PUBLICATIONS OF THE IAHS

Abstract

Gauging stations where the stage—discharge relationship is affected by hysteresis due to unsteady flow represent a challenge in hydrometry. In such situations, the standard hydrometric practice of fitting a single-valued rating curve to the available stage—discharge measurements is inappropriate. As a solution to this problem, this study provides a method based on the Jones formula and nonlinear regression, which requires no further data beyond the available stage—discharge measurements, given that either the stages before and after each measurement are known along with the duration of each measurement, or a stage hydrograph is available. The regression model based on the Jones formula rating curve is developed by applying the monoclinal rising wave approximation and the generalized friction law for uniform flow, along with simplifying assumptions about the hydraulic and geometric properties of the river channel in conjunction with the gauging station. Methods for obtaining the nonlinear least-squares rating-curve estimates, while factoring in approximated uncertainty, are discussed. The broad practical applicability and appropriateness of the method are demonstrated by applying the model to: (a) an accurate, comprehensive and detailed database from a hydropower-generated highly dynamic flow in the Chattahoochee River, Georgia, USA; and (b) data from gauging stations in two large rivers in the USA affected by hysteresis. It is also shown that the model is especially suitable for post-modelling hydraulic and statistical validation and assessment.     

Existence of the frequentistic estimate for power-law regression with a location parameter, with applications for making discharge rating curves

Practical application of the power-law regression model with an unknown location parameter can be plagued by non-finite least squares parameter estimates. This presents a serious problem in hydrology, since stream flow data is mainly obtained using an estimated stage–discharge power-law rating curve. This study provides a set of sufficient requirements for the data to ensure the existence of finite least squares parameter estimates for a power-law regression with an unknown location parameter. It is shown that in practice, these requirements act as necessary for having a finite least squares solution, in most cases. Furthermore, it is proved that there is a finite probability for the model to produce data having non-finite least squares parameter estimates. The implications of this result are discussed in the context of asymptotic predictions, inference and experimental design. A Bayesian approach to the actual regression problem is recommended.     

陇西地区黄土的强度特性

本文介绍了对陇西地区黄土的强度特性进行的试验研究结果。陇西地区Q_3和Q_4黄土在偏应力作用下的应力—应变关系基本上可用康德纳双曲线模式来表示。对大量的试验数据采用了最小二乘法计算了黄土的强度参数,结果表明其强度参数是比较低的。本文还对几十组黄土的强度参数与其物理性质指标之间的关系进行了回归分析,建立了它们之间的经验公式,该公式可以直接用于陇西地区黄土的强度和土坡稳定性估算。     

Estimation of water cloud model vegetation parameters using a genetic algorithm

Abstract

The water cloud model is used to account for the effect of vegetation water content on radar backscatter data. The model generally comprises two parameters that characterize the vegetated terrain, A and B, and two bare soil parameters, C and D. In the present study, parameters A and B were estimated using a genetic algorithm (GA) optimization technique and compared with estimates obtained by the sequential unconstrained minimization technique (SUMT) from measured backscatter data. The parameter estimation was formulated as a least squares optimization problem by minimizing the deviations between the backscatter coefficients retrieved from the ENVISAT ASAR image and those predicted by the water cloud model. The bias induced by three different objective functions was statistically analysed by generating synthetic backscatter data. It was observed that, when the backscatter coefficient data contain no errors, the objective functions do not induce any bias in the parameter estimation and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the cases considered, the objective function based on the sum of squares of normalized deviations with respect to the computed backscatter coefficient resulted in the best possible estimates. A comparison of the GA technique with the SUMT was undertaken in estimating the water cloud model parameters. For the case considered, the GA technique performed better than the SUMT in parameter estimation, where the root mean squared error obtained from the GA was about half of that obtained by the SUMT.

Editor D. Koutsoyiannis; Associate editor L. See

Citation Kumar, K., Hari Prasad, K.S. and Arora, M.K., 2012. Estimation of water cloud model vegetation parameters using a genetic algorithm. Hydrological Sciences Journal, 57 (4), 776–789.     

