volume 7_engineering modelling

Volume 7 Engineering Modelling

Jabatan Pengairan dan Saliran Malaysia Jalan Sultan Salahuddin 50626 KUALA LUMPUR

GOVERNMENT OF MALAYSIA DEPARTMENT OF IRRIGATION

AND DRAINAGE

DID MANUAL Volume 7

March 2009 i

Disclaimer

Every effort and care has been taken in selecting methods and recommendations that are appropriate to Malaysian conditions. Notwithstanding these efforts, no warranty or guarantee, express, implied or statutory is made as to the accuracy, reliability, suitability or results of the methods or recommendations. The use of this Manual requires professional interpretation and judgment. Appropriate design procedures and assessment must be applied, to suit the particular circumstances under consideration. The government shall have no liability or responsibility to the user or any other person or entity with respect to any liability, loss or damage caused or alleged to be caused, directly or indirectly, by the adoption and use of the methods and recommendations of this Manual, including but not limited to, any interruption of service, loss of business or anticipatory profits, or consequential damages resulting from the use of this Manual.

DID MANUAL Volume 7

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Foreword

The first edition of the Manual was published in 1960 and was actually based on the experiences and knowledge of DID engineers in planning, design, construction, operations and maintenance of large volume water management systems for irrigation, drainage, floods and river conservancy. The manual became invaluable references for both practising as well as officers newly posted to an unfamiliar engineering environment. Over these years the role and experience of the DID has expanded beyond an agriculture-based environment to cover urbanisation needs but the principle role of being the countrys leading expert in large volume water management remains. The challenges are also wider covering issues of environment and its sustainability. Recognising this, the Department decided that it is timely for the DID Manual be reviewed and updated. Continuing the spirit of our predecessors, this Manual is not only about the fundamentals of related engineering knowledge but also based on the concept of sharing experience and knowledge of practising engineers. This new version now includes the latest standards and practices, technologies, best engineering practices that are applicable and useful for the country. This Manual consists of eleven separate volumes covering Flood Management; River Management; Coastal Management; Hydrology and Water Resources; Irrigation and Agricultural Drainage; Geotechnical, Site Investigation and Engineering Survey; Engineering Modelling; Mechanical and Electrical Services; Dam Safety, Inspections and Monitoring; Contract Administration; and Construction Management. Within each Volume is a wide range of related topics including topics on future concerns that should put on record our care for the future generations. This DID Manual is developed through contributions from nearly 200 professionals from the Government as well as private sectors who are very experienced and experts in their respective fields. It has not been an easy exercise and the success in publishing this is the results of hard work and tenacity of all those involved. The Manual has been written to serve as a source of information and to provide guidance and reference pertaining to the latest information, knowledge and best practices for DID engineers and personnel. The Manual would enable new DID engineers and personnel to have a jump-start in carrying out their duties. This is one of the many initiatives undertaken by DID to improve its delivery system and to achieve the mission of the Department in providing an efficient and effective service. This Manual will also be useful reference for non-DID Engineers, other non-engineering professionals, Contractors, Consultants, the Academia, Developers and students involved and interested in water-related development and management. Just as it was before, this DID Manual is, in a way, a record of the history of engineering knowledge and development in the water and water resources engineering applications in Malaysia. There are just too many to name and congratulate individually, all those involved in preparing this Manual. Most of them are my fellow professionals and well-respected within the profession. I wish to record my sincere thanks and appreciation to all of them and I am confident that their contributions will be truly appreciated by the readers for many years to come.

Dato Ir. Hj. Ahmad Husaini bin Sulaiman, Director General, Department of Irrigation and Drainage Malaysia

