Modeling variations in salt composition components of river water

The balance of a component contained in river water is considered taking into account its input with lateral inflow and decay in the aquatic environment. Random changes in lateral inflow causes fluctuations in the parameters of component input and decay. A stochastic equation of component balance is derived and used as the basis for the construction of an equation for the probability density of component concentration. The solution of this equation shows that the probability density follows lognormal law. This theoretical result is applicable to the analysis of time series of water salt composition components, including pH, alkalinity, chlorides, ammonia, iron, and aluminum. The applicability of the lognormal law is proved and distribution parameters are evaluated. The distributions of three components (pH, alkalinity, and chlorides) are found to split into two lognormal branches, describing high and low component concentrations. In the case of pH and alkalinity, this splitting is due to seasonal effects, while in the case of chlorides, it is caused by the difference between concentrations in the surface runoff at the early and final stages of snow melting and rainfalls. The application of the statistical distributions for probabilistic forecasting of extreme component concentrations is considered. The exceedance probability of standard limits of the components is considered. The use of exceedance probability in hydrochemical standardization is demonstrated.     

Analysis of river runoff in the Poyang Lake Basin of China: long-term changes and influencing factors

An analysis of the variation characteristics and evolutionary trends in the runoff of five rivers in the Poyang Lake Basin was conducted using the MK trend test, Morlet wavelet transforms, correlation analyses, and other methods. For 1956–2011, the inflow runoff displays small, statistically insignificant trends. However, for 2000–2011, significant downward trends are present. River runoff in the basin is significantly correlated with precipitation, while water intake and use is less influential; the most significant impact on river runoff is climate variability. To analyse the effects of water conservancy project scheduling and operation, we also compare the inflow and outflow runoff processes of typical large reservoirs before and after peak reservoir construction. The scheduling and operation of large reservoirs in the five rivers is known to play a supplementary role in dry season inflow runoff. The recent reduction in inflow runoff was mainly caused by basin precipitation; reasonable scheduling of water conservancy projects in the five rivers plays a positive role in safeguarding the water required by the dry season ecosystem in Poyang Lake.     

An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization

Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.     

An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization

Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.     

A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model

The estimation of missing rainfall data is an important problem for data analysis and modelling studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood function of measured runoff flows and prior rainfall information, which is presented by uniform distributions in the absence of rainfall data. The likelihood function of measured runoff can be determined via the test of different residual error models in the calibration phase. The application of this method to a French urban catchment indicates that the proposed Bayesian method is able to assess missing rainfall and its uncertainty based only on runoff measurements, which provides an alternative to the reverse model for missing rainfall estimates.     

Modeling the water resources of the Black and Mediterranean Sea river basins and their impact on regional mass changes

For the first time, a dedicated release of the hydrology and water use model WaterGAP3, has been developed to spatially explicit calculate hydrological fluxes within river basins draining into the Mediterranean and Black Sea. The main differences between the new regional version of the global WaterGAP3 model and the previously applied global version WaterGAP2 can be found in the spatial resolution, snow modeling, and water use modeling. Comparison with observations shows that WaterGAP3 features a more realistic representation of modeled river runoff and inflow into both seas. WaterGAP3 generates more inflow to both seas than WaterGAP2. In the WaterGAP3 simulation, contributions to the total runoff into the Black Sea from individual discharge regions show in general a good agreement to climatology derived runoff, but lesser importance of Georgian rivers for the basin's water. After the successful model validation WaterGAP3 has been applied to correct estimates of seawater mass derived from the GRACE gravity mission and to account for freshwater inflow into both basins. The performance of the WaterGAP3 regional solution has been evaluated by comparing the seawater mass derived from GRACE corrected for the leakage of continental hydrology, to an independent estimate derived from steric-corrected satellite altimetry with steric correction from regional oceanographic models. The agreement is higher in the Mediterranean Sea than in the Black Sea. Results using WaterGAP3 and WaterGAP2 are not significantly different. However the agreement with the altimetry-derived results is higher using WaterGAP2, due to the smaller annual amplitude of the continental hydrology leakage from WaterGAP3. We conclude that the regional model WaterGAP3 is capable of realistically quantifying water mass variation in the region, further developments have been identified.     

