ON THE OPTIMAL BACKGROUND ERROR COVARIANCES: DIFFERENT SCALE ERRORS' CONTRIBUTION

The large-scale and small-scale errors could affect background error covariances for a regional numerical model with the specified grid resolution.Based on the different background error covariances influenced by different scale errors,this study tries to construct a so-called"optimal background error covariances"to consider the interactions among different scale errors.For this purpose,a linear combination of the forecast differences influenced by information of errors at different scales is used to construct the new forecast differences for estimating optimal background error covariances.By adjusting the relative weight of the forecast differences influenced by information of smaller-scale errors,the relative influence of different scale errors on optimal background error covariances can be changed.For a heavy rainfall case,the corresponding optimal background error covariances can be estimated through choosing proper weighting factor for forecast differences influenced by information of smaller-scale errors.The data assimilation and forecast with these optimal covariances show that,the corresponding analyses and forecasts can lead to superior quality,compared with those using covariances that just introduce influences of larger-or smallerscale errors.Due to the interactions among different scale errors included in optimal background error covariances,relevant analysis increments can properly describe weather systems(processes)at different scales,such as dynamic lifting,thermodynamic instability and advection of moisture at large scale,high-level and low-level jet at synoptic scale,and convective systems at mesoscale and small scale,as well as their interactions.As a result,the corresponding forecasts can be improved.

Ocean Data Assimilation with Background Error Covariance Derived from OGCM Outputs

The background error covariance plays an important role in modern data assimilation and analysis systems by determining the spatial spreading of information in the data. A novel method based on model output is proposed to estimate background error covariance for use in Optimum Interpolation. At every model level, anisotropic correlation scales are obtained that give a more detailed description of the spatial correlation structure. Furthermore, the impact of the background field itself is included in the background error covariance. The methodology of the estimation is presented and the structure of the covariance is examined. The results of 20-year assimilation experiments are compared with observations from TOGA-TAO (The Tropical Ocean-Global Atmosphere-Tropical Atmosphere Ocean) array and other analysis data.

VARIATIONAL DATA ASSIMILATION USING WAVELET BACKGROUND ERROR COVARIANCE: INITIALIZATION OF TYPHOON KAEMI (2006)

Background error covariance plays an important role in any variational data assimilation system, because it determines how information from observations is spread in model space and between different model variables. In this paper, the use of orthogonal wavelets in representation of background error covariance over a limited area is studied. Based on the WRF model and its 3D-VAR system, an algorithm using orthogonal wavelets to model background error covariance is developed. Because each wavelet function contains information on both position and scale, using a diagonal correlation matrix in wavelet space gives the possibility to represent some anisotropic and inhomogeneous characteristics of background error covariance. The experiments show that local correlation functions are better modeled than spectral methods. The formulation of wavelet background error covariance is tested with the typhoon Kaemi (2006). The results of experiments indicate that the subsequent forecasts of typhoon Kaemi’s track and intensity are significantly improved by the new method.

A background error covariance model of significant wave height employing Monte Carlo simulation

The quality of background error statistics is one of the key components for successful assimilation of observations in a numerical model.The background error covariance(BEC) of ocean waves is generally estimated under an assumption that it is stationary over a period of time and uniform over a domain.However,error statistics are in fact functions of the physical processes governing the meteorological situation and vary with the wave condition.In this paper,we simulated the BEC of the significant wave height(SWH) employing Monte Carlo methods.An interesting result is that the BEC varies consistently with the mean wave direction(MWD).In the model domain,the BEC of the SWH decreases significantly when the MWD changes abruptly.A new BEC model of the SWH based on the correlation between the BEC and MWD was then developed.A case study of regional data assimilation was performed,where the SWH observations of buoy 22001 were used to assess the SWH hindcast.The results show that the new BEC model benefits wave prediction and allows reasonable approximations of anisotropy and inhomogeneous errors.

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.

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.

