Hydrology by Suramanya - PDF

THIRD EDITION  About the Author Dr K Subramanya is a retired Professor of Civil Engineering at the Indian Institute of Technology, Kanpur. He obtained his bachelor’s degree in Civil Engineering from Mysore University and a master’s degree from the Univer- sity of Madras. Fu...

THIRD EDITION  About the Author Dr K Subramanya is a retired Professor of Civil Engineering at the Indian Institute of Technology, Kanpur. He obtained his bachelor’s degree in Civil Engineering from Mysore University and a master’s degree from the Univer- sity of Madras. Further, he obtained another master’s degree and Ph. D from the University of Alberta, Edmonton, Canada. He has taught at IIT Kanpur for over 30 years and has extensive teaching experience in the area of Hydrology and Water Resources Engineering. During his tenure at IIT Kanpur, Prof. Subramanya worked as Visiting Faculty at the Asian Institute of Tech- nology, Bangkok, for a short while. He has authored several successful books for McGraw-Hill Education (India). Besides the current book, his other books include Flow in Open Channels (2nd Ed., TMH, 1997), and 1000 Solved Problems in Fluid Mechanics (TMH, 2005). Dr Subramanya has published over eighty technical papers in national and international journals. He has also presented numerous techni- cal papers in conferences. He is a Fellow of the Institution of Engineers (India); Fellow of Indian Society for Hydraulics; Member of Indian Society of Technical Education and Member of Indian Water Resources Association. Currently, he resides in Bangalore and is active as a practicing consultant in Water Resources Engineering. He can be contacted at [email protected].  THIRD EDITION K Subramanya Former Professor of Civil Engineering Indian Institute of Technology Kanpur Tata McGraw-Hill Publishing Company Limited NEW DELHI McGraw-Hill Offices New Delhi New York St Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Published by the Tata McGraw-Hill Publishing Company Limited, 7 West Patel Nagar, New Delhi 110 008. Copyright © 2008, by Tata McGraw-Hill Publishing Company Limited. 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General Manager—Production: B L Dogra Information contained in this work has been obtained by Tata McGraw-Hill, from sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw- Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at Text-o-Graphics, B1/56 Arawali Apartment, Sector 34, Noida 201 301 and printed at Rashtriya Printers, 1/11955-7D, (M-135), Panchsheel Garden, Naveen Shahdara, Delhi 110 032 Cover Printer: Rashtriya Printers RQLCRRZXRCBLB Dedicated to My Mother  Contents Preface to the Third Edition xiii Preface to the First Edition xv 1. Introduction 1 1.1 Introduction 1 1.2 Hydrologic Cycle 1 1.3 Water Budget Equation 3 1.4 World Water Balance 6 1.5 History of Hydrology 8 1.6 Applications in Engineering 9 1.7 Sources of Data 10 References 11 Revision Questions 11 Problems 11 Objective Questions 12 2. Precipitation 13 2.1 Introduction 13 2.2 Forms of Precipitation 13 2.3 Weather Systems for Precipitation 14 2.4 Characteristics of Precipitation in India 16 2.5 Measurement of Precipitation 20 2.6 Raingauge Network 24 2.7 Preparation of Data 26 2.8 Presentation of Rainfall Data 30 2.9 Mean Precipitation Over an Area 33 2.10 Depth-Area-Duration Relationships 37 2.11 Frequency of Point Rainfall 39 2.12 Maximum Intensity-Duration-Frequency Relationship 43 2.13 Probable Maximum Precipitation (PMP) 48 2.14 Rainfall Data in India 50 References 51 Revision Questions 51 Problems 51 Objective Questions 56 3. Abstractions from Precipitation 59 3.1 Introduction 59 3.2 Evaporation Process 59 LEEE Contents 3.3 Evaporimeters 60 3.4 Empirical Evaporation Equations 63 3.5 Analytical Methods of Evaporation Estimation 64 3.6 Reservoir Evaporation and Methods for its Reduction 66 3.7 Transpiration 68 3.8 Evapotranspiration 69 3.9 Measurement of Evapotranspiration 70 3.10 Evapotranspiration Equations 70 3.11 Potential Evapotranspiration Over India 76 3.12 Actual Evapotranspiration (AET) 76 3.13 Interception 79 3.14 Depression Storage 79 3.15 Infiltration 80 3.16 Infiltration Capacity 81 3.17 Measurement of Infiltration 82 3.18 Modeling Infiltration Capacity 84 3.19 Classification of Infiltration Capacities 91 3.20 Infiltration Indices 92 References 95 Revision Questions 96 Problems 96 Objective Questions 99 4. Streamflow Measurement 101 4.1 Introduction 101 4.2 Measurement of Stage 102 4.3 Measurement of Velocity 105 4.4 Area-Velocity Method 109 4.5 Dilution Technique of Streamflow Measurement 113 4.6 Electromagnetic Method 115 4.7 Ultrasonic Method 116 4.8 Indirect Methods 117 4.9 Stage-Discharge Relationship 122 4.10 Extrapolation of Rating Curve 129 4.11 Hydrometry Stations 131 References 133 Revision Questions 133 Problems 134 Objective Questions 137 5. Runoff 139 5.1 Introduction 139 5.2 Hydrograph 141 5.3 Runoff Characteristics of Streams 142 5.4 Runoff Volume 143 5.5 Flow-Duration Curve 163  Contents EN 5.6 Flow-Mass Curve 166 5.7 Sequent Peak Algorithm 171 5.8 Droughts 175 5.9 Surface Water Resources of India 182 References 187 Revision Questions 187 Problems 188 Objective Questions 192 6. Hydrographs 195 6.1 Introduction 195 6.2 Factors Affecting Flood Hydrograph 196 6.3 Components of a Hydrograph 198 6.4 Base Flow Separation 202 6.5 Effective Rainfall (ER) 203 6.6 Unit Hydrograph 205 6.7 Derivation of Unit Hydrographs 212 6.8 Unit Hydrographs of Different Durations 216 6.9 Use and Limitations of Unit Hydrograph 223 6.10 Duration of the Unit Hydrograph 223 6.11 Distribution Graph 224 6.12 Synthetic Unit Hydrograph 225 6.13 Instantaneous Unit Hydrograph (IUH) 232 References 235 Revision Questions 235 Problems 237 Objective Questions 242 7. Floods 245 7.1 Introduction 245 7.2 Rational Method 245 7.3 Empirical Formulae 251 7.4 Unit Hydrograph Method 253 7.5 Flood Frequency Studies 253 7.6 Gumbel’s Method 255 7.7 Log-Pearson Type III Distribution 263 7.8 Partial Duration Series 266 7.9 Regional Flood Frequency Analysis 266 7.10 Data for Frequency Studies 266 7.11 Design Flood 267 7.12 Design Storm 269 7.13 Risk, Reliability and Safety Factor 271 References 273 Revision Questions 273 Problems 274 Objective Questions 278 N Contents 8. Flood Routing 280 8.1 Introduction 280 8.2 Basic Equations 281 8.3 Hydrologic Storage Routing (Level Pool Routing) 281 8.4 Attenuation 290 8.5 Hydrologic Channel Routing 291 8.6 Hydraulic Method of Flood Routing 296 8.7 Routing in Conceptual Hydrograph Development 297 8.8 Clark’s Method for IUH 298 8.9 Nash’s Conceptual Model 301 8.10 Flood Control 309 8.11 Flood Control in India 313 References 314 Revision Questions 314 Problems 315 Objective Questions 318 9. Groundwater 320 9.1 Introduction 320 9.2 Forms of Subsurface Water 320 9.3 Aquifer Properties 323 9.4 Geologic Formations as Aquifers 330 9.5 Compressibility of Aquifers 330 9.6 Equation of Motion 333 9.7 Wells 343 9.8 Steady Flow into a Well 344 9.9 Open Wells 349 9.10 Unsteady Flow in a Confined Aquifer 351 9.11 Well Loss 356 9.12 Specific Capacity 357 9.13 Recharge 357 9.14 Groundwater Resource 361 9.15 Groundwater Monitoring Network in India 365 References 366 Revision Questions 366 Problems 367 Objective Questions 371 10. Erosion and Reservoir Sedimentation 374 10.1 Introduction 374 10.2 Erosion Processes 374 10.3 Estimation of Sheet Erosion 376 10.4 Channel Erosion 379 10.5 Movement of Sediment from Watersheds 381 10.6 Sediment Yield from Watersheds 382  Contents NE 10.7 Trap Efficiency 386 10.8 Density of Sediment Deposits 388 10.9 Distribution of Sediment in the Reservoir 391 10.10 Life of a Reservoir 400 10.11 Reservoir Sedimentation Control 403 10.12 Erosion and Reservoir Sedimentation Problems in India 405 References 407 Revision Questions 409 Problems 409 Objective Questions 412 Appendix A: Additonal References, Some Useful Websites, Abbreviations 413 Appendix B: Conversion Factors 416 Answers to Objective Questions 417 Index 428  Contents NE 10.7 Trap Efficiency 386 10.8 Density of Sediment Deposits 388 10.9 Distribution of Sediment in the Reservoir 391 10.10 Life of a Reservoir 400 10.11 Reservoir Sedimentation Control 403 10.12 Erosion and Reservoir Sedimentation Problems in India 405 References 407 Revision Questions 409 Problems 409 Objective Questions 412 Appendix A: Additonal References, Some Useful Websites, Abbreviations 413 Appendix B: Conversion Factors 416 Answers to Objective Questions 417 Index 428  Preface to the Third Edition This is the third edition of the book, the first edition of which was published in 1984. While the second edition of the book is receiving very good response from students and teachers alike, a need was felt to update the book to accommodate changes in technology and practice. Towards this, the book was reviewed thor- oughly with a view to enhance its usefulness as a textbook to meet the needs of the present day, as well as that of the near future, in the area of Engineering Hydrology. Through careful pruning of the second edition and appropriate additions of new material, this edition attempts to make the book useful, catering to a wider range of interests by covering additional subject areas. While the book is essen- tially an undergraduate textbook in the subject area of Engineering Hydrology, in its present form it also serves as a useful reference book for post-graduate stu- dents and field engineers in the domain of Hydrology. The book also meets the need of students taking AMIE examinations. Candidates taking competitive ex- aminations like Central Engineering Services examinations and Central Civil Services examinations will find this book very useful in their preparations re- lated to the topic of hydrology. The book has a unique feature of being India centric; the applications, practices, examples and information about water re- sources are all aimed at familiarizing the reader to the present-day Indian water resources scene. As such, students and professionals in the related areas of Wa- tershed development, Water Harvesting, Minor Irrigation, Forestry and Hydro- Geology would find this book a useful source material relating to technical is- sues dealing with water resources in general and hydrology in particular. NGOs working in the water sector would find this book useful in their training activi- ties. The use of mathematics, statistics and probability concepts