Prepared in cooperation with the U.S. Army Corps of Engineers and Federal Emergency Management Agency
Flood-Frequency Comparison from 1995 to 2016 and Trends in Peak Streamflow in Arkansas, Water Years 1930–2016
MISSOURI Eleven Point River
S p r i n White River g Strawberry River R iv Black River Illinois River er
North Sylamore Creek White River
Black River Little Red River TENNESSEE
OKLAHOMA Arkansas River
ARKANSAS James Fork
River Poteau White River Dutch Creek Bayou Meto South Fourche LaFave River Fourche LaFave River Arkansas River
A Cossatot River nto in e R Saline River i v e Saline River r Little Missouri River B a MISSISSIPPI y o Mississippi River u Little River B a r
t
Ouachita River h
o
l
o
m e
Red River S w m a c Bayou Macon kover Creek TEXAS Ouachita River
LOUISIANA
Scientific Investigations Report 2019–5131
U.S. Department of the Interior U.S. Geological Survey Cover. Physiographic sections in Arkansas and surrounding States (modified from figure 1). Flood-Frequency Comparison from 1995 to 2016 and Trends in Peak Streamflow in Arkansas, Water Years 1930–2016
By Paul A. Ensminger and Brian K. Breaker
Prepared in cooperation with the U.S. Army Corps of Engineers and Federal Emergency Management Agency
Scientific Investigations Report 2019–5131
U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior DAVID BERNHARDT, Secretary U.S. Geological Survey James F. Reilly II, Director
U.S. Geological Survey, Reston, Virginia: 2019
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Suggested citation: Ensminger, P.A., and Breaker, B.K., 2019, Flood-frequency comparison from 1995 to 2016 and trends in peak stream- flow in Arkansas, water years 1930–2016: U.S. Geological Survey Scientific Investigations Report 2019–5131, 20 p., https://doi.org/10.3133/sir20195131.
ISSN 2328-0328 (online) iii
Contents
Acknowledgments...... vi Abstract...... 1 Introduction...... 1 Purpose and Scope...... 2 Study Area...... 2 Arkansas Flood-Frequency Reports from 1995 and 2016...... 2 Methods and Results...... 5 Mann-Kendall Tau Test for Trends in Peak Streamflows...... 5 Locally Estimated Scatterplot Smoothing of Peak Streamflows...... 5 One-Percent Annual Exceedance Probability Changes through Time...... 5 Arkansas Regional Regression Equations Comparison...... 9 Summary...... 19 References Cited...... 19 iv
Figures
1. Map showing locations of the 15 selected streamgages and physiographic sections in Arkansas and surrounding States...... 3 2. Map showing food regions and 74 selected locations where the 2016 and 1995 annual exceedance probability floods were computed...... 4 3. Graphs showing locally estimated scatterplot smoothing trend lines of the annual peak streamflow data at the 15 selected streamgages for the full period of record ...... 7 4. Graphs showing the 1-percent annual exceedance probability flood trend for the 15 selected streamgages plotted with the annual peak for the full period of record...... 11 5. Graph showing relation between the log base 10 transformed recurrence interval and the average percentage difference change between the 2016 and 1995 annual exceedance probability flood estimates for the 74 streamflow locations representing 15 streamgages and the 0-, 10-, 50-, and 85-percent locations along the stream, terminating at the Arkansas border...... 14 6. Boxplots showing the range of percentage differences of annual exceedance probability flood estimates from the 1995 to the 2016 regional regression equations by peak streamflow region as designated by Wagner and others (2016)...... 18
Tables
1. The 15 selected streamgages and the associated Mann-Kendall trend results with probability values for the designated period of record...... 6 2. The 15 selected streamgages used in this study and the percentage differences from the initial 1-percent annual exceedance probability flood estimate for each subsequent 1-percent annual exceedance probability flood reevaluation...... 10 3. The percentage difference between the 2016 and 1995 annual exceedance probability floods for the 74 selected streamflow locations, which include the 15 selected streamgage locations and the 0-, 10-, 50-, and 85-percent locations along each of the selected streams, terminating at the Arkansas border, when applicable...... 15 v
Conversion Factors
U.S. customary units to International System of Units
Multiply By To obtain Length inch (in.) 2.54 centimeter (cm) inch (in.) 25.4 millimeter (mm) Flow rate cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)
Datum
Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). Altitude, as used in this report, refers to distance above the vertical datum.
Supplemental Information
A water year is the period from October 1 to September 30 and is designated by the year in which it ends; for example, water year 2015 was from October 1, 2014, to September 30, 2015.
Abbreviations
AEP annual exceedance probability AEPF annual exceedance probability flood EMA Expected Moments Algorithm LOESS locally estimated scatterplot smoothing PD percentage difference RI recurrence interval RRE regional regression equation USGS U.S. Geological Survey vi
Acknowledgments
Thanks to the U.S. Army Corps of Engineers and the Federal Emergency Management Agency, whose valuable support made this report possible.
