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OCR for page 41

4
Inland Flooding
F
EMA has studied nearly 1 million miles of rivers mapped on the landscape and joined by a smooth line
and streams, so considerable experience has to define the floodplain boundary for the Special Flood
been gained in mapping riverine flood hazard, Hazard Area. This process is repeated for a 500-year
and mapping methods are well established. In contrast, storm to define the floodplain boundary for the shaded
approaches to mapping unconfined flows over broad, Zone X, which indicates the outer limits of moderate
low-relief areas and the ponding of floodwaters in flood hazard.
depressions (shallow flooding) are only emerging. This There is no national repository of maps of historical
chapter addresses floodplain mapping associated with flood inundation that can be used to determine actual
riverine flooding and flooding in ponded landscapes. floodplain boundaries. Rather, floodplain boundaries
Riverine flood mapping is typically carried out for must be estimated by indirect means and thus flood
river and stream reaches with drainage areas exceed- maps contain various kinds of uncertainties. Most
ing 1 square mile. Each river reach is considered as a of these uncertainties arise from the interaction of
separate entity, and a collection of reaches is studied in water and land. In any storm, floodwaters flow across
a planning region such as a county. For each reach, the the land as the shape of the land surface and forces
design flood discharge for the 100-year storm event of gravity dictate. The water surface is smooth in all
is estimated using U.S. Geological Survey (USGS) directions—indeed the assumption in one-dimensional
regression equations, rainfall-runoff modeling, or sta- models of riverine flooding is that the water surface is
tistical analysis of peak discharges measured at stream horizontal along a cross-section line perpendicular to
gages. The river channel shape and longitudinal pro- the direction of flow. In contrast, the land surface is
file are described by a stream centerline, and a set of uneven, so the uncertainty in mapping the base flood
cross sections is measured transverse to the centerline. elevation (BFE) is influenced by both the uncertainty
Data for the cross sections may be obtained from an in mapping land surface elevation and the uncertainty
approximate data source, such as the National Eleva- in the depth and extent of flood inundation of the
tion Dataset, and/or by land surveying or aerial map- landscape. There are three main sources of uncertainty
ping. The base flood elevation is computed at each in riverine flood mapping:
cross section using the design discharge and a channel
roughness factor by applying a hydraulic model such 1. Hydrologic uncertainty about the magnitude of
as HEC-RAS (Hydrologic Engineering Center-River the base flood discharge;
Analysis System). The points of intersection of the 2. Hydraulic uncertainty about the water surface
water surface and land surface for each cross section are elevation; and
3. Mapping uncertainty about the delineation of
Presentationto the committee by Michael Godesky, FEMA, the floodplain boundary.
on November 8, 2007.
41

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42 MAPPING THE ZONE
Uncertainties in the base flood discharge create It is true that frequency analysis of stage height
uncertainties in the calculated base flood elevation is not the same thing as frequency analysis of base
and in the delineation of the floodplain boundary. flood elevation because the BFE is defined relative to
For a given base flood discharge, uncertainties in an orthometric datum, the North American Vertical
hydraulic modeling and parameters create uncertainty Datum of 1988 (NAVD 88; see Chapter 3), and the
in the BFE. For a given BFE, uncertainties in terrain stage height is defined relative to an arbitrary gage
elevation and boundary delineation methods create elevation datum. However, it is not necessary to
uncertainties in the location of the floodplain bound- r
econcile these datums because what we are seeking is
ary. Although the discharge, elevation, and extent of not the elevation itself, but rather the uncertainty of
inundation are interrelated, uncertainty increases with the elevation. The difference between the stage height
each step of the mapping process. The purpose of this and the flood elevation is the fixed datum height that
chapter is to define the magnitude of these uncertain- is the same for all measurements and thus does not
ties in relation to the nature of the data and methods affect their variations from year to year. It should be
used in flood mapping. understood that the purpose of this exercise is to gain
insight into the sampling variation of extreme water
UNCERTAINTY OF THE BASE FLOOD surface elevations around a statistically determined
ELEVATION AT STREAM GAGES expected value, not to statistically determine the base
flood elevation. Indeed, because the BFE depends on
A large number of factors have an effect on flood the land surface elevation, which is different at each
map uncertainty. It is helpful to have a benchmark gaging station on a river, and on drainage area and
measure of uncertainty to determine with some level other factors that vary from one location to another,
of objectivity what is or is not significant. The BFE is it is not possible to regionalize the computation of the
a useful benchmark because it separates the hydrology BFE as it is to regionalize the corresponding base flood
and hydraulics analysis from the mapping step. discharge. However, as the following analysis demon-
USGS stream gage sites are the principal places in strates, there is a great deal of commonality among the
the country where flood elevations have been measured sampling uncertainties around statistically estimated
precisely and consistently over many years. Each year extreme stage heights. It is this commonality that lends
of streamflow record includes the stage height (water insight into the corresponding uncertainties in the BFE
height relative to a gage datum elevation) recorded estimated at the same locations. The sampling uncer-
every 15 minutes as well as the maximum stage height tainties of extreme stage heights are a lower bound on
and corresponding maximum discharge for the year. the corresponding and larger uncertainties in the base
The USGS publishes these peak stage heights and flood elevation.
discharges for more than 27,000 stream gages as part The committee analyzed peak flow records in three
of its National Water Information System. This physiographic regions in North Carolina to determine
includes data from the approximately 7,000 USGS whether the uncertainty in the BFE is influenced
gages presently operational, as well as approximately by topography. The stations evaluated included six
20,000 gage sites that were operational for some period gages around mountainous Asheville in Buncombe
in the past but are now closed. Frequency analysis of County, seven gages in the rolling hills near Charlotte
peak discharges is the standard approach for defining in Mecklenburg County, and eight gages distributed
extreme flow magnitudes. Peak stage heights can also along the flat coastal plain (Figure 4.1). The average
be subjected to flood frequency analysis using the same land surface slope, computed from the National Eleva-
approach. Although this approach is unconventional, tion Dataset, is 26.7 percent in Buncombe County,
the uncertainty in the peak stage revealed by frequency 6.1 percent in Mecklenburg County, and 0.304 per-
analysis forms a lower bound on the uncertainties cent in Pasquotank County in the coastal plain. On
inherent in BFE estimation by normal means. average, a 1-foot rise in land elevation in Buncombe
County corresponds to a horizontal run of 3.7 feet,
See
while in Pasquotank County a 1-foot rise corresponds
.

