湖泊三维水动力水质模型研究与应用
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摘要
湖泊是地球上的璀璨明珠。在自然和人类活动的综合影响下，湖泊的水文过程和生态系统结构均发生深刻变化。探索自然和人文因素双重驱动下的湖泊水生态系统演变过程与格局，揭示湖泊水生态系统内大气、水体、沉积物三相界面之间的相互作用规律，为湖泊水环境治理、湖泊生态调控、重大江湖连通工程优化调度提供科学工具，是一项重要而迫切的研究命题。建立湖泊水环境数学模型、开展湖泊水动力与水生态数值模拟是完成这一研究命题的重要途径。然而，湖泊水环境系统集中体现了大气圈、水圈、生物圈之间的物质交换和能量交换过程，各种物理、化学、生物过程交织在一起，在以水动力学为骨架的研究框架下，需同时考虑化学、生物分支以及人类活动影响，极大地增加了研究难度。本研究为应对这一科学挑战，以湖泊（群）为研究对象，建立了三维湖泊水动力水质耦合数值模型，取得了若干具有理论意义和实用价值的成果。论文主要研究工作和创新成果如下：
（1）湖泊水流运动复杂多变、湖流输运和混合作用强烈，为正确地模拟湖泊水动力过程，论文推导建立了Sigma坐标系下由连续性方程、动量方程、温度方程和物质输运方程组成的三维湖泊水动力模型控制方程组。采用κ-ε垂向湍流闭合模型及Smagorinsky水平湍流闭合模型对方程组进行闭合。考虑到数值模型计算需要，推导建立了二维垂向积分方程。在水温模型中，基于经典的传热概念，提出了包含辐射、对流、传导和蒸发项的湖泊自由水面热通量计算方法。该方法简单实用，尽量减少了对实测数据的要求，具有广泛的实用性。
（2）以WASP模型为基础，分析了湖泊中氮、磷等元素的迁移转化规律及其与外界环境和水生生物的相互作用机制，构建了包含溶解氧平衡系统、浮游植物生长系统、氮循环系统和磷循环系统组成的三维湖泊水质模型。
（3）发展了一种基于有限体积法的湖泊三维水动力水质耦合数值模型。该模型采用无结构三角形网格和垂向Sigma坐标来剖分计算区域，空间上模型采用有限体积法离散三维水动力水质方程组，时间上采用模式分裂技术，即首先通过外模求解二维垂向积分方程以获得水深分布，然后利用内模求解三维水流运动方程组获得三维流场细节，进而求解水温模型和水质模型。外模求解中，采用修正的四阶龙格库塔格式求解时变项，运用Osher格式计算跨边界法向通量。求解三维内模动量方程时，模型采用显示与隐式相结合的方法，其中水平对流项及扩散项采用基于Osher格式的黎曼数值解，垂向对流项采用TVD格式，垂向扩散采用隐格式离散。
（4）以武汉大东湖水系为对象开展了数值模型验证工作。开展数值模拟需要高质量的气象水文驱动数据，然而对湖泊这样大面积水体的同步观测极为困难。为解决这一难题，本研究利用多源遥感数据（包括MODIS、Landsat5TM和Landsat7ETM+）开展了湖泊水文水质信息反演工作，利用反演数据为数值模拟提供初始条件并对模型进行验证。此外，本研究在数值模拟中全面引入GIS技术来辅助完成前处理、后处理与可视化任务，大大提高了建模和调试的效率。按照以上技术思路，论文研究并探讨了不同气候背景下大东湖水系中东湖、沙湖、杨春湖、北湖、严西湖和严东湖六个主要湖泊的三维流场结构和水温时空变化规律。此外，重点针对东湖开展了水质时空变化模拟研究，以验证模型有效性。结果表明，该研究思路和技术路线为开展湖泊水环境数值模拟提供了可靠、稳定且易执行的一体化解决方案，为建立湖泊水环境调控长效机制提供了有力技术支撑。
（5）运用建立的数值模型，开展了江湖连通情境下武汉大东湖水系水网调度问题研究。根据大东湖生态水网项目总体规划，提出了初步的水网连通及引水调度方案和方案评价指标体系。运用数值模型开展水网连通研究，分析了不同方案对湖泊水体运动模式、水流形态和水质改善的影响，根据建立的指标体系对比了不同方案的优劣以确定最有利于大东湖水生态环境改善的调度方案。
Lakes are resplendent jewels of the earth. The hydrological process and ecologicalsystem structure in lakes are undergoing deep change due to the dual influence of natureand human behaviors. Exploring evolution procedures and patterns of lakehydro-ecological system, as well as revealing interaction rules between air, water andsediment of the system, are important and necessary research topics. However, intensiveexchanges of substance and energy between atmosphere, hydrosphere and biosphere takeplace in the lake system, resulting in extremely complex mixture of physical, chemical andbiologic procedures. This poses a great challenge on researchers who try to simulate thelake system with numerical models, because a variety of methods and knowledgebelonging to diverse research fields like chemistry and biology have to be integrated intothe hydrodynamics framework, which is the basis for the simulation. In order to meet thischallenge, this paper is focused on the development and application of a three-dimensionalhydrodynamics and water quality lake model using unstructured grid and finite volumemethod (FVM), aiming to provide a general tool for modeling the flow field, transport,and eutrophication processes in lakes. The main contributions and innovations of thiswork are outlined below:
(1) In order to simulate the complicated circulation and mixture schema of lakes, amathematic model consisting of continuity, momentum, temperature and transportationequations was established. The standard k-ε vertical turbulent model and Smagorinskyhorizontal turbulent model were used to close the model physically and mathematically.Two-dimensional vertically integrated equations were also deducted to satisfy requirementof numerical computation. In particular, this work provides a method for estimating heatflux on the free surface of lakes where the flux is determined based on the balance ofincoming solar radiation, net back radiation flux, sensible heat exchange, and evaporativeheat. This method was liveraged in the temperature model and was proved to be a simpleand practical way for simulating lake temperature since it minimized requirements ofmetrological data.
(2) Based on principles of WASP, a3D water quality model was constructed. The model is able to simulate spatial and temporal variations of eight water quality variablesincluding dissolved oxygen, carbon biological oxygen demand, nitrogen andphytoplankton. Specially, the original WASP model was improved by providing methodto calculate nutrient fluxes from the bottom sediment layer, allowing for better simulationof interactions between water column and bottom sediment.
(3) A3D finite volume method for lake hydrodynamics on unstructured grid wasdeveloped. The horizontal computational domain are represented using non-overlappingunstructured triangular meshes, while irregular bottom elevations are represented with astretched or sigma vertical coordinate. The model's time integration employs aninternal-external mode splitting procedure to separate the internal shear mode from theexternal free surface gravity wave. The external mode solution uses a modifiedfourth-order Runge-Kutta time-stepping scheme to calculate the two-dimensional surfaceelevation field and the depth averaged velocities. The model’s internal momentumequation solution is solved numerically using a simple combined explicit and implicitscheme. Specially, the model uses Osher’s scheme to compute numerical flux across theboundary of triangular elements in horizontal direction and use TVD scheme to solvevertical advection.
(4) The3D model was applied to the Great Lake Donghu area in Wuhan city, Chinato evaluate its effectiveness. To provide better boundary and condition data for drivingand validating the model, RS and GIS techniques were employed to extract water depth,temperature and water quality information from RS images including MODIS, LandsatTM and Landsat ETM+. Furthermore, GIS technique was fully leveraged to aidpre-and-post processing involved in the modeling task. With this methodology,hydrodynamics and temperature field of six major lakes (i.e., Lake Donghu, Lake Shahu,Lake Yangchunhu, Lake Beihu, Lake Yanxihu and Lake Yandonghu) located in the studyarea were carefully researched by considering different metrological conditions. Specialfocus was put on simulation of water quality in Lake Donghu. The modeling resultsshowed that the simulated currents, temperature and water quality variables in watercolumn of the six lakes agreed with the observed or estimated data well. The presentedmethodology that integrates GIS, RS into hydrodynamics modeling provides a reliable, easy-to-use and one-stop solution for modeling lake system.
