Journal of Hydrologic Engineering

In order to forecast drainage basin runoff, mathematical models involving diffusion processes are tested against hydrological data obtained from the hydrographic basin of the Saguenay-Lac-St-Jean, located in northeastern Quebec. For one-day-ahead estimates, a bidimensional model using an Ornstein-Uhlenbeck process is seen to give better results than a deterministic model presently in use. The latter model involves the estimation of 18 parameters, while the diffusion process model requires only one parameter, thus making it much simpler and cheaper to implement.

The effects of grid-cell size on surface runoff modeling using a distributed hydrologic model are examined. The raster-based hydrologic CASC2D model is applied to two watersheds in northern Mississippi. Observed streamflow for Goodwin Creek (21 km²) is used in calibrating the model's infiltration, runoff, and routing parameters. The results are extended to Hickahala-Senatobia (560 km²), which has similar physical characteristics. The applicability of CASC2D in simulating rainfall-runoff processes is tested using square grid-cell sizes ranging from 127 to 914 m. Event-based simulation results indicate that coarser grid-cell resolutions can be used in rainfall-runoff simulations as long as parameters are appropriately calibrated. It is demonstrated that the primary effect of increasing grid-cell size on simulation parameters is to require an increase in overland and channel roughness coefficients. The concept of a watershed time-to-equilibrium is used in evaluating the runoff response of overland and channel cells. At different grid-cell sizes, raster maps generated within a GRASS GIS environment provide information regarding the spatial distribution of drainage area, time-to-equilibrium, and equilibrium discharge on Goodwin Creek and Hickahala-Senatobia. It is shown that at increasing grid-cell size, the statistical distribution of drainage areas associated with overland cells is significantly increased, while the statistical distribution of drainage areas associated with channel cells is hardly affected by grid-cell size. It is also demonstrated that flow on overland cells is more sensitive to changes in grid-cell size than is channel flow. Since channel flow dominates the shape of the hydrograph in large watersheds, the results indicate that coarse grid sizes can be used for rainfall-runoff simulations on large watersheds. The results also indicate that coarser grid sizes will be more appropriate when simulating events of high intensity or of long duration.

Time series of daily streamflows are studied with particular emphasis on the behavior of recessions. Long-term and periodic characteristics are modeled through spectral analysis. Gamma autoregressive models are used to simulate time intervals D between consecutive low flows and the conditional duration d of recessions. A similar model is also used for generating the magnitudes of low flows, conditional on D. A nonnormal ARIMA process is adopted for simulating a recession backward in time over a time interval d commencing with the associated low flow. Transformation to stationarity of the recession process is by means of a difference-ratio, which is the difference between the current and antecedent streamflows divided by their average. The rising limb of the hydrograph is simulated using a ranked uniform random number generator. Application is made to four river basins ranging in size from the Po at Pontelagoscuro (70,090 km²) in northern Italy to the Arzino (123 km²) in northeast Italy. Hydrograph characteristics and the distributions of average, low, and peak flows are maintained.

A simple nonlinear conceptual model for simulating Hortonian rainfall-runoff phenomena is presented. The model is based on the concept of a nonlinear storage outflow relationship and assumes a nonlinear loss module. The abstractions can take the form of a constant or an exponential decreasing rate. The analytical model is derived from an approximate perturbation solution of the governing nonlinear ordinary differential equation and relates in an explicit fashion the runoff to the rainfall, the abstractions, and the watershed parameters. The model is function of few parameters that can be estimated efficiently using optimization techniques and nonlinear least-squares regression. The model has been applied to a very small semiarid watershed with considerable success. The proposed model can be considered as an improvement over the classical linear reservoir theory, and an attractive and useful substitute to the linear reservoir components in more complex conceptual rainfall-runoff models.

An innovative stochastic model for the purpose of daily flows simulations is presented in this paper. This model is particularly well suited for the generation of daily river flows in semiarid climates. The previous models have not preserved basic features of daily flow hydrographs, such as peaks and recessions, and have failed to reproduce the long low water and short flood periods due to the temporal distribution of precipitation in semiarid climates such as Sahelian regions. This hybrid stochastic model uses a product model that simulates an intermittent impulse series. The impulse magnitude is the flow increment from one day to the next. The intermittent impulse series enables the definition over time of alternate rising and falling limbs. On the rising limbs, the generated impulse magnitudes help to produce the daily flows. However, on the falling limbs, the flows are produced by a deterministic model using a time-varying recession coefficient that is, for the first time, introduced in stochastic modeling of daily flows. Application of this model for daily flows simulation at the Bakel Station on the Senegal River (West Africa) has provided good results as shown by the analysis of the synthetic daily flow series.

Changes in central tendency in hydrologic data are commonly evaluated with nonparametric statistics because the assumptions of parametric alternatives are not met. The Wilcoxon signed-ranks (WSR) test can be used to infer changes in central tendency in paired comparisons. Standard critical values for the WSR test assume that the data samples are drawn from distributions with equal skew, such that the differences are symmetrically distributed. When the data are drawn from distributions with unequal skews, the WSR test with the zero-skew critical values can lead to incorrect or inaccurate research decisions. This work provides critical values that can be applied to paired data with unequal skews. Skew-dependent critical values were developed by simulation. Equations are presented enabling the estimation of critical values as a function of sample size, skew, and type I error for both positively and negatively skewed data. The new critical values are applied to compare the annual maximum discharge and runoff depths measured at two small agricultural watersheds. The results show that the skew-dependent critical values provide decisions with different statistical significance than those decisions made using the traditional critical values that assume zero skew. The implication is that more rational decisions will be made, using the skew-dependent critical values, when the WSR test is applied to data characterized by unequal skews.

