1 LOW FLOW STATISTICS TOOLS A How -To Handbook for NPDES Permit Writers -833- B-18- 001 October 2018 EPA Office of Water https://www.epa.gov/npdes

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3 Disclaimer The U.S. Environmental Protection Agency (EPA) Office of Water , through its Office of Wastewater Management , funded the preparation of this report under EPA Contract No . EP -C16 -0003. Any opinions, findings, conc lusions, or recommendations do not change or substitute for any statutory or regulatory provisions. This document does not constitute a regulation, impose legally binding requirements, confer legal rights, impose legal obligations, or implement any statuto ry or regulatory provisions. This handbook is a living document and may be revised periodically without public notice. EPA welcomes input on this report at any time. Mention of trade names or commercial products is not intended to constitute endorsement or recommendation for use. Acknowledgements This document was notably improved by input from USGS and several NPDES permit writers representing both EPA and state programs. Photos reproduced on the cover of this document were provided courtesy of PG Enviro nmental , Zak . Erickson, and Anthony D’Angelo ii

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5 Disclaimer ... ii ii Acknowledgements ... 1 book ... 1-1 An Introduction to Low Flow Statistics and This Hand Who Is the Intended Audience for This Hand book? ... 1-1 1.1 What Is a Low Flow Statistic? 1.2 1-1 ... 1.3 What Topics Does This Hand book Cover? ... 1-2 1-2 1.4 What So ftware Tools Are Discussed in This Hand book? ... 1.5 When Should I Use Each of These Tools? ... 1-2 2-1 2 Investigating the Watershed ... Introduction ... 2.1 2-1 2-1 2.2 -by -Step Instructions for Exploring with StreamStats ... Step 3 Estimating Low Flow Statistics with SWToolbox and WREG ... 3-1 3.1 Intro duction ... 3-1 3.2 Using SWToolbox to Estimate Low Flow Statistics on a Gaged Waterbody ... 3-1 3.3 Using WREG to Estimate Low Flow Statistics on an Ungaged Waterbody ... 3-8 4 tions ... 4-1 Frequently Asked Ques 4.1 General Questions ... 4-1 4.2 Troubleshooting Tips ... 4-6 5 References ... 5-1 A-1 ... Appendix A: K Values Tables iv

6 1 T h is Hand book An Introduction to Low Flow Statistics and Who Is the Intended Audience for T his Hand book ? 1.1 Elimination System (NPDES) National Pollutant Discharge often need to calculate low flow permit writers water quality -based effluent limitation ( statistics for reasonable potential analyses and ) WQBEL calculation s or to confirm estimates provided by the permittee during the NPDES permit development process. The typical calculation procedures for low flow statistics are complex and cumbersome to execute by hand or with spreadsheet -based tools. However, several software app lications that greatly permit simplify this process are available to permit writers. The purpose of this hand book is to help low flow statistic values in a variety of situations using these free, publicly available estimate writers tools. Flo w What Is a Low Statistic? 1.2 Low f low statistics are estimates of the lowest flow event in a stream or river that would be expected to occur over some period of record. NPDES permit writers typically use these estimates when authorizing a regulatory mixing zone and associated dilution cred its or dilution factors for use in reasonable As described in potential analyses and/or WQBEL calculations. of EPA’s 3.2 Section Technical Support Document for Water Most permitting authorities Quality- based Toxics Control (hereafter, the Technical Support use either the term “credit” or Document), dilution credits EPA recommends that authorized “factor” to refer to the level of reflect the behavior of a permitted discharge as it mixes with the dilution authorized in a permit. receiving water. In flowing rivers and streams, dilution credits are For convenience, this , which are based on the critical conditions of the receiving water typi cally defined in the applicable water quality standards (e.g., document primarily uses the . Critical conditions are conservatively 7Q10 receiving water flow) term “dilution credit,” but both the based on receiving water low flow estimates to ensure are equally valid terms. ove discharge does not cause or contribute to an excursion ab water q uality standards. hydrologic design or biological design basis. Both are equally Low flow values are defined on a acceptable for use in NPDES permitting. Low flow values are expressed in terms of their averaging -day average flow o period (for example, a 4 7-day average flow) and their recurrence frequency r a 3 years for biologically based years for hydrologically 10 (generally once in based flows and once in flows). low flow is computed using the single lowest flow event from each ye ar of A hydrologically based record, followed by application of distributional models (typically the Log Pearson Type III distribution is -day average flow that occurs (on assumed) to infer the low flow value. The 1Q10 is the lowest one average) once every 10 years. The 7Q10 is the lowest 7-day average flow that occurs (on average) once every 10 years. A biologically low flow is computed based on all low flow events within a period of record, even if based several occur in one year, and reflects the empirically observed frequency of biological exposure during a period of record. The 4B3 is the lowest four occurs once every three years. The -day average flow that occurs once every three years. 1B3 is the lowest one -day average flow that 1 1 - An Introduction to Low Flow Statistics

