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Timothy A. Cohn

Publications and source records attributed to Timothy A. Cohn.

At least 19 recordsLinked to original sources
USGS2019

Methods for estimating regional coefficient of skewness for unregulated streams in New England, based on data through water year 2011

The magnitude of annual exceedance probability floods is greatly affected by the coefficient of skewness (skew) of the annual peak flows at a streamgage. Standard flood frequency methods recommend weighting the station skew with a regional skew to better represent regional and stable conditions. This study presents an updated analysis of a regional skew for New England developed using a robust Bayesian weighted and generalized least squares regression model. Nineteen explanatory variables for 153 streamgages were tested in the regression analysis, but none were statistically significant and, as a result, a constant model was selected to define the regional skew for New England. The constant model for the New England region has, in log units, a skew of 0.37, a model error variance of 0.13, and an average variance of prediction at a new site of 0.14. An assessment of the selected regional skew model was conducted using a Monte Carlo analysis. The Monte Carlo simulations reveal that the perceived pattern in the station skews among the 153 streamgages is an artifact of the sample variability and the covariance structure of the errors.

Connecticut, Maine, Massachusetts, New Hampshire, ↗
USGS2019

Evaluation of recommended revisions to Bulletin 17B

For the past 36 years, Bulletin 17B, published by the Interagency Committee on Water Data in 1982, has guided flood-frequency analyses in the United States. During this period, much has been learned about both hydrology and statistical methods. In keeping with the tradition of periodically updating the Bulletin 17B guidelines in light of advances in our understanding and methods, the Hydrologic Frequency Analysis Work Group (HFAWG) was charged by the Subcommittee on Hydrology (SOH) of the Advisory Committee on Water Information (ACWI) to consider possible updates to Bulletin 17B. The purpose of this report is to consider the statistical performance of possible revisions to Bulletin 17B procedures. Of particular interest are procedures designed to accommodate more general forms of flood information. The concern is how the proposed procedures would affect the precision, accuracy and robustness of flood-frequency estimates. The investigations reported here focus on techniques for the following: incorporating information related to historical flooding that occurred outside the period of systematic streamgaging; and identification of potentially influential low floods (PILFs). The proposed changes, which mostly involve generalizing Bulletin 17B’s method-of-moments procedures by using the Expected Moments Algorithm (EMA), are relatively modest, at least in the sense that they would not affect the main features of Bulletin 17B. The proposed methods include the following: continued use of the log-Pearson Type 3 (LP3) distribution; continued use of the Method-of-Moments fitting method applied to the logarithms of annual-peak-flow data; and a generalization of the Grubbs-Beck test used in Bulletin 17B to identify low outliers. The new multiple Grubbs-Beck test is sensitive to multiple PILFs. The hydrological literature already provides extensive support for the theory behind the proposed changes. The remaining question is practical: How well do the proposed methods perform under typical and realistic conditions and, specifically, with difficult records occasionally encountered in practice? In order to answer these questions, the HFAWG commissioned the work reported here. The following four major sets of results are provided: Monte Carlo simulations of fitting procedures employing data drawn from simulated LP3 populations; Monte Carlo simulations of fitting procedures employing data drawn from non-LP3 populations that were selected to reflect likely deviations of flood series from LP3 distributions, based on the experience of HFAWG members; a direct comparison of the fitted LP3 distributions for 82 real “test sites” identified by an independent data group as both “typical” and “challenging” for flood-frequency estimation; and simulations of fitting procedures using records obtained by resampling with replacement from the longest of the 82 test-site records. Collectively, these studies provide a reasonably comprehensive, valid, and robust assessment of the properties of the Bulletin 17B methods and proposed alternatives. The experiments and analysis indicate that the flood quantile estimators, proposed as a revision of Bulletin 17B, do the following: perform generally as well as, and in some cases much better than, Bulletin 17B estimators in terms of the mean square error of flood quantiles estimates; allow for incorporation and efficient statistical treatment of broader classes of flood-frequency data and information, including historical information, binomial data and interval data; and generally confirm studies and the theoretical findings reported in the hydrological literature that would support use of updated estimation procedures that have been developed since Bulletin 17B was published.

