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

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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, conclusions, 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 statutory 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 Environmental, Zak
Erickson, and Anthony D'Angelo.
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Disclaimer	ii
Acknowledgements	ii
1	An Introduction to Low Flow Statistics and This Handbook	1-1
1.1	Who Is the Intended Audience for This Handbook?	1-1
1.2	What Is a Low Flow Statistic?	1-1
1.3	What Topics Does This Handbook Cover?	1-2
1.4	What Software Tools Are Discussed in This Handbook?	1-2
1.5	When Should I Use Each of These Tools?	1-2
2	Investigating the Watershed	2-1
2.1	Introduction	2-1
2.2	Step-by-Step Instructions for Exploring with StreamStats	2-1
3	Estimating Low Flow Statistics with SWToolbox and WREG	3-1
3.1	Introduction	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	Frequently Asked Questions	4-1
4.1	General Questions	4-1
4.2	Troubleshooting Tips	4-6
5	References	5-1
Appendix A: K Values Tables	A-l

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1 An Introduction to Low Flow Statistics and This Handbook
1.1	Who Is the Intended Audience for This Handbook?
National Pollutant Discharge Elimination System (NPDES) permit writers often need to calculate low flow
statistics for reasonable potential analyses and water quality-based effluent limitation (WQBEL)
calculations 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 applications that greatly
simplify this process are available to permit writers. The purpose of this handbook is to help permit
writers estimate low flow statistic values in a variety of situations using these free, publicly available
tools.
1.2	What Is a Low Flow Statistic?
Low flow 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 credits or dilution factors for use in reasonable
potential analyses and/or WQBEL calculations. As described in
Section 3.2 of EPA's Technical Support Document for Water
Quality-based Toxics Control (hereafter, the Technical Support
Document), EPA recommends that authorized dilution credits
reflect the behavior of a permitted discharge as it mixes with the factor to refer to the level of
receiving water. In flowing rivers and streams, dilution credits are dilution authorized in a permit.
based on the critical conditions of the receiving water, which are	For convenience, this
typically defined in the applicable water quality standards (e.g.,	document primarily uses the
7Q10 receiving water flow). Critical conditions are conservatively term "dilution credit," but both
based on receiving water low flow estimates to ensure the	are eqUaUy valid terms
discharge does not cause or contribute to an excursion above		
water quality standards.
Low flow values are defined on a hydrologic design or biological design basis. Both are equally
acceptable for use in NPDES permitting. Low flow values are expressed in terms of their averaging
period (for example, a 4-day average flow or a 7-day average flow) and their recurrence frequency
(generally once in 10 years for hydrologically based flows and once in 3 years for biologically based
flows).
A hydrologically based low flow is computed using the single lowest flow event from each year of
record, followed by application of distributional models (typically the Log Pearson Type III distribution is
assumed) to infer the low flow value. The 1Q10 is the lowest one-day average flow that occurs (on
average) once every 10 years. The 7Q10 is the lowest 7-day average flow that occurs (on average) once
every 10 years.
A biologically based low flow is computed based on all low flow events within a period of record, even if
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-day average flow that occurs once every three years. The
1B3 is the lowest one-day average flow that occurs once every three years.
An Introduction to Low Flow Statistics

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1.3	What Topics Does This Handbook Cover?
Section 2: Investigate the Watershed—Are there stream gages in the watershed of interest? Where are
they and are they useful to the permit writer? This section will provide the permit writer with strategies
for finding and evaluating appropriate streamflow data sources using the StreamStats web application.
Section 3: Estimating Low Flow Statistics with SWToolbox and WREG—After exploring the watershed
and identifying the available data sources, this section will guide permit writers with tips for loading data
and managing settings to obtain the low flow estimates needed for NPDES permit development.
Section 4: Frequently Asked Questions—This section will answer some questions that arise frequently
when permit writers estimate low flow statistics.
1.4	What Software Tools Are Discussed in This Handbook?
This handbook will discuss three pieces of software: StreamStats, SWToolbox, and WREG. The U.S.
Geological Survey (USGS) distributes all three of these publicly available tools on the web.
StreamStats
StreamStats (version 4) is a web application that provides access to an assortment of geographic
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
application can be accessed at: https://water.usgs.gov/osw/streamstats/
SWToolbox
SWToolbox is a desktop application that builds upon past tools, such as SWSTAT and DFLOW, which
permit writers have historically used to estimate low flow statistics from stream gage data. SWToolbox
allows users to compute n-day frequency analyses (i.e., 1Q10 or 7Q10) and biologically based flows. It
also facilitates the use of USGS National Water Information System (NWIS) streamflow data, as well as
user-provided data files. The SWToolbox desktop application can be downloaded at:
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
regional estimation equation results from a multiple-linear regression that relates observable basin
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 Use Each of These Tools?
When deciding which of these tools to use and when to use them, you should consider:
•	The specific need you are attempting to address.
•	The data and information available to you.
•	The uses of the tools at your disposal.
An Introduction to Low Flow Statistics
IB