7 1.3 Topics Does This Handbook Cover? What Investigate the — Are there stream gages in the watershed of interest? Where are Section 2: Watershed they and are they useful to the permit writer? This section will provide the permit writer with strategies data sources using the StreamStats web app lication . for finding and evaluating appropriate streamflow —After Section 3: Estimating Low Flow Statistics with SWToolbox and WREG exploring the watershed identifying the available data sources, this section will guide permit writers with tips for loading data and obtain the low flow estimates need ed for NPDES permit development. and managing settings to Section 4: Frequently Asked Questions —This section will answer some questions that arise frequently when permit writers estimate low flow . statistics What Software 1.4 Are Discussed in T his Hand book ? Tools This hand book will discuss three pieces of software: StreamStats, SWToolbox, and WREG. The U.S. Geological Survey (USGS) distributes all three publicly available tools on the web . of these StreamStats StreamStats (version 4) is a web application that provides access to an assortment of g eographic information system (GIS) analytical tools that are useful for water resources planning and management, as well as engineering and design purposes. StreamStats is an excellent tool for mapping and exploring the drainage area and stream gages near a discharge location of interest. The StreamStats web sgs.gov/osw/streamstats/ application can be accessed at: https://water.u SWToolbox SWToolbox is a desktop application that builds upon past tools, such as SWSTAT and DFLOW, which to estimate permit writers have historically used low flow statistics from stream gage data. SWToolbox ute n-day frequency analyses (i.e., 1Q10 or 7Q10) and biologically based flows. It allows users to comp also s the use of USGS National Water Information System (NWIS) streamflow data, as well as facilitate user data files. The SWToolbox desktop application can be downloaded at: -provided https://water.usgs.gov/osw/swtoolbox/ WREG WREG is a desktop application that is used to develop a regional estimation equation for streamflow characteristics ( e.g ., low flow values) . Users can apply these estimates at ungaged basins, or use them to improve the corresponding estimate at continuous -record streamflow gages with short records. The -linear regression that relates obs ervable basin regional estimation equation results from a multiple characteristics, such as drainage area, to streamflow characteristics. The desktop application and additional supporting documentation for WREG can be downloaded at: https://water.usgs.gov /software/WREG/ 1.5 When Should I U se Each of These Tools ? When deciding which of these tools to use and when to use them, should consider : you • The specific need you are attempting to address . • The data and information available to you . disposal. your • s at The uses of the tool 1 2 - An Introduction to Low Flow Statistics

8 1 displays a decision tree flowchart to help you evaluate Figure the right tool these questions and pick for the job. 1. A decision tree for evaluating which tool to use when calculating low flow statistics. Figure 1 3 - An Introduction to Low Flow Statistics

9 2 the Watershed Investigating 2.1 Introduction Your first step when estimating low flow statistics during the permit writing process is to take stock of you . You should identify the following pieces of the character and quantity of information available to information: The location of the permitted discharge for which you are seeking a dilution credit • . authorization • The availability, location, and proximity of any flow gages upstream or downstream of the discharge location . • The presence and location of any impoundments, tributaries, water withdrawals, other discharges, or other factors that might influence the quantity of flow occurring at the discharge location . • The availability of flow gages within nearby drainage basins if the stream segment where the discharge is occurring is ungaged. In addition, once you identify stream gages, you should evaluate the quality and quantity of historical flow data available for estimating low flow values. tool Several tools are available to help locate USGS flow gages and explore the watershed. The principal discussed in t you may also find the is USGS’ his section s StreamStats web application. However, following alternative s useful: resource • ’s NWIS website provides direct links to a variety of USGS monitoring sites —including USGS streamflow gages —through a searchable map in terface at: https://nwis.waterdata.usgs.gov/nwis SWToolbox also includes a GIS interface allowing users to visually explore a watershed and • identify potentially useful stream gage locations. • Commercial satellite imagery and mapping software (e.g., Google Earth or similar) may be useful for locating the permitted discharge outfall on the waterbody of interest and for identifying other points of interest. StreamStats provides a GIS interface like that of t he NWIS website, but also provides additional mapping may be useful. You can access StreamStats online at and drainage area delineation tools that https://water.usgs.gov/osw/streamstats/ by selecting the “StreamStats Application” button on the navigation bar. 2.2 Step -by -Step Instructions for Exploring with StreamStats Next, let’s discuss some step -by -step instructions a permit writer can use when investigating the watershed with StreamStats. I llustrations accompany the instructions , which you can use to follow along depict own computer. The illustrations on the process of locating potential stream gages for the your Cookeville Wastewater Treatment Plant located at 1870 South Jefferson Ave keville ., Coo , Tennessee. The plant discharges to Pigeon Roost Creek, which is a tributary to the Falling Water River. 2 1 - Investigating the Watershed

10 Step 1. After opening the web application, search for a location of interest in the search bar. You can search using a street address or latitude and longitude coordinates for the facility . Step 2. Select the appropriate “State or Regional Study Area is presented in the search window. ” that should revisit the locat If an appropriate option does not appear, you ion information used in the search and verify its accuracy, or try using different search information. Navigate to the discharge locati Step 3. on of interest and zoom in until the stream network data ) appear layer (i.e., a pixelated, blue tracing of the local stream s. 2 2 - Investigating the Watershed

11 Click the “D Step 4. -hand toolbar, then click on the discharge location elineate ” button on the left within the waterbody. After processing for several moments, StreamStats will display the upstream portion of the basin network that drains to the discharge location. Using the map interface, explore nearby locations Step 5. upstream and downstream of the discharge for StreamStats will present different streamflow gages. If gages are unavailable, sites using various colors to examine nearby watersheds that are similar to the denote useful information for drainage area into which the permitted outfall each gage station. Expand the discharges. “National Layers” button in the After id entifying relevant stations, click on their legend to show an expanded icons to find links to their NWIS and StreamStats legend explaining each symbol pages. used in the map. 2 3 - Investigating the Watershed

12 The NWIS page provides facts about the area that drains to the station (e.g., total drainage area and contributing drainage area) , as well as the monitoring beginning date, monitoring ending date, and number of records available for the site. you On the StreamStats page, information for the can find additional USGS site, which may you are seeking include -calculated low flow statistics. If the appropriate low flow statistic pre is listed on the page, you should obtain the original research report that documents the period of record and other factors the estimate is estimate. You should then verify that the upon are appropriate to the circumstances of using permit authorization before your based the estimate. Most direct estimates reported on the StreamStats gage webpage will be based that are less recent than those available to the permit writer. on streamflow measurements For more in formation on identifying the underlying references these estimates are based upon, please refer to Section 4 , “Frequently Asked Questions. ” Based on the available information, you Step 6. should decide whether sufficient data exist on the or if you stream segment of interest to directly calculate low flow statistics using SWToolbox, estimate on a regression of nearby watershed should base your gages using WREG. Refer to for additional discussion on making this determination. Section Section 1.5 of this hand book and WREG se of 3 further describes the u for more discussion . Refer to Section 4 SWToolbox sufficient for use in your NPDES permit. on determining whether data are 2 4 - Investigating the Watershed

