ESTIMATING PARAMETERS OF EV1 DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The parameters of the extreme value type 1 distribution were estimated for 55 annual flood data sets by seven methods. These are the methods of (1) moments, (2) probability weighted moments, (3) mixed moments, (4) maximum likelihood estimation, (5) incomplete means, (6) principle of maximum entropy, and (7) least squares. The method of maximum likelihood estimation was found to be the best and the method of incomplete means the worst. The differences between the methods of principle of maximum entropy, probability weighted moments, moments, and least squares were only minor. The difference between these methods and the method of maximum likelihood was not pronounced.     

UNIT HYDROGRAPHS – A COMPARATIVE STUDY1

ABSTRACT. Unit hydrographs derived by using two methods, linear programming and least squares, are compared. Test data comprise rainfall and runoff information from four storms over the North Branch Potomac River near Cumberland, Maryland. The mathematical bases of these methods for unit-hydrograph derivation are explained. The linear programming method minimizes the sum of absolute deviations, and the least squares method minimizes the sum of the squares of deviations. Computer subroutines are readily available for application of these methods. The unit hydrographs derived with the two methods are practically the same for storms 2 and 3, but differ somewhat for storms 1 and 4. However, the reconstituted direct surface runoff hydrographs are similar to those observed with the exception of the hydrograph for storm 4 which had a relatively more non-uniform rainfall excess of a considerably larger duration.     

PARAMETRIC ESTIMATION OF COVARIANCES OF REGIONALIZED VARIABLES1

ABSTRACT: The usefulness of stochastic models in describing the spatial variability of hydrogeologic quantities, such as permeability, storativity, piezometric head, seepage velocity, and solute concentrations is now widely recognized. In practice, these quantities are represented as the sum of a well-structured component, or drift, and a more erratic fluctuation component which is described statistically through its covariance function. This paper reviews some of the most recent and most promising methods for the estimation of parameters of these covariances from existing data. They are maximum likelihood, restricted maximum likelihood, minimum-variance unbiased quadratic estimation, and minimum-norm (weighted least squares) estimation. The applicability of such methods to conditional and unconditional probability problems is discussed.     

DERIVATION OF THE GAMMA DISTRIBUTION BY USING THE PRINCIPLE OF MAXIMUM ENTROPY (POME)1

The principle of maximum entropy (POME) was used to derive the two-parameter gamma distribution used frequently in synthesis of instantaneous or finite-period unit hydrographs. The POME yielded the minimally prejudiced gamma distribution by maximizing the entropy subject to two appropriate constraints which were the mean of real values and the mean of the logarithms of real values of the variable. It provided a unique method for parameter estimation. Experimental data were used to compare this method with the methods of moments, cumulants, maximum likelihood estimation, and least squares.     

ANALYSIS OF PUMPING TESTS: SIGNIFICANCE OF WELL DIAMETER,PARTIAL PENETRATION,AND NOISE1

ABSTRACT: The nonlinear least squares (NLS) method was applied to pumping and recovery aquifer test data in confined and unconfined aquifers with finite diameter and partially penetrating pumping wells, and with partially penetrating piezometers or observation wells. It was demonstrated that noiseless and moderately noisy drawdown data from observation points located less than two saturated thicknesses of the aquifer from the pumping well produced an exact or acceptable set of parameters when the diameter of the pumping well was included in the analysis. The accuracy of the estimated parameters, particularly that of specific storage, decreased with increases in the noise level in the observed drawdown data. With consideration of the well radii, the noiseless drawdown data from the pumping well in an unconfined aquifer produced good estimates of horizontal and vertical hydraulic conductivities and specific yield, but the estimated specific storage was unacceptable. When noisy data from the pumping well were used, an acceptable set of parameters was not obtained. Further experiments with noisy drawdown data in an unconfined aquifer revealed that when the well diameter was included in the analysis, hydraulic conductivity, specific yield and vertical hydraulic conductivity may be estimated rather effectively from piezometers located over a range of distances from the pumping well. Estimation of specific storage became less reliable for piezometers located at distances greater than the initial saturated thickness of the aquifer. Application of the NLS to field pumping and recovery data from a confined aquifer showed that the estimated parameters from the two tests were in good agreement only when the well diameter was included in the analysis. Without consideration of well radii, the estimated values of hydraulic conductivity from the pumping and recovery tests were off by a factor of four.     

