基于集合卡尔曼滤波的新安江模型状态变量实时修正方法
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摘要
为了提高洪水预报的精度,基于集合卡尔曼滤波,提出对流域中子流域中间状态量进行全状态量回溯修正方法。该方法根据每个子流域地貌特征和汇流时间不同,分别找出其相应的回溯时间,与新安江模型相结合对各个子流域特定时段前的中间状态量进行全状态量回溯修正,逐步降低误差的累积。采用理想模型验证,结果显示子流域中间状态量得到有效修正,洪量相对误差和洪峰相对误差减小,确定性系数提高。以大坡岭流域为例,采用该方法对流域12场历史洪水进行修正,修正结果表明此方法能有效提高洪水预报的精度,可在实际洪水预报中推广应用。
In order to improve the accuracy of flood forecasting, the paper proposes a retroactive correction method for the whole intermediate state variables of a sub-basin based on the ensemble Kalman filter. According to the different geomorphic feature and confluence time of each sub-basin, its corresponding retroactive time is found, and then, the Xinanjiang model is combined with to correct the state of each sub-basin before a certain time, gradually reducing the accumulation of errors. The results of the ideal model show that the intermediate state of sub-basin is effectively corrected, relative error of peak and volume decreases, and the deterministic coefficient increases. 12 historical floods of the Dapoling Basin, selected as an example, are effectively modified by the proposed method. As a result, the method can effectively improve the accuracy of flood forecasting and can be widely used in actual flood forecasting.
In order to improve the accuracy of flood forecasting, the paper proposes a retroactive correction method for the whole intermediate state variables of a sub-basin based on the ensemble Kalman filter. According to the different geomorphic feature and confluence time of each sub-basin, its corresponding retroactive time is found, and then, the Xinanjiang model is combined with to correct the state of each sub-basin before a certain time, gradually reducing the accumulation of errors. The results of the ideal model show that the intermediate state of sub-basin is effectively corrected, relative error of peak and volume decreases, and the deterministic coefficient increases. 12 historical floods of the Dapoling Basin, selected as an example, are effectively modified by the proposed method. As a result, the method can effectively improve the accuracy of flood forecasting and can be widely used in actual flood forecasting.
引文
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[3]万新宇,王光谦.近60年中国典型洪水灾害与防洪减灾对策[J].人民黄河,2011,33(8):1-4.(WAN Xinyu,WANGGuangqian.Typical flood disasters during last sixty years and strategies of flood control and disaster mitigation in China[J].Yellow River,2011,33(8):1-4.(in Chinese))
[4]瞿思敏,包为民,石朋,等.AR模式误差修正方程参数抗差估计[J].河海大学学报(自然科学版),2003,31(5):497-500.(QU Simin,BAO Weimin,SHI Peng,et al.AR model error correction equation parameter tolerance estimation[J].Journal of Hohai University(Natural Sciences),2003,31(5):497-500.(in Chinese))
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[8]BAO Weimin,SI Wei,QU Simin.Flow updating in real-time flood forecasting based on runoff correction by a dynamic system response curve[J].Journal of Hydrologic Engineering,2014,19(4):747-756.
[9]刘开磊,姚成,李致家,等.水动力学模型实时校正方法对比[J].河海大学学报(自然科学版),2014,42(2):124-129.(LIU Kailei,YAO Cheng,LI Zhijia,et al.Comparison of real time correction methods of hydrodynamic model[J].Journal of Hohai University(Natural Sciences),2014,42(2):124-129.(in Chinese))
[10]葛守西,程海云,李玉荣.水动力学模型卡尔曼滤波实时校正技术[J].水利学报,2005,36(6):687-693.(GE Shouxi,CHENG Haiyun,LI Yurong.Real time updating of hydrodynamic model by using Kalman filtering[J].Journal of Water Engineering,2005,36(6):687-693.(in Chinese))
[11]吴晓玲,王船海.基于卡尔曼滤波的水动力模型实时校正方法[J].武汉大学学报(工学版),2008,41(3):5-8,12.(WUXiaoling,WANG Chuanhai.Real-time correction of hydrodynamic model based on Kalman filter[J].Engineering Journal of Wuhan University,2008,41(3):5-8,12.(in Chinese))
[12]王船海,吴晓玲,周全.卡尔曼滤波校正技术在水动力学模型实时洪水预报中的应用[J].河海大学学报(自然科学版),2008,36(3):300-305.(WANG Chuanhai,WU Xiaoling,ZHOU Quan.Application of Kalman filter technique in real-time flood forecasting[J].Journal of Hohai University(Natural Sciences),2008,36(3):300-305.(in Chinese))
[13]EVENSEN G.Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics[J].Journal of Geophysical Research,1994,99(C5):10143.
