Modeling Hydrologic Change: Statistical Methods - Chapter 13 (end) docx

Frequency Analysis Under Nonstationary Land Use Conditions Glenn E. Moglen 13.1 INTRODUCTION Many hydrologic designs are based on estimates of flood magnitudes associated with a specified return period. Flood-frequency analyses based on data collected by stream gages can be used to determine these flood magnitudes. In the event of land use change associated with urbanization, deforestation, or changes in agricultural practices within the gaged watershed, the annual maximum time series recorded by the gage includes a trend or nonstationary component that reflects the effect of the land use change. Because urbanization typically increases the flood response of a watershed, a flood frequency analysis performed on a nonstationary time series will lead to underestimation of flood magnitudes and insufficient, underdesigned structures. Accounting for this nonstationarity is, therefore, essential for appropriate design. 13.1.1 O VERVIEW OF M ETHOD The method presented in this chapter may be used to adjust a peak-discharge time series that is nonstationary because of changing land use within the gaged watershed over the gaging period. The method has several parts. First, the method focuses on deriving a spatially sensitive time series of land use. This step requires resourceful- ness and creativity on the part of the hydrologist to obtain relevant data and to organize these data into a format, most likely using making use of geographic information systems (GIS) technology, that can be readily used to generate the values necessary as input to the hydrologic model. The next step is to calibrate the hydro- logic model over the gaging period being studied, while taking into account the spatially and temporally varying land use. The final step is to use the calibrated model to generate a synthetic time series of peak discharge, related to the observed time series, but adjusted to reflect a single land use condition such as the current or ultimate land use. This chapter examines the differences in derived flood-frequency behavior between the observed (nonstationary) and adjusted (stationary) peak- discharge time series. 13 L1600_Frame_C13.fm Page 367 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC 13.1.2 I LLUSTRATIVE C ASE S TUDY : W ATTS B RANCH The process of accounting for nonstationarity in the flood record and ultimately performing a flood-frequency analysis based on an adjusted flood series is illustrated for a watershed in the Piedmont region of Maryland just north of Washington, D.C. This watershed, Watts Branch, has a drainage area of 3.7 square miles at the location of U.S. Geological Survey (USGS) gage station 01645200, which was active from 1958 to 1987. According to the Maryland Department of Planning’s assessment as of 2000, it was composed of a mix of residential densities totaling 35% of the land area. Commercial and industrial land uses cover 23%, and other urban uses (insti- tutional and open urban land) cover an additional 15% of the land area. A significant percentage (18%) of agricultural land remains within the watershed with the remain- der (9%) made up of deciduous forest. By comparison, at the time of a 1951 aerial photograph, the rough land use distribution was 15% urban, 64% agricultural, and 21% forest. Figure 13.1 shows a comparison of the spatial distribution of these land uses in 1951 and 2000. As further evidence of the changes this watershed has undergone, see the literature focused on channel enlargement and geomorphic change (e.g., Leopold, Wolman, and Miller, 1964; Leopold, 1973; Leopold, 1994). FIGURE 13.1 Spatial distribution of land use in Watts Branch watershed in 1951, 1987, 2000, and under ultimate development conditions. L1600_Frame_C13.fm Page 368 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC The flood of record took place in 1975 with a discharge of 3400 ft 3 /sec. In 1972, Hurricane Agnes, responsible for the flood of record in many neighboring water- sheds, produced an annual maximum flow of 2900 ft 3 /sec. The Watts Branch water- shed is used throughout subsequent sections to illustrate the various phases of the modeling process. 13.2 DATA REQUIREMENTS In a flood-frequency analysis for a stationary system, the only data required are the observed annual maximum series, Q p,o ( t ). Because of the land use change that induced nonstationarity into Q p,o ( t ), other data are required: an observed causal rainfall time series, P ( t ), and several GIS data sets such as digital elevation models (DEMs), land use, and soils. These data sets are described in greater detail in the following sections. 