城市区域水情仿真和数据同化的理论研究与应用
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摘要
目前,城市雨洪模型多数用于规划阶段的分析,若要更好地服务于城市防洪及排水系统日常管理,须建立能够实时反映排水系统真实运行状态和能对未来一段时间内水情预报的水情仿真与预报系统。本文从城市区域产汇流特性分析等方面入手,构建了一个适用于城市区域的水文水动力耦合模型,研究了模型参数反演和数据同化技术,初步搭建了一个城市水情仿真、校正与预报的实时系统。论文的主要研究成果如下：
(1)提出了以矩阵化形式对水文与水动力模型进行耦合的方法,并结合多种措施对提高计算的稳定性、精度和效率进行了研究,包括：1)采用基流法和窄缝设计法进行干湿交替的处理；2)采用迭代计算处理堰闸等非线性内边界；3)赋予节点蓄水面积以加强系数矩阵的主对角占优性；4)采用迭代法结合矩阵标识法进行方程组的求解；5)研究了固定系数矩阵、只改变方程组右端项以提高计算效率的方法；6)提出了考虑连续方程和动量方程线性化处理后二阶及以上小量的计算方法。
(2)针对定床河道糙率的率定,提出了两个结合先验知识的反演模型：糙率空间分布最平滑模型和糙率估值修正最小模型。数值仿真表明：1)当糙率初值选在合理范围内时,模型受初值选取的影响较小；2)当监测信息较少时,模型亦能获得较为合理的结果,并随着监测信息的增加,反演结果趋于真解；3)模型具有较好的抗噪性,通过控制糙率空间分布平滑项或糙率估值修正项的权重,能有效抑制监测信息误差引起的数值扰动。
(3)以扩展卡尔曼滤波为基础,构造了多个河道糙率动态修正算法。数值仿真表明：结合糙率修正平滑性且以糙率和水情变量为系统状态变量的扩展卡尔曼滤波,能有效防止糙率的突变和失真。
(4)在水位、流量等水情变量的数据同化方面,提出并探索了扩展卡尔曼滤波、集合卡尔曼滤波和广义反演法三种方法。数值仿真表明：1)扩展卡尔曼滤波的数据同化效果好,可同时对糙率、水位、流量等变量进行校正；2)集合卡尔曼滤波的适用范围广,计算简便；3)广义反演法的计算原理简单,可避免状态修正过大而严重破坏原先的水量平衡关系。
(5)在上述研究成果的基础上,针对目前应用较广的城市雨洪管理模型SWMM存在的不足进行了改进,搭建了城市水情实时仿真与预报系统的结构框架,完成了核心计算程序的开发。
The current urban storm water models are mostly applied in the early planning stages of projects. In order to apply urban storm water models into urban flood prevention and drainage system management, it is necessary to establish an urban storm water simulation and prediction system which is capable of reflecting actually the operation of the drainage system and predicting the hydrographic condition during a period of time in the future. Therefore, the thesis will start with an analysis of the characteristics of runoff in urban areas to build an appropriate hydrology-hydrodynamics coupling model, and develop a real-time system that is applicable to storm water simulation, correction and prediction by means of parameter calibration and data assimilation. The research works are as follows:
(1) Drawing up a hydrology-hydrodynamics coupling model that couples the hydrology calculation module and the hydrodynamic calculation module together in a matrix, and using multiple measures to improve the calculation stability, accuracy and efficiency, which include:1) processing the alternation of drying and wetting with base flow method and narrow slit method;2) dealing with nonlinear internal boundaries such as weirs, sluices, etc. using iterative computation method;3) furnishing the nodes with storage area to obtain a diagonally dominant matrix;4) combining iterative computation method with matrix indicator method to solve equations;5) proposing a method where the coefficient matrix is fixed and only the right side of equations is variable in order to improve the computing efficiency;6) putting forward a method of calculating small quantities of second order and above of the linearized continuity equations and momentum equations.
(2) For the research on bed-fixed river roughness inversion combined with prior knowledge, two inversion models are developed based on prior knowledge of roughness:the first is a model of roughness parameters within the smoothest space distribution, and the second is a model of the estimated values of roughness parameters with the least modification. It is demonstrated by numerical simulations that:1) the inversion models are less affected by the selection of initial values;2) reasonable results can be obtained from such models even if there is not much available observation information, and the results tend to be close to the true values along with the increase of observation information;3) the models are of high noise immunity, i.e. numerical disturbance caused by the errors of observation information can be effectively avoided by controlling the weight of the roughness space distribution item or the roughness modification item.
(3) For the research on dynamic identification of roughness parameters, some data assimilation methods are developed based on extended kalman filtering algorithm. It is shown by numerical simulations that:combining with smoothly modification of roughness, the extended kalman filtering algorithm where the roughness parameters and flow variables are seen as system state variables can avoid distortion of roughness parameters, and it can improve the efficiency of data assimilation and the stability of calculation as well.
(4) For the research on data assimilation of flow variables such as water level, discharge, etc., three data assimilation methods are developed including extended kalman filtering algorithm, ensemble kalman filtering algorithm and generalized inversion method. It is demonstrated by numerical simulations that:1) the extended kalman filtering algorithm has a good performance, and can be used to data assimilation of roughness parameters and flow variables at the same time;2) the ensemble kalman filtering algorithm features wide applicability and simple computing process;3) the theory and programming of the generalized inversion method are simple, and the serious damage on the previous water balance caused by too much modification of flow variables can be avoided.
