Geology topics

Andrea G. Veilleux

Publications and source records attributed to Andrea G. Veilleux.

At least 19 recordsLinked to original sources

USGS2023

Magnitude and frequency of floods for rural streams in Georgia, South Carolina, and North Carolina, 2017—Results

Reliable estimates of the magnitude and frequency of floods are an important part of the framework for hydraulic-structure design and flood-plain management in Georgia, South Carolina, and North Carolina. Annual peak flows measured at U.S. Geological Survey streamgages are used to compute flood‑frequency estimates at those streamgages. However, flood‑frequency estimates also are needed at ungaged stream locations. A process known as regionalization was used to develop regression equations to estimate the magnitude and frequency of floods at ungaged locations. A multistate approach was used to update estimates of the magnitude and frequency of floods in rural, ungaged basins in Georgia, South Carolina, and North Carolina. Annual peak-flow data through September 2017 were analyzed for 965 streamgages with 10 or more years of data on rural streams in Georgia, South Carolina, North Carolina, and adjacent parts of Alabama, Florida, Tennessee, and Virginia. Flood‑frequency estimates of the 50‑, 20‑, 10‑, 4‑, 2‑, 1‑, 0.5‑, and 0.2‑percent annual exceedance probability streamflows, which correspond to flood-recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively, were computed for the 965 streamgages following national guidelines. As part of the computation of flood‑frequency estimates for the streamgages, an updated value for the regional skew coefficient (0.048) was developed using a Bayesian generalized least squares regression model. The new regional skew has a mean square error or average variance of prediction of 0.092. Additionally, basin characteristics for these stations were computed using a geographical information system. Exploratory analyses on the 965 streamgages confirmed the five hydrologic regions for Georgia, South Carolina, and North Carolina defined in a previous rural flood‑frequency study. From the 965 streamgages, streamgages with 30 or more years of record were used to complete a peak-flow trend analysis. Of the 965 streamgages, 164 streamgages were found to be redundant and were excluded from the regional regression analyses. Data from the remaining 801 streamgages (292 in Georgia, 75 in South Carolina, 303 in North Carolina, 15 in Alabama, 12 in Florida, 39 in Tennessee, and 65 in Virginia) were used in a regional regression analysis relating basin characteristics to flood‑frequency estimates. This analysis, based on generalized least squares regression, was used to develop a set of predictive equations to estimate the 50‑, 20‑, 10‑, 4‑, 2‑, 1‑, 0.5‑, and 0.2‑percent annual exceedance probability streamflows for rural, ungaged basins in Georgia, South Carolina, and North Carolina. The final set of predictive equations are all functions of drainage area and percentage of the drainage basin within each of the five hydrologic regions. Average errors of prediction for these regression equations range from 35.8 to 44.4 percent. Flood‑frequency estimates also were computed for 72 regulated (for example, a streamgage where flow is altered by a dam or weir) streamgages in Georgia, South Carolina, and North Carolina with 20 or more years of post-regulation record using data through water year 2019. The water year is the annual period from October 1 through September 30 and is designated by the year in which the period ends. Of the 72 regulated streamgages, 18 had pre-regulated periods of record that also were analyzed as part of this study. Flow adjustments were applied to historic peaks and large floods from the pre-regulated period, if available, for use in the post-regulation frequency analysis. Estimates of large floods provide valuable information in frequency analysis and, thus, were included in the post-regulation frequency analysis.

Georgia, North Carolina, South Carolina↗

USGS2023

Magnitude and frequency of floods on Kauaʻi, Oʻahu, Molokaʻi, Maui, and Hawaiʻi, State of Hawaiʻi, based on data through water year 2020