are kept at the minimal level necessary for understanding the subject matter and emphasis is placed on engineering applications of hydrology. The significant additions in the present edition are the following: l The SCS–CN method of estimating Runoff volume l A new chapter entitled Erosion and Reservoir Sedimentation l Thoroughly revised and rewritten section on infiltration with descriptions of various infiltration models l Revised and enlarged section on Yield of River Basins to cover current Indian practice l A new section dealing with SCS–dimensionless unit hydrograph and SCS –Triangular unit hydrograph l Improvements to the chapter on Groundwater by including sections on dug wells and recuperation tests of tube wells and dug wells NEL Preface to the Third Edition l A new section dealing with various aspects of recharge of groundwater l A section on water harvesting l Improved coverage of droughts l Revised information on water resources of India l Additional worked examples, revision questions, problems and objec- tive questions The contents of the book cover essentially the entire subject areas normally covered in an undergraduate course in Engineering Hydrology. Each of the chap- ters covers not only the basic topics in detail but also includes some advanced topics at an introductory level. The book is designed as a textbook with clear explanations, illustrations and sufficient worked examples. As hydrology is best learned by solving problems, a vast number of them, amounting to more than 200 problems, with answers are provided in the book. Additionally, the sets of Re- vision questions and Objective questions (with answers) provided at the end of each chapter help not only in the comprehension of the subject matter but also in preparing well for competitive examinations. Most of the problems can be solved by use of a spreadsheet (such as MS Excel) and this in fact can be made use of in designing interesting teaching and tutorial sessions. The Online Learning Center of this book can be accessed at http://www.mhhe.com/subramanya/eh3e. The site contains a Solution Manual and PowerPoint Slides for Instructors; and Sample Question Papers with Solutions and Sample Case studies for students. I have received a large number of feed- back, both formally and informally, towards the improvement of the book. The following reviewers of the typescript have provided valuable inputs for the con- tents of this edition. Mohammed Jamil Department of Civil Engineering, Z H College of Engineering and Technology, Aligarh Muslim University, Aligarh Molly Kutty M V Department of Civil Engineering, Crescent Engineering College, Chennai Thiruvenkatasamy K Department of Civil Engineering, Bharath University, Chennai Jothi Prakash V Department of Civil Engineering, Indian Institute of Technology, Mumbai M R Y Putty National Institute of Engineering, Mysore I would also like to express my sincere thanks to all those who have directly or indirectly helped me in bringing out this revised edition. Comments and sugges- tions for further improvement of the book would be greatly appreciated. I can be contacted at the following e-mail address: [email protected]. K SUBRAMANYA April 2008  Preface to the First Edition Water is vital to life and development in all parts of the world. In Third World countries where the agricultural sector plays a key role in their economic growth, the management of water resources is an item of high priority in their develop- mental activities. The basic inputs in the evaluation of water resources are from hydrological parameters and the subject of hydrology forms the core in the evalu- ation and development of water resources. In the civil engineering curriculum, this subject occupies an important position. During my long teaching experience, I have felt a strong need for a textbook oriented to the Indian environment and written in a simple and lucid style. The present book is a response to the same. This book is intended to serve as a text for a first course in engineering hydrology at the undergraduate level in the civil engineering discipline. Students specializing in various aspects of water-resources engineering, such as water-power engineering and agricultural engineering will find this book useful. This book also serves as a source of useful information to professional engineers working in the area of water-resources evaluation and development. Engineering hydrology encompasses a wide spectrum of topics and a book like the present one meant for the first course must necessarily maintain a bal- ance in the blend of topics. The subject matter has been developed in a logical and coherent manner and covers the prescribed syllabi of various Indian univer- sities. The mathematical part is kept to the minimum and emphasis is placed on the applicability to field situations relevant to Indian conditions. SI units are used throughout the book. Designed essentially for a one-semester course, the material in the book is presented in nine chapters. The hydrologic cycle and world-water balance are covered in Chap. 1. Aspects of precipitation, essentially rainfall, are dealt in suf- ficient detail in Chap. 2. Hydrologic abstractions including evapotranspiration and infiltration arc presented in Chap. 3. Streamflow-measurement techniques and assessment of surface-flow yield of a catchment form the subject matter of Chaps. 4 and 5 respectively. The characteristics of flood hydrographs and the unit hydrograph theory together with an introduction to instantaneous unit hydrograph are covered in sufficient detail with numerous worked examples in Chap. 6. Floods, a topic of considerable importance, constitute the subject matter of Chap. 7 and 8. While in Chap. 7 the flood-peak estimation and frequency studies are described in detail, Chap. 8 deals with the aspects of flood routing, flood control and forecasting. Basic information on the hydrological aspects of groundwater has been covered in Chap. 9. NLE Preface to the First Edition Numerous worked examples, a set of problems and a set of objective type multiple-choice questions are provided at the end of each chapter to enable the student to gain good comprehension of the subject. Questions and problems in- cluded in the book are largely original and are designed to enhance the capabili- ties of comprehension, analysis and application of the student. I am grateful to: UNESCO for permission to reproduce several figures from their publication, Natural Resources of Humid Tropical Asia—Natural Resources Research XII, ** UNESCO, 1974; the Director-General of Meteorology, India Meteorological Department, Government of India for permission to reproduce several maps; M/s Leupold and Stevens, Inc., Beaverton, Oregon, USA, for pho- tographs of hydrometeorological instruments; M/s Alsthom-Atlantique, Neyrtec, Grenoble France, for photographs of several Neyrtec Instruments; M/s Lawrence and Mayo. (India) Pvt. Ltd., New Delhi for the photograph of a current meter. Thanks are due to Professor KVGK Gokhale for his valuable suggestions and to Sri Suresh Kumar for his help in the production of the manuscript. I wish to thank my student friends who helped in this endeavour in many ways. The finan- cial support received under the Quality Improvement Programme (QIP), Gov- ernment of India, through the Indian Institute of Technology, Kanpur, for the preparation of the manuscript is gratefully acknowledged.  Abbreviations AET Actual Evapotranspiration AIAridity Index AMC Antecedent Moisture Condition CBIP Central Board of Irrigation and Power (India) CGWB Central Groundwater Board (India) CN Curve Number CWC Central Water Commission (India) DAD Maximum Depth-Area-Duration DRH Direct Runoff Hydrograph DVC Damodar Valley Corporation ERH Effective Rainfall Hyetograph FAO Food and Agriculture Organisation FEM Finite Element Method FRL Full Reservoir Level GOI Government of India IMD India Meteorological Department IUH Instantaneous Unit Hydrograph KWM Kentucky Watershed Model MAI Moisture Availability Index MCM Million Cubic Meter MDDL Minimum Drawdown Level MOC Method of Characteristics MSL Mean Sea Level MUSLE Modified Universal Soil Loss Equation NBSS&LUP National Bureau of Soil Survey and Land Use Planning NCIWRD National Commission for Integrated Water Resources Development (1999) NRSA National Remote Sensing Agency PET Potential Evapotranspiration PI Palmer Index PMF Probable Maximum Flood PMP Probable Maximum Precipitation RBA Rashtriya Barh Ayog (National Flood Commission) RTWH Roof Top Water Harvesting SCS US Soil Conservation Service SDR Sediment Delivery Ratio SPF Standard Project Flood NLEEE Abbreviations SPS Standard Project Storm SWM Stanford Watershed Model TMC Thousand Million Cubic Feet UH Unit Hydrograph UNESCO United Nations Economic, Social and Cultural Organisa- tion USLE Universal Soil Loss Equation WMO World Meteorological Organisation  Chapter 1 INTRODUCTION 1.1 INTRODUCTION Hydrology means the science of water. It is the science that deals with the occurrence, circulation and distribution of water of the earth and earth’s atmosphere. As a branch of earth science, it is concerned with the water in streams and lakes, rainfall and snow- fall, snow and ice on the land and water occurring below the earth’s surface in the pores of the soil and rocks. In a general sense, hydrology is a very broad subject of an inter-disciplinary nature drawing support from allied sciences, such as meteorology, geology, statistics, chemistry, physics and fluid mechanics. Hydrology is basically an applied science. To further emphasise the degree of ap- plicability, the subject is sometimes classified as 1. Scientific hydrology—the study which is concerned chiefly with academic as- pects. 2. Engineering or applied hydrology—a study concerned with engineering ap- plications. In a general sense engineering hydrology deals with (i) estimation of water resources, (ii) the study of processes such as precipitation, runoff, evapotranspiration and their interaction and (iii) the study of problems such as floods and droughts, and strategies to combat them. This book is an elementary treatment of engineering hydrology with descriptions that aid in a qualitative appreciation and techniques which enable a quantitative evalu- ation of the hydrologic processes that are of importance to a civil engineer. 