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Mapping the Zone: Improving Flood Map Accuracy
4
Inland Flooding
FEMA has studied nearly 1 million miles of rivers and streams,1 so considerable experience has been gained in mapping riverine flood hazard, and mapping methods are well established. In contrast, approaches to mapping unconfined flows over broad, low-relief areas and the ponding of floodwaters in depressions (shallow flooding) are only emerging. This chapter addresses floodplain mapping associated with riverine flooding and flooding in ponded landscapes.
Riverine flood mapping is typically carried out for river and stream reaches with drainage areas exceeding 1 square mile. Each river reach is considered as a separate entity, and a collection of reaches is studied in a planning region such as a county. For each reach, the design flood discharge for the 100-year storm event is estimated using U.S. Geological Survey (USGS) regression equations, rainfall-runoff modeling, or statistical analysis of peak discharges measured at stream gages. The river channel shape and longitudinal profile are described by a stream centerline, and a set of cross sections is measured transverse to the centerline. Data for the cross sections may be obtained from an approximate data source, such as the National Elevation Dataset, and/or by land surveying or aerial mapping. The base flood elevation is computed at each cross section using the design discharge and a channel roughness factor by applying a hydraulic model such as HEC-RAS (Hydrologic Engineering Center-River Analysis System). The points of intersection of the water surface and land surface for each cross section are mapped on the landscape and joined by a smooth line to define the floodplain boundary for the Special Flood Hazard Area. This process is repeated for a 500-year storm to define the floodplain boundary for the shaded Zone X, which indicates the outer limits of moderate flood hazard.
There is no national repository of maps of historical flood inundation that can be used to determine actual floodplain boundaries. Rather, floodplain boundaries must be estimated by indirect means and thus flood maps contain various kinds of uncertainties. Most of these uncertainties arise from the interaction of water and land. In any storm, floodwaters flow across the land as the shape of the land surface and forces of gravity dictate. The water surface is smooth in all directions—indeed the assumption in one-dimensional models of riverine flooding is that the water surface is horizontal along a cross-section line perpendicular to the direction of flow. In contrast, the land surface is uneven, so the uncertainty in mapping the base flood elevation (BFE) is influenced by both the uncertainty in mapping land surface elevation and the uncertainty in the depth and extent of flood inundation of the landscape. There are three main sources of uncertainty in riverine flood mapping:
Hydrologic uncertainty about the magnitude of the base flood discharge;
Hydraulic uncertainty about the water surface elevation; and
Mapping uncertainty about the delineation of the floodplain boundary.
1
Presentation to the committee by Michael Godesky, FEMA, on November 8, 2007.
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Mapping the Zone: Improving Flood Map Accuracy
Uncertainties in the base flood discharge create uncertainties in the calculated base flood elevation and in the delineation of the floodplain boundary. For a given base flood discharge, uncertainties in hydraulic modeling and parameters create uncertainty in the BFE. For a given BFE, uncertainties in terrain elevation and boundary delineation methods create uncertainties in the location of the floodplain boundary. Although the discharge, elevation, and extent of inundation are interrelated, uncertainty increases with each step of the mapping process. The purpose of this chapter is to define the magnitude of these uncertainties in relation to the nature of the data and methods used in flood mapping.
UNCERTAINTY OF THE BASE FLOOD ELEVATION AT STREAM GAGES
A large number of factors have an effect on flood map uncertainty. It is helpful to have a benchmark measure of uncertainty to determine with some level of objectivity what is or is not significant. The BFE is a useful benchmark because it separates the hydrology and hydraulics analysis from the mapping step.
USGS stream gage sites are the principal places in the country where flood elevations have been measured precisely and consistently over many years. Each year of streamflow record includes the stage height (water height relative to a gage datum elevation) recorded every 15 minutes as well as the maximum stage height and corresponding maximum discharge for the year. The USGS publishes these peak stage heights and discharges for more than 27,000 stream gages as part of its National Water Information System.2 This includes data from the approximately 7,000 USGS gages presently operational, as well as approximately 20,000 gage sites that were operational for some period in the past but are now closed. Frequency analysis of peak discharges is the standard approach for defining extreme flow magnitudes. Peak stage heights can also be subjected to flood frequency analysis using the same approach. Although this approach is unconventional, the uncertainty in the peak stage revealed by frequency analysis forms a lower bound on the uncertainties inherent in BFE estimation by normal means.
It is true that frequency analysis of stage height is not the same thing as frequency analysis of base flood elevation because the BFE is defined relative to an orthometric datum, the North American Vertical Datum of 1988 (NAVD 88; see Chapter 3), and the stage height is defined relative to an arbitrary gage elevation datum. However, it is not necessary to reconcile these datums because what we are seeking is not the elevation itself, but rather the uncertainty of the elevation. The difference between the stage height and the flood elevation is the fixed datum height that is the same for all measurements and thus does not affect their variations from year to year. It should be understood that the purpose of this exercise is to gain insight into the sampling variation of extreme water surface elevations around a statistically determined expected value, not to statistically determine the base flood elevation. Indeed, because the BFE depends on the land surface elevation, which is different at each gaging station on a river, and on drainage area and other factors that vary from one location to another, it is not possible to regionalize the computation of the BFE as it is to regionalize the corresponding base flood discharge. However, as the following analysis demonstrates, there is a great deal of commonality among the sampling uncertainties around statistically estimated extreme stage heights. It is this commonality that lends insight into the corresponding uncertainties in the BFE estimated at the same locations. The sampling uncertainties of extreme stage heights are a lower bound on the corresponding and larger uncertainties in the base flood elevation.