Open-File Report↗
USGS2018

Guidelines for determining flood flow frequency — Bulletin 17C

Accurate estimates of flood frequency and magnitude are a key component of any effective nationwide flood risk management and flood damage abatement program. In addition to accuracy, methods for estimating flood risk must be uniformly and consistently applied because management of the Nation’s water and related land resources is a collaborative effort involving multiple actors including most levels of government and the private sector. Flood frequency guidelines have been published in the United States since 1967, and have undergone periodic revisions. In 1967, the U.S. Water Resources Council presented a coherent approach to flood frequency with Bulletin 15, “A Uniform Technique for Determining Flood Flow Frequencies.” The method it recommended involved fitting the log-Pearson Type III distribution to annual peak flow data by the method of moments. The first extension and update of Bulletin 15 was published in 1976 as Bulletin 17, “Guidelines for Determining Flood Flow Frequency” (Guidelines). It extended the Bulletin 15 procedures by introducing methods for dealing with outliers, historical flood information, and regional skew. Bulletin 17A was published the following year to clarify the computation of weighted skew. The next revision of the Bulletin, the Bulletin 17B, provided a host of improvements and new techniques designed to address situations that often arise in practice, including better methods for estimating and using regional skew, weighting station and regional skew, detection of outliers, and use of the conditional probability adjustment. The current version of these Guidelines are presented in this document, denoted Bulletin 17C. It incorporates changes motivated by four of the items listed as “Future Work” in Bulletin 17B and 30 years of post-17B research on flood processes and statistical methods. The updates include: adoption of a generalized representation of flood data that allows for interval and censored data types; a new method, called the Expected Moments Algorithm, which extends the method of moments so that it can accommodate interval data; a generalized approach to identification of low outliers in flood data; and an improved method for computing confidence intervals. Federal agencies are requested to use these Guidelines in all planning activities involving water and related land resources. State, local, and private organizations are encouraged to use these Guidelines to assure uniformity in the flood frequency estimates that all agencies concerned with flood risk should use for Federal planning decisions. This revision is adopted with the knowledge and understanding that review of these procedures will be ongoing. Updated methods will be adopted when warranted by experience and by examination and testing of new techniques.

Georgia↗
USGS2017

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10 –3 in scientific notation or for brevity 10 –3 ). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10 –3 to 10 –6 . Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

Scientific Investigations Report↗
USGS2016

Rating curve uncertainty: A comparison of estimation methods

The USGS is engaged in both internal development and collaborative efforts to evaluate existing methods for characterizing the uncertainty of streamflow measurements (gaugings), stage-discharge relations (ratings), and, ultimately, the streamflow records derived from them. This paper provides a brief overview of two candidate methods that may be used to characterize the uncertainty of ratings, and illustrates the results of their application to the ratings of the two USGS streamgages.

Conference Paper↗
USGS2014

Estimating magnitude and frequency of floods using the PeakFQ 7.0 program

Flood-frequency analysis provides information about the magnitude and frequency of flood discharges based on records of annual maximum instantaneous peak discharges collected at streamgages. The information is essential for defining flood-hazard areas, for managing floodplains, and for designing bridges, culverts, dams, levees, and other flood-control structures. Bulletin 17B (B17B) of the Interagency Advisory Committee on Water Data (IACWD; 1982) codifies the standard methodology for conducting flood-frequency studies in the United States. B17B specifies that annual peak-flow data are to be fit to a log-Pearson Type III distribution. Specific methods are also prescribed for improving skew estimates using regional skew information, tests for high and low outliers, adjustments for low outliers and zero flows, and procedures for incorporating historical flood information. The authors of B17B identified various needs for methodological improvement and recommended additional study. In response to these needs, the Advisory Committee on Water Information (ACWI, successor to IACWD; http://acwi.gov/ , Subcommittee on Hydrology (SOH), Hydrologic Frequency Analysis Work Group (HFAWG), has recommended modest changes to B17B. These changes include adoption of a generalized method-of-moments estimator denoted the Expected Moments Algorithm (EMA) (Cohn and others, 1997) and a generalized version of the Grubbs-Beck test for low outliers (Cohn and others, 2013). The SOH requested that the USGS implement these changes in a user-friendly, publicly accessible program.

Fact Sheet↗
USGS2014

Evaluation of the expected moments algorithm and a multiple low-outlier test for flood frequency analysis at streamgaging stations in Arizona