1.2 HYDROLOGIC CYCLE Water occurs on the earth in all its three states, viz. liquid, solid and gaseous, and in various degrees of motion. Evaporation of water from water bodies such as oceans and lakes, formation and movement of clouds, rain and snowfall, streamflow and groundwater movement are some examples of the dynamic aspects of water. The vari- ous aspects of water related to the earth can be explained in terms of a cycle known as the hydrologic cycle. Figure 1.1 is a schematic representation of the hydrologic cycle. A convenient starting point to describe the cycle is in the oceans. Water in the oceans evaporate due to the heat energy provided by solar radiation. The water vapour moves upwards and forms clouds. While much of the clouds condense and fall back to the oceans as rain, a part of the clouds is driven to the land areas by winds. There they condense and precipitate onto the land mass as rain, snow, hail, sleet, etc. A part of the precipitation  Engineering Hydrology Fig. 1.1 The Hydrologic Cycle may evaporate back to the atmosphere even while falling. Another part may be inter- cepted by vegetation, structures and other such surface modifications from which it may be either evaporated back to atmosphere or move down to the ground surface. A portion of the water that reaches the ground enters the earth’s surface through infiltration, enhance the moisture content of the soil and reach the groundwater body. Vegetation sends a portion of the water from under the ground surface back to the atmosphere through the process of transpiration. The precipitation reaching the ground surface after meeting the needs of infiltration and evaporation moves down the natural slope over the surface and through a network of gullies, streams and rivers to reach the ocean. The groundwater may come to the surface through springs and other outlets after spending a considerably longer time than the surface flow. The portion of the precipitation which by a variety of paths above and below the surface of the earth reaches the stream channel is called runoff. Once it enters a stream channel, runoff becomes stream flow. The sequence of events as above is a simplistic picture of a very complex cycle that has been taking place since the formation of the earth. It is seen that the hydrologic cycle is a very vast and complicated cycle in which there are a large number of paths of varying time scales. Further, it is a continuous recirculating cycle in the sense that there is neither a beginning nor an end or a pause. Each path of the hydrologic cycle involves one or more of the following aspects: (i) transportation of water, (ii) tempo- rary storage and (iii) change of state. For example, (a) the process of rainfall has the  Introduction ! change of state and transportation and (b) the groundwater path has storage and trans- portation aspects. The main components of the hydrologic cycle can be broadly classified as trans- portation ( flow) components and storage components as below: Transportation Storage components components Precipitation Storage on the land surface (Depression storage, Ponds, Lakes, Reservoirs, etc) Evaporation Soil moisture storage Transpiration Groundwater storage Infiltration Runoff Schematically the interdepen- dency of the transportation compo- nents can be represented as in Fig. 1.2. The quantities of water going through various individual paths of the hydrological cycle in a given system can be described by the continuity principle known as water budget equation or hydro- logic equation. It is important to note that the total water resources of the earth Fig. 1.2 Transportation Components of the are constant and the sun is the Hydrologic Cycle source of energy for the hydrologic cycle. A recognition of the various processes such as evaporation, precipitation and groundwater flow helps one to study the science of hydrology in a systematic way. Also, one realises that man can interfere with virtually any part of the hydrologic cycle, e.g. through artificial rain, evaporation suppression, change of vegetal cover and land use, extraction of groundwater, etc. Interference at one stage can cause seri- ous repercussions at some other stage of the cycle. The hydrological cycle has important influences in a variety of fields including agriculture, forestry, geography, economics, sociology and political scene. Engineer- ing applications of the knowledge of the hydrologic cycle, and hence of the subjects of hydrology, are found in the design and operation of projects dealing with water sup- ply, irrigation and drainage, water power, flood control, navigation, coastal works, salinity control and recreational uses of water. 1.3 WATER BUDGET EQUATION Catchment Area The area of land draining into a stream or a water course at a given location is known as catchment area. It is also called as drainage area or drainage basin. In USA, it is known as watershed. A catchment area is separated form its neighbouring areas by a  " Engineering Hydrology ridge called divide in USA and wa- tershed in UK (Fig. 1.3). The areal extent of the catchment is obtained by tracing the ridge on a topographic map to delineate the catchment and meas- uring the area by a planimeter. It is obvious that for a river while mention- ing the catchment area the station to which it pertains (Fig. 1.3) must also be mentioned. It is normal to assume the groundwater divide to coincide with the surface divide. Thus, the Fig. 1.3 Schematic Sketch of Catchment catchment area affords a logical and of River A at Station M convenient unit to study various as- pects relating to the hydrology and water resources of a region. Further it is probably the singlemost important drainage characteristic used in hydro- logical analysis and design. Water Budget Equation For a given problem area, say a catchment, in an interval of time Dt, the continuity equation for water in its various phases is written as Mass inflow – mass outflow = change in mass storage If the density of the inflow, outflow and storage volumes are the same Vi - V0 = DS (1.1) where Vi = inflow volume of water into the problem area during the time period, V0 = outflow volume of water from the problem area during the time period, and DS = change in the storage of the water volume over and under the given area during the given period. In applying this continuity equation [Eq. (1.1)] to the paths of the hydro- logic cycle involving change of state, the volumes considered are the equivalent vol- umes of water at a reference temperature. In hydrologic calculations, the volumes are often expressed as average depths over the catchment area. Thus, for example, if the annual stream flow from a 10 km2 catchment is 107 m3, it corresponds to a depth of æ 107 ö çè 10 ´ 106 ÷ø = 1 m = 100 cm. Rainfall, evaporation and often runoff volumes are expressed in units of depth over the catchment. While realizing that all the terms in a hydrological water budget may not be known to the same degree of accuracy, an expression for the water budget of a catchment for a time interval Dt is written as P – R – G – E – T = DS (1.2-a) In this P = precipitation, R = surface runoff, G = net groundwater flow out of the catchment, E = evaporation, T = transpiration and DS = change in storage. The storage S consists of three components as S = Ss + Ssm + Sg where Ss = surface water storage Ssm = water in storage as soil moisture and Sg = water in storage as groundwater.  Introduction # Thus in Eq. (1.2-a) DS = DSs + DSsm + DSg All terms in Eq. (1.2-a) have the dimensions of volume. Note that all these terms can be expressed as depth over the catchment area (e.g. in centimetres), and in fact this is a very common unit. In terms of rainfall–runoff relationship, Eq. (1.2-a) can be represented as R=P–L (1.2-b) where L = Losses = water not available to runoff due to infiltration (causing addition to soil moisture and groundwater storage), evaporation, transpiration and surface stor- age. Details of various components of the water budget equation are discussed in subsequent chapters. Note that in Eqs (1.2-a and b) the net import of water into the catchment, from sources outside the catchment, by action of man is assumed to be zero. EXAMPLE 1.1 A lake had a water surface elevation of 103.200 m above datum at the beginning of a certain month. In that month the lake received an average inflow of 6.0 m3/s from surface runoff sources. In the same period the outflow from the lake had an average value of 6.5 m3/s. Further, in that month, the lake received a rainfall of 145 mm and the evaporation from the lake surface was estimated as 6.10 cm. Write the water budget equation for the lake and calculate the water surface elevation of the lake at the end of the month. The average lake surface area can be taken as 5000 ha. Assume that there is no contribution to or from the groundwater storage. SOLUTION: In a time interval D t the water budget for the lake can be written as Input volume – output volume = change in storage of the lake ( I Dt + PA) – ( Q Dt + EA) = DS where I = average rate of inflow of water into the lake, Q = average rate of outflow from the lake, P = precipitation, E = evaporation, A = average surface area of the lake and D S = change in storage volume of the lake. Here D t = 1 month = 30 ´ 24 ´ 60 ´ 60 = 2.592 ´ 106 s = 2.592 Ms In one month: Inflow volume = I Dt = 6.0 ´ 2.592 = 15.552 M m3 Outflow volume = Q Dt = 6.5 ´ 2.592 = 16.848 M m3 14.5 ´ 5000 ´ 100 ´ 100 Input due to precipitation = PA = M m3 = 7.25 M m3 100 ´ 10 6 6.10 5000 ´ 100 ´ 100 Outflow due to evaporation = EA = ´ = 3.05 M m3 100 106 Hence DS = 15.552 + 7.25 – 16.848 – 3.05 = 2.904 M m3 DS 2.904 ´ 106 Change in elevation Dz = = = 0.058 m A 5000 ´ 100 ´ 100 New water surface elevation at the end of the month = 103.200 + 0.058 = 103.258 m above the datum. EXAMPLE 1.2 A small catchment of area 150 ha received a rainfall of 10.5 cm in 90 minutes due to a storm. At the outlet of the catchment, the stream draining the catchment was dry before the storm and experienced a runoff lasting for 10 hours with an average discharge of 1.5 m3/s. The stream was again dry after the runoff event. (a) What is the amount of water which was not available to runoff due to combined effect of infiltration, evaporation and transpiration? What is the ratio of runoff to precipitation?  $ Engineering Hydrology SOLUTION: The water budget equation for the catchment in a time D t is R=P–L (1.2-b) where L = Losses = water not available to runoff due to infiltration (causing addition to soil moisture and groundwater storage), evaporation, transpiration and surface storage. In the present case Dt = duration of the runoff = 10 hours. Note that the rainfall occurred in the first 90 minutes and the rest 8.5 hours the precipi- tation was zero. (a) P = Input due to precipitation in 10 hours = 150 ´ 100 ´ 100 ´ (10.5/100) = 157,500 m3 R = runoff volume = outflow volume at the catchment outlet in 10 hours = 1.5 ´ 10 ´ 60 ´ 60 = 54,000 m3 Hence losses L = 157,500 – 54,000 = 103,500 m3 (b) Runoff/rainfall = 54,000/157,500 = 0.343 (This ratio is known as runoff coefficient and is discussed in Chapter 5) 1.4 WORLD WATER BALANCE The total quantity of water in the world is estimated to be about 1386 million cubic kilometres (M km3). About 96.5% of this water is contained in the oceans as saline water. Some of the water on the land amounting to about 1% of the total water is also saline. Thus only about 35.0 M km3 of fresh water is available. Out of this about 10.6 M km3 is both liquid and fresh and the remaining 24.4 M km3 is contained in frozen state as ice in the polar regions and on mountain tops and glaciers. An estimated distribution of water on the earth is given in Table 1.1. Table 1.1 Estimated World Water Quantities Item Area Volume Percent Percent (M km2) (M km3) total water fresh water 1. Oceans 361.3 1338.0 96.5 — 2. Groundwater (a) fresh 134.8 10.530 0.76 30.1 (b) saline 134.8 12.870 0.93 — 3. Soil moisture 82.0 0.0165 0.0012 0.05 4. Polar ice 16.0 24.0235 1.7 68.6 5. Other ice and snow 0.3 0.3406 0.025 1.0 6. Lakes (a) fresh 1.2 0.0910 0.007 0.26 (b) saline 0.8 0.0854 0.006 — 7. Marshes 2.7 0.01147 0.0008 0.03 8. Rivers 148.8 0.00212 0.0002 0.006 9. Biological water 510.0 0.00112 0.0001 0.003 10. Atmospheric water 510.0 0.01290 0.001 0.04 Total: (a) All kinds of water 510.0 1386.0 100.0 (b) Fresh water 148.8 35.0 2.5 100.0 Table from WORLD WATER BALANCE AND WATER RESOURCES OF THE EARTH, © UNESCO, 1975. Reproduced by the permission of UNESCO.  Introduction % The global annual water balance is shown in Table 1.2. Table 1.2 Global Annual Water Balance Item Ocean Land 2 1. Area (M km ) 361.30 148.8 2. Precipitation (km3/year) 458,000 119,000 (mm/year) 1270 800 3. Evaporation (km3/year) 505,000 72,000 (mm/year) 1400 484 4. Runoff to ocean (i) Rivers (km3/year) 44,700 (ii) Groundwater (km3/year) 2,200 Total Runoff (km3/year) 47,000 (mm/year) 316 Table from WORLD WATER BALANCE AND WATER RESOURCES OF THE EARTH, © UNESCO, 1975. Reproduced by the permission of UNESCO. It is seen from Table 1.2 that the annual evaporation from the world’s oceans and inland areas are 0.505 and 0.072 M km3 respectively. Thus, over the oceans about 9% more water evaporates than that falls back as precipitation. Correspondingly, there will be excess precipitation over evaporation on the land mass. The differential, which is estimated to be about 0.047 M km3 is the runoff from land mass to oceans and groundwater outflow to oceans. It is interesting to know that less than 4% of this total river flow is used for irrigation and the rest flows down to sea. These estimates are only approximate and the results from different studies vary; the chief cause being the difficulty in obtaining adequate and reliable data on a global scale. The volume in various phases of the hydrologic cycle (Table 1.1) as also the rate of flow in that phase (Table 1.2) do vary considerably. The average duration of a particle of water to pass through a phase of the hydrologic cycle is known as the residence time of that phase. It could be calculated by dividing the volume of water in the phase by the average flow rate in that phase. For example, by assuming that all the surface runoff to the oceans comes from the rivers, From Table 1.1, the volume of water in the rivers of the world = 0.00212 M km3 From Table 1.2, the average flow rate of water in global rivers = 44700 km3/year Hence residence time of global rivers, Tr = 2120/44700 = 0.0474 year = 17.3 days. Similarly, the residence time for other phases of the hydrological cycle can be calculated (Prob. 1.6). It will be found that the value of Tr varies from phase to phase. In a general sense the shorter the residence time the greater is the difficulty in predict- ing the behaviour of that phase of the hydrologic cycle. Annual water balance studies of the sub-areas of the world indicate interesting facts. The water balance of the continental land mass is shown in Table 1.3(a). It is interesting to see from this table that Africa, in spite of its equatorial forest zones, is  & Engineering Hydrology the driest continent in the world with only 20% of the precipitation going as runoff. On the other hand, North America and Europe emerge as continents with highest runoff. Extending this type of analysis to a smaller land mass, viz. the Indian subcontinent, the long term average runoff for India is found to be 46%. Table 1.3(a) Water Balance of Continents2 mm/year Continent Area Precipitation Total Runoff as % Evaporation (M km2) runoff of precipitation Africa 30.3 686 139 20 547 Asia 45.0 726 293 40 433 Australia 8.7 736 226 30 510 Europe 9.8 734 319 43 415 N. America 20.7 670 287 43 383 S. America 17.8 1648 583 35 1065 Water balance studies on the oceans indicate that there is considerable transfer of water between the oceans and the evaporation and precipitation values vary from one ocean to another (Table 1.3(b)). Table 1.3(b) Water Balance of Oceans2 mm/year Ocean Area Precipitation Inflow from Evaporation Water (M km2) adjacent exchange with continents other oceans Atlantic 107 780 200 1040 –60 Arctic 12 240 230 120 350 Indian 75 1010 70 1380 –300 Pacific 167 1210 60 1140 130 Each year the rivers of the world discharge about 44,700 km3 of water into the oceans. This amounts to an annual average flow of 1.417 Mm3/s. The world’s largest river, the Amazon, has an annual average discharge of 200,000 m3/s, i.e. one-seventh of the world’s annual average value. India’s largest river, the Brahmaputra, and the second largest, the Ganga, flow into the Bay of Bengal with a mean annual average discharges of 16,200 m3/s and 15,600 m3/s respectively. 1.5 HISTORY OF HYDROLOGY Water is the prime requirement for the existence of life and thus it has been man’s endeavour from time immemorial to utilise the available water resources. History has instances of civilizations that flourished with the availability of dependable water sup- plies and then collapsed when the water supply failed. Numerous references exist in Vedic literature to groundwater availability and its utility. During 3000 BC groundwater development through wells was known to the people of the Indus Valley civilizations as revealed by archaeological excavations at Mohenjodaro. Quotations in ancient Hindu scriptures indicate the existence of the knowledge of the hydrologic cycle even as far back as the Vedic period. The first description of the raingauge and its use is contained  Introduction ' in the Arthashastra by Chanakya (300 BC). Varahamihira’s (AD 505–587) Brihatsamhita contains descriptions of the raingauge, wind vane and prediction pro- cedures for rainfall. Egyptians knew the importance of the stage measurement of riv- ers and records of the stages of the Nile dating back to 1800 BC have been located. The knowledge of the hydrologic cycle came to be known to Europe much later, around AD 1500. Chow1 classifies the history of hydrology into eight periods as: 1. Period of speculation—prior to AD 1400 2. Period of observation—1400–1600 3. Period of measurement—1600–1700 4. Period of experimentation—1700–1800 5. Period of modernization—1800–1900 6. Period of empiricism—1900–1930 7. Period of rationalization—1930–1950 8. Period of theorization—1950–to–date Most of the present-day science of hydrology has been developed since 1930, thus giving hydrology the status of a young science. The worldwide activities in water- resources development since the last few decades by both developed and developing countries aided by rapid advances in instrumentation for data acquisition and in the computer facilities for data analysis have contributed towards the rapid growth rate of this young science. 1.6 APPLICATIONS IN ENGINEERING Hydrology finds its greatest application in the design and operation of water-resources engineering projects, such as those for (i) irrigation, (ii) water supply, (iii) flood con- trol, (iv) water power, and (v) navigation. In all these projects hydrological investiga- tions for the proper assessment of the following factors are necessary: 1. The capacity of storage structures such as reservoirs. 2. The magnitude of flood flows to enable safe disposal of the excess flow. 3. The minimum flow and quantity of flow available at various seasons. 4. The interaction of the flood wave and hydraulic structures, such as levees, reser- voirs, barrages and bridges. The hydrological study of a project should necessarily precede structural and other detailed design studies. It involves the collection of relevant data and analysis of the data by applying the principles and theories of hydrology to seek solutions to practical problems. Many important projects in the past have failed due to improper assessment of the hydrological factors. Some typical failures of hydraulic structures are: (i) overtopping and consequent failure of an earthen dam due to an inadequate spill- way capacity, (ii) failure of bridges and culverts due to excess flood flow and (iii) inability of a large reservoir to fill up with water due to overestimation of the stream flow. Such failure, often called hydrologic failures underscore the uncertainty aspect inherent in hydrological studies.   Engineering Hydrology Various phases of the hydrological cycle, such as rainfall, runoff, evaporation and transpiration are all nonuniformly distributed both in time and space. Further, practi- cally all hydrologic phenomena are complex and at the present level of knowledge, they can at best be interpreted with the aid of probability concepts. Hydrological events are treated as random processes and the historical data relating to the event are ana- lysed by statistical methods to obtain information on probabilities of occurrence of various events. The probability analysis of hydrologic data is an important component of present-day hydrological studies and enables the engineer to take suitable design decisions consistent with economic and other criteria to be taken in a given project. 