Model Development and Calibration of a Saltwater Intrusion Model in Southern California1

Abstract: A nine‐layered confined‐unconfined flow and transport model is developed for the Alamitos saltwater intrusion barrier in Southern California. The conceptual model is based on the geological structure of the coastal aquifer system. The key parameters in the flow and transport models are calibrated using a two‐phase procedure which matches the types of data available for calibration. Because of the abundance of point measurements of hydraulic conductivity, the heterogeneous and random hydraulic conductivity field for each of the five aquifers is estimated by the geostatiscal method of natural‐neighbor‐kriging in Phase 1. In Phase 2, the longitudinal and transverse dispersivities in the transport model are estimated by a traditional inverse procedure that minimizes the least‐squares error for concentration (LSE‐CON). The minimum LSE‐CON is achieved near 15.2 and 1.52 m for the longitudinal and transverse dispersivities, respectively. Additional simulations with increasing transport parameter complexity did not yield significant improvements in LSE‐CON. Also, tracking least‐squares error for head while parametrically varying the transport parameters revealed there is a negligible interaction between predicted head and transport parameters.     

GENERALIZED LOW-FLOW FREQUENCY RELATIONSHIPS FOR UNGAGED SITES IN MASSACHUSETTS1

ABSTRACT: Regional hydrologic procedures such as generalized least squares regression and streamflow record augmentation have been advocated for obtaining estimates of both flood-flow and low-flow statistics at ungaged sites. While such procedures are extremely useful in regional flood-flow studies, no evaluation of their merit in regional low-flow estimation has been made using actual streamflow data. This study develops generalized regional regression equations for estimating the d-day, T-year low-flow discharge, Q_{d, t}, at ungaged sites in Massachusetts where d = 3, 7, 14, and 30 days. A two-parameter lognormal distribution is fit to sequences of annual minimum d-day low-flows and the estimated parameters of the lognormal distribution are then related to two drainage basin characteristics: drainage area and relief. The resulting models are general, simple to use, and about as precise as most previous models that only provide estimates of a single statistic such as Q_7,10. Comparisons are provided of the impact of using ordinary least squares regression, generalized least squares regression, and streamflow record augmentation procedures to fit regional low-flow frequency models in Massachusetts.     

ERRORS IN ESTIMATED STREAMFLOW PARAMETERS AND STORAGES FOR UNGAUGED CATCHMENTS1

ABSTRACT: For a set of 81 catchments in southeast Victoria, Australia, predictive equations were developed by least squares regression of the mean and coefficient of variation of annual Streamflow against a variety of rainfall and physiographic parameters. The data were also divided into subsets according to catchment size, subregion, or record length of investigate if the relationships differed significantly between subsets. Only the catchment area and some rainfall statistical parameters were found to be significant. Streamflow parameters predicted by the regression equations were used to estimate storage requirements in ungauged catchments. The influence of errors in the Streamflow parameters on the storage error was examined.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

ABSTRACT: The purpose of this article is to discuss the importance of uncertainty analysis in water quality modeling, with an emphasis on the identification of the correct model specification. A wetland phosphorus retention model is used as an example to illustrate the procedure of using a filtering technique for model structure identification. Model structure identification is typically done through model parameter estimation. However, due to many sources of error in both model parameterization and observed variables and data, error-in-variable is often a problem. Therefore, it is not appropriate to use the least squares method for parameter estimation. Two alternative methods for parameter estimation are presented. The first method is the maximum likelihood estimator, which assumes independence of the observed response variable values. In anticipating the possible violation of the independence assumption, a second method, which coupled a maximum likelihood estimator and Kalman filter model, was presented. Furthermore, a Monte Carlo simulation algorithm is presented as a preliminary method for judging whether the model structure is appropriate or not.     

