U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2018–5148

Supersedes USGS Water-Resources Investigations Report 91–4037

Prepared in cooperation with the Mississippi Department of Transportation

Flood Frequency of Rural Streams in Mississippi, 2013

397

407 406 405

404 423

422

418

416

417

415

414 412

393

392 389

GULF OF MEXICO

MISSISSIPPI

ALABAMA

TENNESSEE

ARKANSAS

FLORIDA

MISSISSIPPI

LOUISIANA

FLORIDA
 
Flood Frequency of Rural Streams in 

Mississippi, 2013

By Brandon T. Anderson

Prepared in cooperation with the Mississippi Department of Transportation

Scientific Investigations Report 2018–5148

Supersedes USGS Water-Resources Investigations Report 91–4037

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

Supersedes USGS Water-Resources Investigations Report 91–4037

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Suggested citation:

Anderson, B.T., 2018, Flood frequency of rural streams in Mississippi, 2013: U.S. Geological Survey Scientific 

Investigations Report 2018–5148, 12 p., https://doi.org/10.3133/sir20185148. [Supersedes USGS Water-Resources 

Investigations Report 91–4037.]

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

ISBN 978-1-4113-4264-4
iii

Acknowledgments

The following U.S. Geological Survey personnel are acknowledged for their assistance in 

developing the computations for this project and helping to complete the report. T. Scott 

Hedgecock, Hydrologist in the U.S. Geological Survey Lower Mississippi-Gulf Water Science 

Center (USGS LMGWSC) Montgomery, Alabama, office, provided mentorship during the project. 

Andrea Veilleux, Hydrologist in the USGS Integrated Modeling and Prediction Division, Analysis 

and Prediction Branch, Reston, Virginia, assisted in the development of the study-specific skew 

and provided project support. Brian Breaker, Hydrologist in the USGS LMGWSC, Little Rock, 

Arkansas, office helped with statistical software. Stephanie Kula, Biologist in the USGS OhioKentucky-Indiana Water Science Center, provided geographic information system (GIS) data for 

the development of StreamStats and provided GIS-derived basin characteristics.

v

Contents

Acknowledgments .......................................................................................................................................iii

Abstract ..........................................................................................................................................................1

Introduction ....................................................................................................................................................1

Purpose and Scope .............................................................................................................................1

Description of Study Area ..................................................................................................................1

Previous Investigations .......................................................................................................................3

Data Compilation ...........................................................................................................................................3

Peak-Flow Data and Basin Characteristics ....................................................................................3

Analysis of Flow at Gaged Locations ...............................................................................................3

Development of a Study-Specific Skew Coefficient ......................................................................5

Regional Regression Analysis ...........................................................................................................5

Application of Methods ................................................................................................................................8

Flood-Frequency Estimates at Gaged Sites in Mississippi ...........................................................8

Flood-Frequency Estimates at Ungaged Locations on Gaged Streams .....................................9

Flood-Frequency Estimates at Locations on Ungaged Streams ..................................................9

Accuracy and Limitations of Regional Regression Equations .....................................................9

Summary and Conclusions ........................................................................................................................11

References Cited .........................................................................................................................................11

Figures

1. Map showing locations of streamgages included in this study and the four newly 

developed flood regions in Mississippi, 2013 ..........................................................................2

2. Map showing locations of streamgages used to compute the study-specific 

skew coefficient in select subregional watersheds in Mississippi ....................................6

Tables

1. Basin characteristics used in the regional regression analysis for determining 

flood frequency of rural streams in Mississippi, 2013 ...........................................................4

2. T-year recurrence intervals with corresponding annual exceedance probability 

and P-percent chance exceedance for flood-frequency flow estimates ..........................5

3. Streamgages used to compute the study-specific skew in select subregional 

watersheds in Mississippi—the Middle Tennessee-Elk, Mobile-Tombigbee, 

Lower Mississippi-Big Black, Pearl, and Pascagoula ...........................................................7

4. Final regional regression equations for estimating annual exceedance 

probability flows and generalized least squares model diagnostics for 

unregulated streams in Mississippi ........................................................................................10

5. Number of streamgages used in regional regression analysis and ranges of 

drainage area in each flood region of Mississippi ...............................................................10
vi

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F – 32) / 1.8.

Datum

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). 

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88) or the National Geodetic Vertical Datum of 1929 (NGVD 29).

Elevation, as used in this report, refers to distance above the vertical datum.
vii

Abbreviations

AEP Annual exceedance probability

AVP Average variance of prediction

EMA Expected moments algorithm

GIS Geographic information system

GLS Generalized least squares

HUC Hydrologic unit code

LP3 Log-Pearson type III

MAP Mississippi Alluvial Plain

MGB Multiple Grubbs-Beck test

MSE Mean square error

MSEp Mean square error of prediction

NWIS National Water Information System

OLS Ordinary least squares

PILFs Potentially influential low floods

RRE Regional regression equation

SEM Standard error of the model

SEP Standard error of prediction

USGS U.S. Geological Survey

WREG Weighted-multiple-linear regression program

Flood Frequency of Rural Streams in Mississippi, 2013

By Brandon T. Anderson

Abstract 

To improve flood-frequency estimates at rural streams 

in Mississippi, annual exceedance probability flows at 

gaged streams and regional regression equations used to 

estimate annual exceedance probability flows for ungaged 

streams were developed by using current geospatial data, 

new analytical methods, and annual peak-flow data through 

the 2013 water year. The regional regression equations were 

derived from statistical analyses of peak-flow data and basin 

characteristics for 281 streamgages and incorporated a newly 

developed study-specific skew coefficient at streamgages 

located in five subregional watersheds (Middle TennesseeElk, Mobile-Tombigbee, Lower Mississippi-Big Black, Pearl, 

and Pascagoula) in Mississippi. Three flood regions—A, 

B, and C—were identified based on residuals from the 

regional regression analyses and contain sites with similar 

basin characteristics. Analysis was not conducted for the 

fourth flood region, the Mississippi Alluvial Plain, because 

of insufficient long-term streamflow data and poorly defined 

basin characteristics. 