1.7 SOURCES OF DATA Depending upon the problem at hand, a hydrologist would require data relating to the various relevant phases of the hydrological cycle playing on the problem catchment. The data normally required in the studies are: l Weather records—temperature, humidity and wind velocity l Precipitation data l Stream flow records l Evaporation and evapotranspiration data l Infiltration characteristics of the study area l Soils of the area l Land use and land cover l Groundwater characteristics l Physical and geological characteristics of the area l Water quality data In India, hydro-meteorological data are collected by the India Meteorological De- partment (IMD) and by some state government agencies. The Central Water Commis- sion (CWC) monitors flow in major rivers of the country. Stream flow data of various rivers and streams are usually available from the State Water Resources/Irrigation Department. Groundwater data will normally be available with Central Groundwater Board (CGWB) and state Government groundwater development agencies. Data re- lating evapotranspiration and infiltration characteristics of soils will be available with State Government organizations such as Department of Agriculture, Department of Watershed development and Irrigation department. The physical features of the study area have to be obtained from a study of topographical maps available with the Survey of India. The information relating to geological characteristics of the basin under study will be available with the Geological Survey of India and the state Geology Directo- rate. Information relating to soils at an area are available from relevant maps of National Bureau of Soil Survey and Land Use Planning (NBSS&LUP), 1996. Further additional or specific data can be obtained from the state Agriculture Department and the state Watershed Development Department. Land use and land cover data would generally be available from state Remote sensing Agencies. Specific details will have to be derived through interpretation of multi-spectral multi-season satellite images available from National Remote Sensing Agency (NRSA) of Government of India. Central and State Pollution Control Boards, CWC and CGWB collect water quality data.  Introduction  REFERENCES 1. Chow, V.T., (Ed), Handbook of Applied Hydrology, McGraw-Hill, New York, NY, 1964. 2. Schendel, V., “The world’s water resources and water balance”, Natural Resources and Development, Vol. 1, 1975, Inst. for Sci. Coop, Hannover, Germany, pp. 8–14. 3. UNESCO, “World Water Balance and Water Resources of the Earth”, Studies and Reports in Hydrology, 25, UNESCO, Paris, France, 1978. 4. Van der Leeden, Water Resources of the World, Water Information Center, Port Wash- ington, N.Y., USA, 1975. REVISION QUESTIONS 1.1 Describe the Hydrologic cycle. Explain briefly the man’s interference in various parts of this cycle. 1.2 Discuss the hydrological water budget with the aid of examples. 1.3 What are the significant features of global water balance studies? 1.4 List the major activities in which hydrological studies are important. 1.5 Describe briefly the sources of hydrological data in India. PROBLEMS 1.1 Two and half centimetres of rain per day over an area of 200 km2 is equivalent to average rate of input of how many cubic metres per second of water to that area? 1.2 A catchment area of 140 km2 received 120 cm of rainfall in a year. At the outlet of the catchment the flow in the stream draining the catchment was found to have an average rate of 2.0 m3/s for 3 months, 3.0 m3/s for 6 months and 5.0 m3/s for 3 months. (i) What is the runoff coefficient of the catchment? (ii) If the afforestation of the catchment re- duces the runoff coefficient to 0.50, what is the increase in the abstraction from precipi- tation due to infiltration, evaporation and transpiration, for the same annual rainfall of 120 cm? 1.3 Estimate the constant rate of withdrawal from a 1375 ha reservoir in a month of 30 days during which the reservoir level dropped by 0.75 m in spite of an average inflow into the reservoir of 0.5 Mm3/day. During the month the average seepage loss from the reservoir was 2.5 cm, total precipitation on the reservoir was 18.5 cm and the total evaporation was 9.5 cm. 1.4 A river reach had a flood wave passing through it. At a given instant the storage of water in the reach was estimated as 15.5 ha.m. What would be the storage in the reach after an interval of 3 hours if the average inflow and outflow during the time period are 14.2 m3/ s and 10.6 m3/s respectively? 1.5 A catchment has four sub-areas. The annual precipitation and evaporation from each of the sub-areas are given below. Assume that there is no change in the groundwater storage on an annual basis and calcu- late for the whole catchment the values of annual average (i) precipitation, and (ii) evapo- ration. What are the annual runoff coefficients for the sub-areas and for the total catch- ment taken as a whole? Sub-area Area Annual precipitation Annual evaporation Mm2 mm mm A 10.7 1030 530 B 3.0 830 438 C 8.2 900 430 D 17.0 1300 600  Engineering Hydrology 1.6 Estimate the residence time of (a) Global atmospheric moisture. (b) Global groundwater by assuming that only the fresh groundwater runs off to the oceans. (c) Ocean water. OBJECTIVE QUESTIONS 1.1 The percentage of earth covered by oceans is about (a) 31% (b) 51% (c) 71% (d) 97% 1.2 The percentage of total quantity of water in the world that is saline is about (a) 71% (b) 33% (c) 67% (d) 97% 1.3 The percentage of total quantity of fresh water in the world available in the liquid form is about (a) 30% (b) 70% (c) 11% (d) 51% 1.4 If the average annual rainfall and evaporation over land masses and oceans of the earth are considered it would be found that (a) over the land mass the annual evaporation is the same as the annual precipitation (b) about 9% more water evaporates from the oceans than what falls back on them as precipitation (c) over the ocean about 19% more rain falls than what is evaporated (d) over the oceans about 19% more water evaporates than what falls back on them as precipitation. 1.5 Considering the ratio of annual precipitation to runoff = r0 for all the continents on the earth, (a) Asia has the largest value of the ratio r0. (b) Europe has the smallest value of r0. (c) Africa has the smallest value of r0. (d) Australia has the smallest value of r0. 1.6 In the hydrological cycle the average residence time of water in the global (a) atmospheric moisture is larger than that in the global rivers (b) oceans is smaller than that of the global groundwater (c) rivers is larger than that of the global groundwater (d) oceans is larger than that of the global groundwater. 1.7 A watershed has an area of 300 ha. Due to a 10 cm rainfall event over the watershed a stream flow is generated and at the outlet of the watershed it lasts for 10 hours. Assum- ing a runoff/rainfall ratio of 0.20 for this event, the average stream flow rate at the outlet in this period of 10 hours is (a) 1.33 m3/s (b) 16.7 m3/s (c) 100 m3/minute (d) 60,000 m3/h 1.8 Rainfall of intensity of 20 mm/h occurred over a watershed of area 100 ha for a duration of 6 h. measured direct runoff volume in the stream draining the watershed was found to be 30,000 m3. The precipitation not available to runoff in this case is (a) 9 cm (b) 3 cm (c) 17.5 mm (d) 5 mm 1.9 A catchment of area 120 km2 has three distinct zones as below: Zone Area (km2) Annual runoff (cm) A 61 52 B 39 42 C 20 32 The annual runoff from the catchment, is (a) 126.0 cm (b) 42.0 cm (c) 45.4 cm (d) 47.3 cm  Chapter 2 PRECIPITATION 2.1 INTRODUCTION The term precipitation denotes all forms of water that reach the earth from the atmos- phere. The usual forms are rainfall, snowfall, hail, frost and dew. Of all these, only the first two contribute significant amounts of water. Rainfall being the predominant form of precipitation causing stream flow, especially the flood flow in a majority of rivers in India, unless otherwise stated the term rainfall is used in this book synonymously with precipitation. The magnitude of precipitation varies with time and space. Differ- ences in the magnitude of rainfall in various parts of a country at a given time and variations of rainfall at a place in various seasons of the year are obvious and need no elaboration. It is this variation that is responsible for many hydrological problems, such as floods and droughts. The study of precipitation forms a major portion of the subject of hydrometeorology. In this chapter, a brief introduction is given to familiar- ize the engineer with important aspects of rainfall, and, in particular, with the collec- tion and analysis of rainfall data. For precipitation to form: (i) the atmosphere must have moisture, (ii) there must be sufficient nuclei present to aid condensation, (iii) weather conditions must be good for condensation of water vapour to take place, and (iv) the products of condensation must reach the earth. Under proper weather conditions, the water vapour condenses over nuclei to form tiny water droplets of sizes less than 0.1 mm in diameter. The nuclei are usually salt particles or products of combustion and are normally available in plenty. Wind speed facilitates the movement of clouds while its turbulence retains the water droplets in suspension. Water droplets in a cloud are somewhat similar to the particles in a colloidal suspension. Precipitation results when water droplets come together and coalesce to form larger drops that can drop down. A considerable part of this precipitation gets evaporated back to the atmosphere. The net precipitation at a place and its form depend upon a number of meteorological factors, such as the weather elements like wind, temperature, humidity and pressure in the volume region enclos- ing the clouds and the ground surface at the given place. 