河道洪水实时概率预报模型与应用

通过数据同化方法合理地将实时水文观测数据融入到洪水预报模型中,可提高洪水预报模型的实时性和精确度。选取沿程断面流量、水位和糙率系数作为代表水流状态的基本粒子,以监测断面实测水位数据作为观测信息,建立了基于粒子滤波数据同化算法的河道洪水实时概率预报模型。模型应用于黄河中下游河道洪水预报计算的结果表明,采用粒子滤波方法同化观测水位后,不仅可以直接校正水位,同时也可以有效地校正流量和糙率,为未来时刻模型预报计算提供更准确的水流初始条件和糙率取值区间,进而有效地提高模型预报结果的精度,给出合理的概率预报区间。不同预报期的预报结果表明,随着预报期的增长,同化效果减弱,模型预报结果的精度会有所降低,水位概率预报结果受粒子间糙率不同的影响不确定性增加,而流量概率预报结果受给定模型边界条件的影响不确定性降低。所提出模型可以有效同化真实水位观测数据,适合应用于实际的洪水预报工作中。     

黄河下游高含沙洪水过程一维水沙耦合数学模型

采用浑水控制方程,建立了基于耦合解法的一维非恒定非均匀沙数学模型,用于模拟高含沙洪水演进时的河床冲淤过程.然后采用黄河下游游荡段1977年7—8月实测高含沙洪水资料对该模型进行率定,基于水沙耦合解法的各水文断面流量、总含沙量及分组含沙量的计算过程与实测过程符合更好,计算的沿程最高水位及累计河段冲淤量与实测值也较为符合.最后还采用2004年8月高含沙洪水资料对该模型进行了验证.模型率定及验证计算结果表明,采用一维水沙耦合模型计算高含沙洪水过程,能取得较高的精度.     

动态实时洪水风险分析及管理系统

当前洪水风险分析按照典型设计标准洪水进行计算的模式难以满足实际防洪管理需要,为了提高洪水风险分析的实时性以及适应洪水演进的动态性,设计了动态实时洪水风险分析框架。在本框架中,先采用一维和二维动态耦合水动力学数值方法耦合溃堤模型,然后在樵桑联围防洪保护区建立洪水演进模拟模型,通过灵活处理模型计算边界条件以及动态设置溃堤功能,计算不同设计标准洪水发生时,堤防出现单一溃口或者组合溃口后保护区内洪水演进过程。按照上述框架开发了樵桑联围动态实时洪水风险图编制与管理应用系统,并利用历史洪水资料开展模型验证,验证结果表明,2008-06洪水马口站、三水站、大熬站、甘竹（一）站的实测最高水位和模型计算最高水位的绝对误差分别为-0.10、0.10、0.09、0.04 m,均满足洪水模拟精度要求。利用模型计算了西江发生200年一遇的洪水情况下,江根堤防出现溃口后的洪水流量及溃口内外洪水水位变化过程,模拟溃口宽度168 m,最大溃口洪水流量达到5 190 m³,分析了堤防溃决后3、6和24 h洪水漫延导致村落淹没情况,结果表明其满足合理性分析。     

城市暴雨内涝数学模型的研究与应用

以城市地表与明渠、河道水流运动为主要模拟对象,研制了模拟城市暴雨内涝积水的数学模型。模型以平面二维非恒定流的基本方程和无结构不规则网格划分技术为骨架,同时,针对小于离散网格尺度的河道或明渠,应用了一维非恒定流方程的算法。采用分类简化处理的方法,将通道分为河道型、路面型、特殊通道型(城市内的二级河道),根据不同类型简化动量方程,求任意网格各个通道上的单宽流量。采用一维非恒定流方程模拟地下排水管网内的水流,并给出泵站、闸门、淹没出流管道等排水系统的处理方法。根据无结构不规则网格的设计思路,按照天津、南京、南昌三市的地形地貌特征分别设计多边形的计算网格。介绍了城市面雨量的计算方法以及数学模型在天津市、南京市、南昌市的应用情况和误差分析。     