13.2.1 R AINFALL D ATA R ECORDS Rainfall data are collected through a nationwide network of rain gages and, more recently, radar and satellite imagery. These data are archived and readily available on the Internet at a number of websites, the most accessible being the National Climatic Data Center (NCDC, 2001). This site provides free download access for point rainfall data. Data are stored in a database that is accessed through the website allowing the location and extraction of rainfall data that suits a range of selection criteria such as latitude/longitude, state/county/city name, ZIP code, or station iden- tification number. 13.2.2 S TREAMFLOW R ECORDS Streamflow data are collected and archived by the USGS and are similarly made available for extraction via a web-based interface that allows for a range of potential selection criteria (U.S. Geological Survey, 2001b). Data are organized and archived in two forms: daily averaged flows and the annual maximum series. In the case of the annual maximum series data, the discharge is accompanied by a field that also identifies the date of occurrence of the annual maximum. This chapter will focus on the annual maximum series and any trends that may be present in this series as a result of land use change within the gaged watershed. 13.2.3 GIS D ATA Rainfall-runoff estimates of peak discharge could be developed with a range of potential models. This chapter uses Natural Resources Conservation Service (NRCS; U.S. Soil Conservation Service, 1985, 1986) methods to develop such estimates. Although the details of using other models to perform a similar analysis would certainly differ, the spirit of the approach presented here is consistent with any model. As stated earlier, several different types of GIS data are required for the hydro- logic modeling of the annual maximum discharges. First and foremost, topographic data in the form of a DEM is probably the most fundamental data type required for L1600_Frame_C13.fm Page 369 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC this analysis. The DEM serves first to determine flow paths and provide an automated delineation of the study watershed that provides an estimate of the watershed area. The DEM then allows for the estimation of slopes and times of concentration that are central to the analysis as well. These data are made available by the USGS (U.S. Geological Survey, 2001c) at several map scales. The data used in the case study presented here are derived from the 1:24,000 map scale and have a resolution of 30 meters. NRCS methods depend heavily on the estimation of a curve number, requiring information about the area distribution of both land use and hydrologic soil type. Thus, coverages of both land use and hydrologic soil type are required. Land use coverages may be obtained from a number of sources. The USGS GIRAS (Mitchell et al., 1977) is probably the oldest, widely available data set. It tends to reflect land use of an approximately 1970s vintage. These data are now commonly distributed as part of the core data set in the BASINS model (U.S. Environmental Protection Agency, 2001a). Newer data may also exist on a more regionally varied level, such as the MRLC data set (Vogelmann et al., 1998a; Vogelmann, Sohl, and Howard, 1998b; U.S. Environmental Protection Agency, 2001b) that covers many states in the eastern United States and dates to approximately the early 1990s. Other more high-quality data sets will likely be available on an even more limited basis, perhaps varying by state, county, or municipality. Generally, the higher-quality data will reflect condi- tions from periods more recent than the GIRAS data mentioned earlier. Knowledge of land use from before the 1970s will likely need to be gleaned from nondigital sources such as historical aerial photography or paper maps. Soils data are generally obtained from the NRCS. The NRCS publishes two different sets of digital soils data: STATSGO (NRCS, 2001a) and SSURGO (NRCS, 2001b). The STATSGO data are the coarser of the two and are digitized from 1:250,000 scale maps (except in Alaska where the scale is 1:1,000,000) with a minimum mapping unit of about 1544 acres. These data are available anywhere within the United States. The SSURGO data are digitized from map scales ranging from 1:12,000 to 1:63,360. SSURGO is the most detailed level of soil mapping done by the NRCS. These data are in production at this time and availability varies on a county-by-county basis. In the case study presented here, Watts Branch lies entirely within Montgomery County, Maryland, one of the counties for which SSURGO data are available. 