Time-Expanded Sampling for Ensemble-Based Filters: Assimilation Experiments with Real Radar Observations

By sampling perturbed state vectors from each ensemble prediction run at properly selected time levels in the vicinity of the analysis time, the recently proposed time-expanded sampling approach can enlarge the ensemble size without increasing the number of prediction runs and, hence, can reduce the computational cost of an ensemble-based filter. In this study, this approach is tested for the first time with real radar data from a tornadic thunderstorm. In particular, four assimilation experiments were performed to test the time-expanded sampling method against the conventional ensemble sampling method used by ensemble- based filters. In these experiments, the ensemble square-root filter (EnSRF) was used with 45 ensemble members generated by the time-expanded sampling and conventional sampling from 15 and 45 prediction runs, respectively, and quality-controlled radar data were compressed into super-observations with properly reduced spatial resolutions to improve the EnSRF performances. The results show that the time-expanded sampling approach not only can reduce the computational cost but also can improve the accuracy of the analysis, especially when the ensemble size is severely limited due to computational constraints for real-radar data assimilation. These potential merits are consistent with those previously demonstrated by assimilation experiments with simulated data.     

模式误差动力特征：模式参数误差和物理过程描绘缺失误差

模式变最初始场误差和模式误差都是制约数值天气预报准确性提高的重要因素,传统数值预报和变分同化均忽略模式误差的影响.随着研究的深入,关于模式误差对数值预报影响的研究显得尤为重要.本文从非线性动力方程出发,推导出在模式存在参数误差和物理过程描绘缺失误差情况下的模式预报误差演变方程及短时间内误差平方均值近似表达式,并利用Li...     

数值预报误差订正技术中相似-动力方法的发展

Due to the increasing requirement for high-level weather and climate forecasting accuracy, it is necessary to exploit a strategy for model error correction while developing numerical modeling and data assimilation techniques. This study classifies the correction strategies according to the types of forecast errors, and reviews recent studies on these correction strategies. Among others, the analogue-dynamical method has been developed in China, which combines statistical methods with the dynamical model, corrects model errors based on analogue information, and effectively utilizes historical data in dynamical forecasts. In this study, the fundamental principles and technical solutions of the analogue-dynamical method and associated development history for forecasts on different timescales are introduced. It is shown that this method can effectively improve medium- and extended-range forecasts, monthly-average circulation forecast, and short-term climate prediction. As an innovative technique independently developed in China, the analogue- dynamical method plays an important role in both weather forecast and climate prediction, and has potential applications in wider fields.     

4DSVD分析误差与样本选取方法和样本容量的关系初探

分析误差与样本选取方法和样本容量的关系是4DSVD同化方法一个亟需研究的重要问题。获得支撑大气模式空间和观测空间吸引子的基向量是4DSVD研究的关键部分,样本的好坏和样本容量的范围是决定4DSVD基向量和分析结果质量的一个重要前提条件。首先利用Lorenz28变量模式,用4DSVD方法做了一些简单三维同化试验,探讨了Lorenz28变量模式的分析误差与样本容量和样本选取方法的关系。数值试验结果表明,对一个具体的模式,有限的样本容量就能够获得较高精度的分析结果;在模式系统和观测系统不变情况下,用一定样本容量得到的支撑模式空间和观测空间的基向量具有很好的稳定性,即一旦获得一组较好的基向量,在观测系统和模式系统不变的情况下,对同化任何时刻的观测适用;分析结果对选取方法没有太大的依赖性,但具体的样本容量要视不同模式和样本选取方法而定。用WRF模式做的4DSVD四维观测系统模拟试验结果表明,若样本选取方法得当,所需要的样本容量要远远小于模式自由度。4DSVD要真正获得较高精度的分析结果,需要的条件是尽可能的在吸引子上取样并选取充足的样本容量;间隔取样可以一定程度上减少计算量。根据数值试验结果提出了4DSVD在实际同化时样本选取的一些初步的方法。     

EnKF中误差协方差优化方法及在资料同化中应用

集合卡尔曼滤波 (the Ensemble Kalman Filter,简称EnKF) 中将预报集合的统计协方差作为预报误差协方差,但该估计可能严重偏离真实的预报误差协方差,影响同化精度。基于极大似然估计理论,发展了一种优化预报误差协方差矩阵的实时膨胀方法,即MLE (the Maximum Likelihood Estimation) 方法。利用蒙古国基准站Delgertsgot (简称DGS站) 观测资料,基于EnKF方法和MLE方法,在通用陆面模式 (the Common Land Model,简称CoLM) 中同化了地表温度和10 cm土壤温度观测资料,建立了土壤温度同化系统。结果表明:MLE方法对地表温度和各层土壤温度 (尤其深层土壤温度) 的估计比EnKF方法准确。考虑到浅层和深层土壤温度的差别,在实施MLE方法时对浅层和深层土壤温度采用了不同的膨胀因子。对比膨胀因子为单一标量时的结果,多因子膨胀能缓解深层土壤温度的不合理膨胀,改善同化效果。     

