Volume 34 Number 506 Derivation of hydrographs for small Article 1 watersheds from measurable physical characteristics June 1962 Derivation of hydrographs for small watersheds from measurable physical characteristics Don M. Gray Iowa State University of Science & Technology Follow this and additional works at: http://lib.dr.iastate.edu/researchbulletin Part of the Agriculture Commons, and the Bioresource and Agricultural Engineering Commons Recommended Citation Gray, Don M. (1962) "Derivation of hydrographs for small watersheds from measurable physical characteristics," Research Bulletin (Iowa Agriculture and Home Economics Experiment Station): Vol. 34 : No. 506 , Article 1. Available at: http://lib.dr.iastate.edu/researchbulletin/vol34/iss506/1 This Article is brought to you for free and open access by the Iowa Agricultural and Home Economics Experiment Station Publications at Iowa State University Digital Repository. It has been accepted for inclusion in Research Bulletin (Iowa Agriculture and Home Economics Experiment Station) by an authorized editor of Iowa State University Digital Repository. For more information, please contact [email protected]. Derivation of Hydrographs for Small Watersheds From Measurable Physical Characteristics by Don M. Gray Department of Agricultural Engineering AGRICULTURAL AND HOME ECONOMICS EXPERIMENT STATION IOWA STATE UNIVERSITY of Science and Technology RESEARCH BULLETIN 506 JUNE 1962 AMES, IOWA SYNOPSIS This study was concerned with the development slope of a representative sample of first-order of n method for synthesizing the unit hydrograph streams taken from the same watershed, S1' for small watersheds from topographic character­ Hydrologic Characteristics istics. The topographic and hydrologic character­ istics from 42 watersheds located in Illinois, Iowa, The rainfall and runoff characteristics from a Uissoul'i, Nebraska, Ohio and Wisconsin were in­ number of unit storms occurring over each water­ vcs~igated. These watersheds varied in size from shed were analyzed. The results showed that the 0_23 to 33.00 square miles. period of rise, PH' could be used in place of .lag time, t r" as a time parameter to relate t~e sahent features of rainfall and runoff. For practIcal work, Topographic Characteristics PIl=tr.. • • t 'b For each watershed, a representatIve dIS 1'1 u- Five watershed characteristics were measured tion graph was developed and modified to a on e::cch basin: drainage-area size, A; length of the dimensionless form based on the use of PRJ as main stream, L; length to the center of area, Lea; the time parameter. Recent hy.drologic investiga­ slope of the main stream, Sc; and mean land slope, tions have shown that the umt hydro graph can Sr,. An initial attempt to relate these factors with be described by a two-parameter equation which hydl"Ograph properties by employing the prin­ is identical in form to the equation describing the ciples of dimensional analysis proved unsuccess­ two-parameter statistical gamma ?istriJ;>ution. ful. As a result, a preliminary analysis of the top­ This distribution was fitted to each dImensIOnless ographic data was undertaken to ascertain the O"raph and estimators of its parameters, q and y', reason for this failure. ;'ere 'obtained by machine calculation. It was The study indicated that the three length fac­ found that, in most cases, the two-paramete.r gam­ tors-A. L and Lea-for the watersheds were ma distribution could be employed to descrIbe the highly correlated and could not be used as inde­ dimensionless graph; however, additional work is pendent terms. In addition. the results showed required in evaluating the goodness of fit in terms that the watersheds adopted a relatively consist­ of hydrologic acceptance. ent shape, intermediary between ovoid and pear­ A set of relationships was derived to enable shap3d. For all practical purposes, in the water­ evaluation of the three variables, PR, q and y'. shedB studied, L"a=0.50L. With these values known, the dimensionless Tests indicated that the variables, Land Se, are graph, distribution gral~h or unit hydrograI!h of a related if consideration is given to the effect of given area can be descrIbed. A successful lInkage regional influence. between hydro graph properties and watershed An empirical relation was found between the characteristics was obtained by relating the stor­ mean land slope of a watershed, Sr" and the mean agefactorPR/y', with the watershed factor L/VS,.. 514 CONTENTS Introduction _____________________________ ._____________________ :__________________________________________________ 517 Review of literature ____________ .______________________ ._____________________ .________________________________ 518 Surface runoff phenomena _________________________ , ____________________________________________ 518 The hydrograph _______________ .