The Effect of Varying Unit Periods on Shape of Unit

THESIS: THE EFFECT OF VARYING UNIT PERIODS ON SHAPE OP UNIT HYDROGRAPHS BY ELUDERIO SALVO, C. E. SUBMITTED FOR THE DEGREE OF MASTER OP ENGINEERING i960 UNIVERSITY OP NEW SOUTH WALES SCHOOL OP CIVIL ENGINEERING BROADWAY, SYDNEY, N, S, W. AUSTRALIA ^^ OF FOREiORO The germ of the idea to investigate the unit storm concept of lUsler and Brater using large watersheds (areas greater than 10 square miles) was stimulated by Associate Profess©r H, R, Vallentins, Officer- in-Charge, I'/ater Research Laboratory, University of New 3©uth vfeles, With the approval and subsequent encouragement and guidance of Professor C, H, Munro, Head, School of Civil Engineering, University of New South Wales, the pjriter made preliminary investigations using data from South Creek Catchment, an experimental watershed maintained by the University* Uppn the writer's return t© the Philippines, hydrol©gic data fr©m the watersheds ©f Belubula River and Tarcutta Creek were forwarded t® him by Mr, G, Whitehouse, Technical Staff Member, Hydrelsgy Section, Scheel of Civil Engineering, U. N, S, W, The results of the investigations and analyses are all embodied in this thesis. It may be said that this thesis has a tendency to over simplifica^- tion. There is a grain of truth in that. But is it not the end of every engineer to simplify the intricacies of mathematics and make the application to engineering pr©blems practical and easy? The theory of the unit hydrograph, first advanced by L, K, Sherman in 1932, is a simplified version of the mathematical treatment by J. A, Folse in his book, "A New Methsd of Estimating Stream Flow upon a New Evaporation Formula," The theory is based on the observed facts that the unit hydrograph ©f a stream has a characteristic shape that ^ ii is not generally modified by the different factors affecting the hydrograph of a stream. In other words, all the variables are integrated and evaluated in the shape of the hydrograph of a stream. The mathematical derivations of unit hydrographs, such as the Collins Method and Solution by Least Squares are excluded from the text. Instead, the simplified method set out by Wisler and Brater in "Hydro- logy" is utilized through out. It is believed that the simplifying assumptions and methods used are within the limits of accuracy and jus- tified by the paucity of data and intrinsic inaccuracies of the funda- mental assumptions of the theory of the unit hydrograph. The writer wishes to express his sincere gratitude to Professor C, H, Munro for his encouragement, interest and guidance; to Associate Professor H, R. Vallentine for directing the writer's attention to this particular phase of research; to f^lr, G, Whitehouse for his unstinted help in data collection and enlightening discussions on the subject; . and to the other members of the Hydrology Section, Messrs, N, Body, F, Bell and F, Stein for their clarifying ideas and views* Furthermore, the writer would thank Professor D, Ilio, College of Engineering, University of the Philippines, for his guidance and super- vision in the preparation of this thesis; Mr, Marcelo Franco, civil engineering student who assisted the writer in the preparation of the graphs and lastly, his ivife, for proof reading the whole text. - Ill - TABLE CF CONTENTS TITLE PAGE 1 1. INTKIDUCTICN 2 2. THE UNIT GRAPH AND THE UNIT HYDRGGRAPH 4 2, 1. Sherman's Original Unit Graph, 2. 2, Sherman's Unit Hydrograph. 3. THE HltDROGRAPH Of A STREAM 8 1. The Runoff Process, 3, 2, Separation of the Hydrograph to Various Components. 3. 3, Factors Affecting the Hydrograph 4. THE THEORY CF THE UNIT HYDROGRAPH 13 4. 1, Assumptions and Practical Substantiation of the Theory 5. THE UNIT STORM CONCEPT 16 5. 1. The First Principle, 5. 2. Period of Rise. 5. 3. The Second Principle. 5, 4, Discussion on the Derivation, 6. WISLER AND BRATER'S FINDINGS 23 6. 1. Peak Percentages of Distribution Graphs, 6, 2, Dis- tribution Graphs From Similar Watersheds. 6, 3.. Conclu- sions of IVisler and Brater. 7. THE UNIT STORM CONCEPT APPLIED TO UiRGE AUSTRALIAN imTERSHEDS 25 7. 1, General Procedure. 7. 2. Belubula River lâtershed, T.-* 7, 3, South Creek Vâtershed. 7. 4. Tarcutta Creek Watershed. 8. GENERAL DISCUSSION OF THE PROCEDURE 31 8, 1, Hydrographs. 8. 2. Isohyetal Maps. 8, 3, Mean Mass Rain- fall Curiae, 8. 4, Durations of Rainfall Excess. 8, 5, End of Rainfall to Peak. 9. SNYDER'S SYNTHETIC UNIT-GRAPH 34 10. APPLICATION OF SNYDER'S EQUATIONS ' 36 - iV - 10, 1, Application to Belubula River Watershed. IG, 2, Appli- tion to South Creek Catchment, 10. 3. Application to Tarcu- tta Creek VJatershed, 11, m\K PEF^CENTAGE/SQUARE MILE/TBIE INTERVAL VS. AREA 41 12, PERIOD OF RISE VS. WATERSHED FACTOR 46 12, 1, Computations for South Creek Catchment 12, 2 Computa- tions for Belubula River Watershed. 