13 and Step 7. Before leaving StreamStats, you should return to the discharge location ’s delineation collect information on its size. You can do this by clicking on “Continue” and collecting the basin characteristics , as these are likely to be useful later . “Basin Characteristics Report ” as a comma separated values (.csv) StreamStats will export a which can be saved and viewed later using a spreadsheet application. In addition, the file, for use in n be downloaded as a shapefile (or in other formats) delineation for the basin ca . other GIS applications In the case of the Cookeville Wastewater Treatment Plant, there are no gages upstream of the permitted outfall , but there are two downstream gages. The first is approxi mately 1.8 miles downstream (Station ID No. 03422900) but does not have data available for download the or information on any data associated with station. The second is 4 miles downstream on the Falling Water River (Station ID No. 03423000) and has data a vailable for download dating from 1932 to 2018. In general, the first station is preferable in terms of its location (i.e., nearby and on the same ; however stream segment) not available for review. The second station, are , the flow data while farther down and has a substantial amount of data representative stream, is likely to be available for use. 2 5 - Investigating the Watershed

14 3 Estimating Low Flow Statistics with SWToolbox and WREG Introduction 3.1 In this section, we will discuss how to use SWToolbox and WREG to estimate low flow statistics. As tee’ 2, you would use SWToolbox for situations where the permit s outfall discussed in Sections 1 and location and a stream gage are on the same stretch of a er. WREG is typically used when it is not stream or riv ly measure the waterbody’s low flow possible to direct Some experienced readers will have statistics. Instead, low flow statistics are calculated for used other tools, such as DFLOW, nearby, gaged basins (e.g., using SWToolbox) and related Basins, and SWSTAT, to estimate to the discharge location of interest via regression low flow statistics on a gaged equations. stream in the past. EPA and USGS s step -by -step instructions for using This section provide developed SWToolbox to replace while writing permits these applications . This hand book these applications. SWToolbox will use SWToolbox to access and assumes that you incorporates the functionality and download daily flow measurements for USGS gage computational methods used in all stations. However, please note that this information may three legacy applications. also be obtained manually from the NWIS website. For more information on manually loading data sets into SWToolbox and , or to learn about uses of the WREG beyond , please refer to the applications software calculating low flow statistics ’ user manuals. Using SWToolbox to Estimate Low Flow Statistics on a Gaged Waterbody 3.2 to calculate low flow values. The Next, let’s walk through step -by -step instructions u sing SWToolbox general workflow when using SWToolbox is as follows: In SWToolbox, locate the flow monitoring stations identified while investigating the watershed. 1. 2. the flow station data into SWToolbox. Import 3. Define the ca lculations you wish to run. 4. Run the analysis. own computer. The can use to follow along on you , which Illustrations accompany the instructions your the City of Claremont Wastewater illustrations depict the process for calculating a 7Q 10 value for Hampshire, ) using USGS’s nearby Treatment Plant (located at 338 Plains Road , Claremont, N ew 03743 01152500 . Both the permitted outfall and the gage are located on the Sugar Station ID No. River in New Hampshire, as illustrated on the StreamStats screenshot below. 3 1 - Estimating Low Flow Statistics with SWToolbox and WREG

15 OUTFALL Gage No 01152500 Step 1. Open SWToolbox and start a “New Project .” location of the stream gage to Step 2. A map of the United States will appear. Zoom and pan to the No. 01152500 in our example) to estimate flow statistics. (Hint: Add state, Station ID be used ( , and major roads to the map in the left menu to help navigate to the -hand “Legend” county location of interest.) 3 - 2 Estimating Low Flow Statistics with SWToolbox and WREG

16 Click “Select” in the toolbar and click on the drainage basin that includes the stream gage of Step 3. selected hlighted yellow. basin will be hig interest. The Step 4. ” dialog window. Save the map Build New USGS SW Toolbox Project Click “Build” in the “ and then display data layers projection to the default location. The software will download associated with the basin. selected 3 3 - Estimating Low Flow Statistics with SWToolbox and WREG

17 Using zoom and pan, n avigate to the stream gage previously identified in StreamStats. Click Step 5. on the “Identify” button in the toolbar and click on the stream gage to display identifying information. The selected object will be highlighted yellow. Zoom so only the station of inte rest is visible. Step 6. .” A Under the File menu, click “Download Data dialog box will appear to select the data to Alternatively, permit writers download. In the “Regions to Download” can directly specify the gage dropdown menu, select “View Rectangle .” Under station if they already know its “Data Values from US Geographical Service ID number from StreamStats, lect “Daily National Water Information System ,” se and they can download its data Discharge .” Click “Download” at the bottom. by selecting the “Station IDs” option in the “Region to Download” dropdown menu. 3 4 - Estimating Low Flow Statistics with SWToolbox and WREG

18 ,” will appear. In the window, select the station of A new dialog window, “Data Sources Step 7. Then (Hint: This dialog box will label stations according to their station number.) interest. ” under the Analysis menu. Next, select the station Integrated Design Flow (IDF) select “ USGS ” of interest and click “ OK. 3 5 - Estimating Low Flow Statistics with SWToolbox and WREG

19 Step 8. The “Integrated Design Flow” window will appear. Under the “Select Dates” tab, specify “Low” “Flow Condition ” window, the water year in the will be used in the boundaries that /season calculation, and the timespan of data to include in the analysis. For more discussion on what a “water year” is and how it fits into these calculations, please refer to Section 4 , “Frequently Asked Questions. ” –March 31 water year and use all data available from example, we will specify an April 1 For our this station (i.e., Station ID No. 01152500). Step 9. Next, click o . Specify the averaging period of the low -Day, Trend, Frequency” tab n the “N ,” as well as flow statistics of interest (e.g., 1 for 1Q10, 7 for 7Q10) under “Number of Days based estimates). Make sure to leave the recurrence interval (typically 10 for hydrologically the “Logarithmic” toggle selected. to calculate the values of the Click on the “Frequency Grid” or “Frequency Report” buttons selected flow statistics. 3 6 - Estimating Low Flow Statistics with SWToolbox and WREG