________________________________________________________________________ 518 Topographic factors and the hydrograph ______________________________________________ 519 Unit hydrograph___________________________________________________________ .____________________________ 520 Distribution graph _______________________________________________________ .____________________________ 522 Synthetic unit hydrographs __ ._________________________________________________________________ 522 Investigations, results and discussion ___________________________________________________ .. _______ 524 Basic data _________________________________ . ________________________________________________________________ 524 Topographic characteristics ____________________________________________________________________ 524 Preliminary hydrograph analysis __________________________________________________________ 526 Fitting the two-parameter gamma distribution to the dimensionless graph __________________________________________________________________ 529 Selection of the time parameter____________________________________________________________ 531 Relation between parameters, q and y' __________________________________________________ 532 Estimation of the storage factor, PRI/, from basin characteristics ________________________________________________________________________ 533 Relation of period of rise, P R , and parameter, /---_______________________________ 537 Application of results ___________________________ . ___________________ -- _______________________________ 539 Summary__________________________________________________________________________________________________ .___________ 539 Selected bibliography _______________ .__ . _______________________ ---------------------- _____________ .__________ 540 Appendix A: Glossary of terms and symbols _______ .... __________________________ . __________ 5011 Appendix B: Equational forms of the unit hydrograph ______ ._. ____________________ .542 Appendix C: Topographic and hydrologic data-__________________ ...... _____ . _____________ 544 Appendix D: Distribution graphs and empirical graphs _________ . ___________ . __ . _____ 547 Appendix E: Dimensionless graphs __________________________________ ._____________ -- __________ . ___ 559 Appendix F: Application of results._ ... _._ ...... _...... __ .. ___ . ___ ._. _____ .. ______ . ________________ 570 515 Derivation of Hydrographs for Small Watersheds From Measurable Physical Characteristics1 by Don M. Gray' Wisler and Brater (59, p. 1) define hydrology vestigations on watersherls of intermediate size as "the science that deals with the processes gov­ is relatively small. erning the depletion and replenishment of the For design purposes engineers require a knowl­ waters of the land areas of the earth." Thus, edge of the time-rate distribution of surface-runoff hydrology is concerned with the transportation of volumes. This distribution is depicted graphically the water through the air, over the ground sur­ by the hydro graph as a continuous plot of the in­ face and through the strata of the earth. stantaneous discharge rate with time. The design The manner in which water passes to a stream of small hydraulic structures-such as road cul­ channel governs the terminology of the flow. The verts and chutes, water-conveyance channels, de­ accepted components of stream-flow are interflow, tention structures, weirs, spillways, drop inlets ground water, channel precipitation and surface and others, as recommended for use for conveyance, runoff. Of primary importance in this study is control or conservation of surface runoff by the surface runoff, or water which passes to a stream Bureau of Public Roads and the Soil Conservation channel by traveling over the soil surface. Its Service-depends largely on the discharge-time origin may be water arising from melting snow or relationships resulting from intense rains occur­ ice, or rainfall which falls at rates in excess of the ring on basins of an area of only a few square soil infiltration capacity. miles. The majority of work completed concerning the In many areas of the country for which rainfall phenomena of surface runoff has been in two dis­ records are available, there is a lack of stream­ tinct area groups: (a) those hydrologic studies ap­ gaging stations in operation. For these ungaged plied to large. basins varying in size from 100 to areas, the surface-runoff hydrograph for a given several thousand square miles and (b) those stud­ storm may be approximated by two techniques: ies applied to small areas of a hundredth-acre to a 1. Use of a recorded hydrograph from a like few acres. Work on the larger areas