非恒定水流计算的最优控制问题及其变分求解

为综合利用各类可用的信息源(如水流运动规律,观测资料和统计信息),在反问题的框架下构建了非恒定水流计算的变分模型.针对模型预测的可能误差来源,给出了初始条件、边界条件、物理参数三类独立参量及综合控制问题的定义.在此基础上,阐述了变分法求解这类偏微分方程最优化控制问题的基本原理及模型求解步骤.同时,为便于应用参考,选取初始条件、边界条件和物理参数作为控制向量,以实际常用的水流运动微分方程为基础,导出了一、二维非恒定水流计算的通用伴随方程.并以珠江黄浦至大虎段二维潮流计算为例,展示了变分模型的应用.     

黄河下游河道悬移质泥沙与床沙交换计算研究

在前人研究成果的基础上,根据挟沙水流任一粒径组泥沙在输移过程中质量守恒原理,建立了一维非恒定挟沙水流悬移质泥沙和床沙交换基本方程;通过引入平衡冲淤物粒径的概念,建立了河床处于淤积与冲刷时冲淤物粒径的计算公式,并提出了一套完整的一维非恒定挟沙水流悬移质泥沙和床沙交换计算方法。将该成果引入黄河下游一维扩展泥沙数学模型中,采用黄河下游1977年高含沙洪水与1999年汛后至2002年汛前冲刷系列进行了验证。结果表明,该方法能较好地模拟悬沙与床沙的交换过程,克服分组挟沙力方法的缺陷,使得非均匀沙计算理论上更加完善,应用上更加方便。     

河道洪水实时预报的半自适应模型研究

提出和讨论了基于马斯京根流量演算河道洪水实时预报的半自适应滤波模型.在该模型中量测误差系列的协方差矩阵可以通过信息更新系列实时估计出来,只有模型误差系列的协方差矩阵需要预先给出.提出了一个处理区间入流较为合理、方便的方法.通过验证和应用说明了该模型的合理性.     

基于神经网络理论的河道水情预报模型

河道水流运动过程特别是洪水演进过程是一个复杂的非线性动力学过程,鉴于神经网络具有很强的处理大规模复杂非线性动力学系统的能力,本文将神经网络理论用于河道水情预报的研究,以期识别水流运动变化过程与其影响因子之间的复杂非线性关系,为河道水情预报提供了一条新的途径。在此基础上建立了螺山站洪水预报的非线性动力学模型,通过分析研究得出近年来特别是1998年长江中游出现的小流量高水位现象与螺山汉口河段累计淤积有关并得到螺山站水位变化与河床淤积之间的定量关系。     

长江中游洞庭湖防洪系统水流模拟——Ⅰ．建模思路和基本算法

针对长江中游洞庭湖防洪系统规模庞大、水流复杂、资料短缺和预报时限紧迫的实际条件,提出了具有层次和模块结构特点、一维与二维水流模拟、水力学与水文学方法、理论模型与补充信息相结合的建模途径.所建模型的湖泊部分采用无结构网格二维非恒定流高性能有限体积格式,以适应湖区复杂的边界形状和保持水量平衡;河网部分采用一维非恒定流守恒型显格式,避免隐格式矩阵算法的复杂性,同时有利于与二维模型的耦合及与各种复杂连通关系的显式连接.这种一、二维混合非恒定流模型可用于长江干流、洞庭湖河网及湖泊、堤垸区的洪水演进和防洪调度的水流仿真.     

水电站进水口快速闸门水力学分析

主要分析水电站进水口快速闸门在动水关闭过程中流量、临界开度和闸门受水流作用力(闸顶水压力、闸底水压力和闸门水平压力)等问题。根据模型试验所观测的水力现象和非恒定流计算理沦,提出了计算电站闸门、引水管道的水力参数(流量、水头和通气孔水位等)的数学模型。实例计算结果和模型试验结果基本吻合。     