20 For this gage location, the 7Q10 flow was estimated at 34.6 cubic feet per second (22.4 million gallons per day [MGD]). You can copy t he data report to the clipboard and save it in the project f ile for future reference on this or subsequent permit reissuances. Step 10. Finally, make any adjustments necessary to account for differences in the locations of the permitted outfall and stream gage. For example, if the outfall is located some distance downstrea m of the gage (as is the case with the Claremon t Wastewater Treatment Plant), would likely the low flow statistic be slightly greater in magnitude at the outfall location than contributing flow to the outfall at the gage location. This is due to the larger area that is location. Conversely, an outfall located upstream of the gage location would have a smaller low flow statistic. If there are no other contributors of flow between the outfall and gage location ( e.g. , other permitted discharges) , and if no ma n-made impoundments or water withdrawal system s are intervening, adjustment roportions (i.e., by multiplying you can make the ule of p using the r gage low flow value by a ratio of the outfall drainage area and the gage drainage area). Th e following equation demonstrates this procedure : 퐴퐴 표표표표표표표표표표표표표표 푄푄 = 푄푄 × 표표표표표표표표표표표표표표 푔푔표표 푔푔푔푔 퐴퐴 푔푔표표 푔푔푔푔 3 7 - Estimating Low Flow Statistics with SWToolbox and WREG

21 : Where = Low flow statistic at outfall location Q outfall Q = Low flow statistic at gage location gage A = Area draining to outfall outfall A = Area draining to gage gage ule of proportions method for adjusting low flow values will provide more In general, the r size. According to accurate results when the two drainage areas are roughly the same Hortness (2006), a good rule of thumb is to apply this method when the rati o between the A is around 0.5 to 1.5. /A gage outfall elineation tool in In the Claremont Wastewater Treatment Plant example, we will use the d StreamStats (refer to Section 2 , Step 7) to estimate the area of the watershed draining to the outfall (272 square m No. 01152500 (269 square miles). iles) and the NWIS page for Station ID Therefore, the 7Q10 estimate for the outfall is given by: 푚푚푚푚푚푚푠푠푠푠 푠푠푠푠푠푠푠푠푠푠푠푠 272 푄푄 × 22 = 푀푀푀푀푀푀 푀푀푀푀푀푀 .4 = 22 .6 표표표표표표표표표표표표표표 269 푠푠푠푠푠푠푠푠푠푠푠푠 푚푚푚푚푚푚푠푠푠푠 If intervening flow sources, impoundments, or withdrawal systems exist, you may need to these sources to better understand how they are likely obtain supplementary data regarding to influence low flows within the waterbody near the discharge. 3.3 to Estimate Low Flow Statistics on a n Ung aged Waterbody Using WREG let’s walk through step -by -step instructions for using WREG to calculate low flow values on Next, ungaged waterbodies. The general workflow when using WREG is as follows: Create input files for use in WREG. 1. 2. Create a WREG project directory with all input files and the WREG executable file . 3. Run WREG and define the variables for the regression analysis. 4. Create regression equations in WREG. 5. Estimate dependent variables for the ungaged basin and enter them into the regression equation to estimate ungaged basin low flow statistics. Regression relationships between basin characteristics and low flow statistics are not plug -and -play tools —once developed , the user should perform diagnostic and quality control evaluations to determine the ac curacy and reliability of the derived models. This hand book section focuse s on the use of the . More in WREG software package -depth discussion of quality control evaluation diagnostics of regression relationships is its scope , but you may find the fo llowing additional resources useful beyond when designing regression models: • Helsel, D.R. , and R. M. Hirsch . 2002. Statistical Methods in Water Resources Techniques of Water (Chapters 9 . U.S. Geological Survey. Resources Investigations –11) https://pubs.usgs.gov/twri/twri4a3/ . • Ries, K.G., J.B. Atkins, P.R. Hummel, M. Gray, R. Dusenbury, M.E. Jennings, W.H. Kirby, H.C. : A The National Streamflow Statistics Program 2007. Riggs, V.B. Sauer, and W.O. Thomas, Jr. 3 8 - Estimating Low Flow Statistics with SWToolbox and WREG

22 Comp uter Program for Estimating Streamflow Statistics for Ungaged Sites . U.S. Geological https://md.water.usgs.gov/publications/tm -4-a6/ Survey. . Stedinger, J ., and G Regional Hydrologic Analysis : 1. Ordinary, Weighted, and • .D. Tasker. 1985. “ ” Water Resources Research 21 Generalized Least Squares Compared. –1432. : 1421 https://doi.org/10.1029/WR021i009p01421 . WREG requires the manual creation of a variety of input files. The WREG user’s manual (Eng et al., 2009) includes detailed instructions for creating these files using Microsoft Excel or text editors, and should refer to this resource for the mechanics of creating the text input files. This hand you book will walk you through calculating the distributional shape parameters and basin characteristics for use in the input files. Illustrations accompany the instructions , which you can use to follow along on your own computer. The illustrations de pict for the City of West Liberty Sewage the process of calculating a 7Q10 value ., West Liberty 52776) , which discharges to Treatment Plant (located at 615 East A St , Iowa, . The creek Wapsinonoc Creek is ungaged near the discharge. Step 1. Using the gages selected, download the station timeseries data from the relevant NWIS websites (which can be accessed through StreamStats) or following the data download procedures for SWToolbox ( Section 3.2 , Steps 1–6). gage stations located in nearby drainage areas For West Liberty’s plant, we will use five (Station ID Nos. 05454090, 05454300, 05454500 , 05455700, and 054 650 00 ). Step 2. WREG requires input files that de scribe site, basin, and flow characteristics for the gage locations of interest, as well as -Pearson Type III distributions shape parameters for the Log fit to the flow data for those locations. In addition, you that may also include two additional files wh en using a weighted least squares or generalized least squares regression method — when using ordinary least squares regression, these optional files are not required. This book will assume the use of a weighted least squares hand tion regression. For more informa on other regression techniques, refer to the WREG user’s manual or to the (Eng et al., 2009) 4. supplementary resources listed both above and in Section 1 (reproduced from the WREG user’s manual) describes the input files needed. Table Table 1. WREG Input Files File Name Description WREG Requir ements SiteInfo.txt Site information and basin characteristics to Always required be used in the regression (the independent variables) Flow characteristics to be used in the Always required FlowChar.txt regression (the dependent variables) LP3G.txt Skew for Log - Pearson Type III distribution Always required LP3K.txt K for Log - Pearson Type III distribution Always required Always required Pearson Type III - LP3s.txt Standard deviation for Log distribution 3 9 - Estimating Low Flow Statistics with SWToolbox and WREG

