LOW FLOW STATISTICS TOOLS
A How-To-Handbook for NPDES Permit Writers
Second Edition
EPA-833-B-23-001
https://www. epo. qov/npdes
January 2023
Office of Water
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Disclaimer
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 document has been
reviewed in accordance with U.S. Environmental Protection Agency policy and approved for distribution.
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Table of Contents
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 Hydrologic Toolbox and WREG 3-1
3.1 Introduction 3-1
3.2 Using Hydrologic Toolbox 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
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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
receiving water. In flowing rivers and streams, dilution credits are
based on the critical conditions of the receiving water, which are
typically defined in the applicable water quality standards (e.g.,
7Q10 receiving water flow). Critical conditions are conservatively
based on receiving water low flow estimates to ensure the
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.
1—An Introduction to Low Flow Statistics and This Handbook
Most permitting authorities
use either the term "credit" or
"'factor" to refer to the level of
dilution authorized in a permit.
For convenience, this
document primarily uses the
term "dilution credit," but both
are equally valid terms.
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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 Hydrologic Toolbox 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, Hydrologic Toolbox, 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/
Hydrologic Toolbox
Hydrologic Toolbox is a desktop application that builds upon past tools, such as SWSTAT, DFLOW, and
SWToolbox, which permit writers have historically used to estimate low flow statistics from stream gage
data. Hydrologic Toolbox 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 Hydrologic Toolbox desktop application can be
downloaded at:
https://www.sciencebase.gov/catalog/item/6197980bd34eb622f692b481
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.
1—An Introduction to Low Flow Statistics and This Handbook
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• The data and information available to you.
• The uses of the tools at your disposal.
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 StreamStats 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
Hydro logic Toolbox for 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 isungagged, ttie permit
writer should consider developing a regression
relationship between the basin of interest and other
nearby watershed which are gaged.
For some basins, StreamStats 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).
Hydrologic
Toolbox
Using Hydrologic Too.box and its G(S
interface, locate and download
strearnflow 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 ungagged waterbodies.
Figure 1. A decision tree for evaluating which tool to use when calculating low flow statistics.
1—An Introduction to Low Flow Statistics and This Handbook
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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
• Hydrologic Toolbox 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
2—Investigating the Watershed
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Cookevilie 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.
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.
USGS
StreamStats
I Report 0 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
Illinois
0
Kentucky
0
Missouri St Louis
North Carolina
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TENNESSEE
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Columbia
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.
2—Investigating the Watershed
2-2
-------
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.
= ZUSGS StreamStats * Report O About ? Help
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.
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.
2—Investigating the Watershed
2-3
-------
After identifying relevant stations, click on their icons to find links to their NWIS and
StreamStats pages.
USGS
StreamStats
¦ Report 0 About ? Help
S Exploration Tools
*¦ Lee ssrninJ7 Kct
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.
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Station ID: 03423000
Station Name: FALLING WATER RIVER NEAR
COOKEVILLE, TN
Latitude: 36.07731
Longitude: -85.52153
NWIS page: link
StreamStats Gage page: link
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Zoom Level: 13
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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.
On the StreamStats page, you can find additional USGS information for the site, which may
include pre-calculated low flow statistics. If the appropriate low flow statistic you are seeking
is listed on the page, you should obtain the original research report that documents the
estimate. When reviewing the original research report, you should look for the following
information within the report:
• When was the underlying data used in the analysis collected, and is that date range
sufficiently representative of current climate conditions and other conditions that
contribute to in-stream flow (e.g., land use pattern)?
• What is the geographic region or area of applicability for the estimate? Does the
waterbody of interest and the discharge location fall within that area or region? If not,
the estimate will not be applicable to the discharge location.
• Is the estimate derived from a reputable source that utilizes peer review or other
suitable quality control procedures? Typically, estimates produced by USGS will be
developed using suitable quality control procedures.
2—Investigating the Watershed
2-
a
-------
Most direct estimates reported on the StreamStats gage webpage will be based on
streamflow measurements that are less recent than those available to the permit writer. For
more information on identifying the underlying references these estimates are based upon,
please refer to Section 4, "Frequently Asked Questions."
Step 6 Based on the available information, you should decide whether sufficient data exist on the
stream segment of interest to directly calculate low flow statistics using Hydrologic Toolbox,
or if you should base your estimate on a regression of nearby watershed gages using WREG.