The committee analyzed peak flow records in three physiographic regions in North Carolina to determine whether the uncertainty in the BFE is influenced by topography. The stations evaluated included six gages around mountainous Asheville in Buncombe County, seven gages in the rolling hills near Charlotte in Mecklenburg County, and eight gages distributed along the flat coastal plain (Figure 4.1). The average land surface slope, computed from the National Elevation Dataset, is 26.7 percent in Buncombe County, 6.1 percent in Mecklenburg County, and 0.304 percent in Pasquotank County in the coastal plain. On average, a 1-foot rise in land elevation in Buncombe County corresponds to a horizontal run of 3.7 feet, while in Pasquotank County a 1-foot rise corresponds
2
See <http://nwis.waterdata.usgs.gov/usa/nwis/peak>.
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Mapping the Zone: Improving Flood Map Accuracy
FIGURE 4.1 Map of stream gages analyzed in this report.
to a horizontal run of 329 feet. In the mountains, flood discharges for a given drainage area are large, but the floodwaters are confined within narrow valley floodplains. In the coastal plain, lower terrain slope leads to less flood discharge for a given drainage area, but once the banks overflow, floodwaters spread over a broader floodplain. The relationship between the terrain slope and the river slope is discussed below (see “Channel Slope”).
Peak stage data were also studied from 10 gages in southwest Florida (Table 4.1), which has a pitted landscape with many sinkholes where water ponds in depressions and flows from one pond to another until it reaches a stream or river. These stage height data were analyzed to determine whether BFE uncertainties were different in pitted landscapes compared to landscapes with dendritic drainage patterns. Altogether, 31 stream gage records were examined from North Carolina and Florida. The gages have an average length of record of 54 years and an average drainage area of 458 square miles. Although the spatial distribution of USGS stream gages is biased toward larger streams and rivers, the drainage area of the gages examined varied by three orders of magnitude—from approximately 5 square miles to approximately 5,000 square miles—which is a reasonable representation of the range of drainage areas for stream reaches used in floodplain mapping.
At each stream gage site, the historical record of both flood discharges and flood stage was analyzed using the U.S. Army Corps of Engineers (USACE) Statistical Software Package HEC-SSP.3 Although some stream gage records include estimates of “historical” floods before the period of gaged record, these were not included in the present study. In some gage records, there are notes that the flood flows were affected by factors such as urbanization or releases from upstream reservoirs. The committee did not separate out these records in the belief that riverine environments must be mapped, regardless of whether such events occurred. In a few of the coastal gages, the times of occurrence of the maximum flood stage and maximum flood discharge differ slightly, and in those cases, the largest value was used. For each gage, the log-Pearson III distribution was applied to both discharges and stage heights, as
3
<http://www.hec.usace.army.mil/software/hec-ssp/>.
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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
With lacoochee River near Trilby, Fla.
570
76
02312500
With lacoochee River near Croom, Fla.
810
67
02313000
With lacoochee 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 the Swannanoa River at Biltmore.
It is evident in Figure 4.2 that both the flood discharges and the stage heights have a similar frequency pattern. The base flood discharge is the value for the computed curve (red line) at exceedance probability 0.01 (20,672 cubic feet per second [cfs]), and the corresponding base flood stage height is 22.65 feet above gage datum. The uncertainty of the base flood is quantified by the dashed confidence limits in the graphs, a range from 16,024 to 28,514 cfs for the flow and 19.54 to 27.30 feet for the stage height.
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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 the HEC-SSP program.
These confidence limits were computed using the noncentral t-distribution as defined in Bulletin 17-B (IACWD, 1982).4 This range represents approximately 1.645 standard errors above and below the estimate of the mean, so a good measure of the sampling error in the base flood elevation can be derived from the range in the confidence limits. This estimate of the sampling error provides a sense of how much inherent uncertainty exists in BFEs derived from measured annual flood elevations at gages with long flood records.
Figure 4.3 plots the estimated sampling error of the
4
Bulletin 17B does not include regional skew information for peak stage analysis. Thus, the confidence limits calculated by this method provide only an approximate estimate of the sampling error of the peak stage data. This is sufficient and appropriate for the purpose that these limits are used in this study.
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FIGURE 4.3 Sampling error of the 100-year stage height at 31 Florida and North Carolina stream gage sites.
computed 100-year stage heights against drainage area at all 31 stream gages. This graph displays a surprising result: there is no correlation of the sampling error with drainage area or topography across the three regions of North Carolina, nor is there any significant difference in the results from the Florida gages compared with those from North Carolina. One large outlier in the sampling error (5.6 feet) occurs at Hominy Creek in Candler, North Carolina, and was caused by a couple of unusually large floods that significantly skewed the stage frequency curve at that stream gage site. If this value is omitted, the average value of the remaining standard errors is 1.06 feet, with a range of 0.3 foot to 2.4 feet.
This frequency analysis of stage heights has a number of limitations: no regional skew estimates were included (none exist for stage height data), the number of stream gages was relatively small (31 gages of 27,000 for which the USGS has peak gage records), and only a small region of the nation was examined. This analysis should be considered as indicative but not definitive of what a more comprehensive study of such data across the nation might reveal. Despite these limitations, a reasonable statistical interpretation of the result is that a null hypothesis cannot be rejected, namely that the sampling error of the 100-year stage height, or equivalently the 100-year BFE, does not vary with drainage area or geographic location over the gages studied. Moreover, the average sampling error was 1 foot with a range from 0.3 foot to 2.4 feet for 30 of the 31 sites. In other words, even at locations with long records of measured peak floods, the BFE cannot be estimated more accurately than approximately 1 foot, no matter what mapping or modeling approach is used. This value provides a benchmark against which the effects of variations in methods can be evaluated—a variation that produces a change in BFE of more than 1 foot may be significant. At ungaged sites, uncertainties in the BFE are necessarily higher.
