观测与模式的频率匹配改进模式预报等方法。     

Forecasting quantitative rainfall over India using multi-model ensemble technique

A new approach to ensemble forecasting of rainfall over India based on daily outputs of four operational numerical weather prediction (NWP) models in the medium-range timescale (up to 5 days) is proposed in this study. Four global models, namely ECMWF, JMA, GFS and UKMO available on real-time basis at India Meteorological Department, New Delhi, are used simultaneously with adequate weights to obtain a multi-model ensemble (MME) technique. In this technique, weights for each NWP model at each grid point are assigned on the basis of unbiased mean absolute error between the bias-corrected forecast and observed rainfall time series of 366 daily data of 3 consecutive southwest monsoon periods (JJAS) of 2008, 2009 and 2010. Apart from MME, a simple ensemble mean (ENSM) forecast is also generated and experimented. The prediction skill of MME is examined against observed and corresponding outputs of each constituent model during monsoon 2011. The inter-comparison reveals that MME is able to provide more realistic forecast of rainfall over Indian monsoon region by taking the strength of each constituent model. It has been further found that the weighted MME technique has higher skill in predicting daily rainfall compared to ENSM and individual member models. RMSE is found to be lowest in MME forecasts both in magnitude and area coverage. This indicates that fluctuations of day-to-day errors are relatively less in the MME forecast. The inter-comparison of domain-averaged skill scores for different rainfall thresholds further clearly demonstrates that the MME algorithm improves slightly above the ENSM and member models.     

A Model Output Machine Learning Method for Grid Temperature Forecasts in the Beijing Area

In this paper, the model output machine learning (MOML) method is proposed for simulating weather consultation, which can improve the forecast results of numerical weather prediction (NWP). During weather consultation, the forecasters obtain the final results by combining the observations with the NWP results and giving opinions based on their experience. It is obvious that using a suitable post-processing algorithm for simulating weather consultation is an interesting and important topic. MOML is a post-processing method based on machine learning, which matches NWP forecasts against observations through a regression function. By adopting different feature engineering of datasets and training periods, the observational and model data can be processed into the corresponding training set and test set. The MOML regression function uses an existing machine learning algorithm with the processed dataset to revise the output of NWP models combined with the observations, so as to improve the results of weather forecasts. To test the new approach for grid temperature forecasts, the 2-m surface air temperature in the Beijing area from the ECMWF model is used. MOML with different feature engineering is compared against the ECMWF model and modified model output statistics (MOS) method. MOML shows a better numerical performance than the ECMWF model and MOS, especially for winter. The results of MOML with a linear algorithm, running training period, and dataset using spatial interpolation ideas, are better than others when the forecast time is within a few days. The results of MOML with the Random Forest algorithm, year-round training period, and dataset containing surrounding gridpoint information, are better when the forecast time is longer.     

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     

用一种新的同化方法同化降水量资料

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three-dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard four- dimensional variational data assimilation at a much lower computational cost.     

A Simplified Extended Kalman Filter assimilation of soil moisture for the SL-AV global medium-range forecast model

The implementation of the Simplified Extended Kalman Filter (SEKF) for the deep soil moisture initialization in the SL-AV global atmosphere model is described. Special attention is paid to the calculation of the observation operator and analysis increment. SL-AV screen-level parameters forecasts are estimated with SEKF and optimal interpolation initialization methods. It is demonstrated that the implementation of the assimilation algorithm improves the model forecast quality for screen-level temperature and relative humidity.     