Flooding is among the costliest natural disasters in terms of loss of life and property in Arizona, which is why the accurate estimation of flood frequency and magnitude is crucial for proper structural design and accurate floodplain mapping. Current guidelines for flood frequency analysis in the United States are described in Bulletin 17B (B17B), yet since B17B’s publication in 1982 (Interagency Advisory Committee on Water Data, 1982), several improvements have been proposed as updates for future guidelines. Two proposed updates are the Expected Moments Algorithm (EMA) to accommodate historical and censored data, and a generalized multiple Grubbs-Beck (MGB) low-outlier test. The current guidelines use a standard Grubbs-Beck (GB) method to identify low outliers, changing the determination of the moment estimators because B17B uses a conditional probability adjustment to handle low outliers while EMA censors the low outliers. B17B and EMA estimates are identical if no historical information or censored or low outliers are present in the peak-flow data. EMA with MGB (EMA-MGB) test was compared to the standard B17B (B17B-GB) method for flood frequency analysis at 328 streamgaging stations in Arizona. The methods were compared using the relative percent difference (RPD) between annual exceedance probabilities (AEPs), goodness-of-fit assessments, random resampling procedures, and Monte Carlo simulations. The AEPs were calculated and compared using both station skew and weighted skew. Streamgaging stations were classified by U.S. Geological Survey (USGS) National Water Information System (NWIS) qualification codes, used to denote historical and censored peak-flow data, to better understand the effect that nonstandard flood information has on the flood frequency analysis for each method. Streamgaging stations were also grouped according to geographic flood regions and analyzed separately to better understand regional differences caused by physiography and climate. The B17B-GB and EMA-MGB RPD-boxplot results showed that the median RPDs across all streamgaging stations for the 10-, 1-, and 0.2-percent AEPs, computed using station skew, were approximately zero. As the AEP flow estimates decreased (that is, from 10 to 0.2 percent AEP) the variability in the RPDs increased, indicating that the AEP flow estimate was greater for EMA-MGB when compared to B17B-GB. There was only one RPD greater than 100 percent for the 10- and 1-percent AEP estimates, whereas 19 RPDs exceeded 100 percent for the 0.2-percent AEP. At streamgaging stations with low-outlier data, historical peak-flow data, or both, RPDs ranged from −84 to 262 percent for the 0.2-percent AEP flow estimate. When streamgaging stations were separated by the presence of historical peak-flow data (that is, no low outliers or censored peaks) or by low outlier peak-flow data (no historical data), the results showed that RPD variability was greatest for the 0.2-AEP flow estimates, indicating that the treatment of historical and (or) low-outlier data was different between methods and that method differences were most influential when estimating the less probable AEP flows (1, 0.5, and 0.2 percent). When regional skew information was weighted with the station skew, B17B-GB estimates were generally higher than the EMA-MGB estimates for any given AEP. This was related to the different regional skews and mean square error used in the weighting procedure for each flood frequency analysis. The B17B-GB weighted skew analysis used a more positive regional skew determined in USGS Water Supply Paper 2433 (Thomas and others, 1997), while the EMA-MGB analysis used a more negative regional skew with a lower mean square error determined from a Bayesian generalized least squares analysis. Regional groupings of streamgaging stations reflected differences in physiographic and climatic characteristics. Potentially influential low flows (PILFs) were more prevalent in arid regions of the State, and generally AEP flows were larger with EMA-MGB than with B17B-GB for gaging stations with PILFs. In most cases EMA-MGB curves would fit the largest floods more accurately than B17B-GB. In areas of the State with more baseflow, such as along the Mogollon Rim and the White Mountains, streamgaging stations generally had fewer PILFs and more positive skews, causing estimated AEP flows to be larger with B17B-GB than with EMA-MGB. The effect of including regional skew was similar for all regions, and the observed pattern was increasingly greater B17B-GB flows (more negative RPDs) with each decreasing AEP quantile. A variation on a goodness-of-fit test statistic was used to describe each method’s ability to fit the largest floods. The mean absolute percent difference between the measured peak flows and the log-Pearson Type 3 (LP3)-estimated flows, for each method, was averaged over the 90th, 75th, and 50th percentiles of peak-flow data at each site. In most percentile subsets, EMA-MGB on average had smaller differences (1 to 3 percent) between the observed and fitted value, suggesting that the EMA-MGB-LP3 distribution is fitting the observed peak-flow data more precisely than B17B-GB. The smallest EMA-MGB percent differences occurred for the greatest 10 percent (90th percentile) of the peak-flow data. When stations were analyzed by USGS NWIS peak flow qualification code groups, the stations with historical peak flows and no low outliers had average percent differences as high as 11 percent greater for B17B-GB, indicating that EMA-MGB utilized the historical information to fit the largest observed floods more accurately. A resampling procedure was used in which 1,000 random subsamples were drawn, each comprising one-half of the observed data. An LP3 distribution was fit to each subsample using B17B-GB and EMA-MGB methods, and the predicted 1-percent AEP flows were compared to those generated from distributions fit to the entire dataset. With station skew, the two methods were similar in the median percent difference, but with weighted skew EMA-MGB estimates were generally better. At two gages where B17B-GB appeared to perform better, a large number of peak flows were deemed to be PILFs by the MGB test, although they did not appear to depart significantly from the trend of the data (step or dogleg appearance). At two gages where EMA-MGB performed better, the MGB identified several PILFs that were affecting the fitted distribution of the B17B-GB method. Monte Carlo simulations were run for the LP3 distribution using different skews and with different assumptions about the expected number of historical peaks. The primary benefit of running Monte Carlo simulations is that the underlying distribution statistics are known, meaning that the true 1-percent AEP is known. The results showed that EMA-MGB performed as well or better in situations where the LP3 distribution had a zero or positive skew and historical information. When the skew for the LP3 distribution was negative, EMA-MGB performed significantly better than B17B-GB and EMA-MGB estimates were less biased by more closely estimating the true 1-percent AEP for 1, 2, and 10 historical flood scenarios.

