impact of multicollinearity on small sample hydrologic regression models 1 often hydrologic regression models are developed with ordinary least squares ols procedures the use of ols with highly correlated explanatory variables produces multicollinearity which creates highly sensitive parameter estimators with inflated variances and improper model selection it is not clear how to best address multicollinearity in hydrologic regression models here a monte carlo simulation is developed to compare four techniques to address multicollinearity ols ols with variance inflation factor screening vif principal component regression pcr and partial least squares regression pls the performance of these four techniques was observed for varying sample sizes correlation coefficients between the explanatory variables and model error variances consistent with hydrologic regional regression models the negative effects of multicollinearity are magnified at smaller sample sizes higher correlations between the variables and larger model error variances smaller r2 the monte carlo simulation indicates that if the true model is known multicollinearity is present and the estimation and statistical testing of regression parameters are of interest then pcr or pls should be employed if the model is unknown or if the interest is solely on model predictions is it recommended that ols be employed since using more complicated techniques did not produce any improvement in model performance a leave one out cross validation case study was also performed using low streamflow data sets from the eastern united states results indicate that ols with stepwise selection generally produces models across study regions with varying levels of multicollinearity that are as good as biased regression techniques such as pcr and pls

fourth order time stepping for stiff pdes a modification of the exponential time differencing fourth order runge kutta method for solving stiff nonlinear pdes is presented that solves the problem of numerical instability in the scheme as proposed by cox and matthews and generalizes the method to nondiagonal operators a comparison is made of the performance of this modified exponential time differencing etd scheme against the competing methods of implicit explicit differencing integrating factors time splitting and fornberg and driscoll s sliders for the kdv kuramoto sivashinsky burgers and allen cahn equations in one space dimension implementation of the method is illustrated by short matlab programs for two of the equations it is found that for these applications with fixed time steps the modified etd scheme is the best

numerical simulation of singular solutions to the two dimensional cubic schrodinger equation numerical simulations of the cubic nonlinear schrodinger equation are presented in dimension n 2 the emphasis is on a detailed mechanism of blow up the numerical results indicate that the blow up is not restricted to the case where the problem is posed in the entire r2 space but also occurs with periodic boundary conditions the structure of the solution as the singular time t is approached has been investigated using examples with and without radial symmetry and or periodicity in most cases we observe that the amplitude develops something like the peaked self similar profile predicted by zakharov and synakh 38 which has a t t 2 3 maximum amplitude and a t t 2 3 width

estimation of distributional parameters for censored trace level water quality data 1 estimation techniques a recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations their reliabilities were evaluated by a monte carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels eight methods were used to estimate the mean standard deviation median and interquartile range criteria were developed based on the distribution of uncensored observations for determining the best performing parameter estimation method for any particular data det the most robust method for minimizing error in censored sample estimates of the four distributional parameters over all simulation conditions was the log probability regression method with this method censored observations are assumed to follow the zero to censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores when method performance was separately evaluated for each distributional parameter over all simulation conditions the log probability regression method still had the smallest errors for the mean and standard deviation more but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range when data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions the ranking of estimation methods was similar but the accuracy of error estimates was markedly improved over those without classification less

exponential time differencing crank nicolson method with a quartic spline approximation for nonlinear schrodinger equations abstract this paper studies a central difference and quartic spline approximation based exponential time differencing crank nicolson etd cn method for solving systems of one dimensional nonlinear schrodinger equations and two dimensional nonlinear schrodinger equations a local extrapolation is employed to achieve a fourth order accuracy in time the numerical method is proven to be highly efficient and stable for long range soliton computations numerical examples associated with dirichlet neumann and periodic boundary conditions are provided to illustrate the accuracy efficiency and stability of the method proposed

estimation of descriptive statistics for multiply censored water quality data this paper extends the work of gilliom and helsel 1986 on procedures for estimating descriptive statistics of water quality data that contain less than observations previously procedures were evaluated when only one detection limit was present here we investigate the performance of estimators for data that have multiple detection limits probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use therefore simple substitution procedures e g substitution of the detection limit should be avoided probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown when utilized correctly less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them

