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

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 t

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 OVERVIEW OF METHOD

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

13.1.2 ILLUSTRATIVE CASE STUDY: WATTS BRANCH

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

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The flood of record took place in 1975 with a discharge of 3400 ft3/sec In 1972, Hurricane Agnes, responsible for the flood of record in many neighboring water- sheds, produced an annual maximum flow of 2900 ft3/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, Qp,o( t ) Because of the land use change that induced nonstationarity into Qp,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 RAINFALL DATA RECORDS

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 STREAMFLOW RECORDS

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 DATA

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 logic modeling of the annual maximum discharges First and foremost, topographic

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 periodL1600_Frame_C13.fm Page 370 Friday, September 20, 2002 10:25 AM

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, t1, indicated by the earlier of the two land use maps This land use is denoted by LU ( x , t1) If t1 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 t1= 1951 and t2= 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 , t1) coverage as a starting point, the land use is then allowed to transition to LU ( x , t2) 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 t1 < t* < t2 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 oped and gray parcels are not developed Note that all parcels shown become developed by

The GIS treats all parcels shown in gray (undeveloped parcels) to remain in their original land use at time t = t1, while those shown in white (developed parcels) have transitioned to their final land use at time t = t2 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 SELECTING A MODEL

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

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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 waterwater-shed

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

Qp,s( t ) = qu( t ) AQ ( t ) (13.1)

where Qp,s( t ) is the simulated peak discharge in ft3/sec, qu( t ) is the unit peak discharge

in ft3/sec-in of runoff, A is the area of the watershed in mi2, 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, Ia( 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, qu( t ), is a function of two quantities, time of

concen-tration, tc( t), and the ratio of the initial abstraction to the precipitation, Ia(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

where r(t) is determined from

(13.5)

and C0, C1, and C2, 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, tc(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

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 C0, C1, and C2 Used in Equation 13.4 for the SCS Type II Storm Distribution

Source: U.S Soil Conservation Service, Urban

Hydrol-ogy for Small Watersheds, Technical Release 55, U.S

Department of Agriculture, Washington, DC, 1986

r t I t

P t

a

( ) ( ) ( )

=

t t

L

CN t Y

where I(t) is the time-varying imperviousness of the watershed in percentages, and

D0, D1, D2, and D3 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

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 tc

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 Qp,s[t, P(t)] is the simulated peak discharge in year, t, and assuming a causal precipitation depth, P(t) Qp,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

MAXIMUM-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: Qp,1951(t) (earliest land use),

Qp,1987(t) (last year of the gage record), Qp,2000(t) (“present” conditions), and Qp,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,

the observed [Qo(t)] and simulated runoff volumes, [Q1951(t), Q1987(t), Q2000(t), and

Qult.(t)], are provided first in Table 13.4.)

With these new time series determined, it is important to clearly understand what they represent Each of the simulated time series represents the discharges that

would have been observed at the stream gage, had the land use been fixed at t* conditions over the entirety of the gaging period Thus, the 1951 time series, Qp,1951(t),

P obs 1 Day before Peak (in.)

P obs on Day of Peak (in.)

P obs 1 Day after Peak (in.)

Maximum Observed

FIGURE 13.4 Comparison of observed and causal (simulated) precipitation depths associated

with the annual maximum discharges in Watts Branch The line shown corresponds to perfectagreement

FIGURE 13.5 Time series plot showing observed and adjusted annual maximum discharges.

Year

conditions present in 1951 Note that the observed discharges lie between those associated with the 1951 and 1987 land use conditions This is to be expected since the gaging period is from 1958 to 1987 It is also of interest to note that the 1987

discharge in the Qp,1987(t) time series is identical to that in the observed record In

other words, under the method described here, adjustment is not made to this discharge when determining the peak discharge under 1987 land use conditions If gaging were to have taken place in 1951 or to have continued in 2000, we would expect the discharges in both of these years under these land use conditions to also

be identical to the observed record for the particular year in question Each of these time series is valuable, because each obeys a major assumption of flood-frequency

land-use time series are stationary; the trend of increasing discharges due to ization has been removed.

urban-A few words are merited in the description of the ultimate land use condition Zoning data were obtained from the Maryland Department of Planning spanning the area associated with the study watershed As of 2000, the watershed is already highly urbanized; however, zoning for this watershed indicates that the remaining 18% of agricultural land and a significant proportion of the forest cover would be converted to commercial and/or residential land uses Forest cover within 100 feet

of existing streams is assumed to remain due to efforts to retain a buffer zone adjacent

TABLE 13.5

Observed and Simulated Annual Maximum Discharges in

Watts Branch, Maryland

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 return periods In stream restoration, discharges that approximate bank-full flow conditions have a return frequency of 1.5 to 2 years (Leopold, 1994) The design of bridges, culverts, detention ponds, and outlet structures may depend on frequencies ranging from 2 to 100 years depending on the structure and design specifications regulated

by the state From an engineering perspective, the consequences of the analyses presented in this chapter are on the differences in flood frequency between the various time series we have determined.

