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Estimating Background Error Covariance in Regional 3DVAR of WRF
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摘要: 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。Abstract: In order to explore the statistical structure of background error covariance ( B ) and its impact on initial field and three-dimensional variational data assimilation system, based on day by day WRF model forecast data from May to October in 2008, B is estimated using NMC method. The statistical structure of B is analyzed and validated with single ideal experiment, showing that it can reasonably reflect the geostrophic balance relationships and the relationships among multivariable in middle and lower latitudes. The characteristics of B structure are presented as well.A B file provided in three-dimensional variational data assimilation system, it is a generic background error statistics file called CV3- B that can be used for any resolution or area case. The CV3- B is the NCEP background error covariance, which is estimated in grid space by the NMC method. The statistics are estimated with the differences of 24 and 48-hour GFS forecasts with T170 resolution valid at the same time for 357 cases distributed over a period of one year. The major differences between these two kinds of B are the vertical covariance. CV3- B uses the vertical recursive filter to model the vertical covariance but the modified B uses the empirical orthogonal function (EOF) to represent the vertical covariance. In order to compare the difference of the two B in detail, a simulation experiment for June 2009 with two different B are performed to comparatively analyze the initial fields and precipitation distributing of strong rainfall case, and test the simulation effect in a month precipitation. The results show that different B lead to great differences in data assimilation processes. With the same background fields and observation, the minimizing convergence standards are equal to 0.01, the iterative step is about twenty using updated B , while the iterative step is about forty using CV3- B .And using updated B , for most instances it's monotonic decreasing during the iteration except for few iterative steps, and the decrease velocity is more rapid. But using CV3- B the value fluctuates from time to time. From data assimilation process, the efficiency in the iteration is higher using updated B , and the convergence of object function is steadier. The heavy rainfall process triggered by shear on 30 June 2009 in Yunnan Province is selected to analyze the effect of using different B on initial fields and precipitation distribution.Assimilating the sounding data of Tengchong in the west of Yunnan Province, the increment fields of wind vector on 700 hPa is analyzed. It is found that the increment impact spreads to the whole Yunnan Province using CV3- B , which is unreasonable. Using modified B the increment impact is within the adjacent area of the shear, leading to a relatively reasonable result. The precipitation simulation also indicate that using updated B which is consistent with model fields and all kinds of parameter, the TS in moderate rain or over is higher than using CV3- B .The whole simulating effect using updated B is remarkably superior to that using CV3- B . Thus estimating B afresh is important when three-dimensional variational data assimilation system is applied.
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图 1 背景误差协方差与控制变量转换算子的关系
Fig. 1 The relation between background error covariance and control variable transformation operator
图 2 平衡势函数、平衡温度与其完整场的比值
Fig. 2 The ratio between balanced and full velocity potential, temperature
图 6 纬向风单点观测同化试验 (a) 纬向风分析增量场 (单位：m·s-1)，(b) 经向风分析增量场 (单位：m·s-1)，(c) 气压分析增量场 (单位：Pa)，(d) 温度分析增量场 (单位：K)
Fig. 6 The assimilation test of zonal wind speed single observation
(a) zonal wind increment structure (unit:m·s-1), (b) meridional wind increment structure (unit:m·s-1), (c) pressure increment structure (unit:Pa), (d) temperature increment structure (unit:K)
图 7 温度单点观测同化试验
a) 温度分析增量场 (单位：K), (b) 纬向风分析增量场 (单位：m·s-1)，(c) 经向风分析增量场 (单位：m·s-1)，(d) 气压分析增量场 (单位：Pa)
Fig. 7 The assimilation test of temperature single observation
a) temperature increment structure (unit:K), (b) zonal wind increment structure (unit:m·s-1), (c) meridional wind increment structure (unit:m·s-1), (d) pressure increment structure (unit:Pa)
图 8 纬向风 (a，b) 和温度 (c，d) 单点观测同化试验
(a) 纬向风分析增量场 (单位：m·s-1)，(b) 经向风分析增量场 (单位：m·s-1)，(c) 温度分析增量场 (单位：K), (d) 纬向风分析增量场 (单位：m·s-1)，
Fig. 8 The assimilation test of zonal wind (a, b) and temperature (c, d) single observations
(a) zonal wind increment structure (unit:m·s-1), (b) meridional wind increment structure (unit:m·s-1), (c) temperature increment structure (unit:K), (d) zonal wind increment structure (unit:m·s-1)
图 9 2009年6月30日20:00 700 hPa风矢量
(a) 初始场, (b) 应用CV3-B的增量场, (c) 应用本地化B的增量场
Fig. 9 The wind vector fields of 700 hPa at 20:00 30 June 2009
(a) initial guess field, (b) the increment field using CV3-B, (c) the increment field using the updated B
图 10 2009年6月30日20：00—7月1日08：00降水量 (单位：mm)
(a) 实况，(b) 应用本地化B模拟，(c) 应用CV3-B模拟，(d) 模拟差值 (本地化B-CV3-B)
Fig. 10 Accumulated precipitation from 20:00 30 June to 08:00 7 July in 2009(unit:mm)
(a) observation, (b) simulated precipitation using updated B, (c) simulated precipitation using CV3-B, (d) the difference of simulated precipitation with different B(updated B minus CV3-B)
表 1 CV3-B和本地化B作为背景误差协方差WRF模式降水预报检验
Table 1 The precipitation forecast test with CV3-B and updated B in WRF
量级 TS/% ETS 偏差 CV3-B 本地化B CV3-B 本地化B CV3-B 本地化B 小雨 71.880 68.738 0.583 0.554 1.48 1.63 中雨 17.179 19.850 0.096 0.116 1.77 1.97 大雨 8.091 8.729 0.060 0.059 1.75 1.21 暴雨 6.783 7.719 0.045 0.052 1.88 1.71 
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