基于概率描述的宏观尺度空间均化流域水文模型研究
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摘要
传统的物理性流域水文模型以“点”尺度的水文过程控制方程为基础构建,与概念性模型相比有显著的优越性,但存在由于方程非线性和下垫面条件不均匀性所导致的方程适用尺度和模型应用尺度间不匹配的问题。基于对下垫面条件不均匀性的概率描述,通过空间均化构建宏观尺度的水文过程控制方程,是解决水文尺度问题的一种新途径。
流域水文过程的数学描述是流域水文模型构建的基础,论文建立了主要水文过程的宏观尺度空间均化方程:基于概率密度函数和土壤垂向分层对饱和导水率空间变异性进行了全面描述,建立了空间均化分层土壤入渗模型和空间均化壤中流模型,能模拟饱和导水率水平和垂直方向都不均匀条件下土壤的入渗和壤中流出流过程。基于沟道参数均匀假设,改进了Yoon等建立的沟道-坡面耦合坡面流模型,使模型参数能够根据DEM确定。
在所建立的水文过程空间均化方程的基础上,构建了具有自己特色的空间均化流域水文模型——SAWH模型。模型中流域下垫面特性的宏观不均匀性通过流域划分和模型计算单元(MCU)内分区进行考虑,土壤饱和导水率和地形的微观不均匀性通过概率密度函数进行描述。模型应用建立的宏观尺度空间均化方程描述MCU上的主要水文过程,在保持传统物理性水文模型机理性的同时从理论上避免了方程适用尺度和模型应用尺度不匹配的问题。
空间均化流域模型在半干旱半湿润的沁河流域和湿润的美国Baron Fork River流域展开了应用,流域出口流量过程的对比表明模型具有较高的计算精度,Nash效率系数均在0.70以上,水量平衡指数在10%以内。由于SAWH模型应用了宏观尺度的水文过程控制方程,模型可在较大空间计算单元上计算,在上述两个典型流域的应用表明了模型具有较高的计算效率,为大中尺度流域的水文模拟提供了新的方法。
在沁河流域汛期的参数敏感性分析表明了土壤的饱和导水率的不均匀性对模拟结果有较大影响,以Baron Fork River流域以两次洪水过程为例,对降雨空间分布和土壤饱和导水率统计参数的不确定性及其对模型模拟结果的影响进行了分析。
The current generation of physically based distributed hydrological models is based on the point scale equations. They have distinct advantages compared with the conceptual models, but also suffer from serious shortcomings, of which the essential one is the inconsistence between the equation applicable scale and model application scale. Such scale inconsistency makes the physical meaning of the equations as well as the parameters uninterpretable. To address this problem, Kavvas et al. proposed a new hydrological modeling approach which upscales the point scale equations to macro scale through the spatial averaging based on the probability description of landscape heterogeneity.
The mathematical equations controlling the hydrological processes serve as the basis of watershed hydrological modeling. As the first attempt of hydrological modeling based on spatial averaging approach, the equations and hydrological model developed by Kavvas et al. have obvious deficiencies such as ignoring of soil properties variance in vertical direction and over-demanding of data. In this thesis, the equations controlling the major hillslope processes have been improved: the spatial averaging infiltration model for layered soil (SAI model) and spatial averaging interflow model (SAIF model) are developed, which incorporating spatial heterogeneity of soil properties in both horizontal and vertical aspects. Besides, the new surface flow model for the hillslope with rill-interrill configurations is developed by simplifying Yoon’s model so that the parameters can be derived from digital elevation model directly.
Based on macro-scale equation controlling hydrological processes, a new watershed hydrological model, Spatial Averaging Hydrological Model (SAWH model), is developed. The mathematical description of watershed heterogeneity is improved and the parameters estimation is significantly simplified and can be easilier applied compared with former models based on spatial averaging approach, i.e. WEHY model. In the SAWH model, the watershed is divided into model computation units (MCU) according to topograph, and the MCU is then partitioned to several sub-regions according to land use, the heterogeneity of soil hydraulic conductivity and micro topograph is descriped by propobility density function and incorporated into the upscaled equations. The inconsistency between the equation applicable scale and the model application scale is avoided through using the upscale equations, while the physically meaning of point scale equations and their parameters are preserved.
The SAWH model is applied at two typical watersheds with different climate, one is Qin River basin with semi-arid climate and the other is Baron Fork River basin with humid climate. The model can capture the observed streamflow pattern with high computation efficiency which suggests the macro-scale spatial averaging approach can serve as an alternative approach for continuous hydrological modeling in large watershed.
The analysis of model parameter sensitivities in Qin River basin shows the heterogeneity of soil hydraulic conductivity have significant influence to the watershed hydroligcal responses.