Storage capacity, yield, and reliability of a reservoir are random variables. Conditional distributions of these variables are studied by Monte Carlo simulation for operating periods up to 100 years. It is shown that these distributions are affected by the length of the period of operation due to the assumption of an initially full reservoir. Results of the study will aid in the reliability based reservoir design by clarifying the connection among the storage variables. The relationship between the steady-state reliability and the probability of failure-free operation over an N-year planning period is also investigated, and it is shown that the effect of the initial storage can be neglected only when the ratio of regulation is low.

The harmonic mean has numerous engineering applications including characterization of the large-scale effective permeability in layered porous media, characterization of petrochemical properties of heterogeneous media, and the design of declining rate filter beds. The U.S. EPA also recommends the use of the harmonic mean daily streamflow as a design streamflow for the protection of human health against lifetime exposure to suspected carcinogens. The sampling properties of various estimators of the harmonic mean are derived and compared for observations arising from a lognormal distribution. Previous applications have recommended the use of a moment estimator of the harmonic mean. We document that the moment estimator of the harmonic mean exhibits significant upward bias and large root-mean-square error, particularly for large skews. A maximum likelihood estimator of the harmonic mean is generally preferred because it is nearly unbiased and can provide dramatic reductions in the root-mean-square error, compared with the moment estimator. In addition, a maximum likelihood estimator of the generalized mean (or p-norm) of a lognormal distribution is introduced.

Genetic algorithm (GA) is considered to be a robust technique for solving ground-water optimization problems. Often these problems are difficult to solve using traditional gradient-based techniques as these are nonlinear, nonconvex, and discontinuous. In this manuscript, recent research related to application of GA in solving these problems is critically reviewed, and three areas of potential enhancement to GA are identified and explored. These enhancement methods to GA are fitness reduction method (FRM), search bound sampling method (SBSM), and optimal resource allocation guideline (ORAG). In order to assess these methods, a nonlinear ground-water problem with fixed and variable costs is selected (from literature) where the corresponding optimal solution using a gradient-based nonlinear programming (NLP) technique is available. The problem is resolved using GA coupled with the enhancement methods, and the GA solutions are compared with the NLP solution. In addition, the sensitivity of these methods to various GA parameters are studied. The results of the analysis using the enhancement methods show the following: (1) FRM enhances efficiency of GA in handling constraints; (2) SBSM enhances accuracy of GA in solving problems with fixed costs; (3) ORAG enhances reliability of GA by providing some convergence guarantee for a given computational resource; and (4) when applied with FRM and SBSM, accuracy of GA is marginally increased from near-optimal to global-optimal by tuning any one of the several parameters. There appears to be little need to embark on a full-scale analysis for achieving the increase.

This paper presents an adaptive multigrid approach, combining multigrid methods and adaptive local grid refinement, to solve 3D density-dependent flow and transport problems in the subsurface. This approach is incorporated with the Galerkin finite-element method to solve the modified Richards' equation in the flow module and the Lagrangian-Eulerian finite-element method to solve the advection-dispersion equation in the transport module, which are coupled through density effects. With multigrid methods, the linear/linearized matrix equations can be solved with O(n) manipulations to save computer time. With adaptive local grid refinement, computational accuracy is improved by refining only rough regions of the problem domain and the computation is efficiently achieved because computer efforts are focused on those regions. In this work, rough regions are determined by examining the mesh Péclet number during each nonlinear iteration of the flow module and by checking the smoothness of the Lagrangian concentrations over global elements in the Lagrangian step of the transport module. Based on the detected rough regions, a modular setting of grid generation is employed to generate local zooming grids as well as to prepare the information needed for applying multigrid methods. Two examples are given to demonstrate the success of this approach.

The numerical simulation of seawater intrusion with a considerable transition zone requires simultaneous solution of the discretized ground-water flow and transport equations. A nonlinear optimization method for solving the embedded governing equations for simulation of seawater intrusion is proposed. The main advantage of this optimization based method is that sequential iterative solution of the flow and transport equations is not necessary. Also, simultaneous solution of the flow and transport equations using the optimization approach uniquely suits the transformation of this simulation approach to a management model. Both steady-state and transient simulations are performed by using this methodology. The solutions obtained by using the proposed methodology are compared with results reported by other researchers. The obtained solutions compared satisfactorily with the known solutions. The formulation and solution of a nonlinear optimization model for maximizing total sustainable yield from specified locations of the aquifer, while satisfying stipulated salinity constraints, are presented to demonstrate the feasibility of integrating this simulation approach within a coastal aquifer management model.

Assessment of water quality monitoring networks requires potential methods to delineate the efficiency and cost-effectiveness of current monitoring programs. To this end, the concept of entropy has been considered a promising method in previous studies as it quantitatively measures the information produced by a network. This paper revises the entropy methodology developed in an earlier study and introduces a new approach for the assessment of combined spatial/temporal frequencies of monitoring networks. The results are demonstrated in the case of water quality data observed along the Mississippi River in Louisiana.

The linear Muskingum method continues to be a simple and popular procedure for river flood routing. An alternative algorithm for the numerical estimation of the Muskingum routing parameters is presented. Fully implicit and semi-implicit finite-difference schemes are compared for accuracy with respect to the traditional graphical procedure. A stability analysis and an objective criterion for the application of each scheme in the light of different measurement intervals for the inflow and outflow hydrographs is discussed. An application example and recommendations are included.