Finding. The sampling error of the base flood elevation estimated using flood frequency analysis of annual maximum stage heights measured at 30 long-record USGS stream gage sites in North Carolina and Florida does not vary with drainage area, topography, or landscape type and has an average value of approximately 1 foot.
DETERMINING THE FLOOD DISCHARGE
Riverine flood studies involve a combination of statistical, hydrologic (rainfall-runoff), and hydraulic models. Determining the BFE involves first determining the base flood discharge. This can be done three ways:
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Mapping the Zone: Improving Flood Map Accuracy
A hydrologic model is used to predict the peak discharge associated with a design storm (hypothetical event of a desired frequency),
The peak discharge that has a 1 percent chance of occurring in a given year is observed directly (by frequency analysis at a gage site), or
The peak discharge is inferred using regional regression equations.
In all cases, a hydraulic model is subsequently used to compute the BFE, and geographic information system (GIS) mapping methods are required to overlay the computed flood elevation on the surrounding topography to determine the extent of the floodplain. Figure 4.4 illustrates the hydrologic and hydraulic modeling processes and input involved in riverine floodplain mapping.
Three hydrologic methods are used in flood mapping studies:
Flood frequency analysis—statistical estimation of flood discharges as illustrated above for the gage studies in North Carolina and Florida;
Rainfall-runoff models—hydrologic simulation models that convert storm rainfall to stream discharge applied using standardized design storms; and
USGS regional regression equations—simple methods for estimating the flood discharge as a function of drainage area and sometimes other parameters.
In a flood mapping study, each river reach between significant tributaries is treated as a separate entity and a corresponding flood discharge must be defined for it. Approximate studies use USGS regional regression equations, and limited detailed studies use regression equations or gage data (Table 2.1). In detailed studies, a mixture of methods is used—rainfall-runoff models in about half of the studies and flood frequency analysis or regression equations in the others (Table 4.2).
Flood Frequency Analysis
About 30 percent of detailed mapping studies use flood frequency analysis to establish the peak flow for the 100-year flood event (Table 4.2). The log-Pearson III is the U.S. standard of practice for flood frequency analysis for gaged sites (IACWD, 1982). Three statistical quantities (mean, standard deviation, and skewness coefficient) are required to estimate the parameters of the probability distribution. The Interagency Advisory Committee on Water Data (IACWD, 1982) guidelines identify procedures for the use of regional estimates of
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 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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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 distinguished between two kinds of uncertainty:
Natural variability deals with inherent variability in the physical world; by assumption, this “randomness” is irreducible. In the water resources context, uncertainties related to natural variability include things such as streamflow, assumed to be a random process in time, or soil properties, assumed to be random in space. Natural variability is also sometimes referred to as aleatory, external, objective, random, or stochastic uncertainty.
Knowledge uncertainty deals with a lack of understanding of events and processes or with a lack of data from which to draw inferences; by assumption, such lack of knowledge is reducible with further information. Knowledge uncertainty is also sometimes referred to as epistemic, functional, internal, or subjective uncertainty.
Estimation of flood peaks at return periods of interest for determining 100-year and 500-year (1 and 0.2 percent annual chance) floods illustrates the concepts of natural variability and knowledge uncertainty. Figure 4.5 shows the same kind of flood frequency curves illustrated in Figure 4.2 except that the confidence limits computed by the HEC-SSP program for specific flood probabilities are highlighted. These data are for the French Broad River at the Asheville, N.C. gage site (gage 3451500) in Buncombe County, which has 85 years of peak discharge record, the longest
FIGURE 4.5 Return periods for flood discharge at the French Broad River at Ashville, N.C., for the expected flood discharge and its upper and lower confidence limits (dotted lines).
flow record in this study. As in Figure 4.2, natural variability is represented by the central red line and expresses the relation between the magnitude of the flood discharge and its return period or likelihood of occurrence. Knowledge uncertainty is expressed by the spread of the confidence limits around this estimated line. As more data are used in a frequency analysis, the confidence band around the flood frequency curve becomes narrower.
For this gage, reading up from the horizontal axis value of 100 years return period for flood discharge and across to the vertical axis yields an equivalent return period of 50 years for the lower confidence interval discharge and 180 years for the upper confidence interval discharge. The corresponding values for the 500-year flood range from a 200-year to a 1,000-year return period. Similar results were obtained for confidence limits on the 100-year flood stage. This means that knowledge uncertainty is significant even when frequency analysis is performed on long gage records.
Rainfall-Runoff Models
Rainfall-runoff models are mathematical representations of the natural system’s complex transformation
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of rainfall into runoff. To compute the flow discharge at the watershed’s outlet, hydrologic models include basic flow routing techniques and one-dimensional representations of overland flow and channel hydraulics. These approximations permit several subbasins to be nested into a single model, allowing better accounting for spatial variability and computation of the flow hydrograph (time record of discharge) within the watershed. Hydrologic models can be event-based or continuous, depending on whether the initial conditions of model parameters such as soil moisture are assumed or updated using information gathered between storms. The Federal Emergency Management Agency (FEMA) accepts 13 event-based and 3 continuous hydrologic modeling software programs for determining flow hydrographs.5
The natural variability of quantities such as precipitation, soil moisture, and soil physical and hydraulic properties is typically described using probabilistic models (Merz and Thieken, 2005). Knowledge uncertainty is associated with the structure of the model and its ability to capture the behavior of the studied system in part or as a whole, the model parameters used to quantify the relationships between the various components of the system, and model input and output.