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INLAND FLOODING 43
FIGURE 4.1 Map of stream gages analyzed in this report.
to a horizontal run of 329 feet. In the mountains, flood orders of magnitude—from approximately 5 square
discharges for a given drainage area are large, but the miles to approximately 5,000 square miles—which is a
floodwaters are confined within narrow valley flood- reasonable representation of the range of drainage areas
plains. In the coastal plain, lower terrain slope leads to for stream reaches used in floodplain mapping.
less flood discharge for a given drainage area, but once At each stream gage site, the historical record of
the banks overflow, floodwaters spread over a broader both flood discharges and flood stage was analyzed
floodplain. The relationship between the terrain slope using the U.S. Army Corps of Engineers (USACE)
and the river slope is discussed below (see “Channel Statistical Software Package HEC-SSP. Although
Slope”). some stream gage records include estimates of “histori-
Peak stage data were also studied from 10 gages cal” floods before the period of gaged record, these were
in southwest Florida (Table 4.1), which has a pitted not included in the present study. In some gage records,
landscape with many sinkholes where water ponds in there are notes that the flood flows were affected by
depressions and flows from one pond to another until it factors such as urbanization or releases from upstream
reaches a stream or river. These stage height data were reservoirs. The committee did not separate out these
analyzed to determine whether BFE uncertainties were records in the belief that riverine environments must be
different in pitted landscapes compared to landscapes mapped, regardless of whether such events occurred. In
with dendritic drainage patterns. Altogether, 31 stream a few of the coastal gages, the times of occurrence of the
gage records were examined from North Carolina and maximum flood stage and maximum flood discharge
Florida. The gages have an average length of record of differ slightly, and in those cases, the largest value was
54 years and an average drainage area of 458 square used. For each gage, the log-Pearson III distribution
miles. Although the spatial distribution of USGS was applied to both discharges and stage heights, as
stream gages is biased toward larger streams and rivers,
the drainage area of the gages examined varied by three .

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44 MAPPING THE ZONE
TABLE 4.1 Stream Gages Used for Flood Frequency Analysis
USGS Site Site Name Drainage Area (square miles) Years of Record
Buncombe County
03448000 French Broad River at Bent Creek, N.C. 676 54
03448500 Hominy Creek at Candler, N.C. 79.8 37
03451000a Swannanoa River at Biltmore, N.C. 130 78
03451500 French Broad River at Asheville, N.C. 945 85
03450000 Beetree Creek near Swannanoa, N.C. 5.46 72
03449000 North Fork Swannanoa River near Black Mountain, N.C. 23.8 32
Mecklenburg County
02142900a Long Creek near Paw Creek, N.C. 16.4 41
02146750 McAlpine Creek below McMullen Creek near Pineville, N.C. 92.4 31
02146600 McAlpine Creek at Sardis Road near Charlotte, N.C. 39.6 45
02146700 McMullen Creek at Sharon View Road near Charlotte, N.C. 6.95 44
02146507 Little Sugar Creek at Archdale Drive at Charlotte, N.C. 42.6 29
02146500 Little Sugar Creek near Charlotte, N.C. 41 52
02146300 Irwin Creek near Charlotte, N.C. 30.7 44
North Carolina Coastal Plain
02092500 Trent River near Trenton, N.C. 168 51
02093000 New River near Gum Branch, N.C. 94 44
02105900 Hood Creek near Leland, N.C. 21.6 34
02105769 Cape Fear River at Lock #1 near Kelly, N.C. 5,255 37
02108500 Rockfish Creek near Wallace, N.C. 69.3 26
02053500a Ahoskie Creek at Ahoskie, N.C. 63.3 57
02084500 Herring Run near Washington, N.C. 9.59 31
02084557 Van Swamp near Hoke, N.C. 23 27
Southwest Florida
02256500 Fisheating Creek at Palmdale, Fla. 311 75
02295637 Peace River at Zolfo Springs, Fla. 826 74
02296750 Peace River at Arcadia, Fla. 1,367 77
02298830 Myakka River near Sarasota, Fla. 229 70
02300500 Little Manatee River near Wimauma, Fla. 149 68
02303000 Hillsborough River near Zephyrhills, Fla. 220 67
02310000 Anclote River near Elfers, Fla. 72.5 62
02312000 Withlacoochee River near Trilby, Fla. 570 76
02312500 Withlacoochee River near Croom, Fla. 810 67
02313000 Withlacoochee River near Holder, Fla. 1,825 75
aLocations of detailed flood hydrology and hydraulic studies.
illustrated in Figure 4.2 for the 78 years of record on 0.01 (20,672 cubic feet per second [cfs]), and the
the Swannanoa River at Biltmore. c
orresponding base flood stage height is 22.65 feet
It is evident in Figure 4.2 that both the flood dis- above gage datum. The uncertainty of the base flood
charges and the stage heights have a similar frequency is quantified by the dashed confidence limits in the
pattern. The base flood discharge is the value for the graphs, a range from 16,024 to 28,514 cfs for the
computed curve (red line) at exceedance probability flow and 19.54 to 27.30 feet for the stage height.

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INLAND FLOODING 45
Figure 4-2.eps
FIGURE 4.2 Frequency analysis of flood discharge and stage height for gage 03451000, the Swannanoa River at Biltmore, North
Carolina, computed using USGS peak flow data and thebitmap image
HEC-SSP program.
These confidence limits were computed using the 1.645 standard errors above and below the estimate of
noncentral t-distribution as defined in Bulletin 17-B the mean, so a good measure of the sampling error in
(IACWD, 1982). This range represents approximately the base flood elevation can be derived from the range
in the confidence limits. This estimate of the sampling
Bulletin 17B does not include regional skew information for error provides a sense of how much inherent uncer-
peak stage analysis. Thus, the confidence limits calculated by this tainty exists in BFEs derived from measured annual
method provide only an approximate estimate of the sampling error flood elevations at gages with long flood records.
of the peak stage data. This is sufficient and appropriate for the
Figure 4.3 plots the estimated sampling error of the
purpose that these limits are used in this study.

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46 MAPPING THE ZONE
0
1
FIGURE 4.3 Sampling error of the 100-year stage height at 31 Florida and North Carolina stream gage sites.
Figure 4-3.eps
bitmap image
computed 100-year stage heights against drainage area Moreover, the average sampling error was 1 foot with
at all 31 stream gages. This graph displays a surprising a range from 0.3 foot to 2.4 feet for 30 of the 31 sites.
result: there is no correlation of the sampling error with In other words, even at locations with long records of
drainage area or topography across the three regions of measured peak floods, the BFE cannot be estimated
North Carolina, nor is there any significant difference more accurately than approximately 1 foot, no matter
in the results from the Florida gages compared with what mapping or modeling approach is used. This
those from North Carolina. One large outlier in the value provides a benchmark against which the effects
sampling error (5.6 feet) occurs at Hominy Creek in of variations in methods can be evaluated—a variation
Candler, North Carolina, and was caused by a couple of that produces a change in BFE of more than 1 foot
unusually large floods that significantly skewed the stage may be significant. At ungaged sites, uncertainties in
frequency curve at that stream gage site. If this value is the BFE are necessarily higher.
omitted, the average value of the remaining standard
errors is 1.06 feet, with a range of 0.3 foot to 2.4 feet. Finding. The sampling error of the base flood eleva-
This frequency analysis of stage heights has a tion estimated using flood frequency analysis of
number of limitations: no regional skew estimates were annual maximum stage heights measured at 30 long-
included (none exist for stage height data), the number record USGS stream gage sites in North Carolina and
of stream gages was relatively small (31 gages of 27,000 Florida does not vary with drainage area, topography,
for which the USGS has peak gage records), and only a or landscape type and has an average value of approxi-
small region of the nation was examined. This analysis mately 1 foot.
should be considered as indicative but not definitive of
what a more comprehensive study of such data across DETERMINING THE FLOOD DISCHARGE
the nation might reveal. Despite these limitations, a
reasonable statistical interpretation of the result is that Riverine flood studies involve a combination of
a null hypothesis cannot be rejected, namely that the statistical, hydrologic (rainfall-runoff ), and hydraulic
sampling error of the 100-year stage height, or equiva- models. Determining the BFE involves first determin-
lently the 100-year BFE, does not vary with drainage ing the base flood discharge. This can be done three
area or geographic location over the gages studied. ways:

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INLAND FLOODING 47
1. A hydrologic model is used to predict the peak 3. USGS regional regression equations—simple
discharge associated with a design storm (hypothetical methods for estimating the flood discharge as a function
event of a desired frequency), of drainage area and sometimes other parameters.
2. The peak discharge that has a 1 percent chance
of occurring in a given year is observed directly (by In a flood mapping study, each river reach between
frequency analysis at a gage site), or significant tributaries is treated as a separate entity and
3. The peak discharge is inferred using regional a corresponding flood discharge must be defined for
regression equations. it. Approximate studies use USGS regional regression
equations, and limited detailed studies use regression
In all cases, a hydraulic model is subsequently used equations or gage data (Table 2.1). In detailed studies,
to compute the BFE, and geographic information a mixture of methods is used—rainfall-runoff models
system (GIS) mapping methods are required to over- in about half of the studies and flood frequency analysis
lay the computed flood elevation on the surrounding or regression equations in the others (Table 4.2).
topography to determine the extent of the floodplain.
Figure 4.4 illustrates the hydrologic and hydraulic Flood Frequency Analysis
modeling processes and input involved in riverine
floodplain mapping. About 30 percent of detailed mapping studies use
Three hydrologic methods are used in flood map- flood frequency analysis to establish the peak flow for
ping studies: the 100-year flood event (Table 4.2). The log-Pearson
III is the U.S. standard of practice for flood frequency
1. Flood frequency analysis—statistical estimation analysis for gaged sites (IACWD, 1982). Three statisti-
of flood discharges as illustrated above for the gage cal quantities (mean, standard deviation, and skewness
studies in North Carolina and Florida; coefficient) are required to estimate the parameters of
2. Rainfall-runoff models—hydrologic simulation the probability distribution. The Interagency Advisory
models that convert storm rainfall to stream discharge Committee on Water Data (IACWD, 1982) guidelines
applied using standardized design storms; and identify procedures for the use of regional estimates of
Rainfall-Runoff
Models
Base Maps &
(Precipitation, Streamflow)
Surveys
Hydrometeorological Data
Statistical Hydraulic Flood
Qp WSE
Analysis Models Map
DEM
Regional/Local
Regression
FIGURE 4.4 Schematic of an idealized flood mapping study showing the type of input, models, and output used. The outputs from
each step are used as inputs to the next step. Digital elevation models (DEMs) and surveys are used first to configure and provide input
Figure 4-4.eps
to the hydraulic model in the form of cross sections, structures, and roughness coefficients, and later as input to flood map creation.
NOTE: Qp = flood peak flow; WSE = water surface elevation.

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48 MAPPING THE ZONE
TABLE 4.2 Methods Used to Compute the Peak
Discharge in Detailed Flood Mapping Studies
Method Percentage Used
USGS regional regression equations 22
Rainfall-runoff models 48
Flood frequency analyses 30
SOURCE: Presentation to the committee by Michael Godesky, FEMA,
on November 8, 2007.
the skewness coefficient when the data record is not
sufficiently long and for the treatment of outliers and
other data anomalies. Even when all the guidelines are
followed however, sampling uncertainty remains and
is characterized by the confidence intervals of the peak
flood estimates, as shown above for flood flows and
stage heights.
A National Research Council (NRC, 2000) report
FIGURE 4.5 Return periods for flood discharge at the French
distinguished between two kinds of uncertainty:
Broad River at Ashville, N.C., for the expected flood discharge
and its upper and lower confidence limits (dotted lines).
1. Natural variability deals with inherent vari-
ability in the physical world; by assumption, this
“randomness” is irreducible. In the water resources
context, uncertainties related to natural variability flow record in this study. As in Figure 4.2, natural
include things such as streamflow, assumed to be a variability is represented by the central red line and
random process in time, or soil properties, assumed expresses the relation between the magnitude of the
to be random in space. Natural variability is also flood discharge and its return period or likelihood of
sometimes referred to as aleatory, external, objec- occurrence. Knowledge uncertainty is expressed by the
tive, random, or stochastic uncertainty. spread of the confidence limits around this estimated
2. Knowledge uncertainty deals with a lack of line. As more data are used in a frequency analysis,
understanding of events and processes or with a the confidence band around the flood frequency curve
lack of data from which to draw inferences; by becomes narrower.
assumption, such lack of knowledge is reducible For this gage, reading up from the horizontal axis
with further information. Knowledge uncertainty value of 100 years return period for flood discharge and
is also sometimes referred to as epistemic, func- across to the vertical axis yields an equivalent return
tional, internal, or subjective uncertainty. period of 50 years for the lower confidence interval
discharge and 180 years for the upper confidence
Estimation of flood peaks at return periods of interval discharge. The corresponding values for the
interest for determining 100-year and 500-year (1 and 500-year flood range from a 200-year to a 1,000-year
0.2 percent annual chance) floods illustrates the con- return period. Similar results were obtained for confi-
cepts of natural variability and knowledge uncertainty. dence limits on the 100-year flood stage. This means
Figure 4.5 shows the same kind of flood frequency that knowledge uncertainty is significant even when
curves illustrated in Figure 4.2 except that the con- frequency analysis is performed on long gage records.
fidence limits computed by the HEC-SSP program
for specific flood probabilities are highlighted. These Rainfall-Runoff Models
data are for the French Broad River at the Asheville,
N.C. gage site (gage 3451500) in Buncombe County, Rainfall-runoff models are mathematical represen-
which has 85 years of peak discharge record, the longest tations of the natural system’s complex transformation