A stochastic collocation based Kalman filter for data assimilation

In this paper, a stochastic collocation-based Kalman filter (SCKF) is developed to estimate the hydraulic conductivity from direct and indirect measurements. It combines the advantages of the ensemble Kalman filter (EnKF) for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, the random log hydraulic conductivity field is first parameterized by the Karhunen–Loeve (KL) expansion and the hydraulic pressure is expressed by the PCE. The coefficients of PCE are solved with a collocation technique. Realizations are constructed by choosing collocation point sets in the random space. The stochastic collocation method is non-intrusive in that such realizations are solved forward in time via an existing deterministic solver independently as in the Monte Carlo method. The needed entries of the state covariance matrix are approximated with the coefficients of PCE, which can be recovered from the collocation results. The system states are updated by updating the PCE coefficients. A 2D heterogeneous flow example is used to demonstrate the applicability of the SCKF with respect to different factors, such as initial guess, variance, correlation length, and the number of observations. The results are compared with those from the EnKF method. It is shown that the SCKF is computationally more efficient than the EnKF under certain conditions. Each approach has its own advantages and limitations. The performance of the SCKF decreases with larger variance, smaller correlation ratio, and fewer observations. Hence, the choice between the two methods is problem dependent. As a non-intrusive method, the SCKF can be easily extended to multiphase flow problems.     

Ensemble filter methods with perturbed observations applied to nonlinear problems

The ensemble Kalman filter (EnKF) has been shown repeatedly to be an effective method for data assimilation in large-scale problems, including those in petroleum engineering. Data assimilation for multiphase flow in porous media is particularly difficult, however, because the relationships between model variables (e.g., permeability and porosity) and observations (e.g., water cut and gas–oil ratio) are highly nonlinear. Because of the linear approximation in the update step and the use of a limited number of realizations in an ensemble, the EnKF has a tendency to systematically underestimate the variance of the model variables. Various approaches have been suggested to reduce the magnitude of this problem, including the application of ensemble filter methods that do not require perturbations to the observed data. On the other hand, iterative least-squares data assimilation methods with perturbations of the observations have been shown to be fairly robust to nonlinearity in the data relationship. In this paper, we present EnKF with perturbed observations as a square root filter in an enlarged state space. By imposing second-order-exact sampling of the observation errors and independence constraints to eliminate the cross-covariance with predicted observation perturbations, we show that it is possible in linear problems to obtain results from EnKF with observation perturbations that are equivalent to ensemble square-root filter results. Results from a standard EnKF, EnKF with second-order-exact sampling of measurement errors that satisfy independence constraints (EnKF (SIC)), and an ensemble square-root filter (ETKF) are compared on various test problems with varying degrees of nonlinearity and dimensions. The first test problem is a simple one-variable quadratic model in which the nonlinearity of the observation operator is varied over a wide range by adjusting the magnitude of the coefficient of the quadratic term. The second problem has increased observation and model dimensions to test the EnKF (SIC) algorithm. The third test problem is a two-dimensional, two-phase reservoir flow problem in which permeability and porosity of every grid cell (5,000 model parameters) are unknown. The EnKF (SIC) and the mean-preserving ETKF (SRF) give similar results when applied to linear problems, and both are better than the standard EnKF. Although the ensemble methods are expected to handle the forecast step well in nonlinear problems, the estimates of the mean and the variance from the analysis step for all variants of ensemble filters are also surprisingly good, with little difference between ensemble methods when applied to nonlinear problems.     

Application of the EnKF and Localization to Automatic History Matching of Facies Distribution and Production Data