Time-Expanded Sampling Approach for Ensemble Kalman Filter:Experiment Assimilation of Simulated Soundings

In the Ensemble Kalman Filter (EnKF) data assimilation-prediction system, most of the computationtime is spent on the prediction runs of ensemble members. A limited or small ensemble size does reduce thecomputational cost, but an excessively small ensemble size usually leads to filter divergence, especially whenthere are model errors. In order to improve the efficiency of the EnKF data assimilation-prediction systemand prevent it against filter divergence, a time-expanded sampling approach for EnKF based on the WRF(Weather Research and Forecasting) model is used to assimilate simulated sounding data. The approachsamples a series of perturbed state vectors from Nb member prediction runs not only at the analysis time(as the conventional approach does) but also at equally separated time levels (time interval is △t) beforeand after the analysis time with M times. All the above sampled state vectors are used to construct theensemble and compute the background covariance for the analysis, so the ensemble size is increased fromNb to Nb+2M￡Nb=(1+2M)×Nb) without increasing the number of prediction runs (it is still Nb). Thisreduces the computational cost. A series of experiments are conducted to investigate the impact of △t (thetime interval of time-expanded sampling) and M (the maximum sampling times) on the analysis. The resultsshow that if △t and M are properly selected, the time-expanded sampling approach achieves the similareffect to that from the conventional approach with an ensemble size of (1+2M)×Nb, but the number ofprediction runs is greatly reduced.     

全球海洋资料同化系统ZFL_GODAS的研制和初步评估试验

本研究发展了一个全球海洋资料同化系统ZFL_GODAS。该系统是一个短期气候数值预测业务系统的子系统,为短期气候预测海气耦合模式提供全球海洋初始场。系统能够同化的观测资料包括卫星高度计资料、卫星海表温度(SST)资料,以及Argo、XBT、TAO等各种不同来源的现场温盐廓线资料。系统使用的海洋模式为中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室开发的气候系统海洋模式LICOM1.0,同化方案为集合最优插值(EnOI)方案。系统使用一个由海洋模式自由积分得到的静态样本来估计背景场误差协方差。这样的基于集合样本的背景场误差协方差具有多变量协变、各向异性的特征,且能反映海洋物理过程固有的空间尺度特征。针对EnOI同化程序的特点,开发了一套特色鲜明、负载均衡、高效的并行化同化程序。本文通过与不同类型观测资料的比较,对同化系统的性能进行了评估。通过比较海表温度和海面高度的年际变率,海表温度异常随时间的变化,SST、海面高度异常(SLA)以及次表层温盐预报产品的均方根误差,5年平均温度偏差廓线、平均盐度廓线、平均纬向流速廓线等发现:系统工作正常、同化效果较好;经过同化以后,各变量都更加接近观测,误差更小,与观测场的相关性更好,可以为短期气候预测系统提供较好的海洋初始场,也可以为物理海洋学的研究提供有效的再分析资料。     

GRAPES全球模式的误差评估和订正

以欧洲中期预报中心的ERA-interim再分析资料为参考,对GRAPES全球模式的数值预报结果误差进行了评估,并运用基于历史资料的模式距平积分订正（ANO）方法,对数值预报结果进行了订正试验,检验了ANO方法对GRAPES模式全球中期天气预报的订正改进效果。对1984~2014逐年7月15~24日10天的预报结果订正前后对比分析表明,ANO方法对不同区域位势高度、温度等要素预报订正效果明显,31个个例200 hPa位势高度一周预报距平相关系数平均提高0.05、均方根误差减少12 gpm。其它各层误差订正也显示类似结果,验证了ANO方法对提高GRAPES全球模式10天数值天气预报技巧的有效性,并与MOS（Model Output Statistics）方法对比,更便利、更经济,具有更好的可操作性以及业务预报应用能力。     

Wind Speed and Altitude Dependent AMDAR Observational Error and Its Impacts on Data Assimilation and Forecasting

