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Flood Hydrograph and Peak Flow Frequency Analysis March 1979 Approved for Public Release. Distribution Unlimited. TP-62

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6. AUTHOR(S) Arlen D. Feldman

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12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES Presented at Engineering Foundation Conference on Improved Hydrologic Forecasting and also published in their proceedings, Asilomar, California, March 1979. 14. ABSTRACT Several methods for estimating flood hydrographs and flood peaks of various frequencies are discussed. The methods include frequency analysis of historical streamflows, statistical equations, empirical formulas, single event watershed models, and continuous watershed models. Methods for computing modified frequency curves due to changing watershed conditions and water management activities are described. 15. SUBJECT TERMS flood hydrology, flood frequency, peak discharge, regional methods, design storms, continuous simulation, math model, river basin hydrology 16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON a. REPORT U

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Flood Hydrograph and Peak Flow Frequency Analysis

March 1979 US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center 609 Second Street Davis, CA 95616 (530) 756-1104 (530) 756-8250 FAX www.hec.usace.army.mil TP-62

Papers in this series have resulted from technical activities of the Hydrologic Engineering Center. Versions of some of these have been published in technical journals or in conference proceedings. The purpose of this series is to make the information available for use in the Center's training program and for distribution with the Corps of Engineers. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products.

Flood Hydrograph and Peak Flow Frequency Analysis

Arlen D. Feldman*

The accurate prediction of streamflows i s essent ial t o the planning of our water resource systems. This paper addresses the practical s t a t e - of-the-art of techniques t o predict flood peaks and t h e i r associated frequency of occurrence; and techniques f o r predicting c r i t i c a l flood hydrographs (o r se r i e s of hydrographs) and t h e i r frequencies of occur- rence. S ta t i s t i ca l re lat ionships, empirical equations, and watershed models will be investigated as means fo r predicting the peak discharges and flood hydrographs .

Peak discharge information i s required t o determine the appropriate s i z e of water conveyance systems such as natural channels, diversion canals, storm drains, bridge openings, e tc . The frkquency of the peak discharges i s necessary t o determine how often the con- veyance' system capacity i s exceeded. Cr i te r ia for s iz ing conveyance systems are derived from socio-economic responses to the inconveniences associated with the exceedence of system conveyance capacities and the cost of providing those systems.

Flood control studies usually base flood damages on peak discharges as representati ve of damage due to several associated flood problems. I t i s especially convenient to be able to express flood damages in terms of discharge (s tage) , however, other factors such as flow veloci t ies and duration of flooding may need t o be considered separately. Flood control measures may take the form of increasing the capacity of conveyance systems o r regulating the flood waters through storage, diversions, or local control measures. Flood damage reduction measures include these items plus nonstructaral measures such as flood proofing s t ruc tures , e t c .

The tradeoff between conveyance capacity and storage i n a flood con- t ro l system i s a c lass ic consideration. This analysis i s appropriate for small urban drainage systems (storm and combined sani tary) up to the 1 arge r i ver/reservoi r networks. Many techniques have been devel oped, tes ted, and implemented f o r s iz ing these systems. In general, the la rger or more complex the drainage system becomes, the more the analysis s h i f t s from predicting peaks to predicting the whole hydrograph. The

"Flood Hydrograph and Peak Flow Frequency Analysis", Arlen D. Feldman, Chief, Research Branch, U.S. Army Corps of Engineers, The Hydrologic Engineering Center, Davis, Cali forni a. Presented a t Enaineering Foundation Conference on Improved Hydrologic Forecasting, Asilomar, California, March 1979.

techniques addressed in t h i s paper are separated i n t ~ the following catagories :

Frequency analysis of his tor ical streamflows S t a t i s t i c a l equati ons Empi r ica l formul ae Single e v e n t watershed models Continuous watershed models

The single event watershed models are fur ther broken down into tech- niques using hypothetical storms and h is tor ica l storms. Continuous watershed models are discussed in terms of relat ively simple models and a l s o the more complex ccunplete so i l moisture accounting models. In one of the proposed methods of analysis, a simple continuous model i s used to screen the his tor ical rainfall-runoff record t o determine important individual events which are then simulated i n more detai l with a s ingle event model. A d is t inct ion wil l also be made between techniques which predict peak flows from urban and nonurban areas. Much emphasis has been placed on urban runoff in recent years and several techniques have been developed to meet those needs (1 ) .

The s t a t i s t i c a l equations and empirical formulae are best used t o predict peak flow ra tes f o r small areas, less than 50 mi2. When analyzing larger areas, the storage and routing ef fec ts i n the basin usually require the use of a watershed model f o r adequate definit ion of the hydrograph.

Peak Flow Estimation Techniques.--Peak flows may be estimated d i rec t ly as functions of h is tor ica l streamflow records o r s t a t i s t i c a l / empirical relationships. The peak flow techniques referred to in t h i s paper are those te~hniques which predict only the peak flow - not including the whole hydrograph. The techniques which predict the whole hydrograph o r ser ies of hydrographs also compute a peak flow but they wil l be discussed in the Watershed Modeling sections. The peak flow techniques are functions of rain fa1 1 in tens i ty o r runoff frequency and various geographic characteris t i c s of the basin. Usually the annual peak flow frequency curve i s derived e i t h e r d i rec t ly from an equation o r by estimating a se r i e s of flood peaks which are then analyzed with standard frequency techniques.

Frequency Analysis o f Historical Streamflows. --Histori cal stream- flow records may be used d i r ec t ly to estimate discharges a t various frequencies. I f adequate streamflow records e x i s t and the watershed has remained re la t ive ly unchanged during the course of tha t record, then those observed s treamfl ows are probably the best indicator of the potential flood responses of the watershed in i t s present con- di t ion. The Water Resource Counci 1 ' s guide1 ines (2) describe the currently recommended techniques. Those guidelines describe the use of the Pearson Type I11 d is t r ibut ion and associated topics of high and 1 ow out1 i e r s , generalized skew, two-station comparisons, mixed populations, confidence 1 imits , flood estimates from precipitation data, and equivalent accuracy fo r independent estimates for analysis of his- tor ica l flood peaks.

I f i t i s desired t o predict the magnitude-frequency of streamflows under some future watershed land use development or regulated condition, then the h is tor ica l streamflow records cannot be used d i rec t ly . In th i s case one must usual ly resort t o a watershed model. The same requirement ar ises where long term his tor ical streamflow records e x i s t b u t the watershed has undergone signi f icant changes during tha t time. T h u s , a nonstationary streamflow ser ies ex is t s and cannot be used d i rec t ly in the frequency analysis. The nonstationary se r i e s problem can also be unraveled through the use of watershed models ( 3 ) .

