TIME-PARAMETER ESTIMATION FOR APPLICABLE TEXAS WATERSHEDS

Transcription

1 TIME-PARAMETER ESTIMATION FOR APPLICABLE TEXAS WATERSHEDS Meghan C. Roussel 1, Davd B. Thompson 2, Xng Fang 3, Theodore G. Cleveland 4, C. Amanda Garca 1 1 U.S. Geologcal Survey, 2 Texas Tech Unversty, 3 Lamar Unversty, 4 Unversty of Houston Submtted to Texas Department of Transportaton Research Report Department of Cvl Engneerng College of Engneerng Lamar Unversty Beaumont, Texas

2 NOTICE The Unted States Government and the State of Texas do not endorse products or manufacturers. Trade or manufacturers names appear heren solely because they are consdered essental to the objectves of ths report.

3 1. Report No. FHWA/TX-05/ Ttle and Subttle Tme-Parameter Estmaton for Applcable Texas Watersheds 2. Government Accesson No. 3. Recpent s Catalog No. 7. Author(s) Meghan C. Roussel, Davd B. Thompson, Xng Fang, Theodore G. Cleveland, and C. Amanda Garca 9. Performng Organzaton Name and Address U.S. Geologcal Survey Texas Water Scence Center 8027 Exchange Drve Austn, Texas Sponsorng Agency Name and Address Texas Department of Transportaton Research and Technology Implementaton Offce P.O. Box 5080 Austn, TX Techncal Report Documentaton Page 5. Report Date August Performng Organzaton Code 8. Performng Organzaton Report No Work Unt No. (TRAIS) 11. Contract or Grant No. Project Type of Report and Perod Covered Techncal Report September 2004 August Sponsorng Agency Code 15. Supplementary Notes Project conducted n cooperaton wth the Texas Department of Transportaton and the Federal Hghway Admnstraton. 16. Abstract Characterzaton of hydrologc processes of a watershed n the context of dranage desgn requres estmaton of specfc tmeresponse characterstcs. The tme-response characterstcs of a watershed frequently are represented by two conceptual tme parameters, the tme of concentraton and the tme to peak dscharge. The study descrbed n ths report assesses varous approaches for estmatng watershed characterstcs necessary to estmate tme of concentraton for applcable Texas watersheds, assesses varous establshed approaches of estmatng tme of concentraton, descrbes a preferable approach for tme of concentraton estmaton, and evaluates the converson of values of tme of concentraton from the preferable method to values of tme to peak. A comparson of varous approaches (manual and automated) for estmatng watershed characterstcs ndcates that tme of concentraton s relatvely nsenstve to the specfc approach. For the 92 watersheds consdered n the study (applcable watersheds), dranage areas are approxmately 0.25 to 150 square mles, man- lengths are approxmately 1 to 50 mles, and dmensonless man- slopes are approxmately to Based on the analyss, the preferable approaches for estmaton of tme of concentraton are the Krpch-nclusve approaches and more specfcally, the Kerby- Krpch approach for applcable watersheds. The preference s based on smplcty of approach and ease of nput-data acquston. The Kerby-Krpch approach s straghtforward to use and produces tme of concentraton values, whch, through the conventonal Natural Resources Conservaton Servce converson, mmc tme to peak from auxlary analyss of observed ranfall and runoff data for the 92 watersheds. Comparson of tme of concentraton and tme to peak values substantates the preferable method. Vsually fttng a lnear relaton between tme of concentraton and tme to peak ndcates that alternatve conversons to the Natural Resources Conservaton Servce converson are more approprate when the Kerby-Krpch approach s used. 17. Key Words Tme Parameter, Tme of Concentraton, Watershed, Texas 19. Securty Classf. (of report) Unclassfed 20. Securty Classf. (of ths page) Unclassfed 18. Dstrbuton Statement No restrctons. 21. No. of pages Prce Form DOT F (8-72) Reproducton of completed page authorzed

4 TIME-PARAMETER ESTIMATION FOR APPLICABLE TEXAS WATERSHEDS by Meghan C. Roussel, Cvl Engneer U.S. Geologcal Survey, Austn, Texas Davd B. Thompson, Assocate Professor Department of Cvl Engneerng, Texas Tech Unversty Xng Fang, Assocate Professor Department of Cvl Engneerng, Lamar Unversty Theodore G. Cleveland, Assocate Professor Department of Cvl and Envronmental Engneerng, Unversty of Houston C. Amanda Garca, Cvl Engneer U.S. Geologcal Survey, Austn, Texas Research Report Texas Department of Transportaton Research Project Number Research Project Ttle: Estmatng Tme Parameters of Drect Runoff and Unt Hydrographs for Texas Watersheds Prepared n cooperaton wth the Texas Department of Transportaton and the Federal Hghway Admnstraton August 2005 Department of Cvl Engneerng College of Engneerng Lamar Unversty Beaumont, Texas

5 DISCLAIMER The contents of ths report reflect the vews of the authors, who are responsble for the facts and accuracy of the data presented heren. The contents do not necessarly reflect the offcal vew or polces of the Federal Hghway Admnstraton or the Texas Department of Transportaton (TxDOT). Ths report does not consttute a standard, specfcaton, or regulaton. The researcher n charge of ths project s Dr. Xng Fang, Lamar Unversty. No nventon or dscovery was conceved or frst actually reduced to practce n the course of or under ths contract, ncludng any art, method, process, machne, manufacture, desgn, or composton of matter, or any new useful mprovement thereof, or any varety of plant, whch s or may be patentable under the patent laws of the Unted States of Amerca or any foregn country.