Aircraft Meteorological Data Relay (AMDAR) observations have been widely used in numerical weather prediction (NWP) because of its high spatiotemporal resolution. The observational error of AMDAR is influenced by aircraft flight altitude and atmospheric condition. In this study, the wind speed and altitude dependent observational error of AMDAR is estimated. The statistical results show that the temperature and the observational error in wind speeds slightly decrease as altitude increases, and the observational error in wind speed increases as wind speed increases. Pseudo single AMDAR observation assimilation tests demonstrate that the wind speed and altitude dependent observational error can provide more reasonable analysis increment. Furthermore, to assess the performance of wind speed and altitude dependent observational error on data assimilation and forecasting, two-month 3-hourly cycling data assimilation and forecast experiments based on the Weather Research and Forecasting Model (WRF) and its Data Assimilation system (WRFDA) are performed for the period during 1 September-31 October, 2017. The results of the two-month 3-hourly cycling experiments indicate that new observational error improves analysis and forecast of wind field and geo-potential height, and has slight improvements on temperature. The Fractions Skill Score (FSS) of the 6-h accumulated precipitation shows that new wind speed and altitude dependent observational error leads to better precipitation forecast skill than the default observational error in the WRFDA does.     

Improvement in Background Error Covariances Using Ensemble Forecasts for Assimilation of High-Resolution Satellite Data

Satellite data obtained over synoptic data-sparse regions such as an ocean contribute toward improving the quality of the initial state of limited-area models. Background error covariances are crucial to the proper distribution of satellite-observed information in variational data assimilation. In the NMC (National Meteorological Center) method, background error covariances are underestimated over data-sparse regions such as an ocean because of small differences between different forecast times. Thus, it is necessary to reconstruct and tune the background error covariances so as to maximize the usefulness of the satellite data for the initial state of limited-area models, especially over an ocean where there is a lack of conventional data. In this study, we attempted to estimate background error covariances so as to provide adequate error statistics for data-sparse regions by using ensemble forecasts of optimal perturbations using bred vectors. The background error covariances estimated by the ensemble method reduced the overestimation of error amplitude obtained by the NMC method. By employing an appropriate horizontal length scale to exclude spurious correlations, the ensemble method produced better results than the NMC method in the assimilation of retrieved satellite data. Because the ensemble method distributes observed information over a limited local area, it would be more useful in the analysis of high-resolution satellite data. Accordingly, the performance of forecast models can be improved over the area where the satellite data are assimilated.     

复杂地形下地面观测资料同化II. 模式地形与观测站地形高度差异代表性误差

第I部分研究结果(徐枝芳等,2007)表明模式与实际观测站地形高度差异对地面观测资料同化效果有较大影响。此文在MM5_3DVAR同化系统中利用近地层相似理论将地面观测资料进行直接三维变分同化分析,考虑模式与实际观测站地形高度差异对同化效果的影响,提出在地面观测误差中增加地形代表性误差来解决这个问题。研究结果表明:地面资料同化分析时,在其观测误差中加入一项新的误差——地形代表性误差,能较好地解决地面资料同化分析中模式与观测站地形高度差异问题;地面资料参与同化分析,在观测误差中加入与模式和实际观测站地形高度差异大小相关的地形代表性误差时,地面观测值对分析值的影响随着地形高度差异代表性误差的加入而减小,同时又部分地将地面观测信息通过变分分析融进分析场,使得低层分析更接近真实场,且地面资料利用率更高,24小时降水数值预报(模拟)的效果较好。     

复杂地形下地面观测资料同化Ⅱ.模式地形与观测站地形高度差异代表性误差

第Ⅰ部分研究结果 (徐枝芳等, 2007) 表明模式与实际观测站地形高度差异对地面观测资料同化效果有较大影响.此文在MM5_3DVAR同化系统中利用近地层相似理论将地面观测资料进行直接三维变分同化分析, 考虑模式与实际观测站地形高度差异对同化效果的影响, 提出在地面观测误差中增加地形代表性误差来解决这个问题.研究结果表明: 地面资料同化分析时, 在其观测误差中加入一项新的误差--地形代表性误差, 能较好地解决地面资料同化分析中模式与观测站地形高度差异问题; 地面资料参与同化分析, 在观测误差中加入与模式和实际观测站地形高度差异大小相关的地形代表性误差时, 地面观测值对分析值的影响随着地形高度差异代表性误差的加入而减小, 同时又部分地将地面观测信息通过变分分析融进分析场, 使得低层分析更接近真实场, 且地面资料利用率更高, 24小时降水数值预报 (模拟) 的效果较好.     