I f a s ta t ionary se r i e s of data i s available, b u t not a t the specif ic locations of i n t e r e s t , then a regional frequency analysis may be under- taken (4). The regional analysis allows one to t ransfer the parameters of the flood frequency dis t r ibut ion a t gaged locations t o other locations of in t e re s t . This i s accomplished through relat ing frequency parameters to geographic and meteorologic charac ter i s t ics which are known a t the gaged and ungaged locations.

Water Resource Counci 1 ' s Ungaged Areas F l m d Frequency Study. --The Water Resaurces Counci 1 - Hydrology Committee, work group for peak flow frequency f o r ungaged areas, has recently begun a study of the follow- ing e i ght flood frequency estimation techniques.

S ta t i s t i ca l estimation of Qp S t a t i s t i c a l estimation by moments Index flood method Transfer method Empi ri cal equations Single storm Multiple discrete events Continuous simulation

The f i r s t phase of the WRC study has just been completed for selected watersheds i n the northwestern and central U.S. and they expect t o publish a report in November 1979 (personal communication with John Miller, National Weather Service). The methods reported in the p i l o t t e s t s are: USGS Equations, FHWA, Reich, Snowmel t, Index Flood, Rational Formula, TR55, (RPl49), TR55 (TC) , TR20, and HEC-1. They are encouraging the widest possible review of th i s work before going on with s imilar applica- t ions in the southwestern and southeastern U.S. A l a t e r phase of the WRC studies wil l include urban areas.

Preliminary resu l t s of the WRC study show there to be a f a i r amount of variation within the application of the same method on the same watershed by d i f fe rent par t ic ipants . This was observed even with the apparently s t r a i g h t forward methods such as the USGS Sta te Equations and FHWA where a l l t ha t i s needed i s drainage area and other simple geographic location parameters. The r e su l t s varied even more, as one would expect, as more judgement/experience factors were required to use the methods such as SCS' TR-20 and The Corps of Engineers' HEC-1. The above observations were made from a very preliminary review of the p i l o t study raw data. The WRC Ungaged Watershed Group i s now in the process of ed i t ing and analyzing tha t data and preparing t h e i r report .

Sta t i s t i ca l Flood Peak Estimation Techniques. - -S ta t i s t ica l flood peak estimation techniques predict instantaneous peak flows of prescti bed frequencies through a regression analysis of. geographic variables affect- ing the flood runoff. An excellent discussion of drainage basin and meteorologic charac ter i s t ics which can be used to explain behavior of streamflows is given i n Thomas and Benson (21). They analyzed over twenty character is t ics and discuss the relat ive a f fec ts of each. Drain- age basin area and normal annual precipitation were among the most s igni- f icant . Certainly some of the most widely available examples of these techniques are the U .S. Geological Survey (USGS) "State Regression Equations," ( 5 ) .

Patterson and Gamble ( 5 ) , developed relationships between drainage area and mean annual flood in d i f fe rent hydrologic areas. The mean annual flood i s reduced in proportion to the lake storage in the basin i f applicable, and the peak flows for recurrence intervals from 1.1 t o 50 years may be determined from a graph of recurrence interval vs. r a t i o of discharge t o mean annual flood as in figure 1.

A generalized procedure i s also used by the Federal Highway Adminis- t ra t ion (FHWA), (6) f o r small rural watersheds, generally less than 100 square miles. In th i s procedure the 10-year event is determined as a function of the drainage area, an iso-erodent factor , and a difference in elevation in the watershed. Separate equations are given f o r each of twenty four hydrophysiographic zones in the U.S. and Puerto Rico. A fixed relationship i s given between the 2-year, 100-year peaks and the 10-year peak.

Other techniques use watershed runoff charac ter i s t ics and precipi- tation in tens i t ies to predict the peak runoff rates . A time on concen- t ra t ion and i n f i l t r a t i o n index may be determined d i rec t ly from watershed character is t ics such as length and elevation change of main channel, so i l characteris t i c s , and 1 and cover. The x-minute ra infa l l in tens i ty f o r the desired frequency i s obtained from TP40 or HYDRO-35 ( 7 ) . A peak discharge per square mile may be derived from the time-of-concentration, i n f i l t r a t ion index, and peak 30-minute intensi ty . Adjustments can be made for antecedent precipi ta t ion. This method i s subject t o the standard cr i t ic isms of assuming the frequency of the runoff i s the same as the r a in fa l l .

Empirical Equations .--The most popular and long las t ing of the empirical equations i s the Rational formula (8). Despite the many more sophisticated methods available today, the rational formula i s s t i l l popular because of i t s easy and economic use. The regression equations previously discussed are simi l a r to th i s except tha t the coeff ic ients in the equations are determined by a minimum e r r o r s t a t i s t i c a l tech- niques. Application of the Rational method has even been inconsistent (37) .

Runoff vs, Rainfall Based Methods .--Many of the s t a t i s t i c a l estima- t iontechniques fo r peak flow are direct ly streamflow based and do not go through the ra infa l l -to-runoff analysis. The flow estimates are determined by anaiyzing streamf iows of known frequencies in a hydrologic region and re1 at ing them to basin character is t i cs, primarily drainage area and sometimes general meteor01 ogi c measures such as average annual

Drainage Area m i 2

1 . I 2 5 20 50 100

Recurrence In te rva l

Ratio o f

Discharge t 0

Me an Annual

Flood

Figure 1. Area Regression Equation Method

I

precipitation. I t i s generally more d i f f i c u l t t o develop these relation- ships in urbanizing basins because of the nonhomogeneous nature of the runoff ser ies .

As urbanization occurs the ra infa l l runoff response function changes and additional parameters must be brought in to the relationship to explain that variation. Usually the percent of impervious area and watershed conveyance factors a re found to be su i tab le measures of urban- ization ( 9 ) . Rainfall i s also brought into these relationships so tha t impact of changed precipitation loss ra tes can be analyzed d i rec t ly instead of trying to r e f l ec t change only in the routing parameters.

There are two general classes of ra infa l l based flood prediction methods: 1) runoff frequency i s assumed t o be the same as the ra infa l l frequency, and 2 ) the runoff frequency is computed independently of the ra infa l l frequency. The assumption tha t runoff frequency equals rain- fa1 1 frequency is generally agreed t o be undesireable (10) h u t i s often- times used because i t s implif ies the requi red analysis. Preci pi- t a t i sn frequency analysis i s discussed i n a l a t e r section. Rainfall of some frequency can be applied t o several d i f fe rent antecedent moisture conditions in the same watershed and largely d i f fe rent runoff may resu l t . As the frequency of the event becomes more rare, the runoff i s less affected by the antecedent moisture condition and the ensuing loss rates . The s ingle event models can be used on many h i s to r i c events and then the runoff peaks ranked and the frequencies determined by standard methods. Continuaus simulation models take the f inal s tep of analyzing the en t i r e precipitation runoff record maintaining consistency with respect t o soi 1 moisture storages. The continuous process modelers claim) to have the most real i s t i c basis for computing flood frequencies.

