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。     

台风预报误差的流依赖特征及混合资料同化中最优耦合系数

基于集合卡尔曼变换与三维变分(ETKF-3DVAR)混合资料同化系统和欧洲中期天气预报中心(ECWMF)的全球集合预报,以"梅花"台风为例,分析了台风系统预报误差的流依赖特征,讨论了耦合系数在混合同化和预报中的敏感性及其对预报质量的影响。结果显示,台风系统的预报误差协方差具有显著的中小尺度结构特征,集合估计的预报误差协方差结构能够再现其流依赖属性。相对于3DVAR方案,混合资料同化方案的最优耦合系数对台风系统的分析和预报质量具有更好的改善;但不同的耦合系数对台风路径预报有明显的影响,不合适的耦合系数甚至可能导致更坏的结果,只有耦合了相对合适的预报误差协方差的流依赖信息,混合资料同化方案才可能对分析和预报质量有正效果。这表明在混合资料同化系统中,构造一种具有自适应能力的耦合权重函数,实现相对最优权重的自动选择,对充分发挥混合资料同化方案的潜在优势具有重要意义。     

Estimating the Soil Moisture Profile by Assimilating Near-Surface Observations with the Ensemble Kalman Filter （EnKF）

The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter （EnKF） assimilation scheme, including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The ＂true＂ soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d^-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.     

集合卡尔曼滤波同化多普勒雷达资料的数值试验

利用集合卡尔曼滤波(EnKF)在云数值模式中同化模拟多普勒雷达资料,并考察了不同条件下EnKF同化方法的性能.结果显示,经过几个同化周期后,EnKF分析结果非常接近真值.单多普勒雷达资料EnKF同化对雷达位置不太敏感,双雷达资料同化结果在同化的初期阶段比单雷达资料同化结果准确.同化由反射率导出的雨水比直接同化反射率资料更有效,联合同化径向速度和雨水有利于提高同化分析效果.协方差对EnKF同化效果起着非常重要的作用,考虑模式全部预报变量与径向速度协方差的同化效果比仅考虑速度场与径向速度协方差的同化效果好.雷达资料缺值降低了同化效果,此时增加地面常规观测资料的同化可以明显提高同化分析效果.EnKF同化技术对雷达观测资料误差不太敏感.初始集合对同化分析有较大影响.EnKF同化受集合大小和观测资料影响半径.同化对模式误差较敏感.利用EnKF同化双多普勒雷达资料,分析了一次梅雨锋暴雨过程的中尺度结构.结果表明,EnKF同化技术能够从双多普勒雷达资料反演暴雨中尺度系统的动力场、热力场和微物理场,反演的风场是较准确的,反演的热力场和微物理场分布也是基本合理的.中低层切变线是此次暴雨的主要动力特征,对流云表现为低层辐合、高层辐散并有垂直上升运动伴随,其热力特征表现为低层是低压区,高层为高压区,中部为暖区而上、下部为冷区,水汽、云水和雨水分别集中在对流云体内、上升气流区和强回波区.     

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。     

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。     

An Ensemble-Based Three-Dimensional Variational Assimilation Method for Land Data Assimilation

Land surface models are often highly nonlinear with model physics that contain parameterized discontinuities. These model attributes severely limit the application of advanced variational data assimilation methods into land data assimilation. The ensemble Kalman filter （EnKF） has been widely employed for land data assimilation because of its simple conceptual formulation and relative ease of implementation. An updated ensemble-based three-dimensional variational assimilation （En3-DVar） method is proposed for land data assimilation This new method incorporates Monte Carlo sampling strategies into the 3-D variational data assimilation framework. The proper orthogonal decomposition （POD） technique is used to efficiently approximate a forecast ensemble produced by the Monte Carlo method in a 3-D space that uses a set of base vectors that span the ensemble. The data assimilation process is thus significantly simplified. Our assimilation experiments indicate that this new En3-DVar method considerably outperforms the EnKF method by increasing assimilation precision. Furthermore, computational costs for the new En3-DVar method are much lower than for the EnKF method.     