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Figure 1 displays a decision tree flowchart to help you evaluate these questions and pick the right tool
for the job.
State the
Problem
Identify: (1)the discharge
location of interest, and (2) the
critical low flow statistics
needed by the permit writer
Explore the
Watershed
Using Stream Stats or a similar
tool, explore the drainage area
where the discharge is
occurring. Identify points of
interest, like USGS stream
gages, impoundments, and
tributary flows to the waterbody
of interest.
Decision Point
If stream gages are present on
the stream or river of interest
with sufficient data to support
an estimation of the low flow
statistics needed for the
permit, select SWToolboxfor
use and proceed to Step 4.
If stream gages are not
available on the waterbody but
other nearby watersheds are
gaged, proceed to Step 5.
Ungaged Basins
When the waterbody of interest is ungaged,
the permit writer should consider
developing a regression relationship
between the basin of interest and other
nearby watersheds which are gaged.
For some basins, Stream Stats may have
pre-computed regression relationships
(Step 6}which the permit writer may use.
Otherwise, the permit writer should use
WREG to estimate low flow values (Step 7).
SWToolbox
Using SWToolbox and its GIS interface,
locate and download streamflow data
from the USGS station which best
reflects flow conditions at the permitted
discharge location. Then use the
software to calculate the critical low flow
statistics of interest.
StreamStats
Use StreamStats for basins with pre-computed
watershed regression relationships. The permit
writer can identify basins with regression
relationships within StreamStats.
WREG
Use WREG for basins without pre-computed
watershed regression relationships on ungaged
waterbodies.
Figure 1. A decision tree for evaluating which tool to use when calculating low flow statistics,
An Introduction to Low Flow Statistics
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2 Investigating the Watershed
2.1	Introduction
Your first step when estimating low flow statistics during the permit writing process is to take stock of
the character and quantity of information available to you. You should identify the following pieces of
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.
Several tools are available to help locate USGS flow gages and explore the watershed. The principal tool
discussed in this section is USGS's StreamStats web application. However, you may also find the
following alternative resources useful:
•	USGS's NWIS website provides direct links to a variety of USGS monitoring sites—including
streamflow gages—through a searchable map interface 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 the NWIS website, but also provides additional mapping
and drainage area delineation tools that may be useful. You can access StreamStats online at
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. Illustrations accompany the instructions, which you can use to follow along
on your own computer. The illustrations depict the process of locating potential stream gages for the
Cookeville Wastewater Treatment Plant located at 1870 South Jefferson Ave., Cookeville, Tennessee.
The plant discharges to Pigeon Roost Creek, which is a tributary to the Falling Water River.
Investigating the Watershed
19

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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" that is presented in the search window.
If an appropriate option does not appear, you should revisit the location information used in
the search and verify its accuracy, or try using different search information.
iUSGS
StreamStats
SELECT A STATE / REGION >
Step 2: You have zoomed in sufficiently to
select a state or regional study area. Your
selection will dictate the data used to
perform basin delineation and flow
statistics calculation.
Click to select a State or Regional Study Area
o
O
Missouri St Louis	0
Kentucky
) 8
Ml Exploration Tools
0W°
# Paducah
¦ Report O About ? Help
KENTUC
Campbellsville
Bowling Green,
Hop kins ville
Murray
Clarksville
Nashville*
.Gallatin
Lebanon
Cookeville
TENNESSEE
Zoom Level: 8
Map Scale: 1:2,311,162
Lat: 37.0727, Lon: -85.4022
'30 km
Murfreesboro
Columbia
North Carolin
Virginia
Tennessee
Step 3. Navigate to the discharge location of interest and zoom in until the stream network data
layer (i.e., a pixelated, blue tracing of the local stream) appears.
investigating the Watershed
2-2

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Step 4,
Click the "Delineate" button on the left-hand toolbar, then click on the discharge location
within the waterbody. After processing for several moments, StreamStats will display the
upstream portion of the basin network that drains to the discharge location.
USGS
StreamStats
B Exploration Tools
Mckinley St
Horace i,
Zoom Level: 15
9 Delineate
IDENTIFY A STUDY AREA >
Map Scale: 1:18,055
Lat: 36.1073, Lon: -85.4938
, v
300 m 1
Tennessee O
Step 3: Use your mouse or finger to click
or tap a blue stream cell on the map
Step 5. Using the map interface, explore nearby locations
upstream and downstream of the discharge for
streamflow gages. If gages are unavailable,
examine nearby watersheds that are similar to the
drainage area into which the permitted outfall
discharges.
After identifying relevant stations, click on their
icons to find links to their NWIS and StreamStats
pages.
StreamStats will present different
sites using various colors to
denote useful information for
each gage station. Expand the
"National Layers" button in the
legend to show an expanded
legend explaining each symbol
used in the map.
POWERED BY WIM
USGS Home Contact USGS Search USGS
Accessibility FOIA Privacy Policy &
Notices
Investigating the Watershed
2-3

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StreamStats
¦ Report O About ? Help
B Exploration Tools
Tennessee 0
IDENTIFY A STUDY AREA
Basin Delineated >
Step 5: Your delineation is complete. You
can now clear, edit, or download your
basin, or choose a state or regional study
specific function (if available). Click
continue when you are ready.
Of Edit Basin
£ Download Basin"
or

Lee se^J1? R
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Step 7. Before leaving StreamStats, you should return to the discharge location's delineation and
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.
USGS
StreamStats
Tennessee O
IDENTIFY A STUDY AREA
Basin Delineated >
Step 5: Your delineation is complete. You
can now clear, edit, or download your
basin, or choose a state or regional study
specific function (if available). Click
continue when you are ready.
® Clear Basin
JL Download Basins
Exploration Tools
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3 Estimating Low Flow Statistics with SWToolbox and WREG
3.1	Introduction
In this section, we will discuss how to use SWToolbox and WREG to estimate low flow statistics. As
discussed in Sections 1 and 2, you would use SWToolbox for situations where the permittee's outfall
location and a stream gage are on the same stretch of a
stream or river. WREG is typically used when it is not
possible to directly measure the waterbody's low flow
statistics. Instead, low flow statistics are calculated for
nearby, gaged basins (e.g., using SWToolbox) and related
to the discharge location of interest via regression
equations.
This section provides step-by-step instructions for using
these applications while writing permits. This handbook
assumes that you will use SWToolbox to access and
download daily flow measurements for USGS gage
stations. However, please note that this information may
also be obtained manually from the NWIS website. For
more information on manually loading data sets into
SWToolbox and WREG, or to learn about uses of the
software beyond calculating low flow statistics, please refer to the applications' user manuals.
3.2	Using SWToolbox to Estimate Low Flow Statistics on a Gaged Waterbody
Next, let's walk through step-by-step instructions using SWToolbox to calculate low flow values. The
general workflow when using SWToolbox is as follows:
1.	In SWToolbox, locate the flow monitoring stations identified while investigating the watershed.
2.	Import the flow station data into SWToolbox.
3.	Define the calculations you wish to run.
4.	Run the analysis.
Illustrations accompany the instructions, which you can use to follow along on your own computer. The
illustrations depict the process for calculating a 7Q10 value for the City of Claremont Wastewater
Treatment Plant (located at 338 Plains Road, Claremont, New Hampshire, 03743) using USGS's nearby
Station ID No. 01152500. Both the permitted outfall and the gage are located on the Sugar River in New
Hampshire, as illustrated on the StreamStats screenshot below.
Some experienced readers will have
used other tools, such as DFLOW,
Basins, and SWSTAT, to estimate
low flow statistics on a gaged
stream in the past. EPA and USGS
developed SWToolbox to replace
these applications. SWToolbox
incorporates the functionality and
computational methods used in all
three legacy applications.
Estimating Low Flow Statistics with SWToolbox and WREG
n
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USGS
StreamStats
I Report O About ? Help
Exploration Tools
Zoom Level: 13
I. ,
OUTFALL
~