13.3 DEVELOPING A LAND-USE TIME SERIES The particular emphasis of this chapter is to consider the effect of changing land use on peak discharge; land use is not static, but rather continually changing in both time and space throughout the time series. A practical problem that generally arises is that the GIS data to support the modeling of peak discharge on an annual basis do not exist. In general, one has access to, at best, several different maps of land use corresponding to different “snapshots” in time. This section provides and illus- trates a method to develop a land-use time series on an annual time step. The data required to develop a land-use time series are two different maps of land use covering the extents of the watershed and spanning the same time period L1600_Frame_C13.fm Page 370 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC as the available annual maximum discharge record. Additionally, data are required that convey the history of land use development at times between the two land use snapshots. Such data are typically available in the form of tax maps. In the example provided here, the Maryland Department of Planning publishes such data (Maryland Department of Planning, 2001) that indicate tax map information at the detailed level of individual parcel locations. One of the attributes associated with these data is the date of construction of any structure on the property. The notation LU ( x,t ) is used here to indicate the land use across all locations in the vector x within the watershed being studied, and t is any generic time in years. The land-use time series is initialized to be the land use at time, t 1 , indicated by the earlier of the two land use maps. This land use is denoted by LU ( x , t 1 ). If t 1 is earlier than approximately 1970, it is likely that the required land use data are not available digitally, but rather in the form of a paper map or aerial photograph. Such data will need to be georeferenced and then digitized into a hierarchical land-use classification scheme such as the one created by Anderson et al. (1976). Figure 13.1 shows land use over the study watershed at times t 1 = 1951 and t 2 = 2000. (For completeness, this figure also shows the watershed at an intermediate time, t = 1987, and at some future time corresponding to ultimate development conditions. These land use con- ditions are discussed later in this chapter.) Using the LU ( x , t 1 ) coverage as a starting point, the land use is then allowed to transition to LU ( x , t 2 ) in the specific year, t* , that the tax map information indicates is the year of construction for that individual parcel. Applying this rule over all years t 1 < t* < t 2 and for all parcels within the watershed allows the modeler to recreate land use change on an annual time step. This process is illustrated in Figure 13.2, which shows a view of several rows of parcels in a subdivision over the years 1969 and 1970. The date shown within each parcel is the year in which the tax map data indicates that it was developed. FIGURE 13.2 Parcel-level view of land-use change model. Parcels shown in white are devel- oped and gray parcels are not developed. Note that all parcels shown become developed by 1970. L1600_Frame_C13.fm Page 371 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC The GIS treats all parcels shown in gray (undeveloped parcels) to remain in their original land use at time t = t 1 , while those shown in white (developed parcels) have transitioned to their final land use at time t = t 2 . Figure 13.3 shows the aggregate change in the land use distribution within the Watts Branch watershed between 1951 and 2000. Note that land use does not simply change linearly between these two known times, but rather it changes in an irregular fashion following the actual patterns of development as they were realized within the watershed. 13.4 MODELING ISSUES A wide range of modeling issues confront the hydrologist performing this type of study. First and foremost is the simple selection of the model to use. Other issues include methods for calibrating the model and ultimately using the model to simulate the discharge behavior of the study watershed in a predictive sense. This section presents a discussion of these wide-ranging issues and argues for a particular series of choices throughout the modeling process, recognizing that different choices might be selected by others. The decisions presented here reflect the pragmatic needs of the engineer wishing to make use of a valuable gage record, but also recognizing the influence that urbanization has on that record. 