The performance of the ensemble Kalman filter (EnKF) for continuous updating of facies location and boundaries in a reservoir model based on production and facies data for a 3D synthetic problem is presented. The occurrence of the different facies types is treated as a random process and the initial distribution was obtained by truncating a bi-Gaussian random field. Because facies data are highly non-Gaussian, re-parameterization was necessary in order to use the EnKF algorithm for data assimilation; two Gaussian random fields are updated in lieu of the static facies parameters. The problem of history matching applied to facies is difficult due to (1) constraints to facies observations at wells are occasionally violated when productions data are assimilated; (2) excessive reduction of variance seems to be a bigger problem with facies than with Gaussian random permeability and porosity fields; and (3) the relationship between facies variables and data is so highly non-linear that the final facies field does not always honor early production data well. Consequently three issues are investigated in this work. Is it possible to iteratively enforce facies constraints when updates due to production data have caused them to be violated? Can localization of adjustments be used for facies to prevent collapse of the variance during the data-assimilation period? Is a forecast from the final state better than a forecast from time zero using the final parameter fields?To investigate these issues, a 3D reservoir simulation model is coupled with the EnKF technique for data assimilation. One approach to enforcing the facies constraint is continuous iteration on all available data, which may lead to inconsistent model states, incorrect weighting of the production data and incorrect adjustment of the state vector. A sequential EnKF where the dynamic and static data are assimilated sequentially is presented and this approach seems to have solved the highlighted problems above. When the ensemble size is small compared to the number of independent data, the localized adjustment of the state vector is a very important technique that may be used to mitigate loss of rank in the ensemble. Implementing a distance-based localization of the facies adjustment appears to mitigate the problem of variance deficiency in the ensembles by ensuring that sufficient variability in the ensemble is maintained throughout the data assimilation period. Finally, when data are assimilated without localization, the prediction results appear to be independent of the starting point. When localization is applied, it is better to predict from the start using the final parameter field rather than continue from the final state.     

Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. By comparison with a more standard implementation of the EnKF, the NS-EnKF gives better results with regard to histogram preservation, uncertainty assessment, and transport predictions.     

基于集合卡尔曼平滑算法的土壤水分同化

为研究观测资料稀少情况下土壤质地及有机质对土壤水分同化的影响,发展了集合卡尔曼平滑(Ensemble Kalman Smooth, EnKS)的土壤水分同化方案。利用黑河上游阿柔冻融观测站2008年6月1日至10月29日的观测数据,使用EnKS算法将表层土壤水分观测数据同化到简单生物圈模型(Simple Biosphere Model 2, SiB2)中,分析不同方案对土壤水分估计的影响,并与集合卡尔曼滤波算法(EnKF)的结果进行比较。研究结果表明,土壤质地和有机质对表层土壤水分模拟结果影响最大而对深层的影响相对较小;利用EnKF和EnKS算法同化表层土壤水分观测数据,均能够显著提高表层和根区土壤水分估计的精度,EnKS算法的精度略高于EnKF且所受土壤质地和有机质的影响小于EnKF;当观测数据稀少时,EnKS算法仍然可以得到较高精度的土壤水分估计。     

Improved initial sampling for the ensemble Kalman filter

In this paper, we discuss several possible approaches to improving the performance of the ensemble Kalman filter (EnKF) through improved sampling of the initial ensemble. Each of the approaches addresses a different limitation of the standard method. All methods, however, attempt to make the results from a small ensemble as reliable as possible. The validity and usefulness of each method for creating the initial ensemble is based on three criteria: (1) does the sampling result in unbiased Monte Carlo estimates for nonlinear flow problems, (2) does the sampling reduce the variability of estimates compared to ensembles of realizations from the prior, and (3) does the sampling improve the performance of the EnKF? In general, we conclude that the use of dominant eigenvectors ensures the orthogonality of the generated realizations, but results in biased forecasts of the fractional flow of water. We show that the addition of high frequencies from remaining eigenvectors can be used to remove the bias without affecting the orthogonality of the realizations, but the method did not perform significantly better than standard Monte Carlo sampling. It was possible to identify an appropriate importance weighting to reduce the variance in estimates of the fractional flow of water, but it does not appear to be possible to use the importance weighted realizations in standard EnKF when the data relationship is nonlinear. The biggest improvement came from use of the pseudo-data with corrections to the variance of the actual observations.     