13.5.1 IMPLICATIONS FOR HYDROLOGIC DESIGN

The USGS PeakFQ program (U.S Geological Survey, 2001a) automates the mination of the flood frequency distribution for any annual maximum time series, producing estimates consistent with Bulletin 17B (Interagency Advisory Committee

deter-on Water Data, 1982) guidelines The four time series presented in Table 13.5 were analyzed 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 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

adjust-TABLE 13.6

Flood Frequency Distributions for Observed and Simulated Annual

Maximum Discharges in Watts Branch, Maryland

Return Period

(years)

Observed Time Series (ft 3 /sec)

1951 Land Use (ft 3 /sec)

1987 Land Use (ft 3 /sec)

2000 Land Use (ft 3 /sec)

Ultimate Land Use (ft 3 /sec)

dis-the observed frequency distribution, dis-the consequences of dis-the discharge adjustment method become clear Consider, for example, developing a hydrologic design for a bridge located at the stream gage based on a 50-year return frequency In the absence

of an adjustment method, the design discharge would be 3459 ft3/sec Given that the gaging ended relatively recently in 1987, one might be tempted to simply use the discharges adjusted to 1987 land use conditions In this case, the design discharge would increase by 269 ft3/sec to 3728 ft3/sec If adjustments are made for urbaniza- tion that has taken place since the end of the gage record, the design discharge would increase to 3852 ft3/sec In Maryland, where ultimate development determines the design discharge for new bridges, the 50-year peak discharge based on adjustment

of the gage record to ultimate development land-use conditions is 5063 ft3/sec This

is 1604 ft3/sec greater than the unadjusted discharge from the gage record The consequences on engineering design are clear: failure to adjust the observed dis- charge record in the face of known urbanization can lead to systematic underdesign

of the structure Depending on the structure, this underdesign might manifest itself

in increased flooding, a discharge structure failing to pass the required flow and being overtopped, or in scour of a magnitude much greater than anticipated In any case, underdesign will lead to a greater likelihood of failure of the engineered structure.

It is important to note that the adjustment procedure outlined here is of value, even if land use is relatively unchanged over the period of record of the stream gage This is because there may still have been significant development since the gage record was collected or ultimate development conditions may represent a large degree of urbanization that was not present at the time of gaging In both of these cases, adjusted discharges would be greater, and potentially much greater, than those associated with the observed flood-frequency distribution.

FIGURE 13.6 Observed and adjusted flood-frequency distributions.

13.5.2 ASSUMPTIONS AND LIMITATIONS

Although the method outlined here is a valuable approach for adjusting nonstationary annual maximum discharges, it is not without its assumptions and limitations, which should be enumerated explicitly The method, as presented, lumps all uncertainty in the modeling process into a time series of precipitation estimates that reproduce the observed peak discharge using the TR-55 method This precipitation time series has been referred to throughout this chapter as the “causal precipitation time series.” Actual differences in the hydrologic response may be due to any number of other assumptions in the TR-55 model as employed here For instance, the curve number table that was used may not be appropriate, the antecedent conditions (assumed normal) may be dry or wet, the impervious surfaces (assumed to be directly con- nected to the drainage system) may instead be disconnected, subareas within the watershed may need to be considered separately, and detention storage has been ignored altogether Design criteria instituted since the end of the gage record may mean that the ultimate land use conditions include a significant storage component; thus, peak discharges associated with ultimate development as portrayed here are much greater than would be expected in the face of stormwater management prac- tices If a larger 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 allowed to transition from

one initial land use at time t = t1 to another final land use at time t = t2 A more robust model that would be relatively easy to incorporate would allow the landscape

to transition from/to multiple land use conditions at discrete points in time This

model would then require n different snapshots in time and n – 1 spatially referenced

data sets that convey when the conversion of each bit of landscape from condition

at time t = ti, to condition at time t = ti+1, occurs In the land use model presented

earlier, there were only n = 2 snapshots in time and the subscript, i, took on only the value i = 1 The most likely limitation that the hydrologic modeler will encounter

in this context is a distinct lack of land use “snapshots” at fixed points in time, and

of spatially referenced data sets to convey the land use change history.

