A MONTHLY WATER BALANCE MODEL INCLUDING DEEP INFILTRATION AND CANAL LOSSES / Un modèle mensuel du bilan hydrologique inclusive l'infiltration profonde et les pertes des canaux

Abstract

A monthly water balance model is being successfully applied to the Grote Nete test basin (553 km²) in the North of Belgium. This low region has a complex geological structure, its boundaries are more or less unknown and deep infiltration into a deep aquifer is most likely to occur. Moreover, the area is crossed by several navigation canals which import and export an unknown volume of water.

The inputs are monthly precipitation and Penman potential evapotranspiration values. The model computes actual evapotranspiration, water storage in the basin, direct runoff and infiltration, baseflow and total stream discharge, deep infiltration loss into the underlying aquifer and constant seepage from the canals. The ‘pattern search’ procedure has been used for automatic optimization of the six model parameters. All parameters have a physical meaning and can be evaluated initially.

For the calibration period 1967–1972, total stream discharge has been calculated with a precision of 0.2 per cent compared to total measured volume. The correlation coefficient is 92 per cent for the same calibration period. Prediction for the period 1973–1974 gave a volume precision of 8.7 per cent and a correlation coefficient of 93 per cent.     

The unsteady plane flow of ice-sheets: A parabolic problem with two moving boundaries

Abstract

Finite difference algorithms have been developed to solve a one-dimensional non-linear parabolic equation with one or two moving boundaries and to analyse the unsteady plane flow of ice-sheets. They are designed to investigate the response of an ice-sheet to changes in climate, and to reconstruct climatic changes implied by past ice-sheet variations inferred from glacial geological data. Two algorithms are presented and compared. The first, a fixed domain method, replaces time as an independent variable with span. The grid interval in real space is kept constant, and thus the number of grid points changes with span. The second, a moving mesh method, retains time as one of the independent variables, but normalises the spatial variable relative to the span, which now enters the diffusion and advection coeficients in the parabolic equation for the surface profile.

Crank-Nicholson schemes for the solution of the equations are constructed, and iterative schemes for the solution of the resulting non-linear equations are considered.

Boundary (margin) motion is governed by the surface slope at the margin. Differentiation of the evolution equations results in an evolution equation for the margin slopes. It is shown that incorporation of this evolution equation, while not formally increasing the accuracy of the finite difference schemes, in practice increases accuracy of the solution.     

CALCULATION OF AREAL RAINFALL USING FINITE ELEMENT TECHNIQUES WITH ALTITUDINAL CORRECTIONS

ABSTRACT

A procedure for calculating areal rainfall, based on recent innovations in finite element analysis, is presented. The procedure involves the use of interpolation functions, allowing an accurate representation of the shape and relief of the catchment, with numerical integration performed by Gaussian quadrature. Each raingauge is allotted two weights, one associated with the rainfall reduced to a datum, and the other with the rainfall-altitude relationship. The latter weight effectively removes any systematic errors due to altitudinal bias of the network.

The rainfall-altitude relationship, derived for individual storms and for synoptic situations for a small area, is used to show that errors due to the bias of the network can be considerable.     

On the generation,propagation and radiation of magneto–acoustic–gravity waves with application to stars

Abstract

The study of the mechanisms controlling the stratification in closed fluid regions is an important branch of geophysical fluid dynamics. Part of this subject can be handled with a simple linear model, consisting of a buoyancy layer at the non-horizontal boundaries of a container and an advective-diffusive interior coupled by volume continuity. The model is valid under the following conditions: firstly, the buoyancy-frequency characterizing the solution must be sufficiently large to give rise to a flow pattern of boundary layer type and, secondly, the non-horizontal walls must not have too large thermal conductivity.

The main purpose of the present paper is to summarise previous work done by the authors in this field and to present some consequences of their theory not previously discussed.

Three important cases are discussed; certain stationary solutions, the decay of a given stratification and the build up of a stratification in a homogeneous fluid. The experimental results concerning the afore-mentioned cases are presented.     