Watershed Modeling.--When i s i t necessai-y and/or desirable to use a watershed model instead of the simplified s t a t i s t i c a l and empirical techniques? The watershed models are generally requi red when : an ent i re hydrograph i s desired; analyzing complex areas ; o r when the past o r proposed future watershed response functions are changing. Watershed models are par t i cul a r ly desi rabl e when analyzing the e f f ec t of various water management schemes.

Watershed models range widely i n complexi ty. Brandstetter (1 1, compares many d i f fe rent models f o r urban storm runoff and many of these models are equally good f o r nonurban cases. Some are nothing more than simple empi r i cal equations within a subbasin network routing/combining framework. Others perform a complex accounting of so i l moisture and water in various stages of runoff. The following discussion of water- shed model ing looks a t the pract i cal s ta te -of - the-ar t in s ingle event and continuous models and combinations thereof. The attendent pre- c i p i tat ion analyses requi red with both techniques i s also discussed.

Hydrographs are necessary when storage projects (reservoirs of d i f fe rent forms) are being investigated as flood control measures. A frequency analysis of runoff can be made to determine the expected frequency of vari ous f'low biirations ( 4 ) . I f a cer tain f? cw-duraticr, relationship i s desired f o r project design, i t can be determined separately, as ju s t mentioned, and then the simulated hydrograph can be

balanced (1 1) t o conform to tha t flood duration. Continuous event simulation models are often preferred fo r storage analysis i f i t i s a sequence of storms which cause the flood problem as opposed to one large, s ingle event.

Single Event Models.--A single event model i s one tha t i s used ~ r i m a r i l v f o r individual-storm events, although i t may be of long duration* and mu1 t i -peaked. Two factors usual iy constrain the i r use to s ingle events: the continuity of so i l moisture ( loss ra tes ) i s not simulated, and/or the model simulates in such de ta i l and requires time consuming~computations s o tha t i t i s not economical to run over long periods. Many of the s ingle event models can be used equally we1 l in urban and nonurban areas but have usually been developed for a specif ic purpose and then generalized to meet more needs. Some of the most widely used s ingle event models are:

HEC-1: Flood Hydrograph Package (1 1 )

TR-20: Computer Pr~gram fo r Project Formulation Hydrology (1 2 )

MITCAT: MIT Catchment Model (13)

USGS Rainfall-Runoff Simulator (14)

SWMM: Storm Water Management Model (15)

Many other models e x i s t and some contain more advanced representation of various aspects of the precipitation-runoff process. Many comparisons of such models have been made (1, 16). Few models are more comprehensi ve and/or widely used than those above. These models are generally well supported by government agencies o r private engineering consultants and are continually being improved to meet new needs. The HEC-1 model, f o r example, goes beyond the basic rain fa1 1 /snowme1 t runoff simul ation pro- cess and has special options for computation of expected annual flood damages, automati cal ly s iz ing components of a flood control sys tem fo r maximum net benefi ts , and simulation of dam overtopping and fa i lure per the requirements of the National Dam Safety Inspection Program.

The current tendency in watershed model ing, both s ingle event and continuous, i s t o incorporate parameters with real i s t i c re1 ationships to the physical process and tha t can be determined d i rec t ly from readily avail able geographic data. Because of th i s strong in t e res t in re1 ating watershed model parameters to geographic charac ter i s t ics , the Soi 1 Conservation Service's (SCS) curve number technique has received much increased in t e res t and usage. The SCS curve number technique i s the only one i n which both the precipitation loss ra te and the water excess- to- runoff transformation (un i t hydrograph) can be determined from readily available geographic data. The data used are: 1 and cover, hydrologic so i l type, average slope of the watershed, and length of the main water course. Curve numbers have been recommended fo r various land cover - hydrologic so i l group combinations i n both urban and nonurban areas (17) as shown i n Table 1. Calibration with observed ra infa l l runoff data i s s t i 11 required. The curve number technique, a1 though a rather simp1 i s t i c

representation of the runoff process, appears to work well in many cases. Further research i s being currently undertaken by the HEC and Espey, Huston & Assoc. to t e s t the val idi ty of the technique in urbanizing watersheds.

Table 1. Runoff Curve Numbers f o r

Selected Land Uses (from Table 2.2 (17))

Hydro1 ogi c Soi 1 Group Land Use A B C D

Cultivated 1 and 72 81 88 91

Pasture o r range land 68 79 86 89

Wood o r Forest land 25 55 70 77

Residential, 114 acre l o t s 61 75 83 87

Commercial (85% imperv. ) 89 92 94 95

Industri a1 (72% imperv. ) 8 1 88 91 9 3

Paved parking l o t s , roofs, 98 98 98 98 driveways, e tc .

A par t icular ly in te res t ing and powerful benefi t of using geographi- cal ly re1 ated watershed parameters i s t h a t of interconnecting watershed models with geographi c information systems. This concept was used in a project fo r Fairfax County, VA in which a geographic grid cel l information system was used as the basis fo r computation of watershed model parameters (18). This study made use of the MITCAT watershed model and parameters were estimated from a geographic data bank of land use, e tc .

The Hydrologic Engineering Center, (19), made a practical appl i ca- tion of a geographic information system f o r automatically computing hydrolag-i c and economi c parameters in the Oconee Ri ver Expanded Flood Plain Information study, figure 2. This concept has been expanded in to a comprehensive flood plain planning tool (20), and i s now being implemented as a regular tool in Corps of Engineers' project investiga- tion.

As s ingle event models became more geographical ly based and capable of eas i ly predicting s t a r t i n g conditions, ( i n i t i a l values of model par- ameters), the less necessary continuous watershed models would appear to be. With this capabi l i ty , the s ingle event model could be s t a r t ed before every s igni f icant event. S t a t i s t i c a l analysis of the output peak flows and volumes could be performed to make predictions fo r design purposes. Using a s ingle event model fo r many storm events and using the resul t ing frequency curve, overcomes the common cr i t ic i sm of s ingle event models - t h a t runoff frequency equals rainfal l frequency.