2.2 FORMS OF PRECIPITATION Some of the common forms of precipitation are: rain, snow, drizzle, glaze, sleet and hail. Rain It is the principal form of precipitation in India. The term rainfall is used to describe precipitations in the form of water drops of sizes larger than 0.5 mm. The maximum size of a raindrop is about 6 mm. Any drop larger in size than this tends to  " Engineering Hydrology break up into drops of smaller sizes during its fall from the clouds. On the basis of its intensity, rainfall is classified as: Type Intensity 1. Light rain trace to 2.5 mm/h 2. Moderate rain 2.5 mm/h to 7.5 mm/h 3. Heavy rain > 7.5 mm/h Snow Snow is another important form of precipitation. Snow consists of ice crys- tals which usually combine to form flakes. When fresh, snow has an initial density varying from 0.06 to 0.15 g/cm3 and it is usual to assume an average density of 0.1 g/ cm3. In India, snow occurs only in the Himalayan regions. Drizzle A fine sprinkle of numerous water droplets of size less than 0.5 mm and intensity less than 1 mm/h is known as drizzle. In this the drops are so small that they appear to float in the air. Glaze When rain or drizzle comes in contact with cold ground at around 0º C, the water drops freeze to form an ice coating called glaze or freezing rain. Sleet It is frozen raindrops of transparent grains which form when rain falls through air at subfreezing temperature. In Britain, sleet denotes precipitation of snow and rain simultaneously. Hail It is a showery precipitation in the form of irregular pellets or lumps of ice of size more than 8 mm. Hails occur in violent thunderstorms in which vertical currents are very strong. 2.3 WEATHER SYSTEMS FOR PRECIPITATION For the formation of clouds and subsequent precipitation, it is necessary that the moist air masses cool to form condensation. This is normally accomplished by adiabatic cooling of moist air through a process of being lifted to higher altitudes. Some of the terms and processes connected with the weather systems associated with precipitation are given below. Front A front is the interface between two distinct air masses. Under certain fa- vourable conditions when a warm air mass and cold air mass meet, the warmer air mass is lifted over the colder one with the formation of a front. The ascending warmer air cools adiabatically with the consequent formation of clouds and precipitation. Cyclone A cyclone is a large low pressure region with circular wind motion. Two types of cyclones are recognised: tropical cyclones and extratropical cyclones. Tropical cyclone: A tropical cyclone, also called cyclone in India, hurricane in USA and typhoon in South-East Asia, is a wind system with an intensely strong de- pression with MSL pressures sometimes below 915 mbars The normal areal extent of a cyclone is about 100–200 km in diameter. The isobars are closely spaced and the winds are anticlockwise in the northern hemisphere. The centre of the storm, called the eye, which may extend to about 10–50 km in diameter, will be relatively quiet. However, right outside the eye, very strong winds/reaching to as much as 200 kmph  Precipitation # exist. The wind speed gradually decreases towards the outer edge. The pressure also increases outwards (Fig. 2.1). The rainfall will normally be heavy in the entire area occupied by the cyclone. Fig. 2.1 Schematic Section of a Tropical Cyclone During summer months, tropical cyclones originate in the open ocean at around 5– 10° latitude and move at speeds of about 10–30 kmph to higher latitudes in an irregu- lar path. They derive their energy from the latent heat of condensation of ocean water vapour and increase in size as they move on oceans. When they move on land the source of energy is cut off and the cyclone dissipates its energy very fast. Hence, the intensity of the storm decreases rapidly. Tropical cyclones cause heavy damage to life and property on their land path and intense rainfall and heavy floods in streams are its usual consequences. Tropical cyclones give moderate to excessive precipitation over very large areas, of the order of 103 km2, for several days. Extratropical Cyclone: These are cyclones formed in locations outside the tropical zone. Associated with a frontal system, they possess a strong counter-clockwise wind circulation in the northern hemisphere. The magnitude of precipitation and wind velocities are relatively lower than those of a tropical cyclone. However, the duration of precipitation is usually longer and the areal extent also is larger. Anticyclones These are regions of high pressure, usually of large areal extent. The weather is usually calm at the centre. Anticyclones cause clockwise wind circula- tions in the northern hemisphere. Winds are of moderate speed, and at the outer edges, cloudy and precipitation conditions exist. Convective Precipitation In this type of precipitation a packet of air which is warmer than the surrounding air due to localised heating rises because of its lesser density. Air from cooler surroundings flows to take up its place thus setting up a con- vective cell. The warm air continues to rise, undergoes cooling and results in precipi- tation. Depending upon the moisture, thermal and other conditions light showers to thunderstorms can be expected in convective precipitation. Usually the areal extent of such rains is small, being limited to a diameter of about 10 km. Orographic Precipitation The moist air masses may get lifted-up to higher altitudes due to the presence of mountain barriers and consequently undergo cooling,  $ Engineering Hydrology condensation and precipitation. Such a precipitation is known as Orographic precipi- tation. Thus in mountain ranges, the windward slopes have heavy precipitation and the leeward slopes light rainfall. 2.4 CHARACTERISTICS OF PRECIPITATION IN INDIA From the point of view of climate the Indian subcontinent can be considered to have two major seasons and two transitional periods as: l South-west monsoon (June–September) l Transition-I, post-monsoon (October–November) l Winter season (December–February) l Transition-II, Summer, (March–May) The chief precipitation characteristics of these seasons are given below. South-West Monsoon (June–September) The south-west monsoon (popularly known as monsoon) is the principal rainy season of India when over 75% of the annual rainfall is received over a major portion of the country. Excepting the south-eastern part of the peninsula and Jammu and Kashmir, for the rest of the country the south-west monsoon is the principal source of rain with July as the month which has maximum rain. The monsoon originates in the Indian ocean and heralds its appearance in the southern part of Kerala by the end of May. The onset of monsoon is accompanied by high south-westerly winds at speeds of 30–70 kmph and low-pressure regions at the advancing edge. The monsoon winds advance across the country in two branches: (i) the Arabian sea branch, and (ii) the Bay of Bengal branch. The former sets in at the extreme southern part of Kerala and the latter at Assam, almost simultaneously in the first week of June. The Bay branch first covers the north-eastern regions of the country and turns westwards to advance into Bihar and UP. The Arabian sea branch moves northwards over Karnataka, Maharashtra and Gujarat. Both the branches reach Delhi around the same time by about the fourth week of June. A low-pressure region known as monsoon trough is formed between the two branches. The trough extends from the Bay of Bengal to Rajasthan and the precipitation pattern over the country is generally determined by its position. The monsoon winds increase from June to July and begin to weaken in September. The withdrawal of the monsoon, marked by a substantial rainfall activity starts in September in the northern part of the country. The onset and withdrawal of the monsoon at various parts of the country are shown in Fig. 2.2(a) and Fig. 2.2(b). The monsoon is not a period of continuous rainfall. The weather is generally cloudy with frequent spells of rainfall. Heavy rainfall activity in various parts of the country owing to the passage of low pressure regions is common. Depressions formed in the Bay of Bengal at a frequency of 2–3 per month move along the trough causing exces- sive precipitation of about 100–200 mm per day. Breaks of about a week in which the rainfall activity is the least is another feature of the monsoon. The south-west monsoon rainfall over the country is indicated in Fig. 2.3. As seen from this figure, the heavy rainfall areas are Assam and the north-eastern region with 200–400 cm, west coast and western ghats with 200–300 cm, West Bengal with 120–160 cm, UP, Haryana and the Punjab with 100–120 cm. The long term average monsoon rainfall over the coun- try is estimated as 95.0 cm.  Precipitation % (a) (b) Fig. 2.2 (a) Normal Dates of Onset of Monsoon, (b) Normal Dates of With- drawal of Monsoon (Reproduced from Natural Resources of Humid Tropical Asia—Natural Resources Research, XII. © UNESCO, 1974, with permission of UNESCO) The territorial waters of India extend into the sea to a distance of 200 nautical miles measured from the appro- priate baseline Responsibility for the correctness of the internal details on the map rests with the publisher.  & Engineering Hydrology Fig. 2.3 Southwest Monsoon Rainfall (cm) over India and Neighbourhood (Reproduced with permission from India Meteorological Department) Based upon Survey of India map with the permission of the Surveyor General of India © Government of India Copyright 1984 The territorial waters of India extend into the sea to a distance of 200 nautical miles measured from the appropriate baseline Responsibility for the correctness of the internal details on the map rests with the publisher. Post-Monsoon (October–November) As the south-west monsoon retreats, low-pressure areas form in the Bay of Bengal and a north-easterly flow of air that picks up moisture in the Bay of Bengal is formed. This air mass strikes the east coast of the southern peninsula (Tamil Nadu) and causes rainfall. Also, in this period, especially in November, severe tropical cyclones form in the Bay of Bengal and the Arabian sea. The cyclones formed in the Bay of Bengal are about twice as many as in the Arabian sea. These cyclones strike the coastal areas and cause intense rainfall and heavy damage to life and property. Winter Season (December–February) By about mid-December, disturbances of extra tropical origin travel eastwards across Afghanistan and Pakistan. Known as western disturbances, they cause moderate to  Precipitation ' heavy rain and snowfall (about 25 cm) in the Himalayas, and, Jammu and Kashmir. Some light rainfall also occurs in the northern plains. Low-pressure areas in the Bay of Bengal formed in these months cause 10–12 cm of rainfall in the southern parts of Tamil Nadu. Summer (Pre-monsoon) (March-May) There is very little rainfall in India in this season. Convective cells cause some thun- derstorms mainly in Kerala, West Bengal and Assam. Some cyclone activity, domi- nantly on the east coast, also occurs. Annual Rainfall The annual rainfall over the country is shown in Fig. 2.4. Considerable areal variation exists for the annual rainfall in India with high rainfall of the magnitude of 200 cm in Fig. 2.4 Annual Rainfall (cm) over India and Neighbourhood (Reproduced from Natural Resources of Humid Tropical Asia—Natural Resources Research, XII. © UNESCO, 1974, with permission of UNESCO) Based upon Survey of India map with the permission of the Surveyor General of India © Government of India Copyright 1984 The territorial waters of India extend into the sea to a distance of 200 nautical miles measured from the appropriate baseline Responsibility for the correctness of the internal details on the map rests with the publisher.   