Introduction

Improved flood-frequency information is important 

for the effective management of flood plains, including the 

safe and economic design of bridges, culverts, dams, levees, 

and other structures near streams. The last flood-frequency 

study for Mississippi was published more than 25 years ago 

(Landers and Wilson, 1991). Since that time, improvements in 

estimation techniques have increased the accuracy of floodfrequency estimates. One such technique is the expected 

moments algorithm (EMA), which allows historical data to 

be represented as intervals (Cohn and others, 1997). Another 

is the multiple Grubbs-Beck (MGB) test, which increases 

the accuracy of peak-flow statistics by objectively and 

systematically detecting and removing low, highly variable 

peak flows, and can be used with the EMA (Cohn and others, 

2013). In 1982, the Interagency Advisory Committee on Water 

Data presented a generalized regional skew coefficient map

for the United States that was developed using peak-flow data 

collected through 1976 (Interagency Advisory Committee 

on Water Data, 1982). Since then, an additional 37 years of 

peak-flow data have been collected and can be used to develop 

updated skew coefficients. 

In 2000, the U.S. Geological Survey (USGS), 

in cooperation with the Mississippi Department of 

Transportation, began a study to update the regional regression 

equations (RRE) and annual exceedance probability (AEP) 

flows for rural streams in Mississippi using recent geospatial 

data, new analytical methods, and additional annual peakflow data through the 2013 water year.1

 Results of the study, 

including the updated AEP flows and RRE information, would 

be published and also incorporated into the USGS StreamStats 

application, which is an online tool that provides flood plain 

planners and water managers in Mississippi with basin 

characteristics and estimates of flow statistics at gaged and 

ungaged stream sites (http://water.usgs.gov/osw/streamstats/). 

Purpose and Scope

The purposes of this report are to (1) describe the 

development of a study-specific skew coefficient that was 

applied to sites located in five subregional watersheds 

in Mississippi; (2) update flood regions for all areas in 

Mississippi except the Mississippi Alluvial Plain (MAP); 

(3) update the annual exceedance probability flows at gaged 

locations; and (4) update regional flood-frequency equations 

(regional regression equations) for use at ungaged locations 

in Mississippi. The MAP was not included in this analysis 

because of insufficient long-term streamflow data and poorly 

defined basin characteristics. All data used in support of 

the analysis presented in this report, including geographic 

information system (GIS) data for the four flood regions in 

Mississippi, are available from Anderson (2018). This report 

supersedes the flood-frequency analysis published by Landers 

and Wilson (1991).

Description of Study Area

The study area (fig. 1) includes the State of Mississippi 

and selected locations in Louisiana, Alabama, Tennessee, 

and Florida. Rainfall in Mississippi generally is associated 

1

The water year is the annual period from October 1 through September 30 

and is designated by the year in which the period ends. For example, the 2013 

water year is from October 1, 2012, through September 30, 2013.
2 Flood Frequency of Rural Streams in Mississippi, 2013

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0 20 40 MILES

0 20 40 KILOMETERS

EXPLANATION

Mississippi Alluvial 

 Plain

Flood region B

Flood region C

Flood region A Stream

Streamgage used in study. 

 Number corresponds to 

 table 1 in Anderson (2018)

91° 90° 89° 88°

35°

34°

33°

32°

31°

GULF OF MEXICO

MISSISSIPPI

ALABAMA

TENNESSEE

ARKANSAS

FLORIDA

MISSISSIPPI

LOUISIANA

FLORIDA

Base from U.S. Geological Survey digital data

and National Watershed Boundary Dataset

Figure 1. Locations of streamgages included in this study and the four newly developed flood regions in Mississippi, 

2013.
Data Compilation 3

with the movement of warm and cold fronts across the State 

from November through April and isolated thunderstorms 

from May through October. From June to September, tropical 

storms or hurricanes occasionally enter the State along the gulf 

coast and produce unusually heavy amounts of rainfall. The 

average annual precipitation for Mississippi is 54.16 inches 

(U.S. Climate Data, 2017). The average annual high and 

low temperatures are 75.5 and 53.6 degrees Fahrenheit, 

respectively (U.S. Climate Data, 2017). 

Previous Investigations

Wilson and Trotter (1961) developed techniques for 

estimating the magnitude and frequency of floods at streams in 

Mississippi. Colson and Hudson (1976) used a multiple-linear 

regression model to update those techniques. Landers (1985) 

used linear regressions to develop updated techniques for 

estimating the magnitude and frequency of floods at streams 

located in the alluvial plain of the lower Mississippi River. 

Landers and Wilson (1991) used a generalized least-squares 

regression to develop updated techniques for estimating 

the magnitude and frequency of flows in streams located in 

Mississippi. From the residuals in the 1991 analysis, Landers 

and Wilson defined three flood regions in Mississippi (East, 

West, and the MAP). 