Refer to Section 1.5 of this handbook for additional discussion on making this determination.
Section 3 further describes the use of Hydrologic Toolbox and WREG. Refer to Section 4 for
more discussion on determining whether data are sufficient for use in your NPDES permit.
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.
9 Clear Basin
G? Edit Basin
J. Download Basin-*-
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StreamStats will export a "Basin Characteristics Report" as a comma separated values (.csv)
file, which can be saved and viewed later using a spreadsheet application. In addition, the
delineation for the basin can be downloaded as a shapefile (or in other formats) for use in
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 approximately 1.8
2—Investigating the Watershed
2-5
-------
miles downstream (Station ID No. 03422900) but does not have data available for download
or information on any data associated with the station. The second is 4 miles downstream on
the Falling Water River (Station ID No. 03423000) and has data available 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
stream segment); however, the flow data are not available for review. The second station,
while farther downstream, is likely to be representative and has a substantial amount of data
available for use.
2—Investigating the Watershed
2-6
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3 Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3.1 Introduction
In this section, we will discuss how to use Hydrologic Toolbox and WREG to estimate low flow statistics.
As discussed in Sections 1 and 2, you would use Hydrologic Toolbox 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 Hydrologic Toolbox)
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 Hydrologic Toolbox 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
Hydrologic Toolbox 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 Hydrologic Toolbox to Estimate Low Flow Statistics on a Gaged Waterbody
Next, let's walk through step-by-step instructions using Hydrologic Toolbox to calculate low flow values.
The general workflow when using Hydrologic Toolbox is as follows:
1. In Hydrologic Toolbox, locate the flow monitoring stations identified while investigating the
watershed.
2. Import the flow station data into Hydrologic Toolbox.
3. Define the calculations you wish to run.
4. Run the analysis.
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 Hydrologic Toolbox to
replace these applications.
Hydrologic Toolbox incorporates the
functionality and computational
methods used in all three legacy
applications.
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
-------
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.
Mi Exploration Tools
Mill Rd j?
OUTFALL
Gage No
01152500
Wapja A-
Moody
Park
jS Zoom Level: 13
Leaflet I Esri
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Base Maps
NH Map Layers
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Step 1 Open Hydrologic Toolbox and select "Build New Project."
jSGS Hydrologic Toolbox
~ X I
File Project Data Time-Series Tools GW Tools SW Tools Help
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3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-2
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Step 2 A map of the United States wiii appear. Zoom and pan to the location of the stream gage to
be used (Station ID No. 01152500 in our example) to estimate flow statistics. (Hint: Add
state, county, and major roads to the map in the left-hand "Legend" menu to heip navigate
to the location of interest.)
Step 3 Click "Select" in the toolbar and click on the drainage basin that includes the stream gage of
interest. The selected basin's outline will be highlighted cyan.
^ USGS Hydrologic Toolbox - national
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Step 4 Click "Build" in the "Build New USGS Hydrologic Toolbox (1.0.0) 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.
Build New USGS Hydrologic Toolbox (1,0.0) Project
X
To Build a New USGS Hydnologic Toolbox
(1.0.0) 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:
01Q8010S: Black-Ottauquechee
Build
Cancel
3—Estimating Low Flow Statistics with Hydrologic Toolbox 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 cyan. Zoom so only the station of
interest is visible.
^ USGS Hydrotogic Toolbox - 01080106-2.dspx
File Project Data Time-Series Tools GW Tools SW Tools Help
a m i=«,i« ® a @ & a o ,i s
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B ^ ;Map Layers
B H9 Observed Data Stations
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B IS NWIS Daily Groundwater
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station_nm
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site_tp_cd
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Ready.
Step 6 Under the File menu, click "Download Data." A dialog
box will appear to select the data to download. In the
"Regions to Download" dropdown menu, select "View
Rectangle."
Alternatively; permit writers
can directly specify the gage
station if they already know its
ID number from StreamStats,
and they can download its data
by selecting the Station IDs"
option in the "Region to
Download" dropdown menu.
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-
a
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Under "Data Values from US Geographical Survey National Water Information System/'
select "Daily Discharge." Click "Download" at the bottom.