不同模式误差方案在集合Kalman滤波土壤湿度同化中的比较试验

本文主要目的是探讨不同模式误差方案在土壤湿度同化中的性能。基于集合Kalman滤波同化方法和AVIM (Atmosphere-Vegetation Interaction Model) 陆面模式, 利用理想试验对膨胀因子方案 (Covariance Inflation, 简称CI)、 直接随机扰动方案 (Direct Random Disturbance, 简称DRD)、 误差源扰动方案 (Source Random Disturbance, 简称SRD) 等3种模式误差方案的同化效果进行了比较, 讨论了各方案在不同观测误差、 观测层数、 观测间隔情况下的同化性能。试验结果表明在观测误差估计完全准确的情况下, 3种方案都能获得较好的同化效果, 并且SRD方案相对于真值的均方根误差最小。当观测误差估计不准确时, SRD方案的同化效果仍能基本得以保持, 而CI和DRD方案则对观测误差估计更为敏感, 同化效果下降明显。当同化多层观测时, CI和DRD方案由于难以保持不同层观测之间的匹配关系, 同化结果反而变差, 而SRD方案能有效协调同化多层观测, 增加观测层后同化结果有了进一步的改善。当观测时间间隔较大时, CI和DRD方案的同化效果显著下降; 而SRD方案由于包含了一定的误差订正功能, 在观测稀疏时仍能保持较好的同化效果。     

Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction(NWP).To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations,hydrometeor control variables are necessary.Common data assimilation systems theoretically require that the probability density functions(PDFs)of analysis,background,and observation errors should satisfy the Gaussian unbiased assumptions.In this study,a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables,which is modified from the Softmax function and renamed as Quasi-Softmax transform.The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform.The spatial distribution,the non-Gaussian nature of the background errors,and the characteristics of the background errors of hydrometeors in each method are studied.Compared to the logarithmic and Softmax transform,the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent.The results of the D′Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods.The Gaussian transform has been added to the control variable transform to estimate the background error covariances.Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method.The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system,and are promising control variables for data assimilation systems.     

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。     

秒级探空数据随机误差评估

利用2007年6月和2008年6—7月国内GPS探空仪同步比对试验数据及2010年中国阳江国际探空系统比对试验数据,基于现有的探空仪随机误差的间接计算方法,深入分析不同的探空原始数据平滑处理程度对随机误差评估的影响。分析表明:现有的探空仪随机误差评估方法不能完全适用于秒级探空数据,特别是对风、平流层温度和对流层相对湿度这3个要素的随机误差的评估。在同步比对施放中,如果对探空原始数据的平滑处理程度一致,可以利用现有的随机误差评估方法,不会产生明显偏差;反之,如果平滑处理程度差异较大,则间接计算得出的随机误差会明显偏大。在比对施放方案中,为了更好地获取某种型号探空仪的随机误差,建议将多个同型号探空仪同球施放进行比对观测,避免作为参考仪器的其他型号探空仪自身的误差参与计算,影响待测探空仪随机误差的评估。同型号探空仪同球施放的探空仪越多,获取的有效统计数据越多,随机误差的分析越准确。     

中尺度模式的四维伴随同化系统及其同化试验

以中尺度模式MM4为基础，利用伴随码技术改进、完善了MM4伴随模式同化系统，并利用该系统进行了常规资料和非常规资料的伴随模式同化试验，例如加入了可降水量资料等。试验表明：在伴随模式同化系统中加入常规和非常规资料，可以改进初始场，从而改善预报场。     

两种四维奇异值分解同化方法的比较及误差分析

4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。     

两种四维SVD同化方法的比较及误差分析

4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。     

基于地面资料集合均方根滤波同化方案的京津冀暴雨模拟研究

为了更加有效地同化地面自动气象站观测资料,针对模式地形与观测站地形存在的高度差异对同化效果的影响,提出了相应的解决方案。在同化系统的位温和露点观测误差中分别引入位温和露点地形代表性误差,在WRF模式中应用集合均方根滤波方法（EnSRF）同化地面自动气象站观测资料,并对2016年一次京津冀暴雨个例进行数值试验。研究结果表明,同化地面资料后,同化阶段的均方根误差、预报阶段的降水TS评分和前13个时次各要素预报均有整体改进。在观测误差中引入地形代表性误差与引入前相比,风场均方根误差得到整体改进;位温和露点的均方根误差在前期表现并不稳定,在后期有所改进;预报阶段前24 h累计降水与后24 h累计降水TS评分在整体上均有所提高。新方案能够减少高度差异对同化效果的影响。