Ensemble-based diurnally varying background error covariances and their impact on short-term weather forecasting

Background error covariance(BEC)plays an essential role in variational data assimilation.Most variational data assimilation systems still use static BEC.Actually,the characteristics of BEC vary with season,day,and even hour of the background.National Meteorological Center-based diurnally varying BECs had been proposed,but the diurnal variation characteristics were gained by climatic samples.Ensemble methods can obtain the background error characteristics that suit the samples in the current moment.Therefore,to gain more reasonable diurnally varying BECs,in this study,ensemble-based diurnally varying BECs are generated and the diurnal variation characteristics are discussed.Their impacts are then evaluated by cycling data assimilation and forecasting experiments for a week based on the operational China Meteorological Administration-Beijing system.Clear diurnal variation in the standard deviation of ensemble forecasts and ensemble-based BECs can be identified,consistent with the diurnal variation characteristics of the atmosphere.The results of one-week cycling data assimilation and forecasting show that the application of diurnally varying BECs reduces the RMSEs in the analysis and 6-h forecast.Detailed analysis of a convective rainfall case shows that the distribution of the accumulated precipitation forecast using the diurnally varying BECs is closer to the observation than using the static BEC.Besides,the cycle-averaged precipitation scores in all magnitudes are improved,especially for the heavy precipitation,indicating the potential of using diurnally varying BEC in operational applications.

基于GRAPES全球分析系统的Hybrid-3DVAR混合同化研究

本文基于我国自主研发的GRAPES全球3DVAR同化系统,利用NCEP全球集合预报产品和time-lagged方法,针对膨胀系数、集合样本数和集合权重系数,开展了每日4次、连续一周的GRAPES全球Hybrid-3DVAR混合同化研究。结果表明:所有试验中,集合样本取60个、集合权重取0.5时,得到的混合同化分析和预报误差最小;在该混合同化系统中,在高层也考虑静态背景误差协方差和集合背景误差协方差的耦合,可避免混合同化方案分析场误差在150 hPa及以上过大,并超过3DVAR分析场误差的情况。

INFLUENCE OF DIFFERENT-SCALE ERRORS INTERACTIONS ON ANALYSIS AND FORECAST OF REGIONAL NWP MODEL

In the previous study, the influences of introducing larger- and smaller-scale errors on the background error covariances estimated at the given scales were investigated, respectively. This study used the eovariances obtained in the previous study in the data assimilation and model forecast system based on three-dimensional variational method and the Weather Research and Forecasting model. In this study, analyses and forecasts from this system with different covariances for a period of one month were compared, and the causes for differing results were presented. The varia- tions of analysis increments with different-scale errors are consistent with those of variances and correlations of back- ground errors that were reported in the previous paper. In particular, the introduction of smaller-scale errors leads to greater amplitudes in analysis increments for medium-scale wind at the heights of both high- and low-level jets. Tem- perature and humidity analysis increments are greater at the corresponding scales at the middle- and upper-levels. These analysis increments could improve the intensity of the jet-convection system that includes jets at different levels and the coupling between them that is associated with latent heat release. These changes in analyses will contribute to more ac- curate wind and temperature forecasts in the corresponding areas. When smaller-scale errors are included, humidity analysis increments are significantly enhanced at large scales and lower levels, to moisten southern analyses. Thus, dry bias can be corrected, which will improve humidity forecasts. Moreover, the inclusion of larger- （smaller-） scale errors will be beneficial for the accuracy of forecasts of heavy （light） precipitation at large （small） scales because of the ampli- fication （diminution） of the intensity and area in precipitation forecasts.

CMA-MESO逐时快速更新同化预报系统及其短临预报效果初步分析

基于CMA-MESO模式水平3 km分辨率3 h循环的快速更新同化预报系统,本文建立逐小时的分析预报循环系统,并且通过采用5种尺度叠加的高斯相关模型和引入各向异性的水平相关尺度方案来改进背景误差水平相关结构,同时考察引入全球大尺度信息方案对逐小时循环的分析和预报影响。通过对2020年7月19日华东强对流天气过程的数值模拟表明:(1)逐小时循环吸收了更多的高频观测资料和循环中采用更临近的1 h预报场作为背景场,分析和降水短临预报质量整体比3 h循环有所提高;(2)在区域分析中逐时引入全球预报场的大尺度信息会削弱区域观测资料的影响,对预报会有不利影响;(3)改进的五种尺度叠加高斯相关模型和各向异性的水平相关尺度主要使风场背景误差水平相关系数的描述更接近样本的统计结果,因而在逐1 h循环中风场分析更靠近观测,华东强对流过程的组合反射率和降水短临预报更接近实况。