6 ACKNOWLEDGMENTS The authors recognze the contrbutons of Jame Vllena-Morales, Austn Dstrct, Project Drector ; Davd Stolpa, Desgn Dvson, Program Coordnator for Project ; and the followng Project Advsors : George Herrmann, San Angelo Dstrct; Rose Mare Klee, Desgn Dvson; Amy Ronnfeldt, Desgn Dvson; and Davd Zwernemann, Desgn Dvson. v

7 TABLE OF CONTENTS Abstract Introducton Purpose and Scope Estmaton of Watershed Characterstcs Prevous Studes Tme-Parameter Estmaton for Applcable Texas Watersheds Travel Tme for Overland Flow Travel Tme for Shallow Concentrated Flow and Channel Flow Dscusson Conclusons References Supplement: Gudance for Estmaton of Tme of Concentraton n Texas v

8 LIST OF FIGURES 1. Locatons of U.S. Geologcal Survey streamflow-gagng statons used n study Relaton between manual-based watershed characterstcs and automatc-based watershed characterstcs derved from a 30-meter dgtal elevaton model Relaton between dranage area and tme of concentraton from evaluated approaches Relaton between dranage area and tme of concentraton from evaluated approaches wth dstncton of Krpch-nclusve approaches Relaton between tme of concentraton and tme to peak Relaton between tme of concentraton and tme to peak showng alternatve tme-ofconcentraton to tme-to-peak conversons v

9 LIST OF TABLES 1. U.S. Geologcal Survey streamflow-gagng statons used n the study Summary of travel-tme and tme-of-concentraton computatons for 92 watersheds n Texas by U.S. Geologcal Survey researchers Summary of travel-tme and tme-of-concentraton computatons for 92 watersheds n Texas by Lamar Unversty researchers Summary of travel-tme and tme-of-concentraton computatons for 92 watersheds n Texas by Texas Tech Unversty researchers v

10 TIME-PARAMETER ESTIMATION FOR APPLICABLE TEXAS WATERSHEDS Meghan C. Roussel 1, Davd B. Thompson 2, Xng Fang 3, Theodore G. Cleveland 4, C. Amanda Garca 1 1 U.S. Geologcal Survey, 2 Texas Tech Unversty, 3 Lamar Unversty, 4 Unversty of Houston ABSTRACT Characterzaton of hydrologc processes of a watershed n the context of dranage desgn requres estmaton of specfc tme-response characterstcs. The tme-response characterstcs of a watershed frequently are represented by two conceptual tme parameters, the tme of concentraton and the tme to peak dscharge. The study descrbed n ths report assesses varous approaches for estmatng watershed characterstcs necessary to estmate tme of concentraton for applcable Texas watersheds, assesses varous establshed approaches of estmatng tme of concentraton, descrbes a preferable approach for tme of concentraton estmaton, and evaluates the converson of values of tme of concentraton from the preferable method to values of tme to peak. A comparson of varous approaches (manual and automated) for estmatng watershed characterstcs ndcates that tme of concentraton s relatvely nsenstve to the specfc approach. For the 92 watersheds consdered n the study (applcable watersheds), dranage areas are approxmately 0.25 to 150 square mles, man- lengths are approxmately 1 to 50 mles, and dmensonless man- slopes are approxmately to Based on the analyss, the preferable approaches for estmaton of tme of concentraton are the Krpchnclusve approaches and more specfcally, the Kerby-Krpch approach for applcable watersheds. The preference s based on smplcty of approach and ease of nput-data acquston. The Kerby-Krpch approach s straghtforward to use and produces tme of concentraton values, whch, through the conventonal Natural Resources Conservaton Servce converson, mmc tme to peak from auxlary analyss of observed ranfall and runoff data for the 92 watersheds. Comparson of tme of concentraton and tme to peak values substantates the preferable method. Vsually fttng a lnear relaton between tme of concentraton and tme to peak ndcates that alternatve conversons to the Natural Resources Conservaton Servce converson are more approprate when the Kerby-Krpch approach s used

11 INTRODUCTION Characterzaton of hydrologc processes of a watershed n the context of dranage desgn requres estmaton of tme-response characterstcs. Tme-response characterstcs are used n hydrologc models and nfluence model response to ranfall from real or desgn storms. Ranfall and runoff models that ncorporate tme parameters are used by engneers and others for hydrologc desgn ncludng the desgn of brdges and culverts. Durng 2004 and 2005, a consortum of researchers at the U.S. Geologcal Survey (USGS), Texas Tech Unversty (TTU), Lamar Unversty (LU), and Unversty of Houston (UH), n cooperaton wth the Texas Department of Transportaton (TxDOT) Research Management Commttee 3, nvestgated approaches for estmatng tme parameters for applcable Texas watersheds (TxDOT Research Project ). The tme-response characterstcs of a watershed frequently are represented by two conceptual tme parameters, tme of concentraton ( ) and tme to peak ( T p ). The generally s defned as the tme t takes for runoff to travel from the most hydraulcally dstant pont n a watershed to the outlet. The T p generally s defned as the tme from the begnnng of storm runoff to the peak streamflow value of a unt-runoff hydrograph. Hydrologc models typcally requre an adjustment or converson of to T p because models commonly use T p ; yet n practce often s consdered easer to conceptualze. For ths study, 92 watersheds n Texas wth USGS streamflow-gagng statons were selected for estmaton. The necessary ranfall and runoff data (Asquth and others, 2004) for T p nvestgaton are avalable for these watersheds. Data for more than 1,600 storms are avalable. Locatons of the 92 statons are shown n fgure 1. Ancllary staton nformaton s lsted n table 1. Each watershed s categorzed on the bass of a qualtatve land-use classfcaton as ether developed (D) or undeveloped (U). The dstncton s provded by the orgnal data sources dentfed n Asquth and others (2004). Dranage areas for the 92 watersheds consdered for the study are about 0.25 to 150 square mles, man- lengths (length from the outlet to the watershed dvde) are about 1 to 50 mles, and dmensonless man- slopes (the dfference n elevaton between the outlet and the watershed dvde dvded by the man- length) are about to Values for T p are avalable from auxlary analyss of observed ranfall and runoff data for the 92 watersheds by four methods as part of TxDOT Research Project (W.H. Asquth, U.S. Geologcal Survey, wrtten commun., 2005), whch s a research project contemporaneous to ths TxDOT Research Project. The four methods of computng T p are (1) the tradtonal unt hydrograph approach, (2) the Gamma Unt Hydrograph Analyss System (GUHAS) unthydrograph approach usng a gamma dstrbuton hydrograph model, (3) the lnear-programmng unt-hydrograph approach, and (4) the nstantaneous unt-hydrograph approach usng a Raylegh dstrbuton hydrograph model

