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4 Inland Flooding F EMA has studied nearly 1 million miles of Ârivers 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) directionsâindeed 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

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 Â 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 Â 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 Â 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 <http://nwis.waterdata.usgs.gov/usa/nwis/peak>.

INLAND FLOODING 43 FIGURE 4.1â Map of stream gages analyzed in this report. to a horizontal run of 329 feet. In the mountains, flood orders of magnitudeâfrom approximately 5 square discharges for a given drainage area are large, but the miles to approximately 5,000 square milesâwhich 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 âChannel Statistical Software Package HEC-SSP. Although Slopeâ). some stream gage records include estimates of âhistori- Peak stage data were also studied from 10 gages calâ 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 <http://www.hec.usace.army.mil/software/hec-ssp/>.

44 MAPPING THE ZONE TABLE 4.1â 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 Â 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.

INLAND FLOODING 45 Figure 4-2.eps FIGURE 4.2â 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 Âerror 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.

46 MAPPING THE ZONE 0 1 FIGURE 4.3â 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 Âmatter 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 evaluatedâa 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:

INLAND FLOODING 47 1. A hydrologic model is used to predict the peak 3. USGS regional regression equationsâsimple 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 usedârainfall-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 analysisâstatistical 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 modelsâhydrologic 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 4.4â 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.

48 MAPPING THE ZONE TABLE 4.2â 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 4.5â 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 ârandomnessâ 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 Âlongest tations of the natural systemâs complex transformation

INLAND FLOODING 49 of rainfall into runoff. To compute the flow discharge Sorooshian and Gupta, 1983; Sorooshian et al., 1983; at the watershedâs 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 Â 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 Administrationâs (NOAAâs) 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 <http://www.fema.gov/plan/prevent/fhm/en_hydro.shtm>. <http://hdsc.nws.noaa.gov/hdsc/pfds/pfds_docs.html>. subset of gaged sites with similar basin characteristics

50 MAPPING THE ZONE FIGURE 4.6â 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 basinâs 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 = Î±AÎ², 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 4.3â 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 â7 13 Weighted least squares â4 â4 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 â1 â2 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.

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 4.7â Summary of rural peak flow regression equations by date of completion. SOURCE: USGS. Figure 4-7.eps peak, A is the catchment area, and Î± and Î² 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 Î± and Î² 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 regionsâthe 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 ÂCarolina 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 ÂCarolina. 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 ÂMecklenburg County (Âpiedmont), and (as the committee has treated in the flood study in Ahoskie Creek in Â 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

52 MAPPING THE ZONE FIGURE 4.8â 100-year flood peak discharges estimated from regression equations in three physiographic regions of North Carolina. reaches. Some characteristics of the study reaches are 3. 95 percent lower and upper confidence limits summarized in Table 4.4. The reaches have similar (REGLOW and REGUP). The limits of the 95 percent lengths, in the range of 5 to 7 miles, but significantly confidence interval around the regional regression value different upstream drainage areas, ranging from 8 to (plus or minus 42 to 47 percent of the base flood dis- 108 square miles. charge) were used to estimate the 100-year peak flow. In all cases, the effect of variations in flood Âmethods 4. Adjusted regional regression (ADJREG). The peak is compared to a base case of hydrology using a discharges from the rural regional regression equations r Â ainfall-runoff model (if available), hydraulics using were adjusted at and near the gages to match estimates HEC-RAS with survey of structures in the floodplain, from flood frequency analysis of stream gage data. and terrain mapped by lidar. Four variants of hydrologic m Â ethods for determining the flood peak discharge were A typical result for the effect of these variations in examined: flood discharge on the BFE is shown in Figure 4.10. The water surface profiles for the rainfall-runoff, rural 1. Rainfall runoff model (RR). Both HEC-1 and regression, and adjusted regression methods are virtu- HEC-Hydrologic Modeling System were used and ally identical, within a sampling error of 1 foot. Use of calibrated using historical peak flows recorded at stream the lower and upper limits of the regression equation gages. The calibrated models were then used to calcu- confidence limits (upper and lower lines in Figure 4.10) late the 100-year flood peak flow. changes the water surface elevation profile by an aver- 2. Regional regression (REG). USGS regional age of about 2 feet along Long Creek. However, the regression equations for rural watersheds in North standard practice is to use flow values at the fitted Carolina were used to obtain the 100-year peak flow. regression line. Choosing flows at the range of the

landscape Figure 4-9.eps 4 bitmap images w/ vector arrows FIGURE 4.9â Location of the study reaches. Source NCFMP (2008). Used with permission. 53