Assessment of transmission losses and groundwater recharge from runoff events in a wadi under shortage of data on lateral inflow,Negev, Israel

A hydrological–lithostratigraphical model was developed for assessment of transmission losses and groundwater recharge from runoff events in arid water courses where hydrological and meteorological records are incomplete. Water balance equations were established for reaches between hydrometric stations. Because rainfall and tributary flow data are scarce, lateral inflow, which is an essential component of the water balance equation, could not be estimated directly. The solution was obtained by developing a method which includes a hydrological–lithostratigraphical analogy. This is based on the following assumptions: (a) runoff resulting from a given rainfall event is related to the watershed surface lithology; (b) for a given event, the spatial distribution of runoff reflects the distribution of rainfall: and (c) transmission losses are uniquely related to the total inflow to the reach. The latter relationship, called the loss function, and the water balance equation comprise a model which simultaneously assesses lateral inflow and transmission losses for runoff events recorded at the terminal stations. The model was applied to three reaches of the arid Nahal Tsin in Israel. In this case study, the transmission losses were of the same order of magnitude as the flow at the major hydrometric stations. The losses were subdivided into channel moistening, which subsequently evaporates, and deep percolation, which recharges groundwater. For large runoff events, evaporation was substantially smaller than the losses. The mean annual recharge of groundwater from runoff events in the Tsin watershed was 4·1×10⁶ m³, while the mean annual flow volume at the major stations ranged from 0·6 to 1·5×10⁶ m³. Once in 100 years, the annual recharge may be seven times higher than the mean annual value, but the recharge during most years is very small. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling of stormwater biofilters under random hydrologic variability: a case study of a car park at Monash University,Victoria (Australia)

Biofiltration systems represent an effective technology for the management of urban stormwater runoff volumes and quality. The performance of these systems, although largely dependent on their physical characteristics, is also strongly affected by the natural variability of runoff occurrence and volumes. This article presents a model that describes the statistical behaviour of the main variables involved in the water balance of a biofiltration system, given its main physical properties (filter media and vegetation types) and accounting for the natural inflow variability in terms of occurrence and water volumes. The model permits the analytical derivation of the long‐term (e.g. annual) probability density function of the soil water content in the filter media and the estimation of the main statistics of water fluxes, that is, outflow, evapotranspiration and overflow. By relating the soil water content in the filter media before inflow events to the outflow total nitrogen concentrations, the model also gives estimates of the statistics of nitrogen removal performance as a function of inflow variability. The model was tested against field data collected at a stormwater biofiltration system in Melbourne, Australia. The model could be used to rapidly assess the hydrologic and nitrogen treatment performance of alternative applications of biofiltration for stormwater management across a range of climates. Copyright © 2011 John Wiley & Sons, Ltd.     

Reservoir attenuation of floods from ungauged basins

Abstract

In a typical reservoir routing problem, the givens are the inflow hydrograph and reservoir characteristic functions. Flood attenuation investigations can be easily accomplished using a hydrological or hydraulic routing of the inflow hydrograph to obtain the reservoir outflow hydrograph, unless the inflow hydrograph is unavailable. Although attempts for runoff simulation have been made in ungauged basins, there is only a limited degree of success in special cases. Those approaches are, in general, not suitable for basins with a reservoir. The objective of this study is to propose a procedure for flood attenuation estimation in ungauged reservoir basins. In this study, a kinematic-wave based geomorphic IUH model was adopted. The reservoir inflow hydrograph was generated through convolution integration using the rainfall excess and basin geomorphic information. Consequently, a fourth-order Runge-Kutta method was used to route the inflow hydrograph to obtain the reservoir outflow hydrograph without the aid of recorded flow data. Flood attenuation was estimated through the analysis of the inflow and outflow hydrographs of the reservoir. An ungauged reservoir basin in southern Taiwan is presented as an example to show the applicability of the proposed analytical procedure. The analytical results provide valuable information for downstream flood control work for different return periods.     

Long‐term runoff forecasting by combining hydrological models and meteorological records

Reservoir operation is generally based on the inflows of the upstream catchment of the reservoir. If the arriving inflows can be forecasted, that can benefit reservoir operation and management. This study attempts to construct a long‐term inflow‐forecasting model by combining a continuous rainfall–runoff model with the long‐term weather outlook from the Central Weather Bureau of Taiwan. The analytical results demonstrate that the continuous rainfall–runoff model has good inflow simulation performance by using 10‐day meteorological and inflow records over a 33‐year period for model calibration and verification. The long‐term inflow forecasting during the dry season was further conducted by combining the continuous rainfall–runoff model and the long‐term weather outlook, which was found to have good performance. Copyright © 2005 John Wiley & Sons, Ltd.     