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INLAND FLOODING 49
of rainfall into runoff. To compute the flow discharge Sorooshian and Gupta, 1983; Sorooshian et al., 1983;
at the watershed’s outlet, hydrologic models include Yapo et al., 1996, 1998).
basic flow routing techniques and one-dimensional
representations of overland flow and channel hydrau- Recommendation. FEMA should calibrate hydro-
lics. These approximations permit several subbasins logic models using actual storm rainfall data from
to be nested into a single model, allowing better multiple historical events, not just flood design
accounting for spatial variability and computation of storms.
the flow hydrograph (time record of discharge) within
the watershed. Hydrologic models can be event-based Hydrologic modeling uncertainty is often described
or continuous, depending on whether the initial con- in the form of a probability distribution of model out-
ditions of model parameters such as soil moisture put (e.g., peak discharge for the required return period).
are assumed or updated using information gathered By changing the distribution of model parameters, it
between storms. The Federal Emergency Manage- is possible to identify both the impact of uncertainty
ment Agency (FEMA) accepts 13 event-based and 3 in model parameters on hydrologic predictions and
continuous hydrologic modeling software programs for the effects of uncertainties in model input and model
determining flow hydrographs. structure on predictive uncertainty. Figure 4.6 demon-
The natural variability of quantities such as pre- strates that addressing only parameter uncertainty can
cipitation, soil moisture, and soil physical and hydraulic lead to biased and, in some cases, incorrect assessment
properties is typically described using probabilistic of total uncertainty.
models (Merz and Thieken, 2005). Knowledge uncer-
tainty is associated with the structure of the model and USGS REGIONAL REGRESSION EQUATIONS
its ability to capture the behavior of the studied system
in part or as a whole, the model parameters used to USGS regional regression equations are used to
quantify the relationships between the various compo- compute flood discharges in nearly all approximate
nents of the system, and model input and output. mapping studies and in about 20 percent of detailed
Model calibration and parameter estimation are studies. A state is divided into regions, each with a
perhaps the most important aspects of hydrologic set of USGS regression equations that allow flood
modeling and are a major contribution to knowledge map practitioners to compute flood discharges for
uncertainty. FEMA (2003) guidelines allow models to the required recurrence intervals. When the USGS
be calibrated using (1) historical rainfall observations, d
evelops these equations, peak discharges at ungaged
which can improve model performance under different sites are regionalized by developing empirical rela-
rainfall conditions, or (2) a design storm, such as those tionships between the peak discharge and basin
defined in the National Oceanic and Atmospheric characteristics using statistical analyses of annual
Administration’s (NOAA’s) Atlas 14, against the maximum flows at gaged sites. Regionalization was
corresponding peak flow of the same return period originally accomplished through nonlinear regression
(frequency). The typical procedure is to estimate the analysis. With this procedure, records from gaged
return period of the peak flow of a historical flood, sites were used to define a set of empirical relations
use the design storm for that return period, and then between selected recurrence interval discharges and
calibrate the hydrologic model so it reproduces the a set of exogenous or independent variables, always
observed flood flow. The optimized parameters are including drainage area. These relations were then
then used to calculate the 100-year peak flow. How- used to estimate discharges at selected recurrence
ever, using a single peak flow calibration may prove to intervals for ungaged sites. A more recent approach to
be inadequate, given the demonstrated importance of regionalization is the region of influence generalized
long records with a sufficiently large number of events least squares method, in which an interactive proce-
(storm hydrographs) to estimate parameters (e.g., dure is used to estimate recurrence interval discharges
(Tasker and Stedinger, 1989). For each ungaged site, a
.
.
subset of gaged sites with similar basin characteristics

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50 MAPPING THE ZONE
FIGURE 4.6 Streamflow hydrograph prediction uncertainty associated with estimated parameters (dark gray) for the Sacramento Soil
Figure 4-6 redrafted.eps
Moisture Accounting (SAC-SMA) model and 95 percent confidence interval for prediction of observed flow (light gray) for water year
bitmap image
1957 at the Leaf River basin’s outlet (USGS Station 02472000 Leaf River, near Collins, Mississippi). The last few peaks are enlarged to
better show the uncertainty distributions. The 95 percent confidence interval represents the total likely uncertainty arising from model,
parameter, and input uncertainties. It is noteworthy that the 95 percent confidence interval in model prediction is very large at or near
peak flow events. SAC-SMA is the core hydrologic model in the National Weather Service River Forecasting System. SOURCE: After
Ajami et al. (2007). Copyright 2007 American Geophysical Union. Reproduced by permission of AGU.
is selected and regression techniques are used to deter- Figure 4.7 shows the age of the regression equa-
mine the relation between flood discharge and basin tions used at the state level for rural basins. Most states
characteristics at gaged sites. This relation is then used have updated their regional regression equations since
to estimate flood discharges at ungaged sites. Tests of 1996. However, basins that cross state boundaries may
this approach in Texas (Tasker and Slade, 1994) and be analyzed using regression equations of different
Arkansas (Hodge and Tasker, 1995) yielded estimates ages and different regression methodologies, creating
with lower prediction errors than those produced inconsistent results across the basin.
using traditional regional regression techniques. The Regression equations in North Carolina generally
region of influence method was used for the North take the form QT = αAβ, where QT is the T-year flood
Carolina regional regression equations (Pope et al.,
2001) discussed in this chapter.
Regression methods have evolved from ordinary
least squares to weighted least squares to generalized TABLE 4.3 Methods Used to Derive Empirical Flood
least squares. Because of the different climate, physio- Equations
graphic, and hydrologic conditions across the country, Number of States Percentage of
Regression Method or Regions Total
more than 200 explanatory variables are used at one
location or another. The equations are developed by Ordinary least squares 7 13
Weighted least squares 4 4
state-level studies, so problems can arise at state bound- Generalized least squares 43 81
aries if different equations are used for the same variable Multiple linear regression 1 2
on either side of the boundary. Table 4.3 summarizes NOTE: These numbers do not include USGS Water Science Centers
the methods currently used to derive flood discharge that use region of influence analyses in addition to one of these regression
methods.
equations. SOURCE: USGS.

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INLAND FLOODING 51
WA
MT ND ME
OR MN VT
NH
ID SD NY
WI MA
WY MI CT RI
NE IA PA NJ
NV UT IL IN OH *DE
CA CO KS WV VA MD
MO KY
TN NC
AZ OK SC Years Equations Published
NM AR
MS AL GA 1974-1985
TX LA 1986-1990
FL
1991-1995
1996-2000
2001-2007
AK HI-AS Regional-regression equations
PR-VI may not be representative of
the entire state.
FIGURE 4.7 Summary of rural peak flow regression equations by date of completion. SOURCE: USGS.
Figure 4-7.eps
peak, A is the catchment area, and α and β are regres- piedmont region. The USGS is currently revising the
sion coefficients. Catchment area, or the area draining regression equations for the Blue Ridge region using
to a defined point on the stream system, is the single additional stream gages from adjacent states with
most important independent variable. In effect, all the similar topography.
other variables that might influence the peak discharge
are bound up in the coefficients α and β of the regres- Finding. The variation in peak flow predictions
sion equation, which are assumed constant within a between regions illustrates the importance of devel-
particular region. In North Carolina, regression equa- oping regression equations at the river basin level,
tions are defined for three regions—the Blue Ridge- independent of state boundaries. States with sig-
piedmont region, the sand hills area, and the coastal nificantly outdated regression equations that should
plains. The discharges calculated using the equations be updated include Michigan, Massachusetts, New
are shown in Figure 4.8. For a 100-square-mile drain- Jersey, California, and New Hampshire.
age area, the 100-year flood discharge estimate is
13,250 cfs in the Blue Ridge-piedmont area, 6,340 cfs
North Carolina Case Study of Flood Discharge
in the coastal plain, and 3,400 cfs in the sand hills area.
Estimation
Hence, flood discharge in the flat coastal plain is about
one-half of the discharge in the Blue Ridge-piedmont At the request of the committee, the North Carolina
area. The low discharge in the sand hills area may reflect Floodplain Management Program (NCFMP) conducted
the presence of more absorbent soils. case studies of flood hydrology, hydraulics, and mapping
Although the USGS regression equations are the in three study reaches in North Carolina. These included
same for the Blue Ridge and piedmont regions, these Swannanoa River in Buncombe County (mountains),
regions are physiographically distinct from one another Long Creek in Mecklenburg County (piedmont), and
(as the committee has treated in the flood study in Ahoskie Creek in Hertford County (coastal plain;
North Carolina). When the equations were being Figure 4.9). Lidar (light detection and ranging) topo-
derived, there were insufficient stream gages in the Blue graphic data and detailed studies yielding BFEs and
Ridge Mountains to distinguish it statistically from the floodplain boundaries were available for all three study

