Estimating Background Error Covariance in Regional 3DVAR of WRF

Wang Man; Li Huahong; Duan Xu; Liu Jianyu; Fu Rui; Chen Xinmei

Vol.22, NO.4, 2011

Article Contents

Article Navigation > Journal of Applied Meteorological Science > 2011 > 22(4): 482-492

Wang Man, Li Huahong, Duan Xu, et al. Estimating background error covariance in regional 3DVAR of WRF. J Appl Meteor Sci, 2011, 22(4): 482-492.

Citation:

Wang Man, Li Huahong, Duan Xu, et al. Estimating background error covariance in regional 3DVAR of WRF. J Appl Meteor Sci, 2011, 22(4): 482-492.

Wang Man, Li Huahong, Duan Xu, et al. Estimating background error covariance in regional 3DVAR of WRF. J Appl Meteor Sci, 2011, 22(4): 482-492.

Citation:

Wang Man, Li Huahong, Duan Xu, et al. Estimating background error covariance in regional 3DVAR of WRF. J Appl Meteor Sci, 2011, 22(4): 482-492.

PDF( 2771 KB)

Estimating Background Error Covariance in Regional 3DVAR of WRF

Wang Man^{1,2
,
,},
Li Huahong³,
Duan Xu¹,
Liu Jianyu¹,
Fu Rui¹,
Chen Xinmei¹

1.
Yunnan Institute of Meteorology, Kunming 650034
2.
Chendu Institute of Plateau Meteorology, China Meteorological Administration, Chendu 610071
3.
Meteorological Observatory of Yunnan Province, Kunming 650034

Received Date: 2010-10-20
Rev Recd Date: 2011-04-03
Publish Date: 2011-08-31

Abstract

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.
- background error covariance;
- single observation test;
- numerical experiment;
- WRF model

FullText(HTML)

References(25)

Figures and Tables

Fig. 1 The relation between background error covariance and control variable transformation operator

DownLoad: Full-Size Img PowerPoint

Fig. 2 The ratio between balanced and full velocity potential, temperature

DownLoad: Full-Size Img PowerPoint

Fig. 3 The five eigenvectors of control variables

DownLoad: Full-Size Img PowerPoint

Fig. 4 The eigenvalues of control variables

DownLoad: Full-Size Img PowerPoint

Fig. 5 Lengthscales of control variables

DownLoad: Full-Size Img PowerPoint

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)

DownLoad: Full-Size Img PowerPoint

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)

DownLoad: Full-Size Img PowerPoint

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)

DownLoad: Full-Size Img PowerPoint

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

DownLoad: Full-Size Img PowerPoint

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)