Engineering Hydrology Assam and north-eastern parts and the western ghats, and scanty rainfall in eastern Rajasthan and parts of Gujarat, Maharashtra and Karnataka. The average annual rain- fall for the entire country is estimated as 117 cm. It is well-known that there is considerable variation of annual rainfall in time at a place. The coefficient of variation, 100 ´ standard deviation Cv = mean of the annual rainfall varies between 15 and 70, from place to place with an average value of about 30. Variability is least in regions of high rainfall and largest in regions of scanty rainfall. Gujarat, Haryana, Punjab and Rajasthan have large variability of rainfall. Some of the interesting statistics relating to the variability of the seasonal and an- nual rainfall of India are as follows: l A few heavy spells of rain contribute nearly 90% of total rainfall. l While the average annual rainfall of the country is 117 cm, average annual rain- fall varies from 10 cm in the western desert to 1100 cm in the North East region. l More than 50% rain occurs within 15 days and less than 100 hours in a year. l More than 80% of seasonal rainfall is produced in 10–20% rain events each lasting 1–3 days. 2.5 MEASUREMENT OF PRECIPITATION A. Rainfall Precipitation is expressed in terms of the depth to which rainfall water would stand on an area if all the rain were collected on it. Thus 1 cm of rainfall over a catchment area of l km2 represents a volume of water equal to 104 m3. In the case of snowfall, an equivalent depth of water is used as the depth of precipitation. The precipitation is collected and measured in a raingauge. Terms such as pluviometer, ombrometer and hyetometer are also sometimes used to designate a raingauge. A raingauge essentially consists of a cylindrical-vessel assembly kept in the open to collect rain. The rainfall catch of the raingauge is affected by its exposure condi- tions. To enable the catch of raingauge to accurately represent the rainfall in the area surrounding the raingauge standard settings are adopted. For siting a raingauge the following considerations are important: l The ground must be level and in the open and the instrument must present a horizontal catch surface. l The gauge must be set as near the ground as possible to reduce wind effects but it must be sufficiently high to prevent splashing, flooding, etc. l The instrument must be surrounded by an open fenced area of at least 5.5 m ´ 5.5 m. No object should be nearer to the instrument than 30 m or twice the height of the obstruction. Raingauges can be broadly classified into two categories as (i) nonrecording raingauges and (ii) recording gauges. Nonrecording Gauges The nonrecording gauge extensively used in India is the Symons’ gauge. It essentially consists of a circular collecting area of 12.7 cm (5.0 inch) diameter connected to a  Precipitation ! Mass Curve of Rainfall The mass curve of rainfall is a plot of the accumulated precipitation against time, plotted in chronological order. Records of float type and weighing bucket type gauges are of this form. A typical mass curve of rainfall at a station during a storm is shown in Fig. 2.9. Mass curves of rainfall are very useful in extracting the information on the duration and magnitude of a storm. Also, intensities at various time intervals in a storm can be obtained by the slope of the curve. For nonrecording raingauges, mass curves are prepared from a knowledge of the approximate beginning and end of a storm and by using the mass curves of adjacent recording gauge stations as a guide. Fig. 2.9 Mass Curve of Rainfall Hyetograph A hyetograph is a plot of the intensity of rainfall against the time interval. The hyetograph is derived from the mass curve and is usually represented as a bar chart (Fig. 2.10). It is a very con- venient way of representing the characteristics of a storm and is particularly important Fig. 2.10 Hyetograph of a Storm in the development of design storms to predict extreme floods. The area under a hyetograph represents the total precipitation received in the period. The time interval used depends on the purpose, in urban-drainage problems small durations are used while in flood-flow computations in larger catchments the intervals are of about 6 h. Point Rainfall Point rainfall, also known as station rainfall refers to the rainfall data of a station. Depending upon the need, data can be listed as daily, weekly, monthly, seasonal or annual values for various periods. Graphically these data are represented as plots of  ! Engineering Hydrology magnitude vs chronological time in the form of a bar diagram. Such a plot, however, is not convenient for discerning a trend in the rainfall as there will be considerable vari- ations in the rainfall values leading to rapid changes in the plot. The trend is often discerned by the method of moving averages, also known as moving means. Moving average Moving average is a technique for smoothening out the high frequency fluctuations of a time series and to enable the trend, if any, to be noticed. The basic principle is that a window of time range m years is selected. Start- ing from the first set of m years of data, the average of the data for m years is calcu- lated and placed in the middle year of the range m. The window is next moved sequentially one time unit (year) at a time and the mean of the m terms in the window is determined at each window location. The value of m can be 3 or more years; usually an odd value. Generally, the larger the size of the range m, the greater is the smoothening. There are many ways of averaging (and consequently the plotting position of the mean) and the method described above is called Central Simple Moving Average. Example 2.4 describes the application of the method of moving averages. EXAMPLE 2.4 Annual rainfall values recorded at station M for the period 1950 to 1979 is given in Example 2.3. Represent this data as a bar diagram with time in chrono- logical order. (i) Identify those years in which the annual rainfall is (a) less than 20% of the mean, and (b) more than the mean. (ii) Plot the three-year moving mean of the annual rainfall time series. SOLUTION: (i) Figure 2.11 shows the bar chart with height of the column representing the annual rainfall depth and the position of the column representing the year of occur- rence. The time is arranged in chronological order. The mean of the annual rainfall time series is 568.7 mm. As such, 20% less than the mean = 426.5 mm. Lines representing these values are shown in Fig. 2.11 as horizontal lines. It can be seen that in 6 years, viz. 1952, 1960, 1969, 1972, 1975 and 1978, the Fig. 2.11 Bar Chart of Annual Rainfall at Station M  Precipitation !! annual rainfall values are less than 426.5 mm. In thirteen years, viz. 1950, 1951, 1955, 1963, 1964, 1965, 1966, 1967, 1968, 1970, 1976, 1977 and 1978, the annual rainfall was more than the mean. (ii) Moving mean calculations are shown in Table 2.2. Three-year moving mean curve is shown plotted in Fig. 2.12 with the moving mean value as the ordinate and the time in chronological order as abscissa. Note that the curve starts from 1951 and ends in the year 1978. No apparent trend is indicated in this plot. Table 2.2 Computation of Three-year Moving Mean 1 2 3 4 Annual Three consecutive year 3-year moving Year Rainfall (mm) total for moving mean mean Pi (Pi–1 + Pi + Pi + 1) (Col. 3/3)* 1950 676 1951 578 676 + 578 + 95 = 1349 449.7 1952 95 578 + 95 + 462 = 1135 378.3 1953 462 95 + 462 + 472 = 1029 343.0 1954 472 462 + 472 + 699 = 1633 544.3 1955 699 472 + 699 + 479 = 1650 550.0 1956 479 699 + 479 + 431 = 1609 536.3 1957 431 479 + 431 + 493 = 1403 467.7 1958 493 431 + 493 + 503 = 1427 475.7 1959 503 493 + 503 + 415 = 1411 470.3 1960 415 503 + 415 + 531 = 1449 483.0 1961 531 415 + 531 + 504 = 1450 483.3 1962 504 531 + 504 + 828 = 1863 621.0 1963 828 504 + 828 + 679 = 2011 670.3 1964 679 828 + 679 + 1244 = 2751 917.0 1965 1244 679 + 1244 + 999 = 2922 974.0 1966 999 1244 + 999 + 573 = 2816 938.7 1967 573 999 + 573 + 596 = 2168 722.7 1968 596 573 + 596 + 375 = 1544 514.7 1969 375 596 + 375 + 635 = 1606 535.3 1970 635 375 + 635 + 497 = 1507 502.3 1971 497 635 + 497 + 386 = 1518 506.0 1972 386 497 + 386 + 438 = 1321 440.3 1973 438 386 + 438 + 568 = 1392 464.0 1974 568 438 + 568 + 356 = 1362 454.0 1975 356 568 + 356 + 685 = 1609 536.3 1976 685 356 + 685 + 825 = 1866 622.0 1977 825 685 + 825 + 426 = 1936 645.3 1978 426 825 + 426 + 162 = 1863 621.0 1979 612 *The moving mean is recorded at the mid span of 3 years. 