flood frequency censoring errors associated with daily read flood observations 1 the effects of daily read discharges discharges derived from a single daily observation say at 9 am are examined in the context of flood frequency analysis these discharges underestimate the true peak discharge because the actual peak is unlikely to occur at the single observation time the resultant error in discharge estimates can be quite large up to a factor of 10 several maximum likelihood methods are proposed to deal with these daily read or censored discharges three methods are evaluated censored as gauged cag which treats daily read discharges as the true peak binomial censoring bc which uses binomial censoring and random dependent censoring rdc which incorporates the dependence between the the daily read and true peak discharges the performance of the methods is evaluated using a monte carlo study the rdc method is found preferable to the cag method because it provides better performance in terms of root mean squared error and bias and is theoretically sound the bc method performs very poorly and is not recommended

log pearson type 3 quantile estimators with regional skew information and low outlier adjustments 1 the recently developed expected moments algorithm ema cohn et al 1997 does as well as maximum likelihood estimations at estimating log pearson type 3 lp3 flood quantiles using systematic and historical flood information needed extensions include use of a regional skewness estimator and its precision to be consistent with bulletin 17b another issue addressed by bulletin 17b is the treatment of low outliers a monte carlo study compares the performance of bulletin 17b using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers including an extended ema estimator the conditional probability adjustment cpa from bulletin 17b and an estimator that uses probability plot regression ppr to compute substitute values for low outliers estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator for lp3 data the low outlier rejection procedure generally results in no loss of overall accuracy and the differences between the mses of the estimators that used an informative regional skew are generally modest in the skewness range of real interest samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment

invariant algebraic surfaces of the lorenz system in this paper we provide a complete classification of the darboux invariants of the irreducible darboux polynomials of the rational first integrals and of the algebraic integrability for the classical lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

confidence intervals for expected moments algorithm flood quantile estimates historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied however the federal guidelines for flood frequency analysis set forth in bulletin 17b rely on an inefficient weighting procedure that fails to take advantage of historical and paleoflood information this has led researchers to propose several more efficient alternatives including the expected moments algorithm ema which is attractive because it retains bulletin 17b s statistical structure method of moments with the log pearson type 3 distribution and thus can be easily integrated into flood analyses employing the rest of the bulletin 17b approach the practical utility of ema however has been limited because no closed form method has been available for quantifying the uncertainty of ema based flood quantile estimates this paper addresses that concern by providing analytical expressions for the asymptotic variance of ema flood quantile estimators and confidence intervals for flood quantile estimates monte carlo simulations demonstrate the properties of such confidence intervals for sites where a 25 to 100 year streamgage record is augmented by 50 to 150 years of historical information the experiments show that the confidence intervals though not exact should be acceptable for most purposes

the validity of a simple statistical model for estimating fluvial constituent loads an empirical study involving nutrient loads entering chesapeake bay we consider the appropriateness of rating curves and other log linear models to estimate the fluvial transport of nutrients split sample studies using data from tributaries to the chesapeake bay reveal that a minimum variance unbiased estimator mvue based on a simple log linear model provides satisfactory load estimates even in some cases where the model exhibited significant lack of fit for total nitrogen tn the average difference between the mvue estimates and the observed loads ranges from 8 to 2 at the four sites the corresponding range for total phosphorus tp is 6 to 5 none of these differences is statistically significant the observed variability of the mvue load estimates for tn and tp which ranges from 7 to 25 depending on the case is accurately predicted by statistical theory