(5) On the basis of the current research as stated above, suggestions are proposed on how to remedy the deficiencies of the current widely-used urban storm water management model SWMM, and a framework of an urban storm water simulation and prediction system is established.
(1)提出了以矩阵化形式对水文与水动力模型进行耦合的方法,并结合多种措施对提高计算的稳定性、精度和效率进行了研究,包括：1)采用基流法和窄缝设计法进行干湿交替的处理；2)采用迭代计算处理堰闸等非线性内边界；3)赋予节点蓄水面积以加强系数矩阵的主对角占优性；4)采用迭代法结合矩阵标识法进行方程组的求解；5)研究了固定系数矩阵、只改变方程组右端项以提高计算效率的方法；6)提出了考虑连续方程和动量方程线性化处理后二阶及以上小量的计算方法。
(2)针对定床河道糙率的率定,提出了两个结合先验知识的反演模型：糙率空间分布最平滑模型和糙率估值修正最小模型。数值仿真表明：1)当糙率初值选在合理范围内时,模型受初值选取的影响较小；2)当监测信息较少时,模型亦能获得较为合理的结果,并随着监测信息的增加,反演结果趋于真解；3)模型具有较好的抗噪性,通过控制糙率空间分布平滑项或糙率估值修正项的权重,能有效抑制监测信息误差引起的数值扰动。
(3)以扩展卡尔曼滤波为基础,构造了多个河道糙率动态修正算法。数值仿真表明：结合糙率修正平滑性且以糙率和水情变量为系统状态变量的扩展卡尔曼滤波,能有效防止糙率的突变和失真。
(4)在水位、流量等水情变量的数据同化方面,提出并探索了扩展卡尔曼滤波、集合卡尔曼滤波和广义反演法三种方法。数值仿真表明：1)扩展卡尔曼滤波的数据同化效果好,可同时对糙率、水位、流量等变量进行校正；2)集合卡尔曼滤波的适用范围广,计算简便；3)广义反演法的计算原理简单,可避免状态修正过大而严重破坏原先的水量平衡关系。
(5)在上述研究成果的基础上,针对目前应用较广的城市雨洪管理模型SWMM存在的不足进行了改进,搭建了城市水情实时仿真与预报系统的结构框架,完成了核心计算程序的开发。
The current urban storm water models are mostly applied in the early planning stages of projects. In order to apply urban storm water models into urban flood prevention and drainage system management, it is necessary to establish an urban storm water simulation and prediction system which is capable of reflecting actually the operation of the drainage system and predicting the hydrographic condition during a period of time in the future. Therefore, the thesis will start with an analysis of the characteristics of runoff in urban areas to build an appropriate hydrology-hydrodynamics coupling model, and develop a real-time system that is applicable to storm water simulation, correction and prediction by means of parameter calibration and data assimilation. The research works are as follows:
(1) Drawing up a hydrology-hydrodynamics coupling model that couples the hydrology calculation module and the hydrodynamic calculation module together in a matrix, and using multiple measures to improve the calculation stability, accuracy and efficiency, which include:1) processing the alternation of drying and wetting with base flow method and narrow slit method;2) dealing with nonlinear internal boundaries such as weirs, sluices, etc. using iterative computation method;3) furnishing the nodes with storage area to obtain a diagonally dominant matrix;4) combining iterative computation method with matrix indicator method to solve equations;5) proposing a method where the coefficient matrix is fixed and only the right side of equations is variable in order to improve the computing efficiency;6) putting forward a method of calculating small quantities of second order and above of the linearized continuity equations and momentum equations.
(2) For the research on bed-fixed river roughness inversion combined with prior knowledge, two inversion models are developed based on prior knowledge of roughness:the first is a model of roughness parameters within the smoothest space distribution, and the second is a model of the estimated values of roughness parameters with the least modification. It is demonstrated by numerical simulations that:1) the inversion models are less affected by the selection of initial values;2) reasonable results can be obtained from such models even if there is not much available observation information, and the results tend to be close to the true values along with the increase of observation information;3) the models are of high noise immunity, i.e. numerical disturbance caused by the errors of observation information can be effectively avoided by controlling the weight of the roughness space distribution item or the roughness modification item.
(3) For the research on dynamic identification of roughness parameters, some data assimilation methods are developed based on extended kalman filtering algorithm. It is shown by numerical simulations that:combining with smoothly modification of roughness, the extended kalman filtering algorithm where the roughness parameters and flow variables are seen as system state variables can avoid distortion of roughness parameters, and it can improve the efficiency of data assimilation and the stability of calculation as well.
(4) For the research on data assimilation of flow variables such as water level, discharge, etc., three data assimilation methods are developed including extended kalman filtering algorithm, ensemble kalman filtering algorithm and generalized inversion method. It is demonstrated by numerical simulations that:1) the extended kalman filtering algorithm has a good performance, and can be used to data assimilation of roughness parameters and flow variables at the same time;2) the ensemble kalman filtering algorithm features wide applicability and simple computing process;3) the theory and programming of the generalized inversion method are simple, and the serious damage on the previous water balance caused by too much modification of flow variables can be avoided.
(5) On the basis of the current research as stated above, suggestions are proposed on how to remedy the deficiencies of the current widely-used urban storm water management model SWMM, and a framework of an urban storm water simulation and prediction system is established.
引文
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