DownLoad: Full-Size Img PowerPoint

Table 1 The precipitation forecast test with CV3-B and updated B in WRF

量级	TS/%		ETS		偏差
量级	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

DownLoad: Download CSV

References

[1]	Cardinali C, Pezzulli S, Anderson E. Influence-matrix diagnostic of a data aysimilation system. Quart J Roy Meteor Soc, 2004, 130: 2767-2786. doi: 10.1256/qj.03.205
[2]	Ajjaji Radi, Al-Katheri A A, Dhanhani A.Tuning of WRF 3D-Var Data Assimilation System over Middle-East and Arabian Peninsula.The 8th WRF User Workshop, 2007.
[3]	龚建东, 赵刚.全球资料同化中误差协方差三维结构的准确估计与应用:背景误差协方差调整与数值试验分析.气象学报, 2006, 64(6):669-682. doi: 10.11676/qxxb2006.065
[4]	Parrish D F, Derber J C.The National Meteorological Center's spectral statistical interpolation analysis system.Mon Wea Rev, 1992, 120: 1747-1763. doi: 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2
[5]	朱立娟. 背景场误差协方差估计技术的应用研究. 南京: 南京信息工程大学, 2005: 1-60.
[6]	范水勇, 张朝林, 仲跻芹.MM5三维变分系统在北京地区冷暖季背景场误差的对比分析.高原气象, 2006, 25(5):855-861. http://www.cnki.com.cn/Article/CJFDTOTAL-GYQX200605011.htm
[7]	范水勇, 郭永润, 陈敏, 等.高分辨率WRF三维变分同化在北京地区降水预报中的应用.高原气象, 2008, 27(6):1181-1188. http://www.cnki.com.cn/Article/CJFDTOTAL-GYQX200806001.htm
[8]	刘磊, 费建芳, 程小平, 等.我国东部海区不同气候背景条件下背景误差协方差的性质对比分析.海洋预报, 2009, 26(4):25-35. doi: 10.11737/j.issn.1003-0239.2009.04.004
[9]	曹小群, 黄思训, 张卫民, 等.区域三维变化同化中背景误差协方差的模拟.气象科学, 2008, 28(1):8-14. http://www.cnki.com.cn/Article/CJFDTOTAL-QXKX200801004.htm
[10]	庄照荣. 背景场误差的结构特征及其对三维变分同化影响的研究. 北京: 中国气象科学研究院, 2004: 1-87.
[11]	庄照荣, 薛纪善, 庄世宇, 等.资料同化中背景场位势高度误差统计分析的研究.大气科学, 2006, 30(3):533-544. http://www.cnki.com.cn/Article/CJFDTOTAL-DQXK200603015.htm
[12]	张华, 薛纪善, 庄世宇, 等.GRAPES三维变分同化系统的理想试验.气象学报, 2004, 62(1):31-41. doi: 10.11676/qxxb2004.004
[13]	黄丽萍, 伍湘君, 金之雁.GRAPES模式标准初始化方案设计与实现.应用气象学报, 2005, 16(3):374-384. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20050346&flag=1
[14]	庄世宇, 薛纪善, 朱国富, 等.GRAPES全球三维变分同化系统——基本设计方案与理想试验.大气科学, 2005, 29(6):872-884. http://www.cnki.com.cn/Article/CJFDTOTAL-DQXK200506003.htm
[15]	马旭林, 庄照荣, 薛纪善, 等.GRAPES非静力数值预报模式的三维变分资料同化系统的发展.气象学报, 2009, 67(1):50-60. doi: 10.11676/qxxb2009.006
[16]	薛纪善, 陈德辉.数值预报系统GRAPES的科学设计与应用.北京:科技出版社, 2008:1-61.
[17]	刘红亚, 薛纪善, 沈桐立, 等.探空气球漂移及其对数值预报影响的研究.应用气象学报, 2005, 16(4):518-526. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20050465&flag=1
[18]	陈炯, 王建捷.北京地区夏季边界层结构日变化的高分辨模拟对比.应用气象学报, 2006, 17(4):403-411. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20060469&flag=1
[19]	徐广阔, 孙建华, 雷霆, 等.多普勒天气雷达资料同化对暴雨模拟的影响.应用气象学报, 2009, 20(1):36-46. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20090105&flag=1
[20]	苗世光, 孙桂平, 马艳, 等.青岛奥帆赛高分辨率数值模式系统研制与应用.应用气象学报, 2009, 20(3):370-379. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20090315&flag=1
[21]	董佩明, 王海军, 韩威, 等.水物质对云雨区卫星微波观测模拟影响.应用气象学报, 2009, 20(6):682-691. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20090605&flag=1
[22]	仲跻芹, 陈敏, 范水勇, 等.AMDAR资料在北京数值预报系统中的同化应用.应用气象学报, 2010, 21(1):19-28. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20100103&flag=1
[23]	Skamarock W C, Klemp J B, Dudhia J, et a1.A Description of the Advanced Research WRF Vesion 3.NCAR Tech Note, NCAR/TN-475+STR, 2008:125.
[24]	Wu W S, Purser R J, Parrish D F. Three dimensional variational analysis with spatially inhomogeneous covariance. Mon Wea Rev, 2002, 130:2905-2916. doi: 10.1175/1520-0493(2002)130<2905:TDVAWS>2.0.CO;2
[25]	Derber J, Bouttier F. A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 1999, 51: 195-221. doi: 10.3402/tellusa.v51i2.12316