Data Compilation

USGS streamgages in Mississippi, Louisiana, Alabama, 

Florida, and Tennessee that have 10 or more years of annual 

peak-flow data were used in this analysis. Streamgages with 

annual peak-flow data are either continuous-record gages 

or crest-stage gages. Continuous-record streamgages are 

equipped with instrumentation to record the water-surface 

elevation, or stage, of the water body at fixed-time intervals. 

The stage data are transmitted by satellite to the local 

USGS offices and are applied to a stage-discharge rating to 

determine flow for the given stage value. Crest-stage gages 

record only the peak stage of a flood; the peak stage is then 

applied to a stage-discharge rating to determine the associated 

flow. Hereafter, these two types of gages are referred to as 

streamgages. 

Peak-Flow Data and Basin Characteristics

This analysis was conducted by using data from 

424 streamgages (341 in Mississippi and 83 from adjacent 

States) that had 10 or more years of annual peak-flow 

data (systematic and historic peaks) collected through the 

end of the 2013 water year (fig. 1). Peak-flow data for the 

streamgages were downloaded from the USGS National 

Water Information System (NWIS) database (U.S. Geological 

Survey, 2017a). The drainage areas for the 424 streamgages 

range from 0.04 to 1,144,500 square miles (mi2). The drainage 

areas of the 341 streamgages in Mississippi (excluding the 

Mississippi River at Vicksburg, MS, streamgage) range from 

0.05 to 13,400 mi2. Annual peak-flow data were analyzed 

for trends using the Mann-Kendall test. Trends in annual 

peak-flow data could bias the AEP flow analyses because 

an assumption of probability analyses is that annual peak 

flows are independent and stationary through time. However, 

annual peak-flow data can exhibit some serial correlation 

that can cause the Mann-Kendall trend test to indicate a 

significant trend when there is none, especially at streamgages 

with less than 30 years of peak-flow data (Hodgkins and 

Martin, 2003). For this reason, the Mann-Kendall trend test 

was not considered for streamgages with less than 30 years 

of peak-flow data. A statistically significant trend (p≤0.05) 

in peak flow was shown at 27 streamgages, representing 

approximately 6 percent of the total sites. A positive trend 

was indicated for 11 and a negative trend indicated for 

16 streamgage annual peak flows. These sites represent 

a minority of the total sites, are distributed almost evenly 

between positive and negative trends, and are believed to be 

chance occurrences rather than true trends; therefore, no sites 

were removed from the analyses.

Twenty-one basin characteristics for each site included 

in this study were obtained by using the USGS map-based 

web application StreamStats (U.S. Geological Survey, 2017b). 

Because soil types and land use can influence runoff, the GISderived basin characteristics from StreamStats were compiled 

for each basin by using the 2011 National Land Cover 

Database (Homer and others, 2015) (table 1).

Analysis of Flow at Gaged Locations

Flood-frequency estimates for gaged locations 

were computed by fitting a Log-Pearson Type III (LP3) 

mathematical probability distribution to the series of annual 

peak flows as described in Bulletin 17B (Interagency Advisory 

Committee on Water Data, 1982). The LP3 distribution is 

a three-parameter distribution that requires estimates of 

the mean, standard deviation, and skew coefficient of the 

population of logarithms of annual peak flow at each gaged 

site (Parrett and others, 2011). The EMA method produces 

estimates of the three LP3 statistics that are identical to those 

produced by the standard LP3 method described in Bulletin 

17B. The EMA method improves upon the standard LP3 

method by allowing for the analysis of historical peak datasets 

containing censored observations, historical data, low outliers, 

and uncertain data points and accommodates the interval data 

by using perception thresholds and flow intervals (Cohn and 

others, 1997).
4 Flood Frequency of Rural Streams in Mississippi, 2013

Basin characteristic definition Units Abbreviation Source(s)

Area that drains to a point on a stream Square miles DRNAREA StreamStats, version 3.0

Change in elevation between points 10 and 85 percent of length along 

main channel to basin divide divided by length between points ft 

per mi

Feet per mile CSL10_85fm StreamStats, version 3.0

Latitude of Basin Centroid Decimal degrees LAT_CENT StreamStats, version 3.0

Longitude of Basin Centroid Decimal degrees LONG_CENT StreamStats, version 3.0

Maximum basin elevation Feet ELEVMAX StreamStats, version 3.0

Minimum basin elevation Feet MINBELEV StreamStats, version 3.0

Length of longest flow path Mile LFPLENGTH StreamStats, version 3.0

Area of developed land-use from NLCD 2011 classes 21-24 Square miles LC11ADEV StreamStats, version 3.0; NLCD

Percentage of developed (urban) land from NLCD 2011 classes 21-24 Percent LC11DEV StreamStats, version 3.0; NLCD

Area of developed open land from NLCD 2011 class 21 Square miles LC11ADVOPN StreamStats, version 3.0; NLCD

Area of developed land, low intensity, from NLCD 2011 class 22 Square miles LC11ADEVLO StreamStats, version 3.0; NLCD

Area of developed land, medium intensity, NLCD 2011 class 23 Square miles LC11ADEVMD StreamStats, version 3.0; NLCD

Area of developed land, high intensity, NLCD 2011 class 24 Square miles LC11ADEVHI StreamStats, version 3.0; NLCD

Percentage drainage area that is in low to high developed land-use 

classes 22-24 from NLCD 2011

Percent LC11DEVLMH StreamStats, version 3.0; NLCD

Impervious percentage computed as 

((.10*A21+.25*A22+.65*A23+.90*A24)/DA)*100 

from NLCD 2011

Percent LC11DINT StreamStats, version 3.0; NLCD

Percentage of forest from NLCD 2011 classes 41-43 Percent LC11FOREST StreamStats, version 3.0; NLCD

Area of water from NLCD 2011 class 11 Square miles LC11AWATER StreamStats, version 3.0; NLCD

Percent of open water, class 11, from NLCD 2011 Percent LC11WATER StreamStats, version 3.0; NLCD

Area of wetlands from NLCD 2011 classes 90 and 95 Square miles LC11AWETL StreamStats, version 3.0; NLCD

Percentage of wetlands, classes 90 and 95, from NLCD 2011 Percent LC11WETLND StreamStats, version 3.0; NLCD

Percentage of water bodies and wetlands determined from the 

NLCD 2011

Percent LC11STOR StreamStats, version 3.0; NLCD

Table 1. Basin characteristics used in the regional regression analysis for determining flood frequency of rural streams in 

Mississippi, 2013.

