Summary:
Extreme flooding can threaten life and property in flood-prone areas, as well as cause damage to critical infrastructure along roadways and canals. The effective management of these areas, and appropriate design of structures along rivers and streams, relies on understanding the magnitude and frequency of floods at gaged locations, and the ability to estimate these data at ungaged streams. Peak flow analysis and development of regional regression equations to estimate peak flow frequency and magnitude for New York have not been updated using any new data collected since 1999 (Lumia, 2006). As more data and newer technology have become available there is a need to update these data. The updated regression equations will provide more accurate estimates of flood magnitude and frequency at ungaged sites by incorporating 22 more years (water years 2000 – 2021) of streamflow data. These new regression equations will be incorporated into StreamStats to make the best available data easily accessible to all users.
Problem:
Information about the magnitude and frequency of floods is required for the safe and economical design of homes, businesses, highway bridges, culverts, and other structures on and near to streams. This knowledge is utilized by Federal, State and local entities, such as the Federal Emergency Management Agency (FEMA) to establish flood plain boundaries, and the New York State Department of Transportation (DOT) is charged with reviewing the bridge and culvert design for all major highways in the state, including the hydrology and hydraulics for these structures. Estimates of flood magnitude and frequency commonly are needed at ungaged streamflow sites. Therefore, it is necessary to transfer flood-frequency data from gaged sites to ungaged sites. This estimation can be achieved by defining regression relations between peak discharges of selected frequencies and basin or climate characteristics.
Flood-frequency characteristics are typically determined by fitting a log-Pearson Type III (LPIII) distribution to a time series of annual-peak streamflows. Typically, streamflow records should include observations from 10 or more years at a streamflow gage to reasonably estimate the mean, variance, and skewness of the log-transformed annual-peak streamflow time series to compute the LPIII flood quantiles. Those quantiles describe the annual exceedance probabilities (AEPs) associated with peak flows of various magnitudes across the range of flows modeled. For example, the 0.01-quantile corresponds to the 1-percent AEP (i.e. 100-year recurrence interval).
Bayesian generalized least-squares (GLS) regression methods for estimating regional skew have been shown to provide more reliable error metrics than other methods, especially those that ignore differences in at-site station skew reliability and cross correlations of station skews (Veilleux, 2009). Since the previous flood frequency study in New York was completed, there have been updates and improvements in computational methods (the Expected Moments Algorithm and the multiple Grubbs-Beck test) for flood-frequency analysis which have been recommended in Bulletin 17C (England, 2019), which supersedes the guidelines from Bulletin 17B (IACWD, 1982). The Expected Moments Algorithm (EMA) (Cohn and others, 1997, 2001) generalizes, extends, and simplifies the Bulletin 17B methods (IACWD, 1982). This permits the incorporation of information about uncertainty in the peak-flow values computed under Bulletin 17C guidelines. By incorporating non-exceedance information from determination of observation thresholds, EMA also improves how periods of missing record are handled (Cohn and others, 1997, 2001).
The multiple Grubbs-Beck (MGB) test (Cohn and others, 2013) provides improvements in the detection of more than a single low outlier, which is typically the limit when using he single Grubbs-Beck (SGB) test suggested in Bulletin 17B, even when multiple low outliers are present. Low outliers, because of their high leverage and influence on skew, can significantly affect estimates of higher magnitude flows (lower AEPs). The MGB test correctly identifies multiple low outliers (when they exist) based on the reasonable assumption that peak-flow data are drawn from a log-normal population.
The previous reporting of peak-streamflow equations for New York has become outdated. Since the last peak-streamflow regressions were developed (Lumia, 2006), over 20 more years of streamflow data have been collected and many additional streamgage records are now available to be included.
The recent publications of regional skew values for application of Bulletin 17C methods provide updated skew values for most of the State (Veilleux and Wagner, 2019, Veilleux and others, 2019, Veilleux and others, 2021). Digitally determined basin characteristics used in earlier studies can be improved and expanded using newer and newly available data sets which may improve accuracy of basin characteristics used in the peak-streamflow regression analysis. Computing up to date, at-site basin characteristics for streamgages, and regionally determined skews, will help provide more accurate at-site AEP estimates at ungaged locations in New York to estimate flood risk and infrastructure design specifications.
Objectives:
The objectives of the proposed study are:
- Calculate magnitude of peak flows for 80-, 67-, 50-, 20- 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent Annual Exceedance Probabilities (AEP) at selected streamgages in New York, and neighboring states, using Bulletin 17C methods and data collected through the 2020 water year.