快速更新循环同化系统的背景场误差协方差日变化特征研究及初步应用

目前多数快速更新循环同化系统在各分析时刻常使用固定的背景场误差协方差。为在快速更新循环同化系统中采用日变化的背景场误差协方差,基于RMAPS-ST系统分析了其夏季和冬季日变化背景场误差协方差特征,并进行了同化及预报对比试验。结果表明,该系统夏、冬两季的背景场误差协方差均呈现出明显的日变化特征,且夜间各变量(U、V、T、RH)的误差标准差与特征值均大于日间,反映模式系统夜间的预报误差大于日间;而夏季各变量误差标准差和特征值大于冬季,也说明系统在夏季的模式预报误差比冬季大;连续3 d的循环同化试验初步表明,采用日变化背景场误差协方差可以提高同化及预报效果。

GSI-3DVAR背景误差协方差水平相关特征尺度对地面自动气象站资料同化的适应性研究

基于华东地区3 km分辨率WRF(Weather Research and Forecasting)模式和高密度地面自动气象站(AWS)观测,研究GSI-3DVAR同化系统的R_(HZSCL)对AWS观测的地面温度和风观测同化的敏感性。结果表明:运用GSI-3DVAR同化地面AWS观测时,R_(HZSCL)的取值较为敏感;选取合适的R_(HZSCL)能有效改进地面分析场精度,相较于背景场地面温度和地面矢量风差(VWD)RMSE均可减小35%以上。当R_(HZSCL)过大会导致温度高、低值中心的影响范围过大,风分析场较为平滑,无法反映出中小尺度环流结构。但R_(HZSCL)过小则会使得温度分析场增加误差,并导致风分析场出现虚假大风。观测密度稀疏化的敏感性试验结果表明,地面温度场及风场所适应的最优R_(HZSCL)皆随着观测密度的增大而相应减小。

不同控制变量方案对广州暴雨过程雷达资料同化和预报的影响

为了探讨WRFDA同化系统中不同控制变量方案(CV5,CV6和CV7)所构建的背景误差协方差对雷达资料同化的影响,本文以2017年5月7日发生在广州的一次暖区暴雨为研究个例,开展了不同控制变量方案的单点观测同化试验和雷达同化试验(Exp-CV5,Exp-CV6和Exp-CV7),并对同化试验结果进行诊断分析。单点试验和单次雷达资料同化试验的分析结果表明,Exp-CV6对湿度场的影响最大且在大气中层的比湿均方根误差最小,而Exp-CV7分析增量的影响更集中且梯度更大,更有利于保留中小尺度信息,对风场的模拟效果最好。经过3 h雷达资料循环同化后,Exp-CV7可以更准确地模拟出对流系统的结构,并对本次暖区暴雨雨带与强降水中心位置的预报效果最佳,其次是Exp-CV6。这主要是因为CV7方案对动力场的调整更有利于局地对流的发展,而CV6方案对湿度场的调整较CV5方案更有优势。

The importance of data assimilation components for initial conditions and subsequent error growth

Despite a specific data assimilation method,data assimilation(DA)in general can be decomposed into components of the prior information,observation forward operator that is given by the observation type,observation error covariances,and background error covariances.In a classic Lorenz model,the influences of the DA components on the initial conditions(ICs)and subsequent forecasts are systematically investigated,which could provide a theoretical basis for the design of DA for different scales of interests.The forecast errors undergo three typical stages:a slow growth stage from 0 h to 5 d,a fast growth stage from 5 d to around 15 d with significantly different error growth rates for ensemble and deterministic forecasts,and a saturation stage after 15 d.Assimilation strategies that provide more accurate ICs can improve the predictability.Cycling assimilation is superior to offline assimilation,and a flow-dependent background error covariance matrix(Pf)provides better analyses than a static background error covariance matrix(B)for instantaneous observations and frequent time-averaged observations;but the opposite is true for infrequent time-averaged observations,since cycling simulation cannot construct informative priors when the model lacks predictive skills and the flow-dependent Pf cannot effectively extract information from low-informative observations as the static B.Instantaneous observations contain more information than time-averaged observations,thus the former is preferred,especially for infrequent observing systems.Moreover,ensemble forecasts have advantages over deterministic forecasts,and the advantages are enlarged with less informative observations and lower predictive-skill model priors.