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56 MAPPING THE ZONE
tions, which greatly simplifies the equations required approximations, the flow velocity is assumed to vary
to model the motion of water and to compute the only in the direction of the longitudinal channel slope.
surface water elevation within the channel. However, The flow velocity is averaged over both the depth and
equations are still needed to account for (1) changes in the width of the flow at each cross section. A single
the water surface profile caused by the irregular shapes water surface elevation value is computed, and the
of natural channels, which create flow resistance, and depth of water over all points in the cross section is
(2) structures and flow impediments, which increase determined by extending a horizontal water surface
the height of the water surface upstream and create a elevation line across the channel. The floodplain
backwater effect. boundary is delineated at the location where the water
In practical open-channel hydraulics, the depth- surface elevation line intersects the topographic surface
averaged velocity is a good representation of the flow of land surface elevation.
velocity. As a result, the flow can be approximated using Most one-dimensional hydraulic models require
one- or two-dimensional models. In one-dimensional significant input data (Figure 4.12). The study domain
FIGURE 4.12 A typical three-dimensional representation of a one-dimensional model of a detailed flood study along a segment
of a study reach on the Swannanoa River, North Carolina, Figure the information required for the U.S. Army Corps of Engineers’
showing 4-12.eps
one-dimensional HEC-RAS model. The vertical scale is exaggerated toimage cross-sectional features. Solid black lines represent
bitmap highlight
the channel cross section. Blue areas represent the water surface computed for given discharge. Gray areas are structures that extend
across the channel and for a reasonable distance along the channel. Black areas are structures that can be represented by a vertical
plane as flow impediments. Dashed areas indicate where water can pond. Numbers at the right side of some cross sections refer to
the distance (here in feet) from the downstream end of the reach. Data from the North Carolina Floodplain Mapping Program.

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INLAND FLOODING 57
is generally extended beyond the upstream and down- are computed in directions both parallel and perpen-
stream boundaries of the targeted reach to ensure dicular to the longitudinal channel slope. The resultant
that backwater effects are taken into account and that velocity is then quantified in magnitude and direction.
numerical errors in the computed surface water profile These models solve the complex flow equations using
are minimized. A stream centerline is then defined, numerical algorithms that iteratively advance the solu-
and the cross-section geometry is determined at regular tion in space and time over computational quadrilateral
intervals along the centerline and at structures, river or triangular meshes. The size and shape of the mesh
bends, and major points of change in channel slope grids depend on factors such as the numerical solution
and/or cross-section geometry. Accurate representa- method, available terrain data, level of required detail,
tion of structures and river bends is important for and available computational resources.
identifying flow constrictions and areas where water Two-dimensional models are computationally
can pond, such as at bridges and roadway embank- demanding and require considerable expertise to
ments. Finally, information about surface roughness prepare and execute. However, FEMA flood studies
(i.e., flow resistance) must be gathered for each cross require only a single discharge value for the peak
section. Several equations that relate surface rough- flow of the 100-year event, so flood mapping analyses
ness to flow characteristics are available, but the most are performed assuming steady flow. In steady flow
popular in open-channel flow computation is the the water surface elevation is constant over time; in
Manning equation. Modelers generally determine the unsteady flow the water surface elevation is computed
Manning roughness coefficient at several points across for each cross section or grid point location as a func-
the channel and floodplain by visual examination and tion of time. The steady flow assumption simplifies
use of standardized tables and photographs of channels the data requirements, particularly with respect to
of known roughness. b
oundary conditions, and greatly reduces the compu-
One-dimensional models are computationally effi- tational demand.
cient and are considered by many engineers to produce Two-dimensional models offer many advantages
reasonably accurate surface water profiles (Büchele et over one-dimensional models, including more accu-
al., 2006), although the accuracy must be checked at rate resolution of the actual surface water elevation
river junctions, loops, branches, and significant lateral and direct determination of floodplain extent. A study
inflows. Because the output of one-dimensional models comparing the two types of models found that two-
must be superimposed on digital elevation data to pro- dimensional models have significantly greater ability
duce a Flood Insurance Rate Map, the final mapping to determine flow velocity and direction than one-
product is sensitive to variations in surface elevation dimensional models (TRB, 2006). Computing velocity
that were not captured in the cross sections. This may is an important element of flood damage calculations,
cause inconsistent model results, particularly in urban particularly in urban areas where measurable damage to
areas where roads, walls, and other structures can create buildings and other properties can result from fast flow.
preferential flow paths. Since the flood map is drawn The Transportation Research Board (TRB, 2006) study
on a topographic surface and the water surface eleva- found that the difference between one-dimensional
tion is determined by a hydraulic model using cross and two-dimensional models is smallest within the
sections, it is important for the topographic surface confines of the main channel (green), increases across
and cross sections to be consistent with one another. the channel and floodplain, and is largest near the
This may not be the case if the cross sections are smaller branch of the river (Figure 4.13). This diver-
defined by land surveying and the topographic surface gence across the channel and floodplain results from
is defined by aerial photogrammetry (Tate et al., 2002). the inability of the one-dimensional model to capture
Careful adjustment and reconciliation of topographic complex features, such as braided streams, multiple
and cross-section data sources are needed for detailed openings, and bridge crossings near channel bends.
mapping studies. Consequently, the choice of model can significantly
In two-dimensional models, the velocity is aver- affect determination of floodplain elevations and the
aged over only the flow depth, and velocity components vertical extent of the channel.

