集合Kalman滤波在土壤湿度同化中的应用

基于非饱和土壤水模型和集合卡尔曼滤波 (Ensemble Kalman Filter, 简称EnKF) 并结合陆面水文模型——可变下渗能力模型 (Variable Infiltration Capacity, 简称VIC模型) 发展了一个土壤湿度同化方案。利用1998年6~8月淮河流域能量和水循环试验 (HUBEX) 项目外场观测试验区——史灌河流域梅山站土壤湿度逐日观测资料及1986~1993年合肥和南阳两站点的土壤湿度旬观测资料进行同化试验, 结果表明该同化方案能完整估计土壤湿度廓线, 同化的土壤湿度与观测资料基本吻合, 反映了土壤湿度的日、 旬、 月、 季变化, 同化方案是合理的。与基于扩展卡尔曼滤波 (Extended Kalman Filter, 简称EKF) 的土壤湿度同化方案的结果比较, 基于EnKF的土壤湿度同化方案易于实现, 且通过选择恰当的集合样本数其同化效果总体上略优于EKF同化方案, 但前者同化时需要花费较多的计算时间。     

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.     

Assimilation of Doppler Radar Observations with an Ensemble Square Root Filter：A Squall Line Case Study

The effectiveness of using an Ensemble Square Root Filter（EnSRF） to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12July 2005 in midwest Shandong Province using the Weather Research and Forecasting（WRF） model.The experimental results show that：（1） The EnSRF system has the potential to initiate a squall line accurately by assimilation of real Doppler radar data.The convective-scale information has been added into the WRF model through radar data assimilation and thus the analyzed fields are improved noticeably.The model spin-up time has been shortened,and the precipitation forecast is improved accordingly.（2） Compared with the control run,the deterministic forecast initiated with the ensemble mean analysis of EnSRF produces more accurate prediction of microphysical fields.The predicted wind and thermal fields are reasonable and in accordance with the characteristics of convective storms.（3） The propagation direction of the squall line from the ensemble mean analysis is consistent with that of the observation,but the propagation speed is larger than the observed.The effective forecast period for this squall line is about 5-6 h,probably because of the nonlinear development of the convective storm.     

WRF-EnKF系统对中国南方一次暴雨过程确定性预报的试验

文章利用美国宾州州立大学的WRF EnKF(Ensemble Kalman Filter)实时预报系统(Real time Penn State WRF EnKF System),针对2013年5月15—16日发生在中国南方的暴雨过程进行了数值预报试验,以初步检验该系统对我国南方降水确定性预报的效果。数值试验采用2013年5月14日08时（北京时）起报的6 h间隔的1°×1° NCEP GFS (globle forecast system) 60 h预报数据（预报到5月16日20时）作为初始条件和边界条件。其中,控制试验不同化任何观测资料,同化试验通过集合卡尔曼滤波方法同化常规探空资料,分别进行确定性预报。结果表明：利用WRF EnKF系统同化常规探空资料,显著改善了数值预报的初始场,减小了各物理量的预报偏差和预报均方根误差,进而提高了此次暴雨过程的降水落区和强度的预报准确率。     

Using analysis state to construct a forecast error covariance matrix in ensemble Kalman filter assimilation

Correctly estimating the forecast error covariance matrix is a key step in any data assimilation scheme. If it is not correctly estimated, the assimilated states could be far from the true states. A popular method to address this problem is error covariance matrix inflation. That is, to multiply the forecast error covariance matrix by an appropriate factor. In this paper, analysis states are used to construct the forecast error covariance matrix and an adaptive estimation procedure associated with the error covariance matrix inflation technique is developed. The proposed assimilation scheme was tested on the Lorenz-96 model and 2D Shallow Water Equation model, both of which are associated with spatially correlated observational systems. The experiments showed that by introducing the proposed structure of the forecast error covariance matrix and applying its adaptive estimation procedure, the assimilation results were further improved.     