[NLCD, National Land Cover Database from Homer and others (2015); A21, area of developed open land from NLCD class 21; A22, area of developed 

land, low intensity, from NLCD class 22; A23, area of developed land, medium intensity, NLCD 2011 class 23; A24, area of developed land, high intensity, 

NLCD class 24]

The basic equation for fitting the LP3 distribution to a 

measured series of annual peak flows is

logQp= X+KpS, (1)

where

Qp is the P-percent AEP flow in cubic feet per 

second;

X is the mean of the logarithms of the annual 

peak flows;

Kp is a factor based on the skew coefficient and 

the given percentage of annual exceedance 

probability, which can be obtained from 

appendix 3 of Bulletin 17B (Interagency 

Advisory Committee on Water Data, 

1982); and

S is the standard deviation of the logarithms of the 

annual peak flows.

In previous USGS reports about floods in Mississippi, the 

term “recurrence interval, in years” has been used to characterize 

flood frequency (50-year flood, and so forth). The USGS and 

other Federal agencies now refer to the P-percent chance of 

occurrence as an annual exceedance probability (AEP). For 

example, the 0.02 percent (Q2%) AEP flood has a 2-percent 

chance of occurring in any given year and corresponds to a 

recurrence interval of 50 years (reciprocal of the AEP; table 2) 

(Griffis and Stedinger, 2007). An increase in the number of 

years of peak-flow record at a streamgage increases the level of 

confidence in computed AEP flows. For example, a stream with 

30 years of historical peak-flow data will have a lower variance 

than a stream with 10 years of record, thus increasing the 

confidence of the estimated AEP flow.
Data Compilation 5

T-year 

recurrence 

interval

Annual

exceedance

probability

P-percent annual

exceedance

probability

2 0.5 50

5 0.2 20

10 0.1 10

25 0.04 4

50 0.02 2

100 0.01 1

200 0.005 0.5

500 0.002 0.2

Table 2. T-year recurrence intervals with corresponding annual 

exceedance probability and P-percent chance exceedance for 

flood-frequency flow estimates (Feaster and others, 2009).

The MGB test, a generalization of the Grubbs-Beck 

method, provides a standard procedure for identifying lowflow outliers and multiple potentially influential low floods 

(PILFs) (Cohn and others, 2013). PILFs are annual peaks 

that meet three criteria: (1) their magnitude is much smaller 

than the flood quantile of interest; (2) they occur below a 

statistically significant break in the flood-frequency plot; and 

(3) they have excessive influence on the estimated frequency 

of large floods. The USGS PeakFQ software version 7.1, 

available for download from https://water.usgs.gov/software/

PeakFQ/ (U.S. Geological Survey, 2014), was used to conduct 

the EMA/MGB test. 

Development of a Study-Specific Skew 

Coefficient

The skew coefficient measures the asymmetry of the 

probability distribution of a set of annual peak flows, which 

is affected by the presence of high or low outliers (Wagner 

and others, 2016). Peak-flow data available through wateryear 2013 were used to develop a skew coefficient, hereafter 

referred to as the study-specific skew coefficient, for five 

subregional watersheds in Mississippi: Middle Tennessee-Elk, 

Mobile-Tombigbee, Lower Mississippi-Big Black, Pearl, and 

Pascagoula (fig. 2). 

Two criteria were required to ensure consistency with 

the skew analysis outlined in Bulletin 17B (Interagency 

Advisory Committee on Water Data, 1982) and compatibility 

with previous flood-frequency studies across the region. 

Streamgage sites selected for the study-specific skew 

coefficient development could not have substantial 

urbanization, regulation, diversion, or tidal influence. Station 

skew coefficients at altered sites could be location specific 

based on the type and degree of alteration and have the 

potential to affect the skew analysis. The other criterion 

was that a streamgage station needed 25 years or more of 

systematic peak-flow record. Based on these criteria, 93 rural 

streamgage stations were selected for use in computing 

the study-specific skew coefficient and mean square error 

(MSE). Station skew coefficient statistics were compiled for 

each of the 93 candidate stations (table 3) using the software 

PeakFQ, version 7.1 (https://water.usgs.gov/software/PeakFQ/; 

U.S. Geological Survey, 2014). The arithmetic mean of the 

93 individual station skew coefficients yielded a study-specific 

skew coefficient of −0.08, and the MSE was computed to 

be 0.22. This study-specific skew coefficient replaced the 

generalized skew coefficient from Bulletin 17B (Interagency 

Advisory Committee on Water Data, 1982) in the five 

subregional watersheds that contained all 93 streamgages and 

was weighted with the station skew coefficient at each site to 

calculate the AEP flows. In all other areas of Mississippi and 

areas of adjacent States (fig. 2), the Bulletin 17B generalized 

skew coefficient was used for station weighting. It is important 

to note that the study-specific skew coefficient cannot be 

applied in other subregional watersheds in Mississippi. 