DID MANUAL Volume 7

March 2009 iii

Acknowledgements

Steering Committee: Dato Ir. Hj. Ahmad Husaini bin Sulaiman, Dato Nordin bin Hamdan, Dato Ir. K. J. Abraham, Dato Ong Siew Heng, Dato Ir. Lim Chow Hock, Ir. Lee Loke Chong, Tuan Hj. Abu Bakar bin Mohd Yusof, Ir. Zainor Rahim bin Ibrahim, En. Leong Tak Meng, En. Ziauddin bin Abdul Latiff, Pn. Hjh. Wardiah bte Abd. Muttalib, En. Wahid Anuar bin Ahmad, Tn. Hj. Zulkefli bin Hassan, Ir. Dr. Hj. Mohd. Nor bin Hj. Mohd. Desa, En. Low Koon Seng, En. Wan Marhafidz Shah bin Wan Mohd. Omar, Sr. Md Fauzi bin Md Rejab, En. Khairuddin bin Mat Yunus, Cik Khairiah bt Ahmad, Coordination Committee: Dato Nordin bin Hamdan, Dato Ir. Hj. Ahmad Fuad bin Embi, Dato Ong Siew Heng, Ir. Lee Loke Chong, Tuan Hj. Abu Bakar bin Mohd Yusof, Ir. Zainor Rahim bin Ibrahim, Ir. Cho Weng Keong, En. Leong Tak Meng, Dr. Mohamed Roseli Zainal Abidin, En. Zainal Akamar bin Harun, Pn. Norazia Ibrahim, Ir. Mohd. Zaki, En. Sazali Osman, Pn. Rosnelawati Hj. Ismail, En. Ng Kim Hoy, Ir. Lim See Tian, Sr. Mohd. Fauzi bin Rejab, Ir. Hj. Daud Mohd Lep, Tn. Hj. Muhamad Khosim Ikhsan, En. Roslan Ahmad, En. Tan Teow Soon, Tn. Hj. Ahmad Darus, En. Adnan Othman, Ir. Hapida Ghazali, En. Sukemi Hj. Sidek, Pn. Hjh. Fadzilah Abdul Samad, Pn. Hjh. Salmah Mohd. Som, Ir. Sahak Che Abdullah, Pn. Sofiah Mat, En. Mohd. Shafawi Alwi, En. Ooi Soon Lee, En. Muhammad Khairudin Khalil, Tn. Hj. Azmi Md Jafri, Ir. Nor Hisham Ghazali, En. Gunasegaran M., En. Rajaselvam G., Cik Nur Hareza Redzuan, Ir. Chia Chong Wing, Pn Norlida Mohd. Dom, , Ir. Lee Bea Leang, Dr. Hj. Md. Nasir Md. Noh, Pn Paridah Anum Tahir, Pn. Nurazlina Mohd Zaid, PWM Associates Sdn. Bhd., Institut Penyelidikan Hidraulik Kebangsaan Malaysia (NAHRIM), RPM Engineers Sdn. Bhd., J.U.B.M. Sdn. Bhd. Working Group: En. Ng Kok Seng, Ir. Mohd. Noor bin Bidin, En. Ferdaos bin Mohamed, Pn. Noor Hanisah Wok, Dr. Mohamed Roseli Zainal Abidin, En. Adnan bin Othman, Ir Dr Ng Chee Hock, En. Chong Ing Keong, En. Irwandee Reduan, En. Teoh Boon Pin, Ir. Mohd. Adnan Mohd. Nor, Ir. Liam We Lin, Ir. Liang Kee Ming, En. Ratna Rajah Sivapiragasam, Dr. Heng Hock Hwee, En. Ahmad Ashrin Abdul Jalil.

DID MANUAL Volume 7

iv March 2009

Registration of Amendments

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DID MANUAL Volume 7

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Table of Contents

Disclaimer .................................................................................................................................. i

Foreword .................................................................................................................................. ii

Acknowledgements ................................................................................................................... iii

Registration of Amendments ...................................................................................................... iv

Table of Contents ...................................................................................................................... v

List of Volumes ........................................................................................................................ vi

List of Symbols ........................................................................................................................ vii

List of Abbreviations ................................................................................................................ viii

List of Glossary ......................................................................................................................... ix

Chapter 1 INTRODUCTION

Chapter 2 HYDROLOGICAL AND HYDRAULIC MODELS

Chapter 3 GEOTECHNICAL MODELLING

Chapter 4 STRUCTURAL MODELLING

DID MANUAL Volume 7

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List of Volumes

Volume 1 FLOOD MANAGEMENT Volume 2 RIVER MANAGEMENT Volume 3 COASTAL MANAGEMENT Volume 4 HYDROLOGY AND WATER RESOURCES Volume 5 IRRIGATION AND AGRICULTURAL DRAINAGE Volume 6 GEOTECHNICAL MANUAL, SITE INVESTIGATION AND ENGINEERING SURVEY Volume 7 ENGINEERING MODELLING Volume 8 MECHANICAL AND ELECTRICAL SERVICES Volume 9 DAM SAFETY, INSPECTIONS AND MONITORING Volume 10 CONTRACT ADMINISTRATION Volume 11 CONSTRUCTION MANAGEMENT