Improvement on the estimation of constant-rate drawdown in large-diameter wells

Abstract

Papadopulos and Cooper's (PC) solution can be used to describe the drawdown resulting from pumping with a constant rate at a large-diameter well. However, this solution is too complicated to be accurately evaluated due to the oscillatory nature of the Bessel functions. The PC approach resulted in tabulated values of dimensionless drawdown at the well with an accuracy of four or fewer digits for selected values of dimensionless storage coefficient versus dimensionless time. Some researchers have fitted the tabulated values with interpolation formulas that are easy to use in engineering applications. Those formulas may be more accurate if the tabulated values are computed with greater accuracy. In this study, we propose an efficient numerical procedure, including a root search scheme, to find the roots of the integrand, Gaussian quadrature for numerical integration, and Shanks transform to accelerate convergence of infinite series. The proposed procedure can evaluate the dimensionless drawdown with greater accuracy and is useful in practice if there is a need for high accuracy for the observation either at the well or in the aquifer at some distance from the pumping well

Editor D. Koutsoyiannis

Citation Chang, Y.C., Yeh, H.D., and Wang, C.T., 2013. Improvement on the estimation of constant-rate drawdown in large-diameter wells. Hydrological Sciences Journal, 58 (3), 716–727.     

Effects of dissipation on internal waves in a contained rotating stratified fluid

Abstract

Boundary layer techniques are used to examine the modifications due to dissipation in the normal modes of a uniformly rotating, density stratified, Boussinesq fluid in a rigid container. Arbitrary relative influence of rotation and stratification is considered. The existence of critical regions of the container boundary is discussed. In cylindrical geometry a formula is derived for the decay factor on the homogeneous “spin-up” time scale which reveals how the dominant dissipation varies as a function of several parameters. For the situation where the buoyancy and inertial frequency are exactly equal, all boundaries are everywhere critical. In this case the method of multiple time-scales is employed to investigate the confluence inertial-gravity mode which is shown to persist until the diffusive time-scale is achieved.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

A study on hydrological series of the Niger River

Abstract

The Hubert segmentation procedure has been applied to historical series of annual average discharges of the Niger River at Koulikoro (Mali), Niamey (Niger) and Lokoja (Nigeria) stations. The breaks, especially those identified at Koulikoro and Niamey, match well with those identified in the Senegal River series at Bakel using the same procedure. Lokoja departs from this regional pattern, as it shows in the late 1980s a return to wetter conditions much earlier than the other three stations. The magnitudes of the variation of the inter-annual means between the alternating wet and dry periods are significant and similar. These results seem to suggest that phenomena causing non-stationarity in hydrological series can have a sub-continental impact or, in contrast, may be more limited in their spatial coverage.

Editor Z.W. Kundzewicz; Associate editor H. Aksoy

Citation Abrate, T., Hubert, P., and Sighomnou, D., 2013. A study on hydrological series of the Niger River. Hydrological Sciences Journal, 58 (2), 271–279.     

Defining an estuary using the Hilbert-Huang transform

Abstract

Researchers have used various physical, chemical, or topographic features to define estuaries, based on the needs of their particular subject. The principal features of estuaries are the tides that influence their water stages; thus, the boundaries of an estuary can be determined based on whether the water stage is subject to tidal influence. However, the water stage is also influenced by the upstream river discharge. A hydrograph of water stage will therefore include both non-stationary and nonlinear features. Here, we use the Hilbert-Huang Transform (HHT), which allows us to process such non-stationary and nonlinear signals, to decompose the water-stage hydrographs recorded at different gauging stations in an estuary into their intrinsic mode function (IMF) components and residuals. We then analyse the relationships between the frequencies of IMFs and known tidal components. A frequency correlation indicates that the water stage of the station is subject to tidal influences and is located within the estuary. The spatial distribution of the stations that are subject to tidal influences can then be used to define the estuary boundaries. We used data from gauging stations in the estuary region of Taiwan's Tanshui River to assess the feasibility of using the HHT to define an estuary. The results show that the HHT is a dependable and easy method for determining the boundaries of an estuary.

Citation Chen, Y.-C., Kao, S.-P., and Chiang, H.-W., 2013. Defining an estuary using the Hilbert-Huang transform. Hydrological Sciences Journal, 58 (4), 841–853.     