&
Base Maps
>/ NH Map Layers
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Step 3,
Click "Select" in the toolbar arid click on the drainage basin that includes the stream gage of
interest. The selected basin will be highlighted yellow.
USGS SW Toolbox 1.0.2 - national*	— ~
e Analysis Compute Layer View Bookmarks Plug-ins Shapefile Editor Converters Help
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Select
Deselect Measure Identify
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0D Counties	~
~ Reference
SD Major Roads ^
fVl unnamed ~ I X: -8.332.690.889 Y: 5.492 200,129 Meters Lafc 44.173 Long: -74.854
1:2877436
Preview Map
Step 4. Click "Build" in the "Build New USGS SW Toolbox Project" dialog window. Save the map
projection to the default location. The software will download and then display data layers
associated with the selected basin.
4 Build New USGS SW Too I box 1.0.2 Project
To Build a New USGS SW Toolbox 1.0.2 Project, zoom/pan to your geographic
area of interest, select (highlight) it, and then click 'Build'.
If your area is outside the USA or you do not want to use the map, click 'Build' with
no features selected to create an empty project.
Selected Features:
010801D4 : Upper Connecticut-Mascoma. New Hampshire, Vermon
Build
Cancel
Estimating Low Flow Statistics with SWToolbox and WREG
3-3
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Step 5, Using zoom and pan, navigate to the stream gage previously identified in StreamStats. Click
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
interest is visible.
USGS SW Toolbox 1.0.2 - 01080104'
File Analysis Compute Layer
J <1 & s 9
New Open Save Print Settings
View Bookmarks Plug-ins Shapefile Editor Converters Help
La La Lq
Add Remove Clear
m,
;«¦ Q [ft?
Select Deselect Measure
O
Identify
Preview Map