23 File Name WREG Requir ements Description User - specified weighting matrix Req uired only if the user - UserWLS.txt defined WLS option is selected USGS ########.txt Annual timeseries of flow at streamflow - Required only when using gaging stations the GLS option. When needed, one file is required -gaging for each streamflow station listed in SiteInfo.txt. Tips for Creating Input Files: • The WREG distribution package comes with example input files —try copying the se example input files into the project directory and editing them using Microsoft Excel or another spreadsheet application. This is often easier than creating them from scratch . • Note that the same gage stations must appear in all input files. In addition, WREG presented in the same order in each input file. You expects the stations to be may find it helpful to use your ’s “Sort” function to put the spreadsheet application stations in numeric/alphabetical order in each of the input sheets to ensure consistency. SiteInfo.txt & FlowChar.txt : Consistent with the instructions in the WREG manual, enter the basin information and flow values that you wish to use in the regression analysis. Note that StreamStats is a good resource for information on basin characteristics. For the flow characteristics, make sure to enter the flow statistics that are needed for the ungaged basin (e.g., 7Q10, 1Q10). In the example for the West Liberty Sewage Treatment Plant, information on the basin drainage area, basin length, and mean annual precipitation for each of the gages and for the permitted outfall location are available and were collected from StreamStats. LP3G that define the Log -Pearson .txt, LP3K.txt, and LP3s.txt: These files contain parameters Type III distribution , which was fitted to each gage station ’s flow data when estimating their respective low flow statistics. These parameters are the skew coefficient (entered into LP3G.txt), K values for the distribution (entered into LP3GK.txt), and the standard deviation of the annual timeseries of low flow values (entered into LP3s.txt). Step 3. To estimate the abovementioned shape parameters needed for WREG input files, follow station of interest. flow data for each gage Steps 1 –6 of Section 3.2 to collect and download When presented with the “Data Sources” window, select “USGS Integrated Design Flow OK. (IDF)” under the “Analysis” Menu. Next, select one of the stations of interest and click “ ” 3 10 - Estimating Low Flow Statistics with SWToolbox and WREG

24 Step 4. The “Integrated Design Flow” window will appear. Under the “Select Dates” tab, specify will be used “Low” in the “Flow Condition /season boundaries that ” window, the water year in the calculation, and the timespan of data to include in the analysis. –March 31 water year and use For o ur West Liberty plant example, we will specify an April 1 all data available from this station (i.e., Station ID No. 0545570). Next, click o Step 5. -Day, Trend, Frequency” tab . Specify the averaging period of the low n the “N ,” as well as flow statistics of interest (e.g., 1 for 1Q10, 7 for 7Q10) under “Number of Days based estimates). Make sure to leave the recurrence interval (typically 10 for hydrologically 3 11 - Estimating Low Flow Statistics with SWToolbox and WREG

25 the “Logarithmic” toggle selected. gen Click the “N -Day Timeseries List” to erate an annual timeseries of the estimate of interest (e.g., the lowest seven -day average observed each water year) for export and separate own calculations of distributional shape parameters analysis . This allows you to perform your (N could generate the annual low flow time ote that this is also how you would like. if you series files for use in the generalized least squares technique.) By selecting the “Separate N -Day Plots” toggle and clicking the “Frequency Graph” button , -Pearson Type III curve the Log -fitted to the timeseries data . The you can generate plots with associated skew and standard deviation estimates used in WREG will also appear on the plots. 3 12 - Estimating Low Flow Statistics with SWToolbox and WREG

26 The skew values and standard deviation from the plots may be entered into the input files. To compute the K value, use the statistic’s skew value and exceedance probability with the K- s are table . These value table Error! Bookmark not defined. s found in reproduced from 3 13 - Estimating Low Flow Statistics with SWToolbox and WREG

27 (Interagency Advisory USGS’ Flood Flow Frequency Guidelines for Determining s Bulletin 17B: 2). Committee on Water Data, 198 The exceedance probability can be calculated using the low flow statistics recurrence interval (T) as follows: 1 푃푃푠푠푃푃푃푃 푠푠푃푃 푚푚푚푚푚푚 푃푃푃푃 = 1 − 퐸퐸퐸퐸퐸퐸 푠푠푠푠 퐸퐸푠푠퐸퐸퐸퐸푠푠 푇푇 So, for a 7Q10 statistic that has a recurrence interval of 10, the exceedance probability would d statistic (e.g., 4B3) that has a recurrence interval of 3, the base be 0.9. For a biologically exceedance probability would be 0.67. For Station ID No. 05455700, the skew is 1.6736, and the exceedance probability for the -1 ( 7Q10 low flow is 0.9. Using Table A Error! Bookmark not defined . ), you would interpolate -0.976. to estimate a K value of approximately You should tabulate each of the statistical parameters for each station of interest and enter The screenshot below reproduces the input files for the them into th e appropriate input file. West Liberty Sewage Treatment Plant. Step 6. Next, create a project folder on the computer’s hard drive, and copy and paste the WREG executable file (WREGv1_05.exe) and input files into the folder. Open the WREGv1_05.exe file to start WREG. On the first screen that appears, select the dependent variable of interest (e.g., 7Q10) and the independent variables to be used (press the “Ctrl” key on the keyboard g to select multiple independent variables). Click “OK when clickin .” In this example, the regression relationship will use the basin drainage areas and mean annual precipitation values as the dependent variables. 3 14 - Estimating Low Flow Statistics with SWToolbox and WREG