Accurate estimates of flood magnitude and frequency are needed to (1) optimize the design and location of infrastructure, including dams, culverts, bridges, industrial buildings, and highways, and (2) inform flood-zoning and flood-insurance studies. The U.S. Geological Survey (USGS), in cooperation with the State of Hawaiʻi Department of Transportation, estimated flood magnitudes for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (AEP) for unregulated streamgages in Kauaʻi, Oʻahu, Molokaʻi, Maui, and Hawaiʻi, State of Hawaiʻi, using data through water year 2020. Regression equations were developed to estimate flood magnitude and associated frequency at ungaged streams. This study improves upon a previous USGS flood-frequency report (Oki and others, 2010) by including more peak-flow data, implementing new statistical methods in flood-frequency analysis, and using updated techniques to estimate the regional-skewness coefficient (regional skew). Flood magnitude and frequency at 238 streamgages were estimated—following national guidelines established in Bulletin 17C (England and others, 2019)—by fitting annual peak-flow data to the Log-Pearson Type III distribution using the expected moments algorithm and the PeakFQ flood-frequency software. Potentially influential low outliers in the data were identified and removed using the Multiple Grubbs-Beck Test. An updated regional skew for Hawaiʻi was estimated using the Bayesian weighted least squares/Bayesian generalized least squares method. The updated regional skew employs a constant model for the five islands in the study area and has a value of −0.157 (mean square error of 0.212). Multiple linear regression techniques were used to develop regression equations that relate basin and climatic characteristics to peak flows at streamgages. The regression equations can be applied to estimate flood magnitude and frequency at ungaged sites. The study area was split into 10 regions—2 regions per island, generally following a leeward/windward division—containing from 9 to 49 streamgages each. The final regression equations for each region were determined with generalized least-squares analysis using the USGS weighted-multiple-linear regression (WREG) program. The standard error of prediction at the 1-percent AEP for the regression equations ranged from 18 to 164 percent; the pseudo coefficient of determination (pseudo-R2) at the 1-percent AEP ranged from 46 to 100 percent. The regression equations performed well for all regions except leeward Molokaʻi and southern Island of Hawaiʻi; for all other regions, the pseudo-R2 values ranged from about 75 to 100 percent. Compared to the regression equations developed by Oki and others (2010), the regression equations in this study generally showed modest improvements, although the magnitude of differences varied for each region. Peak-flow estimates at the 238 streamgages included in this study are improved by weighting the at-site statistics computed with PeakFQ and the predicted flows based on the regression equations. Results of this study—including the final peak-flow estimates at streamgages and the regional regression equations—are implemented in the USGS StreamStats web application (U.S. Geological Survey, 2023, StreamStats: https://streamstats.usgs.gov/ss/ ). StreamStats provides a consistent approach for obtaining peak-flow estimates at streamgages and for applying the regional regression equations for estimating peak flows at ungaged locations.

Hawaii↗

USGS2021

Methods for estimating regional skewness of annual peak flows in parts of eastern New York and Pennsylvania, based on data through water year 2013

Bulletin 17C (B17C) recommends fitting the log-Pearson Type III (LP−III) distribution to a series of annual peak flows at a streamgage by using the method of moments. The third moment, the skewness coefficient (or skew), is important because the magnitudes of annual exceedance probability (AEP) flows estimated by using the LP–III distribution are affected by the skew; interest is focused on the right-hand tail of the distribution, which represents the larger annual peak flows that correspond to small AEPs. For streamgages having modest record lengths, the skew is sensitive to extreme events like large floods, which cause a sample to be highly asymmetrical or “skewed.” For this reason, B17C recommends using a weighted-average skew computed from the skew of the annual peak flows for a given streamgage and a regional skew. This report presents an estimate of regional skew for a study area encompassing parts of eastern New York and Pennsylvania. A total of 232 candidate U.S. Geological Survey streamgages that were unaffected by extensive regulation, diversion, urbanization, or channelization were considered for use in the skew analysis; after screening for redundancy and pseudo record length ( P RL ) of at least 36 years, 183 streamgages were selected for use in the study. Flood frequencies for candidate streamgages were analyzed by employing the expected moments algorithm, which extends the method of moments so that it can accommodate interval, censored, and historical/paleo flow data, as well as the multiple Grubbs-Beck test to identify potentially influential low floods in the data series. Bayesian weighted least squares/Bayesian generalized least squares regression was used to develop a regional skew model for the study area that would incorporate possible variables (basin characteristics) to explain the variation in skew in the study area. Ten basin characteristics were considered as possible explanatory variables; however, none produced a pseudo coefficient of determination greater than 1 percent; as a result, these characteristics did not help to explain the variation in skew in the study area. Therefore, a constant model that had a regional skew coefficient of 0.32 and an average variance of prediction at a new streamgage ( AVP new , which corresponds to the mean square error [MSE] of 0.11) was selected. The AVP new corresponds to an effective record length of 68 years, a marked improvement over the Bulletin 17B national skew map, whose reported MSE of 0.302 indicated a corresponding effective record length of only 17 years.