F i gure 2 . Spati a1 Data Management and Hydrologi c Analysis System

Analysis of Flood Control Measures and Land Use Changes.--The hydra- logic engineer i s often asked to determine the impact of land use changes o r flood control management measures on spec i f ic design floods and the e n t i r e flow frequency curve. This can be accomplished with e i the r the s ingle event o r continuous watershed model. Both methods require the abi 1 i ty to change watershed parameters to r e f l e c t new watershed response functions.

Watershed modelers use many d i f fe rent character is t ics affecting the runoff process with which to predict the parameters of the model. The common procedure i s t o establ ish a relationship between the model para- meters, say 1 oss r a t e s , and runoff t rans formations (uni t g r a ~ h and kinematic wave), and basin character is t ics . Basin character is t ics are discussed in re1 ation to runoff production by Thomas and Benson (21). Urbanization factors a re included i f the basin has been o r i s being devel- oped ( 9 ) .

For evaluating flood control management a1 te rna t i ves, the watershed modelers simply r u n the model in the with and without project control modes to determine the impact of the project. In the continuous models, one usually simulates the en t i r e record with and without the modified land use and/or flood control projects. The annual peak flows, for each case, are subjected t o t radi t ional frequency analysis and the modified frequency curve i s obtained.

Single event models can be used t o develop a modified frequency curve by simulating several storms, of varying magnitude, under each dev- elopment condition (1 1 ). A base case frequency curve i s required and can he delreloped by- any preferred method- -Usually a frequency curve i s "adopted" which may be some specif ic curve o r combination of curves. The frequency of the base case computed peak flow, for each storm mag- nitude, i s determined from the adopted frequency curve, f igure 3 . The same storm i s simulated again under the modified conditions and the frequency of the runoff i s assumed to be the same. The modified fre- quency curve i s determined as shown i n f igure 3 . A potential fa l lacy w i t h t h i s approach i s t ha t the storm runoff may change in frequency for the modified watershed development. That i s , the ranking of peaks flows might change under the modified condition.

Precipitation Frequency Analysis. --Many studies have been made of precipitation frequency and c r i t i c a l design events such as the probable maximum preci p i t a t i on and various frequenc in tensi ty-durati on re1 a t i on- ships of the National Weather Service (NlJS f (7). A recent analysis by Marsalek (10) reviewed the Chicago and I l l i n o i s design storm methods and compared them w i t h resul ts obtained from continuous simul ation. Marsalek reinforced those common feelings about the p i t f a l l s of design storms, a t l e a s t f o r the limited geographic area analyzed.

Nevertheless, design storms are a commonly used tool and must be given serious consideration, especi a1 ly because of thei r economic at t ract iveness . Several s ingle event watershed modelers have developed t h e i r own ra in fa l l frequency analysis techniques (22) and l ink these techniques di rect l w i t h t h e i r watershed models. These techniques as we1 1 as the AWS ( 7 f publications can be used effect ively as long as the

1 Modified

Discharge Q t 2

Q 92

Q ' 1

curve

/

I E x i s t i n g -7 - Adopted curve

I

f l f2

Frequency ( f )

'i = peak d i scha rge f o r des ign s torm i

fi = f requency o f Qi from given curve

Q t i = peak d i scha rge from des ign s torm i under modif ied watershed c o n d i t i o n

Figure 3. Modifying Frequency Curves

impact of the antecedent preci pi t a t i on assumptions are fu l ly real i zed. A study by Yen (23) demonstrates the use of synthet ic storms in design- ing projects for the Federal Highway Administration. One of the major problems occurs when the part icular sequence of precipitation events causes the c r i t i c a l flood s i tua t ion as opposed t o the magnitude of any one par t of the multiple events. This type of problem leads one t o prefer the analysis found in the continuous models.

The use of continuous watershed models does not solve a1 1 of one's rain fa1 1 analysis problems. Granted, i t i s the most comprehensi ve analysis of the hydrology of the basin and much i s to be gained from tha t insight. These models have a major dependence upon the precipita- tion measured o r synthetical ly generated; and the precipitation data are usually the l eas t well known par t of the runoff process. The d i f f icu l ty comes in the spat ia l variation of precipi ta t ion; point measurements are made and spat i a1 averages are inferred.

The construction of a long-record precipitation ser ies i s a d i f f i - cu l t task. As one goes back in time, the observation s ta t ions become fewer, and one m u s t make more and more assumptions about the spa t ia l and temporal variation of the precipitation. The National Weather Service maintains tape f i l e s of daily precipi ta t ion records since 1948 and shorter interval precipitation measurements f o r selected s ta t ions and time periods. Before 1948, most precipi ta t ion data were not in computer compatible format and t h u s , extensive preparation by the analyst i s required. The Hydrologic Engineering Center estimated tha t approximately 4 t o 6 person-months of e f f o r t would be required t o construct the precipitation record from 1900 to 1948 f o r a 130 mi2 basin near Chicago, IL.

Continuous Watershed Models.--Most of today's highly sophisticated continuous watershed models are deri ved from the Stanford Watershed Model (24). Another model, developed a t about the same time, i s the SSARR model of' the Corps of Engineers (25). The SSARR model does not have a l l of the complexity of the Stanford derived models, but has been shown t o be comparable in resu l t s wi t h the more comprehensi ve models (26) .

The Stanford Watershed Model has been elaborated upon a t several universit ies: Kentucky (27) ; Texas (28) ; Ohio (20) ; and others. Notable among these i s the Kentucky version, en t i t l ed OPSET, where the parameters of the model are derived automatically by an optimization routine. The National Weather Service also used the Stanford Watershed-Model as the basis f o r i t s NWSRFS model (30). The National Weather Service Sacramento Model (31 ) has more comprehensive soi 1 moisture accounting a1 gori t h m s , but may be considered less sophisticated in i t s runoff transformation via l i nea r uni t graphs and the fac t tha t i t does not route stream flows in a comp rehens i ve r i ve r sys tern.

One of the most highly developed vers,ions of the Stanford Watershed Model ex is t ing today i s the Hydrocomp HSP Model (32). The HSP system of programs incorporates the precipitation-runoff model as one piece of an army o f study tools ranging from water qual i ty simulation to unsteady flow dam break flood routings. The technical analysis tools a l l l ink together with a comprehensive data management sys tem whi ch arranges input and saves output fo r fur ther analysis.

Efficient data management in continuous watershed simulation models i s an exceedingly important requirement. The HSP system i s probably the most advanced and comprehensive i n t h i s regard. The continuous models a re frequently c r i t i c i zed fo r t h e i r enormous appetite f o r data. In f ac t , the cost of assembling the necessary data often negates the use of these models in a l l but the most comprehensive s tudies which require a we1 1 orchestrated analysis of competing interdiscipl inary uses of water.