PROCESS-ORIENTED ESTIMATION OF SUSPENDED SEDIMENT CONCENTRATION1

ABSTRACT: Least squares regression and ARIMA models were developed from suspended sediment data for the Ausable River, Southern Ontario, Canada. A poor correlation between discharge and suspended sediment concentration results from the dynamics of the physical system, including seasonality, antecedent conditions, and hysteresis. Regression model results were significantly improved by the division of the data set into seasons and the addition of simple. but physically meaningful variables. Misleading improvements obtained from the regression of sediment load and discharge are discussed. ARIMA models provided accurate forecasts of sediment concentration on a real-time basis, but the rigorous data requirements limit their use in modeling suspended sediment concentrations in Canadian rivers.     

NONLINEAR MODELING AND PREDICTION OF A RIVER FLOW SYSTEM1

ABSTRACT: Model estimation and prediction of a river flow system are investigated using nonlinear system identification techniques. We demonstrate how the dynamics of the system, rainfall, and river flow can be modeled using NARMAX (Nonlinear Autoregressive Moving Average with eXogenuous input) models. The parameters of the model are estimated using an orthogonal least squares algorithm with intelligent structure detection. The identification of the nonlinear model is described to represent the relationship between local rainfall and river flow at Enoree station (inputs) and river flow at Whitmire (output) for a river flow system in South Carolina.     

CATCHMENT RESPONSE TIME AS A PREDICTOR OF FLOOD QUANTILES1

ABSTRACT: A regression analysis using a generalized least squares approach on flow data from the driftless area of Wisconsin indicates that the ratio of drainage area to time-to-peak is a good predictor of flood quantiles. The estimation of time-to-peak (or some other measure of basin response time) requires direct measurement of river stage and possibly rainfall at the site of which the quantiles are to be estimated. The cost-effectiveness of such an approach must yet be determined.     

火焰原子吸收法测定总铜不确定度的评定

依据线性最小二乘法的数学特性,提出采用火焰原子吸收法测定地表水中总铜的不确定度的简化评定方法,通过识别和分析不确定度源,对不确定度进行量化,计算合成标准不确定度。此方法适用于地下水、地表水和废水中的总铜含量直接法测定中不确定度的快速评定。     

NONSTEADY FLOW TO A WELL WITH TIME DEPENDENT DRAWDOWN1

Confined flow toward a single well of finite radius in an extensive aquifer of uniform transmissibility is studied under the assumption of time-dependent drawdown. Three particular cases are considered: (a) linear drawdown (including constant drawdown); (b) exponential drawdown; (c) periodic (sinusoidal) drawdown. The differential equation governing unsteady axial symmetric flow toward a single well in a confined aquifer is solved for the three different situations by the use of the Laplace transform method. The resulting expressions are integrated by adapting a modified Gemant scheme. General computer programs have been developed and operated for several combinations of characteristics. The results are plotted to show the effect of time dependent drawdown on the variation of the well discharge and the piezometric head distribution.     

Linking Biological Integrity and Watershed Models to Assess the Impacts of Historical Land Use and Climate Changes on Stream Health

Land use change and other human disturbances have significant impacts on physicochemical and biological conditions of stream systems. Meanwhile, linking these disturbances with hydrology and water quality conditions is challenged due to the lack of high-resolution datasets and the selection of modeling techniques that can adequately deal with the complex and nonlinear relationships of natural systems. This study addresses the above concerns by employing a watershed model to obtain stream flow and water quality data and fill a critical gap in data collection. The data were then used to estimate fish index of biological integrity (IBI) within the Saginaw Bay basin in Michigan. Three methods were used in connecting hydrology and water quality variables to fish measures including stepwise linear regression, partial least squares regression, and fuzzy logic. The IBI predictive model developed using fuzzy logic showed the best performance with the R ² = 0.48. The variables that identified as most correlated to IBI were average annual flow, average annual organic phosphorus, average seasonal nitrite, average seasonal nitrate, and stream gradient. Next, the predictions were extended to pre-settlement (mid-1800s) land use and climate conditions. Results showed overall significantly higher IBI scores under the pre-settlement land use scenario for the entire watershed. However, at the fish sampling locations, there was no significant difference in IBI. Results also showed that including historical climate data have strong influences on stream flow and water quality measures that interactively affect stream health; therefore, should be considered in developing baseline ecological conditions.     

