MODELING AND FORECASTING MONTHLY AVERAGE WATER LEVELS BASED ON THE ELLIPTIC ORBIT MODEL

Evaluation and forecasting of water‐level fluctuation for one river is of increasing importance since it is intimately associated with human welfare and socioeconomic sustainability development. In this study, it is found that time series of monthly water‐level fluctuation exhibits annual cyclical variation. Then with annual periodic extension for monthly water‐level fluctuation, the so‐called “elliptic orbit model” is proposed for describing monthly water‐level fluctuation by mapping its time series into the polar coordinates. Experiments and result analysis indicate potentiality of the proposed method that it yields satisfying results in evaluating and forecasting monthly water‐level fluctuation at the monitoring stations in the Yangtze River of China. It is shown that the monthly water‐level fluctuation is well described by the proposed elliptic orbit model, which offers a vivid approach for modeling and forecasting monthly water‐level fluctuation in a concise and intuitive way.     

垂直与水平渗透作用下潜水非稳定渗流运动规律

对河渠边界控制的半无限含水层,建立垂向入渗与河渠水平渗透共同作用下的潜水非稳定渗流模型;利用Boussinesq第一线性化方法,通过Laplace变换,给出模型的解析解. 证明相关经典公式与模型特定解之间的转换关系,分析经典公式适用范围．根据模型解,逐一定量研究下述变量,如垂向入渗强度、河渠水位变动幅度、含水层结构参数如给水度和导压系数、计算点与边界之间的距离,对渗流过程的影响．这些变量的变化,对潜水位获最大上升速度的时间产生延迟效应;论证一些变量间产生等效延迟效应的条件．根据解的数学特征,讨论其对应的物理意义和潜水位变动规律．     

Two-dimensional modelling of the river Rhine

The system for operational water level forecast and prediction of (fortunately not daily) pollutant transport for the river Rhine is in daily use. This model is based on the Saint-Venant or one-dimensional shallow water equations.The model is augmented by additional terms and equations to model the effect of dead zones and the transport of soluble components.The next step is to move towards two-dimensional models. An important problem that arises is that the domain of the fluid is not fixed by the given data, but depends on the water level and is therefore part of the solution of the model. Even worse, depending on the topography of the river bed, even the topology of the fluid domain may change, as islands may appear at low water and get flooded at high water situations.     

COLLECTIVE DECISION MAKING IN AN INTERNATIONAL RIVER POLLUTION MODEL

In this paper, we study international river pollution problems. We introduce a model in which countries located along a river from upstream to downstream derive benefits from causing pollution, but also incur environmental costs from experiencing its own pollution and the pollution of all its upstream countries. The total welfare, being the sum of all benefits minus the sum of all costs, is maximized when all countries cooperate. Several principles from international water law are applied to find reasonable and fair distributions of the total welfare that can be obtained under full cooperation. Such a distribution of the welfare at efficient pollution levels can be implemented by monetary compensations.     

一类输水线路的最佳布线问题

主要解决了如下问题 :对于从河流 L取水并输送到 L同岸的两个用水点 A,B的输水工程(图 1) ,当修建各段输水管道的耗资系数分别为 k1,k2 ,k3 时 ,如何确定抽水点 P及分水点 O才能使加权和值w =k1OA+ k2 OB+ k3OP为最小 .     

Optimization of the production of hydroelectric power systems with a variable head

We present in this paper a new approach for optimization of the production of hydroelectric power systems with a variable head. The problem is formulated as a minimum norm problem.The method takes into account the water head variation. To avoid underestimation of production for rising water levels and overestimation for falling water level, an average head (of begin and end of time step) is used. The method also takes into account the stochasticity of the river flows. Numerical results for a real system in operation including up to six reservoirs are reported for different water conditions. The proposed method is computationally efficient compared to other approaches.This work was supported by the National Research Council of Canada, Grant No. A-4146. The authors would like to acknowledge the data obtained from British Columbia Hydro.     