New York, Pennsylvania↗

USGS2021

Development of regression equations for the estimation of the magnitude and frequency of floods at rural, unregulated gaged and ungaged streams in Puerto Rico through water year 2017

The methods of computation and estimates of the magnitude of flood flows were updated for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent chance exceedance levels for 91 streamgages on the main island of Puerto Rico by using annual peak-flow data through 2017. Since the previous flood frequency study in 1994, the U.S. Geological Survey has collected additional peak flows at additional streamgages, and Puerto Rico has experienced numerous flood events. This updated study was performed using longer annual peak-flow datasets from more stations to provide more representative equations to predict flood flows. Screening criteria for these streamgages included 10 or more years of annual peak-flow data, unregulated flow, and less than 10 percent impervious drainage area. The magnitude and frequency of floods at selected streamgages in Puerto Rico were estimated using updated methods outlined in Bulletin 17C. The new procedures include a regional skew analysis that incorporates Bayesian regression techniques, the Expected Moments Algorithm to better represent missing record and estimate parameters of the log-Pearson Type III distribution, and the Multiple Grubbs-Beck test for low outlier detection. Regional regression equations were developed to estimate peak-flow statistics at ungaged locations by using selected basin and climatic characteristics as explanatory variables. These variables were determined from digital spatial datasets and geographic information systems by using the most recent data available. Ordinary least-squares regression techniques were used to filter the basin characteristics and determine two separate regions, region 1 (west) and region 2 (east), based on residuals. A generalized least-squares procedure was used to account for cross-correlation of sites and develop the final set of equations that have drainage area as the only explanatory variable. The average standard errors of prediction ranged from 18.7 to 46.7 percent in region 1 and 33.4 to 57.6 percent in region 2 for all annual exceedance probabilities (AEPs) examined. The updated statistics showed a greater accuracy of prediction when compared to those from the previous study using drainage area as the only explanatory variable for all AEPs examined in region 1 and the 0.01 and 0.002 AEP flows for region 2. When compared to equations developed in the previous study that have drainage area, mean annual rainfall, and (or) depth-to-rock as explanatory variables, the updated statistics show a greater accuracy of prediction in region 1 at AEP flows of 0.02 and lower (that is, higher flows). Those developed for region 2 do not show a greater accuracy of prediction for any AEP flows when compared to the equations having multiple explanatory variables in the previous study. The calculated regression equations, basin characteristics, and at-site statistics will be incorporated into the U.S. Geological Survey web application, StreamStats ( https://streamstats.usgs.gov/ss/ ). This application allows users to select a location on a stream, whether gaged or ungaged, to obtain estimates of basin characteristics and flow statistics.

Puerto Rico↗

USGS2020

Methods for estimating regional skewness of annual peak flows in parts of the Great Lakes and Ohio River Basins, based on data through water year 2013

Bulletin 17C (B17C) recommends fitting the log-Pearson Type III (LP−III) distribution to a series of annual peak flows at a streamgage by using the method of moments. The third moment, the skewness coefficient (or skew), is important because the magnitudes of annual exceedance probability (AEP) flows estimated by using the LP−III distribution are affected by the skew; interest is focused on the right-hand tail of the distribution, which represents the larger annual peak flows that correspond to small AEPs. For streamgages having modest record lengths, the skew is sensitive to extreme events like large floods, which cause a sample to be highly asymmetrical or “skewed.” For this reason, B17C recommends using a weighted-average skew computed from the station skew for a given streamgage and a regional skew. This report generates an estimate of regional skew for a study area encompassing most of the Great Lakes Basin (hydrologic unit 04) and part of the Ohio River Basin (hydrologic unit 05). A total of 551 candidate streamgages that were unaffected by extensive regulation, diversion, urbanization, or channelization were considered for use in the skew analysis; after screening for redundancy and pseudo record length greater than 36 years, 368 streamgages were selected for use in the study. Flood frequencies for candidate streamgages were analyzed by employing the Expected Moments Algorithm, which extends the method of moments so that it can accommodate interval, censored, and historic/paleo flow data, as well as the Multiple Grubbs-Beck test to identify potentially influential low floods in the data series. Bayesian weighted least squares/Bayesian generalized least squares regression was used to develop a regional skew model for the study area that would incorporate possible variables (basin characteristics) to explain the variation in skew in the study area. Twelve basin characteristics were considered as possible explanatory variables; however, none produced a pseudo coefficient of determination greater than 5 percent; as a result, these characteristics did not help to explain the variation in skew in the study area. Therefore, a constant model having a regional skew coefficient of 0.086 and an average variance of prediction ( AVP new ) (which corresponds to the mean square error [MSE]) of 0.13 at a new streamgage was selected. The AVP new corresponds to an effective record length of 54 years, a marked improvement over the Bulletin 17B national skew map, whose reported MSE of 0.302 indicated a corresponding effective record length of only 17 years.