54 MAPPING THE ZONE TABLE 4.4â Characteristics of the Study Reaches analysis (rainfall-runoff model approach and adjusted Drainage Area Drainage Area at Length regression method), the flood frequency Âanalysis at the at Upstream End Downstream End of Reach stream gage dominates the results. However, regional River (square miles) (square miles) (miles) regression equations, which are not adjusted to gages, Swannanoa River 108 133 4.8 Long Creek ââ 8 â 32 5.7 do not produce flows that are sufficiently different from Ahoskie Creek â 60 136 7.1 the other methods to create significant changes in water surface elevation at any of the study sites. The standard deviations of the differences in base flood elevations at corresponding cross sections between the rainfall-Ârunoff upper and lower confidence limits on the regression model and the regression equations at Long Creek equation illustrates the effect of an extreme variation and the ÂSwannanoa River are 0.04 foot and 0.67 foot, in the design discharge above and below the value that respectively. This means that for these study reaches, the would be used in a flood study. USGS regional regression equation method is estimat- It seems surprising at first that there is so little dif- ing flood discharges with sufficient precision to support ference between the results from rainfall-runoff, flood FEMA flood mapping efforts. frequency analysis, and regional regression equations The average error of prediction for a 100-year flood because the regional regression equations are simple in the USGS regional regression equations differs by empirical expressions that do not involve the precision physiographic region in North Carolina: 47 percent in of rainfall-runoff modeling or flood frequency Âanalysis. the mountain-piedmont area, 42 percent in the coastal However, the results from all these methods are driven plains, and 57 percent in the sand hills area. Table 4.5 by their calibration to the flood frequency curves devel- shows the effect on the BFE of flood discharges set oped at the stream gages, and each of the three study at the upper and lower limits of this prediction error. reaches has a USGS stream gage with long-term records. The values shown are the average effects for all cross For methods where the regression equation flood esti- sections in a study reach. On average, when the flood mate is adjusted to match the results of flood frequency discharge is at its upper prediction error (REGUP), the 670 660 650 Elevation (feet) 640 630 Rainfall Runoff Adjusted Regression 620 Rural Regression Rural Regression Upper Limit Rural Regression Lower Limit 610 STRUCTURE USGS Gage 600 19000 24000 29000 34000 39000 44000 49000 54000 Station FIGURE 4.10â Effect of variations in hydrologic methods on the base flood elevation on Long Creek, North Carolina. SOURCE: NCFMP (2008). Used with permission. Figure 4-10.eps

INLAND FLOODING 55 TABLE 4.5â Effect on Base Flood Elevation of Regression Equation Discharges at the Limits of Their Prediction Error Equation Ahoskie Creek (ft) Long Creek (ft) Swannanoa River (ft) Average (ft) REGUP â 0.71 â 1.93 â 0.65 â 1.10 REGLOW â2.53 â2.66 â4.96 â3.38 BFE is increased by 1.1 feet, and when it is at its lower HYDRAULIC MODELS prediction error (REGLOW), the BFE is reduced by 3.38 feet. Inaccuracies in hydraulic modeling add to inac- curacies associated with the base flood discharge Finding. Flood frequency analysis of stream gage and decrease the accuracy of the BFE. Figure 4.11 records is the most reliable method of defining peak illustrates the potential sources of inaccuracy in open- flood discharges. Discharges calculated from Ârainfall- channel hydraulic modeling. Each model has its own runoff models or from regional regression equa- sources of uncertainties, and the magnitude of errors tions adjusted for flood frequency analysis results in the model results depends on input, parameters, at a nearby gage produce similar BFE profiles. The model structure, and local conditions. Because model USGS regional regression equations also produce uncertainties vary significantly between models, only similar BFE profiles in the three reaches examined in uncertainties associated with parameters and boundary this study. The only hydrologic method that signifi- conditions are discussed below. cantly affects the BFE profile is to change the flood The physics of fluid flow is well understood and discharge to the limits of the prediction error of the is generally captured by mathematical formulations regression equationsâthis raises or lowers the BFE that conserve mass, energy, and momentum. In open- profiles by an average of 1 to 3 feet in the three study c Â hannel flow, both the density and the viscosity of water reaches. can be assumed constant in nearly all practical situa- FIGURE 4.11â Possible sources of inaccuracies in hydraulic modeling for floodplain delineation. Figure 4-11.eps bitmap image

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 4.12â 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 Engineersâ 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.

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 Â 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 Âchannel 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 Â 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 (BÃ¼chele 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.

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 4.13â 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

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 Manningâs d Â 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 Âmodels, 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. commuÂnity. Furthermore, the guidelines require the 4. Approximate (APPROX). Same as for LDSNC mapping partner to check velocities at river bends to except that Manningâs 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 ÂService 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 <http://www.fema.gov/plan/prevent/fhm/en_hydra.shtm>. description of structures.

60 MAPPING THE ZONE FIGURE 4.14â 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 4.15â 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 profileâsometimes 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

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 4.16â Water surface elevation profiles for different hydraulic study types on the Swannanoa River and Ahoskie Creek. SOURCE: NCFMP (2008). Used with permission. of the Âhydraulic 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

62 MAPPING THE ZONE TABLE 4.6â Base Flood Elevation Differences Between Detailed and Approximate-NED Studies Stream Mean (ft) Standard Deviation (ft) Minimum (ft) Maximum (ft) Ahoskie Creek â 0.95 1.30 â3.34 â 2.87 Long Creek 20.89 3.07 13.11 26.45 Swannanoa River â 0.18 3.61 â5.12 â 9.91 studies using lidar terrain data and approximate studies S Â 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 Â 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 Â 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 Âtopography (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

INLAND FLOODING 63 TABLE 4.7â 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 4.8â Channel and Terrain Slopes Terrain Slopea Longitudinal Slope Lateral Slope Lateral Run/Rise Stream (%) (%) (%) (ft/ft) Ahoskie Creek â 0.3 0.05 â 2.4 42 Long Creek â 6.1 0.13 â 9.8 10 Swannanoa River 26.7 0.18 12.9 â8 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 mountainsâin 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 Â 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

64 MAPPING THE ZONE FIGURE 4.17â 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 4.9â 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 â0.7 490 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

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 4.18â 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 committeeâs 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 culvertâif 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

66 MAPPING THE ZONE these landscapes. Such analysis is beyond the resources â¢ 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. â¢ 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 â¢ 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 â¢ 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 â¢ 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 â¢ 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.