The uncertainty of SAWH model is further explored by analyzing two typical flood events in Baron Fork River Basin. The radar based rainfall data is compared with the rain gauge based data for analysis of temporal uncertainty of rainfall data. Also, the spatial uncertainty of rainfall data and its influence on SAWH predictibility are analyzed by comparing different rainfall data resolution. Finally, the model uncertainty caused by model parameters is explored by GLUE approach.
流域水文过程的数学描述是流域水文模型构建的基础,论文建立了主要水文过程的宏观尺度空间均化方程:基于概率密度函数和土壤垂向分层对饱和导水率空间变异性进行了全面描述,建立了空间均化分层土壤入渗模型和空间均化壤中流模型,能模拟饱和导水率水平和垂直方向都不均匀条件下土壤的入渗和壤中流出流过程。基于沟道参数均匀假设,改进了Yoon等建立的沟道-坡面耦合坡面流模型,使模型参数能够根据DEM确定。
在所建立的水文过程空间均化方程的基础上,构建了具有自己特色的空间均化流域水文模型——SAWH模型。模型中流域下垫面特性的宏观不均匀性通过流域划分和模型计算单元(MCU)内分区进行考虑,土壤饱和导水率和地形的微观不均匀性通过概率密度函数进行描述。模型应用建立的宏观尺度空间均化方程描述MCU上的主要水文过程,在保持传统物理性水文模型机理性的同时从理论上避免了方程适用尺度和模型应用尺度不匹配的问题。
空间均化流域模型在半干旱半湿润的沁河流域和湿润的美国Baron Fork River流域展开了应用,流域出口流量过程的对比表明模型具有较高的计算精度,Nash效率系数均在0.70以上,水量平衡指数在10%以内。由于SAWH模型应用了宏观尺度的水文过程控制方程,模型可在较大空间计算单元上计算,在上述两个典型流域的应用表明了模型具有较高的计算效率,为大中尺度流域的水文模拟提供了新的方法。
在沁河流域汛期的参数敏感性分析表明了土壤的饱和导水率的不均匀性对模拟结果有较大影响,以Baron Fork River流域以两次洪水过程为例,对降雨空间分布和土壤饱和导水率统计参数的不确定性及其对模型模拟结果的影响进行了分析。
The current generation of physically based distributed hydrological models is based on the point scale equations. They have distinct advantages compared with the conceptual models, but also suffer from serious shortcomings, of which the essential one is the inconsistence between the equation applicable scale and model application scale. Such scale inconsistency makes the physical meaning of the equations as well as the parameters uninterpretable. To address this problem, Kavvas et al. proposed a new hydrological modeling approach which upscales the point scale equations to macro scale through the spatial averaging based on the probability description of landscape heterogeneity.
The mathematical equations controlling the hydrological processes serve as the basis of watershed hydrological modeling. As the first attempt of hydrological modeling based on spatial averaging approach, the equations and hydrological model developed by Kavvas et al. have obvious deficiencies such as ignoring of soil properties variance in vertical direction and over-demanding of data. In this thesis, the equations controlling the major hillslope processes have been improved: the spatial averaging infiltration model for layered soil (SAI model) and spatial averaging interflow model (SAIF model) are developed, which incorporating spatial heterogeneity of soil properties in both horizontal and vertical aspects. Besides, the new surface flow model for the hillslope with rill-interrill configurations is developed by simplifying Yoon’s model so that the parameters can be derived from digital elevation model directly.
Based on macro-scale equation controlling hydrological processes, a new watershed hydrological model, Spatial Averaging Hydrological Model (SAWH model), is developed. The mathematical description of watershed heterogeneity is improved and the parameters estimation is significantly simplified and can be easilier applied compared with former models based on spatial averaging approach, i.e. WEHY model. In the SAWH model, the watershed is divided into model computation units (MCU) according to topograph, and the MCU is then partitioned to several sub-regions according to land use, the heterogeneity of soil hydraulic conductivity and micro topograph is descriped by propobility density function and incorporated into the upscaled equations. The inconsistency between the equation applicable scale and the model application scale is avoided through using the upscale equations, while the physically meaning of point scale equations and their parameters are preserved.
The SAWH model is applied at two typical watersheds with different climate, one is Qin River basin with semi-arid climate and the other is Baron Fork River basin with humid climate. The model can capture the observed streamflow pattern with high computation efficiency which suggests the macro-scale spatial averaging approach can serve as an alternative approach for continuous hydrological modeling in large watershed.
The analysis of model parameter sensitivities in Qin River basin shows the heterogeneity of soil hydraulic conductivity have significant influence to the watershed hydroligcal responses.
The uncertainty of SAWH model is further explored by analyzing two typical flood events in Baron Fork River Basin. The radar based rainfall data is compared with the rain gauge based data for analysis of temporal uncertainty of rainfall data. Also, the spatial uncertainty of rainfall data and its influence on SAWH predictibility are analyzed by comparing different rainfall data resolution. Finally, the model uncertainty caused by model parameters is explored by GLUE approach.
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