Great Lakes and Ohio River Basins↗

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, ↗

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↗

USGS2016

Magnitude, frequency, and trends of floods at gaged and ungaged sites in Washington, based on data through water year 2014

An investigation into the magnitude and frequency of floods in Washington State computed the annual exceedance probability (AEP) statistics for 648 U.S. Geological Survey unregulated streamgages in and near the borders of Washington using the recorded annual peak flows through water year 2014. This is an updated report from a previous report published in 1998 that used annual peak flows through the water year 1996. New in this report, a regional skew coefficient was developed for the Pacific Northwest region that includes areas in Oregon, Washington, Idaho and western Montana within the Columbia River drainage basin south of the United States-Canada border, the coastal areas of Oregon and western Washington, and watersheds draining into Puget Sound, Washington. The skew coefficient is an important term in the Log Pearson Type III equation used to define the distribution of the log-transformed annual peaks. The Expected Moments Algorithm was used to fit historical and censored peak-flow data to the log Pearson Type III distribution. A Multiple Grubb-Beck test was employed to censor low outliers of annual peak flows to improve on the frequency distribution. This investigation also includes a section on observed trends in annual peak flows that showed significant trends ( p -value < 0.05) in 21 of 83 long-term sites, but with small magnitude Kendall tau values suggesting a limited monotonic trend in the time series of annual peaks. Most of the sites with a significant trend in western Washington were positive and all the sites with significant trends (three sites) in eastern Washington were negative. Multivariate regression analysis with measured basin characteristics and the AEP statistics at long-term, unregulated, and un-urbanized (defined as drainage basins with less than 5 percent impervious land cover for this investigation) streamgages within Washington and some in Idaho and Oregon that are near the Washington border was used to develop equations to estimate AEP statistics at ungaged basins. Washington was divided into four regions to improve the accuracy of the regression equations; a set of equations for eight selected AEPs and for each region were constructed. Selected AEP statistics included the annual peak flows that equaled or exceeded 50, 20, 10, 4, 2, 1, 0.5 and 0.2 percent of the time equivalent to peak flows for peaks with a 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively. Annual precipitation and drainage area were the significant basin characteristics in the regression equations for all four regression regions in Washington and forest cover was significant for the two regression regions in eastern Washington. Average standard error of prediction for the regional regression equations ranged from 70.19 to 125.72 percent for Regression Regions 1 and 2 on the eastern side of the Cascade Mountains and from 43.22 to 58.04 percent for Regression Regions 3 and 4 on the western side of the Cascade Mountains. The pseudo coefficient of determination (where a value of 100 signifies a perfect regression model) ranged from 68.39 to 90.68 for Regression Regions 1 and 2, and 92.35 to 95.44 for Regions 3 and 4. The calculated AEP statistics for the streamgages and the regional regression equations are expected to be incorporated into StreamStats after the publication of this report. StreamStats is the interactive Web-based map tool created by the U.S. Geological Survey to allow the user to choose a streamgage and obtain published statistics or choose ungaged locations where the program automatically applies the regional regression equations and computes the estimates of the AEP statistics.