21 U5GS Hydrologic Toolbox • 010S0106-2.dspx
n
ifl Download Data X
File Project Data Time-Series Tools GW Tools SW Tools Help
llSl"* ~ ¦ |
Region to Download View Rectangle v
Legend Tools
Station Locations from US Geological Survey National Water Information System
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B ~ National Hydrography Dataset
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B ® Cataloging Unit Boundaries
~ 2016 Land Cover
B LH Accounting Unit Boundaries
I I 2016 Impervious
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B 0 State Boundaries
B O County Boundaries
I I Clip to Region 0 Get Newest Help Cancel | Download |
B 0 Transportation
B O Major Roads
B ® Soil. Land Use/Cover
~
B ~ State Soil
Ready.
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.) Next exit
out of this window.
H Data Sources — ~
File Analysis Help
BUSGSRDB
APG L>CCQ^02\Users$\Man ah. Papac'.Des ktop\HydrologicT ool boxl .{MatavDi080 l06-2\NVwS\NWlS_discliarge_01152500. rdb
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1 Timeseries
1.088,112 bytes
Modified 8/15/2022 11:46:1ftAM
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
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Step 8 Then select "USGS Integrated Design Fiow (IDF)" under the SW Tools dropdown. Next, select
the station of interest and click "OK."
2?
~ X
File Project Data Time-Series Tools GW Tools^SW Tocj^ Help
: U Li ,i • |i 4 4 H ® 9 B O
151 Select Data for Integrated Frequency Analysis
~ X
Legend Tools
File Attributes Select Help
Select Attribute Values to Filter Available Data
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B 0 Observed Data Stations
B E NWI5 Periodic Groundwater
Scenario v Location
Constituent
v AGENCY V
OBSERVED 01152500
Streamflow
USGS
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B [NWIS Daily Discharge Stations
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Matching Data {1 of 1)
B 0 Cataloging Unit Boundaries
OBSERVED 01152500 Streamflow USGS
B LH Accounting Unit Boundaries
B HI Political
B 13 State Boundaries
B O County Boundaries
B El Transportation
B ~ Major Roads
B ® Soil, Land Use'Cover
B EZ1 State Soil
Selected Data (1 of 1)
OBSERVED 01152500
Streamflow
USGS
Date Range of Selected Data
All Common
Start 1928/05/25 1928/05/25
l~l Include Provisional Data
l~1 Subset and Rlter Time Series
End 2022/08/14 2022/08/14
Ok | Cancel
Ready.
Step 9 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 [April v|| 1 I
End | March v [ [ 31 |
Years to Include in Analysis
O All: 1928/05/25to 2022/03/28
® Common: 1928/05/25to 2022/03/28
O Custom:
Start Year | 1928 Data Starts 1928/05/25
End Year 2022 Data Ends 2022/G3/2S
Display Basic Statistics
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-6
-------
Step 10 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.
For this gage location, the 7Q10 flow was estimated at 31.7 cubic feet per second
(20.5 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 11 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:
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
-------
Qoutfall Qgage ^ «
A
Where:
lgage
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 (269 square miles) and the NWIS page for Station ID No. 01152500 (270 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/.
Qoutfaii — 20.5 MGD X
269 square miles
= 20.4 MGD
270 square miles
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-8
-------
• 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 Stream/low 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.
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 Hydrologic Toolbox (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 3-1 (reproduced from the WREG user's manual) describes the input files needed.
Table 3-1. 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
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-9
-------
File Name
Description
WREG Requirements
LP3s.txt
Standard deviation for Log-Pearson Type III
distribution
Always required
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).
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-10
-------
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 exit out and return to the main Hydrologic
Toolbox interface. From the SW Tools drop down menu hover over "USGS Integrated Design
Flow (IDF)" and select "Interactive". Next, select one of the stations of interest and click
"OK."
^ USGS Hydrologic Toolbox - 01080106-2.dspx
- ~ X
File Project Data Time-Series Tools GW Tools
SW Tools | Help
I ® H|l # |i ® tl 11 ©•BQ|!
Duration/Compare
Legend Tools
Duration Hydrograph
B Map Layers
USGS Integrated Design Flow (IDF) ~
^^Interactive
El 0 Observed Data Stations
create bvvblAl Batch
B ~ NWIS Periodic Groundwater
Create DFLOW Batch
B 0 NWIS Daily Groundwater
Run Existing Batch
•
B [Zl [NWIS Daily Discharge Stations
¦
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).