Arizona↗
USGS2014

Assessing inundation hazards to nuclear powerplant sites using geologically extended histories of riverine floods, tsunamis, and storm surges

Most nuclear powerplants in the United States are near rivers, large lakes, or oceans. As evident from the Fukushima Daiichi, Japan, disaster of 2011, these water bodies pose inundation threats. Geologic records can extend knowledge of rare hazards from flooding, storm surges, and tsunamis. This knowledge can aid in assessing the safety of critical structures such as dams and energy plants, for which even remotely possible hazards are pertinent. Quantitative analysis of inundation from geologic records perhaps is most developed for and applied to riverine flood hazards, but because of recent natural disasters, geologic investigations also are now used widely for understanding tsunami hazards and coastal storm surges. Layered sedimentary deposits commonly give the most complete geologic record of large floods, storm surges, and tsunamis. Sedimentary layers may be preserved for hundreds or thousands of years in suitable depositional environments, thereby providing an archive of rare, high-magnitude events. All inundation hazards discussed in this report—riverine floods, tsunamis, and storm surges—have had long records extracted from sedimentary sequences, many specifically for hazard assessment. Geologic records commonly are imprecise, so most hazard assessments benefit from evaluation of many sites and rigorous uncertainty assessment. Despite uncertainties, geologic records commonly can improve knowledge of the types and magnitudes of hazards threatening specific sites or regions. New statistical tools and approaches can efficiently incorporate geologic information into frequency assessments. These tools are most developed for riverine flood hazards, but are to some degree transferable to other episodic natural phenomena such as tsunamis and storm surges. Even with these efficient statistical approaches for examining geologic records, systematic landscape changes may reduce the applicability of retrospective assessments. These non-stationarity issues (such as climate change, sea‑level rise, land-use, dams and flow regulation) may all affect the validity of using past experience—no matter how complete the record—to assess future likelihoods. These issues require site-specific consideration for nearly all hazard assessments drawn from geologic evidence. A screening of the 104 nuclear powerplants in the United States licensed by the Nuclear Regulatory Commission (at 64 sites) indicates several sites for which paleoflood studies likely would provide additional flood-frequency information. Two sites—Duane Arnold, Iowa, on the Cedar River; and David-Besse, Ohio, on the Toussaint River—have geologic conditions suitable for creating and preserving stratigraphic records of flooding and few upstream dams that may complicate flood-frequency analysis. One site—Crystal River, Florida1, on the Withlacoochee River and only 4 kilometers from the coast—has high potential as a candidate for assessing riverine and marine inundation hazards. Several sites on the Mississippi River have high geologic potential, but upstream dams almost certainly now regulate peak flows. Nevertheless, studies on the Mississippi River to evaluate long-term flood frequency may provide results applicable to a wide spectrum of regional hazard issues. Several sites in the southeastern United States have high geologic potential, and studies at these sites also may be helpful in evaluating hazards from outburst floods from landslide dams (river blockages formed by mass movements), which may be a regional hazard. For all these sites, closer investigation and field reconnaissance would be needed to confirm suitable deposits and settings for a complete paleoflood analysis. Similar screenings may help identify high-potential sites for geologic investigations of tsunami and storm-surge hazards.

Scientific Investigations Report↗
USGS2012

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.

Reviews of Geophysics↗
USGS2012

Calculating weighted estimates of peak streamflow statistics

According to the Federal guidelines for flood-frequency estimation, the uncertainty of peak streamflow statistics, such as the 1-percent annual exceedance probability (AEP) flow at a streamgage, can be reduced by combining the at-site estimate with the regional regression estimate to obtain a weighted estimate of the flow statistic. The procedure assumes the estimates are independent, which is reasonable in most practical situations. The purpose of this publication is to describe and make available a method for calculating a weighted estimate from the uncertainty or variance of the two independent estimates.

Fact Sheet↗
USGS2011

Stationarity: Wanted dead or alive?