Towards using pedotransfer functions for estimating infiltration parameters

ABSTRACT

Water infiltration into soils is an important component of hydrological processes. Direct measurement of infiltration is time consuming, expensive and often involves large spatial and temporal variability. The objective of this study was to develop and verify parametric pedotransfer functions (PTFs) to predict infiltration parameters. Consequently, 119 double-ring infiltration data were collected. The parameters of Philip, Kostiakov, Kostiakov-Lewis and Horton models were obtained, using the sum of squares error optimization method. Some parametric PTFs were then derived to predict the parameters of the infiltration models, using stepwise regression analysis. The results indicated a reasonable estimation of infiltration parameters by the derived PTFs. These results were more accurate when the land use of the studied area was considered. Overall results of this study suggest infiltration-based PTFs could be established as a reasonable indirect method for estimating infiltration parameters.

Editor M.C. Acreman; Associate editor N. Verhoest     

Empirical statistical characterization and regionalization of amplitude–duration–frequency curves for extreme peak flows in the Lake Victoria Basin,East Africa

Abstract

This paper focuses on a regionalization attempt to partly solve data limitation problems in statistical analysis of high flows to derive discharge–duration–frequency (QDF) relationships. The analysis is based on 24 selected catchments in the Lake Victoria Basin (LVB) in East Africa. Characteristics of the theoretical QDF relationships were parameterized to capture their slopes of extreme value distributions (evd), tail behaviour and scaling measures. To enable QDF estimates to be obtained for ungauged catchments, interdependence relationships between the QDF parameters were identified, and regional regression models were developed to explain the regional difference in these parameters from physiographic characteristics. In validation of the regression models, from the lowest (5 years) to the highest (25 years) return periods considered, the percentage bias in the QDF estimates ranged from –2% for the 5-year return period to 27% for 25-year return period.

Editor D. Koutsoyiannis     

Least squares fitting of the stage–discharge relationship using smooth models with curvilinear asymptotes

Abstract

In this paper we consider the problem of modelling the stage–discharge relationship by curve fitting using the least squares method. Our basic idea is to present new models which are more flexible and have the ability to model phenomena with increasing or unchanging carrying capacity. The new models present a generalization of some sigmoid smooth models commonly used in practice. They are characterized by a curvilinear asymptote and may have several inflection points. The use of these models on six real datasets collected from the US Geological Survey’s website proves their performance and their ability to model hydrological phenomena.

Editor D. Koutsoyiannis; Associate editor S. Yue     

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall‐runoff model, caused by stage–discharge rating‐curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross‐section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel‐bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross‐section form due to scour and re‐deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd.     

EXPERIENCES WITH AUTOMATIC MAGNETIC INTERPRETATION USING THE THICK PLATE MODEL *

Various experiments are described in designing two-dimensional magnetic interpretation algorithms using computer curve fitting techniques. For a single anomaly the position of the anomaly maximum and the half-width of the anomaly give good initial estimates of the plate position and thickness. A nomogram and formulae for improving these estimates is given. Curves and estimates for the effects of finite depth extent of a plate show the limits, when the lower surface of the plate can be neglected in curve fitting. The combined anomaly of two parallel plates can be separated into partial anomalies with no common points using the horizontal derivative of the anomaly. The changes of the anomaly maxima and changes in anomaly half-widths are studied as a function of plate separation. The position of the maxima and the half-widths can be corrected before applying the one-plate procedure for obtaining initial estimates of plate positions and thicknesses. The performance of standard optimization methods of Powell, Davidon, and Marquardt in improving the values of the plate parameters are compared. The Powell method seems to be the most reliable for both single and multi-plate anomalies. All methods become unacceptably slow when the number of plates is greater than 2 or 3. In these cases feasible interpretation times are obtained using the partial anomalies and sequential parabolic search of the parameter values as tailored specially to the thick plate model. Experiments with three different error norms, the classical least squares, weighted least squares and minimax, show that the first norm gives the best overall performance in automatic interpretation. The behaviour of the classical least squares norm as a function of the plate parameters is also briefly described.     

Relationship between the yearly maxima of peak and daily discharge for some basins in Tuscany

ABSTRACT

The paper deals with the estimation of the probability distribution of the yearly maximum of the peak discharge Q by means of the distribution of the maximum of the daily discharge q and the distribution of the ratio R = Q/q. The study was carried out for some catchments in Tuscany, analysing the dependence of the parameters of R on the geomorphic catchment parameters. The values of the discharge Q, relevant to an assigned return period, obtained by the methods given herein agree rather well (the error is about 20%) with those directly obtained from the observed values of Q.     