Model calibration and parameter estimation are perhaps the most important aspects of hydrologic modeling and are a major contribution to knowledge uncertainty. FEMA (2003) guidelines allow models to be calibrated using (1) historical rainfall observations, which can improve model performance under different rainfall conditions, or (2) a design storm, such as those defined in the National Oceanic and Atmospheric Administration’s (NOAA’s) Atlas 14,6 against the corresponding peak flow of the same return period (frequency). The typical procedure is to estimate the return period of the peak flow of a historical flood, use the design storm for that return period, and then calibrate the hydrologic model so it reproduces the observed flood flow. The optimized parameters are then used to calculate the 100-year peak flow. However, using a single peak flow calibration may prove to be inadequate, given the demonstrated importance of long records with a sufficiently large number of events (storm hydrographs) to estimate parameters (e.g., Sorooshian and Gupta, 1983; Sorooshian et al., 1983; Yapo et al., 1996, 1998).
Recommendation. FEMA should calibrate hydrologic models using actual storm rainfall data from multiple historical events, not just flood design storms.
Hydrologic modeling uncertainty is often described in the form of a probability distribution of model output (e.g., peak discharge for the required return period). By changing the distribution of model parameters, it is possible to identify both the impact of uncertainty in model parameters on hydrologic predictions and the effects of uncertainties in model input and model structure on predictive uncertainty. Figure 4.6 demonstrates that addressing only parameter uncertainty can lead to biased and, in some cases, incorrect assessment of total uncertainty.
USGS REGIONAL REGRESSION EQUATIONS
USGS regional regression equations are used to compute flood discharges in nearly all approximate mapping studies and in about 20 percent of detailed studies. A state is divided into regions, each with a set of USGS regression equations that allow flood map practitioners to compute flood discharges for the required recurrence intervals. When the USGS develops these equations, peak discharges at ungaged sites are regionalized by developing empirical relationships between the peak discharge and basin characteristics using statistical analyses of annual maximum flows at gaged sites. Regionalization was originally accomplished through nonlinear regression analysis. With this procedure, records from gaged sites were used to define a set of empirical relations between selected recurrence interval discharges and a set of exogenous or independent variables, always including drainage area. These relations were then used to estimate discharges at selected recurrence intervals for ungaged sites. A more recent approach to regionalization is the region of influence generalized least squares method, in which an interactive procedure is used to estimate recurrence interval discharges (Tasker and Stedinger, 1989). For each ungaged site, a subset of gaged sites with similar basin characteristics
5
<http://www.fema.gov/plan/prevent/fhm/en_hydro.shtm>.
6
<http://hdsc.nws.noaa.gov/hdsc/pfds/pfds_docs.html>.
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FIGURE 4.6 Streamflow hydrograph prediction uncertainty associated with estimated parameters (dark gray) for the Sacramento Soil Moisture Accounting (SAC-SMA) model and 95 percent confidence interval for prediction of observed flow (light gray) for water year 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 determine the relation between flood discharge and basin characteristics at gaged sites. This relation is then used to estimate flood discharges at ungaged sites. Tests of this approach in Texas (Tasker and Slade, 1994) and Arkansas (Hodge and Tasker, 1995) yielded estimates with lower prediction errors than those produced using traditional regional regression techniques. The region of influence method was used for the North 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 least squares. Because of the different climate, physiographic, and hydrologic conditions across the country, more than 200 explanatory variables are used at one location or another. The equations are developed by state-level studies, so problems can arise at state boundaries if different equations are used for the same variable on either side of the boundary. Table 4.3 summarizes the methods currently used to derive flood discharge equations.
Figure 4.7 shows the age of the regression equations used at the state level for rural basins. Most states have updated their regional regression equations since 1996. However, basins that cross state boundaries may be analyzed using regression equations of different ages and different regression methodologies, creating inconsistent results across the basin.
Regression equations in North Carolina generally take the form QT = αAβ, where QT is the T-year flood
TABLE 4.3 Methods Used to Derive Empirical Flood Equations
Regression Method
Number of States or Regions
Percentage of Total
Ordinary least squares
7
13
Weighted least squares
4
4
Generalized least squares
43
81
Multiple linear regression
1
2
NOTE: These numbers do not include USGS Water Science Centers that use region of influence analyses in addition to one of these regression methods.
SOURCE: USGS.
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FIGURE 4.7 Summary of rural peak flow regression equations by date of completion. SOURCE: USGS.
peak, A is the catchment area, and α and β are regression coefficients. Catchment area, or the area draining to a defined point on the stream system, is the single most important independent variable. In effect, all the other variables that might influence the peak discharge are bound up in the coefficients α and β of the regression equation, which are assumed constant within a particular region. In North Carolina, regression equations are defined for three regions—the Blue Ridge-piedmont region, the sand hills area, and the coastal plains. The discharges calculated using the equations are shown in Figure 4.8. For a 100-square-mile drainage area, the 100-year flood discharge estimate is 13,250 cfs in the Blue Ridge-piedmont area, 6,340 cfs in the coastal plain, and 3,400 cfs in the sand hills area. Hence, flood discharge in the flat coastal plain is about one-half of the discharge in the Blue Ridge-piedmont area. The low discharge in the sand hills area may reflect the presence of more absorbent soils.
