基于改进卡尔曼滤波算法的雷达定量降雨估算
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摘要
针对雷达定量降雨估算误差较大的问题,本文提出一种使用改进卡尔曼滤波对雷达估算值进行校准的方法。先确立G/R(自动气象站测量值/天气雷达估算值)校准因子模型,并应用普通卡尔曼滤波方法对G/R校准因子建立预测系统和测量系统,同时引入系统参数的校准过程和系统误差的自适应估计过程,动态调整卡尔曼滤波中各项参数值;最后将滤波后的G/R因子用于校正雷达定量降雨估算,得到较准确的降雨估算值。利用长春市天气雷达2015年8月19-20日和2016年月8月6-7日两次降雨过程的雷达产品和加密自动站逐小时的降雨资料,对卡尔曼滤波方法进行检验分析。结果表明:改进卡尔曼滤波和普通卡尔曼滤波校准后雷达降雨估算结果优于未校准的降雨估算结果,普通卡尔曼滤波方法和改进卡尔曼滤波方法的平均相对误差分别从0.6047减至0.3557和0.2645,从0.8052减至0.3096和0.1715,且改进算法效果优于普通卡尔曼滤波算法,校准后雷达降雨估算准确度明显提高。
To minimum the error of radar rainfall evaluation,an improved Kalman filter method was presented to calibrate the radar quantitative rainfall estimation(QRE).Firstly,the G/R(rain gauge rain rate/radar rain rate) calibration factor model was established.Secondly,the prediction and measurement system of G/R was set up based on the Kalman filter(KF).The calibration process of system parameters and adaptive estimation process of system error was introduced to adjust the parameters of KF dynamically.Thirdly,the G/R calibration ratio was used to correct radar quantitative rainfall estimation.The radar and rain gauge hourly rain data of two rain cases on 2015-08-19-20 and 2016-08-06-07 from Changchun were used to test the efficiency of the proposed method.The results showed that the QRE result with KF calibration was better than that without calibration.And the average relative errors of two rain cases were reduced from 0.6047 to 0.3557 and 0.2645,from 0.8052 to 0.3096 and 0.1715 by ordinary KF and improved KF respectively.Moreover,the improved KF was even better than the ordinary KF.
To minimum the error of radar rainfall evaluation,an improved Kalman filter method was presented to calibrate the radar quantitative rainfall estimation(QRE).Firstly,the G/R(rain gauge rain rate/radar rain rate) calibration factor model was established.Secondly,the prediction and measurement system of G/R was set up based on the Kalman filter(KF).The calibration process of system parameters and adaptive estimation process of system error was introduced to adjust the parameters of KF dynamically.Thirdly,the G/R calibration ratio was used to correct radar quantitative rainfall estimation.The radar and rain gauge hourly rain data of two rain cases on 2015-08-19-20 and 2016-08-06-07 from Changchun were used to test the efficiency of the proposed method.The results showed that the QRE result with KF calibration was better than that without calibration.And the average relative errors of two rain cases were reduced from 0.6047 to 0.3557 and 0.2645,from 0.8052 to 0.3096 and 0.1715 by ordinary KF and improved KF respectively.Moreover,the improved KF was even better than the ordinary KF.