WRF模式三维变分中背景误差协方差估计

利用WRF模式2008年5—10月逐日预报结果,通过NMC方法进行背景误差协方差(B)估计。给出其结构特征,进行单点数值试验,并利用不同B进行1个月的数值模拟试验,检验模拟降水效果。结果表明:通过单点数值试验验证估算的B结构合理。不同的B,资料同化过程差别较大,应用重新统计的B,同化效率更高,目标函数收敛更稳定。模式模拟降水预报效果有所差别,经过重新统计与预报模式区域和各种参数相匹配的B,模式预报效果在中雨及以上量级优于通用的B预报效果。因此,在应用三维变分同化系统时,重新统计B非常必要。

区域三维变分同化中背景误差协方差的模拟

背景误差协方差(B)是变分同化中的一个重要部分,极大地影响同化系统输出的分析场。由于计算和指定B中有关统计量需要巨大的资料存储量和计算量,因此进行相关的研究较为困难。本文首先论述了B在变分同化中的重要性以及进行模拟的必要性;接着介绍了美国NMC方法的原理,并研究将其应用到区域三维变分同化中的方法;然后利用WRF模式生成的预报场差值集合对有关统计量进行了估计。揭示了以下结论:通过使用平衡变换和回归系数,控制变量被限制在较小范围内,保证了分析场的质量;流函数第一全局特征向量在200hPa附近的最大分量,表示了急流层中强西风误差;流函数前五个全局特征向量在低层与中高层之间是负相关的;非平衡温度和相对湿度的特征长度尺度比流函数和非平衡速度势的值要小,说明它们是局地性较强的量。流函数和非平衡速度势的特征长度尺度随垂直模态数的增大快速减小,而相对湿度和非平衡温度的特征长度尺度随垂直模态数的变化较为平缓。

背景误差协方差变量平衡特征及其对台风同化和预报的影响

构造合理的背景场误差协方差是做好资料同化的关键。分析了背景误差协方差中变量相关关系在台风季节和非台风季节隐含的不同动力平衡特征,并讨论其对台风同化和预报的影响。分析发现,与非台风季节相比,在台风季节温度与非平衡速度势具有更强的动力相关性,拟相对湿度与其他控制变量的相关性也更显著。这些动力相关性在背景场误差中协方差的引入,将在同化分析过程中使得观测信息可以合理地对同化分析场产生影响。台风循环同化和预报的结果验证了对变量平衡特征的分析:背景误差协方差中新平衡关系的建立,对同化和预报有较大的正面影响,尤其是相对湿度和其他控制变量相关的建立,明显改善了台风路径、强度和降水的预报效果。

GRAPES全球变分同化背景误差协方差的改进及对分析预报的影响：背景误差协方差三维结构的估计

回顾并详细推导了估计背景误差协方差统计特征的美国国家气象中心(NMC)方法及其优缺点;采用NMC方法系统地估计了新版GRAPES全球模式的背景误差方差、水平相关特征尺度和垂直相关结构,并与欧洲中心模式结果进行了比较。结果表明,目前GRAPES全球模式的背景误差方差比以前有了显著减小;水平相关特征尺度随纬度和高度有显著变化;背景误差垂直相关结构与欧洲中心模式结果非常一致,相比经验公式结果更具物理意义,同时,单点试验结果也表明,更新后的垂直相关结构产生的分析增量更合理。通过与欧洲中心模式背景误差协方差三维结构的对比,分析了不同模式间背景误差协方差的异同及GRAPES全球同化分析系统目前存在的一些不足及可能原因。为新版GRAPES全球模式的三维变分系统提供了基本的背景误差协方差的三维结构。

资料同化中背景场位势高度误差统计分析的研究

在客观分析中,背景误差协方差对观测信息的传播和平滑、反映不同变量之间的关系有着非常重要的作用。构造合理的背景误差协方差矩阵对于同化系统至关重要,甚至会决定同化分析的好坏。作者主要利用观测余差方法,用T213预报资料和无线电探空观测资料统计我国区域的背景位势高度误差协方差样本,分析背景误差协方差场的结构特征和拟合误差场的空间分布。

青藏高原和华东地区背景误差协方差特征的对比研究

背景误差协方差特征与区域的天气气候特征密切相关。为了更好地理解中国华东地区和青藏高原地区的背景误差协方差特征,利用夏季一个月的模拟结果,以最新的多元变量相关的背景误差协方差模型为基础,通过提取隐含背景误差协方差中的变量相关系数、特征值、特征向量和特征长度尺度等,对这两个区域的背景误差协方差特征进行比较和分析。结果表明,相对于华东地区,青藏高原地区变量之间的影响关系更显著,背景场的误差更大,大气特征具有更强的局地性。对青藏高原地区资料同化而言,观测资料占有更大的权重和更小的影响范围,对青藏高原地区观测资料提出了更高的要求。