(5) A project aimed to reestablish hydraulic connectivity between lakes in the GreatLake Donghu area and the Yangtze River is being implemented in Wuhan at present. Withthe purpose of offering a scientific tool for investigating water quality restoration effectsfollowing alternative designs of the project and determining suitable operation strategies,the3D model was utilized once again. After proposing three water network connectivityschemes and operation solutions as well as an assessment indicator system used toevaluate and compare different solutions, the model was applied to analyze watermovement patterns and possible water quality changes responded to different solutions.Advantages and shortcomings of the solutions were compared under the same roof of theindicator system to determine the best one for restoration of the water quality in the lakes.
（1）湖泊水流运动复杂多变、湖流输运和混合作用强烈，为正确地模拟湖泊水动力过程，论文推导建立了Sigma坐标系下由连续性方程、动量方程、温度方程和物质输运方程组成的三维湖泊水动力模型控制方程组。采用κ-ε垂向湍流闭合模型及Smagorinsky水平湍流闭合模型对方程组进行闭合。考虑到数值模型计算需要，推导建立了二维垂向积分方程。在水温模型中，基于经典的传热概念，提出了包含辐射、对流、传导和蒸发项的湖泊自由水面热通量计算方法。该方法简单实用，尽量减少了对实测数据的要求，具有广泛的实用性。
（2）以WASP模型为基础，分析了湖泊中氮、磷等元素的迁移转化规律及其与外界环境和水生生物的相互作用机制，构建了包含溶解氧平衡系统、浮游植物生长系统、氮循环系统和磷循环系统组成的三维湖泊水质模型。
（3）发展了一种基于有限体积法的湖泊三维水动力水质耦合数值模型。该模型采用无结构三角形网格和垂向Sigma坐标来剖分计算区域，空间上模型采用有限体积法离散三维水动力水质方程组，时间上采用模式分裂技术，即首先通过外模求解二维垂向积分方程以获得水深分布，然后利用内模求解三维水流运动方程组获得三维流场细节，进而求解水温模型和水质模型。外模求解中，采用修正的四阶龙格库塔格式求解时变项，运用Osher格式计算跨边界法向通量。求解三维内模动量方程时，模型采用显示与隐式相结合的方法，其中水平对流项及扩散项采用基于Osher格式的黎曼数值解，垂向对流项采用TVD格式，垂向扩散采用隐格式离散。
（4）以武汉大东湖水系为对象开展了数值模型验证工作。开展数值模拟需要高质量的气象水文驱动数据，然而对湖泊这样大面积水体的同步观测极为困难。为解决这一难题，本研究利用多源遥感数据（包括MODIS、Landsat5TM和Landsat7ETM+）开展了湖泊水文水质信息反演工作，利用反演数据为数值模拟提供初始条件并对模型进行验证。此外，本研究在数值模拟中全面引入GIS技术来辅助完成前处理、后处理与可视化任务，大大提高了建模和调试的效率。按照以上技术思路，论文研究并探讨了不同气候背景下大东湖水系中东湖、沙湖、杨春湖、北湖、严西湖和严东湖六个主要湖泊的三维流场结构和水温时空变化规律。此外，重点针对东湖开展了水质时空变化模拟研究，以验证模型有效性。结果表明，该研究思路和技术路线为开展湖泊水环境数值模拟提供了可靠、稳定且易执行的一体化解决方案，为建立湖泊水环境调控长效机制提供了有力技术支撑。
（5）运用建立的数值模型，开展了江湖连通情境下武汉大东湖水系水网调度问题研究。根据大东湖生态水网项目总体规划，提出了初步的水网连通及引水调度方案和方案评价指标体系。运用数值模型开展水网连通研究，分析了不同方案对湖泊水体运动模式、水流形态和水质改善的影响，根据建立的指标体系对比了不同方案的优劣以确定最有利于大东湖水生态环境改善的调度方案。
Lakes are resplendent jewels of the earth. The hydrological process and ecologicalsystem structure in lakes are undergoing deep change due to the dual influence of natureand human behaviors. Exploring evolution procedures and patterns of lakehydro-ecological system, as well as revealing interaction rules between air, water andsediment of the system, are important and necessary research topics. However, intensiveexchanges of substance and energy between atmosphere, hydrosphere and biosphere takeplace in the lake system, resulting in extremely complex mixture of physical, chemical andbiologic procedures. This poses a great challenge on researchers who try to simulate thelake system with numerical models, because a variety of methods and knowledgebelonging to diverse research fields like chemistry and biology have to be integrated intothe hydrodynamics framework, which is the basis for the simulation. In order to meet thischallenge, this paper is focused on the development and application of a three-dimensionalhydrodynamics and water quality lake model using unstructured grid and finite volumemethod (FVM), aiming to provide a general tool for modeling the flow field, transport,and eutrophication processes in lakes. The main contributions and innovations of thiswork are outlined below:
(1) In order to simulate the complicated circulation and mixture schema of lakes, amathematic model consisting of continuity, momentum, temperature and transportationequations was established. The standard k-ε vertical turbulent model and Smagorinskyhorizontal turbulent model were used to close the model physically and mathematically.Two-dimensional vertically integrated equations were also deducted to satisfy requirementof numerical computation. In particular, this work provides a method for estimating heatflux on the free surface of lakes where the flux is determined based on the balance ofincoming solar radiation, net back radiation flux, sensible heat exchange, and evaporativeheat. This method was liveraged in the temperature model and was proved to be a simpleand practical way for simulating lake temperature since it minimized requirements ofmetrological data.