13.4.1 S ELECTING A M ODEL This study is concerned with observed and simulated peak discharges from a small watershed subject to changes in land use over time. The model that is selected must therefore predict peak discharges, be appropriate for a watershed of this size, and be sensitive to land use change in its predictions of peak discharge. The NRCS TR-55 (U.S. Soil Conservation Service, 1986) is one such model. It is selected here over the HEC-HMS model (U.S. Army Corps of Engineers, 2000) because the NRCS models FIGURE 13.3 Aggregate land-use distribution in Watts Branch watershed over time. The bar at the far right gives the ultimate development land-use distribution. L1600_Frame_C13.fm Page 372 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC are the recognized analysis tools required by the Maryland Department of the Environment for all flood discharge studies. TR-55 is chosen over the more general TR-20 (U.S. Soil Conservation Service, 1984) because only peak discharge esti- mates, not entire hydrographs are sought. Furthermore, this model is appropriate in this case because of the small scale of the watershed being studied. A larger water- shed where reach routing is a significant part of the overall travel time, or a watershed with significant detention, would require the more sophisticated TR-20. In any case, although the details specific to the TR-55 graphical method are presented here, the general approach, which is essentially model independent, is emphasized. The TR-55 model determines peak discharge using Q p , s ( t ) = q u ( t ) AQ ( t ) (13.1) where Q p,s ( t ) is the simulated peak discharge in ft 3 /sec, q u ( t ) is the unit peak discharge in ft 3 /sec-in. of runoff, A is the area of the watershed in mi 2 , and Q ( t ) is the runoff depth in inches. The functional dependence of runoff, unit peak discharge, and simulated peak discharge on time is explicitly shown to emphasize the time-varying nature of these quantities due to changes in land use. The runoff depth is determined from (13.2) where the standard assumption is made that the initial abstraction, I a ( t ), is equal to 20 percent of the storage, S ( t ) . Both storage and initial abstraction are in inches units. P ( t ) is the causal precipitation depth associated with the observed annual maximum discharge. This quantity is discussed in greater detail in Section 13.4.2. Storage, S ( t ), is determined as a function of the curve number, CN ( t ) using (13.3) The curve number is determined using a standard “look-up table” approach given the spatial overlap of land use and soils and using the NRCS-defined curve numbers (U.S. Soil Conservation Service, 1985). The time-varying nature of CN ( t ) is due to the time-varying land use within the watershed as discussed earlier in Section 13.3. The unit peak discharge, q u ( t ), is a function of two quantities, time of concen- tration, t c ( t), and the ratio of the initial abstraction to the precipitation, I a (t)/P(t). Again, the dependence of these quantities on time is shown here explicitly. The unit peak discharge is generally determined graphically; however, this procedure is auto- mated with the GIS using the equation (13.4) Qt Pt I t Pt I t St Pt St Pt St a a () [() ()] () () () [() . ()] () . () = − −+ = − + 2 2 02 08 St CN t () () =− 1000 10 log[ ( )] [ ( )] [ ( )] log[ ( )] [ ( )] {log[ ( )]}qt Crt Crt tt Crt tt ucc =+⋅ +⋅ 01 2 2 L1600_Frame_C13.fm Page 373 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC where r(t) is determined from (13.5) and C 0 , C 1 , and C 2 , are tabular functions of this ratio. Values of these constants for the U.S. Soil Conservation Service Type II storm distribution, which is appropriate for the study watershed are provided in Table 13.1. For consistency, the time of concentration, t c (t), was determined in this study using the SCS lag equation (U.S. Soil Conservation Service, 1973), rather than the often-used velocity method. In this case, the dependency of the velocity method on spatially and time-varied surface roughness would be too arbitrary to characterize consistently. The lag equation’s dependency on curve number, which is characterized very carefully throughout this study, was instead chosen as the basis for developing t c estimates. The SCS lag time, t l (t) in minutes, is determined using (13.6) where L is the longest flow path in the watershed in feet, and Y is the basin averaged slope in percentages. The lag time is converted to a time of concentration by multiplying by a factor of 1.67 and also accounting for speedup in runoff rates due to imperviousness introduced in the urbanization process. Time of concentration is thus determined using the following equation (McCuen, 1982): (13.7) TABLE 13.1 Constants C 0 , C 1 , and C 2 Used in Equation 13.4 for the SCS Type II Storm Distribution I a /PC 0 C 1 C 2 0.10 2.55323 −0.61512 −0.16403 0.30 2.46532 −0.62257 −0.11657 0.35 2.41896 −0.61594 −0.08820 0.40 2.36409 −0.59857 −0.05621 0.45 2.29238 −0.57005 −0.02281 0.50 2.20282 −0.51599 −0.01259 Source: U.S. Soil Conservation Service, Urban Hydrol- ogy for Small Watersheds, Technical Release 55, U.S. Department of Agriculture, Washington, DC, 1986. rt It Pt a () () () = tt L CN t Y l () () . . . = −       100 1000 9 1900 08 07 05 t t t t I t D D CN t D CN t D CN t c l () . (){ ()[( () () ()]}=⋅−+⋅+⋅+⋅167 1 01 2 2 3 3 L1600_Frame_C13.fm Page 374 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC where I(t) is the time-varying imperviousness of the watershed in percentages, and D 0 , D 1 , D 2 , and D 3 are −6.789 × 10 −3 , 3.35 × 10 −4 , −4.298 × 10 −7 , and −2.185 × 10 −8 , respectively. Imperviousness was determined as a simple lookup function of land use based on values determined by the Maryland Department of Planning for their generalized land use data. These values are provided in Table 13.2. 