12 EXPLANATION Watershed boundary Streamflow-gagng staton and number Staton located n watershed classfed as developed Staton located n watershed classfed as undeveloped 34 00' 99 00' 98 00' 97 00' 96 00' 30 00' 31 00' ' 29 00' 32 00' ' ' COLORADO RIVER BASIN BRAZOS RIVER BASIN TRINITY RIVER BASIN 95 00' SAN ANTONIO RIVER BASIN Base from U.S. Geologcal Survey dgtal data Scale 1:250,000 Albers equal-area projecton, Datum NAD 83 Standard parallels and 27 25, central merdan ' Study area Fort Worth Dallas MILES TEXAS Bryan KILOMETERS San Antono Austn MILES KILOMETERS LOCATION MAP Fgure 1. Locatons of U.S. Geologcal Survey streamflow-gagng statons used n study

13 Purpose and Scope The purpose of ths report s to (1) qualtatvely assess varous approaches for estmatng watershed characterstcs necessary for estmaton for applcable Texas watersheds, (2) assess varous establshed approaches for estmatng, (3) descrbe a preferable estmaton approach, and (4) evaluate the converson of values from the preferable approach to T p values. Multple ndependent approaches to estmate watershed characterstcs and were appled to 92 selected watersheds to assess a representatve range of establshed approaches for estmatng. All methods for estmatng conceptualze the flow path of a parcel of runoff from the most hydraulcally dstant pont n a watershed to the watershed outlet. values obtaned by the multple approaches are compared to each other and to T p values for the same watersheds from TxDOT Research Project Estmaton of Watershed Characterstcs Methods for estmatng tme parameters generally requre one or more watershed characterstcs. For example, a method mght requre length or slope. Each research entty wthn the consortum ndependently estmated watershed characterstcs for the 92 watersheds n order to mmc actual hydrologc practce. Three manual approaches and one automated approach were used and comparsons between the approaches were made. Manual approaches are based on well-establshed methods such as hand delneaton of dranage area on paper maps, use of planmeters to compute dranage area, and use of a map wheel to determne length. An algorthmc foundaton for automated computaton of basn characterstcs s descrbed by Brown and others (2000). A graphcal comparson of methods for estmaton of watershed characterstcs s shown n fgure 2. The graphs depct manual-based watershed characterstcs, whch were computed by researchers at the Unversty of Houston, on the horzontal axs and automatc-based watershed characterstcs on the vertcal axs. The equal value lne ndcates dfferences between manual- and automatc-based watershed characterstcs and emphaszes the uncertanty nherent n watershed-characterstc estmaton. The dranage-area graph n fgure 2 shows that dranage area s estmated consstently across a wde range of scales, as ndcated by the few devatons from the equal value lne. The man length graph shows that as length decreases, the automatc-based length becomes larger than the manual-based length. The man- slope graph shows that as slope ncreases, the automatc-based slope becomes smaller than the manualbased slope. Despte dfferences n watershed-characterstc values, the authors conclude that the dfferences are few and that t s approprate to estmate watershed characterstcs usng a varety of methods. Dfferences between manual- and automatc-based watershed characterstcs are consdered a comparatvely mnor source of uncertanty n relaton to other sources nherent n tme-parameter estmaton, n partcular, and to hydrologc models ncorporatng tme parameters, n general

14 Prevous Studes The lterature addressng s rch and vared. A contemporaneous and extensve lterature revew s presented by Fang and others (2005). Consequently, only references pertnent to the research reported here are presented n ths secton. Methods for estmatng are classfed nto two broad categores emprcal or regresson-based and hydraulc-based. The regresson-based method uses watershed characterstcs and observatons of tme parameters derved from analyss of ranfall and runoff data. The hydraulc-based method uses estmates of flow velocty usng Mannng's equaton. One of the earlest works on for watersheds s Krpch (1940). Example publcatons that dscuss Krpch (1940) nclude Plgrm and Cordery (1993) and Dngman (2002). Krpch studed the hydrographs of seven small watersheds n Tennessee. Dranage areas ranged from 1.25 to 112 acres and dmensonless slopes from 0.03 to Krpch (1940) concludes that the method s applcable to watersheds wth dranage areas less than about 200 acres. The computed usng the Krpch method s multpled by 0.4 for overland flow on concrete and 0.2 for concrete flow. Kerby (1959) used data gathered by Hathaway (1945) from very small watersheds to develop an equaton for estmatng for overland flow. Watersheds studed by Kerby (1959) have dranage areas less than 10 acres, have dmensonless slopes less than 0.01, and have lengths of overland flow less than 1,200 feet. A method based on the knematc wave approxmaton (Knematc Wave Formula, KWF) to the dynamc wave equatons s presented by Morgal and Lnsley (1965) and Aron and Erborge (1973). The Natural Resources Conservaton Servce )(2004) travel-tme method (herenafter, NRCS travel-tme uses hydraulc-based estmates of flow velocty n the watershed to estmate. Haktanr and Sezen (1990) apply twoparameter gamma and three-parameter beta dstrbutons to approxmate tme parameters usng unt hydrographs for 10 watersheds n Anatola, Turkey. Smas and Hawkns (2002) studed ranfall and runoff relatons ncludng tme parameters for 168 small watersheds throughout the Unted States wth 3,100 observed storms. Watershed dranage area ranged from 0.3 to 3,490 acres