3 integrated Design Flow — ~
X
File Analysis Help
Select Dates N-Day. Trend. Frequency Design Row Group Outlier Test
Flow Condrtion
O H«h
(§) Low
Year / Season Boundaries
Start April v| | 1 |
End March | | 31 |
Years to Indude n Ariafysis
O Al-1928/05/25 to 2018/02/23
<§) Common: 1928/05/25 to 2018/02/23
O Custom
Start Year 1928 Data Starts 19284)6/25
End Year 2018 Data Ends 2018/02/23
Display Baste Statistics
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-11
-------
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 hydrologicaily based estimates). Make sure to leave
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.)
Select Dates N-Day, Trend. Frequency Design Row Group Outlier Test
Number of Days
Recurrence Werval
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
3 303
5
C
N-Day Tntesefles Lot
Trend List
Screening Tests (R)
Frequency Grid
Frequency Report
Frequency Graph
0 Separate N-Day Plots
~ Separate Station Flots
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-12
-------
By selecting the "Separate N-Day Plots" and "Separate Station Plots" toggle and clicking the
"Frequency Graph" button, you can generate plots with the Log-Pearson Type III curve-fitted
to the timeseries data for each station selected. The associated skew and standard deviation
estimates used in WREG will also appear on the plots.
Integrated Design Flow —
File Analysis Help
Select Dates N-Day, Trend, Frequency Design Row Group Outlier Test
Number of Days Recurrence Interval
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
3.333
0 Logarithmic
N-Day Timeseries List
] | * | | - | Default
y Report
Screening Te
sts(R) ]
c
0 Separate N-Day Plots
Xgguency Graph
M Separate Station Plots
:>
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-
alue tables found in Appendix A. These tables are reproduced from USGS's Bulletin 17B:
Guidelines for Determining Flood Flow Frequency (Interagency Advisory Committee on Water
Data, 1982).
g.jcprsnn.nin^.ria.r^
¦Mean: 505.06
Standard Deviation: 448.37
Skew 1 6736
ANNUAL NON-EXCEEDANCE PROBABILITY, PERCENT
Station - 05455700 - Iowa River near Lone Tree, IA
^ Frequency Graph
File Edit View Analysis (11 %, 2,626.2) Help
10,000
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-13
-------
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 (Appendix A), 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.
3^ FlowChar.txt - No... — ~
X 1
£§ LP3G.txt - Notepad
~ X
LP3s.txt - Notepad
~
X
31 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
Station
ID
skew7Q10
skewlQ10
Station
ID
S-7Q10 s
-1Q10
Station ID K7Q10 K1Q10
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
J| Sitelnfo.txt - Notepad
-
X
~
File Edit Format View Help
Station ID Lat Long
No.
Annual
Series
Zeno-lj
;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.
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-14
-------
N WREG ver 1.0-Select Variables
- ~ X
Dependent Variables:
Independent Variables:
¦7Q10
DRNAREA
1Q10
PRECIP
DRNLENGTH
BFI
OK
A
Select only 1 Select no more than 5
Hold 'Ctrl' to select more than one variable
Press 'Alt' + 'PmtScrn' to obtain screen capture.
UATLAfl(R) (c) 1984-2007 Tut UattiWortci
IUSGS
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").
I WREG ver 1.0 - Variable Transformation
Var
None
"*nH
Int-
el 0
[(C1 *(Var)c2+C3)c4]
Dependent
7Q10
Independent
DRNAREA
PRECIP
C1
1
C2
1
Press 'Alt' + 'PmtScm' to obtain screen capture
OK
C3
0
C4
1
IUSGS
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."
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-15
-------
Regressions
® Multiple-Linear Regression
oRegion-of-lnfluence Regression
PRol
GRol
C HRol Geographic Proximity (km):
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
0 0.98 MSE(G ): 0.302
oUser Specified Weights
Press 'Alt' + 'PrntScrn' to obtain
screen capture.
iUSGS
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).
WREG ver 1.0 - Regression Summary
~ X
Regression Summary
Performance Metrics:
SP <%)"
Inf
Pseudo R2 = 8!
3.77
Standard Model Error (%) =
Inf
Regression:
J = -10352.09
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).
3—Estimating Low Flow Statistics with Hydrologic Toolbox and WREG
3-16
-------
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. Many readers will
be tempted to consider all outliers "bad" data which should be removed from the analysis. However,
not all outliers are "bad"—many are observations that document rare, but real conditions in the
waterbody and should not be removed from the analysis.