13.4.2 CALIBRATION STRATEGIES Rainfall data obtained from the NCDC Web site (National Climatic Data Center, 2001) mentioned in Section 13.2.1 were obtained for the Rockville, Maryland rain gage (Coop ID# 187705). Annual precipitation values were determined around a three- dimensional window centered on the date of the annual maximum flood. Because of potential time/date mismatches between the occurrence of precipitation and peak discharge, the observed precipitation associated with the peak discharge was taken to be the maximum of the sum over a 2-day window either beginning on ending on the day associated with the annual maximum discharge. Even allowing for potential time/date mismatches, the observed precipitation is quite small on four occasions (1958, 1964, 1969, and 1981). In fact, no precipitation is observed to explain the annual maximum in 1969. A plausible explanation for this is the relatively small scale of the study watershed. Convectively generated rainfall is highly varied in space compared to frontal-system generated rainfall, and the rain gage, although close, is not actually within the study watershed. Because of the size of the watershed, the annual maximum discharge is likely to be associated with convective summer events rather than the frontal precipitation more common TABLE 13.2 Percent Imperviousness Associated with Various Land Uses Present in Watts Branch, Maryland Land Use Percent Imperviousness Low-density residential 25 Medium-density residential 30 High-density residential 65 Commercial 82 Industrial 70 Institutional 50 Open urban land 11 Cropland 0 Pasture 0 Deciduous forest 0 Mixed forest 0 Brush 0 Source: Weller, personal communication. L1600_Frame_C13.fm Page 375 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC in the cooler months. The data support this hypothesis with 19 of 27 annual maxima observed in the months of June through September. The hydrologic engineer has a number of parameters available to calibrate the above model to the observed annual maximum series. Both curve numbers and t c values are frequent candidates for calibration in a typical analysis. Given the time series implications of this analysis, it did not make sense to adjust either of these quantities since an adjustment of a quantity might be made “up” in one year and “down” in the next. The physical basis for such an adjustment pattern is unclear. Instead, given the presumed inaccuracies in the observed precipitation record, pre- cipitation was used as the only calibration parameter. The causal precipitation, P(t), in Equation 13.2, was calibrated by setting the model outlined in Equations 13.1 through 13.7 into Equation 13.8, such that the observed and simulated annual maximum discharges were the same within a small (0.1%) tolerance. (13.8) where Q p,s [t, P(t)] is the simulated peak discharge in year, t, and assuming a causal precipitation depth, P(t). Q p,o (t) is the observed peak discharge in year, t. The observed and causal precipitation were determined to have a correlation coefficient, R, of 0.67. Table 13.3 and Figure 13.4 provide a summary and comparison of the causal (simulated) and observed precipitation depths. 13.4.3 SIMULATING A STATIONARY ANNUAL M AXIMUM-DISCHARGE SERIES With the causal precipitation time series determined, it is a straightforward process to determine the annual maximum discharge that would have been observed had land use remained constant over the period of record of the stream gage. In fact, the only question facing the hydrologic engineer is what land use to employ in the simulation. As a side-product of the calibration process, representations of land use on an annual time step corresponding to each year from 1951 to 2000 are available. Using any one of these years, t*, and the causal precipitation time series developed in the calibration step, the annual maximum series that would be observed as if the land use were fixed for that particular year, t* can be generated. In more mathematical terms, (13.9) For illustrative purposes, the annual maxima corresponding to the following four different land use conditions have been simulated: Q p,1951 (t) (earliest land use), Q p,1987 (t) (last year of the gage record), Q p,2000 (t) (“present” conditions), and Q p,ult. (t) (projected ultimate condition of watershed given zoning data). These simulated peak discharges are provided in Table 13.5 and shown in Figure 13.5. (For completeness, | [ , ( )] ( ) | () . ,, , QtPt Qt Qt ps po po − < 0 001 QtQtPtLUxt pt ps ,* , () [, (), ( ,*)]= L1600_Frame_C13.fm Page 376 Friday, September 20, 2002 10:25 AM © 2003 by CRC Press LLC [...]