15 TIME-PARAMETER ESTIMATION FOR APPLICABLE TEXAS WATERSHEDS Multple ndependent approaches to estmate were appled to the 92 study watersheds to assess a representatve range of prevously establshed approaches for estmatng. All methods for estmatng conceptualze the flow path of a parcel of runoff from the most hydraulcally dstant pont n a watershed to the watershed outlet. One method uses three dstnct flow paths, or components overland flow, shallow concentrated flow, and flow; other methods use only two components overland flow and flow. In general, the more complex the conceptualzaton of runoff flow path (the more components), the more complex the ensung method for estmatng. For ths study, the selected subset of avalable estmaton approaches conssts of three overland flow methods, one shallow concentrated flow method, and four flow methods. Indvdual tme of travel (flow duraton) of the th component s represented by T t. The T t components are summed to yeld for each watershed. Travel Tme for Overland Flow, the NRCS travel- Three methods were used to calculate the overland flow component of tme method, the Kerby method, and the KWF method. The NRCS travel-tme method was mplemented usng equaton 1 (McCuen, 2005) and Mannng s equaton, = L V and (1) V = R, (2) n h S where s n mnutes; length of overland flow ( L) s n feet; average velocty ( V ) s n feet per second; hydraulc radus ( R h ), or the area dvded by wetted permeter of the, s n feet; S s the dmensonless man- slope; and n s Mannng s roughness coeffcent. Kerby (1959) provdes a method to estmate usng the followng equaton: T 0.67( L N) t = , (3) S 0.5 where T t s n mnutes; length of overland flow ( L) s n feet; S s the dmensonless man slope; and the retardance coeffcent ( N ) s based on condton of the overland flow surface and ranges from 0.1 for bare and packed sol to 0.8 for dense grass or forest

16 AUTOMATED MAIN-CHANNEL SLOPE, AUTOMATED MAIN-CHANNEL AUTOMATED DRAINAGE AREA, IN FEET PER MILE LENGTH, IN MILES IN SQUARE MILES MANUAL DRAINAGE AREA, IN SQUARE MILES MANUAL MAIN-CHANNEL LENGTH, IN MILES EQUAL VALUE LINE EQUAL VALUE LINE EQUAL VALUE LINE MANUAL MAIN-CHANNEL SLOPE, IN FEET PER MILE Fgure 2. Relaton between manual-based watershed characterstcs and automatc-based watershed characterstcs derved from a 30-meter dgtal elevaton model

17 The KWF method (Morgal and Lnsley, 1965; Aron and Erborge, 1973) was mplemented usng T 0.94( L n) 0.6 t = , (4) 0.4 S 0.3 where T t s n mnutes; length of overland flow ( L) s n feet; S s the dmensonless man slope; ranfall ntensty ( ) s n nches per hour; and n s Mannng s roughness coeffcent. Ranfall ntensty for each watershed s estmated usng the 2-year recurrence nterval, and ranfall duraton s computed by an teratve process and s watershed specfc. Ranfall ntensty for Texas was obtaned from Asquth and Roussel (2004). Travel Tme for Shallow Concentrated Flow and Channel Flow Only the NRCS travel-tme method was used to calculate the shallow concentrated flow component of, as that s the only method n whch t s explctly computed. The four methods used to calculate the flow component of are the NRCS travel-tme method, the Krpch method, the Haktanr and Sezen method, and the Smas and Hawkns method. The NRCS travel-tme method was mplemented for shallow concentrated and flow usng equaton 1 by substtutng the length of shallow concentrated flow or the man- length for L as approprate. The average velocty ( V ) was computed for shallow concentrated flow and flow by usng Mannng s equaton (eq. 2) n the equaton of contnuty for steady flow (eqs. 5, 6): Q = AR, and (5) n h S V = Q ---, (6) A where dscharge ( Q) s n cubc feet per second; area ( A) s the cross-sectonal area n square feet for ether shallow concentrated flow or flow; other varables as defned for equaton 2. The Krpch (1940) method was mplemented usng the equaton T t = L 0.77 S 0.385, (7) where T t s n mnutes; length of the longest from basn dvde to outlet ( L ) s n feet; and S s dmensonless watershed slope. The Haktanr and Sezen (1990) method was mplemented usng equaton 8 to estmate (Haktanr and Sezen defne T L as the dfference n tme between when the center of excess ranfall occurs n a basn and when peak streamflow occurs) and equaton 9 to convert T L to : T L T L = 0.401L m and (8)

18 = T L , (9) 0.6 where T L s n hours; man- length ( L m ) s n mles; and s n hours, computed from the NRCS relaton n equaton 9. The Smas and Hawkns (2002) method was mplemented usng equaton 10 to estmate T L (Smas and Hawkns defned T L as the dfference between the center of excess ranfall and the centrod of drect runoff) and equaton 11 to convert T L to S nat T L = W S 0.150, and (10) = 1.417T L, (11) where T L s n hours; watershed wdth ( W ), whch s obtaned by dvdng the watershed area by the watershed length s n feet; S s dmensonless watershed slope; and the maxmum potental retenton ( S nat ) s n nches. The maxmum potental retenton s computed usng the NRCS curve number ( CN) n the equaton S nat = 1, , (12) CN where CN s a ste-specfc value from a study of clmatc adjustments to CN by Thompson and others (2003). Fnally, an analyss of the overland and shallow concentrated flow components of was conducted by researchers at LU to determne whether a consstent travel tme could be assocated wth those two flow components to smplfy calculatons. The analyss ncluded senstvty of to varatons n nput parameters such as roughness and slope. The analyss s not presented n ths report; however, the results are summarzed. For the 92 watersheds, a reasonable estmate of the duraton of the combned overland and shallow concentrated flow components s on the order of 30 mnutes. The authors conclude that, for rapd estmaton, both the overland and shallow concentrated flow components can be accounted for by addng 30 mnutes to -flow duraton for applcable Texas watersheds. Dscusson Estmates of T t and for 92 Texas watersheds are lsted n tables 2 4 (at end of report). Estmates of are not avalable for all methods for all 92 watersheds. The relaton between dranage area and for each method s depcted n fgure 3. Estmates of vary consderably for a gven dranage area. The varaton s expected because a varety of methods are represented and because nput parameter estmates for each method are subject to dfferences n analyst nterpretatons; that s, nterpretatons n estmaton of nput parameter values. estmates from the Smas and Hawkns method generally are greater than those from other estmates. Although, as dranage area ncreases, the dfferences become smaller. The Smas and