Although the USGS regression equations are the same for the Blue Ridge and piedmont regions, these regions are physiographically distinct from one another (as the committee has treated in the flood study in North Carolina). When the equations were being derived, there were insufficient stream gages in the Blue Ridge Mountains to distinguish it statistically from the piedmont region. The USGS is currently revising the regression equations for the Blue Ridge region using additional stream gages from adjacent states with similar topography.
Finding. The variation in peak flow predictions between regions illustrates the importance of developing regression equations at the river basin level, independent of state boundaries. States with significantly outdated regression equations that should be updated include Michigan, Massachusetts, New Jersey, California, and New Hampshire.
North Carolina Case Study of Flood Discharge Estimation
At the request of the committee, the North Carolina Floodplain Management Program (NCFMP) conducted case studies of flood hydrology, hydraulics, and mapping in three study reaches in North Carolina. These included Swannanoa River in Buncombe County (mountains), Long Creek in Mecklenburg County (piedmont), and Ahoskie Creek in Hertford County (coastal plain; Figure 4.9). Lidar (light detection and ranging) topographic data and detailed studies yielding BFEs and floodplain boundaries were available for all three study
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tions, which greatly simplifies the equations required to model the motion of water and to compute the surface water elevation within the channel. However, equations are still needed to account for (1) changes in the water surface profile caused by the irregular shapes of natural channels, which create flow resistance, and (2) structures and flow impediments, which increase the height of the water surface upstream and create a backwater effect.
In practical open-channel hydraulics, the depth-averaged velocity is a good representation of the flow velocity. As a result, the flow can be approximated using one- or two-dimensional models. In one-dimensional approximations, the flow velocity is assumed to vary only in the direction of the longitudinal channel slope. The flow velocity is averaged over both the depth and the width of the flow at each cross section. A single water surface elevation value is computed, and the depth of water over all points in the cross section is determined by extending a horizontal water surface elevation line across the channel. The floodplain boundary is delineated at the location where the water surface elevation line intersects the topographic surface of land surface elevation.
Most one-dimensional hydraulic models require 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, showing the information required for the U.S. Army Corps of Engineers’ one-dimensional HEC-RAS model. The vertical scale is exaggerated to highlight cross-sectional features. Solid black lines represent 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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is generally extended beyond the upstream and downstream boundaries of the targeted reach to ensure that backwater effects are taken into account and that numerical errors in the computed surface water profile are minimized. A stream centerline is then defined, and the cross-section geometry is determined at regular intervals along the centerline and at structures, river bends, and major points of change in channel slope and/or cross-section geometry. Accurate representation of structures and river bends is important for identifying flow constrictions and areas where water can pond, such as at bridges and roadway embankments. Finally, information about surface roughness (i.e., flow resistance) must be gathered for each cross section. Several equations that relate surface roughness to flow characteristics are available, but the most popular in open-channel flow computation is the Manning equation. Modelers generally determine the Manning roughness coefficient at several points across the channel and floodplain by visual examination and use of standardized tables and photographs of channels of known roughness.
One-dimensional models are computationally efficient and are considered by many engineers to produce reasonably accurate surface water profiles (Büchele et al., 2006), although the accuracy must be checked at river junctions, loops, branches, and significant lateral inflows. Because the output of one-dimensional models must be superimposed on digital elevation data to produce a Flood Insurance Rate Map, the final mapping product is sensitive to variations in surface elevation that were not captured in the cross sections. This may cause inconsistent model results, particularly in urban areas where roads, walls, and other structures can create preferential flow paths. Since the flood map is drawn on a topographic surface and the water surface elevation is determined by a hydraulic model using cross sections, it is important for the topographic surface and cross sections to be consistent with one another. This may not be the case if the cross sections are defined by land surveying and the topographic surface is defined by aerial photogrammetry (Tate et al., 2002). Careful adjustment and reconciliation of topographic and cross-section data sources are needed for detailed mapping studies.
In two-dimensional models, the velocity is averaged over only the flow depth, and velocity components are computed in directions both parallel and perpendicular to the longitudinal channel slope. The resultant velocity is then quantified in magnitude and direction. These models solve the complex flow equations using numerical algorithms that iteratively advance the solution in space and time over computational quadrilateral or triangular meshes. The size and shape of the mesh grids depend on factors such as the numerical solution method, available terrain data, level of required detail, and available computational resources.
Two-dimensional models are computationally demanding and require considerable expertise to prepare and execute. However, FEMA flood studies require only a single discharge value for the peak flow of the 100-year event, so flood mapping analyses are performed assuming steady flow. In steady flow the water surface elevation is constant over time; in unsteady flow the water surface elevation is computed for each cross section or grid point location as a function of time. The steady flow assumption simplifies the data requirements, particularly with respect to boundary conditions, and greatly reduces the computational demand.
Two-dimensional models offer many advantages over one-dimensional models, including more accurate resolution of the actual surface water elevation and direct determination of floodplain extent. A study comparing the two types of models found that two-dimensional models have significantly greater ability to determine flow velocity and direction than one-dimensional models (TRB, 2006). Computing velocity is an important element of flood damage calculations, particularly in urban areas where measurable damage to buildings and other properties can result from fast flow. The Transportation Research Board (TRB, 2006) study found that the difference between one-dimensional and two-dimensional models is smallest within the confines of the main channel (green), increases across the channel and floodplain, and is largest near the smaller branch of the river (Figure 4.13). This divergence across the channel and floodplain results from the inability of the one-dimensional model to capture complex features, such as braided streams, multiple openings, and bridge crossings near channel bends. Consequently, the choice of model can significantly affect determination of floodplain elevations and the vertical extent of the channel.
