Journal of Hydrologic Engineering

In the 1940s, Étienne Halphen, a French statistician and hydrologist, developed a set of distributions for frequency analysis of river flows. Halphen's research was fueled by an extensive practical experience with hydrological data combined with a solid knowledge of statistics. Because of their complex form involving Bessel functions and exponential factorial functions, Halphen's distributions have remained for several years in oblivion. This paper revisits the three types of Halphen distributions, in particular their mathematical and statistical properties. Their flexible shapes and tail properties should make them excellent candidates for frequency analysis of extremes. A companion paper presents procedures for estimating parameters and quantiles of Halphen's distribution.

In this paper, the second in a series of two, procedures for the estimation of parameters and quantiles of the Halphen type A, B, and IB distributions are presented. Because the Halphen distributions are members of the exponential class of distributions, parameters can be estimated from sufficient statistics, and maximum likelihood estimators should possess certain optimality characteristics. In some cases, the maximum likelihood system of equations does not allow a solution, and the limiting forms of the Halphen distributions, the gamma and inverse gamma, should alternatively by considered. The asymptotic variance of parameter estimators may be obtained by inverting the Fisher information matrix. The asymptotic variance of quantile estimators is obtained by classical first-order approximations. Practical experience with fitting the Halphen distributions is reported.

Appropriately designed flood control infrastructure should provide for public safety without wasteful over-design. The design-storm duration is a very significant determinant of the computed peak discharge. Presently, most hydrologic design is based on either the 24-h storm duration or a duration equal to the time of concentration. The professional literature, however, has not included a rational basis for using either of these durations. Since the annual maximum discharges are the basis for flood frequency analyses and ultimately flood risk estimates, it is reasonable that the rainfall duration that causes the annual maximum discharge should provide insight into the most appropriate duration for design storms. Use of the time of concentration suggests that the duration should depend on drainage area. Therefore, a range of watershed areas were used to determine whether or not storm duration depends on watershed size. Analysis of annual maximum discharge data for six Maryland watersheds (1.97 ≤ A ≤ 52.6 sq mi) for 1972–1990 shows: (1) that the rainfall duration causing the annual maximum discharge is slightly longer than 24 h, even for watershed areas as small as 2 sq mi; and (2) that storm duration increases only slightly with watershed area. The actual data also suggests that center-loaded design storms are appropriate. Therefore, the Soil Conservation Service Type II storm is an appropriate design hyetograph for prediction of discharges comparable to annual maximum discharges

The uncertainty or reliability of model simulation results produced by rainfall-runoff models is a function of uncertainties in model parameters, input data, and model structure. The present study considers a stochastic instantaneous unit hydrograph (SIUH) model describing the catchment as a single linear reservoir with input and transfer functions treated as random processes. Errors in runoff predictions caused by errors in input data and model parameters are analyzed by solving the governing stochastic differential equation (SDE) analytically, thus quantifying—in a general way—the error propagation structure and the relative importance of input errors and parameter errors. The result shows that the SIUH parameter variance has a direct bearing on the runoff variance, whereas the error contribution from the effective rainfall variance depends on the parameter mean value and the ratio between effective rainfall and simulated runoff. Data from 34 rainstorms are selected to verify the analytical SDE approach. The selected events represent varying: (1) rainfall intensity and duration; (2) single/multiple peak events; and (3) catchment initial losses. The results from the simulations are compared with observed runoff peaks and flood volumes. It is concluded that: (1) the SIUH model is a simple yet robust method, for which the parameter uncertainty can be realistically assessed; (2) the application of a theoretical SDE to estimate the prediction variance is supported by the statistical analysis of simulated and observed runoff; and (3) the estimation of flood peak variance can improve the design of flood control measures.

The Hurst exponent can be estimated by different methods. Two estimation methods are considered in this study. In the first estimate, the rescaled range of a hydrometeorological series is plotted against the lag on a logarithmic scale and the slope of the line fitted by least squares. In the second method, the Hurst exponent is estimated by characterizing the time series by a fractional Gaussian noise (FGN) model, which is a long-memory model. The FGN parameter d, which is related to the Hurst exponent, is estimated by two methods. The Hurst exponent is subsequently estimated using the relationship h = d + 0.5. The Hurst estimate based on the rescaled range is robust and is recommended for use. Estimates based on methods that characterize the hydrologic time series by the FGN model are not robust. Hence, they are not recommended.

An Artificial Neural Network (ANN) methodology was employed to forecast daily runoff as a function of daily precipitation, temperature, and snowmelt for the Little Patuxent River watershed in Maryland. The sensitivity of the prediction accuracy to the content and length of training data was investigated. The ANN rainfall-runoff model compared favorably with results obtained using existing techniques including statistical regression and a simple conceptual model. The ANN model provides a more systematic approach, reduces the length of calibration data, and shortens the time spent in calibration of the models. At the same time, it represents an improvement upon the prediction accuracy and flexibility of current methods.

Regional flood frequency curves are developed by fitting the L-moment based generalized extreme value distribution to annual maximum peak flood data of small-to-medium size catchments of the seven hydrometeorological subzones of Zone 3 and combined Zone 3 of India. These seven subzones cover an area of about 1,041,661 km². Relationships developed between mean annual peak flood and catchment area are coupled with the respective regional flood frequency curves for derivation of the regional flood formulas. The regional flood frequency curves developed for each subzone together with at-site mean annual peak floods may be used for gauged catchments, whereas for ungauged catchments, regional flood formulas developed for the respective subzones may be adopted for obtaining rational flood frequency estimates.