An Optimization Method for Estimating Constituent Mean Concentrations in Base Flow‐Dominated Flow

Pollutant coefficients have been widely used to assess runoff nonpoint source pollution from individual land uses (e.g., agricultural, residential) of a watershed. Pollutant coefficients, known as event mean concentrations (EMCs), were developed by the U.S. Environmental Protection Agency's Nationwide Urban Runoff Program (NURP) to serve as a national measure for characterizing pollutant loading in a receiving water body. The term “baseflow pollutant coefficient (BPC)” is used in this study as a surrogate for EMC to describe mean concentration of pollutants in base flow‐dominated flow. A method for characterizing base flow quantity and quality for different land uses was explored using inverse modeling with two optimization techniques (a least square method and a genetic algorithm [GA] optimization), land use information, and streamflow quantity and quality data. The inverse model was formulated as a constrained minimization problem and demonstrated with data for 15 watersheds in Indiana. Results showed that estimated pollutant coefficients are comparable to the published literature. This indicates that the proposed method has the potential to effectively estimate constituent mean concentrations for pollutant load determination in gauged and ungauged watersheds, albeit more analysis with larger and more robust datasets is desirable to further refine and validate the accuracy of the approach.     

PARAMETER ESTIMATION FOR TPLN DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The principle of maximum entropy (POME) was used to derive an alternative method for parameter estimation for the three parameter lognormal (TPLN) distribution. Six sets of annual peak discharge data were used to evaluate this method and compare it with the methods of moments and maximum likelihood estimation.     

OPTIMAL IDENTIFICATION OF MUSKINGUM ROUTING COEFFICIENTS1

Traditionally, identification of the Muskingum routing coefficients has been based on observations of the linearity of a loop formed by graphically plotting a forward and a reverse path. This graphical procedure is time-consuming and may not minimize the error of estimation. A procedure was developed to improve the drawbacks of the graphical method. This procedure calls for (a) the use of least square regression on the forward and reverse paths to determine their respective slopes, and (b) the use of statistical t-test to evaluate the hypothesis that these two slopes are equal. The computational procedure is repeated, using incremental values of the flow weighting coefficient, x. A graph of the computed t-value versus x can be constructed. The optimal value of x, as read from the graph, occurs at the minimum computed t-value. The procedure has been demonstrated superior to the graphical method for three illustrative examples, resulting in a reduction of the error squares by factors ranging from 5 to 6.     

Optimization of the electrocoagulation process for the removal of copper, lead and cadmium in natural waters and simulated wastewater

Chemical, electrochemical and flow variables were optimized to examine the effectiveness of the electrocoagulation process for the removal of copper, lead and cadmium. The electrochemical process, which uses electrodes of commercial laminate steel, was applied to simulated wastewater containing 12 mg dm(-3) of copper, 4 mg dm(-3) of lead and 4 mg dm(-3) of cadmium. The optimum conditions for the process were identified as pH=7, flow rate=6.3 cm(3) min(-1) and a current density between 31 and 54 A m(-2). When the electrode geometric area and time of electrolysis reached critical values, the copper removal reached a maximum value of 80%. A linear relationship was identified between the current density and the mass of generated sludge. In addition, a linear relationship was found between specific energy consumption and current density. The results of this investigation provide important data for the development of an industrial-scale electrolytic reactor.     

STREAM TYPES IN THE DES MOINES RIVER BASIN1

Stream tributaries in the Des Moines River basin have been classified according to the glacial terrain through which they flow. Three stream types were categorized as follows: (1) streams that flow entirely on Wisconsin drift, (2) streams that flow entirely on Kansan drift, and (3) streams that have their headwaters located on new drift but have their lower reaches flowing on older drift. Selected channel and valley characteristics were measured and used to verify the stream type classification. Five variables were chosen for use in a multiple linear discriminatory analysis, which is a statistical technique developed for the purpose of classifying observations into one of several categories which have been predetermined. The streams in each group were verified with the exception of three anomalies based on the probability associated with the largest linear discriminant function. The rationale for the three anomalous streams is not easily determined. But, they are considered to be associated with pre-glacial drainage or at least pre-Wisconsin age drainage. Otherwise, the analysis shows that the major channels and valleys in the Des Moines River basin tend to reflect the glaciated upland surface.