flood frequency analysis with systematic and historical or paleoflood data based on the two parameter general extreme value models historical and paleoflood data have become an important source of information for flood frequency analysis a number of studies have been proposed in the literature regarding the value of historical and paleoflood information for estimating flood quantiles these studies have been generally based on computer simulation experiments in this paper the value of using systematic and historical paleoflood data relative to using systematic records alone is examined analytically by comparing the asymptotic variances of flood quantiles assuming a two parameter general extreme value marginal distribution type 1 and type 2 censored data and maximum likelihood estimation method the results of this study indicate that the value of historical and paleoflood data for estimating flood quantiles can be small or large depending on only three factors the relative magnitudes of the length of the systematic record n and the length of the historical period m the return period t of the flood quantile of interest and the return period h of the threshold level of perception for instance for n 50 m 50 and t 500 the statistical gain for type 2 censoring becomes significantly larger than for type 1 censoring as h becomes greater than 100 years in addition computer experiments have shown that the results regarding the statistical gain based on asymptotic considerations are valid for the usual sample sizes

dynamics of the lorenz system having an invariant algebraic surface in this paper we characterize all dynamics of the lorenz system x s y x y rx xz y z xy bz having an invariant algebraic surface

plotting positions for historical floods and their precision plotting positions are needed for situations where in addition to a systematically recorded annual flood series one would have a record of any large floods which occurred during an extended historical period if they occurred many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment plotting positions are derived for such experiments using both classical and bayesian viewpoints in general it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank the number of observed historical floods and the lengths of the historical period and the systematic record for the largest flood the coefficient of variation of exceedance probability estimators is of the order of 1 as it is for complete systematic records examples illustrate the bias and precision of a variety of plotting position formulas the differences among the different plotting positions are generally small in comparison to the sampling variability however plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data three appendices consider the effect of misspecification of the length of the historical period the effect of misspecification of the threshold of perception or observation level and plotting positions for situations with several perception thresholds

numerical studies on the split step finite difference method for nonlinear schrodinger equations in this study we use the split step finite difference method to solve various nonlinear schrodinger equations including coupled ones we study the numerical accuracy of the method detailed numerical results including higher dimensions show that the method provides accurate and stable solutions for nonlinear schrodinger equations

formal and analytic integrability of the lorenz system the well known lorenz system can be written as and here we study the first integrals of the lorenz system that can be described by formal power series in particular if s 0 and either b is not a negative rational number or b is a negative rational number and k1b k2 1 s 0 for all k1 and k2 non negative integers with k1 k2 0 then the lorenz system has no analytic first integrals in a neighbourhood of the origin

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

lh moments for statistical analysis of extreme events statistical analysis of extremes is often conducted for predicting large return period events in this paper lh moments a generalization of l moments that are based on linear combinations of higher order statistics are introduced for characterizing the upper part of distributions and larger events in data using lh moments reduces undesirable influences that small sample events may have on the estimation of large return period events the method of lh moments is formulated for the generalized extreme value gev distribution along with two detailed examples monte carlo simulations are conducted to illustrate the performance of using the method of lh moments to fit the gev distribution to both gev and non gev samples lh moment diagrams are constructed using annual maximum flow data for 107 streams worldwide to examine the ability of the gev distribution to model those series

regional hydrologic analysis ordinary and generalized least squares revisited generalized least squares gls regional regression procedures have been developed for estimating river flow quantiles a widely used gls procedure employs a simplified model error structure and average covariances when constructing an approximate residual error covariance matrix this paper compares that gls estimator an idealized gls estimator based on the simplifying assumptions of with true underlying statistics in a region the best possible gls estimator obtained using the true residual error covariarice matrix and the ordinary least squares estimator useful analytic expressions are developed for the variance of and for previously examined cases the average sampling mean square error mses of was the same as the mses of and the mses of usually was larger than the mses of both and the loss in efficiency of was mostly due to estimating streamflow statistics employed in the construction of the residual error covariance matrix rather than the simplifying assumptions in presently employed gls estimators the new analytic expressions were used to compare the performance of the ols and gls estimators for new cases representing greater model variability across sites as well as the effect return period has on the estimators relative performance for a more heteroscedastic model error variance and larger return periods some increase in the mses of relative to the mses of was observed

an element free based solution for nonlinear schrodinger equations using the icvmls ritz method an improved complex variable moving least squares ritz icvmls ritz method is proposed for predicting numerical solution of the two dimensional nonlinear schrodinger equation in this element free solution procedure the icvmls approximation is employed to reduce the number of unknown coefficients in the trial function it follows by the ritz procedure to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear schrodinger equation the central differencing scheme and newton s algorithm are adopted to solve the nonlinear equation system numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element free icvmls ritz method by comparing the computed results with the available analytical solutions