19 20 TIME OF CONCENTRATION, IN HOURS DRAINAGE AREA, IN SQUARE MILES EXPLANATION LINE DEPICTING SQUARE ROOT OF DRAINAGE AREA SIMAS AND HAWKINS METHOD PLUS 30 MINUTES FOR OVERLAND FLOW NRCS TRAVEL-TIME METHOD IMPLEMENTED BY LAMAR UNIVERSITY RESEARCHERS NRCS TRAVEL-TIME METHOD IMPLEMENTED BY TEXAS TECH UNIVERSITY RESEARCHERS NRCS TRAVEL-TIME METHOD IMPLEMENTED BY USGS RESEARCHERS ESTIMATES FROM ALL OTHER APPROACHES CONSIDERED Fgure 3. Relaton between dranage area and tme of concentraton from evaluated approaches

20 S nat Hawkns method uses an estmate of, whch s derved from the NRCS CN. Standard (or tabulated) values of CN generally are greater than those computed from watershed ranfall and runoff for a substantal part of Texas (Thompson and others, 2003), resultng n values that most lkely are too large. As a result, the authors conclude that the Smas and Hawkns method s napproprate for the watersheds of ths study. Addtonally, as CN approaches 100, a value approprate for mpervous cover, T L approaches zero regardless of watershed sze. Logc dctates that T L s greater than zero for any watershed. For ths report, the Smas and Hawkns method s not consdered further. Estmates of from the NRCS travel-tme method vary over about one-half order of magntude and generally are less than estmates from other methods. The effect of a smaller s an ncrease n peak streamflow of the unt hydrograph. An ncrease n the unt-hydrograph peak translates nto an ncrease n the peak streamflow of the drect runoff hydrograph. Many hydrologc desgn decsons are senstve to peak streamflow. Overestmaton of peak streamflow could lead to the overdesgn of dranage structures. Estmates of by the NRCS travel-tme method requre a substantal number of nput parameters, more than any other method presented n ths report. Results from the NRCS travel-tme method are senstve to analyst-selected nputs for overland flow slope and land-use condton; shallow concentrated flow geometry, roughness, and slope; and man geometry, roughness, and slope. The dfferences n the three ndependent computatons of (those of LU, TTU, and USGS) usng the NRCS travel-tme method are attrbuted to dfferng length estmates for each flow component, dfferng estmates of the remanng watershed characterstcs, and dfferng mplementatons of Mannng s equaton for open- flow. Dfferent assumptons were made regardng geometry and Mannng s roughness coeffcent. Precse estmaton of some of the nput parameters for the NRCS travel-tme method s dffcult. In partcular, repeatable applcaton of Mannng s equaton usng generalzed measures of geometry and roughness that are representatve of the hydraulc and hydrologc processes nfluencng of the watershed s dffcult. The potental exsts for analysts to have substantally dfferent estmates as demonstrated by the results n fgure 3. Krpch-nclusve (Kerby-Krpch, KWF-Krpch, and Krpch method plus 30 mnutes approaches) estmates are shown n fgure 4. Whereas estmates usng Krpch-nclusve approaches stll exhbt much varaton, less varablty appears to be n these estmates compared to estmates obtaned usng the NRCS travel-tme method. The smaller varablty n the Krpchnclusve approaches s partally expected because some of the methods used for flow ncorporate overlappng methodology. Krpch-nclusve approaches are preferable from a usablty perspectve. Krpch-nclusve approaches requre fewer nput parameter estmates than the NRCS travel-tme method. The actual number of parameters for Krpch-nclusve approaches s dependent on the partcular method for estmatng the overland flow component. Input parameters for Krpch-nclusve approaches are avalable from publshed resources, such as topographc maps, NRCS county sol surveys, and geographc nformaton software; ths s not the case for NRCS travel-tme nput parameters. Examples of unpublshed nput parameters for the NRCS travel-tme method are the approprate Mannng s roughness coeffcent for the and approprate measures of

21 20 TIME OF CONCENTRATION, IN HOURS DRAINAGE AREA, IN SQUARE MILES EXPLANATION LINE DEPICTING SQUARE ROOT OF DRAINAGE AREA KIRPICH METHOD PLUS 30 MINUTES FOR OVERLAND FLOW IMPLEMENTED BY LAMAR UNIVERSITY RESEARCHERS KERBY-KIRPICH APPROACH IMPLEMENTED BY TEXAS TECH UNIVERSITY RESEARCHERS KERBY-KIRPICH APPROACH IMPLEMENTED BY USGS RESEARCHERS ESTIMATES FROM ALL OTHER METHODS CONSIDERED Fgure 4. Relaton between dranage area and tme of concentraton from evaluated approaches wth dstncton of Krpch-nclusve approaches

22 geometry. Addtonally, dentfcaton of the most approprate method to acqure some of the NRCS nput parameters s dffcult. Another method for estmaton for small watersheds s an ad hoc method that uses the square root of dranage area n square mles, whch reportedly produces n hours (Davd Stolpa, Texas Department of Transportaton, oral commun., 2004). The orgn of the method s uncertan. The method lacks apparent physcal bass and s dependent on the unt system ndcated. Square root of dranage area s supermposed on the graphs of the relatons between and dranage area (fgs. 3, 4). The square root of dranage area equaton solates length by removng unts of length squared. Remarkably, the square root of dranage area passes through the generalzed center of the data n the /dranage area graphs. Although the method produces the correct order of, the authors stress that the method remans an ad hoc method, perhaps best used as a check of other methods. T p The relaton between for each watershed derved from regresson analyss from TxDOT Research Project and from the Kerby-Krpch approach s shown n fgure 5. The conventonal converson (Natural Resources Conservaton Servce, 2004) of to T p s T p = d 2 + T L and T L = 0.6 (form of eq. 9), where d s equal to ranfall duraton. The rato d 2 s assumed neglgble for ths report because 1- and 5-mnute ranfall duratons were consdered for TxDOT Research Project Therefore, T p 0.6 ; ths relaton s shown n fgure 5. An mportant dstncton for the regresson analyss s the watershed development classfcaton. In the graph of the relaton between T p and, the generalzed regons for the two development classfcatons are ndcated by two ellpses. The generalzed regons shown are applcable to three of the unt hydrograph approaches the tradtonal unt hydrograph approach ndcates less nfluence of watershed development. An nterpretaton of the T p graph (fg. 5) s that the NRCS conventonal T p 0.6 converson overestmates T p for developed watersheds and slghtly underestmates T p for undeveloped watersheds. The authors conclude that the NRCS T p 0.6 converson s of the correct order and straddles the dstncton between watershed classfcaton. Inspecton of fgure 5 suggests that a moderate curvlnear relaton between T p and exsts ths s partcularly evdent for undeveloped watersheds wth values less than about 2 hours. Graphcal fttng of alternatve -to- T p conversons onto the data n fgure 5 ndcates that the followng conversons are more approprate when the Kerby-Krpch approach s used, T p T p for developed watersheds, and for undeveloped watersheds. The alternatve -to- T p conversons are shown n fgure 6. T p from the regresson analyss from the tradtonal unt hydrograph approach s not ncluded n fgure 6. Inspecton of the fgure suggests some nonlnearty exsts, partcularly for small values of. Based on relatons depcted n fgure 5, the authors conclude that the Kerby-Krpch approach produces estmates of T p consstent wth observed ranfall and runoff. Whereas consderable varablty exsts n predctons of T p, the Kerby-Krpch approach for estmatng (and hence T p ) s reasonable. The Kerby-Krpch approach thus s useful for estmaton for applcable Texas watersheds