Wave front tracing and asymptotic stability of planar travelling waves for a two-dimensional shallow river model

The propagation of surface water waves in a frictional channel with a uniformly inclined bed is governed by a two-dimensional shallow river model. In this paper, we consider the time-asymptotic stability of weak planar travelling waves for a two-dimensional shallow river model with Darcy's law. We derive an effective parabolic equation to analyze the wave front motion. By employing weighted energy estimates, we show that weak planar travelling waves are time-asymptotically stable under sufficiently small perturbations.     

Practical Extreme Value Modelling of Hydrological Floods and Droughts: A Case Study

Estimation of flood and drought frequencies is important for reservoir design and management, river pollution, ecology and drinking water supply. Through an example based on daily streamflow observations, we introduce a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts. We fit the generalised extreme value (GEV) distribution by the method of block maxima and the generalised Pareto (GP) distribution by applying the peak over threshold method. Maximum likelihood, penalized maximum likelihood and probability weighted moments are used for parameter estimation. We incorporate trends and seasonal variation in the models instead of splitting the data, and investigate how the observed number of extreme events, the chosen statistical model, and the parameter estimation method effect parameter estimates and quantiles. We find that a seasonal variation should be included in the GEV distribution fitting for floods using block sizes less than one year. When modelling droughts, block sizes of one year or less are not recommended as significant model bias becomes visible. We conclude that the different characteristics of floods and droughts influence the choices made in the extreme value modelling within a common inferential strategy.This revised version was published online in March 2005 with corrections to the cover date.     

用概率统计方法预测洪水水位

河流的水位变化从局部时间看是偶然的，但从长远看，这些偶然的数据常常是必然的结果。在自然条件下取得的水位数据，从本质上看都是随机的，正因为其随机性，统计方法尤为重要。本文试用统计方法分析预测河水的最高洪水水位，这对建筑桥梁、修建堤坝具有一定的参考价值。     

CLEANING A RIVER: AN ANALYSIS OF VOLUNTARY JOINT ACTION

Abstract River pollution creates negative externalities to downstream water users. In this paper, we analyze how voluntary joint action of water users can improve pollution abatement when optimal treatment cannot be enforced. We model a transboundary pollution game with a unidirectional pollutant flow. Players are identical except for their location along the river. We find that, surprisingly, the location of coalition members has no impact on coalition stability. Location does, however, affect overall welfare. The more upstream the members of the coalition are, the higher is the overall welfare because the positive externalities of cleaning accrue to a larger number of downstream water users.     

二层不同密度流体作用下的地震动水压力

研究了多泥沙河流中的水工建筑物受地震影响后,在异重分层次流体作用下的地震动水压力.考虑到具有铅直坝面的坝体在地震作用下,刚性地作垂直坝面方向的微幅简谐振动.因此假定河床水平,流体理想不可压缩,上下二层流体密度不同,从而得到一个有连接条件的混合边值问题的拉普拉斯方程.然后利用分离变量法以及共轭函数的方法,得到了方程的广义傅氏级数解.通过对该结果的定性分析,最后得到了异重分层次流体作用在坝面上的动水压力的变化规律性,这些结论具有重要的理论与应用价值.     

Optimization of reservoirs in series on a river with a nonlinear storage curve for long-term regulation

We present in this paper a new approach to finding the monthly optimal operation of a multireservoir power system connected in series on a river. The hydroelectric power generation is a highly nonlinear function of the storage, and the conversion factor assigned to each power plant is also a nonlinear function of the storage. We use for both a quadratic function of the storage; the resulting problem has a highly nonlinear objective function and linear constraints. We propose a transformation such that the system equations are reduced to linear-quadratic form. Lagrange and Kuhn-Tucker multipliers are used to adjoin the equality and inequality constraints to the objective function. Numerical results are presented for a real system in operation consisting of two reservoirs in series on a river for widely different water conditions.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors would like to acknowledge data obtained from B.C. Hydro.     