integrating the nonintegrable analytic structure of the lorenz system revisited abstract a study of the complex time analytic structure of the lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one time dependent integral of motion exists furthermore the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument the analytic techniques used in these studies a systematic resummation of a logarithmic psi series appears to be quite general and can provide explicit representations of a solution even in the chaotic regimes in the neighborhood of a given movable singularity furthermore we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems

comprehensive at site flood frequency analysis using monte carlo bayesian inference in flood frequency applications where the design flood is required to have a specified exceedance probability expected probability should be used its computation however presents formidable difficulties this study presents a monte carlo bayesian method for computing the expected probability distribution as well as quantile confidence limits for any flood frequency distribution using data on gauged flows possibly corrupted by rating curve error and on censored flows this is achieved by a three step process 1 formulate the likelihood function for the given data 2 approximate the likelihood function using a multinomial distribution and 3 integrate the expected probability integral using importance sampling the flike software for performing this is described and an example is given

conservation of phase space properties using exponential integrators on the cubic schrodinger equation the cubic nonlinear schrodinger nls equation with periodic boundary conditions is solvable using inverse spectral theory the nonlinear spectrum of the associated lax pair reveals topological properties of the nls phase space that are difficult to assess by other means in this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach the initial condition used is a perturbation of the unstable plane wave solution which is difficult to numerically resolve our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step while a lower order multisymplectic is not as accurate and too slow to compete

a monte carlo study of some two sample rank tests with censored data abstract the powers of several nonparametric tests for the two sample problem with censored data are compared by simulation the tests studied include gehan s efron s and peto s and prentice s generalized wilcoxon tests along with the logrank test the test with the greatest power changes with the sample sizes censoring mechanism and distribution of the random variables the test that performed the best overall was the peto prentice generalized wilcoxon statistic with an asymptotic variance estimate

exponential factors and darbouxian first integrals of the lorenz system in this article we characterize all the exponential factors and the darbouxian first integrals for the lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

estimating constituent loads several recent articles have called attention to the problem of retransformation bias which can arise when log linear regression models are used to estimate sediment or other constituent loads in some cases the bias can lead to underestimation of constituent loads by as much as 50 and several procedures have been suggested for reducing or eliminating it however some of the procedures recommended for reducing the bias can actually increase it this paper compares the bias and variance of three procedures that can be used with log linear regression models the traditional rating curve estimator a modified rating curve method and a minimum variance unbiased estimator mvue analytical derivations of the bias and efficiency of all three estimators are presented it is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates however other conditions exist where they have substantial bias and a large mean square error these conditions commonly occur when sample sizes are small or when loads are estimated during high flow conditions the mvue however is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct since an efficient unbiased estimator is available there seems to be no reason to employ biased estimators

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

integrals of motion for the lorenz system a direct method is proposed for determining the conditions under which the lorenz system is integrable this method uses only leading singular behavior to recover all known integrals of motion together with a few new ones

development of regional regression relationships with censored data when no discharge record is available for a site a regional regression relationship can be used to estimate low flow quantiles problems arise in the derivation of such models when some at site quantile estimates are reported as zero one concern is that quantile estimates reported as zero may be in the range from zero to the measurement threshold a second concern is that a logarithmic transformation cannot be used with zero quantile estimates so traditional log linear least squares estimators cannot be computed this paper uses visual examples and monte carlo simulation to compare the performance of techniques for estimating the parameters of a regional regression model when some at site quantile estimates are zero ordinary least squares ols techniques employed in practice include adding a small constant to all at site quantile estimates denoted olsc or neglecting all observation reported as zero denoted olsd olsc and olsd performed poorly compared to the use of a tobit model which is a maximum likelihood estimator mle procedure that represents the below threshold estimates as a range from zero to the threshold level for a small amount of censoring the olsd method can be acceptable a weighted tobit model that accounts for the heteroscedasticity of the residuals in the regression model provided relatively little gain over the ordinary tobit model