引文
[1]郑媛媛,谢亦峰,吴林林,等.多普勒雷达定量估测降水的三种方法比较试验[J].热带气象学报,2004,(2):192-197.Zheng Y Y,Xie Y F,Wu L L,et al.Comparative experiment with several quantitative precipitation estimator techniques based on Doppler radar[J].Journal of Tropical Meteorology,2004,(2):192-197.(in Chinese)
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[11]刘勤,严昌荣,何文清.黄河流域干旱时空变化特征及其气候要素敏感性分析[J].中国农业气象,2016,37(6):623-632.Liu Q,Yan C R,He W Q.Drought variation and its sensitivity coefficients to climatic factors in the Yellow River Basin[J].Chinese Journal of Agrometeorology,2016,37(6):623-632.(in Chinese)
[12]王学斌,徐建宏,张章.卡尔曼滤波器参数分析与应用方法研究[J].计算机应用与软件,2012,(6):212-215.Wang X B,Xu J H,Zhang Z.On analysis and application approach for Kalman filter parameters[J].Computer Applications and Software,2012,(6):212-215.(in Chinese)
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[14]殷志远,沈铁元,彭涛.基于雷达和雨量站的权重校准法研究及其应用[J].人民长江,2010,(2):47-51.Yin Z Y,Shen T Y,Peng T.Research and application of weight calibration method based on radars and rainfall stations[J].Yangze River,2010,(2):47-51.(in Chinese)
[15]杨杰,刘黎平,赵城城,等.雷达估测对流性降水的误差空间分布及Z-R关系的优化[J].高原气象,2015,34(6):1785-1796.Yang J,Liu L P,Zhao C C,et al.Spatial distribution of error from the convective precipitation estimation of radar and optimization of Z-R relationship[J].Palateau Meteorology,2015,34(6):1785-1796.(in Chinese)
[16]东高红,吕江津.不同校准方法检验雷达定量估测降水的效果对比[J].气象与环境学报,2012,28(4):38-42.Dong G H,Lv J J.Comparison on quantitative estimation of precipitation using radar based on different calibration methods[J].Journal of Meteorology and Environment,2012,28(4):38-42.(in Chinese)
[17]程进伟,李建勋.卡尔曼滤波算法评估平台的设计与实现[J].系统仿真学报,2013,(11):2567-2574.Cheng J W,Li J X.Design and implementation of software platform to evaluate Kalman filter algorithm[J].Journal of System Simulation,2013,(11):2567-2574.(in Chinese)
[18]张利平,张晓琳,王任超,等.雷达估算降雨的同化方法对比[J].武汉大学学报(工学版),2011,(2):146-150.Zhang L P,Zhang X L,Wang R C,et al.The compare research of the rainfall data assimilation methods based on the radar[J].Engineering Journal of Wuhan University,2011,(2):146-150.(in Chinese)
[19]Marco C,Teresa A.Parameter estimation of state space models for univariate observations[[J].Journal of Statistical Planning and Inference,2010,140(7):1889-1902.
[20]汪瑛,冯业荣,蔡锦辉,等.雷达定量降水动态分级Z-I关系估算方法[J].热带气象学报,2011,27(4):601-608.Wang Y,Feng Y R,Cai J H,et al.An approach for radar quantitative precipitation estimate based on categorical Z-I relations[J].Journal of Tropical Meteorology,2011,27(4):601-608.(in Chinese)
[2]Ahnert P R,Krajewski W F,Johnson E R.Kalman filter estimation of radar-rainfall field bias[C].Preprints,23rd Conf.On Radar Meteor.,Snowmass,CO,Amer.Meteor.Soc.,1986:33-37.
[3]Chumchean S,Seed A,Sharma A.Correcting of real-time radar rainfall bias using a Kalman filtering approach[J].Journal of Hydrology,2006,317(1):123-137.
[4]Sharifah N H S Y,Wardah T,Suzana R,et al.Improved estimation of radar rainfall bias over Klang River Basin using a Kalman filtering approach[J].Bandung:2012 IEEE Symposium on Business,Engineering and Industrial Applications,2012:368-373.
[5]尹忠海,张沛源.利用卡尔曼滤波校准方法估算区域降水量[J].应用气象学报,2005,(2):213-219.Yin Z H,Zhang P Y.Radar rainfall calibration by using the Kalman filter method[J].Journal of Applied Meteorological Science,2005,(2):213-219.(in Chinese)
[6]Monteiro M,Costa M.A comparison between single site modeling and multiple site modeling approaches using Kalman filtering[A].Proceedings of the international conference on numerical analysis and applied mathematics 2014(ICNAAM-2014)[C].AIP Publishing,2015,1648(1):110003.
[7]徐燕.卡尔曼滤波法在西峰雷达估测降水中的应用[J].干旱气象,2008,(1):78-82.Xu Y.Application of Kalman filter in precipitation estimation by radar[J].Aridity Meteorology,2008,(1):78-82.(in Chinese)
[8]Kim J,Yoo C.Use of a dual Kalman filter for real-time correction of mean field bias of radar rain rate[J].Journal of Hydrology,2014,519:2785-2796.