DID MANUAL Volume 7

March 2009 vii

List of Symbols

A Area Q Discharge q Discharge per unit width V Velocity So Bed slope Sc Critical slope Yo Normal flow depth Yc Critical depth g Gravitational acceleration S Energy Slope Qs Sediment discharge rate ds Sediment size L Length Fr Froude Number Re Reynolds Number F Force t Time

DID MANUAL Volume 7

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List of Abbreviations

DID Department of Irrigation and Drainage PWD Public Works Department SWMM Storm Water Management Model GIS Geographic Information System ESRI Economic and Social Research Institute .CSV Comma Separated Values ASCII American Standard Code for Information Interchange SQL Structured Query Language USACE United States Army Corps of Engineers VB Visual Basic VBA Visual Basic for Applications GUI Graphical User Interface CAD Computer-Aided Design DOS Disk Operating System HEC Hydrologic Engineering Control HP Hydrological Procedure

DID MANUAL Volume 7

March 2009 ix

List of Glossary

Term Definition Catchment

An extent of land where water from rain drains downhill into a body of water, such as a river, lake, reservoir, estuary, wetland, sea or ocean. The drainage basin includes both the streams and rivers that convey the water as well as the land surfaces from which water drains into those channels, and is separated from adjacent basins by a drainage divide.

Critical Depth The depth of flow when the Froude Number equals to one. This is the flow depth when discharge is maximum for a given specific energy.

Effective Rainfall

Part of the precipitation that reaches stream and river channels as direct runoff (as opposed to that which is intercepted by vegetation or lost as evaporation and water lost to ground water)

Evaporation The vaporization of water from the earths surface

Finite Difference Method

Numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives

Finite Element Method

Is a numerical method for solving partial differential equations (PDE) and integral equations by approximating the PDE with a system of ordinary differential equations (ODE) and then discretising and simplifying the equations so that they can be solved numerically.

Froude Number

The ratio of inertial forces to gravitational forces in flow.

Head Loss

The loss in energy head due to flow through a culvert, a gate due to friction (e.g. flow through a long pipeline)

Hydraulic Jump

A phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise (a step or standing wave) occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increases in height converting some of the flow's initial kinetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. In an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shockwave forms.

Hydraulic Gradient

The gradient between two or more hydraulic head measurements over the length of the flow path.

Infiltration Downward movement of water through soil to the ground water table

Mathematical Models

Mathematical models use mathematical expressions to describe the behavior of systems. In developing a mathematical model the system being modeled needs to be idealized or simplified to capture the essence of the phenomenon of interest.

DID MANUAL Volume 7

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Term Definition Non-uniform Flow

Flow that varies from section to section, which is the flow condition in a natural stream where river sections change and there are bridge constrictions and channel slope varies from section to section

Open Channel Flow

Flow of water in a conduit which can be a channel or even a pipe where there is a free surface subject to atmospheric pressure. This is opposed to pressure flow in a pipe where flow is not subjected to atmospheric pressure but subjected only to hydraulic pressure.

Physical Models

A smaller or larger physical copy of an object. The object being modelled may be small (for example, an atom) or large (for example, the Solar System).

Specific Energy

The energy per unit mass: J/kg or, in basic SI units: m2/s2 at a channel section measured with respect to the channel bed.

Steady Flow Flow in which all the conditions at any one point are constant with respect to time. An example of flow condition which can be considered almost steady flow would be flow in an irrigation canal in a period where supply and withdrawal ratios are constant.

Stochastic Hydrology

Mainly concerned with the assessment of uncertainty in model predictions. In stochastic hydrology, the assessment of uncertainty is an integral part of hydrological analysis and modelling, being as important as the predictions themselves.

Subcritical Flow

The flow when flow depth is greater than critical and velocity less than critical

Supercritical Flow

The flow when flow depth is less than critical and velocity greater than critical

Surface Runoff The water flow which occurs when soil is infiltrated to full capacity and excess water, from rain, snowmelt, or other sources flows over the land.