28 may be appropriate. Step 7. On the next screen, select any variable transformati ons that Transformations can help linearize the regression relationship. Determining which transformations work best may require you to run several iterations of the model to find the In this example, the best model fit occurs without the use of most reasonable model fit. ations (i.e., option “None”) transform . least Step 8. Next, specify the type of regression model to be used. T his example will use weighted squares multiple linear regression. A discussion of the uses of region -of -influence regression and generalized least squares parameter estimation techniques are beyond the scope of this (Eng et al., ; however, you hand book manual are encouraged to review the WREG user’s Once the desired options have been selected, to learn more about these techniques. 2009) .” press “Form Model 3 15 - Estimating Low Flow Statistics with SWToolbox and WREG

29 The final screen, “Regression Summary ,” provides information on the regression model Step 9. 2 e.g., as reflected by the R produced. If the model fit ( value or other statistical and visual ) is poor, consider revising the model (i.e., applying variable transformations diagnostic tests as described in Step 7). 3 16 - Estimating Low Flow Statistics with SWToolbox and WREG

30 to the you should apply Step 10. The equation in the “Regression” window is the regression model ungaged basin’s ungaged basin. Using this equation, enter the independent variables. For the West Liberty plant, we collected the basin drainage area (DRNAREA; 46.6 square hes) from StreamStats using the the mean annual precipitation (PRECIP; 36.11 inc and miles) 2.2 , Step 7). Using these values, we would predict a 7Q10 basin delineation tool (see Section . .6 MGD) 22 cubic feet per second ( value of 34.9 3 17 - Estimating Low Flow Statistics with SWToolbox and WREG

31 4 Frequently Asked Questions 4.1 General Questions My ga ge is far removed from the discharge location but on the same stream or river . What should I do? ule of proportions, the drainage area of the stream gage, and the drainage area of the Use the r discharge location to estimate a flow multiplier to apply to the stream gage flow. Refer to Section 3.2 , Step 11 , for an illustrated example of the use of this technique. Note that you must separately factor intervening elements between the gage station and the discharge location ( e.g., tributaries , impoundmen ts, or other permitted facilities ); the rule of proportions’ transformation of the gage data . will not adequately represent these elements How data are “sufficient” for computing a low flow statistic? many As with any statistical analysis, y ou should consider the representativeness of the data and the quantity of the available data. Representativeness : Does the gage location adequately represent conditions at the discharge location? In addition, pay Generally speaking, the level of proximity indicates greater representativeness. attention to land use patterns rent low flow behavior than a —a highly urbanized basin will have diffe rural or forested basin. : Do the range of years of data available adequately capture variations in climate ove r time Quantity ? Capturing at least 15 to 20 years of data is a good idea . For example , EPA Region 1 permit writers prefer using a 30- year data window to adequately capture variations in climate . However, if notable directional changes in precipitation patterns, wa ter withdrawals or impervious surfaces have occurred during that time period, a more recent subset of available data may be more representative . data Which should I exclude? When computing low flow statistics, you should exclude d ata ha ve known quality issues (e.g., gage that that USGS has indicated is unreliable) or that is not deemed representative of the conditions you data are attempting to model. Should I be worried about outliers in the stream ga ge data? Outliers, or observations that appear unusually large or small within the context of the broader data set, can occur for several reasons: 1) a measurement or recording error, 2) an atypical external event (e.g., a dam break or failure), or 3) a rare event from a single population that is quite skewed. -representative data and should not be included in the Outliers of the first type are an example of non analysis. -by Outliers of the second and third types should be evaluated on a case -case basis to determine if they the are representative of “normal” operations, even if they are rare. An atypical, but recurring system’s 4 1 - Frequently Asked Questions

32 low flow event —say, due to upstream water withdrawals during a drought , whereas —might be included the catastrophic failure of an impoundment structure might be removed from the a flood caused by nt highly unlikely to ever re cur. data set as an unrepresentative eve SWToolbox includes a module for performing statistical analyses to identify unusual values in flow data this module data, refer to the “Outliers” sets, which may be outliers. For more information on using (Kiang, 2018) . section of the SWToolbox user’s manual What should I do if my watershed has man- made modifications (e.g., impoundments or irrigation channels) that will affect low flow values? Man -made modification s often result in the active management of flow regimes that no longer reflect weather driven flow patterns (e.g., some impoundments are operated on a controlled release -event- pattern). You may need to solicit supplementary data from agencies or individual s that manage the impoundments o r diversion programs. Using these supplementary data, you can pre -process the stream gage data to produce flow values that are representative of appropriate low flow conditions at the discharge location. rmit writers and/or permittees be updating the low flow values used in permits? How often should pe In general, the low flow values should be reasonably representative of current climatic conditions. that Climate alterations and patterns often operate on decadal scales, so a value is only 5 years old may while a value that is 25 years old may require revisiting. reasonably representative be own judgement in evaluating When determining whether an update is warranted, you must use your the age and relevance of the underlying da ta that were used to originally develop the low value . When deciding, use StreamStats to examine if any new gages have been added to the basin or any old developed gages taken offline. For example, you may elect to replace an older low flow value that was using regression approaches (e.g., like those in WREG) if direct measurements of sufficient quality and quantity have become available on the stream segment of interest. When calculating low flow values in SWToolbox, what is the difference between specify ing my water year boundaries based on a calendar year, a seasonal boundary, or a portion of a year? , it is a good idea to specify boundaries such that all dry season days fall in the same water Typically year to avoid biasing estimated statistics. SWToolbo x defaults to an April 1 –March 31 water year, but conditions at the permitted outfall of interest may differ from this. In addition, you may be interested in calculating a low flow statistic for a dilution credit that is only – he year. For example, a surface water discharge may only be permitted May applicable for a portion of t October in may want to calculate the low flow statistic that you a particular waterbody. In this case, October for the pertains during the seasonal discharge window and would only use data from May to historical record. 4 2 - Frequently Asked Questions