... 12 13 2 3 4 5 5 6 7 8 8 9 9 10 10 11 11 12 12 13 13 2 3 4 5 6 6 7 8 8 9 10 10 11 11 12 12 13 13 13 2 3 4 5 6 6 7 8 9 9 10 10 11 12 12 13 13 13 14 (Continued ) © 2003 by CRC Press LLC L1600_Frame_App-A.fm2nd Page 397 Friday, September 20, 2002 10:29 AM TABLE A.5 Critical Values of Runs Test n2 n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 3 4 9 9 5 6 9 10 10 11 11 9 10 11 12 12 13 13 13 13 7... 13. 7 PROBLEMS 1 3-1 You are asked to develop the hydrologic analyses necessary to build a bridge crossing at the location of the Watts Branch stream gage The bridge piers are to be sized based on the 25-year peak flow event Express the 1951, 1987, 2000, and ultimate development peaks for this return period as a percentage of the observed 25-year peak Comment on the magnitudes of these percentages 1 3-2 ... 69 .13 77.93 55.33 64.28 73.29 82.36 61.70 71.14 80.62 90 .13 69.33 79.33 89.33 99.33 77.58 88 .13 98.64 109.14 85.53 96.58 107.56 118.50 90.53 101.88 113. 14 124.34 95.02 106.63 113. 14 129.56 100.42 112.33 124.12 135 .81 104.22 116.32 128.30 140.17 © 2003 by CRC Press LLC L1600_Frame_App-A.fm2nd Page 392 Friday, September 20, 2002 10:29 AM TABLE A.3 Cumulative Distribution of Chi Square L1600_Frame_App-A.fm2nd... with the results presented in Table 13. 6 and Figure 13. 6 The implications for hydrologic design are addressed in this section The main, and most obvious, consequence of performing the discharge adjustment procedure outlined here is the proliferation of peak discharge estimates as shown in Tables 13. 5 and 13. 6 and Figures 13. 5 and 13. 6 Through comparison with TABLE 13. 6 Flood Frequency Distributions... 17 18 19 20 2 3 4 9 9 5 6 9 10 10 11 11 9 10 11 12 12 13 13 13 13 7 8 9 10 1l 12 13 14 15 16 17 18 19 20 11 12 13 13 14 14 14 14 15 15 15 11 12 13 14 14 15 15 16 16 16 16 17 17 17 17 17 13 14 14 15 16 16 16 17 17 18 19 18 18 18 18 13 14 15 16 16 17 17 18 18 18 19 19 19 20 20 13 14 15 16 17 17 18 19 19 19 20 20 20 21 21 13 14 16 16 17 18 19 19 20 20 21 21 21 22 22 15 16 17 18 19 19 20 20 21 21 22 22... Wilcoxon Matched-Pairs Signed-Ranks (T) Test Two-Tailed Level of Significance 0.050 0.02 0.010 One-Tailed Level of Significance N 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 © 2003 by CRC Press LLC 0.025 0.01 0.005 0 2 4 6 8 11 14 17 21 25 30 35 40 46 52 59 66 73 81 89 0 2 3 5 7 10 13 16 20 24 28 33 38 43 49 56 62 69 77 0 2 3 5 7 10 13 16 20 23 28 32 38 43 49 55 61 68 L1600_Frame_App-A.fm2nd Page... with what you would expect from the information contained in this chapter? Discuss 1 3-5 You are asked to generalize the flood-frequency adjustment method presented in this chapter to apply to a 40-mi2 watershed that includes several detention basins and 15 miles of channels Describe how you would go © 2003 by CRC Press LLC L1600_Frame_C13.fm Page 385 Friday, September 20, 2002 10:25 AM about doing this... 10.98 11.69 12.40 13. 12 11.59 12.34 13. 09 13. 85 14.61 13. 24 14.04 14.85 15.66 16.47 16.34 17.24 18.14 19.04 19.94 20.34 21.34 22.34 23.34 24.34 24.93 26.04 27.14 28.24 29.34 29.62 30.81 32.01 33.20 34.38 32.67 33.92 35.17 36.42 37.65 35.48 36.78 38.08 39.36 40.65 38.93 40.29 41.64 42.98 44.31 41.40 42.80 44.18 45.56 46.93 26 27 28 29 11.16 11.81 12.46 13. 12 12.20 12.88 13. 56 14.26 13. 84 14.57 15.31... watershed were considered, TR-55 would need to be replaced with the more sophisticated TR-20 or other rainfall-runoff model that both generates runoff and routes this runoff through a channel network Putting the hydrologic model aside for a moment, there are also assumptions and limitations associated with the land-use change model presented here As depicted in Figures 13. 1 through 13. 3, the land use is only... efforts to retain a buffer zone adjacent © 2003 by CRC Press LLC L1600_Frame_C13.fm Page 381 Friday, September 20, 2002 10:25 AM to streams Land use conditions under ultimate development are reflected in the spatial distribution shown in Figure 13. 1 and in the time series shown in Figure 13. 3 13. 5 COMPARISON OF FLOOD-FREQUENCY ANALYSES Hydrologic design is often based on peak discharges associated with various . discharge adjust- ment procedure outlined here is the proliferation of peak discharge estimates as shown in Tables 13. 5 and 13. 6 and Figures 13. 5 and 13. 6. Through comparison with TABLE 13. 6 Flood. reflected in the spatial distribution shown in Figure 13. 1 and in the time series shown in Figure 13. 3. 13. 5 COMPARISON OF FLOOD-FREQUENCY ANALYSES Hydrologic design is often based on peak discharges. use. This chapter examines the differences in derived flood-frequency behavior between the observed (nonstationary) and adjusted (stationary) peak- discharge time series. 13 L1600_Frame_C13.fm Page