Redundant sites were not considered for the study-specific 

skew coefficient analysis because of potential bias. Redundancy 

occurs when drainage basins of two gaged sites are nested, 

meaning that one is contained inside the other, and the sizes 

of the two basins are similar (Parrett and others, 2011). Thus, 

instead of providing two independent spatial observations 

that relate drainage basin characteristics to skew coefficient 

(or flood quantiles), these two basins likely have the same 

hydrologic response to a given storm and represent only one 

spatial observation (Parrett and others, 2011). When sites are 

considered redundant, statistical analyses using both gaged sites 

incorrectly represent the information in the regional dataset 

(Gruber and Stedinger, 2008). Sites were considered redundant 

if gages on the same stream possessed drainage area ratios 

within 50 percent of each other. When evaluating redundancy 

between two sites in a reach, the site having the longer period of 

record was chosen to represent that reach or sub-reach.

Regional Regression Analysis

Of the 424 streamgages considered for inclusion in this 

study, 281 were used for the regional regression analysis 

(fig. 1). Streamgage information and additional data related to 

the regional regression analysis are provided in the data release 

associated with this study (Anderson, 2018). Streamgages were 

evaluated for backwater, regulation, diversion, channelization, 

and urbanization by compiling historical data and inspecting 

NWIS peak-flow data qualification codes; nested sites and 

sites having any of these attributes were removed. Basins of 

sites having more than 20 percent development also were 

removed. Redundant sites were not considered for the RRE 

analysis because of potential bias. A statewide ordinary least 

squares (OLS) regression equation was developed for the 

State, excluding the MAP, by using drainage area as the only 

explanatory variable for the 1 percent (Q1%) AEP. The residuals 

for each streamgage were evaluated to detect any geographic 

biases or clusters. Residuals for the streamgages represent the 

difference between observed values and the predicted values of 

streamflow using the RREs. 
6 Flood Frequency of Rural Streams in Mississippi, 2013

Pearl

Pascagoula

Mobile-Tombigbee

Lower Mississippi-Yazoo

Lower Mississippi

Boeuf-Tensas

Lower Mississippi-St. Francis

Lower 

MississippiBig Black

Lower Mississippi-Hatchie

Louisiana Coastal

Alabama

Lower Mississippi-Lake Maurepas

Middle 

Tennessee-Elk

Lower Tennessee

Upper White

Lower Red-Ouachita

Lower RedOuachita

ChoctawhatcheeEscambia

Lower Arkansas

91° 90° 89° 88°

35°

34°

33°

32°

31°

30°

GULF OF MEXICO

9

8

98

96

95

93

89

86

85

83

82

81

77

73

72

66

61

60

57

55

56

54

53

51 45

44

42 41

38

18

16

13

11

421

417

413

412

402 404

401

400

396

389

386

383

380 379

374

373

372

365

364

358

347

345

236

235

232

228

222

221

220

211

202

182

181

180

178

177

176

175

168

160

156

155

153

151

146

134 137

130

128

126

123

118 117

112

108

107

104

103

101

100

EXPLANATION

Bulletin 17B skew used (Interagency Advisory 

 Committee on Water Data, 1982)

Computed study-specific skew used

4-digit hydrologic unit code (HUC4) subregion 

 boundary

Streamgages used to compute study-specific 

 skew (see table 3)

160

0 20 40 MILES

0 20 40 KILOMETERS

Base from U.S. Geological Survey digital data

and National Watershed Boundary Dataset

MISSISSIPPI

ALABAMA

TENNESSEE

ARKANSAS

LOUISIANA

Figure 2. Locations of streamgages used to compute the study-specific skew coefficient in select 

subregional watersheds in Mississippi.
Data Compilation 7

Site 

number 

(fig. 2)

Station 

number 

Station 

skew MSE

8 02378500 0.063 0.019

9 02429900 –0.632 0.310

11 02429980 0.978 1.110

13 02430085 0.121 0.039

16 02430615 –0.395 0.102

18 02430880 0.425 0.250

38 02436500 0.847 0.851

41 02437300 –0.742 0.444

42 02437550 0.098 0.030

44 02438000 –0.35 0.075

45 02439400 –0.559 0.234

51 02440400 0.284 0.129

53 02440600 0.182 0.066

54 02440800 –0.611 0.287

55 02441000 –0.729 0.427

56 02441220 –0.253 0.032

57 02441300 0.188 0.069

60 02443000 –0.774 0.488

61 02443500 –0.538 0.214

66 02446500 –0.434 0.129

72 02448000 0.237 0.098

73 02448620 0.807 0.779

77 02467500 0.441 0.267

81 02469800 0.693 0.590

82 02471001 0.113 0.035

83 02471100 –1.001 0.857

85 02471500 –0.649 0.329

86 02472000 0.175 0.063

89 02472500 0.561 0.405

93 02473000 0.387 0.214

95 02473460 0.001 0.000

Site 

number 

(fig. 2)