客观定量预报中降水的预处理

建立预报模型前, 对降水量进行一定的处理会对预报效果有较大的影响。对于降水量为0的样本, 根据对应的相对湿度情况分别赋予0或不同的负值, 并通过神经网络方法, 以中国国家气象中心T213模式、德国气象局业务模式和日本气象厅业务模式相应的降水量预报结果作为预报因子, 利用2003年和2004年夏季资料分别建立了处理后降水量以及未经处理降水量的预报模型。以北京等站为例, 2005年夏季试报结果的对比分析表明:通过相对湿度对降水量进行适当处理后, 预报结果从TS评分、空报率、漏报率及预报偏差来说, 不论是与不进行处理的预报结果还是与模式直接的预报结果相比都有提高, 尤其是减少了空报的情况。该处理方法简单可行, 并且对降水预报效果提高明显。     

Ensemble sensitivity analysis of an extreme rainfall event over the Himalayas in June 2013

Forecast Sensitivity of an extreme rainfall event over the Uttarakhand state located in the Western Himalayas is investigated through Ensemble-based Sensitivity Analysis (ESA). ESA enables the assessment of forecast errors and its relation to the flow fields through linear regression approach. The ensembles are initialized from an Ensemble Kalman Filter (EnKF) Data Assimilation in Weather Research and Forecast (WRF) model. ESA is then applied to evaluate the dynamics and predictability at two different days of the extreme precipitation episode. Results indicate that the precipitation forecast over Uttarakhand is sensitive to the mid-tropospheric trough and moisture fields for both the days, in general. The day 1 precipitation shows negative sensitivity to the trough over upstream regions of the storm location while in day 2, the sensitive region is found to be located over the southward intruded branch of the mid–tropospheric trough. Perturbations introduced in the initial conditions (IC) over the most sensitive region over the west of the storm location indicate significant variations in the forecast location of precipitation. IC perturbed experiments show that the perturbation amplitude is correlated linearly with predicted change in precipitation, which becomes nonlinear as the forecast length increases. ESA performed on convection-permitting ensembles show that precipitation over the Uttarakhand is mostly non-convective. However, when the location of the response function box is moved north-westward of the Uttarakhand, the sensitivity patterns show signs of convection.     

利用MM5模式输出产品制作空气质量预报方法探讨

根据2004年中尺度数值预报模式MM5输出产品和临沂市环境监测中心逐日监测资料建立了各污染物浓度预报方程,在2005年夏季的试报中,该方程的试报效果较差,其预报准确率明显低于其历史拟合率。为了提高预报准确率,利用逐步回归筛选的因子及统计模型研究中的有关数据,探讨了使用卡尔曼滤波方法制作空气污染物浓度预报的问题。分析发现,利用卡尔曼滤波方法制作空气质量预报可以取得比较满意的效果。     

EMD在广西季节降水预报中的应用

气候系统是一种耗散的、具有多个不稳定源的非线性、非平稳系统。该文利用支持向量机(SVM)算法在处理非线性问题中的优越性和经验模态分解(EMD)算法在处理非平稳信号中的优势,采用将EMD与SVM相结合的短期气候预测方法,并应用到广西季节降水预报中。选取广西88个气象观测站1957—2005年6—8月逐年降水量的距平百分率序列作为试验数据,通过EMD算法将标准化处理后的距平百分率序列分解成多个本征模态函数(IMF)分量和一个趋势分量,在分解中针对EMD算法存在的端点极值问题选择两种方法分别进行处理,对比得出极值延拓法效果更好。对每个分量构建不同的SVM模型进行预测,并通过重构形成最后的预测结果。试验中采用不经EMD处理的反向传播(BP)神经网络和SVM算法进行对比验证,结果表明:相对于直接预测方法,该文提出的方案均方误差最小,能够较为准确地反映出降水序列未来几年的变化趋势,具有更高的预测精度和较好的推广前景。     