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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 difference in the magnitude of flow velocity. Positive numbers in d indicate that the two-dimensional model produced higher velocity values, and negative numbers indicate that the one-dimensional model produced higher flow velocity values. SOURCE: TRB (2006).
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This conclusion highlights a potential source of uncertainty in mapping floodplains using one-dimensional models. Models acceptable under current FEMA guidelines include 11 one-dimensional steady flow models, 10 one-dimensional unsteady flow models, and 4 two-dimensional steady-unsteady flow models.7 The guidelines note the limitations of each model and recommend validation and calibration in most cases, but do little to help mapping partners determine which type of models are most appropriate for a given community. Furthermore, the guidelines require the mapping partner to check velocities at river bends to determine potential erosion. For meandering rivers, the TRB (2006) report suggests that such determinations are better made through two-dimensional models. Partnerships with academic institutions and individuals often facilitate the transition of research models into practical applications. For example, the National Weather Service has led two extensive distributed hydrologic model intercomparison projects (Smith et al., 2004, 2008), in part to establish links with researchers developing the next generation of hydrologic models.
Recommendation. FEMA should work toward greater use of two-dimensional flood hydraulic models where warranted by the floodplain geometry, including preferential flood pathways and existing and planned structures.
NORTH CAROLINA FLOOD MAPPING CASE STUDY
Riverine Flooding
The NCFMP (2008) study considered different combinations of three parameters: (1) hydrologic study type, (2) hydraulic study type, and (3) source of terrain information. The effects of variations in hydrologic methods have been described above. The effects of variations in hydraulic and terrain data are now discussed. Five approaches were examined:
Detailed Study (DS). Lidar data were used for topography, field surveys for channel cross sections and for bridge and culvert openings; ineffective flow areas and channel obstructions were defined; and Manning’s n could vary along the channel.
Limited Detailed Study North Carolina (LDSNC). Same as a detailed study except that field surveying of channel structures was estimated or limited.
Limited Detailed Study National (LDSNAT). Same as for LDSNC except no channel structures or obstructions were included and ineffective flow areas were removed near structures.8
Approximate (APPROX). Same as for LDSNC except that Manning’s n was uniform along the channel profile (it can have separate values for the channel and the left and right overbank areas).
Approximate-NED (APPROX-NED). Same as APPROX but the National Elevation Dataset (NED), rather than lidar, was used for terrain representation.
Figure 4.14 shows the differences among these five methods in representing a channel cross section on the Swannanoa River.
Figure 4.15 illustrates the differences between water surface elevation computed using the five different hydraulic study methods on Long Creek. As long as lidar terrain data are used, the effect of variations in the hydraulic methods (DS, LDSNC, LDSNAT, APPROX) is quite small. The cascading appearance of the water surface profile for the APPROX-NED model is due to a horizontal misalignment between the base map planimetric information and the elevation information. In other words, detailed mapping of the stream network within Mecklenburg County shows the correct location of the stream centerline, and when lidar data are used to define elevation, the topographic and base map imagery are correctly aligned. However, when the National Elevation Dataset is used to define topography, the stream centerline and the topography are not correctly aligned and the stream appears to flow over small ridges and gullies rather than down a stream channel. The NED is on average 14.7 feet above the lidar on Long Creek (Table 3.2), hence the elevated water surface profile.
The BFE profiles for Ahoskie Creek and the Swannanoa River are plotted in Figure 4.16 for the five
7
See <http://www.fema.gov/plan/prevent/fhm/en_hydra.shtm>.
8
The LDSNAT variant is specific to the NCFMP (2008) case study and does not imply that FEMA limited detailed studies omit description of structures.
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FIGURE 4.14 Differences in the channel cross section and structure geometry among the five different hydraulic study types for station 16008 of the Swannanoa River reach. Structures are shaded black, and water is shaded blue. The lower-right figure illustrates areas 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.
FIGURE 4.15 Base flood elevation profiles for different hydraulic study types on Long Creek. SOURCE: NCFMP (2008). Used with permission.
hydraulic and mapping study types. In these streams, the profiles reveal a great deal of random variation in the APPROX-NED BFE profile—sometimes it is above the other profiles and sometimes below, and the magnitude of the variations is significantly greater than the magnitude of variations in other hydraulic methods. This result countered expectations that map accuracy is affected at least as much by the accuracy
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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 the accuracy of the topographic data. The case studies, which had the advantage of using precise topographic (lidar) data for analysis, clearly show that topographic data is the most important factor in the accuracy of flood maps in riverine areas.
Table 4.6 quantifies the differences between the flood elevation profiles in Figure 4.16 for detailed
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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 using NED terrain data. The differences are striking, particularly for Long Creek, where on average the BFE is more than 20 feet higher if calculated using the NED rather than lidar. In the other two study reaches, the NED BFE is, on average, fairly close to the lidar BFE, but at particular cross sections the two elevations may differ by up to 10 feet.
Finding. The base flood elevation profile is significantly more influenced by whether the National Elevation Dataset or lidar terrain data are used to define land surface elevation than by any variation of methods for calculating channel hydraulics.