The water resources assessment based on resource exergy for the mainstream Yellow River

Based on the resource exergy theory, a unified exergetic index is proposed to assess both the quantity and quality of the water of the mainstream Yellow River, thus verifying the real available quantity of the river water in an ecological thermodynamics view. The chemical exergy, thermal exergy, potential exergy and sediment exergy of the river water as partial exergies are, respectively, calculated with the field river water intake data of the mainstream Yellow River. Exergetic potential is also defined to describe different working capacities of the river water along the mainstream. Finally, the temporal and spatial variation of the water resources of the mainstream Yellow River is illuminated with the proposed exergetic measure.     

Trading water along a river

A set of agents is located along a river. Each agent consumes certain amount of water he receives from his part of the river basin and may sell certain amount to his downstream agent if it is mutually beneficial. Water trading is restricted to two neighboring agents and an agent can only pass water to his downstream agent. We ask if this restricted trade to neighboring agents can implement an efficient allocation of water. We show that the efficient allocation of water can be achieved through the process of downstream bilateral trading. Specifically, we show that this one way “downstream” trading process implements the unique efficient allocation as well as a welfare distribution. We also show that the welfare distribution is in the core of the associated game of the problem. Moreover, we show that the coalition of agents upstream any agent obtains more welfare with the bilateral trading than with the downstream incremental distribution proposed by Ambec and Sprumont (2002) and less than with the upstream incremental distribution proposed by [Ambec and Ehlers, 2008a] and [Ambec and Ehlers, 2008b].     

再生水补给河流的水质模糊风险评价

采用再生水进行河流补给,对河流生态系统健康产生直接或潜在的危害.探讨河流水环境系统的不确定性,基于忽略弥散的一维河流水质模型,建立了再生水补给影响下的河流水质模型,选用三角模糊数来描述和处理水环境风险评价.应用结果表明,所建模型对于河流水质模拟与风险评价具有很好的适用性和稳定性.     

Eco-friendly location of small hydropower

We address the problem of locating small hydropower dams in an environmentally friendly manner. We propose the use of a multi-objective optimization model to maximize total hydropower production, while limiting negative impacts on river connectivity. Critically, we consider the so called “backwater effects” that dams have on power generation at nearby upstream sites via changes in water surface profiles. We further account for the likelihood that migratory fish and other aquatic species can successfully pass hydropower dams and other artificial/natural barriers and how this is influenced by backwater effects. Although naturally represented in nonlinear form, we manage through a series of linearization steps to formulate a mixed integer linear programing model. We illustrate the utility of our proposed framework using a case study from England and Wales. Interestingly, we show that for England and Wales, a region heavily impacted by a large number of existing river barriers, that installation of small hydropower dams fitted with even moderately effective fish passes can, in fact, create a win-win situation that results in increased hydropower and improved river connectivity.     

CLIMATE CHANGE AND COOPERATION IN TRANSBOUNDARY WATER SHARING: AN APPLICATION OF STOCHASTIC STACKELBERG DIFFERENTIAL GAMES IN VOLTA RIVER BASIN

Abstract As multiple countries share a river, the likelihood of conflicts over distributing water resources increases, particularly under the effects of climate change. In this paper, we demonstrate how countries can cooperate in sustainable transboundary water sharing under such conditions. We examine the case of water distribution in the Volta Basin of West Africa between the upstream country, Burkina Faso, and the downstream country, Ghana. The latter faces an additional tradeoff between the production of hydropower in the south, close to the outlet of the basin, and agricultural water use in the reservoir’s catchment area in the north. In the framework of a stochastic Stackelberg differential game, we show how sustainable water‐sharing agreements can be achieved by linking transboundary flows to hydropower exports. Our results indicate that, through cooperation, Ghana will have an opportunity to increase its water abstraction for agriculture, which has remained largely restricted. We also find that the equilibrium strategies for the long‐run distribution are stable even with increasing variances of water flow.     

Multifractal structure in Latin-American market indices

We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis. Comparing with the results obtained for a developed country (US) we conclude that the multifractality degree is higher for emerging markets. Moreover, we propose a stock market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. Finally, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations of the time series and the broad fat-tail distributions. We find that the multifractal structure of Latin-American market indices can be mainly attributed to the latter.     

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a nonconservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary lagrangian eulerian formulation, in order to compute the solution in the moving domain.