Lake levels are under the influence of climatologic changes, greenhouse effects, and anthropogenic activities. Usual atmospheric and environmental conditions give rise to steady-state time series of hydrometeorologic variables within a lake catchment, in addition to lake-level fluctuations. Under these circumstances, the water balance equation is valid with the substitution of arithmetic averages of input, output, and changes in storage variables. However, unusual lake-level changes, including trends and shifts in means, invalidate the use of averages because the hydrometeorologic time series have unsteady-state conditions. A cumulative departures model of the water balance equation is proposed and applied to precipitation, runoff, evaporation, and lake-level records for the Lake Van catchment location in the eastern part of Turkey. Implementation of the model requires identification of steady-state, long-term periods and their end-times that correspond to the starting points of unsteady dynamic periods, during which there might be unexpected trends and shifts in the mean lake levels.

The impact of vegetation filter strips on runoff, sediment yield, and atrazine loss from a cultivated field was investigated using a physically based, distributed watershed model. The field to which the model is applied has a gentle to flat sloping surface covered by a thin topsoil layer underlain by a claypan and is located in the Goodwater Creek watershed, a USDA research site in central Missouri. The model, which works on a cell basis, was developed to route runoff, sediment, and soluble chemical downslope from one cell to the next. The spatial variability of soil, depth of the topsoil, and vegetation are allowed among cells; each cell, however, is represented as a homogeneous unit. Our investigation indicates that changing waterway cover from natural sparse vegetation to dense grass has great potential for retarding runoff and reducing sediment loss, but it is not effective for controlling atrazine loss on claypan soils.

The Soil Conservation Service-curve number (SCS-CN) method is analytically derived and its basis in the Mockus method analyzed. A modification and a general form of the SCS-CN method are proposed. Using data from five watersheds, the existing SCS-CN method, the proposed modification, and the Mockus method are compared. For these data the modified version is found to be more accurate than the current version.

A numerical model to simulate miscible contaminant transport through unsaturated soils is presented. To account for the influence of multiple nonequilibrium sources on the contaminant transport, six governing phenomena of the miscible contaminant transport (i.e., convection, mechanical dispersion, molecular diffusion, adsorption, degradation, and immobile water effect) are integrated into the present model. The pollutant volumetric concentration in mobile water is taken as primary unknown, whereas the pollutant concentration in immobile water and the solid particles of soils are treated as state variables at the element integration points. Based on a splitting of the generalized convective operator from the diffusive operator, a modified version of the characteristic Galerkin method is developed to discretize the equations governing the contaminant transport phenomena. A fully explicit algorithm is then derived for the numerical solution of the finite-element equations in time domain. The numerical examples illustrate the performance and the capability of the presented model and algorithms.

Modeling of the seepage face in the case of flow toward wells has received considerable attention in the literature. It is evident from the literature that the models applicable to describe the well loss in the confined flow situation have been also employed to represent the seepage face variation in the case of unconfined flow situations. It is only during the past decade that attempts have been made to describe the seepage face in the case of wells located in an unconfined aquifer. In these studies, the seepage face has been related to the aquifer discharge, the duration of pumping test, the time since the start of pumping, etc. With a view to further simplifying the existing seepage face models, the present study approaches the problem of seepage face modeling in the case of a large-diameter well located in an unconfined aquifer using the velocity of flow at the well face. The resulting expression of the seepage face is not only simpler but also converts to the existing seepage face models, or their simplified forms, as a particular case.

On-line sewer flow forecasting is simulated in this study using an autoregressive transfer function rainfall-runoff model and a recursive procedure for parameter estimation. Reliable off-line estimates of the model parameters are assumed to be unavailable. Three recursive estimation algorithms are used: the time-invariant and time-varying versions of the recursive least-squares algorithm, and the Kalman filter interpretation of this algorithm. The sensitivity of the forecasting accuracy to the model order and to the initial conditions of the algorithm is studied using sewer flow data from the Milwaukee Metropolitan Sewerage District. It is observed that increasing the number of model parameters does not automatically improve the on-line forecasting results, although it does improve the off-line results. Also, the asymptotic properties of the recursive estimates appear to be better for the low-order models. It is observed that using the off-line identification results as the initial conditions for the recursive procedure produces more accurate forecasts than the (unreliable) model identified off-line without parameter updating. Forecasting results achieved using the time-invariant recursive least-squares algorithm are compared with those obtained for the time-varying approaches.

Equations for the probability weighted moments (PWMs) of the generalized extreme value (GEV) distribution for minima are derived. The GEV-PWM model and five other models are fitted to the low flow data of 16 streams. The suitability of the models is checked by the probability plot correlation coefficient test. Weibull distribution fits the data better than lognormal. GEV-PWM has the best performance among the three-parameter models, but it frequently leads to infeasible lower bounds. The 10-year minimum flow estimates based on various models are determined. In the majority of cases (11 stations), differences between the largest and the smallest estimates are <20%. However, in a few cases, rather large differences (71%) are found. The estimates from the GEV-PWM and W3-MSO models are usually either the largest or smallest at a station.

A laboratory study was conducted to study inert solute transport in a heterogeneous field. Twenty-one relatively undisturbed soil columns were sampled from a field plot, and chloride tracer tests were carried out in these soil columns. These tests provided local breakthrough curves at the scale of the individual soil columns. A large variability in convective transport in the study area was evidenced by the very rapid solute breakthrough at some soil columns, in contrast to the late arrival and slow passage of solute at others. The spatial variability of two measured transport parameters, velocity V and diffusion coefficient D, was analyzed. It was found that the spatial structure of these two transport parameters can be represented through a set of spherical semivariograms. Validation tests of the selected semivariograms showed that the selected semivariograms were theoretically consistent. The kriging technique, coupled with the simple advection-dispersion equation was used to predict solute concentration at a scale of the entire field. A validation test of this approach showed that kriging is a promising tool for the estimation of transport parameters and prediction of solute transport.