33 I developed a Basins Characteristics Report using StreamStats to get low flow estimates for a location on an ungaged stream. However, the application produced a report that did not include any estimates. Not all watersheds and regions within the United States currently have low flow regression analyses computed. Low flow regression relationships presented in StreamStats come from original research and analysis developed and reported by USGS. If USGS has pr oduced an equation for your ungaged basin, then you will have the option to include low flow statistic estimates in your Basin Characteristics Report with a citation linking to the original report that published the regression equation. If USGS has not pre viously developed and reported an equation applicable to the basin, you will not have the option to include a low flow estimate. -computed USGS flow statistic regression equations and their For a list of all states with pre s Regional Regression Equation Publications USGS’ e refer to by State corresponding publications, pleas website at: https://water.usgs.gov/osw/programs/nss/NSSpubs_Rural.html When using the pre -calculated watershed regression relationships and low flow statistic estimates presented in StreamStats, where can I find supporting information on the data and methods used in the calculations? How can I determine if it is appropriate t o use the regression relationship or low flow statistic in my permit? All values presented on the StreamStats gage pages (i.e., the pages — —along with the NWIS gage page that can be found by clicking on the gage) will generally have a source or citation acco mpanying them. The citation for a given value will be found in the “Citation Number” column of any given table, and the at the bottom of all StreamStats table of c itations (pictured below) provides links to all cited reports gage webpages. When developi , Step 7), StreamStats will 2.2 ng Basin Characteristics Reports (as described in Section append a table of citations (pictured below) referring the user to the ori ginal reports containing the statistics or watershed regression relationships. 4 3 - Frequently Asked Questions

34 When using statistical values and basin regression relationships in StreamStats, you should take care to evaluate the representativeness of the underlying data used to gener ate the statistic or regression —just as equation own estimates. In some cases, the underlying data (which will be would with your you by StreamStats described in the report cited ) will not be sufficiently representative of the conditions permit - may reject using StreamStats pre DES . The most common reason you relevant to the NP to represent computed estimates is that they are based on underlying data that outdated too are current climatic conditions. 4 4 - Frequently Asked Questions

35 To evaluate the potential usefulness of the pre- calculated information, download the cited report referenced in StreamStats. Review the report while paying particular attention to the data used to You the following : develop the estimates. should consider • report’s stream gages located? Where are the How many data w ere used in the calculation and from what time period do the data originate? • If there are seasonal considerations relevant to the permit, are those appropriately accounted • for in the report? • Are sources of uncertainty or data gaps accounted for in the analysis? • Is the resulting estimate sufficiently accurate and representative to demonstrate its use will be protective of water quality? If the answers to any of these questions indicate that the estimate is not sufficiently repr esentative or protective of water quality, then you should not use the StreamStats estimate for NPDES permit development. Where can I find more information on low flow statistics in and on implementing dilution credits NPDE S permits? For more information on evaluating mixing zones and low flow conditions, please refer to EPA’s NPDES Permit Writer’s Manual and the Technical Support Document: • NPDES Permit Writer’s Manual : https://www.epa.gov/npdes/npdes -permit -manual -writers Technical Support Document: https://www3.epa.gov/npdes/pubs/owm0264.pdf • of low flow frequency analysis, please refer to For more information on the statistical underpinnings USGS’ s Bulletin 17B: https://www.fema.gov/media -library/assets/documents/8403 used in WREG For more information on how to develop and evaluate watershed regression analyses and on hydrologic regression analyses more generally , please refer to the following sources: • Helsel, D.R. , and R. M. Hirsch . 2002. Statistical Methods in Water Resources Techniques of Water –11). U.S. Geological Survey. (Chapters 9 Resources Investigations https://pubs.usgs.gov/twri/twri4a3/ . • Ries, K.G., J.B. Atkins, P.R. Hummel, M. Gray, R. Dusenbury, M.E. Jennings, W.H. Kirby, H.C. Riggs, V.B. Sauer , and W.O. Thomas, Jr. 2007. The National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites . U.S. Geological Survey. s.gov/publications/tm https://md.water.usg -4-a6/ . • Stedinger, J ., and G. D. Tasker. 1985. “ Regional Hydrologic Analysis : 1. Ordinary, Weighted, and –1432. : 1421 21 Generalized Least Squares Compared. ” Water Resources Research https://doi.org/10.1029/WR021i009p01421 . For a list of all states with pre -computed USGS flow statistic regression equations and their publications, please refer to USGS’s Regional Regression Equation Publications by State corresponding : https://water.usgs.gov/osw/programs/nss/NSSpubs_Rural.html website For the StreamStats, SWToolbox, and WREG user manuals, please refer to the following webpages: 4 5 - Frequently Asked Questions

36 StreamStats User Manual: https://water.usgs.gov/osw/streamstats/Version4UserInstructions - • 20170928.pdf SWToolbox User Manual: • https://doi.org/10. 3133/tm4A11 • WREG User Manual: https://pubs.usgs.gov/tm/tm4a8/ Tips 4.2 Troubleshooting I enter ed . a location into the search bar in StreamStats but nothing happens and prompt you You may need to zoom into the map near your l ocation befo re the search will execute reach zoom magnification level 8 at a minimum. Your to tate or regional study area . Try to select a s zoom level is shown in the lower left -hand portion of the screen. I’m trying to install or run SWToolbox and WREG, but I keep getting errors about “read access” and/or . file permissions You may need administrative access to install these applications on your computer. Try installing them your organization’s IT d epartment for using an account with administrative permissions or contacting assistance. 4 6 - Frequently Asked Questions