DILUTION GAUGING ON THE RECESSION LIMB: 2. THE INTEGRATION METHOD / Mesures par dilution sur la courbe de tarissement: 2. Méthode par intégration

Abstract

The application of dilution gauging techniques to natural streams and other variable flows incurs a systematic error caused by the change in discharge with time. On the recession limb of a hydrograph the change is usually smooth and gradual, and errors can be expected intuitively to be small. In a preceding paper the author investigated errors arising from this cause in the case of a constant rate tracer injection, and developed formulae for the calculation of bias from known values of the recession constant and the distribution of residence time in the gauging reach. This paper extends the theory of the residence time model to the case of a dilution gauging by the integration method, and presents analogous formulae for the errors.     

综合回归分析与中国东部六省地区Lg波衰减的测定

本文提出了具有共同斜率不同截距的多条测线的ldquo;综合回归分析rdquo;方法.设x, y满足线性关系:Y=KX+Cii=1, 2, hellip;, N则由最小二乘原理解出综合回归系数K和Ci, 及其标准差的代数表达式.选取苏、鲁、豫、皖、冀、浙六省及其附近地区, 19个地震80个台站的短周期DD-1地震仪记录.用综合回归分析法测定了ldquo;波传播速度为3.54km/s, 约1秒Lg波埃里相（LG）的滞弹性衰减系数gamma;Lg=0.00435plusmn;0.00010km-1, Lg非埃里相（MAX）的gamma;max=0.00305plusmn;0.00010km-1.前者即为介质的衰减系数;后者具有统计的意义, 可用于最大震相震级公式的建立.计算中使用了LGZ, LGH, MXZ, MXH四个震相, 各近600组振幅数据, 和555组走时数据。震中距范围约为50——1100km.      

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.     

Combining regression and spatial proximity for catchment model regionalization: a comparative study

Abstract

Spatial error regression is employed to regionalize the parameters of a rainfall–runoff model. The approach combines regression on physiographic watershed characteristics with a spatial proximity technique that describes the spatial dependence of model parameters. The methodology is tested for the monthly abcd model at a network of gauges in southeast United States and compared against simpler regression and spatial proximity approaches. Unlike other comparative regionalization studies that only evaluate the skill of regionalized streamflow predictions in ungauged catchments, this study also examines the fit between regionalized parameters and their optimal (i.e. calibrated) values. Interestingly, the spatial error model produces parameter estimates that better resemble the optimal parameters than either of the simpler methods, but the spatial proximity method still yields better hydrologic simulations. The analysis suggests that the superior streamflow predictions of spatial proximity result from its ability to better preserve correlations between compensatory hydrological parameters.

Editor D. Koutsoyiannis; Associate editor Y. Gyasi-Agyei     

Accuracy of discharge determined from a rating curve

ABSTRACT

An error analysis shows that three types of errors influence the random error of a single discharge measurement determined from a rating curve. They are rating curve error, water level measurement error and an error caused by ignoring all physical parameters, other than water level, that affect discharge. Methods in the literature for evaluating the first two types of errors are reviewed and a method for evaluating the third type is given. The error of average discharge for an arbitrary period is also considered.     

Regional flood frequency analysis using Bayesian generalized least squares: a comparison between quantile and parameter regression techniques

Regression‐based regional flood frequency analysis (RFFA) methods are widely adopted in hydrology. This paper compares two regression‐based RFFA methods using a Bayesian generalized least squares (GLS) modelling framework; the two are quantile regression technique (QRT) and parameter regression technique (PRT). In this study, the QRT focuses on the development of prediction equations for a flood quantile in the range of 2 to 100 years average recurrence intervals (ARI), while the PRT develops prediction equations for the first three moments of the log Pearson Type 3 (LP3) distribution, which are the mean, standard deviation and skew of the logarithms of the annual maximum flows; these regional parameters are then used to fit the LP3 distribution to estimate the desired flood quantiles at a given site. It has been shown that using a method similar to stepwise regression and by employing a number of statistics such as the model error variance, average variance of prediction, Bayesian information criterion and Akaike information criterion, the best set of explanatory variables in the GLS regression can be identified. In this study, a range of statistics and diagnostic plots have been adopted to evaluate the regression models. The method has been applied to 53 catchments in Tasmania, Australia. It has been found that catchment area and design rainfall intensity are the most important explanatory variables in predicting flood quantiles using the QRT. For the PRT, a total of four explanatory variables were adopted for predicting the mean, standard deviation and skew. The developed regression models satisfy the underlying model assumptions quite well; of importance, no outlier sites are detected in the plots of the regression diagnostics of the adopted regression equations. Based on ‘one‐at‐a‐time cross validation’ and a number of evaluation statistics, it has been found that for Tasmania the QRT provides more accurate flood quantile estimates for the higher ARIs while the PRT provides relatively better estimates for the smaller ARIs. The RFFA techniques presented here can easily be adapted to other Australian states and countries to derive more accurate regional flood predictions. Copyright © 2011 John Wiley & Sons, Ltd.     