Aligning engineering practice with natural process behavior would appear, on its face, to be a prudent and reasonable course of action. However, if we do not understand the long-term characteristics of hydroclimatic processes, how does one find the prudent and reasonable course needed for water management? We consider this question in light of three aspects of existing and unresolved issues affecting hydroclimatic variability and statistical inference: Hurst-Kolmogorov phenomena; the complications long-term persistence introduces with respect to statistical understanding; and the dependence of process understanding on arbitrary sampling choices. These problems are not easily addressed. In such circumstances, humility may be more important than physics; a simple model with well-understood flaws may be preferable to a sophisticated model whose correspondence to reality is uncertain.

Journal of the American Water Resources Associatio↗
USGS2011

USGS library for S-PLUS for Windows -- Release 4.0

Release 4.0 of the U.S. Geological Survey S-PLUS library supercedes release 2.1. It comprises functions, dialogs, and datasets used in the U.S. Geological Survey for the analysis of water-resources data. This version does not contain ESTREND, which was in version 2.1. See Release 2.1 for information and access to that version. This library requires Release 8.1 or later of S-PLUS for Windows. S-PLUS is a commercial statistical and graphical analysis software package produced by TIBCO corporation(http://www.tibco.com/). The USGS library is not supported by TIBCO or its technical support staff.

Open-File Report↗
USGS2010

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.

Water Resources Research↗
USGS2007

Estimated Magnitudes and Recurrence Intervals of Peak Flows on the Mousam and Little Ossipee Rivers for the Flood of April 2007 in Southern Maine

Large amounts of rain fell on southern Maine from the afternoon of April 15, 2007, to the afternoon of April 16, 2007, causing substantial damage to houses, roads, and culverts. This report provides an estimate of the peak flows on two rivers in southern Maine--the Mousam River and the Little Ossipee River--because of their severe flooding. The April 2007 estimated peak flow of 9,230 ft3/s at the Mousam River near West Kennebunk had a recurrence interval between 100 and 500 years; 95-percent confidence limits for this flow ranged from 25 years to greater than 500 years. The April 2007 estimated peak flow of 8,220 ft3/s at the Little Ossipee River near South Limington had a recurrence interval between 100 and 500 years; 95-percent confidence limits for this flow ranged from 50 years to greater than 500 years.

Open-File Report↗
USGS2005

Estimating contaminant loads in rivers: An application of adjusted maximum likelihood to type 1 censored data

This paper presents an adjusted maximum likelihood estimator (AMLE) that can be used to estimate fluvial transport of contaminants, like phosphorus, that are subject to censoring because of analytical detection limits. The AMLE is a generalization of the widely accepted minimum variance unbiased estimator (MVUE), and Monte Carlo experiments confirm that it shares essentially all of the MVUE's desirable properties, including high efficiency and negligible bias. In particular, the AMLE exhibits substantially less bias than alternative censored‐data estimators such as the MLE (Tobit) or the MLE followed by a jackknife. As with the MLE and the MVUE the AMLE comes close to achieving the theoretical Frechet‐Cramér‐Rao bounds on its variance. This paper also presents a statistical framework, applicable to both censored and complete data, for understanding and estimating the components of uncertainty associated with load estimates. This can serve to lower the cost and improve the efficiency of both traditional and real‐time water quality monitoring.

Water Resources Research↗
USGS2004

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

LOAD ESTimator (LOADEST) is a FORTRAN program for estimating constituent loads in streams and rivers. Given a time series of streamflow, additional data variables, and constituent concentration, LOADEST assists the user in developing a regression model for the estimation of constituent load (calibration). Explanatory variables within the regression model include various functions of streamflow, decimal time, and additional user-specified data variables. The formulated regression model then is used to estimate loads over a user-specified time interval (estimation). Mean load estimates, standard errors, and 95 percent confidence intervals are developed on a monthly and(or) seasonal basis. The calibration and estimation procedures within LOADEST are based on three statistical estimation methods. The first two methods, Adjusted Maximum Likelihood Estimation (AMLE) and Maximum Likelihood Estimation (MLE), are appropriate when the calibration model errors (residuals) are normally distributed. Of the two, AMLE is the method of choice when the calibration data set (time series of streamflow, additional data variables, and concentration) contains censored data. The third method, Least Absolute Deviation (LAD), is an alternative to maximum likelihood estimation when the residuals are not normally distributed. LOADEST output includes diagnostic tests and warnings to assist the user in determining the appropriate estimation method and in interpreting the estimated loads. This report describes the development and application of LOADEST. Sections of the report describe estimation theory, input/output specifications, sample applications, and installation instructions.

Techniques and Methods↗