- Compile and determine explanatory basin and/or land-use characteristic GIS data sets for developing regional-regression equations.
- Produce new regional regression equations for estimating the 80-, 67-, 50-, 20- 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP flows at ungaged sites in New York, excluding Long Island.
- Document the methods and findings in a USGS Scientific Investigations Report publication, which includes a data release to ScienceBase.
- Incorporate the new peak regression equations into the USGS StreamStats web application.
Approach:
The approach of this project will be to compute the AEP flows at streamgages, develop regression equations relating basin characteristics and the streamgage AEP flows, revise the streamgage AEP flows as weighted estimates of the streamgage and regional regression flows, document the results and methods, and incorporate the new equations into StreamStats.
Objective 1: Calculate the magnitude of peak flows with 80-, 67-, 50-, 20- 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual-exceedance probabilities (AEP) at non-regulated streamflow monitoring sites in and near New York with a minimum of 10 years of peak-discharge data, using data collected through the 2020 water year and recently updated Bulletin 17C methods.
Task 1A: Compile the peak flow data needed for the flood frequency analysis in New York. The data compiled will be from active, discontinued, and partial-record (crest-stage gages) streamgages. Streamgages from surrounding states that are hydrologically connected will also be used. Sites affected by regulation, diversion, urbanization, extensive channelization, or backwater, and sites with less than 10 years of annual peak flow data will be excluded from the analysis. The 2020 Water Year peak flows will be included in the analysis. Most stations included in Lumia, 2006 are already updated through 2014 water year, which will reduce the time needed for this task. All of Long Island will be excluded from this project; there is an active project to evaluate AEP floods on Long Island.
Task 1B: Compute at-site peak flow frequency statistics for all sites for the 80-, 67-, 50-, 20- 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP floods using the EMA and MGB techniques implemented in version 7.3 (or later) of the USGS program PEAKFQ (Veilleux and others, 2014) using the newly developed New York skew maps and Bulletin 17C guidelines. Guidelines in Bulletin 17C recommend using a weighted skew coefficient to reduce the uncertainty in AEP estimates for streamgages. The weighted skew coefficient is calculated by mathematically weighting the station skew and generalized skew coefficients. The generalized skew coefficient provides regional geographic continuity by combining the statistical parameter, coefficient of skew, from many streamgages in a hydrologically similar region.
Objective 2: Calculate explanatory basin and land-use characteristics variables. Basin physical and climate characteristics such as contributing drainage area, main-channel slope, mean annual precipitation, land-use, land-cover, and other characteristics will be compiled for use as potential explanatory variables in regression analysis. Any updated drainage area values will be implemented based on the most recent and appropriately accurate datasets. Basin characteristics need to be readily obtainable and reproducible to be useable in StreamStats. National datasets will be prioritized, as these provide consistency across state boundaries.
Objective 3: Develop regional regression equations using calculated AEPs and basin characteristics.
Task 3A: Use Ordinary-Least Squares (OLS) as an initial screening to determine the combinations of explanatory variables the best predict peak streamflows. The explanatory variables that best describe the variability of AEP flows are selected on the basis of several factors, including (1) standard error (SE) of the estimate, (2) Mallow’s Cp statistic, (3) R2, (4) residual sum of squares (PRESS) statistic, and (5) the statistical significance of the explanatory variables. Explanatory variables that are highly correlated will be screened from simultaneous use in the analysis because covariance between variables can adversely affect multivariate regressions.
Task 3B: Determine if regions need to be redefined to improve results, or if the regions from the previous study (Lumia, 2006) are still appropriate. Regionalization of the regression equations determined in Task 3A will be evaluated based on the regression residuals. Sub regions are indicated if the means of the residuals within regions are significantly different (tested by Wilcoxon signed-rank test or other test not influenced by unequal population distributions). If present, Task 3A will be repeated to determine the best explanatory basin characteristics and OLS regression models within a sub region.
Task 3C: The final predictive equations will be determined by WLS and GLS analysis determined by use of the program WREG (Eng and others, 2009) or R (R Core Team, 2018). WLS and GLS procedures assign weights in the analysis based on record length and the covariance between streamgages. Several performance metrics will be used to evaluate the final regression equation(s): (1) Average Variance of Prediction, AVP; (2) Pseudo R2, (3) Leverage and Influence of points, (4) plots of the residuals, (5) regression model coefficients significance, and (6) collinearity of the variables.