On estimating the reliability of functioning of Moskvoretskaya water system and Volga-Kama chain of hydropower plants in a long dry period

An approach is proposed to assessing the reliability of functioning of a complex water management system under the conditions of a long dry period. The approach involves the specification of scenarios of long-term changes in the annual runoff. A method of simulation of artificial series of inflow to elements of water management system is proposed. Criteria for the choice of estimated inflow series are substantiated. The results of water management and hydropower calculations for different scenarios (models) are discussed. Challenges that may face the water management complex of the Volga basin in extremely dry periods are formulated.     

On the implementation of Prabhu’s exact solution of the stochastic reservoir equation

After 50 years of Prabhu’s paper on the exact solution of the stochastic reservoir equation for the important class of gamma inflow distributions with an integral shape parameter, a detailed implementation of the exact solution is still lacking, despite its potential usefulness from both theoretical and practical points of view. This paper explores some properties of Prabhu’s exact solution and investigates the numerical difficulties associated with its implementation. The solution is also extended to derive the distributions of deficit, spillage, yield, and actual release from the reservoir. Explicit analytical solutions for three relatively simple cases are given in detail as examples and comparisons with approximate numerical solutions are made, which reveal some shortcomings of approximate methods. The implementation of the solution in the general case reveals some numerical problems associated with large values of the shape parameter of the inflow distribution and large ratios of reservoir size to draft, mainly due to accumulation of round-off errors. A Matlab program has been developed to calculate emptying and filling probabilities over a wide range of reservoir parameters using extended precision. Comparison of Prabhu’s solution with the numerical solution of the reservoir integral equation highlights possible problems with the numerical solution, which may produce inaccurate or even invalid results for large reservoirs, large drift, and large skewness of the inflow distribution. A comparison between gamma and lognormal distributions as models of skew revealed that as the reservoir size, drift, and skewness increase, the probability of emptying of the reservoir becomes smaller for the case of gamma inflow than in the case of lognormal flow having the same skewness coefficient.     

Annual runoff assessment in arid and semiarid Mediterranean watersheds under the Budyko's framework

The solution of many practical water problems is strictly connected to the availability of reliable and widespread information about runoff. The estimation of mean annual runoff and its interannual variability for any basin over a wide region, even if ungauged, would be fundamental for both water resources assessment and planning and for water quality analysis. Starting from these premises, the main aim of this work is to show a new approach, based on the Budyko's framework, for mapping the mean annual surface runoff and deriving the probability distribution of the annual runoff in arid and semiarid watersheds. As a case study, the entire island of Sicily, Italy, is here proposed. First, time series data of annual rainfall, runoff, and reconstructed series of potential evapotranspiration have been combined within the Budyko's curve framework to obtain regional rules for rainfall partitioning between evapotranspiration and runoff. Then this knowledge has been used to infer long‐term annual runoff at the point scale by means of interpolated rainfall and potential evapotranspiration. The long‐term annual runoff raster layer has been obtained at each pixel of the drainage network, averaging the upstream runoff using advanced spatial analysis techniques within a GIS environment. Furthermore, 2 alternative methods are here proposed to derive the distribution of annual runoff, under the assumption of negligible interannual variations of basin water storage. The first method uses Monte Carlo simulations, combining rainfall and potential evapotranspiration randomly extracted from independent distributions. The second method is based on a simplification of the Budyko's curve and analytically provides the annual runoff distribution as the derived distribution of annual rainfall and potential evapotranspiration. Results are very encouraging: long‐term annual runoff and its distribution have been derived and compared with historical records at several gauged stations, obtaining satisfactory matching.     

Dynamic-stochastical modeling of long-term fluctuations in Lake Baykal levels and Angara River runoff

The results of modeling of the long-term fluctuations in Lake Baikal levels and Angara River runoff are presented. The dynamic-stochastical model was developed and used to obtain analytical relationships between the statistic characteristics of the Baikal levels fluctuations and the parameters of forcing processes, including water inflow into the lake and the effective evaporation from its surface. The parameter λ determining the inertia of the Baikal levels fluctuations, decreased by about three times after Irkutsk Reservoir filling, resulting in an increase in the variance of the lake levels fluctuations. The dependence of variances of the Baikal levels fluctuations and Angara runoff on parameter λ was studied. It is shown that the decreasing in the variance of the Baikal levels fluctuations corresponds to increasing in the variance of Angara river runoff and vice versa. The results of numerical modeling of Baikal levels fluctuations show that water withdrawal from inflow into the lake has an adverse effect on Angara runoff regime.     