华南暴雨区域集合预报中不同同化方案的影响试验研究

基于全球集合预报系统(GEFS)资料,利用WRF中尺度模式及GEFS动力降尺度获取区域集合预报初值场,通过对同化后的分析场进行模式积分实现华南前汛期区域集合预报。对2019年6月10日的一次华南前汛期暴雨过程进行不同同化方案的试验:混合同化(Hybrid)、三维变分(3Dvar)、集合卡尔曼滤波(EnKF)和对比试验(Ctrl)四组试验的对比分析,探讨具有不同背景误差协方差矩阵的同化方案对区域集合预报集合扰动和集合离散随时间演变特征的影响,评估不同试验的降水模拟效果。(1) Hybrid对模式初始场有较好的改善作用,而3DVar和EnKF对初始场的改善作用不明显。(2) 对风场、温度场和湿度场,在前期预报中Hybrid的预报误差小于3DVar和EnKF,在中后期的预报中,3DVar和EnKF的预报误差得到改善,且好于Hybrid。同样,集合扰动能量,Hybrid和Ctrl在前期预报发展好于3DVar和EnKF,而在中后期的预报3DVar和EnKF好于Hybrid和Ctrl。(3) 从24 h累积降水评分中,整体上同化试验好于Ctrl,3DVar和EnKF好于Hybrid,且3DVar对大中雨级别的降水评分较好,而EnKF对暴雨以上级别的降水评分较好。(4) 对于集合统计检验分析,同化试验的AUC值都大于Ctrl的AUC值,24 h累积降水量阈值在10~100 mm的AUC值,3DVar最好;而125 mm阈值的AUC值,EnKF最好。      

A ＂Dressed＂ Ensemble Kalman Filter Using the Hybrid Coordinate Ocean Model in the Pacific

The computational cost required by the Ensemble Kalman Filter (EnKF) is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation (OI) or three-dimension variational assimilation (3DVAR). Ensemble optimal interpolation (EnOI), a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of ``dressing' a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term ``dressing' means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF (DrEnKF for short) scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model (HYCOM) over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors (RMSE) at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.     

Analyses and forecasts of a tornadic supercell outbreak using a 3DVAR system ensemble

As part of NOAA’s "Warn-On-Forecast" initiative, a convective-scale data assimilation and prediction system was developed using the WRF-ARW model and ARPS 3DVAR data assimilation technique. The system was then evaluated using retrospective short-range ensemble analyses and probabilistic forecasts of the tornadic supercell outbreak event that occurred on 24 May 2011 in Oklahoma, USA. A 36-member multi-physics ensemble system provided the initial and boundary conditions for a 3-km convective-scale ensemble system. Radial velocity and reflectivity observations from four WSR-88 Ds were assimilated into the ensemble using the ARPS 3DVAR technique. Five data assimilation and forecast experiments were conducted to evaluate the sensitivity of the system to data assimilation frequencies, in-cloud temperature adjustment schemes, and fixed- and mixed-microphysics ensembles. The results indicated that the experiment with 5-min assimilation frequency quickly built up the storm and produced a more accurate analysis compared with the 10-min assimilation frequency experiment. The predicted vertical vorticity from the moist-adiabatic in-cloud temperature adjustment scheme was larger in magnitude than that from the latent heat scheme. Cycled data assimilation yielded good forecasts, where the ensemble probability of high vertical vorticity matched reasonably well with the observed tornado damage path. Overall, the results of the study suggest that the 3DVAR analysis and forecast system can provide reasonable forecasts of tornadic supercell storms.     