Finite prandtl number convection in spherical shells

Abstract

Finite amplitude convection in spherical shells with spherically symmetric gravity and heat source distribution is considered. The nonlinear problem of three-dimensional convection in shells with stress-free and isothermal boundaries is solved by expanding the dependent variables in terms of powers of the amplitude of convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. The shell is assumed to be thick and only shells for which the ratio ζ of outer radius to inner radius is 2 or 3 are considered. Three cases, two of which lead to a self adjoint problem, are treated in this paper. The stable solutions are found to be l=2 modes for ζ=3 where l is the degree of the spherical harmonics and an l=3 non-axisymmetric mode which exhibits the symmetry of a tetrahedron for ζ=2. These stable solutions transport the maximum amount of heat. The Prandtl number dependence of the heat transport is computed for the various solutions analyzed in the paper.     

A shell model for anisotropic magnetohydrodynamic turbulence

Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B ₀, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 10⁵ have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B ₀ with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.     

Choice of reliability,resilience and vulnerability estimators for risk assessments of water resources systems / Choix d’estimateurs de fiabilité, de résilience et de vulnérabilité pour les analyses de risque de systèmes de ressources en eau

Abstract

Abstract Definitions and estimators of water resources system reliability (the probability that the system will remain in a non-failure state), resilience (the ability of the system to return to non-failure state after a failure has occurred) and vulnerability (the likely damage of a failure event) have been thoroughly investigated. A behaviour analysis addressing monotonic behaviour, overlap and correlation between the estimators was carried out by routing time series of monthly runoff through a reservoir with a specified storage volume that is operated according to a fixed operation policy. Estimation based on historical time series is shown to be problematic and a procedure encompassing generation of synthetic time series with a length of at least 1000 years is recommended in order to stabilize the estimates. Moreover, the strong correlation between resilience and vulnerability may suggest that resilience should not be explicitly accounted for.     

INTERNATIONAL HYDROLOGICAL DECADE / WORKING GROUP ON “THE INFLUENCE OF MAN ON THE HYDROLOGICAL CYCLE”

Abstract

Floods, as extreme hydrological phenomena, can be described by more than one correlated characteristic, such as peak, volume and duration. These characteristics should be jointly considered since they are generally not independent. For an ungauged site, univariate regional flood frequency analysis (FA) provides a limited assessment of flood events. A recent study proposed a procedure for regional FA in a multivariate framework. This procedure represents a multivariate version of the index-flood model and is based on copulas and multivariate quantiles. The performance of the proposed procedure was evaluated by simulation. However, the model was not tested on a real-world case study data. In the present paper, practical aspects are investigated jointly for flood peak (Q) and volume (V) of a dataset from the Côte-Nord region in the province of Quebec, Canada. The application of the proposed procedure requires the identification of the appropriate marginal distribution, the estimation of the index flood and the selection of an appropriate copula. The results of the case study show that the regional bivariate FA procedure performed well. This performance depends strongly on the performance of the two univariate models and, more specifically, the univariate model of Q. The results show also the impact of the homogeneity of the region on the performance of the univariate and bivariate models.

Editor D. Koutsoyiannis     

On the probability of exceeding a given river flow threshold

ABSTRACT

To obtain estimates of the probability that a river flow will exceed a given threshold at time t + 1, given the flow value at time t, two stochastic models are considered: a filtered Poisson process and a diffusion process with jumps. Estimates derived from linear regression are also considered. The model parameters are assumed to depend on the flow value. An application to the Delaware River is presented.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Symmetric baroclinic instability for small ekman numbers

Abstract

The stability of a zonal shear flow to symmetric baroclinic perturbations is examined when the Ekman number, E, is asymptotically small. It is assumed, following Antar and Fowlis (1982), that the zonal Row is generated by imposing a constant horizontal temperature gradient γ* at the horizontal boundaries, and by maintaining a constant temperature difference δT* between them. The boundaries are at rest relative to a rotating frame.

Features of the neutral stability curve are determined for several ranges of values of δT/E ^1/3, where δT = δT*/Hγ* and H is the depth of the fluid layer, and all values of the Prandtl number, [sgrave]. In some cases it is possible to determine the whole curve analytically. The most important feature of the results is that the neutral stability curve is closed.

The results are compared to the numerical integrations of Antar and Fowlis (1982). The qualitative features of the solutions are in accord and the quantitative results are, in most cases, as good as can be expected for E only as small as ～ 10^?4. The implications of the results for experimental observations of symmetric baroclinic instability are explored.     

Long period divergent planetary waves

Abstract

A simple first order perturbation procedure is used to obtain an equation for divergent planetary waves when the period is much greater than the pendulum day. For unbounded regions the equation is the s2me as one derived by Longuet-Higgins (1965), but in bounded basins it is different. As an example, the eigen frequencies of a rectangular basin are calculated for a number of values of the parameters.