双流机场低能见度天气预报方法研究

在信息量较大, 而预报对象与预报因子的关系又不清楚的状况下, 智能机器学习方法是解决这类问题的较好手段。利用1997—2001年成都站的常规探空资料和双流机场的地面观测资料, 使用支持向量机 (Support Vector Machines, 简称SVM) 方法, 选取多种核函数进行双流机场低能见度天气的预报建模试验。测试结果表明:以径向基函数和拉普拉斯函数构造的SVM预报模型实验效果最好, Ts评分分别为0.287和0.292, 远高于双流机场低能见度天气出现的频率 (0.155)。试验结果还表明:以径向基函数构造的SVM预报模型空报较多, 漏报较少; 而以拉普拉斯函数构造的SVM预报模型空报较少, 漏报较多。因此, 如果强调模型对低能见度天气预报的准确性, 则应采用以拉普拉斯函数构造的预报模型, 如果强调对低能见度天气的预防性, 则应采用以径向基函数构造的预报模型。     

初始扰动振幅和集合样本数对CNOPs集合预报的影响

初始扰动振幅的大小和集合样本数对于集合预报取得更高预报技巧具有重要意义。本文将正交条件非线性最优扰动方法（orthogonal conditional nonlinear optimal perturbations,简称CNOPs）应用于概念模型Lorenz-96模式探讨了初始扰动振幅和集合样本数对集合预报技巧的影响,从而为使用更复杂模式进行集合预报提供指导。结果表明,由于CNOPs扮演了非线性系统中的最优初始扰动,从而使得当初始扰动振幅小于初始分析误差的大小时,CNOPs集合预报获得更高的预报技巧,并且CNOPs集合预报的最高预报技巧总是高于奇异向量法（singular vectors,简称SVs）集合预报的最高预报技巧。结果还表明,CNOPs集合预报倾向于具有一个合适的样本数时,达到最高技巧。更好的集合离散度——预报误差关系和更为平坦的Talagrand图（Talagrand diagram）进一步证明了CNOPs集合预报系统的可靠性,从而夯实了上述结果的合理性。因此,针对CNOPs集合预报,本文认为采用一个适当小于初始分析误差的初始扰动振幅和一个合适的集合样本数,有利于CNOPs集合预报达到最高预报技巧。     

大气中的降水与反降水──''98梅雨锋暴雨的天气学成因分析与预报探讨

对我国Ｔ１０６Ｌ１９（客观分析）模式大气,（１９９８年６～７月）做了大气中所有天气学降水（垂直运动形式）的计算。研究表明,’９８长江流域上空暴雨存在着明显的梅雨锋天气（尺度）系统降水,同时,长时间湿空气团的维持及其输运,和在梅雨锋上的非等熵湿绝热运动并不断形成对流不稳定降水,是强降水发生的天气学成因。因此,用模式大气中各种天气学形式的降水去（概率）统计预报实际大气降水,实现了预报因子和预报对象之间     

支持向量机与卡尔曼滤波集合的西太平洋副热带高压数值预报误差修正

基于T106数值预报产品资料,提出了支持向量机和卡尔曼滤波相结合的方法来进行夏季西太平洋副热带高压数值预报的误差修正与预报优化。首先采用支持向量机方法建立了西太平洋副热带高压面积指数的误差修正模型。基于支持向量机预报优化模型尽管有比较好的拟合精度和预报效果,但与实际副热带高压指数尚有一定的差异。究其原因,除预报对象(副热带高压)本身比较复杂、模型优化因子不够充分以及数值预报误差自身的随机性以外,优化模型的输入、输出基本上是一个静态映射结构,因此前一时刻的预测误差难以得到有效的反馈、调整和修正。为考虑前一时刻预报误差的反馈信息,动态跟踪副高的变化趋势,随后引入卡尔曼滤波方法建立支持向量机-卡尔曼滤波模型,对支持向量机模型的输出结果作进一步的调整和优化。试验结果表明,该方法模型的预报优化效果优于T106数值预报产品以及单纯的神经网络修正模型和卡尔曼滤波修正模型的优化效果,能够较为客观、有效地修正西太平洋副热带高压指数的数值预报误差,改进和优化西太平洋副热带高压的数值预报效果。该方法为副热带高压等复杂天气系统和要素场预报提供了一种新的思路,表现出较好的应用前景。     

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。