One of the simplest and most economical to r u n continuous watershed models is the STORM program (33). The model was or iginal ly developed by Water Resource Engineers, Inc. i n connection w i t h stormwater runoff i n the c i ty of San Francisco. The original model was essent ia l ly a long term hyetograph analysis w i t h a simple rational formula type transfor- mation to runoff. Long term, say 50 years o r more, of hourly precipita- t ion data can eas i ly be analyzed a t an affordable computer cost. The or iginal model was limited to a s ingle subbasin analysis b u t l a t e r versions incorporate multibasin routing and combining.

The STORM program was studied by Brandstetter (1) and i t s character- i s t i c s can eas i ly be compared w i t h other models in tha t report . Another comparison of several continuous and s ingle event watershed models was recently pub1 ished by the ASCE Urban Water Resources Research Program (16). While t h i s comparison was not an exhaustive tes t ing of the models, i t does give good insight in to the re la t ive performance, a t t r ibu tes , and d i f f i c u l t i e s one may find in these models. Another comparison of con- tinuous models was made by Lumb (34).

The Hydrologic Engineering Center has undertaken a detai led analysis of the HSP watershed model (35). The purpose of t h i s analysis was to see how well and prac t ica l ly a comprehensive continuous simulation model could be used in a standard Corps of Engineers flood frequency study. The HSP model was chosen as a state-of-the-art model and applied to the DuPage River Basin near Chicago, IL. This study drew several conclusions:

1) The model can produce reasonable resu l t s when properly cal ibrated. Annual flood events, when analyzed together, exhibited character- i s t i c s simi 1 a r t o recorded flows, a1 though individual years were s igni f icant ly d i f fe rent from the observed.

2) The model can account f o r urbanization but more in theory than was able t o be accomplished in pract ice. The application was begun with f ive land uses fo r runoff production, b u t t h i s was soon re- duced to two, nonurban and urban, together with an impervious area. Without runoff data t o distinguish the urban and nonurban contribu- t ions t o runoff i t was furthermore not possible to make that land use d is t inc t ion . The f inal model was constituted of an urban/rural mixture land use and an impervious area. The theory of the model would lead one t o believe tha t several d i f fe rent land use runoff segments could be used b u t in the end only one could be r e a l i s t i - cal ly used.

3) The model i s re la t ive ly easy to operate in terms of input instruct ions, f i l e organization and manipulation.

I

screening model simulation fo r period of record

frequency screening model resul ts

time single event i n detai l

adjusted frequency curve by (Qi. 9:) function

frequency

Figure 4. Hybrid Single Even t/Continuous Model Analysis

to each storm can be estimated from the continuous simulation resu l t s . A s t a t i s t i c a l analysis of the simple continuous model peak flows and the detailed s ingle event model's peak flows i s made and a regression equation i s developed. The regression equation i s used t o deter- mine a be t te r value for the other simple continuous model peak flows not simulated i n de t a i l . T h i s resu l t s i n an adjusted frequency curve based on the detailed simulation of a few s igni f icant flood events, f igure 4.

Concl usions-.--There are numerous techniques fo r predicting peak flood discharges/vol umes of prescribed frequencies. The budget of one's study and one's fami l ia r i ty with d i f fe rent analytical techniques usual ly determine which approach i s used.

S ta t i s t i ca l and empirical flood peak estimation techniques may be good fo r small areas where r ive r routing/storage e f fec t s are not s ignif icant . For larger watersheds and s tudies requiring analysis of a1 ternat i ve flood con trol/watershed management procedures, the water- shed simulation model i s the best tool. The advantages and disadvan- tages of single event models with design storms and complex continuous simulation models have been discussed. A hybrid approach using a simple continuous model to ident i fy s igni f icant events and a s ingle event model to analyze those events in de ta i l i s a promising method of analysis.

Watershed models are tending t o become more d i rec t ly based on readily measurable geographic parameters. The need fo r continuous accounting of so i l moisture conditions would appear t o be less necessary as one becomes be t te r able to predict watershed model parameters from di rect geographic/ meteorologic measurements. With t h i s capabi 1 i t y , s ingle event models theoretically could be eas i ly s t a r t ed f o r any event i n question.

Geographic information systems and uti 1 i ty programs to compute auto- matical ly the watershed model parameters are a promising techno1 ogy fo r comprehensive r ive r basin s tudies . This technique i s particularly powerful in analyzing many land use and watershed and flood damage reducti on management a1 te rna t i ves .

I f one uses a subjective measure of flood severi ty , such as general public inconvenience, then projects may be sized by methods which are not dependent on a t rue estimate of a flood frequency. That i s , the projects are designed by some consistent method, say design storms, and the severity of the storms i s changed dependent upon the publ ic 's reaction to flooding inconvenience. This i s generally the case in urban s t o m sewer design .

I f an objective estimate of expected economic damage i s to be the design c r i t e r i um, then r e a l i s t i c flood frequencies must be computed. Projects based on spec i f i c flood frequencies, say the 100-year flood of the flood insurance s tudies , would require consistent, b u t not neces- s a r i l y precise, estimates of flood frequenctes. In t ha t case, insur- ance premi ums could be adjusted, as actuari a1 experience indicates , t o made the project viable. The landowners, however, would argue f o r the use of a precise frequency.

References

1. B rands te t te r , A1 b in , "Assessment o f Mathematical Models f o r Storm and Combined Sewer Management," f o r Environmental P r o t e c t i o n Agency, Techno1 ogy Ser ies, EPA-600/2-76-175a, August 1976,

2. Water Resources Council , "Guide1 i nes f o r Determin ing Flood Flow Frequency," B u l l e t i n 1 7A, Hydro1 ogy Committee, June 1977,

3. Gundlach, David L, , "Adjustments o f Peak Discharge Rates f o r Urban- i za t i on , " I r r i g a t i o n and Drainage Journal , American Soc ie t y of C i v i l Engineers, Vol. 104, No, IR3, September 1978,

4. Beard, Leo R., " S t a t i s t i c a l Methods i n Hydrology," U.S, Army Corps o f Engineers, Sacramento D i s t r i c t , January 1962.

5. Pat terson, James L, and C, R. Gamble, "Magnitude and Frequency o f Floods i n the Un i ted States, P a r t 5, Hudson Bay and Upper M iss i s - s i p p i R i v e r Basins ," U.S. Geological Survey, Water Supply Paper 1678, Washington, D.C, 1968.