Station 

number 

Station 

skew MSE

96 02473480 0.07 0.021

98 02473500 –0.023 0.003

100 02473850 –0.388 0.098

101 02474500 0.316 0.153

103 02474600 –0.099 0.001

104 02474650 0.001 0.006

107 02475000 0.178 0.064

108 02475050 –0.282 0.043

112 02475500 0.096 0.029

117 02477000 –0.005 0.005

118 02477050 –0.794 0.516

123 02477330 0.041 0.014

126 02477990 0.2 0.076

128 02478500 0.573 0.420

130 02479000 0.119 0.038

134 02479130 0.719 0.631

137 02479155 0.233 0.095

146 02479300 –0.138 0.004

151 02480500 0.237 0.098

153 02481000 –0.356 0.079

155 02481130 –0.154 0.006

156 02481400 0.35 0.181

160 02481510 0.108 0.034

168 02482000 –0.111 0.001

175 02483000 –0.073 0.000

176 02483500 0.952 1.055

177 02483890 0.121 0.039

178 02484000 0.156 0.054

180 02484600 0.552 0.394

181 02484750 0.008 0.007

182 02484760 0.464 0.215

Site 

number 

(fig. 2)

Station 

number 

Station 

skew MSE

202 02487500 0.073 0.022

211 02487900 0.219 0.087

220 02488700 0.076 0.023

221 02489000 0.457 0.283

222 02489030 0.229 0.093

228 02490500 –0.771 0.484

232 02491500 –0.598 0.239

235 02492360 0.229 0.114

236 03592718 –0.873 0.636

345 07289265 –1.41 1.781

347 07289350 –0.123 0.002

358 07289600 –0.287 0.045

364 07290000 0.074 0.022

365 07290005 –0.134 0.003

372 07290650 0.051 0.016

373 07290690 –0.116 0.002

374 07290830 0.146 0.049

379 07291000 –0.655 0.336

380 07291250 –0.245 0.029

383 07292500 –0.553 0.228

386 07295000 –0.61 0.286

389 07373550 –0.107 0.001

396 07375307 –0.538 0.214

400 07375500 –0.174 0.010

401 07375800 –0.177 0.010

402 07376000 –0.132 0.003

404 07376500 –0.264 0.036

412 07377000 –0.454 0.143

413 07377210 –0.735 0.435

417 07377500 –0.937 0.742

421 07378500 –0.672 0.356

Table 3. Streamgages used to compute the study-specific skew in select subregional watersheds in Mississippi—the Middle 

Tennessee-Elk, Mobile-Tombigbee, Lower Mississippi-Big Black, Pearl, and Pascagoula.

[MSE, mean square error in log10 cubic feet per second]
8 Flood Frequency of Rural Streams in Mississippi, 2013

The flood magnitudes obtained from station LP3 

frequency distributions, which were obtained through analysis 

of streamflow records at gaged sites, were related to basin 

characteristics (table 1) by using generalized least squares 

(GLS) multiple-linear regression analysis. Ordinary least 

squares was used in the initial regression analysis to evaluate 

the statistical significance of each basin characteristic (Wagner 

and others, 2016). The USGS weighted-multiple-linear 

regression program (WREG) version 1.05 (https://water.

usgs.gov/software/WREG/) was used to complete the GLS 

regression analysis (Eng and others, 2009; U.S. Geological 

Survey, 2013b), a method that weights streamgages in the 

regression according to differences in streamflow record 

length, the variance of streamflow measurements in the record, 

and spatial cross correlations of concurrent flows among 

streamgages. The estimates of streamflow at gaged sites were 

weighted with the regional estimates of streamflow to compute 

a final set of AEP flows. 

Other regression diagnostics were reviewed to identify 

streamgages that have high leverage and (or) high influence 

metrics. The leverage metric is used to compare the values of 

independent variables at one streamgage to the values of the 

same variables at all other streamgages. The influence metric 

indicates if data from a streamgage have a high influence 

on the estimated regression metric values (Eng and others, 

2009). A streamgage may have a high leverage metric, 

indicating that its independent variables are substantially 

different from those at all other streamgages, but the same 

streamgage may not have a high influence on the regression 

metrics. Conversely, a streamgage with a high influence may 

not have a high leverage metric. Measurement or transposing 

errors in reported values of some independent variables 

sometimes produce high leverage or influence metrics. Data 

from streamgages with high influence or leverage were given 

additional review to determine if such errors had been made or 

if the data should be excluded for other reasons.

Three flood regions for Mississippi (fig. 1) were 

delineated based upon review of residual plots, previous 

reports, eight-digit hydrologic unit code maps, geologic maps, 

and physiographic maps. A GLS analysis was then performed 

to determine the importance of the explanatory variables in 

each region. For flood regions A, B, and C, drainage area was 

the significant variable in the RREs. Region B is similar to the 

East region from the 1991 study but differs due to the fact that 

the Pearl River Basin was excluded. Regions A and C combine 

to cover the area represented by the West region in the 1991 

study but also include the Pearl River Basin.

Application of Methods

When applying regression equations, users are advised 

not to interpret the empirical results as exact. Regression 

equations are statistical models that must be interpreted 

and applied within the limits of the data and with the 

understanding that the results are best-fit estimates with an 

associated variance. Flood-frequency estimation methods for 

stream AEP flows in Mississippi, excluding sites located in the 

MAP, differed among gaged sites, ungaged locations on gaged 

streams, and ungaged streams. 