Symbology Categories Query Properties Table
. J® H P & *< it IS	Q • • 
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/ \Q la <£b shp shp	j ®
Next Layer New Insert Add Remove Copy Paste Merge Erase Erase beneath Move Rotate
Legend	J?
Layers Toolbox
Hydrology
~ 0 National Hydrography Dat
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0 ~ Accounting Unit Boundarie
0@ Cataloging Unit Boundarie
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Preview Map
unnamed ~ | X: 1,879,769.328 Y: 2,506,579.840 Meters Lat: 43.444 Long: -72.428
Region to Download View Rectangle	v
BASINS
~	Met Stations ~ GIRAS Land Use ~ NHD ~ DEM Grid
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~	All O Bevation Grid	Q Catchments	O Hydrography
Station Locations from US Geological Survey National Water Information System
I I Discharge O Water Quality O Measurements O Daily GW O Periodic
Data Values from US Geological Survey National Water Information System
0	Daily Discharge I	I Water Quality I	j Measurements
1	I Instantaneous Discharge
National Land Cover Data from National Map
I I 2011 Land Cover Q 2006 Land Cover O 2001 Land Cover Q 1992 Land Cover
I I 2011 Impervious O 2006 Impervious O 2001 Impervious O 2001 Canopy
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3 (available when
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I I Grid	]	| Hourly Data (available V
O Clip to Region Q Get Newest
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Help
Step 7. A new dialog window, "Data Sources," will appear. In the window, select the station of
interest. (Hint: This dialog box will label stations according to their station number.) Then
select "USGS Integrated Design Flow (IDF)" under the Analysis menu. Next, select the station
of interest and click "OK."
Data Sources
File Analysts Help
EI-USGS RDB
j C:\USGS-SWldsta\Q10801MNWlS\NWS_discharge_Q114180Q.rdb (1)
I ¦C:\USGS-SMdata\Q108Q1Q4\NWIS\NWIS_discharge_Qll5150Q.rdb (1)
I CAUSGS-SWfteta\010S01O4\NWIS\NWIS_discharge_0i144500.rdb (1)
~ X
:\USGS-SW\data\D10801{M\NWlSNMS_dischar9e_0115250ardb [1)
Timeseries::USGS RDB
C:\USG S-SW'.data\01080104\NWIS\NWIS_discharge_01152500.ndb
1 Timeseries
1.033,048 bytes
Modified 4/22/2013 4:12:15 PM
Estimating Low Flow Statistics with SWToolbox and WREG
3-5
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Step 8. The "Integrated Design Flow" window will appear. Under the "Select Dates" tab, specify "Low"
in the "Flow Condition" window, the water year/season boundaries that will be used in the
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."
For our example, we will specify an April 1-March 31 water year and use all data available from
this station (i.e., Station ID No. 01152500).
^ Integrated Design Flow	— ~ X
File Analysis Help
Select Dates N-Day. Trend. Frequency Design Row Group Outlier Test
Row Condition
O High
® Low
Year / Season Boundaries
Start
foril	~s7| | t |
End j March Z] [IT]
Years to Include in toalysis
O All: 1328/05/25to 2018/02/23
(§> Common: 1928/05/25to 2018/02/23
O Custom:
Start Tear 1928 Data Starts 1928/
End Year 2018 Data Bids 2018/1
Display Basic Statistics
Step 9. Next, click on the "N-Day, Trend, Frequency" tab. Specify the averaging period of the low
flow statistics of interest (e.g., 1 for 1Q10, 7 for 7Q10) under "Number of Days," as well as
the recurrence interval (typically 10 for hydrologically based estimates). Make sure to leave
the "Logarithmic" toggle selected.
Click on the "Frequency Grid" or "Frequency Report" buttons to calculate the values of the
selected flow statistics.
Estimating Low Flow Statistics with SWToolbox and WREG
3-6
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^5 integrated Design Flow	—
File Analysis Help
Select Dates N-Day. Trend. Frequency Design Row Group OutSer Tesi
Number of Days	Recurrence Interval
Derai !
P*
0 Logarithmic
N-Day Timeseiies List
Trend List
Screening Tests (R)
None
1.0001
1.0005
1.001
1.002
1.005
1.0101
1.0204
1	0256
1.0417
1.0526
1.1111
125
1.5
2
3
3 333
5
EG
20
25
40
50
Default
None
Frequency Grid
Frequency Report
Frequency Graph
0 Separate N-Day Plots
0 Separate Station Plots
For this gage location, the 7Q.10 flow was estimated at 34.6 cubic feet per second
(22.4 million gallons per day [MGD]). You can copy the data report to the clipboard and save
it in the project file 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
downstream of the gage (as is the case with the Claremont Wastewater Treatment Plant),
the low flow statistic would likely be slightly greater in magnitude at the outfall location than
at the gage location. This is due to the larger area that is contributing flow to the outfall
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 man-made impoundments or water withdrawal systems are
intervening, you can make the adjustment using the rule of proportions (i.e., by multiplying
gage low flow value by a ratio of the outfall drainage area and the gage drainage area). The
following equation demonstrates this procedure:
A
Qoutfall " Qgcige * a
/l
outfall
QQ.Q6
Estimating Low Flow Statistics with SWToolbox and WREG
m
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Where:
Qoutfaii	= Low flow statistic at outfall location
Qgage	= Low flow statistic at gage location
Aoutfaii	= Area draining to outfall
Agage	= Area draining to gage
In general, the rule of proportions method for adjusting low flow values will provide more
accurate results when the two drainage areas are roughly the same size. According to
Hortness (2006), a good rule of thumb is to apply this method when the ratio between the
Aoutfaii/Agage is around 0.5 to 1.5.
In the Claremont Wastewater Treatment Plant example, we will use the delineation tool in
StreamStats (refer to Section 2, Step 7) to estimate the area of the watershed draining to the
outfall (272 square miles) and the NWIS page for Station ID No. 01152500 (269 square miles).
Therefore, the 7Q10 estimate for the outfall is given by:
If intervening flow sources, impoundments, or withdrawal systems exist, you may need to
obtain supplementary data regarding these sources to better understand how they are likely
to influence low flows within the waterbody near the discharge.
3.3 Using WREG to Estimate Low Flow Statistics on an Ungaged Waterbody
Next, let's walk through step-by-step instructions for using WREG to calculate low flow values on
ungaged waterbodies. The general workflow when using WREG is as follows:
1.	Create input files for use in WREG.
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 accuracy and reliability of the derived models. This handbook section focuses on the use of the
WREG software package. More in-depth discussion of quality control evaluation diagnostics of
regression relationships is beyond its scope, but you may find the following additional resources useful
when designing regression models:
•	Helsel, D.R., and R. M. Hirsch. 2002. Statistical Methods in Water Resources Techniques of Water
Resources Investigations (Chapters 9-11). U.S. Geological Survey.
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
Estimating Low Flow Statistics with SWToolbox and WREG
Qoutfaii ~ 22AMGD X
272 square miles
= 22.6 MGD
269 square miles
-------
Computer Program for Estimating Streamflow Statistics for Ungaged Sites. U.S. Geological
Survey, https://md.water.usgs.gov/publications/tm-4-a6/.
• Stedinger, J., and G.D. Tasker. 1985. "Regional Hydrologic Analysis: 1. Ordinary, Weighted, and
Generalized Least Squares Compared." Water Resources Research 21: 1421-1432.
https://doi.org/10.1029/WR021i009pQ1421.
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
you should refer to this resource for the mechanics of creating the text input files. This handbook
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 depict the process of calculating a 7Q10 value for the City of West Liberty Sewage
Treatment Plant (located at 615 East A St., West Liberty, Iowa, 52776), which discharges to
Wapsinonoc Creek. The 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).
For West Liberty's plant, we will use five gage stations located in nearby drainage areas
(Station ID Nos. 05454090, 05454300, 05454500, 05455700, and 05465000).
Step 2. WREG requires input files that describe site, basin, and flow characteristics for the gage
locations of interest, as well as shape parameters for the Log-Pearson Type III distributions
that fit to the flow data for those locations. In addition, you may also include two additional
files when using a weighted least squares or generalized least squares regression method—
when using ordinary least squares regression, these optional files are not required. This
handbook will assume the use of a weighted least squares regression. For more information
on other regression techniques, refer to the WREG user's manual (Eng et al., 2009) or to the
supplementary resources listed both above and in Section 4.
Table 1 (reproduced from the WREG user's manual) describes the input files needed.
Table 1. WREG Input Files
File Name
Description
WREG Requirements
Sitelnfo.txt
Site information and basin characteristics to
be used in the regression (the independent
variables)
Always required
FlowChar.txt
Flow characteristics to be used in the
regression (the dependent variables)
Always required
LP3G.txt
Skew for Log-Pearson Type III distribution
Always required
LP3K.txt
K for Log-Pearson Type III distribution
Always required
LP3s.txt
Standard deviation for Log-Pearson Type III
distribution
Always required
Estimating Low Flow Statistics with SWToolbox and WREG
3-9
-------
File Name
Description
WREG Requirements
UserWLS.txt
User-specified weighting matrix
Required only if the user-