23 TIME TO PEAK FROM REGRESSION, IN HOURS EQUAL VALUE LINE Generalzed regon for undeveloped watersheds Generalzed regon for developed watersheds TIME OF CONCENTRATION FROM KERBY-KIRPICH APPROACH, IN HOURS EXPLANATION 0.6 (TIME OF CONCENTRATION) TIME TO PEAK FROM REGRESSION ANALYSIS FROM TRADITIONAL UNIT HYDROGRAPH APPROACH TIME TO PEAK FROM REGRESSION ANALYSIS FROM GUHAS UNIT HYDROGRAPH APPROACH TIME TO PEAK FROM REGRESSION ANALYSIS FROM LINEAR PROGRAMMING UNIT HYDROGRAPH APPROACH TIME TO PEAK FROM REGRESSION ANALYSIS FROM INSTANTANEOUS UNIT HYDROGRAPH APPROACH Fgure 5. Relaton between tme of concentraton and tme to peak

24 TIME TO PEAK FROM REGRESSION, IN HOURS TIME OF CONCENTRATION FROM KERBY-KIRPICH APPROACH, IN HOURS EXPLANATION 0.6 (TIME OF CONCENTRATION) MODELED TIME TO PEAK FOR DEVELOPED WATERSHED MODELED TIME TO PEAK FOR UNDEVELOPED WATERSHED Fgure 6. Relaton between tme of concentraton and tme to peak showng alternatve tme-of-concentraton to tmeto-peak conversons

25 CONCLUSIONS Conclusons concernng tme-parameter estmaton n the context of hydrologc desgn are made. The conclusons are applcable for Texas watersheds wth dranage areas about 0.25 to 150 square mles, man- lengths about 1 to 50 mles, and dmensonless man- slopes about to Whereas other observatons are ncluded n the body of the report, the enumerated conclusons n ths secton are deemed most nformatve for hydrologc desgn practtoners. 1. It s approprate to estmate watershed characterstcs usng a varety of methods. Dfferences between manual- and automatc-based watershed characterstcs are a comparatvely mnor source of uncertanty relatve to other sources nherent n tmeparameter estmaton n partcular, and to hydrologc models ncorporatng tme parameters n general. 2. In general, Krpch-nclusve approaches, and specfcally the Kerby-Krpch approach, are approprate for estmaton. Krpch-nclusve approaches requre a small number of nput parameters, and the parameters needed are straghtforward to estmate. Furthermore, Krpch-nclusve approaches have greater repeatablty than some alternatve approaches such as the NRCS travel-tme method because fewer analyst-specfc nterpretatons are needed. A comparson of Kerby-Krpch estmates wth T p from TxDOT Research Project suggests that Kerby-Krpch estmates are more consstent wth the characterstcs of actual storm hydrographs. Therefore, the Kerby-Krpch approach s preferable for applcable Texas watersheds. 3. The number and senstvty of tme-response characterstcs to nput parameters for the NRCS travel-tme method make the method senstve to decsons made by the analyst.whereas the NRCS travel-tme method s ntutvely appealng because of ts relance on hydraulcs-based estmates of flow velocty, determnaton of the many nput parameters necessary requres consderable judgement. Estmates of nput parameters are heavly dependent on analyst assumptons of hydraulc propertes, such as geometry, that are dffcult to measure and lack repeatablty. 4. The NRCS conventonal -to- T p converson can be slghtly mproved to account for watershed development and addtonal emprcal calbraton avalable as part of TxDOT Research Projects and The NRCS T p 0.6 converson s of the correct order and yelds T p values between those assocated wth undeveloped watersheds and those assocated wth developed watersheds obtaned from other methods. Inspecton of a graph showng the relaton between tme of concentraton and tme to peak suggests that a moderate curvlnear relaton between T p and exsts ths s partcularly evdent for the undeveloped watersheds wth values less than about 2 hours. Vsual fttng of alternatve to T p converson to the graph suggests that the followng conversons are more approprate when the Kerby-Krpch approach s used T p 0.4 for developed watersheds, and T p 0.7 for undeveloped watersheds