Washington↗

USGS2016

Methods for estimating annual exceedance probability discharges for streams in Arkansas, based on data through water year 2013

In 2013, the U.S. Geological Survey initiated a study to update regional skew, annual exceedance probability discharges, and regional regression equations used to estimate annual exceedance probability discharges for ungaged locations on streams in the study area with the use of recent geospatial data, new analytical methods, and available annual peak-discharge data through the 2013 water year. An analysis of regional skew using Bayesian weighted least-squares/Bayesian generalized-least squares regression was performed for Arkansas, Louisiana, and parts of Missouri and Oklahoma. The newly developed constant regional skew of -0.17 was used in the computation of annual exceedance probability discharges for 281 streamgages used in the regional regression analysis. Based on analysis of covariance, four flood regions were identified for use in the generation of regional regression models. Thirty-nine basin characteristics were considered as potential explanatory variables, and ordinary least-squares regression techniques were used to determine the optimum combinations of basin characteristics for each of the four regions. Basin characteristics in candidate models were evaluated based on multicollinearity with other basin characteristics (variance inflation factor < 2.5) and statistical significance at the 95-percent confidence level ( p ≤ 0.05). Generalized least-squares regression was used to develop the final regression models for each flood region. Average standard errors of prediction of the generalized least-squares models ranged from 32.76 to 59.53 percent, with the largest range in flood region D. Pseudo coefficients of determination of the generalized least-squares models ranged from 90.29 to 97.28 percent, with the largest range also in flood region D. The regional regression equations apply only to locations on streams in Arkansas where annual peak discharges are not substantially affected by regulation, diversion, channelization, backwater, or urbanization. The applicability and accuracy of the regional regression equations depend on the basin characteristics measured for an ungaged location on a stream being within range of those used to develop the equations.

Arkansas↗

USGS2016

Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois

This report provides two sets of equations for estimating peak discharge quantiles at annual exceedance probabilities (AEPs) of 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002 (recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively) for watersheds in Illinois based on annual maximum peak discharge data from 117 watersheds in and near northeastern Illinois. One set of equations was developed through a temporal analysis with a two-step least squares-quantile regression technique that measures the average effect of changes in the urbanization of the watersheds used in the study. The resulting equations can be used to adjust rural peak discharge quantiles for the effect of urbanization, and in this study the equations also were used to adjust the annual maximum peak discharges from the study watersheds to 2010 urbanization conditions. The other set of equations was developed by a spatial analysis. This analysis used generalized least-squares regression to fit the peak discharge quantiles computed from the urbanization-adjusted annual maximum peak discharges from the study watersheds to drainage-basin characteristics. The peak discharge quantiles were computed by using the Expected Moments Algorithm following the removal of potentially influential low floods defined by a multiple Grubbs-Beck test. To improve the quantile estimates, regional skew coefficients were obtained from a newly developed regional skew model in which the skew increases with the urbanized land use fraction. The skew coefficient values for each streamgage were then computed as the variance-weighted average of at-site and regional skew coefficients. The drainage-basin characteristics used as explanatory variables in the spatial analysis include drainage area, the fraction of developed land, the fraction of land with poorly drained soils or likely water, and the basin slope estimated as the ratio of the basin relief to basin perimeter. This report also provides the following: (1) examples to illustrate the use of the spatial and urbanization-adjustment equations for estimating peak discharge quantiles at ungaged sites and to improve flood-quantile estimates at and near a gaged site; (2) the urbanization-adjusted annual maximum peak discharges and peak discharge quantile estimates at streamgages from 181 watersheds including the 117 study watersheds and 64 additional watersheds in the study region that were originally considered for use in the study but later deemed to be redundant. The urbanization-adjustment equations, spatial regression equations, and peak discharge quantile estimates developed in this study will be made available in the web application StreamStats, which provides automated regression-equation solutions for user-selected stream locations. Figures and tables comparing the observed and urbanization-adjusted annual maximum peak discharge records by streamgage are provided at https://doi.org/10.3133/sir20165050 for download.

Illinois↗

USGS2016

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations. Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R 2 >92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R 2 >95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R 2 <78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows. A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5. The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions. The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Idaho↗

USGS2016

Estimating flood magnitude and frequency at gaged and ungaged sites on streams in Alaska and conterminous basins in Canada, based on data through water year 2012

