Timothy A. Cohn

Load estimator (LOADEST): a FORTRAN program for estimating constituent loads in streams and rivers

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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.

Recent advances in statistical methods for the estimation of sediment and nutrient transport in rivers

This paper reviews advances in methods for estimating fluvial transport of suspended sediment and nutrients. Research from the past four years, mostly dealing with estimating monthly and annual loads, is emphasized. However, because this topic has not appeared in previous IUGG reports, some research prior to 1990 is included. The motivation for studying sediment transport has shifted during the past few decades. In addition to its role in filling reservoirs and channels, sediment is increasingly recognized as an important part of fluvial ecosystems and estuarine wetlands. Many groups want information about sediment transport [Bollman, 1992]: Scientists trying to understand benthic biology and catchment hydrology; citizens and policy-makers concerned about environmental impacts (e.g. impacts of logging [Beschta, 1978] or snow-fences [Sturges, 1992]); government regulators considering the effectiveness of programs to protect in-stream habitat and downstream waterbodies; and resource managers seeking to restore wetlands.

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 17Bs [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.

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 17Bs 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.

Use of historical information in a maximum-likelihood framework

Abstract This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are known, and when only threshold-exceedance information is available. Maximum likelihood, quasi-maximum likelihood and curve fitting methods for simultaneous estimation of 1, 2 and 3 unknown parameters are examined. The information contained in a 100 yr record of historical observations, during which the flood perception threshold was near the 10 yr flood level (i.e., on average, one flood in ten is above the threshold and hence is recorded), is equivalent to roughly 43, 64 and 78 years of systematic record in terms of the improvement of the precision of 100 yr flood estimators when estimating 1, 2 and 3 parameters, respectively. With the perception threshold at the 100 yr flood level, the historical data was worth 13, 20 and 46 years of systematic data when estimating 1, 2 and 3 parameters, respectively.

Climate, hydrology and freshwater: towards an interactive incorporation of hydrological experience into climate research

DEMETRIS KOUTSOYIANNIS, ALBERTO MONTANARI, HARRY F. LINS & TIMOTHY A. COHN 1 Department of Water Resources and Environmental Engineering, Faculty of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 5, GR-157 80 Zographou, Greece dk@itia.ntua.gr 2 Dipartimento di Ingegneria delle Strutture, dei Trasporti, delle Acque, del Rilevamento del Territorio, Faculty of Engineering, University of Bologna, I-40136 Bologna, Italy alberto.montanari@unibo.it 3 US Geological Survey, MS 415, Reston, Virginia 20192, USA hlins@usgs.gov; tacohn@usgs.gov

Estimating Discharge Measurement Uncertainty Using the Interpolated Variance Estimator

AbstractMethods for quantifying the uncertainty in discharge measurements typically identify various sources of uncertainty and then estimate the uncertainty from each of these sources by applying the results of empirical or laboratory studies. If actual measurement conditions are not consistent with those encountered in the empirical or laboratory studies, these methods may give poor estimates of discharge uncertainty. This paper presents an alternative method for estimating discharge measurement uncertainty that uses statistical techniques and on-site observations. This interpolated variance estimator (IVE) estimates uncertainty based on the data collected during the streamflow measurement and therefore reflects the conditions encountered at the site. The IVE has the additional advantage of capturing all sources of random uncertainty in the velocity and depth measurements. It can be applied to velocity-area discharge measurements that use a velocity meter to measure point velocities at multiple vertical...

The scientific legacy of Harold Edwin Hurst (1880–1978)

ABSTRACT Emanating from his remarkable characterization of long-term variability in geophysical records in the early 1950s, Hurst’s scientific legacy to hydrology and other disciplines is explored. A statistical explanation of the so-called “Hurst Phenomenon” did not emerge until 1968 when Mandelbrot and co-authors proposed fractional Gaussian noise based on the hypothesis of infinite memory. A vibrant hydrological literature ensued where alternative modelling representations were explored and debated, e.g. ARMA models, the Broken Line model, shifting mean models with no memory, FARIMA models, and Hurst-Kolmogorov dynamics, acknowledging a link with the work of Kolmogorov in 1940. The diffusion of Hurst’s work beyond hydrology is summarized by discipline and citations, showing that he arguably has the largest scientific footprint of any hydrologist in the last century. Its particular relevance to the modelling of long-term climatic variability in the era of climate change is discussed. Links to various long-term modes of variability in the climate system, driven by fluctuations in sea surface temperatures and ocean dynamics, are explored. Several issues related to the Hurst Phenomenon in hydrology remain as a challenge for future research. Editor M. Acreman; Associate editor A. Carsteanu

Scientific and Practical Considerations Related to Revising Bulletin 17B: The Case for Improved Treatment of Historical Information and Low Outliers

Since 1982, Bulletin 17B (B17B) has provided guidelines for conducting flood frequency analyses in support of federal projects in the U.S. The stability and consistency of B17B is widely recognized as a virtue, but research during the past 25 years suggests that substantially more accu rate frequency estimates could be obtained if some of B17Bs procedures were revised. Among other things, scientists and engineers have developed better methods for incorporating historical flood information into frequency analyses, and for addressing the problem of low outliers and zero flows, that take advantage of computational capabilities that were not available when B17B was published in 1982. Similarly, an additional 30 years of data are available to improve regional skew estimation. In this paper we consider both the technical aspects of proposed changes to B17B and some of the practical issues and implications related to altering procedures that have been in use for more than two decades.