26 REFERENCES Aron, G., and Erborge, C.E., 1973, A practcal feasblty study of flood peak abatement n urban areas: Sacramento, Calf., U.S. Army Corps of Engneers. Asquth, W.H., and Roussel, M.C., 2004, Atlas of depth-duraton frequency of precptaton annual maxma for Texas: U.S. Geologcal Survey Water-Resources Investgatons Report , 106 p. Asquth, W.H., Thompson, D.B., Cleveland, T.G., and Fang, X., 2004, Synthess of ranfall and runoff data used for Texas Department of Transportaton Research Projects and : U.S. Geologcal Survey Open-Fle Report , 1,049 p. Brown, J.R., Ulery, R.L., and Parcher, J.W., 2000, Creatng a standardzed watersheds database for the lower Ro Grande/Ro Bravo, Texas: U.S. Geologcal Survey Open-Fle Report , 13 p. Dngman, S.L., 2002, Physcal hydrology (2d ed.): Upper Saddle Rver, N.J., Prentce Hall, 646 p. Fang, Xng., Cleveland, T.G., Garca, C.A., Thompson, D.B., and Malla, R., 2005, Lterature revew on tme parameters for hydrographs: Texas Department of Transportaton Research Report , Lamar Unversty, 82 p. Haktanr, T., and Sezen, N., 1990, Sutablty of two-parameter gamma and three-parameter beta dstrbutons as synthetc unt hydrographs n Anatola: Journal of Hydrologcal Scences, v. 35, no. 2, p Hathaway, G.A., 1945, Desgn of dranage facltes: Amercan Socety of Cvl Engneers Transacton 110, p Kerby, W.S., 1959, Tme of concentraton for overland flow: Cvl Engneerng, v. 29, no. 3, 174 p. Krpch, Z.P., 1940, Tme of concentraton of small agrcultural watersheds: Cvl Engneerng, v. 10, no. 6, 362 p. McCuen, R.H., 2005, Hydrologc analyss and desgn (3d ed.): Upper Saddle Rver, N.J., Pearson Prentce Hall, 814 p. Morgal, J.R., and Lnsley, R.K., 1965, Compute analyss of overland flow: Amercan Socety of Cvl Engneers Journal of the Hydraulcs Dvson, v. 91, no. HY3, p Natural Resources Conservaton Servce, 2004, Natonal Engneerng Handbook, Part 630, chapter 16: accessed July 28, 2004, at hydro-techref-neh-630.html Plgrm, D.H., and Cordery, Ian, 1993, Flood runoff, chap. 9 of Madment, D.R., ed., Handbook of hydrology, New York, McGraw-Hll. Smas, M.J., and Hawkns, R.H., 2002, Lag tme characterstcs n small watersheds n the Unted States n Second Federal Interagency Hydrologc Modelng Conference, Las Vegas, Nevada, July 28-August 1, 2002, Proceedngs: Washngton D.C., Government Prntng Offce, 6 p. Thompson, D.B., Harle, H., Kester, D., McLendon, D., and Sandrana, S.K., 2003, Clmatc adjustments of Natural Resources Conservaton Servce ) runoff curve numbers: Texas Department of Transportaton Research Project Report , Texas Tech Unversty

27 Table 1. U.S. Geologcal Survey streamflow-gagng statons used n the study. [sub., subwatershed; U, undeveloped watershed; IH, Interstate Hghway; D, developed watershed; US, Unted States; SH, State Table Hghway; 1. U.S. FM, Farm Geologcal to Market. Survey Developed streamflow-gagng and undeveloped statons classfcaton used n was the done study Contnued. a qualtatve bass.] Staton no. (fg. 1) Staton name Lattude Longtude North Creek sub. 28A near Jermyn, Texas 33 14'52" 98 19'19" U North Creek near Jacksboro, Texas 33 16'57" 98 17'53" U Sycamore Creek at IH 35W, Fort Worth, Texas 32 39'55" 97 19'16" D Sycamore Creek trbutary above Semnary South Shoppng Center, Fort Worth, Texas 32 41'08" 97 19'44" D Sycamore Creek trbutary at IH 35W, Fort Worth, Texas 32 41'18" 97 19'11" D Dry Branch at Blandn Street, Fort Worth, Texas 32 47'19" 97 18'22" D Dry Branch at Fan Street, Fort Worth, Texas 32 46'34" 97 17'18" D Lttle Fossl Creek at IH 820, Fort Worth, Texas 32 50'22" 97 19'20" D Lttle Fossl Creek at Mesqute Street, Fort Worth, Texas 32 48'33" 97 17'28" D Elm Fork Trnty Rver sub. 6 near Muenster, Texas 33 37'13" 97 24'15" U Lttle Elm Creek sub. 10 near Gunter, Texas 33 24'33" 96 48'41" U Lttle Elm Creek near Aubrey, Texas 33 17'00" 96 53'33" U Joes Creek at Royal Lane, Dallas, Texas 32 53'43" 96 41'36" D Joes Creek at Dallas, Texas 32 51'33" 96 53'00" D Bachman Branch at Dallas, Texas 32 51'37" 96 51'13" D Turtle Creek at Dallas, Texas 32 48'26" 96 48'08" D Coombs Creek at Sylvan Ave, Dallas, Texas 32 46'01" 96 50'07" D Cedar Creek at Bonnevew Road, Dallas, Texas 32 44'50" 96 47'44" D McKamey Creek at Preston Road, Dallas, Texas 32 57'58" 96 48'11" U Rush Branch at Arapaho Road, Dallas, Texas 32 57'45" 96 47'44" D Cottonwood Creek at Forest Lane, Dallas, Texas 32 54'33" 96 45'54" D Floyd Branch at Forest Lane, Dallas, Texas 32 54'33" 96 45'34" D Ash Creek at Hghland Road, Dallas, Texas 32 48'18" 96 43'04" D Elam Creek at Seco Boulevard, Dallas, Texas 32 44'14" 96 41'36" D Fvemle Creek at Kest Boulevard, Dallas, Texas 32 42'19" 96 51'32" D Fvemle Creek at US Hghway 77W, Dallas, Texas 32 41'15" 96 49'22" D Woody Branch at IH 625, Dallas, Texas 32 40'58" 96 49'22" D Newton Creek at IH 635, Dallas, Texas 32 39'19" 96 44'41" D Whtes Branch at IH 625, Dallas, Texas 32 39'26" 96 44'25" D Prare Creek at US Hghway 175, Dallas, Texas 32 42'17" 96 40'11" D Honey Creek sub. 11 near McKnney, Texas 33 18'12" 96 41'22" U Honey Creek sub.12 near McKnney, Texas 33 18'20" 96 40'12" U Duck Creek at Buckngham Road, Garland, Texas 32 55'53" 96 39'55" D South Mesqute Creek at SH 352, Mesqute, Texas 32 46'09" 96 37'18" D South Mesqute Creek at Mercury Road, Mesqute, Texas 32 43'32" 96 34'12" D Pn Oak Creek near Hubbard, Texas 31 48'01" 96 43'02" U Green Creek sub. 1 near Dubln, Texas 32 09'57" 98 20'28" U Cow Bayou sub. 4 near Brucevlle, Texas 31 19'59" 97 16'02" U Lttle Pond Creek near Burlngton, Texas 31 01'35" 96 59'17" U North Elm Creek near Cameron, Texas 30 55'52" 97 01'13" U Burton Creek at Vlla Mara Road, Bryan, Texas 30 38'48" 96 20'57" D Hudson Creek near Bryan, Texas 30 39'38" 96 17'59" U Mukewater Creek sub. 10A near Trckham, Texas 31 39'01" 99 13'30" U Mukewater Creek sub. 9 near Trckham, Texas 31 41'40" 99 12'18" U Mukewater Creek at Trckham, Texas 31 35'24" 99 13'36" U Development classfcaton