Flood-Frequency Estimates at Gaged Sites in 

Mississippi

The estimates of the AEP flows at gaged sites were 

computed by using EMA and MGB to test for PILFs. Annual 

exceedance probability flows at gaging stations should be 

determined by weighting the station skew coefficient with 

either the generalized skew coefficient from Bulletin 17B 

(Interagency Advisory Committee on Water Data, 1982) or 

the study-specific skew coefficient in the five previously 

identified subregional watersheds. The accuracy of AEP 

flows at gaged sites can be further improved by weighting 

those flows with RRE-predicted AEP flows. The variance of 

prediction is a function of the regression equations and the 

independent variables used to develop the flow estimate. If 

the estimated AEP flows at gaged sites and RRE-predicted 

AEP flows are assumed to be independent and are weighted 

in inverse proportion to the associated variances, the variance 

of the weighted estimate will be less than the variance of 

either of the independent estimates. Once the variances have 

been computed, the two independent flow estimates can be 

weighted by using the following equation:

( )

( ) ( ) ( ) ( )

( ) ( )

, 10 , 10

10

, ,

* * p P g r P g s p P g s P g r

P g w

p P g s p P g r

V log Q V log Q

log Q V V

+ = + , (2)

where

QP(g)w is the weighted-flow estimate for the selected 

recurrence interval, in cubic feet per 

second;

Vp,P(g)r is the variance of prediction at the gaged 

station derived from the applicable RRE 

AEP, in log units;

QP(g)s is the estimate of peak flow at the gaged 

station from the EMA analysis for the 

selected AEP, in cubic feet per second;

Vp,P(g)s is the variance of prediction at the gaged 

station from the EMA analysis for the 

selected AEP, in log units; and

QP(g)r is the estimate of peak flow at the gaged 

station from the RRE for the selected AEP, 

in cubic feet per second.

The weighted-flow estimates for the gaged stations in 

Mississippi are provided in the data release associated with 

this report (Anderson, 2018).
Application of Methods 9

Flood-Frequency Estimates at Ungaged 

Locations on Gaged Streams

The AEP flows for a gaged site on a stream can be 

transferred to an ungaged location by using the area-weighting 

method; however, equation 3 does not weight the ungaged 

AEP flows with the RRE AEP flows for the ungaged site. This 

procedure is suggested if the drainage area at an ungaged site 

is within 50 percent of the drainage at the gaged site (drainage 

area ratio is more than 0.5 or less than 1.5) (Ries and Dillow, 

2006). The AEP flows at a gaged site can be transferred to an 

ungaged site by using the following equation:

( )

( )

( ) ( )

b

u

P u P g w

g

A

Q Q A

 

=      

, (3)

where

QP(u) is the estimate of flood flow for the selected 

P-percent AEP for the ungaged site, u, in 

cubic feet per second;

A(u) is the drainage area of the ungaged site, in 

square miles;

A(g) is the drainage area of the upstream or 

downstream streamgage, in square miles;

QP(g)w is the weighted estimate of flood flow for the 

selected P-percent AEP for the upstream or 

downstream streamgage, in cubic feet per 

second; and

b is the exponent of drainage area from the 

appropriate RRE.

The AEP flows at the gaged site can be transferred and 

weighted with RRE AEP flows for the ungaged site by using 

the following equation:

( ) ( ) ( )

2 2

1 P u w P u r P u

g g

A A

Q Q Q A A

 ∆   ∆  =   +  −          , (4)

where

QP(u)w is the weighted-flow estimate at the ungaged 

site after transferring the weighted peak 

flow from the gaged site, in cubic feet per 

second;

QP(u)r is the RRE flood estimate at the ungaged 

site for the selected recurrence interval, in 

cubic feet per second;

Ag is the drainage area of the gaged site, in 

square miles; 

	 │ΔA│ is the absolute difference in drainage areas 

between the ungaged site and the gaged 

site, in square miles; and

QP(u) is the estimate of flood flow for the selected 

P-percent AEP for the ungaged site, u, in 

cubic feet per second.

If the drainage area at an ungaged site differs by more 

than 50 percent from that of the gaged site, the RRE estimates 

should be used. If an ungaged site is between two gaged 

sites on the same stream, the suggested limitations should 

be applied to determine which gaged site should be used to 

estimate weighted AEP flows at the ungaged site. In general, 

the site with the smallest drainage area ratio and longest period 

of record should be used (Sauer, 1974).

Flood-Frequency Estimates at Locations on 

Ungaged Streams

For locations on ungaged streams, the flood region should 

be determined by using figure 1 or StreamStats (http://water.

usgs.gov/osw/streamstats/). The RREs for the flood region 

should then be used to compute flows for the desired range 

of AEPs (table 4). The standard error of prediction (SEP) is a 

measure of how well the regression relation estimates flood 

magnitudes when applied to ungaged basins. The given SEPs 

for the range of AEPs are listed in table 4.

Accuracy and Limitations of Regional 

Regression Equations

The RREs only apply to rural streams that can be 

described using the basin characteristics listed in table 1 and 

with drainage areas within the ranges of drainage areas listed 

in table 5 that were used to develop the equations. These 

methods should not be used for sites in a watershed that are 

affected substantially by regulation from impoundments, 

channelization, levees, or other man-made structures. The 

methods also should not be used for sites on streams in urban 

areas (impervious area greater than 10 percent) unless the 

effects of urbanization are insignificant. The methods do not 

apply where flooding is influenced by extreme ocean storm 

surge or tidal events. Reliability of the regression relations for 

values outside of the flood region limits are unknown. Because 

the RREs were computed by using basin characteristics that 

were derived from GIS layers in StreamStats (http://water.

usgs.gov/osw/streamstats/), RREs should only be computed by 

using basin characteristics from StreamStats. 

The accuracy of a flood-frequency relation traditionally 

has been expressed in two ways—as the mean standard 

error of the model (SEM) or as the mean SEP. The SEM is a 

measure of how well the regression equation fits the data used 

to derive the relation and represents the standard deviation of 

the differences between station data and the corresponding 

values computed from the regression equation. The SEP is a 

measure of how well the regression relation estimates flood 

magnitudes when applied to ungaged basins. The SEP is the 

square root of the mean square error of prediction (MSEp). 