A Prototype Regional GSI-based EnKF-Variational Hybrid Data Assimilation System for the Rapid Refresh Forecasting System:Dual-Resolution Implementation and Testing Results

A dual-resolution(DR) version of a regional ensemble Kalman filter(EnKF)-3D ensemble variational(3DEnVar) coupled hybrid data assimilation system is implemented as a prototype for the operational Rapid Refresh forecasting system. The DR 3DEnVar system combines a high-resolution(HR) deterministic background forecast with lower-resolution(LR) EnKF ensemble perturbations used for flow-dependent background error covariance to produce a HR analysis. The computational cost is substantially reduced by running the ensemble forecasts and EnKF analyses at LR. The DR 3DEnVar system is tested with 3-h cycles over a 9-day period using a 40/13-km grid spacing combination. The HR forecasts from the DR hybrid analyses are compared with forecasts launched from HR Gridpoint Statistical Interpolation(GSI) 3D variational(3DVar)analyses, and single LR hybrid analyses interpolated to the HR grid. With the DR 3DEnVar system, a 90% weight for the ensemble covariance yields the lowest forecast errors and the DR hybrid system clearly outperforms the HR GSI 3DVar.Humidity and wind forecasts are also better than those launched from interpolated LR hybrid analyses, but the temperature forecasts are slightly worse. The humidity forecasts are improved most. For precipitation forecasts, the DR 3DEnVar always outperforms HR GSI 3DVar. It also outperforms the LR 3DEnVar, except for the initial forecast period and lower thresholds.     

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.     

Assimilating AMSU-a radiance data with the WRF hybrid En3DVAR system for track predictions of Typhoon Megi (2010)

The impact of assimilating radiances from the Advanced Microwave Sounding Unit-A (AMSU-A) on the track prediction of Typhoon Megi (2010) was studied using the Weather Research and Forecasting (WRF) model and a hybrid ensemble three-dimensional variational (En3DVAR) data assimilation (DA) system. The influences of tuning the length scale and variance scale factors related to the static background error covariance (BEC) on the track forecast of the typhoon were studied. The results show that, in typhoon radiance data assimilation, a moderate length scale factor improves the prediction of the typhoon track. The assimilation of AMSU-A radiances using 3DVAR had a slight positive impact on track forecasts, even when the static BEC was carefully tuned to optimize its performance. When the hybrid DA was employed, the track forecast was significantly improved, especially for the sharp northward turn after crossing the Philippines, with the flow-dependent ensemble covariance. The flow-dependent BEC can be estimated by the hybrid DA and was capable of adjusting the position of the typhoon systematically. The impacts of the typhoon-specific BEC derived from ensemble forecasts were revealed by comparing the analysis increments and forecasts generated by the hybrid DA and 3DVAR. Additionally, for 24 h forecasts, the hybrid DA experiment with use of the full flow-dependent background error substantially outperformed 3DVAR in terms of the horizontal winds and temperature in the lower and mid-troposphere and for moisture at all levels.     

GRAPES混合同化方法在青藏高原区域的初步试验

针对青藏高原地区气象观测站点稀少和模式同化分析质量较低的问题,将GRAPES区域集合变分(En-3DVAR)混合同化系统应用于青藏高原地区,进行了单点理想试验和真实观测资料同化分析预报试验,分析评估青藏高原混合同化分析增量及预报误差的水平垂直结构特征及其合理性,并与中国东部平原地区进行比对。单点理想试验表明,En-3DVAR混合同化系统中背景误差协方差具备流依赖属性。真实资料混合同化试验结果表明,基于集合预报估计的分析增量具有流依赖的特征,特别是在高原地区和槽脊系统附近;青藏高原地区分析场的绝对误差总体低于3DVAR系统,其平均绝对误差在中层和高层低于平原地区,说明在青藏高原地区的改进效果略优于平原地区。需要关注的是,青藏高原地区En-3DVAR混合同化分析增量总体大于3DVAR,特别是近地面层u风分量分析增量明显偏大,这可能与青藏高原复杂地形有关。     