基于误差分布估计的三峡水库入库洪水概率预报方法

准确、及时的入库洪水预报,对三峡水库综合效益的发挥和长江流域水旱灾害防御、水资源利用、流域综合管理等具有重要作用。基于预报误差的最优分布估计和分布函数动态参数假定,提出了一种三峡水库入库洪水概率预报方法,并进行了洪水概率预报业务试验。结果表明:本文所提方法科学可行,计算快捷,使用方便,便于在实时作业预报中应用推广;概率预报结果较确定性预报结果,在水量预报、预警效果等方面均有所改善,1～5 d预见期预报的确定性系数提高0.1%～3.4%,水量误差减少0.1%～4.8%,可为三峡水库实时调度提供更可靠的预报信息;所提出的三峡水库入库洪水概率预报业务化产品,可提供更多风险信息,为三峡水库的科学调度,尤其是洪水资源化利用提供更好的优化决策支撑。     

A statistically based runoff‐yield model coupling infiltration excess and saturation excess mechanisms

A statistically based runoff‐yield model is proposed in this paper. The model considers spatial heterogeneities of rainfall, soil infiltration capacity and soil water storage capacity that are main factors controlling runoff‐yield process. It assumes that the spatial variation of rainfall intensity at each time step can be characterized by a probability density function, which is estimated by matching the hyetograph through goodness‐of‐fit measure, whereas the spatial heterogeneities of soil infiltration capacity and soil water storage capacity are described by parabola‐type functions. Surface runoff is calculated according to infiltration excess mechanism; the statistical distribution of surface runoff rate can be deduced with the joint distribution of rainfall intensity and soil infiltration rate, thus obtaining a quasi‐analytical solution for surface runoff. Based on saturation excess mechanism, the groundwater flow (flows below the ground are collectively referred to as groundwater flow) is calculated by infiltration and the probability distribution of soil water storage capacity. Consequently, the total runoff is composed of infiltration excess and saturation excess runoff components. As an example, this model is applied to flood event simulation in Dongwan catchment, a semi‐humid region and a tributary of Yellow River in China. It indicates that the proposed runoff‐yield model could achieve acceptable accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

Sediment and solute transport on soil slope under simultaneous influence of rainfall impact and scouring flow

Soil erosion and nutrient losses with surface runoff in the loess plateau in China cause severe soil quality degradation and water pollution. It is driven by both rainfall impact and runoff flow that usually take place simultaneously during a rainfall event. However, the interactive effect of these two processes on soil erosion has received limited attention. The objectives of this study were to better understand the mechanism of soil erosion, solute transport in runoff, and hydraulic characteristics of flow under the simultaneous influence of rainfall and shallow clear‐water flow scouring. Laboratory flume experiments with three rainfall intensities (0, 60, and 120 mm h⁻¹) and four scouring inflow rates (10, 20, 30, and 40 l min⁻¹) were conducted to evaluate their interactive effect on runoff. Results indicate that both rainfall intensity and scouring inflow rate play important roles on runoff formation, soil erosion, and solute transport in the surface runoff. A rainfall splash and water scouring interactive effect on the transport of sediment and solute in runoff were observed at the rainfall intensity of 60 mm h⁻¹ and scouring inflow rates of 20 l min⁻¹. Cumulative sediment mass loss (Ms) was found to be a linear function of cumulative runoff volume (Wr) for each treatment. Solute transport was also affected by both rainfall intensity and scouring inflow rate, and the decrease in bromide concentration in the runoff with time fitted to a power function well. Reynolds number (Re) was a key hydraulic parameter to determine erodability on loess slopes. The Darcy–Weisbach friction coefficients (f) decreased with the Reynolds numbers (Re), and the average soil and water loss rate (M_l) increased with the Reynolds numbers (Re) on loess slope for both scenarios with or without rainfall impact. Copyright © 2010 John Wiley & Sons, Ltd.     

Streamflow routing in the indian arid zone

A lumped model for streamflow routing in arid ephemeral channels has been developed. The governing equations for movement of flood waves subjected to transmission losses are simplified through a time averaging process to develop an ordinary differential equation describing transmission losses as a function of distance, inflow, channel width, time parameters of flow and effective hydraulic conductivity. The resulting equation has an analytical solution and simulates runoff volume and peak discharge rates for individual storm events. The outflow hydrograph is fairly well approximated with a triangular approximation. The model is simplified and constructed to require a minimum of observed data for calibration. It can also be used for ungauged basins in arid regions through parameterization.     

Interpolation of runoff applying objective methods

The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.