Thanks to Maxwell Lindaman, Hydrologist, U.S. Geological Survey, for his geographic informa- tion system help in generating report figures. Flood-Frequency Comparison from 1995 to 2016 and Trends in Peak Streamflow in Arkansas, Water Years 1930–2016
By Paul A. Ensminger and Brian K. Breaker
Abstract were less than the 1995 AEPFs by 2.53 and 0.31 percent, respectively. In 2016, the U.S. Geological Survey, in cooperation with the U.S. Army Corps of Engineers and the Federal Emergency Management Agency, began a study in Arkansas to investigate Introduction possible increasing trends in annual peak streamflow data and the possible resulting increase in the annual exceedance Significantly increasing peak streamflow trends are of probability flood (AEPF) predictions. Temporal trends of peak concern to local, State, and Federal agencies in Arkansas streamflow were investigated at 15 selected streamgages on because of the corresponding increased flood risk to highway unregulated streams in Arkansas having 30 or more years of structures and surrounding communities. The risk of flooding peak streamflow data through the 2016 water year. For the can be characterized by annual exceedance probability flood period of record at each streamgage, the Mann-Kendall trend (AEPF) predictions, which are developed from peak streamflow test indicated that 14 of the 15 streamgages had no statisti- data and flood-frequency analysis. Transportation and drain- cally significant peak streamflow trends and 1 streamgage age infrastructure, such as bridges, culverts, channels, canals, had a statistically significant decreasing peak streamflow dams, and levees, generally is designed and operated under trend. Visual examination of the locally estimated scatterplot the assumption of stationarity (Milly and others, 2008), which smoothing technique trend lines of the peak streamflow data implies that natural and anthropogenic-induced changes are too indicated a possible increasing peak streamflow trend at 8 of small to significantly affect statistical characteristics like annual the 15 streamgages since the 1990s. peak streamflow (Walter and Vogel, 2010). However, substantial A sequential series analysis of the 1-percent AEPF at natural and anthropogenic changes might result in significant each of the 15 selected streamgages was completed by select- trends within the annual peak streamflow data. ing an initial subset of the oldest peak streamflow data from When completing flood-frequency analyses, the peak each site to estimate the initial 1-percent AEPF. This initial streamflow data are assumed to be stationary and their statisti- peak streamflow data subset was subsequently appended with cal properties are unchanged over time, according to Bulle- 10-year increments of additional peak streamflow data until tin 17B, “Guidelines for Determining Flood Flow Frequency” the full period of peak streamflow data was analyzed. The (Interagency Committee on Water Data, 1982). However, maximum increase in the 1-percent AEPF was 113 percent, stationary and nonstationary peak streamflow data are effec- and the maximum decrease was 31.9 percent. tively indistinguishable because of the paucity of observation Percentage differences between the AEPFs derived records except where changes in the underlying processes are from regional regression equations presented in the 1995 and so dramatic that no statistical assessment is necessary (Lins 2016 Arkansas flood-frequency reports were compared. The and Cohn, 2011). Additionally, there can be multidecadal and average percentage differences for the 74 selected locations century-scale variation in streamflow lending to multiyear indicate that the 4-, 2-, 1-, and 0.2-percent AEPFs computed periods in those records that may indicate uptrends and down- using the 2016 regional regression equations were higher by trends and, thus, are not necessarily indicative of a persistent 3.52, 5.10, 8.59, and 13.31 percent, respectively (25-, 50-, change in the system (Cohn and Lins, 2005). 100-, and 500-year recurrence interval floods), than the same Hirsch (2011) denoted the importance of frequent updates percentage AEPFs computed using the 1995 regional regres- to flood-frequency analyses to assist water-resources man- sion equations. The average percentage differences between agement in the design of structures that are dependent on the 1995 and 2016 AEPFs for the 10-percent AEPF (10-year the hydrologic variables that result from these analyses. In recurrence interval flood) resulted in 2016 AEPF predictions Arkansas, the two most recent flood-frequency reports were being 0.41 percent higher. For the 50- and 20-percent AEPFs published in 1995 (Hodge and Tasker, 1995) and 2016 (Wag- (2- and 5-year recurrence interval floods), the 2016 AEPFs ner and others, 2016) and documented the regional regression 2 Flood-Frequency Comparison from 1995 to 2016 and Trends in Peak Streamflow in Arkansas, Water Years 1930–2016 equations (RREs) used to calculate the 50-, 20-, 10-, 4-, 2-, 1-, retaining the essential structure and moments-based approach and 0.2-percent AEPFs. The U.S. Geological Survey (USGS), procedures for determining flood frequency (Interagency in cooperation with the U.S. Army Corps of Engineers and the Committee on Water Data, 1982). The EMA can accommodate Federal Emergency Management Agency, completed a study interval data, which simplifies the analysis of datasets con- to determine if significant increasing trends exist in annual