6. Trent , R,E,, "FHWA Method f o r Es t ima t ing Peak Flow Rates o f Runoff f rom Small Rural Watersheds ," Federal Highway Admin i s t ra t i on , Off ices o f Research and Devel opment , Envi ronmental Desi gn and Cont ro l D i v- i s i o n , Washington, D,C., 1978,

7. U,S, Weather Bureau, " R a i n f a l l Frequency A t l a s o f t he Un i ted States," Dept. o f Commerce, Technical Paper No, 40, May 1961, and Na t iona l Weather Service, "F i ve t o 60-Minute P r e c i p i t a t i o n Frequency f o r t he Eastern and Cent ra l Un i ted States," NOM Technical Memo NWS HYDRO-35, S i l v e r Spring, MD, June 1977.

8. Gregory, R.L., and C,E, Arnold, "Rat iona l Runof f Formulas," Trans- ac t i ons , American Soc ie t y o f C i v i l Engineers, Vol. 96, 1932,

9. Espey, W i l l i a m H. Jr , , Duke G, Altman, and Char les B. Graves, J r . , "Nornographs f o r Ten-Minute U n i t Hydrographs f o r Small Urban Water- sheds," American Soc ie t y o f C i v i 1 Engineers Urban Water Resources Research Program Technical Memo No, 32, New York, 1977,

10. Marsalek, J i r i , "Research on t h e Design Storm Concept ," American Soc ie t y o f C i v i 1 Engineers Urban Water Resources Research Program, Technical Memo No. 33, New York, 1978,

11. Hydro log ic Engineer ing Center, "F lood Hydrograph Package, HEC-1," U.S. Army Corps o f Engineers, C a l i f o r n i a , 1973.

12. Soi 1 Conservat ion Serv ice, "Computer Program f o r P r o j e c t Formulat ion Hydrology," Technical Release No. 20, U.S. Dept. o f A g r i c u l t u r e , Washington, D.C., 1965.

13. Resource Ana lys is , I nc . , "MITCAT Catchment Simulat 'on Model ," D e s c r i p t i o n and Users Manual, Version 6, Massachusetts, 1975.

14. Dawdy, David R., Robert W, L i c h t y , and James M, Bergmann, "A Rain- f a l l - R u n o f f S imu la t ion Model f o r Es t ima t i on o f Flood Peaks f o r Small Drainage Basins ," U,S, Geol og ica f Survey Pro fess iona l Paper 506-B, Washington, D,C, , 1972.

15. Heaney, James P. and Wayne C, Huber, "Storm Water Management Model : Refinements, Test ing, and Decision-Making," U n i v e r s i t y o f F l o r i d a , 1973,

16. Abbott , Jesse W., "Tes t ing of Several Runof f Models on an Urban Watershed ," American Soc ie t y of C i v i l Engineers Urban Water Resources Research Program Technica l Memo NO, 34, New York, October 1978,

17, S o i l Conservat ion Serv ice, "Urban Hydrology f o r Small Watersheds ," Technical Release No. 55, U,S, Dept. o f A g r i c u l t u r e , Washington, D , C b , January 1975.

18. Michel , Henry L. and W i l l i a m P, Henry, "Flood Cont ro l and Drainage Planning i n the Urban iz ing Zone: F a i r f a x Co, V i r g i n i a , " i n Urban Runof f Q u a n t i t y and Qua1 i ty, Eng ineer ing Foundation and American Soc ie t y o f C i v i l Engineers, New York, 1474.

Hydro1 o g i c Engineer ing Center, "Phase 1 Oconee Basin P i l o t Study, T r a i l Creek Test," U.S. Army Corps of Engineers, C a l i f o r n i a , 1975,

Davis, D a r r y l W. , "Comprehensive F lood P l a i n S tud ies Using Spa t i a1 Data Management Techniques ," Water Resources B u l l e t i n , Vol . 14, No. 3, June 1978.

Thomas, H. and M, Benson, "Genera l i za t i on o f Streamflow Character- i s t i c s , " U,S, Geologica l Survey Water Supply Paper No, 1975, Washington, D.C., 1970.

Resource Ana lys is , Inc . , " R a i n f a l l Ana lys is and Generat ion Model D e s c r i p t i o n and Theo re t i ca l Background ," Boston, MA, March 1975,

Yen, Ben Chie and Ven Te Chow, " F e a s i b i l i t y Study on Research of Local Design Storms ," Prepared f o r Federal Highway Admin i s t ra t i on , Report No. FHWA-RD-78-65, Washington, D,C, , November 1977.

Crawford, Norman H. and Ray K. L i n s l e y , " D i g i t a l S imu la t i on i n Hydrology: S tan fo rd Watershed Model I V , " S tan fo rd U n i v e r s i t y , C i v i l Eng ineer ing Technica l Report No. 39, J u l y 1966,

Rockwood, David M. , "Streamf l ow Synthes is and Reservo i r Regulat ion ," U,S, Army Engineer D i v i s i o n , Nor th P a c i f i c , Technica l B u l l e t i n No, 22, January 1964,

World Meteor01 og i c a l Organ iza t ion , " In te rcompar i son of Conceptual Models Used i n Operat ional Hyd ro log i ca l Forecas t ing ," Operat ional Hydro logy Report No, 7, WMO-No. 429, Geneva, 1975,

27. James, L. Douglas, "An Eva1 u a t i o n of Re1 a t i o n s h i p s Between Stream- f low Pa t te rns and Watershed C h a r a c t e r i s t i c s Through t h e Use of OPSET," Research Report No. 36, Mater Resources I n s t i t u t e , Univer- s i t y o f Kentucky, Lex ington, 1970.

28. Claborn, B.J., and W.L, Morre, "Numerical S imu la t i on o f Watershed Hydrology," Hydrol og i c Engineer ing Laboratory, C i v i 1 Engineer ing Dept, , U n i v e r s i t y of Texas, Technica l Report HYD-14-7001, 1970,

29. Ricca, V.T., "The Ohio S t a t e U n i v e r s i t y Vers ion o f t h e S tan fo rd S t reamf l ow S imu la t i on Model ," Water Resources Research Center, Ohio S t a t e U n i v e r s i t y , 1972.

30. Na t i ona l Weather Serv ice, "Nat iona l Weather Se rv i ce R i v e r Forecast Sys tern Forecast Procedures," NOAA f echn i c a l Memo, NWS HY DRO-14, S i l v e r Spr ing, MD, 1972.