28 Table 1. U.S. Geologcal Survey streamflow-gagng statons used n the study Contnued. Staton no. (fg. 1) Staton name Lattude Longtude Deep Creek sub. 3 near Placd,Texas 31 17'25" 99 09'22" U Deep Creek sub. 8 near Mercury, Texas 31 24'08" 99 07'17" U Bull Creek at Loop 360, Austn, Texas 30 22'19" 97 47'04" U Barton Creek at SH 71, Oak Hll, Texas 30 17'46" 97 55'31" U Barton Creek at Loop 360, Austn, Texas 30 14'40" 97 48'07" U West Bouldn Creek at Rversde Drve, Austn, Texas 30 15'49" 97 45'17" D Shoal Creek at Steck Avenue, Austn, Texas 30 21'55" 97 44'11" D Shoal Creek at Northwest Park, Austn, Texas 30 20'50" 97 44'41" D Shoal Creek at Whte Rock Drve, Austn, Texas 30 20'21" 97 44'50" D Shoal Creek at 12th Street, Austn, Texas 30 16'35" 97 45'00" D Waller Creek at 38th Street, Austn, Texas 30 17'49" 97 43'36" D Waller Creek at 23rd Street, Austn, Texas 30 17'08" 97 44'01" D Boggy Creek at US 183, Austn, Texas 30 15'47" 97 40'20" D Walnut Creek at FM 1325, Austn, Texas 30 24'35" 97 42'41" U Walnut Creek at Dessau Road, Austn, Texas 30 22'30" 97 39'37" U Lttle Walnut Creek at Georgan Drve Austn, Texas 30 21'15" 97 41'52" D Lttle Walnut Creek at IH 35, Austn, Texas 30 20'57" 97 41'34" D Lttle Walnut Creek at Manor Road, Austn, Texas 30 18'34" 97 40'04" D Walnut Creek at Webbervlle Road, Austn, Texas 30 16'59" 97 39'17" D Onon Creek near Drftwood, Texas 30 04'59" 98 00'29" U Onon Creek at Buda, Texas 30 05'09" 97 50'52" U Bear Creek below FM 1826, Drftwood, Texas 30 09'19" 97 56'23" U Bear Creek at FM 1626, Manchaca, Texas 30 08'25" 97 50'50" U Lttle Bear Creek at FM 1626, Manchaca, Texas 30 07'31" 97 51'43" U Slaughter Creek at FM 1826, Austn, Texas 30 12'32" 97 54'11" U Slaughter Creek at FM 2304, Austn, Texas 30 09'43" 97 49'55" U Boggy Creek (south) at Crcle S Road, Austn, Texas 30 10'50" 97 46'55" U Wllamson Creek at Oak Hll, Texas 30 14'06" 97 51'36" D Wllamson Creek at Manchaca Road, Austn, Texas 30 13'16" 97 47'36" D Wllamson Creek at Jmmy Clay Road, Austn, Texas 30 11'21" 97 43'56" D Wlbarger Creek near Pflugervlle, Texas 30 27'16" 97 36'02" U Olmos Creek trbutary at FM 1535, Shavano Park, Texas 29 34'35" 98 32'45" D Olmos Creek at Dresden Drve, San Antono, Texas 29 29'56" 98 30'36" D Alazan Creek at St. Cloud Street, San Antono, Texas 29 27'29" 98 32'59" D Harlendale Creek at West Hardng Street, San Antono, Texas 29 21'05" 98 29'32" D Panther Sprngs Creek at FM 2696 near San Antono, Texas 29 37'31" 98 31'06" U Lorence Creek at Thousand Oaks Boulevard, San Antono, Texas 29 35'24" 98 27'47" D West Elm Creek at San Antono, Texas 29 37'23" 98 26'29" U East Elm Creek at San Antono, Texas 29 37'04" 98 25'41" U Salado Creek trbutary at Btters Road, San Antono, Texas 29 31'36" 98 26'25" D Salado Creek trbutary at Bee Street, San Antono, Texas 29 26'38" 98 27'13" D Leon Creek trbutary at FM 1604, San Antono, Texas 29 35'14" 98 37'40" U Helotes Creek at Helotes, Texas 29 34'42" 98 41'29" U Leon Creek trbutary at Kelly Ar Force Base, Texas 29 23'12" 98 36'00" D Calaveras Creek sub. 6 near Elmendorf, Texas 29 22'49" 98 17'33" U Esconddo Creek sub. 1 near Kenedy, Texas 28 46'41" 97 53'41" U Esconddo Creek sub. 11 near Kenedy, Texas 28 51'39" 97 50'39" U Development classfcaton

29 Table 2. Summary of travel-tme and tme-of-concentraton computatons for 92 watersheds n Texas by U.S. Geologcal Survey researchers. [ Table T t, travel tme for a specfed flow component, n hours; NRCS, Natural Resources Conservaton Servce; KWF, Knematc 2. Summary of travel-tme and tme-of-concentraton computatons for 92 watersheds n Texas by U.S. Wave Formula; T, tme of concentraton, n hours, whch equals a sum of flow components from selected methods] Geologcal c Survey researchers Contnued. Staton no. overland travel tme overland (Kerby overland (KWF shallowconcentrated travel-tme travel-tme T Tc c (Kerbytravel- Krpch tme approach) (Krpch (KWF- Krpch approach)