[14]黄春林,李新.基于集合卡尔曼滤波的土壤水分同化试验[J].高原气象,2006,25(4):665-671.(HUANG Chunlin,LI Xin.Experiments of soil moisture data assimilation system based on ensemble Kalman filter[J].Plateau Meteorology,2006,25(4):665-671.(in Chinese))
[15]SAMUEL J,COULIBALY P,DUMEDAH G,et al.Assessing model state and forecasts variation in hydrologic data assimilation[J].Journal of Hydrology,2014,513(5):127-141.
[16]BURGERS G,LEEUWEN P J V,Evensen G.Analysis scheme in the ensemble Kalman filter[J].Monthly Weather Review,1998,126(6):1719-1724.
[17]岳延兵,李致家,范敏.集合卡尔曼滤波与神经网络融合的洪水预报研究[J].水力发电学报,2014,33(1):23-28.(YUEYanbing,LI Zhijia,FAN Min.Study of flood forecasting by ensemble Kalman filtering and neural network[J].Journal of Hydroelectric,2014,33(1):23-28.(in Chinese))
[18]赖锡军.水动力学模型与集合卡尔曼滤波耦合的实时校正多变量分析方法[J].水科学进展,2009,20(2):241-248.(LAIXijun.Real-updating multivariate analysis for unsteady flows with ensemble Kalman filter[J].Advances in Water Science,2009,20(2):241-248.(in Chinese))
[19]顾炉华,赖锡军.基于集合卡尔曼滤波的实时校正方法[J].水利水电科技进展,2017,37(2):73-77.(GU Xijun,LAIXijun.A real-time alternating method based on ensemble Kalman fiter[J].Advances in Science and Technology of Water Resources,2017,37(2):73-77.(in Chinese))
[20]PAUWELS V R N,DE LANNOY G J M.Improvement of modeled soil wetness conditions and turbulent fluxes through the assimilation of observed discharge[J].Journal of Hydrometeorology,2005,7(3):458-477.
[21]MORADKHANI H,SOROOSHIAN S,GUPTA H V,et al.Dual state-parameter estimation of hydrological models using ensemble Kalman filter[J].Advances in Water Resources,2005,28(2):135-147.
[22]SAMUEL J,COULIBALY P,DUMEDAH G,et al.Assessing model state and forecasts variation in hydrologic data assimilation[J].Journal of Hydrology,2014,513(5):127-141.
[23]MCMILLA H K,HREINSSON E,CLARK M P,et al.Operational hydrological data assimilation with the recursive ensemble Kalman filter[J].Hydrology&Earth System Sciences,2013,17(1):21-38.
[24]赵人俊,王佩兰,胡凤彬.新安江模型的根据及模型参数与自然条件的关系[J].河海大学学报(自然科学版),1992,20(1):52-59.(ZHAO Renjun,WANG Peilan,HU Fengbin.Relation between parameter values and corresponding natural condition of Xinanjiang Model[J].Journal of Hohai University(Natural Sciences),1992,20(1):52-59.(in Chinese))
[2]邱瑞田,王本德,周惠成.水库汛期限制水位控制理论与观念的更新探讨[J].水科学进展,2004,15(1):68-72.(QIURuitian,WANG Bende,ZHOU Huicheng.New idea for controlling the limited elevation of reservoirs in the flood season[J].Advances in Water Science,2004,15(1):68-72.(in Chinese))
[3]万新宇,王光谦.近60年中国典型洪水灾害与防洪减灾对策[J].人民黄河,2011,33(8):1-4.(WAN Xinyu,WANGGuangqian.Typical flood disasters during last sixty years and strategies of flood control and disaster mitigation in China[J].Yellow River,2011,33(8):1-4.(in Chinese))
[4]瞿思敏,包为民,石朋,等.AR模式误差修正方程参数抗差估计[J].河海大学学报(自然科学版),2003,31(5):497-500.(QU Simin,BAO Weimin,SHI Peng,et al.AR model error correction equation parameter tolerance estimation[J].Journal of Hohai University(Natural Sciences),2003,31(5):497-500.(in Chinese))
[5]司伟,包为民,瞿思敏.洪水预报产流误差的动态系统响应曲线修正方法[J].水科学进展,2013,24(4):497-503.(SIWei,BAO Weimin,QU Simin.Runoff error correction in real-time flood forecasting based on dynamic system response curve[J].Advances in Water Science,2013,24(4):497-503.(in Chinese))
[6]张小琴,刘可新,包为民,等.产流误差比例系数的系统响应修正方法[J].水科学进展,2014,25(6):789-796.(ZHANGXiaoqin,LIU Kexin,BAO Weimin,et al.Runoff error proportionality coefficient correction based on system response[J].Advances in Water Science,2014,25(6):789-796.(in Chinese))
[7]SI Wei,BAO Weimin,GUPTA H V.Updating real-time flood forecasts via the dynamic system response curve method[J].Water Resources Research,2015,51(7):5128-5144.