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58 MAPPING THE ZONE
(a) (b)
Large Channel Plan: Confluence3050b 3/21/2005
8870.223 Legend
9000 8423.218 WS PF 1
7976.213
8000 Ground
7436.193 Bank Sta
7000 6851.295 Inef f
5900
5072.7
3606.7
3000
2000
1000
Figure 4-13a.eps
Figure 4-13b.eps
bitmap image
FIGURE 4.13 Differences between one-dimensional and two-dimensional models for an idealized channel with a single opening
bridge downstream of a river confluence. (a) One-dimensional model setup information, (b) surface water elevation at main channel
centerline produced by the one-dimensional model, (c) two-dimensional model setup with computational mesh, and (d) relative differ-
ence in the magnitude of flow 4-13c.eps numbers in d indicate that the two-dimensional model produced higher velocity values,
Figure velocity. Positive Figure 4-13d.eps
and negative numbers indicate that the one-dimensional model produced higher flow velocity values. SOURCE: TRB (2006).
bitmap image bitmap image

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INLAND FLOODING 59
This conclusion highlights a potential source for bridge and culvert openings; ineffective flow areas
of uncertainty in mapping floodplains using one- and channel obstructions were defined; and Manning’s
d
imensional models. Models acceptable under current n could vary along the channel.
FEMA guidelines include 11 one-dimensional steady 2. Limited Detailed Study North Carolina (LDSNC).
flow models, 10 one-dimensional unsteady flow models, Same as a detailed study except that field surveying of
and 4 two-dimensional steady-unsteady flow models. channel structures was estimated or limited.
The guidelines note the limitations of each model 3. Limited Detailed Study National (LDSNAT).
and recommend validation and calibration in most Same as for LDSNC except no channel structures or
cases, but do little to help mapping partners determine obstructions were included and ineffective flow areas
which type of models are most appropriate for a given were removed near structures.
community. Furthermore, the guidelines require the 4. Approximate (APPROX). Same as for LDSNC
mapping partner to check velocities at river bends to except that Manning’s n was uniform along the channel
determine potential erosion. For meandering rivers, profile (it can have separate values for the channel and
the TRB (2006) report suggests that such determi- the left and right overbank areas).
nations are better made through two-dimensional 5. Approximate-NED (APPROX-NED). Same as
models. Partnerships with academic institutions and APPROX but the National Elevation Dataset (NED),
individuals often facilitate the transition of research rather than lidar, was used for terrain representation.
models into practical applications. For example, the
National Weather Service has led two extensive dis- Figure 4.14 shows the differences among these five
tributed hydrologic model intercomparison projects methods in representing a channel cross section on the
(Smith et al., 2004, 2008), in part to establish links Swannanoa River.
with researchers developing the next generation of Figure 4.15 illustrates the differences between
hydrologic models. water surface elevation computed using the five differ-
ent hydraulic study methods on Long Creek. As long
Recommendation. FEMA should work toward as lidar terrain data are used, the effect of variations
greater use of two-dimensional flood hydraulic in the hydraulic methods (DS, LDSNC, LDSNAT,
models where warranted by the floodplain geometry, APPROX) is quite small. The cascading appearance
including preferential flood pathways and existing of the water surface profile for the APPROX-NED
and planned structures. model is due to a horizontal misalignment between
the base map planimetric information and the elevation
NORTH CAROLINA FLOOD MAPPING information. In other words, detailed mapping of the
CASE STUDY stream network within Mecklenburg County shows
the correct location of the stream centerline, and when
lidar data are used to define elevation, the topographic
Riverine Flooding
and base map imagery are correctly aligned. However,
The NCFMP (2008) study considered different when the National Elevation Dataset is used to define
combinations of three parameters: (1) hydrologic study topography, the stream centerline and the topography
type, (2) hydraulic study type, and (3) source of terrain are not correctly aligned and the stream appears to flow
information. The effects of variations in hydrologic over small ridges and gullies rather than down a stream
methods have been described above. The effects of channel. The NED is on average 14.7 feet above the
variations in hydraulic and terrain data are now dis- lidar on Long Creek (Table 3.2), hence the elevated
cussed. Five approaches were examined: water surface profile.
The BFE profiles for Ahoskie Creek and the
1. Detailed Study (DS). Lidar data were used for Swannanoa River are plotted in Figure 4.16 for the five
topography, field surveys for channel cross sections and
The LDSNAT variant is specific to the NCFMP (2008) case
study and does not imply that FEMA limited detailed studies omit
See . description of structures.

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60 MAPPING THE ZONE
FIGURE 4.14 Differences in the channel cross section and structure geometry among the five different hydraulic study types for station
Figure 4-14.eps
16008 of the Swannanoa River reach. Structures are shaded black, and water is shaded blue. The lower-right figure illustrates areas
bitmap image
that are isolated from the main channel by a structure. Such areas of ineffective flow can store water but do not convey it. SOURCE:
North Carolina Floodplain Mapping Program. Used with permission.
690
680
670
660
Elevation (feet)
650
640
630 DS
LDSNC
620 LDSNAT
APPROX
APPROX-NED
610 STRUCTURE
USGS Gage
600
19000 24000 29000 34000 39000 44000 49000 54000
Station
FIGURE 4.15 Base flood elevation profiles for different hydraulic study types on Long Creek. SOURCE: NCFMP (2008). Used with
Figure 4-15.eps
permission.
hydraulic and mapping study types. In these streams, the magnitude of the variations is significantly greater
the profiles reveal a great deal of random variation in than the magnitude of variations in other hydraulic
the APPROX-NED BFE profile—sometimes it is methods. This result countered expectations that map
above the other profiles and sometimes below, and accuracy is affected at least as much by the accuracy

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INLAND FLOODING 61
2060
2050
Swannanoa River
2040
2030
Elevation (feet)
2020
2010
DS
2000 LDSNC
LDSNAT
1990 APPROX
APPROX-NED
STRUCTURE
1980 USGS Gage
1970
0 5000 10000 15000 20000 25000
Station
Figure 4-16 top.eps
45
Ahoskie Creek
40
35
Elevation (feet)
30
DS
25
LDSNC
LDSNAT
APPROX
20 APPROX-NED
STRUCTURE
USGS Gage
15
29000 34000 39000 44000 49000 54000 59000 64000 69000
Station
Figure 4-16 bottom.eps
FIGURE 4.16 Water surface elevation profiles for different hydraulic study types on the Swannanoa River and Ahoskie Creek.
SOURCE: NCFMP (2008). Used with permission.
of the hydraulic model and hydraulic parameters as by data is the most important factor in the accuracy of
the accuracy of the topographic data. The case studies, flood maps in riverine areas.
which had the advantage of using precise topographic Table 4.6 quantifies the differences between the
(lidar) data for analysis, clearly show that topographic flood elevation profiles in Figure 4.16 for detailed