defined WLS option is


selected
USGS########.txt
Annual timeseries of flow at streamflow-
gaging stations
Required only when using
the GLS option. When
needed, one file is required
for each streamflow-gaging
station listed in Sitelnfo.txt.
Tips for Creating Input Files:
•	The WREG distribution package comes with example input files—try copying these
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
expects the stations to be presented in the same order in each input file. You may
find it helpful to use your spreadsheet application's "Sort" function to put the
stations in numeric/alphabetical order in each of the input sheets to ensure
consistency.
Sitelnfo.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.txt. LP3K.txt. and LP3s.txt: These files contain parameters that define the Log-Pearson
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
Steps 1-6 of Section 3.2 to collect and download flow data for each gage station of interest.
When presented with the "Data Sources" window, select "USGS Integrated Design Flow
(IDF)" under the "Analysis" Menu. Next, select one of the stations of interest and click "OK."
Estimating Low Flow Statistics with SWToolbox and WREG
3-10
-------
Data Sources
~
File
B--USC
Analysis Help
Seasonal Attributes
Graph
USGS Surface Water Statistics (SWSTAT)::Duration/Compare
USGS Integrated Design Flow (IDF)
DFLOW
Timeseries::USGS RDB
C:\USGS-SWVJala\07030206\NWIS\NWIS_discharge_05455700.rdb
1 Timeseries
720.989 bytes
Modified 4/2272018 6:44:13 PM
Step 4. The "Integrated Design Flow" window will appear. Under the "Select Dates" tab, specify
"Low" in the "Flow Condition" window, the water year/season boundaries that will be used
in the calculation, and the timespan of data to include in the analysis.
For our West Liberty plant example, we will specify an April 1-March 31 water year and use
all data available from this station (i.e., Station ID No. 0545570).
^ Integrated Design Flow	— ~ X
File Analysis Help
Select Dates N-Day, Trend, Frequency Design Row Group Outlier Test
Row Condition
O High
(§) Low
Year / Season Boundaries
1 April
Hh

| March
v 11311
Years to Include in Analysis
O All: 1956/10/01 to 2018/02/28
® Common: 1956/10/01 to 2018/02/28
O Custom:
Start Year 11956 Data Starts 1956/10/01
End Year 2018 Data Ends 2018/02/28
Display Basic Statistics
Step 5. Next, click on the "N-Day, Trend, Frequency" tab. Specify the averaging period of the low
flow statistics of interest (e.g., 1 for 1Q10, 7 for 7Q10) under "Number of Days," as well as
the recurrence interval (typically 10 for hydrologically based estimates). Make sure to leave
Estimating Low Flow Statistics with SWToolbox and WREG
3-11
-------
the "Logarithmic" toggle selected.
Click the "N-Day Timeseries List" to generate an annual timeseries of the estimate of interest
(e.g., the lowest seven-day average observed each water year) for export and separate
analysis. This allows you to perform your own calculations of distributional shape parameters
if you would like. (Note that this is also how you could generate the annual low flow time
series files for use in the generalized least squares technique.)
^ ntegrated Design Flow	—
File Analysis Help
Select Dates N-Day. Trend. Frequency Design Row Group Outlier Test
Number of Days	Recurrence Interval
1 -C.5
1.0204
1 325G
.04 7
1:5:s
i.iiii
Defauft
Default
None
None
N-Day Timeseries List
Trend List
Screening Tests (R)
Frequency Grid
Frequency Report
Frequency Graph
0 Separate N-Day Rots
f~1 Separate Nation Rots
By selecting the "Separate N-Day Plots" toggle and clicking the "Frequency Graph" button,
you can generate plots with the Log-Pearson Type III curve-fitted to the timeseries data. The
associated skew and standard deviation estimates used in WREG will also appear on the
plots.
Estimating Low Flow Statistics with SWToolbox and WREG
3-12
-------
^ ntegrated Design Flow	—
File Analysis Help
Select Dates N-Day. Trend. Frequency Design Row Group Outlier Tesi
Number of Days	Recurrence Interval
X
Default
0 Logarithmic
N-Day Timeseries List
Trend List
Screening Tests (R)
c
1.0001
1 0005
1.001
1 002
1.005
1 0101
1 0204
1.0256
1.0417
1 0526
1	1111
1.25
1.5
2
3
3333
5	
H
20
25
40
50
Frequency Grid
Frequency Report
Default
None
Frequency Graph
0	Separate N-Day Rots
1	I Separate Station Plots

^ requency Graph
File Edit View Analysis Coordinates Help
10,000
o Yearly Observed L007
V-— Log-Pearson Type III Frequency
—'V- Upper Confidence Limit
.Lower Confidence Limit
o
<
<
X
o
1,000
100
5WSTAT5.0 run 2018-04-23
Standard Deviation: 448.37
Skew: 1.6736
ANNUAL NON-EXCEEDANCE PROBABILITY, PERCENT
Station - 05455700 - Iowa River near Lone Tree, IA
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-
value tables found in Error! Bookmark not defined.. These tables are reproduced from
Estimating Low Flow Statistics with SWToolbox and WREG
3-13
-------
USGS's Bulletin 17B: Guidelines for Determining Flood Flow Frequency (Interagency Advisory
Committee on Water Data, 1982).
The exceedance probability can be calculated using the low flow statistics recurrence interval
(T) as follows:
1
Exceedance Probability = 1 — —
So, for a 7Q10 statistic that has a recurrence interval of 10, the exceedance probability would
be 0.9. For a biologically based statistic (e.g., 4B3) that has a recurrence interval of 3, the
exceedance probability would be 0.67.
For Station ID No. 05455700, the skew is 1.6736, and the exceedance probability for the
7Q10 low flow is 0.9. Using Table A-l (Error! Bookmark not defined.), you would interpolate
to estimate a K value of approximately -0.976.
You should tabulate each of the statistical parameters for each station of interest and enter
them into the appropriate input file. The screenshot below reproduces the input files for the
West Liberty Sewage Treatment Plant.
FlowChar.txt - No... — ~
X 1
LP3G.txt - Notepad


~ X I
1 LP3s.txt - Notepac
i
~
X
LP3K.txt - Notepad —
~ X
File Edit Format View Help