Estimates of the magnitude and frequency of floods are needed across Alaska for engineering design of transportation and water-conveyance structures, flood-insurance studies, flood-plain management, and other water-resource purposes. This report updates methods for estimating flood magnitude and frequency in Alaska and conterminous basins in Canada. Annual peak-flow data through water year 2012 were compiled from 387 streamgages on unregulated streams with at least 10 years of record. Flood-frequency estimates were computed for each streamgage using the Expected Moments Algorithm to fit a Pearson Type III distribution to the logarithms of annual peak flows. A multiple Grubbs-Beck test was used to identify potentially influential low floods in the time series of peak flows for censoring in the flood frequency analysis. For two new regional skew areas, flood-frequency estimates using station skew were computed for stations with at least 25 years of record for use in a Bayesian least-squares regression analysis to determine a regional skew value. The consideration of basin characteristics as explanatory variables for regional skew resulted in improvements in precision too small to warrant the additional model complexity, and a constant model was adopted. Regional Skew Area 1 in eastern-central Alaska had a regional skew of 0.54 and an average variance of prediction of 0.45, corresponding to an effective record length of 22 years. Regional Skew Area 2, encompassing coastal areas bordering the Gulf of Alaska, had a regional skew of 0.18 and an average variance of prediction of 0.12, corresponding to an effective record length of 59 years. Station flood-frequency estimates for study sites in regional skew areas were then recomputed using a weighted skew incorporating the station skew and regional skew. In a new regional skew exclusion area outside the regional skew areas, the density of long-record streamgages was too sparse for regional analysis and station skew was used for all estimates. Final station flood frequency estimates for all study streamgages are presented for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities. Regional multiple-regression analysis was used to produce equations for estimating flood frequency statistics from explanatory basin characteristics. Basin characteristics, including physical and climatic variables, were updated for all study streamgages using a geographical information system and geospatial source data. Screening for similar-sized nested basins eliminated hydrologically redundant sites, and screening for eligibility for analysis of explanatory variables eliminated regulated peaks, outburst peaks, and sites with indeterminate basin characteristics. An ordinary least‑squares regression used flood-frequency statistics and basin characteristics for 341 streamgages (284 in Alaska and 57 in Canada) to determine the most suitable combination of basin characteristics for a flood-frequency regression model and to explore regional grouping of streamgages for explaining variability in flood-frequency statistics across the study area. The most suitable model for explaining flood frequency used drainage area and mean annual precipitation as explanatory variables for the entire study area as a region. Final regression equations for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability discharge in Alaska and conterminous basins in Canada were developed using a generalized least-squares regression. The average standard error of prediction for the regression equations for the various annual exceedance probabilities ranged from 69 to 82 percent, and the pseudo-coefficient of determination (pseudo-R 2 ) ranged from 85 to 91 percent. The regional regression equations from this study were incorporated into the U.S. Geological Survey StreamStats program for a limited area of the State—the Cook Inlet Basin. StreamStats is a national web-based geographic information system application that facilitates retrieval of streamflow statistics and associated information. StreamStats retrieves published data for gaged sites and, for user-selected ungaged sites, delineates drainage areas from topographic and hydrographic data, computes basin characteristics, and computes flood frequency estimates using the regional regression equations.

Alaska↗

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

Methods for estimating magnitude and frequency of 1-, 3-, 7-, 15-, and 30-day flood-duration flows in Arizona

Large floods have historically caused extensive damage in Arizona. Although peak-flow frequency estimates are required for managing the risk posed by floods, estimates of the frequency of sustained flood flow (flood-duration flow) are also useful for planning and assessing the adequacy of retention and conveyance structures and for water-resource planning. This report presents a flood-duration flow frequency analysis for selected durations (1 day, 3 day, 7 day, 15 day, and 30 day) at 173 streamgaging stations throughout Arizona and in western New Mexico. For each n -day duration, a log-Pearson type III distribution was fitted to the annual series of n -day flood-duration flows using the expected moments algorithm with a multiple Grubbs-Beck low-outlier test. Regional skews were developed independently for each n -day duration using a hybrid weighted least squares/generalized least squares method. No basin characteristics were found to adequately explain variation in skew among stations and a constant statewide skew model was used for all n -day durations. The regional skewness coefficient is negative for all n -day durations and becomes increasingly negative for longer n -day durations. Uncertainty associated with the skewness coefficient is estimated using a Bayesian generalized least squares technique. Regression equations, which allow predictions of n -day flood-duration flows for selected annual exceedance probabilities at ungaged sites, were developed using generalized least-squares regression and flood-duration flow frequency estimates at 56 streamgaging stations within a single, relatively uniform physiographic region in the central part of Arizona, between the Colorado Plateau and Basin and Range Province, called the Transition Zone. Drainage area explained most of the variation in the n -day flood-duration annual exceedance probabilities, but mean annual precipitation and mean elevation were also significant variables in the regression models. Standard error of prediction for the regression equations varies from 28 to 53 percent and generally decreases with increasing n -day duration. Outside the Transition Zone there are insufficient streamgaging stations to develop regression equations, but flood-duration flow frequency estimates are presented at select streamgaging stations.