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62 MAPPING THE ZONE
TABLE 4.6 Base Flood Elevation Differences Between Detailed and Approximate-NED Studies
Stream Mean (ft) Standard Deviation (ft) Minimum (ft) Maximum (ft)
Ahoskie Creek 0.95 1.30 –3.34 2.87
Long Creek 20.89 3.07 13.11 26.45
Swannanoa River 0.18 3.61 –5.12 9.91
studies using lidar terrain data and approximate studies S
wannanoa River. As expected, these results demon-
using NED terrain data. The differences are striking, strate that backwater effects from structures increase
particularly for Long Creek, where on average the BFE base flood elevations and that the distance these
is more than 20 feet higher if calculated using the NED effects extend upstream is longest at Ahoskie Creek in
rather than lidar. In the other two study reaches, the the coastal plain and shortest on the Swannanoa River
NED BFE is, on average, fairly close to the lidar BFE, in the mountains of western North Carolina.
but at particular cross sections the two elevations may
differ by up to 10 feet. Finding. Backwater effects of structures influence the
base flood elevation profile on all three study reaches
Finding. The base flood elevation profile is sig- and are most pronounced in the coastal plain.
nificantly more influenced by whether the National
Elevation Dataset or lidar terrain data are used to Channel Slope
define land surface elevation than by any variation of
methods for calculating channel hydraulics. The three study areas were chosen in mountains,
rolling hills, and coastal plains to examine the extent
Backwater Effects of Structures to which differences in terrain affect flood properties.
Table 4.8 shows various measures of the slope in these
One of the key reasons for doing detailed surveys study areas: the longitudinal and lateral slope values
of structures in stream channels is to estimate their were derived from the HEC-RAS models for flood
backwater effects. The structures are shown as black flow. The lateral slope is the value along the stream
squares in Figure 4.16, and it can be seen that the cross sections at the edge of the floodplain, averaged
flood profiles jump upward at some of these loca- for the left and right banks of the cross section and
tions. Bridges and culverts constrain the movement over all cross sections in the reach. The terrain slope
of floodwaters during very large discharges, and the was derived from the NED over the whole county. As
water elevation upstream of a structure increases to one would expect, the longitudinal slopes of the stream
create the energy needed to force the water to flow channels are much lower than the lateral slopes; that
through the structure. Intuitively, these backwater is, the land slopes much more steeply away from the
effects should propagate further upstream in flat channel than along it. Even though the terrain slope for
terrain than in steep terrain, but by how much? The the Swannanoa River (26.7 percent) is nearly 100 times
impact of backwater on the surface water profile was that for Ahoskie Creek (0.3 percent), the longitudinal
the highest in Ahoskie Creek on the coastal plain, channel slopes of those two reaches differ by only a
where six structures caused backwater effects and factor of 3.5 (0.18 percent versus 0.05 percent). In
all of them extended to the next structure upstream other words, despite the large differences in topography
(Table 4.7). On Long Creek, all four structures had between the mountains of western North Carolina
backwater effects and three reached the next struc- and the flat coastal plain, the creeks and rivers in those
ture. On the Swannanoa River, six of nine structures regions are much more similar to one another than to
had backwater effects, including five that reached the the surrounding terrain. The longitudinal slopes of the
next structure. The average distance that a backwater rivers are much flatter than the average slope terrains
effect propagated upstream was 1.12 miles on Ahoskie through which they flow. This may help to explain
Creek, 0.5 mile on Long Creek, and 0.30 mile on the why there are no pronounced regional differences in

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INLAND FLOODING 63
TABLE 4.7 Effect of Backwater Upstream of Structures
Number of Extended to Next Average Elevation Maximum Elevation Distance Upstream
Stream Structures Structurea (ft)b (ft)b (miles)c
Ahoskie Creek 6 6 0.89 2.54 1.12
Long Creek 4 3 0.34 0.73 0.50
Swannanoa River 9 5 0.20 2.02 0.30
aAn elevated backwater effect extended from one structure to the next one upstream.
bRefersto the difference between the two elevation profiles with and without structures.
cAverage distance upstream from a structure from which backwater effects propagate.
TABLE 4.8 Channel and Terrain Slopes
Terrain Slopea Longitudinal Slope Lateral Slope Lateral Run/Rise
Stream (%) (%) (%) (ft/ft)
Ahoskie Creek 0.3 0.05 2.4 42
Long Creek 6.1 0.13 9.8 10
Swannanoa River 26.7 0.18 12.9 8
aTerrain slope is the average for the NED over the county where the reach is located, except for Ahoskie Creek, which is located in Hertford County but
the terrain slope is for an adjacent county (Pasquotank), where relevant data were available.
the sampling error of the 100-year BFE estimates at region (Figure 4.3), it follows that floodplain boundary
stream gages. This is heartening for floodplain map- delineation is more uncertain in the coastal plain than
ping because it suggests that there is a good deal more in the piedmont or mountains—in fact, about four to
similarity in stream flood processes across broad regions five times more uncertain, in proportion to the rise-run
than might be expected. data. This shows that having very accurate topographic
data for floodplain mapping is especially critical in
Finding. The river channels in the three study reaches regions with low relief.
have longitudinal slopes that are much flatter and The dominant effect of terrain data (lidar versus
more similar than are the average terrain slopes of the NED) has been illustrated for the base flood eleva-
landscapes through which the rivers flow. tion (Figures 4.15 and 4.16). Figure 4.17 compares
floodplain delineations based on lidar and the NED.
Delineating Special Flood Hazard Areas The top map in red shows the SFHA defined by the
lidar-detailed study approach; the dark green overlay
Once the BFE profile is determined, the next in the middle map shows the BFE profile from the
step in the flood mapping process is to delineate the lidar-detailed study approach plotted on NED terrain
Special Flood Hazard Areas (SFHAs). This involves information, and the light green overlay in the bottom
transforming vertical elevation profiles into horizontal map shows the approximate study approach with all
area polygons drawn around the stream reach. The data computations done using the NED as the terrain base.
on rise-run in Table 4.8 give an idea of the sensitivity There are significant discrepancies in the floodplain
of the lateral spreading of water to variations in the boundaries among these different approaches. An
flood elevation. At Ahoskie Creek, a 1-foot change in evaluation of the economic impact of the location of
vertical elevation changes the horizontal location of the floodplain boundaries is presented in Chapter 6.
floodplain boundary by 1/0.024 = 42 feet. A 1-foot rise A simple way to compare floodplain maps is to
in flood elevation will change the floodplain bound- count the number of acres in the floodplain, as sum-
ary on average by 10 feet at Long Creek and 8 feet marized in Table 4.9. The values correspond to the top
on the Swannanoa River. Since there is no inherent and bottom maps in Figure 4.17. At Ahoskie Creek,
difference in the sampling uncertainty in BFE by the SFHA is 1,756 acres for the lidar-detailed study

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64 MAPPING THE ZONE
FIGURE 4.17 Inundated areas in Swannanoa River Figure 4-17.eps
using different hydraulic study types. SOURCE: North Carolina Floodplain
Mapping Program. Used with permission.
bitmap image
TABLE 4.9 Differences in Inundated Area for Various Hydraulic Study Types
Ahoskie Creek Swannanoa River Long Creek
Area Percent Area Percent Area Percent
Topographic Source (acre) Difference (acre) Difference (acre) Difference
Lidar-DS 1,756 NA 485 NA 325 NA
NED-APPROX 1,744 −0.7 490 0.9 390 20.1
NOTE: NA = not applicable.
and 1,744 acres for the approximate-NED study, a errors in the NED at Long Creek than at Ahoskie
0.7 percent difference. On the Swannanoa River, the Creek and the Swannanoa River.
two areas are 485 and 490 acres, a 0.9 percent differ-
ence. On Long Creek, the areas are 325 and 390 acres, Finding. In the three reaches examined, approximate
a difference of 20.1 percent, which reflects the larger study methods yield a good estimate of the number