File Edit
Format View Help


File Edit
Format
View Help


File Edit
Format View Help

Station ID 7Q10 1Q10
a
Station
ID
skew7Q10

skewlQ10
Station
ID
S-7Q10 s
-1Q10

Station
ID K7Q10 K1Q10
A
5454090 1.1101 0.89327

5454090
0.69392
0.98421


5454090
1.1243
1.0367


5454090
-1.184 -1.13069905

5454300 0.80843 0.55451

5454300
1.9225
1.9388


5454300
9.1067
7.5833


5454300
-1.2145 -1.218721624

5454500 75.991 58.127

5454500
2.2501
2.2523


5454500
277.16
226.25


5454500
-0.8317 -0.83118161

5455700 141.71 128.36

5455700
1.6736
1.6718


5455700
448.37
392.2


5455700
-0.9762 -0.9766

5465000 553.68 466.56

5465000
1.703
1.271


5465000
751.5
644.87


5465000
-0.969 -1.0705

JH Sitelnfo.txt - Notepad












-
~ X
File Edit Format View Help














Station ID Lat Long
No.
Annual
Series
Zero-1;
NonZero-2
FreqZero
Regional Skew
Cont-ljPR-2
DRNAREA PRECIP DRNLENGTH
BFI
5454090 41.7003 -91.5627
10
2
0
-99.99
1
8.58
36.15
5.16
0.491371





5454300 41.677 -91.599
63
2
0
-99.99
1
98.1
35.77

0.386|





5454500 41.9688 -91.4873
112 2
0
-99.99
1
25.2
36.25
7.59
0.50654





5455700 41.423 -91.478
60
2
0
-99.99
1
4293
34.99
196.89
0.521539





5465000 41.409 -91.29
77
2
0
-99.99
1
7787
34.45
228.97
0.560702





Step 6. Next, create a project folder on the computer's hard drive, and copy and paste the WREG
executable file (WREGvl_05.exe) and input files into the folder. Open the WREGvl_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
when clicking to select multiple independent variables). Click "OK."
In this example, the regression relationship will use the basin drainage areas and mean
annual precipitation values as the dependent variables.
Estimating Low Flow Statistics with SWToolbox and WREG
3-14
-------
-> WREG ver 1.0 - Select Variables
Dependent Variables:

Independent Variables:


7Q10

DRNAREA
*


1Q10

PRECIP
DRNLENGTH
BFI







OK

V


V

Select only 1

Select no more than 5


Hold 'Ctrf to select more than one variable


Press 'Alt' + 'PmtScrn' to obtain screen capture ^ USGS
MAHAB(R) (c) 1984-2007 The UathWorts. Inc.
Step 7. On the next screen, select any variable transformations that may be appropriate.
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
most reasonable model fit. In this example, the best model fit occurs without the use of
transformations (i.e., option "None").
j-^ ]WREG ver 1.0 - Variable Transformation	— ~ X
Var
None
iog,„[-l
ln[—]
el 1
[(C1 *(Var)c2+C3)C4]
Dependent




C1
C2
C3
C4
7Q10

o
O
O
1
1
0
1
Independent








DRNAREA

0
o
Q
1
1
0
1
PRECIP

o
o
O
1
1
0
1
Press 'Alt' + 'PmtScrn' to obtain screen capture.	O K J	rusGS
Step 8. Next, specify the type of regression model to be used. This example will use weighted least
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
handbook; however, you are encouraged to review the WREG user's manual (Eng et al.,
2009) to learn more about these techniques. Once the desired options have been selected,
press "Form Model."
Estimating Low Flow Statistics with SWToolbox and WREG
3-15
-------
WREG ver 1.0 - Model Selection — D
X




Regressions


©Multiple-Linear Regression


o Region-of-lnfluence Regression



@ PRol



C GRol



. HRol Geographic Proximity (km): 250



No. of Sites: [ 10



Parameter Estimation


O Ordinary-Least Squares


®Weighted-Least Squares


o Generalized-Least Squares



Summary of Selected Values




Correlation Function Uncertainty in Skew




Concurrent Years: 30 Off Peak Flow




a 0.01 T-Year: 100




9 0.98 MSE(Gr): 0.302



o User Specified Weights

Press Alt + PrntScrn to obtain | c ., . ,
Form Model
screen capture- *UoUj
iiWjuy rwAf
Step 9. The final screen, "Regression Summary/' provides information on the regression model
produced. If the model fit (e.g., as reflected by the R2 value or other statistical and visual
diagnostic tests) is poor, consider revising the model (i.e., applying variable transformations
as described in Step 7).
Estimating Low Flow Statistics with SWToolbox and WREG
3-16
-------
WREG ver 1.0 - Regression Summary
Regression Summary
Performance Metrics:

sp (%> =
Inf
Pseudo R2 =
89.77
Standard Model Error (%) =
Inf
Regression:
(1.00*(7Q10)1°°+0.00)1 00 = -10352.09
+0.123*(1.00*(DRNAREA)1 00+0.00)lo°
+287.491*(1.00*(PRECIP)1'00+0.00)1 00
Press 'Alt' + 'PrntScrn' to obtain
screen capture.
Close
iUSGS
Step 10. The equation in the "Regression" window is the regression model you should apply to the
ungaged basin. Using this equation, enter the ungaged basin's independent variables.
For the West Liberty plant, we collected the basin drainage area (DRNAREA; 46.6 square
miles) and the mean annual precipitation (PRECIP; 36.11 inches) from StreamStats using the
basin delineation tool (see Section 2.2, Step 7). Using these values, we would predict a 7Q10
value of 34.9 cubic feet per second (22.6 MGD).
Estimating Low Flow Statistics with SWToolbox and WREG
3-17
-------
4 Frequently Asked Questions
4.1 General Questions
My gage is far removed from the discharge location but on the same stream or river. What should I
do?
Use the rule of proportions, the drainage area of the stream gage, and the drainage area of the
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,
impoundments, or other permitted facilities); the rule of proportions' transformation of the gage data
will not adequately represent these elements.
How many data are "sufficient" for computing a low flow statistic?
As with any statistical analysis, you 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?
Generally speaking, the level of proximity indicates greater representativeness. In addition, pay
attention to land use patterns—a highly urbanized basin will have different low flow behavior than a
rural or forested basin.
Quantity: Do the range of years of data available adequately capture variations in climate over time?
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, water withdrawals or impervious surfaces have occurred during that
time period, a more recent subset of available data may be more representative.
Which data should I exclude?
When computing low flow statistics, you should exclude data that have known quality issues (e.g., gage
data that USGS has indicated is unreliable) or that is not deemed representative of the conditions you
are attempting to model.
Should I be worried about outliers in the stream gage 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.
Outliers of the first type are an example of non-representative data and should not be included in the
analysis.
Outliers of the second and third types should be evaluated on a case-by-case basis to determine if they
are representative of the system's "normal" operations, even if they are rare. An atypical, but recurring
Frequently Asked Questions
-------
low flow event—say, due to upstream water withdrawals during a drought—might be included, whereas
a flood caused by the catastrophic failure of an impoundment structure might be removed from the
data set as an unrepresentative event highly unlikely to ever recur.
SWToolbox includes a module for performing statistical analyses to identify unusual values in flow data
sets, which may be outliers. For more information on using this module data, refer to the "Outliers"
section of the SWToolbox user's manual (Kiang, 2018).
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 modifications often result in the active management of flow regimes that no longer reflect
weather-event-driven flow patterns (e.g., some impoundments are operated on a controlled release
pattern). You may need to solicit supplementary data from agencies or individuals that manage the
impoundments or 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.
How often should permit writers and/or permittees be updating the low flow values used in permits?
In general, the low flow values should be reasonably representative of current climatic conditions.
Climate alterations and patterns often operate on decadal scales, so a value that is only 5 years old may
be reasonably representative while a value that is 25 years old may require revisiting.
When determining whether an update is warranted, you must use your own judgement in evaluating
the age and relevance of the underlying data 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
gages taken offline. For example, you may elect to replace an older low flow value that was developed
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 specifying my water
year boundaries based on a calendar year, a seasonal boundary, or a portion of a year?
Typically, it is a good idea to specify boundaries such that all dry season days fall in the same water year
to avoid biasing estimated statistics. SWToolbox 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
applicable for a portion of the year. For example, a surface water discharge may only be permitted May-
October in a particular waterbody. In this case, you may want to calculate the low flow statistic that
pertains during the seasonal discharge window and would only use data from May to October for the
historical record.
Frequently Asked Questions
-------
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 produced 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
previously developed and reported an equation applicable to the basin, you will not have the option to
include a low flow estimate.
For a list of all states with pre-computed USGS flow statistic regression equations and their
corresponding publications, please refer to USGS's Regional Regression Equation Publications by State
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 to 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 accompanying them.
The citation for a given value will be found in the "Citation Number" column of any given table, and the
table of citations (pictured below) provides links to all cited reports at the bottom of all StreamStats
gage webpages.
Citations
Citation	Citation Name and URL
Number
30	Imported from NWIS file
41	Wolock. P.M.. 2003. Flow characteristics at U.S. Geological Survey streamgages in the conterminous United States: U.S.
Geological Survey Open-File Report 03-146. digital data set
42	Wolock. P.M.. 2003. Base-flow index grid for the conterminous United States: U.S. Geological Survey Open-File Report
03-263. digital data set
325	Granato G.E.. Ries. K.G.. Ill, and Steeves. P.A.. 2017. Compilation of streamflow statistics calculated from daily mean
streamflow data collected during water years 1901&2015 for selected U.S. Geological Survey streamgages: U.S. Geological
Survey Open-File Report 2017A1108. 17 p.
When developing Basin Characteristics Reports (as described in Section 2.2, Step 7), StreamStats will
append a table of citations (pictured below) referring the user to the original reports containing the
statistics or watershed regression relationships.
Frequently Asked Questions
-------
LOW-FlOW Statistics P3r3m0tsr3 _"v- Centra' ard East 2Q0S 5159.
Parameter	Min Max
Code	Parameter Name Value Units	Limit Limit
DRNAREA
Drainage Area
2.02
square miles
1.3
14441
RECESS
Recession Index
50
days per log
cycle
32
175
CLIMFAC2YR
Tennessee
Climate Factor 2
Year
2.332
dimensionless
2.056
2.46
SOILPERM
Average Soil
Permeability
1.214
inches per
hour
0.45
9.72
PERMGTE2IN Percent	71.075 percent	2	100
permeability gte
2 in per hr
LOW-FlOW Statistics Row Report [Lev/ -cw Centra anc East teg^nns 2009 51
Pll: Prediction Interval-Lower, Piu: Prediction Interval-Upper, SEp: Standard Error of
Prediction, SE: Standard Error (other — see report)
Statistic
Value
Unit
SEp
7 Day 10 Year Low Flow
0.0567
ft*3/s
89
30 Day 5 Year Low Flow
0.101
ftA3/s
70.2
Low-How Statistics Citations
Law, G.S., Tasker, G.D., and Ladd, D.E.,2009, Streamflow-characteristic
estimation methods for unregulated streams of Tennessee: U.S.
Geological Survey Scientific Investigations Report 2009-5159, 212 p., 1
pi.
When using statistical values and basin regression relationships in StreamStats, you should take care to
evaluate the representativeness of the underlying data used to generate the statistic or regression
equation—just as you would with your own estimates. In some cases, the underlying data (which will be
described in the report cited by StreamStats) will not be sufficiently representative of the conditions
relevant to the NPDES permit. The most common reason you may reject using StreamStats pre-
computed estimates is that they are based on underlying data that are too outdated to represent
current climatic conditions.
Frequently Asked Questions
-------
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
develop the estimates. You should consider the following:
•	Where are the report's stream gages located?
•	How many data were 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 representative 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 and on implementing dilution credits in
NPDES 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-writers-manual
•	Technical Support Document: https://www3.epa.gov/npdes/pubs/owm0264.pdf
For more information on the statistical underpinnings of low flow frequency analysis, please refer to
USGS's Bulletin 17B: https://www.fema.gov/media-librarv/assets/documents/8403
For more information on how to develop and evaluate watershed regression analyses used in WREG 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
Resources Investigations (Chapters 9-11). U.S. Geological Survey.
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, https://md.water.usgs.gov/publications/tm-4-a6/.
•	Stedinger, J., and G.D. Tasker. 1985. "Regional Hydrologic Analysis: 1. Ordinary, Weighted, and
Generalized Least Squares Compared." Water Resources Research 21: 1421-1432.
https://doi.org/10.1029/WR021i009pQ1421.
For a list of all states with pre-computed USGS flow statistic regression equations and their
corresponding publications, please refer to USGS's Regional Regression Equation Publications by State
website: https://water.usgs.gov/osw/programs/nss/NSSpubs Rural.html
For the StreamStats, SWToolbox, and WREG user manuals, please refer to the following webpages:
Frequently Asked Questions
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•	StreamStats User Manual: https://water.usgs.gov/osw/strearnstats/Version4Userlnstructions-
20170928.pdf
•	SWToolbox User Manual: https://doi.org/10.3133/tm4All
•	WREG User Manual: https://pubs.usgs.gov/tm/tm4a8/
4.2 Troubleshooting Tips
I entered a location into the search bar in StreamStats but nothing happens.
You may need to zoom into the map near your location before the search will execute and prompt you
to select a state or regional study area. Try to reach zoom magnification level 8 at a minimum. Your
zoom level is shown in the lower left-hand portion of the screen.
USGS
StreamStats
* Report O About ? Help
SELECT A STATE / REGION >
Step 2; You have zoomed in sufficiently to
select a state or regional study area, Your
selection will dictate the data used to
perform basin delineation and flow
statistics calculation-
Click to select a State or Regional Study Area
Kentucky
Missouri St. Louis
North Carolina
O