(2) Based on principles of WASP, a3D water quality model was constructed. The model is able to simulate spatial and temporal variations of eight water quality variablesincluding dissolved oxygen, carbon biological oxygen demand, nitrogen andphytoplankton. Specially, the original WASP model was improved by providing methodto calculate nutrient fluxes from the bottom sediment layer, allowing for better simulationof interactions between water column and bottom sediment.
(3) A3D finite volume method for lake hydrodynamics on unstructured grid wasdeveloped. The horizontal computational domain are represented using non-overlappingunstructured triangular meshes, while irregular bottom elevations are represented with astretched or sigma vertical coordinate. The model's time integration employs aninternal-external mode splitting procedure to separate the internal shear mode from theexternal free surface gravity wave. The external mode solution uses a modifiedfourth-order Runge-Kutta time-stepping scheme to calculate the two-dimensional surfaceelevation field and the depth averaged velocities. The model’s internal momentumequation solution is solved numerically using a simple combined explicit and implicitscheme. Specially, the model uses Osher’s scheme to compute numerical flux across theboundary of triangular elements in horizontal direction and use TVD scheme to solvevertical advection.
(4) The3D model was applied to the Great Lake Donghu area in Wuhan city, Chinato evaluate its effectiveness. To provide better boundary and condition data for drivingand validating the model, RS and GIS techniques were employed to extract water depth,temperature and water quality information from RS images including MODIS, LandsatTM and Landsat ETM+. Furthermore, GIS technique was fully leveraged to aidpre-and-post processing involved in the modeling task. With this methodology,hydrodynamics and temperature field of six major lakes (i.e., Lake Donghu, Lake Shahu,Lake Yangchunhu, Lake Beihu, Lake Yanxihu and Lake Yandonghu) located in the studyarea were carefully researched by considering different metrological conditions. Specialfocus was put on simulation of water quality in Lake Donghu. The modeling resultsshowed that the simulated currents, temperature and water quality variables in watercolumn of the six lakes agreed with the observed or estimated data well. The presentedmethodology that integrates GIS, RS into hydrodynamics modeling provides a reliable, easy-to-use and one-stop solution for modeling lake system.
(5) A project aimed to reestablish hydraulic connectivity between lakes in the GreatLake Donghu area and the Yangtze River is being implemented in Wuhan at present. Withthe purpose of offering a scientific tool for investigating water quality restoration effectsfollowing alternative designs of the project and determining suitable operation strategies,the3D model was utilized once again. After proposing three water network connectivityschemes and operation solutions as well as an assessment indicator system used toevaluate and compare different solutions, the model was applied to analyze watermovement patterns and possible water quality changes responded to different solutions.Advantages and shortcomings of the solutions were compared under the same roof of theindicator system to determine the best one for restoration of the water quality in the lakes.
引文
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