31. Burnash, Robert J. C. , R. L a r r y F e r r a l and Richard McGui re , " A Gen- e r a l i z e d Streamfl ow S imu la t i on System," J o i n t Federal -S ta te R ive r Forecast Center, Sacramento, CA 1973,

32. Hydrocomp, Inc . , "Hydrocomp Simul a t i o n Programming Operat ions Manual, Four th E d i t i o n ,It Palo A1 t o , C a l i f o r n i a , January 1976,

33. Hydrol og i c Eng ineer ing Center, "Storage, Treatment, Ove r f l ow, Run- o f f Model, STORM," U,S, A r m y Corps s f Engineers, C a l i f o r n i a , 1976.

34. Lumb, A1 an M. , "Comparison of t h e Georgia Tech, Kansas, Kentucky, Stanford, and TVA Watershed Models i n Georgia," Georgia I n s t i t u t e o f Technology, January 1976.

35. Cermak, Robert J., "Continuous Hydro log ic S imu la t i on o f t h e West Branch DuPage R i v e r Above West Chicago: An A p p l i c a t i o n o f Hydro- comp's HSP ," Hydrol o g i c Engineer ing Center, U.S. Army Corps o f Engineers, C a l i f o r n i a , D r a f t , November 1978.

36. Peters, John C., "Techniques f o r Developing Frequency Curves i n Urban Areas," Lec tu re Notes, Hydro1 og i c Engi n e e r i ng Center, U. S. Army Corps o f Engineers, C a l i f o r n i a 1978.

37. A r d i s , Col b y V, , K. J. Dueker, and A.T. Lenz, "Storm Drainage P r a c t i c e s o f T h i r ty-Two C i t i e s ,It American Soc ie t y o f C i v i 1 Engi n- eers, Journa l o f t h e Hydrau l i cs D i v i s i o n , Vol . 95, No. 1 , January 1969.

Technical Paper Series TP-1 Use of Interrelated Records to Simulate Streamflow TP-2 Optimization Techniques for Hydrologic

Engineering TP-3 Methods of Determination of Safe Yield and

Compensation Water from Storage Reservoirs TP-4 Functional Evaluation of a Water Resources System TP-5 Streamflow Synthesis for Ungaged Rivers TP-6 Simulation of Daily Streamflow TP-7 Pilot Study for Storage Requirements for Low Flow

Augmentation TP-8 Worth of Streamflow Data for Project Design - A

Pilot Study TP-9 Economic Evaluation of Reservoir System

Accomplishments TP-10 Hydrologic Simulation in Water-Yield Analysis TP-11 Survey of Programs for Water Surface Profiles TP-12 Hypothetical Flood Computation for a Stream

System TP-13 Maximum Utilization of Scarce Data in Hydrologic

Design TP-14 Techniques for Evaluating Long-Tem Reservoir

Yields TP-15 Hydrostatistics - Principles of Application TP-16 A Hydrologic Water Resource System Modeling

Techniques TP-17 Hydrologic Engineering Techniques for Regional

Water Resources Planning TP-18 Estimating Monthly Streamflows Within a Region TP-19 Suspended Sediment Discharge in Streams TP-20 Computer Determination of Flow Through Bridges TP-21 An Approach to Reservoir Temperature Analysis TP-22 A Finite Difference Methods of Analyzing Liquid

Flow in Variably Saturated Porous Media TP-23 Uses of Simulation in River Basin Planning TP-24 Hydroelectric Power Analysis in Reservoir Systems TP-25 Status of Water Resource System Analysis TP-26 System Relationships for Panama Canal Water

Supply TP-27 System Analysis of the Panama Canal Water

Supply TP-28 Digital Simulation of an Existing Water Resources

System TP-29 Computer Application in Continuing Education TP-30 Drought Severity and Water Supply Dependability TP-31 Development of System Operation Rules for an

Existing System by Simulation TP-32 Alternative Approaches to Water Resources System

Simulation TP-33 System Simulation of Integrated Use of

Hydroelectric and Thermal Power Generation TP-34 Optimizing flood Control Allocation for a

Multipurpose Reservoir TP-35 Computer Models for Rainfall-Runoff and River

Hydraulic Analysis TP-36 Evaluation of Drought Effects at Lake Atitlan TP-37 Downstream Effects of the Levee Overtopping at

Wilkes-Barre, PA, During Tropical Storm Agnes TP-38 Water Quality Evaluation of Aquatic Systems

TP-39 A Method for Analyzing Effects of Dam Failures in Design Studies

TP-40 Storm Drainage and Urban Region Flood Control Planning

TP-41 HEC-5C, A Simulation Model for System Formulation and Evaluation

TP-42 Optimal Sizing of Urban Flood Control Systems TP-43 Hydrologic and Economic Simulation of Flood

Control Aspects of Water Resources Systems TP-44 Sizing Flood Control Reservoir Systems by System

Analysis TP-45 Techniques for Real-Time Operation of Flood

Control Reservoirs in the Merrimack River Basin TP-46 Spatial Data Analysis of Nonstructural Measures TP-47 Comprehensive Flood Plain Studies Using Spatial

Data Management Techniques TP-48 Direct Runoff Hydrograph Parameters Versus

Urbanization TP-49 Experience of HEC in Disseminating Information

on Hydrological Models TP-50 Effects of Dam Removal: An Approach to

Sedimentation TP-51 Design of Flood Control Improvements by Systems

Analysis: A Case Study TP-52 Potential Use of Digital Computer Ground Water

Models TP-53 Development of Generalized Free Surface Flow

Models Using Finite Element Techniques TP-54 Adjustment of Peak Discharge Rates for

Urbanization TP-55 The Development and Servicing of Spatial Data

Management Techniques in the Corps of Engineers TP-56 Experiences of the Hydrologic Engineering Center

in Maintaining Widely Used Hydrologic and Water Resource Computer Models

TP-57 Flood Damage Assessments Using Spatial Data Management Techniques

TP-58 A Model for Evaluating Runoff-Quality in Metropolitan Master Planning

TP-59 Testing of Several Runoff Models on an Urban Watershed

TP-60 Operational Simulation of a Reservoir System with Pumped Storage

TP-61 Technical Factors in Small Hydropower Planning TP-62 Flood Hydrograph and Peak Flow Frequency

Analysis TP-63 HEC Contribution to Reservoir System Operation TP-64 Determining Peak-Discharge Frequencies in an

Urbanizing Watershed: A Case Study TP-65 Feasibility Analysis in Small Hydropower Planning TP-66 Reservoir Storage Determination by Computer

Simulation of Flood Control and Conservation Systems

TP-67 Hydrologic Land Use Classification Using LANDSAT

TP-68 Interactive Nonstructural Flood-Control Planning TP-69 Critical Water Surface by Minimum Specific

Energy Using the Parabolic Method

TP-70 Corps of Engineers Experience with Automatic Calibration of a Precipitation-Runoff Model