Outliers of the first type (i.e., measurement or recording errors) are an example of non-representative
data and should not be included in the analysis. These values should be removed from the analysis
4—Frequently Asked Questions
-------
because they represent true errors and do not represent or reflect true conditions within the
waterbody.
Outliers of the second and third types should be included in the analysis unless the permit writer can
identify and articulate a strong rationale for their removal. These values 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 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.
As a rule-of-thumb, values should only be eliminated from the analysis if they represent errors or are
due to events that are not expected to reoccur (and thus are not representative data). All other data
should be included in the analysis.
Hydrologic Toolbox 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
"Surface-Water (SW) Tools" section of the Hydrologic Toolbox user's manual (Barlow, et al., 2022). For
more discussion on the analysis of outliers in surface water data, refer to the textbook Statistical
Methods in Water Resources (Helsel, et al., 2022).
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.
4—Frequently Asked Questions
¦
-2
-------
When calculating low flow values in Hydrologic Toolbox, 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. Hydrologic Toolbox 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.
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.
4—Frequently Asked Questions
¦
-3
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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 2017^1108, 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.
Low-Flow Statistics Parameters iu» a™ c*
na! and Easz Regions 2009 515$)
Parameter
Code
Parameter Name
Value
Units
Min
Limit
Max
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 ftnvHowCottri and East Regans 2009 51 si
PIl: Prediction Interval-Lower, Plu: 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 ftA3/s 89
30 Day 5 Year Low Flow 0.101 ftA3/s 70.2
Low-Fkw Statistics Citations
Law, G.S., Tasker, G.D., and Ladd, D.E.,2009, Streamfiow-characteristic
estimation methods for unregulated streams of Tennessee: U.S.
Geological Survey Scientific Investigations Report 2009-5159, 212 p., 1
ol
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.
4— 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.
This report discusses several different ways of obtaining low flow statistic values for a discharge point.
How should I think about the relative accuracy of these different approaches? When multiple low flow
statistic estimates are available for a discharge point, which should I use for my NPDES permit?
All else being equal, a low flow statistic that is based on information that is more closely related to the
discharge point in time and space will more accurately reflect the flow characteristics of the receiving
water. For example, a low flow statistic computed from recent data collected near the discharge
location will be more accurate than an estimate computed from a state- or regional-regression model
developed a decade ago.
When multiple potential low flow statistic estimates are available for a particular discharge point, values
based on direct measurements of the waterbody of interest are preferable to values based on
geographically broad based statistical models (e.g., the estimates available in StreamStats or developed
using WREG). In addition, you should typically prefer an estimate based on more recent and more
complete streamflow and watershed data, to those based on older and less complete datasets.
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:
4—Frequently Asked Questions
¦
-5
-------
• Helsel, D.R., Hirsch, R.M., Ryberg, K.R., Archfield, S.A., and Gilroy, E.J.. 2022. Statistical methods
in water resources: U.S. Geological Survey Techniques and Methods, book 4, chap. A3.
https://doi.org/10.3133/tm4a3
• 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, Hydrologic Toolbox, and WREG user manuals, please refer to the following
webpages:
• StreamStats User Manual: https://www.usgs.gov/media/files/streamstats-version-4-user-
instructions
• Hydrologic Toolbox User Manual: https://doi.org/10.3133/tm4D3
• 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.
I'm trying to install or run Hydrologic
Toolbox and WREG, but I keep getting
errors about "read access" and/or file
permissions.
You may need administrative access to insta
these applications on your computer. Try
installing them using an account with
administrative permissions or contacting
your organization's IT department for
assistance.
ill
Zoom Level: 8
Map Scale: 1:2,311,162
4— Frequently Asked Questions
¦
-6
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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.
Barlow, P.M., McHugh, A.R., Kiang, J.E., Zhai, T., Hummel, P., Duda, P., and Hinz, S., 2022, U.S. Geological
Survey Hydrologic Toolbox—A graphical and mapping interface for analysis of hydrologic data: U.S.
Geological Survey Techniques and Methods, book 4, chap. D3, 23 p.,
https://doi.org/10.3133/tm4D3.
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.
5—References
-------
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
B *71
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
Appendix A—K Values Tables
A-l
-------
Table A-2: K Values for Negative Skew Estimates
Exceedance
Skew Estimates
Probability
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
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—K Values Tables
A-2
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