[8]BAO Weimin,SI Wei,QU Simin.Flow updating in real-time flood forecasting based on runoff correction by a dynamic system response curve[J].Journal of Hydrologic Engineering,2014,19(4):747-756.
[9]刘开磊,姚成,李致家,等.水动力学模型实时校正方法对比[J].河海大学学报(自然科学版),2014,42(2):124-129.(LIU Kailei,YAO Cheng,LI Zhijia,et al.Comparison of real time correction methods of hydrodynamic model[J].Journal of Hohai University(Natural Sciences),2014,42(2):124-129.(in Chinese))
[10]葛守西,程海云,李玉荣.水动力学模型卡尔曼滤波实时校正技术[J].水利学报,2005,36(6):687-693.(GE Shouxi,CHENG Haiyun,LI Yurong.Real time updating of hydrodynamic model by using Kalman filtering[J].Journal of Water Engineering,2005,36(6):687-693.(in Chinese))
[11]吴晓玲,王船海.基于卡尔曼滤波的水动力模型实时校正方法[J].武汉大学学报(工学版),2008,41(3):5-8,12.(WUXiaoling,WANG Chuanhai.Real-time correction of hydrodynamic model based on Kalman filter[J].Engineering Journal of Wuhan University,2008,41(3):5-8,12.(in Chinese))
[12]王船海,吴晓玲,周全.卡尔曼滤波校正技术在水动力学模型实时洪水预报中的应用[J].河海大学学报(自然科学版),2008,36(3):300-305.(WANG Chuanhai,WU Xiaoling,ZHOU Quan.Application of Kalman filter technique in real-time flood forecasting[J].Journal of Hohai University(Natural Sciences),2008,36(3):300-305.(in Chinese))
[13]EVENSEN G.Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics[J].Journal of Geophysical Research,1994,99(C5):10143.
[14]黄春林,李新.基于集合卡尔曼滤波的土壤水分同化试验[J].高原气象,2006,25(4):665-671.(HUANG Chunlin,LI Xin.Experiments of soil moisture data assimilation system based on ensemble Kalman filter[J].Plateau Meteorology,2006,25(4):665-671.(in Chinese))
[15]SAMUEL J,COULIBALY P,DUMEDAH G,et al.Assessing model state and forecasts variation in hydrologic data assimilation[J].Journal of Hydrology,2014,513(5):127-141.
[16]BURGERS G,LEEUWEN P J V,Evensen G.Analysis scheme in the ensemble Kalman filter[J].Monthly Weather Review,1998,126(6):1719-1724.
[17]岳延兵,李致家,范敏.集合卡尔曼滤波与神经网络融合的洪水预报研究[J].水力发电学报,2014,33(1):23-28.(YUEYanbing,LI Zhijia,FAN Min.Study of flood forecasting by ensemble Kalman filtering and neural network[J].Journal of Hydroelectric,2014,33(1):23-28.(in Chinese))
[18]赖锡军.水动力学模型与集合卡尔曼滤波耦合的实时校正多变量分析方法[J].水科学进展,2009,20(2):241-248.(LAIXijun.Real-updating multivariate analysis for unsteady flows with ensemble Kalman filter[J].Advances in Water Science,2009,20(2):241-248.(in Chinese))
[19]顾炉华,赖锡军.基于集合卡尔曼滤波的实时校正方法[J].水利水电科技进展,2017,37(2):73-77.(GU Xijun,LAIXijun.A real-time alternating method based on ensemble Kalman fiter[J].Advances in Science and Technology of Water Resources,2017,37(2):73-77.(in Chinese))
[20]PAUWELS V R N,DE LANNOY G J M.Improvement of modeled soil wetness conditions and turbulent fluxes through the assimilation of observed discharge[J].Journal of Hydrometeorology,2005,7(3):458-477.
[21]MORADKHANI H,SOROOSHIAN S,GUPTA H V,et al.Dual state-parameter estimation of hydrological models using ensemble Kalman filter[J].Advances in Water Resources,2005,28(2):135-147.
[22]SAMUEL J,COULIBALY P,DUMEDAH G,et al.Assessing model state and forecasts variation in hydrologic data assimilation[J].Journal of Hydrology,2014,513(5):127-141.
[23]MCMILLA H K,HREINSSON E,CLARK M P,et al.Operational hydrological data assimilation with the recursive ensemble Kalman filter[J].Hydrology&Earth System Sciences,2013,17(1):21-38.
[24]赵人俊,王佩兰,胡凤彬.新安江模型的根据及模型参数与自然条件的关系[J].河海大学学报(自然科学版),1992,20(1):52-59.(ZHAO Renjun,WANG Peilan,HU Fengbin.Relation between parameter values and corresponding natural condition of Xinanjiang Model[J].Journal of Hohai University(Natural Sciences),1992,20(1):52-59.(in Chinese))