Arizona↗

USGS2014

Methods for estimating annual exceedance-probability discharges and largest recorded floods for unregulated streams in rural Missouri

Regression analysis techniques were used to develop a set of equations for rural ungaged stream sites for estimating discharges with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. Basin and climatic characteristics were computed using geographic information software and digital geospatial data. A total of 35 characteristics were computed for use in preliminary statewide and regional regression analyses. Annual exceedance-probability discharge estimates were computed for 278 streamgages by using the expected moments algorithm to fit a log-Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data from water year 1844 to 2012. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized multiple Grubbs-Beck test was used to detect potentially influential low floods. Annual peak flows less than a minimum recordable discharge at a streamgage were incorporated into the at-site station analyses. An updated regional skew coefficient was determined for the State of Missouri using Bayesian weighted least-squares/generalized least squares regression analyses. At-site skew estimates for 108 long-term streamgages with 30 or more years of record and the 35 basin characteristics defined for this study were used to estimate the regional variability in skew. However, a constant generalized-skew value of -0.30 and a mean square error of 0.14 were determined in this study. Previous flood studies indicated that the distinct physical features of the three physiographic provinces have a pronounced effect on the magnitude of flood peaks. Trends in the magnitudes of the residuals from preliminary statewide regression analyses from previous studies confirmed that regional analyses in this study were similar and related to three primary physiographic provinces. The final regional regression analyses resulted in three sets of equations. For Regions 1 and 2, the basin characteristics of drainage area and basin shape factor were statistically significant. For Region 3, because of the small amount of data from streamgages, only drainage area was statistically significant. Average standard errors of prediction ranged from 28.7 to 38.4 percent for flood region 1, 24.1 to 43.5 percent for flood region 2, and 25.8 to 30.5 percent for region 3. The regional regression equations are only applicable to stream sites in Missouri with flows not significantly affected by regulation, channelization, backwater, diversion, or urbanization. Basins with about 5 percent or less impervious area were considered to be rural. Applicability of the equations are limited to the basin characteristic values that range from 0.11 to 8,212.38 square miles (mi 2 ) and basin shape from 2.25 to 26.59 for Region 1, 0.17 to 4,008.92 mi 2 and basin shape 2.04 to 26.89 for Region 2, and 2.12 to 2,177.58 mi 2 for Region 3. Annual peak data from streamgages were used to qualitatively assess the largest floods recorded at streamgages in Missouri since the 1915 water year. Based on existing streamgage data, the 1983 flood event was the largest flood event on record since 1915. The next five largest flood events, in descending order, took place in 1993, 1973, 2008, 1994 and 1915. Since 1915, five of six of the largest floods on record occurred from 1973 to 2012.

Missouri↗

USGS2014

Methods for estimating magnitude and frequency of floods in Arizona, developed with unregulated and rural peak-flow data through water year 2010