[9]赵坤,刘国庆,葛文忠.用卡尔曼滤波确定变分方法中的权重系数进行雨量校正[J].气候与环境研究,2001,6(2):180-185.Zhao K,Liu G Q,Ge W Z.Precipitation calibration by using Kalman filter to determine the coefficients of the variational equation[J].Climatic and Environmental Research,2001,6(2):180-185.(in Chinese)
[10]勾亚彬,刘黎平,杨杰,等.基于雷达组网拼图的定量降水估测算法业务应用及效果评估[J].气象学报,2014,72(4):731-748.Gou Y B,Liu L P,Yang J,et al.Operational application and evaluation of the quantitative precipitation estimates algorithm based on the multi-radar mosaic[J].Acta Meteorologica Sinica,2014,72(4):731-748.(in Chinese)
[11]刘勤,严昌荣,何文清.黄河流域干旱时空变化特征及其气候要素敏感性分析[J].中国农业气象,2016,37(6):623-632.Liu Q,Yan C R,He W Q.Drought variation and its sensitivity coefficients to climatic factors in the Yellow River Basin[J].Chinese Journal of Agrometeorology,2016,37(6):623-632.(in Chinese)
[12]王学斌,徐建宏,张章.卡尔曼滤波器参数分析与应用方法研究[J].计算机应用与软件,2012,(6):212-215.Wang X B,Xu J H,Zhang Z.On analysis and application approach for Kalman filter parameters[J].Computer Applications and Software,2012,(6):212-215.(in Chinese)
[13]岳晓奎,袁建平.一种基于极大似然准则的自适应卡尔曼滤波算法[J].西北工业大学学报,2005,23(4):469-474.Yue X K,Yuan J P.An adaptive Kalman filtering algorithm based on maximum-likelihood criterion[J].Journal of Northwestern Polytechnical University,2005,23(4):469-474.(in Chinese)
[14]殷志远,沈铁元,彭涛.基于雷达和雨量站的权重校准法研究及其应用[J].人民长江,2010,(2):47-51.Yin Z Y,Shen T Y,Peng T.Research and application of weight calibration method based on radars and rainfall stations[J].Yangze River,2010,(2):47-51.(in Chinese)
[15]杨杰,刘黎平,赵城城,等.雷达估测对流性降水的误差空间分布及Z-R关系的优化[J].高原气象,2015,34(6):1785-1796.Yang J,Liu L P,Zhao C C,et al.Spatial distribution of error from the convective precipitation estimation of radar and optimization of Z-R relationship[J].Palateau Meteorology,2015,34(6):1785-1796.(in Chinese)
[16]东高红,吕江津.不同校准方法检验雷达定量估测降水的效果对比[J].气象与环境学报,2012,28(4):38-42.Dong G H,Lv J J.Comparison on quantitative estimation of precipitation using radar based on different calibration methods[J].Journal of Meteorology and Environment,2012,28(4):38-42.(in Chinese)
[17]程进伟,李建勋.卡尔曼滤波算法评估平台的设计与实现[J].系统仿真学报,2013,(11):2567-2574.Cheng J W,Li J X.Design and implementation of software platform to evaluate Kalman filter algorithm[J].Journal of System Simulation,2013,(11):2567-2574.(in Chinese)
[18]张利平,张晓琳,王任超,等.雷达估算降雨的同化方法对比[J].武汉大学学报(工学版),2011,(2):146-150.Zhang L P,Zhang X L,Wang R C,et al.The compare research of the rainfall data assimilation methods based on the radar[J].Engineering Journal of Wuhan University,2011,(2):146-150.(in Chinese)
[19]Marco C,Teresa A.Parameter estimation of state space models for univariate observations[[J].Journal of Statistical Planning and Inference,2010,140(7):1889-1902.
[20]汪瑛,冯业荣,蔡锦辉,等.雷达定量降水动态分级Z-I关系估算方法[J].热带气象学报,2011,27(4):601-608.Wang Y,Feng Y R,Cai J H,et al.An approach for radar quantitative precipitation estimate based on categorical Z-I relations[J].Journal of Tropical Meteorology,2011,27(4):601-608.(in Chinese)