nonparametric variable kernel estimation with historical floods and paleoflood information extending a data record back in time using historical or paleoflood data has the potential to provide a considerable amount of information on very large floods parametric estimation methods are readily applicable to flood frequency analysis when historical or paleoflood estimates are available however all parametric approaches need an assumption about the underlying parent distribution which is never known exactly in recent years nonparametric methods of estimating probability density functions have been developed each of these involves the use of a suitable smoothing function known as a kernel a new nonparametric variable kernel estimation model is proposed results obtained from a limited amount of real data and from simulation experiments show that quantiles estimated by the nonparametric method are better than those estimated by some selected parametric models both in descriptive ability and in predictive ability the uncertainty in the choice of the threshold value of perception of a historical flood is also discussed

censored data correlation and principal component dynamic programming a principal component stochastic dynamic programming algorithm for stochastic multireservoir hydropower system operation optimization was proposed by saad and turgeon 1988 the dimension of the state space of the system is reduced by using only the major principal components of the system s state as determined by a principal component analysis of the results of a deterministic optimization a significant refinement of the procedure is to employ censored data principal component analysis the more sophisticated statistical analysis provides a better model of the full dynamic range of the reservoir system s state explains more observed variability of the reservoir volumes and provides more accurate estimates of the statistical description s parameters in an example presented of a four reservoir system the first component of the censored data principal component analysis for a given month explained all but 7 of the uncensored system s variability whereas the standard analysis for the same month left 12 of the observed system s variability unexplained

solving the generalized nonlinear schrodinger equation via quartic spline approximation this paper is concerned with a new conservative finite difference method for solving the generalized nonlinear schrodinger gnls equation iut uxx f u 2 u 0 the numerical scheme is constructed through the semidiscretization and an application of the quartic spline approximation central difference and extrapolation formulae are used for approximating the neumann boundary conditions introduced both continuous and discrete energy conservation and the stability property are investigated the numerical method provides an efficient and reliable way for computing long time solitary solutions given by the gnls equation numerical examples are given to demonstrate our conclusions

generalized extreme value distribution fitted by lh moments for low flow frequency analysis 1 this study introduces a method based on lh moments to use the generalized extreme value gev distribution for low flow frequency analysis and investigates the capability of the gev distribution fitted by lh moments to effectively model the lower tail of the low flow frequency curve without explicitly censoring the data sample the performance of the gev l moment the gev distribution fitted by l moments and gev lh moment the gev distribution fitted by lh moments methods are assessed by evaluating the bias mean square error and relative accuracy of quantile estimates through monte carlo simulations it is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution both gev l2 moment and gev l moment methods make equally accurate quantile estimates however when frequent low flows and extreme low flows do not follow a single trend the bias of the gev l2 moment estimator is negligible while the bias of the gev l moment estimator is significant at large annual recurrence intervals on average the gev l2 moment quantile estimator displays less bias than the gev l moment quantile estimator furthermore as the annual recurrence interval increases the relative accuracy of the gev l2 moment method consistently improves over the gev l moment method the gev lh moment method is thus considered to be the more suitable method to model low flows

l moment diagrams for censored observations observed data sets containing values above or below the analytical threshold of measuring equipment are referred to as censored such data are frequently encountered in quality and quantity monitoring applications of water soil and air samples most of the previous literature on the statistical analysis of censored data relates to the problems of moment parameter and quantile estimation methods such estimation methods usually assume an underlying probability distribution few goodness of fit methods exist for censored data we introduce l moment diagrams for the evaluation of the goodness of fit of alternative distributional hypotheses for left censored data experiments with artificial censored data sets document the conditions under which l moment diagrams should be useful our approach like hosking s 1995 approach for right censoring derived l moment diagrams for left censored observations from partial probability weighted moments