A direct three-parameter Muskingum procedure incorporating lateral inflow

ABSTRACT

An efficient method of analysis is presented which yields directly estimates of the coefficients in the Muskingum flood routing equation:

O_j+1 = c₁I_j + c₂I_j+1 + c₃O_j

that are best in the least squares sense. A simple conceptual model of lateral inflow is proposed and leads to an extended version of the Muskingum method that has a lateral inflow parameter in addition to the standard storage and weighting parameters, K and x. Applications to a number of flood events are given, and proposals for further studies suggested.     

AUTOMATIC PICKING OF FIRST ARRIVALS AND PARAMETERIZATION OF TRAVELTIME CURVES*

One of the methods for studying the near-surface low-velocity zone and for subsequent determination of static corrections is the technique of employing first arrivals. During the past few years several computer algorithms, based on some simplifying assumptions, have been suggested for automatic determination of first arrivals. This paper suggests a new method for automatic picking of first arrivals, which works under quite general assumptions concerning the character of the data. The method is based on the use of correlation properties of signals and the application of a statistical criterion for the estimation of first arrivals time. A number of dimensionless parameters is used in the algorithm making it possible to regulate the level of reliability and the resolution of the picking procedure. The second stage of the algorithm is the parameterization of the traveltime curve, that is a division of the previously obtained t—x curve into separate rectilinear segments. The suggested algorithm of parameterization is based on an heuristic use of some properties of maximum likelihood estimates. This permits location of the breakpoints of the t—x curve and the estimation of the parameters of each rectilinear segment. A computer program has been written based on the picking and parameterization algorithm. This program has been tested on a large amount of field data and the results show that it works at least as well as the hand procedure.     

The effect of geometrical parameters on the discharge capacity of meandering compound channels

A number of methods and formulae has been proposed in the literature to estimate the discharge capacity of compound channels. When the main channel has a meandering pattern, a reduction in the conveyance capacity for a given stage is observed, which is due to the energy dissipations caused by the development of strong secondary currents and to the decrease of the main channel bed slope with respect to the valley bed slope. The discharges in meandering compound channels are usually assessed applying, with some adjustments, the same methods used in the straight compound channels. Specifically, the sinuosity of the main channel is frequently introduced to account for its meandering pattern, although some methods use different geometric parameters.In this paper the stage—discharge curves for several compound channels having identical cross-sectional area, roughness and bed slope but different planimetric patterns are numerically calculated and compared, in order to identify which geometric parameter should be efficaciously used in empirical formulae to account for meandering patterns. The simulations are carried out using a 3D finite-volume model that solves the RANS equations using a k-ε turbulence model. The numerical code is validated against experimental data collected in both straight and meandering compound channels.The numerical results show that the sinuosity is the main parameter to be accounted for in empirical formulae to assess the conveyance capacity of meandering compound channels. Comparison of the stage—discharge curves in the meandering compound channels with that obtained in a straight channel having identical cross-sectional area clearly shows the reduction of discharge due to the presence of bends in the main channel. The effect of other geometric parameters, such as the meander-belt width and the mean curvature radius, results very weak.     

Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification

Abstract

The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hydrograph through uniform rectangular cross-section channels and comparing the results with the corresponding numerical solutions of the St. Venant equations. The stage hydrographs as computed by the method are also compared with the corresponding St. Venant solutions. It is demonstrated that the method closely reproduces the St. Venant solutions for the discharge and stage hydrographs subject to the compliance of the assumptions of the method by the routing process.