The MSEp is the sum of two components—the MSE resulting 

from the model and the sampling MSE, which results 

from estimating the model parameters from samples of the 

population. 
10 Flood Frequency of Rural Streams in Mississippi, 2013

Regional regression 

equation

MSE 

(log ft3/s)

AVP 

(log ft3/s)2

SEP 

(percent)

Pseudo-R2

(percent)

Flood region A (27 streamgages)

Q50%=661(A)0.552 0.018 0.016 30 91

Q20%=955(A)0.564 0.015 0.015 28 92

Q10%=1,148(A)0.571 0.016 0.015 28 92

Q4%=1,380(A)0.580 0.017 0.016 29 92

Q2%=1,514(A)0.587 0.018 0.016 30 92

Q1%=1,660(A)0.593 0.020 0.017 31 92

Q0.5%=1,820(A)0.599 0.022 0.018 32 92

Q0.2%=1,995(A)0.606 0.025 0.019 33 91

Flood region B (134 streamgages)

Q50%=269(A)0.601 0.030 0.027 39 94

Q20%=455(A)0.608 0.023 0.019 33 96

Q10%=593(A)0.612 0.022 0.017 31 97

Q4%=776(A)0.614 0.024 0.018 31 97

Q2%=912(A)0.617 0.027 0.021 34 96

Q1%=1,052(A)0.619 0.032 0.022 35 96

Q0.5%=1,197(A)0.621 0.037 0.026 38 95

Q0.2%=1,390(A)0.624 0.046 0.032 43 94

Flood region C (120 streamgages)

Q50%=337(A)0.607 0.036 0.032 43 94

Q20%=512(A)0.628 0.027 0.023 36 96

Q10%=632(A)0.638 0.027 0.022 35 96

Q4%=787(A)0.648 0.030 0.023 36 96

Q2%=908(A)0.654 0.034 0.027 39 96

Q1%=1,026(A)0.660 0.039 0.029 41 95

Q0.5%=1,148(A)0.664 0.045 0.033 43 95

Q0.2%=1,309(A)0.670 0.053 0.037 46 94

Table 4. Final regional regression equations for estimating annual exceedance probability flows and 

generalized least squares model diagnostics for unregulated streams in Mississippi.

[MSE, mean square error in log10 cubic feet per second; AVP, Average Variance of Prediction in log10 cubic feet per second; 

SEP, standard error of prediction; Pseudo-R2, Pseudo coefficient of determination; Q, flood quantiles, in cubic feet per 

second; A, contributing drainage area in square miles]

Region

(see fig. 1)

Number of 

streamgages Range of drainage area

A 27 1.41 to 612 mi2

B 134 0.15 to 1,750 mi2

C 120 0.05 to 1,010 mi2

Table 5. Number of streamgages used in regional regression 

analysis and ranges of drainage area in each flood region of 

Mississippi.

[mi2, square miles]
References Cited 11

Summary and Conclusions

Flood-frequency estimates for rural Mississippi streams 

had not been updated in over 25 years (Landers and Wilson, 

1991), and since that time, improvements in estimation 

techniques and additional streamflow data were expected 

to improve the accuracy these estimates. Thus, the U.S. 

Geological Survey performed analyses to estimate annual 

exceedance probability (AEP) flows at gaged streams and 

regional regression equations (RREs) to estimate AEPs 

at ungaged locations. Twenty-one basin characteristics 

were analyzed, and those that were significant were used 

in the RREs. In addition, the RREs incorporated a newly 

developed study-specific skew coefficient (−0.08) at 

93 streamgages located in five subregional watersheds of 

Mississippi: the Middle Tennessee-Elk, Mobile-Tombigbee, 

Lower Mississippi-Big Black, Pearl, and Pascagoula. RREs 

established for the other subregional watersheds in the State 

utilized the generalized skew coefficient published in Bulletin 

17B (Interagency Advisory Committee on Water Data, 1982). 

Using the regression residuals and basin characteristics 

derived from geographic information system data, this study 

defined four flood regions (A, B, C, and the Mississippi 

Alluvial Plain) for the State of Mississippi, which differed 

from that of Landers and Wilson (1991) who identified three 

flood regions (East, West, and the Mississippi Alluvial Plain) 

in the previous flood-frequency study. The West region from 

the 1991 study was separated into two regions in the current 

study—flood region A and flood region C that includes the 

Pearl River Basin. 

Extreme flow events have the potential for devastating 

impacts to the economy, infrastructure, and the landscape. 

Keeping flood-frequency analysis current and updated will 

offer water-resource managers the information needed to 

make educated decisions regarding flood-response planning. 

By broadening the regional approach for the development 

of flood-frequency RREs across State lines, flood-frequency 

estimates have the potential to be more accurate and applicable 

to a larger study area. Finally, providing the analysis results on 

a publicly accessible web interface, StreamStats, allows a user 

to select a site of interest and obtain the AEP flows for that site 

at any time. 

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For more information about this publication, contact

Director, Lower Mississippi-Gulf Water Science Center

U.S. Geological Survey

640 Grassmere Park, Suite 100

Nashville, Tennessee 37211

For additional information, visit 

https://www.usgs.gov/centers/lmg-water

Publishing support provided by

Lafayette Publishing Service Center
 
Anderson—Flood Frequency of Rural Streams in Mississippi, 2013—SIR 2018–5148

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20185148

Supersedes USGS WRIR 91–4037

I SBN 978- 1- 4113-4264- 4

9 7 8 1 4 1 1 342 644