37 5 References Eng, K ., Y-Y. Chen, and J. Kiang . 2009. User’s Guide to the Weighted- Multiple -Linear -Regression Program version 1.0) (WREG p. : Techniques and Methods 4–A8 . U.S. Geological Survey, 21 p http://pubs.usgs.gov/tm/tm4a8 . Interagency Advisory Committee on Water Data . 1982 . Guidelines for Determining Flood Flow Frequency: Bull etin #17B of the Hydrology Subcommittee . Office of Water Data Coordination, U.S. Geological Survey, Reston, VA, 183 p p. Streams in Idaho: Hortness, J.E. 2006 . Estimating Low -Flow Frequency Statistics for U nregulated Scientific Investigations Report 2006 . U.S. Geological Survey, 31 p p. 35 –50 https://pubs.usgs.gov/sir/2006/5035/pdf/sir20065035.pdf . Kiang, J.E., K.M. Flynn, T. Zhai, P. Hummel, and G. Granato . 2018 . SWToolbox: A S urface -Water Tool -Box Series: Techniques and Methods for Statistical Analysis of Streamflow Time . U.S. Geological 4–A11 Survey p. https://doi.org/10.3133/tm4A11 , 33 p . Ries, K.G., III, J.K. Newson, M.J. Smith, J.D. Thompson, hrie, P.A. Steeves, T.L. Haluska, K.R. Kolb, R.F. Gut Version 4 Sheet StreamStats, . . U.S. Geological Survey R.D. Santoro, and H.W. Vraga. 2017 , Fact p. https://doi.org/10.3133/fs20173046 3046, 4 p 2017– . 5 1 - References

38 Appendix A: K Values Tables -2 partially reproduce “ Tables A B. Appendix 3: Tables of K Values -1 and A ” from Bulletin 17 ositive Table A -1: K V Skew Estimates alues for P Skew Estimate Exceedance 8 7 5 4 3 2 1 0 Probability 9 6 - 0.22222 - 0.25 - 0.28571 - 0.33333 0.999 0.4 - 0.5 - 0.66667 - 0.999 - 1.78572 - 3.09023 - 0.22222 - 0.25 - 0.28571 - 0.33333 - 0.4 - 0.5 - 0.66663 - 0.98995 - 1.58838 - 2.32635 0.99 - - 0.22222 - 0.25 - 0.28571 - 0.33333 - 0.4 - 0.49986 - 0.66023 - 0.89464 - 1.12762 - 1.28155 0.90 0.28571 0.22222 - 0.25 - 0.80 - 0.33333 - 0.39993 - 0.49784 - 0.63569 - 0.77686 - 0.85161 - 0.84162 - 0.48902 - 0.25 - 0.28571 - 0.3333 - 0.39914 - 0.22222 - 0.58783 - 0.64333 - 0.61815 - 0.5244 0.70 - - 0.22222 - 0.25 - 0.28569 - 0.33285 - 0.39482 0.60 - 0.46496 - 0.51073 - 0.48917 - 0.39434 - 0.25335 0.50 - 0.22222 - 0.24996 - 0.28528 - 0.32974 - 0.37901 - 0.41265 - 0.39554 - 0.30685 - 0.16397 0 0.40 - 0.22214 - 0.24933 - 0.28169 - 0.31472 - 0.33336 - 0.31159 - 0.22726 - 0.08371 0.08763 0.25335 0.24214 0.30 - 0.2203 - - 0.25899 - 0.2575 - 0.21843 - 0.1253 0.02279 0.20397 0.38111 0.5244 0.20 0.19338 - 0.18249 - 0.14434 - 0.06662 0.05798 0.22617 0.4204 0.60944 0.75752 0.84162 - 0.23929 0.40026 0.58933 0.79548 1.00079 1.18006 1.30259 1.34039 1.28155 0.10 0.11146 12.04437 11.46855 10.81343 10.06812 9.21961 8.25289 7.15235 5.90776 4.53112 3.09023 0.001 Table A alues for N egative Skew Estimates -2: K V Skew Estimate Exceedance 0 - 1 - 2 - 3 - Probability - 5 - 6 - 7 - 8 - 9 4 0.999 - 3.09023 - 4.53112 - 5.90776 - 7.15235 - 8.25289 - 9.21961 - 10.06812 - 10.81343 - 11.46855 - 12.04437 - 0.99 2.32635 - 3.02256 - 3.60517 - 4.05138 - 4.36777 - 4.57304 - 4.6868 - 4.72613 - 4.70514 - 4.63541 0.90 - 1.28155 - 1.34039 - 1.30259 - 1.18006 - 1.00079 - 0.79548 - 0.58933 - 0.40026 - 0.23929 - 0.11146 0.80 - 0.84162 - 0.75752 - 0.60944 - 0.4204 - 0.22617 - 0.05798 0.06662 0.14434 0.18249 0.19338 0.70 - 0.5244 - 0.38111 - 0.20397 - 0.02279 0.1253 0.21843 0.2575 0.25899 0.24214 0.2203 0.22214 0.24933 0.28169 0.60 - 0.25335 - 0.08763 0.08371 0.22726 0.31159 0.33336 0.31472 A 1 - Appendix A

39 Skew Estimate Exceedance 0 - 1 - 2 - 3 - Probability - 5 - 6 - 7 - 8 - 9 4 0.50 0 0.16397 0.30685 0.39554 0.41265 0.37901 0.32974 0.28528 0.24996 0.22222 0.40 0.25335 0.39434 0.48917 0.51073 0.46496 0.39482 0.33285 0.28569 0.25 0.22222 0.22222 0.30 0.5244 0.25 0.61815 0.64333 0.58783 0.48902 0.39914 0.3333 0.28571 0.84162 0.85161 0.77686 0.63569 0.49784 0.39993 0.33333 0.28571 0.25 0.22222 0.20 0.10 1.28155 1.12762 0.89464 0.66023 0.49986 0.4 0.33333 0.28571 0.25 0.22222 0.22222 0.001 3.09023 1.78572 0.999 0.66667 0.5 0.4 0.33333 0.28571 0.25 A. A 2 - Appendix A