13.6 SUMMARY

This chapter has illustrated a GIS-based method to model land use change over time

on an annual time step and at the parcel level of spatial detail These land-use change data were used to drive a simple hydrologic model that is sensitive to land use change The hydrologic model was calibrated to reproduce the observed discharges

of the period of record of an actual gaged case-study watershed in Maryland Once calibrated, the hydrologic model was then used to determine the annual maximum discharges that would have resulted in the case study watershed for fixed (rather than time-varying) land use corresponding to past, present, and future land use

conditions Using flood-frequency analysis, the fixed land-use, annual-maximum flood-frequency distributions were compared to the flood-frequency distribution for the actual observed distribution The implications of not adjusting an annual maxi- mum time series derived from a gaged watershed under urbanizing (nonstationary) land use conditions are that design discharges associated with any return frequency are likely to be underestimated and lead to the underdesign of a structure and a greater likelihood for that structure to ultimately fail.

13.7 PROBLEMS

13-1 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.

13-2 Assuming a fixed rectangular cross-sectional channel geometry that is 20 feet wide, with a slope of 0.005 ft./ft., and a Manning’s roughness of 0.03, (a) Determine the normal depth associated with the observed, 1951, 1987,

2000, and ultimate development 100-year discharges.

(b) If the bridge was constructed in 1987 with the deck placed to just pass the 100-year discharge at that time, by how much will it be overtopped

by the 100-year event in 2000? At ultimate development conditions? 13-3 Download the PeakFQ program from the Web: http://water.usgs.gov/soft -

pro-gram and the values in Table 13.5 to verify the Qp,o and Qp,2000 frequency analysis values provided in Table 13.6 You will need to indicate

flood-“STA” for the skew computation option to indicate that you are using the station skew option rather than the default weighted skew option.

13-4 Let the runoff ratio time series, RR(t), be defined as:

where Q(t) is the runoff depth (in inches) defined in Equation 13.2 and

provided in Table 13.4 and P(t) is the causal precipitation depth (in inches) also described as part of Equation 13.2 and provided in Table 13.3 Plot

RR(t) for the Qp,o(t) and Qp,2000(t) time series Perform a regression on these

ratios versus time Report the slopes that you determine from these sions in both cases Are these slopes consistent with what you would expect from the information contained in this chapter? Discuss.

regres-13-5 You are asked to generalize the flood-frequency adjustment method sented 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

pre-R t Q t

P t

R( ) ( ) ( )

=

about doing this What additional information beyond that used in the case study presented here would be necessary?

13-6 You are given access to additional land use coverages corresponding to

1964 and 1975 conditions Describe how the land-use change model presented in this chapter would be modified to accommodate such data Are there any inconsistencies that might arise? Would additional data be necessary?

13-7 You are given access to an additional land use coverage corresponding to

1937 conditions Describe how the land-use change model presented in this chapter would be modified to accommodate such data Are there any inconsistencies that might arise? Would additional data be necessary? 13-8 This chapter makes the claim that the relatively small scale of the study watershed makes it more likely to have convective summer thunderstorms drive the annual-maximum peak flow series Outline a small study that would use only the USGS annual-maximum flow database to determine the scale (in mi2) at which the annual maximum shifts from summer thunderstorms to cooler-season frontal events.

Appendix A Statistical Tables

TABLE A.1 Standard Normal Distribution

TABLE A.2

Critical Values of the t Statistic

Level of Significance, One-Tailed 0.25 0.20 0.10 0.05 0.025 0.0125 0.005 0.0025 0.0005

Level of Significance, Two-Tailed

TABLE A.2

Critical Values of the t Statistic ( Continued )

Level of Significance, One-Tailed 0.25 0.20 0.10 0.05 0.025 0.0125 0.005 0.0025 0.0005

Level of Significance, Two-Tailed

TABLE A.4

Values of F Distribution

5% in Upper Tail df2

TABLE A.4

Values of F Distribution ( Continued )

5% in Upper Tail df2

TABLE A.4

Values of F Distribution ( Continued )

1% in Upper Tail df2

TABLE A.4

Values of F Distribution ( Continued )

1% in Upper Tail df2