Flooding is among the worst natural disasters responsible for loss of life and property in Arizona, underscoring the importance of accurate estimation of flood magnitude for proper structural design and floodplain mapping. Twenty-four years of additional peak-flow data have been recorded since the last comprehensive regional flood frequency analysis conducted in Arizona. Periodically, flood frequency estimates and regional regression equations must be revised to maintain the accurate estimation of flood frequency and magnitude. Annual peak-flow data collected through water year 2010 were compiled from 448 unregulated streamflow-gaging stations, hereafter referred to as streamgages, in Arizona having a minimum of 10 years of record. Flood frequency estimates were first computed with station (or at-site) skew using the Expected Moments Algorithm with a multiple Grubbs-Beck test to identify multiple potentially influential low flows to fit a Pearson Type III distribution. Next, a multiple step Bayesian least-squares-regression approach was used to determine a new statewide regional skew of −0.09. No basin characteristics analyzed were statistically significant in explaining the variation in skew and as a result, the constant model was chosen as the best regional skew model for the Arizona study area. The mean square error used in Bulletin 17B (B17B) of the Interagency Advisory Committee on Water Data is used to describe the precision of the regional skew. The constant model had a mean square error equal to 0.08, which corresponds to an effective record length of 85 years. This is a marked improvement over a previous Arizona regional skew analysis, with a reported mean square error of 0.31, for a corresponding effective record length of around 17 years. Thus the new regional model had almost five times the information content (as measured by effective record length) of that calculated in USGS Water Supply Paper 2433, published in 1997, or the value of 0.302 reported in the B17B generalized skew map. The flood frequency estimates were recalculated using a weighted skew of the station and regional skew. Station flood frequency estimates for each streamgage are presented for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities. Geographical information systems were used to compute basin characteristic information for each streamgage for the purpose of developing regional equations to estimate flood statistics at ungaged basins. Five hydrologic flood regions in Arizona were defined in a multivariate regionalization process based on mean basin elevation, mean annual precipitation, and soil permeability. A regional generalized least-squares-regression analysis was used to develop five sets of equations from 344 nonredundant streamgages, corresponding to five regions, for estimating the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities at ungaged basins in Arizona. The regression equations developed for these five regions were based on one or more of the statistically significant explanatory variables: drainage area, mean basin elevation, and mean annual precipitation. Average standard errors of prediction for the regression regions for the five regions ranged from 27 to 122 percent and the pseudo-coefficients of determination (pseudo-R 2 ), a measure of the proportion of peak-flow variation that is explained by the basin characteristics, ranged from 68 to 98 percent. Regression equations for Central Highlands (region 4) had the lowest model error and the greatest pseudo-R 2 metrics. The equations for Colorado Plateau (region 2) regression equations generally had greater model error and lower pseudo-R 2 metrics. The improvement of regional regression equation model error and pseudo-R 2 metrics was related to higher numbers of streamgages, longer period of record, and even spatial coverage within a region. The regional regression equations were integrated into the U.S. Geological Survey’s StreamStats program. The StreamStats program is a national map-based web application that allows the public to easily access published flood frequency and basin characteristic statistics. The interactive web application allows a user to select a point within a watershed (gaged or ungaged) and retrieve flood-frequency estimates derived from the current regional regression equations and geographic information system data within the selected basin. StreamStats provides users with an efficient and accurate means for retrieving the most up to date flood frequency and basin characteristic data. StreamStats is intended to provide consistent statistics, minimize user error, and reduce the need for large datasets and costly geographic information system software.

Arizona↗

USGS2013

Methods for estimating annual exceedance-probability discharges for streams in Iowa, based on data through water year 2010

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance-probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedance-probability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized least-squares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized least-squares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

Iowa↗

USGS2012

Parameter estimation method and updating of regional prediction equations for ungaged sites in the desert region of California

The U.S. Geological Survey (USGS) is currently updating at-site flood frequency estimates for USGS streamflow-gaging stations in the desert region of California. The at-site flood-frequency analysis is complicated by short record lengths (less than 20 years is common) and numerous zero flows/low outliers at many sites. Estimates of the three parameters (mean, standard deviation, and skew) required for fitting the log Pearson Type 3 (LP3) distribution are likely to be highly unreliable based on the limited and heavily censored at-site data. In a generalization of the recommendations in Bulletin 17B, a regional analysis was used to develop regional estimates of all three parameters (mean, standard deviation, and skew) of the LP3 distribution. A regional skew value of zero from a previously published report was used with a new estimated mean squared error (MSE) of 0.20. A weighted least squares (WLS) regression method was used to develop both a regional standard deviation and a mean model based on annual peak-discharge data for 33 USGS stations throughout California’s desert region. At-site standard deviation and mean values were determined by using an expected moments algorithm (EMA) method for fitting the LP3 distribution to the logarithms of annual peak-discharge data. Additionally, a multiple Grubbs-Beck (MGB) test, a generalization of the test recommended in Bulletin 17B, was used for detecting multiple potentially influential low outliers in a flood series. The WLS regression found that no basin characteristics could explain the variability of standard deviation. Consequently, a constant regional standard deviation model was selected, resulting in a log-space value of 0.91 with a MSE of 0.03 log units. Yet drainage area was found to be statistically significant at explaining the site-to-site variability in mean. The linear WLS regional mean model based on drainage area had a Pseudo- 2 R of 51 percent and a MSE of 0.32 log units. The regional parameter estimates were then used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins. The final equations are functions of drainage area.Average standard errors of prediction for these regression equations range from 214.2 to 856.2 percent.

California↗