再分析资料和陆面数据同化资料土壤湿度产品在中国北方地区的适用性评估

土壤湿度是地球系统模拟的重要参数之一,准确获得其时空分布和变化特征是研究陆-气相互作用的基础。再分析资料和陆面数据同化资料均可提供全球或区域高分辨率土壤湿度产品,但在使用前需要对其进行评估分析。利用土壤湿度观测数据,计算ERA5、ERA5-Land、NCEP-DOE R2、CRA40再分析资料和GLDAS-Noah、GLDAS-CLSM、CLDAS陆面数据同化资料土壤湿度产品与观测数据的中位数、模拟偏差、相关系数等统计指标,并分季节和气候区讨论不同土壤湿度产品在中国北方地区的模拟效果。结果表明：整体来看,CRA40与观测值的相关性最好,ERA5和ERA5-Land分别对干中心、湿中心模拟效果更好,GLDAS-Noah对于较干土壤地区模拟略偏湿,CLDAS对较湿土壤地区模拟结果以系统性偏干为主,NCEP-DOE R2和GLDAS-CLSM模拟效果较差;ERA5、ERA5-Land、NCEP-DOE R2、GLDAS-Noah和CLDAS在所有季节均为模拟正偏差,春季模拟效果较好的是CRA40、ERA5-Land,夏季和秋季ERA5-Land、ERA5和CRA40与观测值相关性较好,不同产...     

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。     

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。     

Assimilating Best Track Minimum Sea Level Pressure Data Together with Doppler Radar Data Using an Ensemble Kalman Filter for Hurricane Ike (2008) at a Cloud-Resolving Resolution

Extending an earlier study, the best track minimum sea level pressure (MSLP) data are assimilated for landfalling Hurricane Ike (2008) using an ensemble Kalman filter (EnKF), in addition to data from two coastal ground-based Doppler radars, at a 4-km grid spacing. Treated as a sea level pressure observation, the MSLP assimilation by the EnKF enhances the hurricane warm core structure and results in a stronger and deeper analyzed vortex than that in the GFS (Global Forecast System) analysis; it also improves the subsequent 18-h hurricane intensity and track forecasts. With a 2-h total assimilation window length, the assimilation of MSLP data interpolated to 10-min intervals results in more balanced analyses with smaller subsequent forecast error growth and better intensity and track forecasts than when the data are assimilated every 60 minutes. Radar data are always assimilated at 10-min intervals. For both intensity and track forecasts, assimilating MSLP only outperforms assimilating radar reflectivity (Z) only. For intensity forecast, assimilating MSLP at 10-min intervals outperforms radar radial wind (Vr) data (assimilated at 10-min intervals), but assimilating MSLP at 60-min intervals fails to beat Vr data. For track forecast, MSLP assimilation has a slightly (noticeably) larger positive impact than Vr(Z) data. When Vr or Z is combined with MSLP, both intensity and track forecasts are improved more than the assimilation of individual observation type. When the total assimilation window length is reduced to 1h or less, the assimilation of MSLP alone even at 10-min intervals produces poorer 18-h intensity forecasts than assimilating Vr only, indicating that many assimilation cycles are needed to establish balanced analyses when MSLP data alone are assimilated; this is due to the very limited pieces of information that MSLP data provide.     

THE EFFECT OF SAMPLE OPTIMIZATION ON THE ENSEMBLE KALMAN FILTER IN FORECASTING TYPHOON RAMMASUN (2014)

In a limited number of ensembles, some samples do not adequately reflect the true atmospheric state and can in turn affect forecast performance. This study explored the feasibility of sample optimization using the ensemble Kalman filter (EnKF) for a simulation of the 2014 Super Typhoon Rammasun, which made landfall in southern China in July 2014. Under the premise of sufficient ensemble spread, keeping samples with a good fit to observations and eliminating those with poor fit can affect the performance of EnKF. In the sample optimization, states were selected based on the sample spatial correlation between the ensemble state and observations. The method discarded ensemble states that were less representative and, to maintain the overall ensemble size, generated new ensemble states by reproducing them from ensemble states with a good fit by adding random noise. Sample selection was performed based on radar echo data. Results showed that applying EnKF with optimized samples improved the estimated track, intensity, precipitation distribution, and inner-core structure of Typhoon Rammasun. Therefore, the authors proposed that distinguishing between samples with good and poor fits is vital for ensemble prediction, suggesting that sample optimization is necessary to the effective use of EnKF.