approximate confidence intervals for design floods for a single site using a neural network a basic problem in hydrology is the computation of confidence levels for the value of the t year flood when it is obtained from a log pearson iii distribution using the estimated mean estimated standard deviation and estimated skew here we give a practical method for finding approximate one sided or two sided confidence intervals for the 100 year flood based on data from a single site these confidence intervals are generally accurate to within a percent or two as tested by simulations and are obtained by use of a neural network

estimation of moments and quantiles using censored data censored data sets are often encountered in water quality investigations and streamflow analyses a monte carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets these techniques include a lognormal maximum likelihood estimator mle a log probability plot regression estimator and a new log partial probability weighted moment estimator data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables a robust fill in method which circumvents transformation bias in the real space moments was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation regardless of the underlying distribution the mle generally performed as well as or better than the other estimators though the moment and quantile estimators using all three techniques had comparable log space root mean square errors rmse for censoring at or below the 20th percentile for samples sizes of n 10 the 40th percentile for n 25 and the 60th percentile for n 50 comparison of the log space rmse and real space rmse indicated that a log space rmse was a better overall metric of estimator precision

correlated rating curve error in flood frequency inference an incremental rating curve error model is proposed to describe the systematic error introduced when a rating curve is extended by methods such as slope conveyance log log extrapolation or fitting to indirect discharge estimates extension can introduce a systematic or highly correlated error which is anchored by the more extensively measured part of the rating curve a likelihood function is developed which explicitly accounts for such error and accepts both gauged and binomial censored data a sampling experiment based on the three parameter generalized extreme value distribution was conducted to assess the performance of maximum likelihood quantile estimators this experiment revealed that substantial and in some cases massive degradation in the performance of quantile estimators can occur in the presence of correlated rating curve error rating error comparison of maximum likelihood estimators allowing for and ignoring rating error produced mixed results as rating error impact and or information content increased estimators allowing for rating error tended to perform better and in some cases significantly better than estimators ignoring rating error it is also shown that in the presence of rating error the likelihood surface may have multiple optima that may result in nonunique solutions for hill climbing search methods moreover in the presence of multiple optima and constraints on parameters the likelihood surface may be poorly described by asymptotic approximations

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

plotting positions of annual flood extremes considering extraordinary values a generalized plotting position formula for estimation of the recurrence interval or its reciprocal the exceedance probability of hydrologic events in an incomplete data sample containing both extraordinarily large and small historical values is derived the derivation is based on order statistics analysis and is independent of the probability distribution of the hydrologic variable it is shown that the weibull formula is a special case of the generalized formula

comparisons of two moments based estimators that utilize historical and paleoflood data for the log pearson type iii distribution 1 the expected moments algorithm ema cohn et al 1997 and the bulletin 17b interagency committee on water data 1982 historical weighting procedure b17h for the log pearson type iii distribution are compared by monte carlo computer simulation for cases in which historical and or paleoflood data are available the relative performance of the estimators was explored for three cases fixed threshold exceedances a fixed number of large floods and floods generated from a different parent distribution ema can effectively incorporate four types of historical and paleoflood data floods where the discharge is explicitly known unknown discharges below a single threshold floods with unknown discharge that exceed some level and floods with discharges described in a range the b17h estimator can utilize only the first two types of historical information including historical paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone ema performed significantly better than b17h in nearly all cases considered b17h performed as well as ema for estimating x100 in some limited fixed threshold exceedance cases ema performed comparatively much better in other fixed threshold situations for the single large flood case and in cases when estimating extreme floods equal to or greater than x500 b17h did not fully utilize historical information when the historical period exceeded 200 years robustness studies using gev simulated data confirmed that ema performed better than b17h overall ema is preferred to b17h when historical and paleoflood data are available for flood frequency analysis