Backwater Effects of Structures
One of the key reasons for doing detailed surveys of structures in stream channels is to estimate their backwater effects. The structures are shown as black squares in Figure 4.16, and it can be seen that the flood profiles jump upward at some of these locations. Bridges and culverts constrain the movement of floodwaters during very large discharges, and the water elevation upstream of a structure increases to create the energy needed to force the water to flow through the structure. Intuitively, these backwater effects should propagate further upstream in flat terrain than in steep terrain, but by how much? The impact of backwater on the surface water profile was the highest in Ahoskie Creek on the coastal plain, where six structures caused backwater effects and all of them extended to the next structure upstream (Table 4.7). On Long Creek, all four structures had backwater effects and three reached the next structure. On the Swannanoa River, six of nine structures had backwater effects, including five that reached the next structure. The average distance that a backwater effect propagated upstream was 1.12 miles on Ahoskie Creek, 0.5 mile on Long Creek, and 0.30 mile on the Swannanoa River. As expected, these results demonstrate that backwater effects from structures increase base flood elevations and that the distance these effects extend upstream is longest at Ahoskie Creek in the coastal plain and shortest on the Swannanoa River in the mountains of western North Carolina.
Finding. Backwater effects of structures influence the base flood elevation profile on all three study reaches and are most pronounced in the coastal plain.
Channel Slope
The three study areas were chosen in mountains, rolling hills, and coastal plains to examine the extent to which differences in terrain affect flood properties. Table 4.8 shows various measures of the slope in these study areas: the longitudinal and lateral slope values were derived from the HEC-RAS models for flood flow. The lateral slope is the value along the stream cross sections at the edge of the floodplain, averaged for the left and right banks of the cross section and over all cross sections in the reach. The terrain slope was derived from the NED over the whole county. As one would expect, the longitudinal slopes of the stream channels are much lower than the lateral slopes; that is, the land slopes much more steeply away from the channel than along it. Even though the terrain slope for the Swannanoa River (26.7 percent) is nearly 100 times that for Ahoskie Creek (0.3 percent), the longitudinal channel slopes of those two reaches differ by only a factor of 3.5 (0.18 percent versus 0.05 percent). In other words, despite the large differences intopography between the mountains of western North Carolina and the flat coastal plain, the creeks and rivers in those regions are much more similar to one another than to the surrounding terrain. The longitudinal slopes of the rivers are much flatter than the average slope terrains through which they flow. This may help to explain why there are no pronounced regional differences in
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TABLE 4.7 Effect of Backwater Upstream of Structures
Stream
Number of Structures
Extended to Next Structurea
Average Elevation (ft)b
Maximum Elevation (ft)b
Distance Upstream (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.
bRefers to 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
Stream
Terrain Slopea (%)
Longitudinal Slope (%)
Lateral Slope (%)
Lateral Run/Rise (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 stream gages. This is heartening for floodplain mapping because it suggests that there is a good deal more similarity in stream flood processes across broad regions than might be expected.
Finding. The river channels in the three study reaches have longitudinal slopes that are much flatter and more similar than are the average terrain slopes of the landscapes through which the rivers flow.
Delineating Special Flood Hazard Areas
Once the BFE profile is determined, the next step in the flood mapping process is to delineate the Special Flood Hazard Areas (SFHAs). This involves transforming vertical elevation profiles into horizontal area polygons drawn around the stream reach. The data on rise-run in Table 4.8 give an idea of the sensitivity of the lateral spreading of water to variations in the flood elevation. At Ahoskie Creek, a 1-foot change in vertical elevation changes the horizontal location of the floodplain boundary by 1/0.024 = 42 feet. A 1-foot rise in flood elevation will change the floodplain boundary on average by 10 feet at Long Creek and 8 feet on the Swannanoa River. Since there is noinherent difference in the sampling uncertainty in BFE by region (Figure 4.3), it follows that floodplain boundary delineation is more uncertain in the coastal plain than in the piedmont or mountains—in fact, about four to five times more uncertain, in proportion to the rise-run data. This shows that having very accurate topographic data for floodplain mapping is especially critical in regions with low relief.
The dominant effect of terrain data (lidar versus NED) has been illustrated for the base flood elevation (Figures 4.15 and 4.16). Figure 4.17 compares floodplain delineations based on lidar and the NED. The top map in red shows the SFHA defined by the lidar-detailed study approach; the dark green overlay in the middle map shows the BFE profile from the lidar-detailed study approach plotted on NED terrain information, and the light green overlay in the bottom map shows the approximate study approach with all computations done using the NED as the terrain base. There are significant discrepancies in the floodplain boundaries among these different approaches. An evaluation of the economic impact of the location of floodplain boundaries is presented in Chapter 6.
A simple way to compare floodplain maps is to count the number of acres in the floodplain, as summarized in Table 4.9. The values correspond to the top and bottom maps in Figure 4.17. At Ahoskie Creek, the SFHA is 1,756 acres for the lidar-detailed study
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FIGURE 4.17 Inundated areas in Swannanoa River using different hydraulic study types. SOURCE: North Carolina Floodplain Mapping Program. Used with permission.
TABLE 4.9 Differences in Inundated Area for Various Hydraulic Study Types
Topographic Source
Ahoskie Creek
Swannanoa River
Long Creek
Area (acre)
Percent Difference
Area (acre)
Percent Difference
Area (acre)
Percent 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 0.7 percent difference. On the Swannanoa River, the two areas are 485 and 490 acres, a 0.9 percent difference. On Long Creek, the areas are 325 and 390 acres, a difference of 20.1 percent, which reflects the larger errors in the NED at Long Creek than at Ahoskie Creek and the Swannanoa River.