Task 3D: Combine the at-site estimates with an independent regional estimate to obtain a weighted estimated of the peak flow statistics at each streamgage. The weighted estimate is considered an improved estimate, particularly those with short records (IACWD, 1982). After the regional regression equations are developed, the streamgage AEP peak flows will be recomputed using weighted independent estimate determined from the values and uncertainties determined from the at-site analyses and the regional-regression equation.
Objective 4: Document the methods used to estimate peak flows at streamgages and the development of peak-flow regression equations in a USGS Scientific Investigations Report.
Objective 5: Incorporate the new peak-flow regression equations into the USGS StreamStats web application.
References
Cohn, T.A., England, J.F., Berenbrock, C.E., Mason, R.R., Stedinger, J.R., and Lamontagne, J.R., 2013. A generalized grubbs-beck test statistic for detecting multiple potentially influential low outliers in flood series. Water Resources Research, 49(8):5047-5058.
Cohn, T.A., Lane, W.L., and Baier, W.G., 1997. An algorithm for computing moments-based flood quantile estimators when historical flood information is available. Water Resources Research, 33(9):2089-2096.
Cohn, T.A., Lane, W.L., and Stedinger, J.R., 2001. Confidence intervals for Expected Moments Algorithm flood quantile estimators. Water Resources Research, 37(6):1695-1706.
Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide to the weighted-multiple-linear-regression program (WREG version 1.0): U.S. Geological Survey Techniques and Methods, book 4, chap. A8, 21 p., available at http://pubs.usgs.gov/tm/tm4a8/.
England, J.F., Jr., Cohn, T.A., Faber, B.A., Stedinger, J.R., Thomas, W.O., Jr., Veilleux, A.G., Kiang, J.E., and Mason, R.R., Jr., 2019, Guidelines for determining flood flow frequency—Bulletin 17C (ver. 1.1, May 2019): U.S. Geological Survey Techniques and Methods, book 4, chap. B5, 148 p., https://doi.org/10.3133/tm4B5.
Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flow frequency: Reston, Va., U.S. Geological Survey, Office of Water Data Coordination, Hydrology Subcommittee Bulletin 17B [variously paged].
Lumia, Richard, and Baevsky, Y.H., 2000, Development of a contour map showing generalized skew coefficients of annual peak discharges of rural, unregulated streams in New York, excluding Long Island: U.S. Geological Survey Water Resources Investigations Report 00-4022, 11 p.
Lumia, Richard, Freehafer, D.A., and Smith, M.J., 2006, Magnitude and frequency of floods in New York: U.S. Geological Survey Scientific Investigations Report 2006–5112, 152 p
R Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
U.S. Geological Survey, 2016, The StreamStats program, online at http://streamstats.usgs.gov.
Veilleux, A.G., and Wagner, D.M., 2021, Methods for estimating regional skewness of annual peak flows in parts of eastern New York and Pennsylvania, based on data through water year 2013: U.S. Geological Survey Scientific Investigations Report 2021–5015, 38 p., https://doi.org/10.3133/sir20215015.
Veilleux, A.G., Cohn, T.A., Flynn, K.M., Mason, R.R., Jr., and Hummel, P.R., 2014, Estimating magnitude and frequency of floods using the PeakFQ 7.0 program: U.S. Geological Survey Fact Sheet 2013–3108, 2 p., https://dx.doi.org/10.3133/fs20133108.
Veilleux, A.G., Zariello, P.J., Hodgkins, G.A., Ahearn, E.A., Olson, S.A., and Cohn, T.A., 2019, Methods for estimating regional coefficient of skewness for unregulated streams in New England, based on data through water year 2011: U.S. Geological Survey Scientific Investigations Report 2017–5037, 29 p., https://doi.org/10.3133/sir20175037.
Veilleux, A.G., and Wagner, D.M., 2019, 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: U.S. Geological Survey Scientific Investigations Report 2019–5105, 26 p., https://doi.org/10.3133/sir20195105.
Wall, G.R., Murray, P.M., Lumia, Richard, and Suro, T.P., 2014, Maximum known stages and discharges of New York streams and their annual exceedance probabilities through September 2011: U.S. Geological Survey Scientific Investigations Report 2014–5084, 16 p., http://dx.doi.org/10.3133/sir20145084.
Watson, K.M., and Schopp, R.D., 2009, Methodology for estimation of flood magnitude and frequency for New Jersey streams: U.S. Geological Survey Scientific Investigations Report 2009–5167, 51 p.