TP-71 Determination of Land Use from Satellite Imagery for Input to Hydrologic Models

TP-72 Application of the Finite Element Method to Vertically Stratified Hydrodynamic Flow and Water Quality

TP-73 Flood Mitigation Planning Using HEC-SAM TP-74 Hydrographs by Single Linear Reservoir Model TP-75 HEC Activities in Reservoir Analysis TP-76 Institutional Support of Water Resource Models TP-77 Investigation of Soil Conservation Service Urban

Hydrology Techniques TP-78 Potential for Increasing the Output of Existing

Hydroelectric Plants TP-79 Potential Energy and Capacity Gains from Flood

Control Storage Reallocation at Existing U.S. Hydropower Reservoirs

TP-80 Use of Non-Sequential Techniques in the Analysis of Power Potential at Storage Projects

TP-81 Data Management Systems of Water Resources Planning

TP-82 The New HEC-1 Flood Hydrograph Package TP-83 River and Reservoir Systems Water Quality

Modeling Capability TP-84 Generalized Real-Time Flood Control System

Model TP-85 Operation Policy Analysis: Sam Rayburn

Reservoir TP-86 Training the Practitioner: The Hydrologic

Engineering Center Program TP-87 Documentation Needs for Water Resources Models TP-88 Reservoir System Regulation for Water Quality

Control TP-89 A Software System to Aid in Making Real-Time

Water Control Decisions TP-90 Calibration, Verification and Application of a Two-

Dimensional Flow Model TP-91 HEC Software Development and Support TP-92 Hydrologic Engineering Center Planning Models TP-93 Flood Routing Through a Flat, Complex Flood

Plain Using a One-Dimensional Unsteady Flow Computer Program

TP-94 Dredged-Material Disposal Management Model TP-95 Infiltration and Soil Moisture Redistribution in

HEC-1 TP-96 The Hydrologic Engineering Center Experience in

Nonstructural Planning TP-97 Prediction of the Effects of a Flood Control Project

on a Meandering Stream TP-98 Evolution in Computer Programs Causes Evolution

in Training Needs: The Hydrologic Engineering Center Experience

TP-99 Reservoir System Analysis for Water Quality TP-100 Probable Maximum Flood Estimation - Eastern

United States TP-101 Use of Computer Program HEC-5 for Water Supply

Analysis TP-102 Role of Calibration in the Application of HEC-6 TP-103 Engineering and Economic Considerations in

Formulating TP-104 Modeling Water Resources Systems for Water

Quality

TP-105 Use of a Two-Dimensional Flow Model to Quantify Aquatic Habitat

TP-106 Flood-Runoff Forecasting with HEC-1F TP-107 Dredged-Material Disposal System Capacity

Expansion TP-108 Role of Small Computers in Two-Dimensional

Flow Modeling TP-109 One-Dimensional Model for Mud Flows TP-110 Subdivision Froude Number TP-111 HEC-5Q: System Water Quality Modeling TP-112 New Developments in HEC Programs for Flood

Control TP-113 Modeling and Managing Water Resource Systems

for Water Quality TP-114 Accuracy of Computer Water Surface Profiles -

Executive Summary TP-115 Application of Spatial-Data Management

Techniques in Corps Planning TP-116 The HEC's Activities in Watershed Modeling TP-117 HEC-1 and HEC-2 Applications on the

Microcomputer TP-118 Real-Time Snow Simulation Model for the

Monongahela River Basin TP-119 Multi-Purpose, Multi-Reservoir Simulation on a PC TP-120 Technology Transfer of Corps' Hydrologic Models TP-121 Development, Calibration and Application of

Runoff Forecasting Models for the Allegheny River Basin

TP-122 The Estimation of Rainfall for Flood Forecasting Using Radar and Rain Gage Data

TP-123 Developing and Managing a Comprehensive Reservoir Analysis Model

TP-124 Review of U.S. Army corps of Engineering Involvement With Alluvial Fan Flooding Problems

TP-125 An Integrated Software Package for Flood Damage Analysis

TP-126 The Value and Depreciation of Existing Facilities: The Case of Reservoirs

TP-127 Floodplain-Management Plan Enumeration TP-128 Two-Dimensional Floodplain Modeling TP-129 Status and New Capabilities of Computer Program

HEC-6: "Scour and Deposition in Rivers and Reservoirs"

TP-130 Estimating Sediment Delivery and Yield on Alluvial Fans

TP-131 Hydrologic Aspects of Flood Warning - Preparedness Programs

TP-132 Twenty-five Years of Developing, Distributing, and Supporting Hydrologic Engineering Computer Programs

TP-133 Predicting Deposition Patterns in Small Basins TP-134 Annual Extreme Lake Elevations by Total

Probability Theorem TP-135 A Muskingum-Cunge Channel Flow Routing

Method for Drainage Networks TP-136 Prescriptive Reservoir System Analysis Model -

Missouri River System Application TP-137 A Generalized Simulation Model for Reservoir

System Analysis TP-138 The HEC NexGen Software Development Project TP-139 Issues for Applications Developers TP-140 HEC-2 Water Surface Profiles Program TP-141 HEC Models for Urban Hydrologic Analysis

TP-142 Systems Analysis Applications at the Hydrologic Engineering Center

TP-143 Runoff Prediction Uncertainty for Ungauged Agricultural Watersheds

TP-144 Review of GIS Applications in Hydrologic Modeling

TP-145 Application of Rainfall-Runoff Simulation for Flood Forecasting

TP-146 Application of the HEC Prescriptive Reservoir Model in the Columbia River Systems

TP-147 HEC River Analysis System (HEC-RAS) TP-148 HEC-6: Reservoir Sediment Control Applications TP-149 The Hydrologic Modeling System (HEC-HMS):

Design and Development Issues TP-150 The HEC Hydrologic Modeling System TP-151 Bridge Hydraulic Analysis with HEC-RAS TP-152 Use of Land Surface Erosion Techniques with

Stream Channel Sediment Models

TP-153 Risk-Based Analysis for Corps Flood Project Studies - A Status Report

TP-154 Modeling Water-Resource Systems for Water Quality Management

TP-155 Runoff simulation Using Radar Rainfall Data TP-156 Status of HEC Next Generation Software

Development TP-157 Unsteady Flow Model for Forecasting Missouri and

Mississippi Rivers TP-158 Corps Water Management System (CWMS) TP-159 Some History and Hydrology of the Panama Canal TP-160 Application of Risk-Based Analysis to Planning

Reservoir and Levee Flood Damage Reduction Systems

TP-161 Corps Water Management System - Capabilities and Implementation Status