Finding. In the three reaches examined, approximate study methods yield a good estimate of the number
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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 downstream. 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 exercise 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 next downstream pond. This process continues until a developed stream or river is reached, at which point the flow dynamics become similar to those in dendritic drainage landscapes.
The committee’s frequency analysis of stage heights included 10 stream gages with long-term flow records in southwest Florida (Figure 4.3). No significant differences in the sampling uncertainty of the 100-year flood stage were found for the Florida gages compared to the 21 gages that were studied in North Carolina.
Finding. Despite the difference in landscape flow processes between the dendritic stream river systems of North Carolina and the ponding landscapes in Florida, the resulting river base flood elevations determined at USGS gage sites have a similar sampling uncertainty.
FEMA guidelines do not specify procedures for dealing with the hydrology and hydraulics of ponded landscapes. The Southwest Florida Water Management District (SWFWMD) has developed some sophisticated tools for delineating drainage areas in
FIGURE 4.18 Drainage areas (red lines) of a ponded landscape in Florida. SOURCE: Southwest Florida Water Management District. Used with permission.
pitted landscapes. The InterConnected Pond Routing model (ICPR) uses broad-crested weir equations to compute the hydraulics of flow between ponds. These equations determine the flow over a berm between one pond and the next as a function of the elevation of water above the berm. The interaction of one pond with the next is treated like upstream and downstream flow through a culvert—if the water elevation in the downstream pond is high enough, it can affect the discharge from the upstream pond. Other factors that are important include the volume of the water temporarily stored in the depressions, the duration of the critical design storm, and the rate of percolation of floodwaters through the base of the ponds or pits. Surface sediments can absorb significant quantities of water during a long design storm, but hydrologic methods that account for percolation have not yet been incorporated into FEMA flood mapping guidelines. Significant work remains to lay the scientific foundation for flood modeling of
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these landscapes. Such analysis is beyond the resources of this committee.
Recommendation. FEMA should commission a scientific review of the hydrology and hydraulics needed to produce guidelines for flood mapping in ponded landscapes.
CONCLUSIONS
The main insights arising from case studies of elevation uncertainty at stream gages and flood mapping uncertainty are the following:
The sampling uncertainty of the base flood elevation at 31 USGS stream gages in North Carolina and Florida is 1 foot with a range of 0.3 foot to 2.4 feet, as inferred from frequency analysis of long records of annual maximum stage heights. This uncertainty does not show any systematic pattern of variation with drainage area or geographic location at these sites. Thus, there is a lower bound of approximately 1 foot on the uncertainty of the BFE as normally determined in floodplain mapping, since indirect methods of computing BFEs at ungaged sites will have uncertainty at least as great as uncertainties observed at stream gages.
On three stream reaches in North Carolina, the lateral slope at the boundary of the floodplain is such that a 1-foot change in flood elevation has a corresponding horizontal uncertainty in the floodplain boundary of 8 feet in the mountains, 10 feet in the rolling hills, and 40 feet in the coastal plain.
Observed flood discharges at stream gages are the most critical component for estimating the base flood discharge in the three study reaches because all hydrologic methods are calibrated using these data and each stream reach contained a stream gage. BFEs computed from the peak discharge estimated from the various hydrologic methods do not differ much, so the choice of hydrologic method does not introduce much uncertainty in the BFE beyond the lower bound uncertainty (1 foot) estimated by frequency analysis of USGS stage records. The most significant effect of hydrologic variations on BFEs is produced by introducing the average error of prediction into the regression flow estimates (from 42 to 47 percent), which changes the BFE by an average of 1 to 3 feet at the three study sites.
Structures in the channel induce backwater in all three study reaches, with backwater effects extending over the entire length of the reach in the coastal plain but less far in the rolling hills and mountains. The maximum backwater elevation increase found was 2.5 feet in the coastal plain reach, and the backwater effect extended an average of 1.1 miles upstream. In the mountains, the backwater effect extended an average of 0.3 mile upstream.
The greatest effect by far of any variant on the BFE is from the input data for land surface elevation: lidar or the National Elevation Dataset. At Long Creek, the BFE computed on the NED is 21 feet higher than on lidar because of a misalignment of the stream location on the NED. At the other two study sites, the average elevation of the BFEs for the two terrain data sources is about the same, but differs at particular locations by 3 to 10 feet. This result overturns the conventional view that map accuracy is affected at least as much by the accuracy of the hydraulic model and hydraulic parameters as by the accuracy of the topographic data.
The floodplain boundaries produced using lidar and the NED differ from one another, but at two of the three study sites the number of acres enclosed within the Special Flood Hazard Area is about the same for a detailed study using lidar data and an approximate study using the NED. At the third site (Long Creek), the difference in the number of acres within these areas is about 20 percent. This suggests that while floodplain boundary locations are more uncertain in approximate studies than in detailed studies, the total areas they encompass can be reasonably similar, provided the stream and topographic data are properly aligned.
These conclusions were based on limited studies in small areas of North Carolina and Florida, which were carried out to examine the uncertainty of riverine flood mapping quantitatively rather than qualitatively. They are indicative but not definitive of what more comprehensive analyses of a similar character done nationwide might reveal. The importance of the results lies not in the specific numbers but rather in the insights they provide about the relative effect of variations in hydrologic, hydraulic, and terrain methods on flood map accuracy.