Dynamic routing modeling for flash flood forecast in river system

A real-time flood-forecasting method coupled with the one-dimensional unsteady flow model was developed for the Danshuei River system in northern Taiwan. Based on the flow at current time, the flow at new time is calculated to provide the water stage forecasting during typhoons. Data, from two typhoons in 2000: Bilis and Nari, were used to validate and evaluate the model capability. First, the developed model was applied to validate and evaluate with and without discharge corrections at the Hsin-Hai Bridge in Tahan Stream, Chung-Cheng Bridge in Hsintien Stream, and Sir-Ho Bridge in the Keelung River. The results indicate that the calculated water stage profiles approach the observed data. Moreover, the water stage forecasting hydrograph with discharge correction is close to the observed water stage hydrograph and yields a better prediction than that without discharge correction. The model was then used to quantify the difference in prediction between different methods of real-time water stage correction. The model results reveal that water stages using the 1–6 h forecast with real-time stage correction exhibits the best lead times. The accuracy for 1–3 h lead time is higher than that for 4–6 h lead time, suggesting that the flash flood forecast in the river system is reasonably accurate for 1–3 h lead time only. The method developed is effective for flash flood forecasting and can be adopted for flood forecasting in complicated river systems.     

基于LHS方法的地下水随机模拟及开采量风险性 评价

地下水流数值模拟过程中,水文地质参数的不确定性对模拟结果影响很大。以内蒙古鄂尔多斯市某水源地为例,利用拉丁超立方抽样(LHS)方法获得了含水层渗透参数的随机组合,进行地下水流随机模拟。通过对观测资料与计算水位的绝对值平均(MAE)误差和误差均方根(RMSE)的统计分析,获得了模型较为稳定的随机模拟次数是243次。利用该随机模型对水源地设计开采量进行水位预测,并给出允许降深的风险性分布图。结果表明,预测水位和标准差分布符合实际情况,水位降深大于35 m的风险性最大达到75%。     

考虑预报偏差的迭代式集合卡尔曼滤波在地下水水流数据同化中的应用

集合卡尔曼滤波（Ensemble Kalman Filter,EnKF）方法已广泛应用于地下水水流和污染物运移模拟相关问题的求解。但前人研究多建立在同化系统预报模型是准确的基础上,忽视了模型概化的不确定性。当模型概化不准确时,将导致预报偏差,可能带来错误的系统估计。因此,文章提出考虑模型预报偏差的迭代式集合卡尔曼滤波（Bias aware Ensemble Kalman Filter with Confirming Option,Bias-CEnKF）方法。以地下水水流数据同化为例,研究模型概化存在不确定条件下,边界条件、初始条件、源汇项概化不准确时新方法的有效性。结果表明,当预报模型概化不准确时,使用标准EnKF方法进行数据同化,可能会导致滤波发散,造成同化失败。Bias-CEnKF方法不仅保留了较好的同化性能,同时减小了参数、变量、偏差项非线性关系带来的不一致性。针对文章中4种情景,Bias-CEnKF同化获得的含水层渗透系数场以及水头场均接近真实场,且预报结果可靠。本研究进一步提升了模型概化不确定时EnKF方法的适用性,为实际野外复杂条件下地下水水流数据同化问题提供了可靠的方法。     

Geometry and kinematics of dunes during steady and unsteady flows in the Calamus River, Nebraska, USA

The geometry and kinematics of river dunes were studied in a reach of the Calamus River, Nebraska. During day-long surveys, dune height, length, steepness, migration rate, creation and destruction were measured concurrently with bedload transport rate, flow depth, flow velocity and bed shear stress. Within a survey, individual dune heights, lengths and migration rates were highly variable, associated with their three-dimensional geometry and changes in their shape through time. Notwithstanding this variability, there were discernible changes in mean dune height, length and migration rate in response to changing discharge over several days. Changes in mean dune height and length lagged only slightly behind changes in discharge. Therefore, during periods of both steady and unsteady flow, mean dune lengths were quite close to equilibrium values predicted by theoretical models. Mean dune steepnesses were also similar to predicted equilibrium values, except during high, falling flows when the steepness was above that predicted. Variations in mean dune height and length with discharge are similar to those predicted by theory under conditions of low mean dune excursion and discharge variation with a short high water period and long low water period. However, the calculated rates of change of height of individual dunes vary considerably from those measured. Rates of dune creation and destruction were unrelated to discharge variations, contrary to previous results. Instead, creations and destructions were apparently the result of local variations in bed shear stress and sediment transport rate. Observed changes in dune height during unsteady flows agree with theory fairly well at low bed shear stresses, but not at higher bed shear stresses when suspended sediment transport is significant.