taining censored observations, historical and (or) paleo data, peak streamflow data from Arkansas and to compare the per- low outliers, and uncertain data points while also providing centage differences (PDs) of the AEPF estimates from the two enhanced confidence intervals for the estimated streamflows most recently published flood-frequency reports for Arkansas. (Veilleux and others, 2014). The 2016 report (Wagner and others, 2016) also incorporated an updated regional skew coefficient, which was developed for Arkansas using Bayesian weighted least-squares/generalized least-squares regression Purpose and Scope (Veilleux, 2009, 2011). The 1995 Arkansas flood-frequency analysis (Hodge This report presents (1) an analysis of trends within peak and Tasker, 1995) defined four flood regions and used data streamflow data for 15 selected streamgage sites in Arkansas collected through 1993 from 204 streamgages to develop the and (2) the PDs between the 1995 and 2016 Arkansas AEPFs RREs. In comparison, the 2016 Arkansas flood-frequency for the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent AEPFs at the analysis (Wagner and others, 2016) documented five flood 15 selected sites and at ungaged sites at the 0-, 10-, 50-, and regions (dividing region B of the 1995 report into subre- 85-percent lengths of each of the 15 selected streams where gions B1 and B2; fig. 2) and used data collected through 2013 those locations were within the boundaries of the State. from 281 streamgages to develop RREs. The 1995 and 2016 RREs included some similar basin characteristics; however, the 2016 RREs typically included additional basin and cli- Study Area matic variables compared to the 1995 RREs. As a result, for the same streamflow location, the AEPF estimates from the The geographic scope of this report encompasses most 1995 (Hodge and Tasker, 1995) and 2016 (Wagner and others, of Arkansas (fig. 1). Arkansas is characterized by a diverse 2016) flood-frequency reports may be different. topography and contains parts of six physiographic sections: With respect to floods, the annual exceedance probability the Springfield-Salem Plateaus, Boston Mountains, Arkansas estimates the likelihood, in percent, of a specific magnitude Valley, Ouachita Mountains, West Gulf Coastal Plain, and flood occurring in any given year. For instance, a 1-percent Mississippi Alluvial Plain (Wagner and others, 2016). The AEPF is a flood with a 1-percent probability of occurring dur- climate in Arkansas is mild and moderately humid. For the ing any given year. Traditionally, AEPFs have been expressed period 1951–2011, mean annual precipitation for the State was as a recurrence interval (RI), in years, where 50-, 20-, 10-, 4-, 49.8 inches (in.) and ranged from 44 in. in the Springfield- 2-, 1-, 0.5-, and 0.2-percent AEPFs were reported as 2-, 5-, Salem Plateaus near the Missouri State line and the Arkansas 10-, 25-, 50-, 100-, 200-, and 500-year RI floods, respectively Valley near the Oklahoma State line to 64 in. in the Ouachita (Holmes and Dinicola, 2010). In terms of probability of occur- Mountains (Pugh and Westerman, 2014). rence, this means there is a 1 in 100 chance (or 1-percent prob- ability) that in any single year, the 100-year flood (1-percent AEPF) will occur at a given location. However, some have erroneously interpreted the “100-year flood” to mean that a Arkansas Flood-Frequency Reports flood of that magnitude would be expected to occur only once from 1995 and 2016 during a 100-year period. In fact, a 1-percent AEPF (100-year flood) has a 1-percent probability of occurring in any given Wagner and others (2016) used data collected through year, regardless of past flooding events. 2013 and the Expected Moments Algorithm (EMA) for fit- The probability P that a flood with an annual exceedance ting the Log-Pearson Type III distribution of the annual peak probability, in percent, will occur at least once in an N-year streamflow data that were used to estimate AEPFs (Cohn and period is shown in the following equation: others, 1997, 2001; Griffis and others, 2004). The use of the EMA method to estimate AEPF events was recommended by P=(1−[1−(AEP)]N) (1) the Subcommittee on Hydrology as a revision to Bulletin 17B (Advisory Committee on Water Information, Subcommittee on where Hydrology, Hydrologic Frequency Analysis Work Group, writ- P is the probability of the annual exceedance ten commun., 2013). The EMA method applies the Grubbs- probability (AEP) flood occurring over Beck test to screen multiple potentially influential low floods N-year period; that are not relevant to the processes associated with larger AEP is the annual exceedance probability, in floods (Cohn and others, 2013). The EMA addresses several percent; and methodological concerns identified in Bulletin 17B while N is the number of years. Arkansas Flood-Frequency Reports from 1995 and 2016 3
9 92 90
MISSOURI Eleven Point River
S p r 3 in White River g 07072000 Strawberry River Ri 2 Black River Illinois River ve 4 r 07069500 6 07074000 North Sylamore Creek 1 07194800 White River 36 07060710
Black River Little Red River 5 TENNESSEE 07075300 OKLAHOMA Arkansas River
ARKANSAS 7 James Fork 07249400 07260000 8 9 teau River White River Po 07263000 Dutch Creek Bayou Meto South Fourche LaFave River
Fourche LaFave River Arkansas River
07340300
Cossatot River A 10 nto in e
Saline River R i v Saline River e
r 07364120 Little Missouri11 07361500 River 14 3 a MISSISSIPPI o Mississippi River Little River 13 a