The energy density of planetary waves is also considered with results which correct those of Buchwald (1972) in the case of bounded basins.     

PUBLICATIONS DE L'ASSOCIATION INTERNATIONALE DES SCIENCES HYDROLOGIQUES

ABSTRACT

The purpose of an hydrometric network is to obtain data giving answers to problems raised by the use of water. The methodology suggested in this paper is essentially based on the regional identification of the actual and potential uses of water, on the estimate of the intensity of their use and on the determination of the hydrological characteristics related to this demand.

The level of accuracy required for these characteristics is an important feature in the rationalization procedure.

The various types of stations are defined according to the purpose of their use and the network considered is on a dynamic basis depending on the evolution of uses. The major results obtained for Quebec by the application of this method are described.     

Multiple criteria rainfall–runoff model calibration using a parallel genetic algorithm in a cluster of computers / Calage multi-critères en modélisation pluie–débit par un algorithme génétique parallèle mis en œuvre par une grappe d'ordinateurs

Abstract

Genetic algorithms are among of the global optimization schemes that have gained popularity as a means to calibrate rainfall–runoff models. However, a conceptual rainfall–runoff model usually includes 10 or more parameters and these are interdependent, which makes the optimization procedure very time-consuming. This may result in the premature termination of the optimization process which will prejudice the quality of the results. Therefore, the speed of optimization procedure is crucial in order to improve the calibration quality and efficiency. A hybrid method that combines a parallel genetic algorithm with a fuzzy optimal model in a cluster of computers is proposed. The method uses the fuzzy optimal model to evaluate multiple alternatives with multiple criteria where chromosomes are the alternatives, whilst the criteria are flood performance measures. In order to easily distinguish the performance of different alternatives and to address the problem of non-uniqueness of optimum, two fuzzy ratios are defined. The new approach has been tested and compared with results obtained by using a two-stage calibration procedure. The current single procedure produces similar results, but is simpler and automatic. Comparison of results between the serial and parallel genetic algorithms showed that the current methodology can significantly reduce the overall optimization time and simultaneously improve the solution quality.     

A) A. I. H. S. / A) A. I. H. S.

Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.     

Risk analyses for a water supply system: Occoquan Reservoir,Fairfax and Prince William Counties,Virginia, USA / Des analyses aléatoires d'un système d'approvisionnement en eau: Occoquan Reservoir,Fairfax et Prince William Counties,Virginia, USA

Abstract

This report demonstrates two techniques for evaluating risks in the operation of a water supply system. Both rely on reconstructed historical streamflow data to develop estimates of the probabilities of certain specific events occurring in the future. These techniques are applied to the Occoquan Reservoir which was experiencing an unprecedented low level of storage in the autumn of 1977. The two techniques are used respectively to evaluate the overall adequacy of the existing reservoir and to evaluate the risks in the 1977 crisis.

In the first technique, the general risk analysis model (GRAM), simulations of the reservoir's contents are carried out under a set of assumptions about withdrawal rates and emergency procedures. The results of the GRAM simulation for the Occoquan Reservoir are in the form of estimates of the probabilities that in any year contain emergency procedures will have to be invoked. These estimates are given for a range of rates of withdrawals and for four different stages of emergency actions. Also given are the estimated probabilities of entering emergency conditions in one year given that an emergency has occurred in the previous year. Due to the year-to-year persistence of low flows, these latter (conditional) probabilities are higher than the former (marginal) probabilities.

The second technique used is position analysis. In this procedure probability distributions of future storages are estimated under existing storage conditions and an assumed rate of withdrawal from the reservoir. The position analysis which was initialized at the 1 October 1977 conditions indicates that the probability of entering a Stage III emergency (the prohibition of all uses of water non-essential to life, health, and safety) in the autumn of 1977 or winter of 1978 was 10 per cent at that time. With a reduction in water use by 8 million gallons per day, however, this probability would have fallen to 4 per cent.

If a long reconstructed historical streamflow record is available to a water supply agency, then the agency will have the capability to undertake its own risk analyses. It can carry out comparisons of alternative operating policies by using techniques such as GRAM. It can also evaluate the short-term risks of different plans of operation during crisis situations by using position analysis.