2.9 MEAN PRECIPITATION OVER AN AREA As indicated earlier, raingauges represent only point sampling of the areal  !" Engineering Hydrology Fig. 2.12 Three-year Moving Mean distribution of a storm. In practice, however, hydrological analysis requires a knowl- edge of the rainfall over an area, such as over a catchment. To convert the point rainfall values at various stations into an average value over a catchment the following three methods are in use: (i) Arithmetical-mean method, (ii) Thiessen-polygon method, and (iii) Isohyetal method. Arithmetical-Mean Method When the rainfall measured at various stations in a catchment show little variation, the average precipitation over the catchment area is taken as the arithmetic mean of the station values. Thus if P1, P2, , Pi, Pn are the rainfall values in a given period in N stations within a catchment, then the value of the mean precipitation P over the catch- ment by the arithmetic-mean method is P + P2 + ¼ + Pi + ¼ + Pn 1 N P= 1 = åP (2.7) N N i =1 i In practice, this method is used very rarely. Thiessen-Mean Method In this method the rainfall recorded at each station is given a weightage on the basis of an area closest to the station. The procedure of determining the weighing area is as follows: Consider a catchment area as in Fig. 2.13 containing three raingauge stations. There are three stations outside the catchment but in its neighbourhood. The catchment area is drawn to scale and the positions of the six stations marked on it. Stations 1 to 6 are joined to form a network of triangles. Perpendicular bisectors for each of the sides of the triangle are drawn. These bisectors form a polygon around each station. The boundary of the catchment, if it cuts the bisectors is taken as the outer limit of the polygon. Thus for station 1, the bounding polygon is abcd. For station 2, kade is taken as the bounding polygon. These bounding polygons are called Thiessen polygons. The areas of these six Thiessen polygons are determined either with a planimeter or  Precipitation !# A = total catchment area Station Bounded Area Weightage by 1 abcd A1 A1/A 2 kade A2 A2/A 3 edcgf A3 A3/A 4 fgh A4 A4/A 5 hgcbj A5 A5/A 6 jbak A6 A6/A Fig. 2.13 Thiessen Polygons by using an overlay grid. If P1 P2, , P6 are the rainfall magnitudes recorded by the stations 1, 2, , 6 respectively, and A1, A2, , A6 are the respective areas of the Thiessen polygons, then the average rainfall over the catchment P is given by P1 A1 + P2 A2 + ¼ + P6 A6 P= ( A1 + A2 + ¼ + A6 ) Thus in general for M stations, M å Pi Ai i =1 M Ai P= = å Pi (2.8) A i =1 A Ai The ratio is called the weightage factor for each station. A The Thiessen-polygon method of calculating the average percipitation over an area is superior to the arithmetic-average method as some weightage is given to the various stations on a rational basis. Further, the raingauge stations outside the catchment are also used effectively. Once the weightage factors are determined, the calculation of P is relatively easy for a fixed network of stations. Isohyetal Method An isohyet is a line joining points of equal rainfall mag- nitude. In the isohyetal method, the catchment area is drawn to scale and the raingauge stations are marked. The recorded val- ues for which areal average P is to be determined are then marked on the plot at appropriate stations. Neigh- bouring stations outside the catchment are also consid- ered. The isohyets of vari- ous values are then drawn by considering point rain- Fig. 2.14 Isohyetals of a Storm  !$ Engineering Hydrology falls as guides and interpolating between them by the eye (Fig. 2.14). The procedure is similar to the drawing of elevation contours based on spot levels. The area between two adjacent isohyets are then determined with a planimeter. If the isohyets go out of catchment, the catchment boundary is used as the bounding line. The average value of the rainfall indicated by two isohyets is assumed to be acting over the inter-isohyet area. Thus P1, P2, , Pn are the values of isohyets and if a1, a2, , an-1 are the inter-isohyet areas respectively, then the mean precipitation over the catchment of area A is given by æ P + P2 ö æ P2 + P3 ö æ Pn - 1 + Pn ö a1 ç 1 + a2 ç + ¼ + an - 1 ç è 2 ÷ø è 2 ÷ø è 2 ÷ø P= (2.9) A The isohyet method is superior to the other two methods especially when the sta- tions are large in number. EXAMPLE 2.5 In a catchment area, approximated by a circle of diameter 100 km, four rainfall stations are situated inside the catchment and one station is outside in its neigh- bourhood. The coordinates of the centre of the catchment and of the five stations are given below. Also given are the annual precipitation recorded by the five stations in 1980. Determine the average annual precipitation by the Thiessen-mean method. Centre: (100, 100) Diameter: 100 km. Distance are in km Station 1 2 3 4 5 Coordinates (30, 80) (70, 100) (100, 140) (130, 100) (100, 70) Precipitation (cm) 85.0 135.2 95.3 146.4 102.2 SOLUTION: The catchment area is drawn to scale and the stations are marked on it (Fig. 2.15). The stations are joined to form a set of triangles and the perpendicular bisector of each side is then drawn. The Thiessen-polygon area enclosing each station is then identified. It may be noted that station 1 in this problem does not have any area of influence in the catchment. The areas of various Thiessen poly- gons are determined either by a planimeter or by placing an overlay grid. Fig. 2.15 Thiessen Polygons— Example 2.5 Station Boundary Area Fraction of total Rainfall Weighted of area (km2) area P (cm) (col. 4 ´ col. 5) 1 — — — 85.0 — 2 abcd 2141 0.2726 135.2 36.86 3 dce 1609 0.2049 95.3 19.53 4 ecbf 2141 0.2726 146.4 39.91 5 fba 1963 0.2499 102.2 25.54 Total 7854 1.000 121. 84 Mean precipitation = 121.84 cm.  Precipitation !% EXAMPLE 2.6 The isohyets due to a storm in a catchment were drawn (Fig. 2.14) and the area of the catchment bounded by isohyets were tabulated as below. Isohyets Area (cm) (km2) Station–12.0 30 12.0–10.0 140 10.0–8.0 80 8.0–6.0 180 6.0–4.0 20 Estimate the mean precipitation due to the storm. SOLUTION: For the first area consisting of a station surrounded by a closed isohyet, a precipitation value of 12.0 cm is taken. For all other areas, the mean of two bounding isohyets are taken. Isohytes Average Area (km2) Fraction of Weighted value of P total area P (cm) (cm) (col. 3/450) (col. 2 ´ col. 4) 1 2 3 4 5 12.0 12.0 30 0.0667 0.800 12.0–10.0 11.0 140 0.3111 3.422 10.0–8.0 9.0 80 0.1778 1.600 8.0–6.0 7.0 180 0.4000 2.800 6.0–4.0 5.0 20 0.0444 0.222 Total 450 1.0000 8.844 Mean precipitation P = 8.84 cm 2.10 DEPTH-AREA-DURATION RELATIONSHIPS The areal distribution characteristics of a storm of given duration is reflected in its depth-area relationship. A few aspects of the interdependency of depth, area and dura- tion of storms are discussed below. Depth-Area Relation For a rainfall of a given duration, the average depth decreases with the area in an exponential fashion given by P = P0 exp (–KAn) (2.10) where P = average depth in cm over an area A km2, P0 = highest amount of rainfall in cm at the storm centre and K and n are constants for a given region. On the basis of 42 severemost storms in north India, Dhar and Bhattacharya3 (1975) have obtained the following values for K and n for storms of different duration: Duration K n 1 day 0.0008526 0.6614 2 days 0.0009877 0.6306 3 days 0.001745 0.5961  !& Engineering Hydrology Since it is very unlikely that the storm centre coincides over a raingauge station, the exact determination of P0 is not possible. Hence in the analysis of large area storms the highest station rainfall is taken as the average depth over an area of 25 km2. Equation (2.10) is useful in extrapolating an existing storm data over an area. Maximum Depth-Area-Duration Curves In many hydrological studies involving estimation of severe floods, it is necessary to have information on the maximum amount of rainfall of various durations occurring over various sizes of areas. The development of relationship, between maximum depth- area-duration for a region is known as DAD analysis and forms an important aspect of hydro-meteorological study. References 2 and 9 can be consulted for details on DAD analysis. A brief description of the analysis is given below. First, the severemost rainstorms that have occurred in the region under question are considered. Isohyetal maps and mass curves of the storm are compiled. A depth-area curve of a given duration of the storm is prepared. Then from a study of the mass curve of rainfall, various durations and the maximum depth of rainfall in these durations are noted. The maximum depth-area curve for a given duration D is prepared by assuming the area distribution of rainfall for smaller duration to be similar to the total storm. The procedure is then repeated for different storms and the envelope curve of maximum depth-area for duration D is obtained. A similar procedure for various values of D results in a family of envelope curves of maximum depth vs area, with duration as the third parameter (Fig. 2.16). These curves are called DAD curves. Figure 2.16 shows typical DAD curves for a catchment. In this the average depth denotes the depth averaged over the area under consideration. It may be seen that the maximum depth for a given storm decreases with the area; for a given area the maxi- mum depth increases with the duration. Fig. 2.16 Typical DAD Curves Preparation of DAD curves involves considerable computational effort and requires meteorological and topographical information of the region. Detailed data on severemost storms in the past are needed. DAD curves are essential to develop design  Precipitation !' storms for use in computing the design flood in the hydrological design of major structures such as dams. Table 2.3 Maximum (Observed) Rain Depths (cm) over Plains of North India4, 5 Area in km2 ´ 104 Duration.026 0.13 0.26 1.3 2.6 5.2 7.8 10.5 13.0 1 day 81.0* 76.5* 71.1 47.2* 37.1 * 26.4 20.3† 18.0† 16.0† 2 days 102.9* 97.5* 93.2* 73.4* 58.7* 42.4* 35.6† 31.5† 27.9† 3 days 121.9† 110.7† 103.l† 79.2† 67.1† 54.6† 48.3† 42.7† 38.9† Note: *—Storm of 17–18 September 1880 over north-west U.P. †—Storm of 28–30 July 1927 over north Gujarat. Maximum rain depths observed over the plains of north India are indicated in Ta- ble 2.3. These were due to two storms, which are perhaps the few severe most re- corded rainstorms over the world. 2.11 FREQUENCY OF POINT RAINFALL In many hydraulic-engineering applications such as those concerned with floods, the probability of occurrence of a particular extreme rainfall, e.g. a 24-h maximum rainfall, will be of importance. Such information is obtained by the frequency analysis of the point-rainfall data. The rainfall at a place is a random hydrologic process and a sequence of rainfall data at a place when arranged in chronological order constitute a time series. One of the commonly used data series is the annual series composed of annual values such as annual rainfall. If the extreme values of a specified event occurring in each year is listed, it also constitu