an algorithm for computing moments based flood quantile estimates when historical flood information is available this paper presents the expected moments algorithm ema a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies ema can utilize three types of at site flood information systematic stream gage record information about the magnitude of historical floods and knowledge of the number of years in the historical period when no large flood occurred ema employs an iterative procedure to compute method of moments parameter estimates initial parameter estimates are calculated from systematic stream gage data these moments are then updated by including the measured historical peaks and the expected moments given the previously estimated parameters of the below threshold floods from the historical period the updated moments result in new parameter estimates and the last two steps are repeated until the algorithm converges monte carlo simulations compare ema bulletin 17b s united states water resources council 1982 historically weighted moments adjustment and maximum likelihood estimators when fitting the three parameters of the log pearson type iii distribution these simulations demonstrate that ema is more efficient than the bulletin 17b method and that it is nearly as efficient as maximum likelihood estimation mle the experiments also suggest that ema has two advantages over mle when dealing with the log pearson type iii distribution it appears that ema estimates always exist and that they are unique although neither result has been proven ema can be used with binomial or interval censored data and with any distributional family amenable to method of moments estimation

a new class of time discretization schemes for the solution of nonlinear pdes we consider issues of stability of time discretization schemes withexacttreatment of thelinear part elp schemes for solving nonlinear pdes a distinctive feature of elp schemes is the exact evaluation of the contribution of the linear term that is if the nonlinear term of the equation is zero then the scheme reduces to the evaluation of the exponential function of the operator representing the linear term computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient it turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices for a finite but arbitrary accuracy this observation makes our approach practical in a number of applications in particular we consider applications of elp schemes to advection diffusion equations we study the stability of these schemes and show that both explicit and implicit elp schemes have distinctly different stability properties if compared with known implicit explicit schemes for example we describe explicit schemes with stability regions similar to those of typical implicit schemes used for solving advection diffusion equations

local discontinuous galerkin methods for nonlinear schrodinger equations in this paper we develop a local discontinuous galerkin method to solve the generalized nonlinear schrodinger equation and the coupled nonlinear schrodinger equation l 2 stability of the schemes are obtained for both of these nonlinear equations numerical examples are shown to demonstrate the accuracy and capability of these methods

minimum variance streamflow record augmentation procedures traditional approaches for augmentation of short streamflow records have exploited the cross correlation among flows at two or more gages to obtain maximum likelihood estimates of the mean and variance of the flows at the short record gage while such estimators asymptotically have minimum variance among all asymptotically unbiased estimators they are not necessarily optimal for the small samples of interest in hydrology improved estimators of the mean and variance of the flows at the short record gage are developed the gains in information transfer associated with the use of both the traditional and improved estimators of the mean and variance are documented monte carlo results illustrate the performa1 ce of these estimators when the true cross correlation of the flows must be estimated the information transfer gains when the true cross correlation must be estimated are com parable to the gains achieved when the cross correlation is known the potential advantages and limi tations of these new estimators are discussed within the framework of augmentation and or extension of both peak annual floods and also monthly streamflow records

uncorrelated measurement error in flood frequency inference when measurement error me is present the true value of the annual maximum discharge and of the censoring threshold discharge is unknown the impact of using estimated rather than true discharges on the inference of flood quantiles is considered the likelihood function is formulated for data which consist of annual maximum discharges systematic data and occurrences of floods above some threshold discharge binomial censored data the formulation makes explicit allowance for the corruption of discharges by statistically independent me this formulation can be used to get maximum likelihood estimates or perform a bayesian analysis a limited sampling experiment was conducted to assess the performance of two parameter lognormal maximum likelihood quantile estimators in the presence of simple uncorreiated discontinuous me it was found that me reduces the information content of systematic and binomial censored data with the reduction being greatest for distributions with low coefficients of variation when only using systematic data it was found that the performance of estimators making allowance for me was at best only modestly better than that of estimators ignoring me the principal finding however was that the performance of maximum likelihood estimators using binomial censored data but ignoring me can be substantially worse than that of estimators making explicit allowance for me in fact the loss in performance can be so great that in some cases it may be preferable to ignore the binomial censored data finally it is shown that a bayesian analysis of flood data affected by me provides insights not offered by maximum likelihood estimation when the threshold discharge is in error the posterior distribution of the lognormal parameters can become bimodal as the length of the binomial censored record increases indicating an inconsistency between the information in the systematic and binomial censored data