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INLAND FLOODING 65
of acres in the Special Flood Hazard Area, provided
the stream location and topographic information are
properly aligned.
SHALLOW FLOODING
In some regions, drainage is dominated by water
flow from one ponded area to the next. Rivers still exist
in such landscapes, but the mechanisms by which water
reaches them are different than in the normal dendritic
stream and channel systems that carry flow down-
stream. Ponding landscapes are common in Florida,
where surficial sedimentary deposits overlie limestone
formations. Dissolution within the limestone causes
pitting, subsidence, and in some cases, collapse of the
surface to form sinkholes.
The land surface terrain in these landscapes has
low slope, so watershed delineation becomes an exer-
cise in determining the drainage area surrounding each
depression (Figure 4.18), rather than the drainage area
of a point on a stream network. During severe storms,
water accumulates in each land surface depression until
it reaches the lowest elevation on its drainage divide
with a neighboring depression and flows into the
FIGURE 4.18 Drainage areas (red lines) of a ponded land-
Figure 4-18 - PittedTerrainCatchments.eps
next downstream pond. This process continues until scape in Florida. SOURCE: Southwest Florida Water Manage-
a developed stream or river is reached, at which point bitmap image
ment District. Used with permission.
the flow dynamics become similar to those in dendritic
drainage landscapes.
The committee’s frequency analysis of stage heights pitted landscapes. The InterConnected Pond Routing
included 10 stream gages with long-term flow records model (ICPR) uses broad-crested weir equations to
in southwest Florida (Figure 4.3). No significant differ- compute the hydraulics of flow between ponds. These
ences in the sampling uncertainty of the 100-year flood equations determine the flow over a berm between
stage were found for the Florida gages compared to the one pond and the next as a function of the elevation
21 gages that were studied in North Carolina. of water above the berm. The interaction of one pond
with the next is treated like upstream and downstream
Finding. Despite the difference in landscape flow flow through a culvert—if the water elevation in the
processes between the dendritic stream river systems downstream pond is high enough, it can affect the dis-
of North Carolina and the ponding landscapes in charge from the upstream pond. Other factors that are
Florida, the resulting river base flood elevations important include the volume of the water temporarily
determined at USGS gage sites have a similar sam- stored in the depressions, the duration of the critical
pling uncertainty. design storm, and the rate of percolation of floodwaters
through the base of the ponds or pits. Surface sediments
FEMA guidelines do not specify procedures for can absorb significant quantities of water during a long
dealing with the hydrology and hydraulics of ponded design storm, but hydrologic methods that account for
landscapes. The Southwest Florida Water Manage- percolation have not yet been incorporated into FEMA
ment District (SWFWMD) has developed some flood mapping guidelines. Significant work remains
sophisticated tools for delineating drainage areas in to lay the scientific foundation for flood modeling of

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66 MAPPING THE ZONE
these landscapes. Such analysis is beyond the resources • Structures in the channel induce backwater in
of this committee. all three study reaches, with backwater effects extend-
ing over the entire length of the reach in the coastal
Recommendation. FEMA should commission a sci- plain but less far in the rolling hills and mountains.
entific review of the hydrology and hydraulics needed The maximum backwater elevation increase found was
to produce guidelines for flood mapping in ponded 2.5 feet in the coastal plain reach, and the backwater
landscapes. effect extended an average of 1.1 miles upstream. In the
mountains, the backwater effect extended an average of
CONCLUSIONS 0.3 mile upstream.
• The greatest effect by far of any variant on the
The main insights arising from case studies of BFE is from the input data for land surface elevation:
elevation uncertainty at stream gages and flood map- lidar or the National Elevation Dataset. At Long
ping uncertainty are the following: Creek, the BFE computed on the NED is 21 feet
higher than on lidar because of a misalignment of the
• The sampling uncertainty of the base flood stream location on the NED. At the other two study
elevation at 31 USGS stream gages in North Carolina sites, the average elevation of the BFEs for the two
and Florida is 1 foot with a range of 0.3 foot to 2.4 feet, terrain data sources is about the same, but differs at
as inferred from frequency analysis of long records of particular locations by 3 to 10 feet. This result overturns
annual maximum stage heights. This uncertainty does the conventional view that map accuracy is affected at
not show any systematic pattern of variation with least as much by the accuracy of the hydraulic model
drainage area or geographic location at these sites. and hydraulic parameters as by the accuracy of the
Thus, there is a lower bound of approximately 1 foot on topographic data.
the uncertainty of the BFE as normally determined in • The floodplain boundaries produced using lidar
floodplain mapping, since indirect methods of comput- and the NED differ from one another, but at two of the
ing BFEs at ungaged sites will have uncertainty at least three study sites the number of acres enclosed within
as great as uncertainties observed at stream gages. the Special Flood Hazard Area is about the same for
• On three stream reaches in North Carolina, a detailed study using lidar data and an approximate
the lateral slope at the boundary of the floodplain is study using the NED. At the third site (Long Creek),
such that a 1-foot change in flood elevation has a cor- the difference in the number of acres within these areas
responding horizontal uncertainty in the floodplain is about 20 percent. This suggests that while floodplain
boundary of 8 feet in the mountains, 10 feet in the boundary locations are more uncertain in approximate
rolling hills, and 40 feet in the coastal plain. studies than in detailed studies, the total areas they
• Observed flood discharges at stream gages are encompass can be reasonably similar, provided the
the most critical component for estimating the base stream and topographic data are properly aligned.
flood discharge in the three study reaches because all
hydrologic methods are calibrated using these data These conclusions were based on limited studies in
and each stream reach contained a stream gage. BFEs small areas of North Carolina and Florida, which were
computed from the peak discharge estimated from the carried out to examine the uncertainty of riverine flood
various hydrologic methods do not differ much, so the mapping quantitatively rather than qualitatively. They
choice of hydrologic method does not introduce much are indicative but not definitive of what more compre-
uncertainty in the BFE beyond the lower bound uncer- hensive analyses of a similar character done nation-
tainty (1 foot) estimated by frequency analysis of USGS wide might reveal. The importance of the results lies
stage records. The most significant effect of hydrologic not in the specific numbers but rather in the insights
variations on BFEs is produced by introducing the aver- they provide about the relative effect of variations in
age error of prediction into the regression flow estimates hydrologic, hydraulic, and terrain methods on flood
(from 42 to 47 percent), which changes the BFE by an map accuracy.
average of 1 to 3 feet at the three study sites.