12, 3, Computations for Tarcutta Creek Watershed. 12. 4, Results of Correlation, 13, CONCLUSIONS 49 14, SmiMARY 51 APPEr'ÎX A - PROPERTIES OF DERIVED UNIT HYDROGRAPHS 52 APPEFÎX B - DATA TABULATIONS FOR BELUBULA RIVER 57 APPErÎDIX C - DATA TABULATIONS FOR SOUTH CREEK 93 APPEN^DIX D - DATA TABULATIONS FOR TARCUTTA CREEK 121 BIBLICK^RAPHY 138 ILLUSTRATIONS; FIGURE I: UNIT HYDROGRAPH AND UNIT GRAPH 7 FIGURE 2: DISTRIBUTION GRAPH 19 FIGURE A-l.UP TO FIGURE A - 5 APPENDIX A FIGURE B-1 UP TO FIGURE B - 10 APPENDIX B FIGURE C-1 UP TO FIGURE C ~ 9 APPENDIX C FIGUIÊ D - 1 UP TO FIGURE D - 6 APPENDIX D - V - 2 - INTROOUCTION In 1932, Leroy K, Sherman first presented the theory of the unit graph^, Ke postulated the tm basic propositions of the unit graph theory, namely; 1, That all hydrographs of a particular drainage basin resulting from rainfalls of given duration, regardless of intensity will have the same length of base, 2. The ordinates of the corresponding hydrographs due to uniform rainfalls of the same length but of different intensities will be in the same proportion as the volumes of surface runoff. Since then, various refinements to the knowledge of this powerful hydrologic tool have been presented by several authors among them are Bernard^, Horner and Flynt^^, Wisler and Brater^, Snyderl2, Collinsl^, Langbein^^, Clark and Johnstone^^ - to name but a few. As a consequence of the works of these authors, the unit hydrograph has been given a slightly different meaning than the unit graph. Nowhere in the book "Slementsrof Applied Hydrology" by Johnstone and Cross^ is mentioned the word unit hydrograph while sHsler and Brater^ in "Hydrology" referred to the unit graph only ivhen quoting the works of Sherman. The U, S. Bureau of Heclamation makes a distinction between a unit hydrograph and a unit graph. Furthermore, Wisler and i/SNGINEERING f^m. R^clORp, 1932, p, 501 Streamflow from Rainfall by Unit Graph Mdthod by Leroy K, Sherman, 2/mmEmS of applied hydrology by Johnstone and Cross, 3/i-IYDROLOGY by Wisler and Brater, 5/rRAre\CTI0^j3 OF THE AMERICAN SOCIETY OF CIVIL E^l^mmS^ 1935, 100 p.- 347, An Approach to Determinate Stream Flow by Merrill M, Bernard, - 3 o Brater^ introduced the concept of unit storms ivhich further muddled the theoretically unsound assumptions of the theory of the unit hydrograph. To an amateur hydrologist, this seemingly different concepts con- fuse the theory. An attempt therefore, is made to clarify these different schools of thought. mj CIVIL Kmimmim, Sept. 1939, p. 559. Runoff Distribution Graph From Precipitation Occurring in More Than One Unit of Time by VI, T, Collins^ 12/ XeAWSACTIONS OF THE GEOPHYSICAL UNION. 1938, Port I, pp. 447 - 454. Synthetic Unit Graph by Franklin F. Sjmder. W XRA^SACTIO^S OF HIE AMERICAN SOCIETY OF CIVIL S^^GINggT^S. 1936, Vol, 101 pp. 140 - 206, Relation Between Rainfall and Runoff From Small Urban Areas by Horner and F. L. Flynt. 11/ TRArvÂCTICNS OF Hm AKEKICAN GSOPHYSIGAL UNION, 1940, pp. 620 -627. Some Channel Storage and Unit Hydrograph Studies by ^^ B, Langbein. 3/ HYD^?CLCK^Y by Wisler and Brater, Chapter II p. 31 and Chapter VIII p« 309. ' - 4 - 2. THE UNIT GRAPH AF^ UNIT HYORCGBAPH The vjriter firmly believes that the unit graph and unit hydrograph are substantially the same. The basic assumptions are the same. If there is any difference at all, it is in the method of derivation. The lAjriter also believes that the root of all these seeming disparity of views is Sherman, the originator of the theory. Why this is so can be gleaned from his works, t 2.1. SHSEFAW^S O'ÎGIfÂL UNIT GR/^PH Shermanl in his original paper stated, "From the known hydrograph the *unit graph* must be determined representing 1 inch of runoff from a 24-hour rainfall". He stated further, "For the same drainage area, hov;ever, there is a definite total flood period corresponding to a given rainfall, and all one day rainfalls, regardless of intensity, will give the same length of base of the hydrograph." From the preceding statements of Sherman, a unit graph must in- variably have a volume of runoff equal to 1 inch. If not, the hydrograph must be converted to a unit graph. Also, that rainfalls having the same durations (one day in his case) regardless of intensity must have the same unit graph. This original paper by Sherman was subjected to criticism by several eminent hydraulic engineers^, Kany found the unit graph theory sound after application to American streams, 1/ Er-iGIrEERIKG "El^ RECC^Ô, 1932 p, 501, Strearaflow from Sainfall by Unit Graph Method by Leroy K, Sherman, i/ EFGIK'SS^TFx^ mm R£COI''D.

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