集合卡尔曼滤波同化多普勒雷达资料的观测系统模拟试验

本文将集合卡尔曼滤波同化技术应用到对流尺度系统中,实施了基于WRF模式的同化单部多普勒雷达径向风和反射率因子的观测系统模拟试验,验证了其在对流尺度中应用的可行性和有效性,并对同化系统的特性进行了探讨。试验表明:WRF-EnKF雷达资料同化系统能较准确分析模式风暴的流场、热力场、微物理量场的细致特征;几乎所有变量的预报和分析误差经过同化循环后都能显著下降,同化分析基本上能使预报场在各层上都有所改进,对预报场误差较大层次的更正更为显著;约8个同化循环后,EnKF能在雷达反射率、径向风观测与背景场间建立较可靠的相关关系,使模式各变量场能被准确分析更新,背景场误差协方差在水平方向和垂直方向都有着复杂的结构,是高度非均匀、各项异性和流依赖的;集合平均分析场做的确定性预报在短时间内能较好保持真值场风暴的细节结构,但预报误差增长较快。     

Assimilation of Hourly Surface Observations with the Canadian High-Resolution Ensemble Kalman Filter

An hourly-cycling ensemble Kalman filter (EnKF) working at 2.5?km horizontal grid spacing is implemented over southern Ontario (Canada) to assimilate Meteorological Terminal Aviation Routine Weather Reports (METARs) in addition to the observations assimilated operationally at the Canadian Meteorological Centre. This high-resolution EnKF (HREnKF) system employs ensemble land analyses and perturbed roughness length to prevent an ensemble spread that is too small near the surface. The HREnKF then performs continuously for a four-day period, from which twelve-hour ensemble forecasts are launched every six hours. The impact on analyses and short-term forecasts of assimilating METAR data is given special attention.

It is shown that using ensemble land surface analyses increases near-surface ensemble spreads for temperature and specific humidity. Perturbing roughness length enlarges the spread for surface wind. Given sufficient ensemble spread, the four-day case study shows that the near-surface model state is brought closer to surface observations during the cycling process. The impact of assimilating surface data can also be seen at higher levels by using aircraft reports for verification. The ensemble forecast verification suggests that METAR data assimilation improves ensemble forecasts of air temperature and dewpoint near the surface up to a lead time of six hours or even longer. However, only minor improvement is found in surface wind forecasts.     

Hybrid ETKF-3DVAR方法同化多普勒雷达速度观测资料Ⅰ:模拟资料试验

利用WRF(Weather research and forecasting)模式及模式模拟的资料,采用Hybrid ETKF-3DVAR(ensemble transform Kalman filter-three-dimensional variational data assimilation)方法同化模拟雷达观测资料。该混合同化方法将集合转换卡尔曼滤波(ensemble transform Kalman filter)得到的集合样本扰动通过转换矩阵直接作用到背景场上,利用顺序滤波的思想得到分析扰动场;然后通过增加额外控制变量的方式把"流依赖"的集合协方差信息引入到变分目标函数中去,在3DVAR框架基础下与观测数据进行融合,从而给出分析场的最优估计。试验结果表明,Hybrid ETKF-3DVAR同化方法相比传统3DVAR可以提供更为准确的分析场,Hybrid方法雷达资料初始化模拟的台风涡旋结构与位置比3DVAR更加接近"真实场",对台风路径预报也有明显改进。通过对比Hybrid S试验与Hybrid F试验发现,Hybrid的正效果主要来源于混合背景误差协方差中的"流依赖"信息,集合平均场代替确定性背景场带来的效果并不显著。     

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。     

Dust storm ensemble forecast experiments in East Asia

The ensemble Kalman filter (EnKF), as a unified approach to both data assimilation and ensemble forecasting problems, is used to investigate the performance of dust storm ensemble forecasting targeting a dust episode in the East Asia during 23–30 May 2007. The errors in the input wind field, dust emission intensity, and dry deposition velocity are among important model uncertainties and are considered in the model error perturbations. These model errors are not assumed to have zero-means. The model error me...     

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。