Tennessee
0
Exploration Tools J
¦ j I k
RENTUCI
Campbellsville
Bowling Green ,
, Padueah
Hopkinsville
Murray
C arksvi e
Gallatin
Lebanon
Nashvi e
Zoom Level: 8
Map Scale: 1:2,311,162
Lat: 35.4249, Lon: -87,9236
Columbia
:i< n
Cookeville
TENNESSEE
Murfreesboro
JF
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
using an account with administrative permissions or contacting your organization's IT department for
assistance.
Frequently Asked Questions
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5 References
Eng, K., Y-Y. Chen, and J. Kiang. 2009. User's Guide to the Weighted-Multiple-Linear-Regression Program
(WREG version 1.0): Techniques and Methods 4-A8. U.S. Geological Survey, 21 pp.
http://pubs.usgs.gov/tm/tm4a8.
Interagency Advisory Committee on Water Data. 1982. Guidelines for Determining Flood Flow
Frequency: Bulletin #17B of the Hydrology Subcommittee. Office of Water Data Coordination, U.S.
Geological Survey, Reston, VA, 183 pp.
Hortness, J.E. 2006. Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho:
Scientific Investigations Report 2006-5035. U.S. Geological Survey, 31 pp.
https://pubs.usgs.gov/sir/2006/5035/pdf/sir20065Q35.pdf.
Kiang, J.E., K.M. Flynn, T. Zhai, P. Hummel, and G. Granato. 2018. SWToolbox: A Surface-Water Tool-Box
for Statistical Analysis of Streamflow Time Series: Techniques and Methods 4-A11. U.S. Geological
Survey, 33 pp. https://doi.org/10.3133/tm4All.
Ries, K.G., III, J.K. Newson, M.J. Smith, J.D. Guthrie, P.A. Steeves, T.L. Haluska, K.R. Kolb, R.F. Thompson,
R.D. Santoro, and H.W. Vraga. 2017. StreamStats, Version 4. U.S. Geological Survey, Fact Sheet
2017-3046, 4 pp. https://doi.org/10.3133/fs20173046.
References
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Appendix A: K Values Tables
Tables A-l and A-2 partially reproduce "Appendix 3: Tables of K Values" from Bulletin 17B.
Table A-l: K Values for Positive Skew Estimates
Exceedance
Probability
Skew Estimate
9
8
7
6
5
4
3
2
1
0
0.999
-0.22222
-0.25
-0.28571
-0.33333
-0.4
-0.5
-0.66667
-0.999
-1.78572
-3.09023
0.99
-0.22222
-0.25
-0.28571
-0.33333
-0.4
-0.5
-0.66663
-0.98995
-1.58838
-2.32635
0.90
-0.22222
-0.25
-0.28571
-0.33333
-0.4
-0.49986
-0.66023
-0.89464
-1.12762
-1.28155
0.80
-0.22222
-0.25
-0.28571
-0.33333
-0.39993
-0.49784
-0.63569
-0.77686
-0.85161
-0.84162
0.70
-0.22222
-0.25
-0.28571
-0.3333
-0.39914
-0.48902
-0.58783
-0.64333
-0.61815
-0.5244
0.60
-0.22222
-0.25
-0.28569
-0.33285
-0.39482
-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
0.30
-0.2203
-0.24214
-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
0.10
0.11146
0.23929
0.40026
0.58933
0.79548
1.00079
1.18006
1.30259
1.34039
1.28155
0.001
12.04437
11.46855
10.81343
10.06812
9.21961
8.25289
7.15235
5.90776
4.53112
3.09023
Table A-2: K Values for Negative Skew Estimates
Exceedance
Probability
Skew Estimate
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
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
0.60
-0.25335
-0.08763
0.08371
0.22726
0.31159
0.33336
0.31472
0.28169
0.24933
0.22214
Appendix A
A-l
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Exceedance
Probability
Skew Estimate
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
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
0.30
0.5244
0.61815
0.64333
0.58783
0.48902
0.39914
0.3333
0.28571
0.25
0.22222
0.20
0.84162
0.85161
0.77686
0.63569
0.49784
0.39993
0.33333
0.28571
0.25
0.22222
0.10
1.28155
1.12762
0.89464
0.66023
0.49986
0.4
0.33333
0.28571
0.25
0.22222
0.001
3.09023
1.78572
0.999
0.66667
0.5
0.4
0.33333
0.28571
0.25
0.22222
Appendix A
A-2
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