Uniform Flow

Flow that does not vary along the channel or conduit and this will occur for steady flow over a long conduit or channel whose slope and sections are constant. In practice flows are seldom perfectly uniform but for practical purposes an example of flow which is almost uniform would be a long conveyance channel whose sections and slope are constant and flow rates steady and constant

Unit Hydrograph

A hypothetical unit response of the watershed to a unit input of rainfall

Unsteady Flow

The flow where the velocity at a point varies with time

CHAPTER 1 INTRODUCTION


March 2009 1-i

Table of Contents

Table of Contents .................................................................................................................... 1-i

1.1 OBJECTIVE OF MANUAL ........................................................................................... 1-1

1.2 INTRODUCTION TO MODELLING .............................................................................. 1-1

1.3 CONTENTS OF MANUAL ........................................................................................... 1-2


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March 2009 1-1

1 INTRODUCTION

1.1 OBJECTIVE OF MANUAL This volume of the DID Manual covers engineering modelling. Engineering modelling in many instances is a computer based mathematical model. But this is not necessarily so especially in the area of hydraulics where there are instances where scaled physical models are preferred or are used to complement mathematical models. The manual covers hydrological modelling and hydraulic modelling which are the two main areas of studies carried out in most DID projects. In the development of concept design for water resources projects, engineering analyses are more focused on hydrology and hydraulics but eventually the proposed system will have to consider earthworks (e.g. channelization and bunds) and structures (outlet structures, pump sump etc.) and in these areas, geotechnical models and structural models are often applied. Hence the inclusion of such models in this manual. 1.2 INTRODUCTION TO MODELLING Models are representations of real systems be it a catchment, a drainage network, a structure, an earthwork design, a river improvement work, etc. Engineers resort to models because the real system is too complex or the system is not in existence yet (a proposed system). As expected models are simplifications of the real system. To be effective in terms of effort, time and money while getting results which is realistic and helpful in decision making or to enhance understanding of systems, models should not be far too complex than it needs to be. The factors that influence the choice of models are:

Availability of expertise and experience to configure and run the models and equally important the experience to interpret the results of the model. Models that come with user friendly data entry tools and default parameters are easy to set up and run but the results obtain may need experience and knowledge to review and adopt. A modeler may need experience and knowledge to be aware of assumptions adopted and simplifications to either a complex computational scheme or simplifications made in conceptualizing the real system.

Availability of data to feed complex models. If data is scarce or the quality of available data not good, feeding the data into a very detailed and complex model would probably be not effective. Simple models are often more robust to erroneous or inaccurate data compared to complex models. The rule of parsimony may be applied where the simplest model able to explain the phenomena being studied should be adopted.

In modelling, there is a need to concentrate on components that are important to the issue being studied and to remove less important components. Complicating the modelling effort with less important components tends to distract effort and attention from the more important components. Sometimes sensitivity analyses are carried out to test the importance of certain parameters of the model. Models configured for a certain study may be sensitive to certain parameters and less sensitive to other parameters. Attention and effort should be focus on the simulation of the more sensitive parameters or input data.

Other factors would include costs of model, cost in computer time, familiarity with the model, ease of use of model, the technical support available, the popularity of the model and the user base, etc.


1-2 March 2009

1.3 CONTENTS OF MANUAL This manual covers engineering modelling in the following areas:

Hydrology Hydraulics Geotechnics Structure

In hydrological modelling rainfall-runoff models are the most commonly applied and hence emphasis was given to this category of models. Besides rainfall-runoff models there are statistical models and such models are covered under time-series modelling. In hydraulic modelling, models of varying degree of complexity starting with simple steady uniform flow, to non-uniform flow to hydrodynamic flow models were described. Fluvial hydraulic models deal with sediment transport and are included because of growing concern in sedimentation and erosion issues. The sections on geotechnical and structural modelling describe empirical and simplified models. The description also extends to numerical and physical models. The application and selection of these models were also discussed. Mathematic models in the various areas of interest, often involve complex and voluminous computational effort. The computation involved can sometimes be handled using a computer spreadsheet software such as Microsoft Excel. Most, however, would rely on third party software. Some of the more well known software are introduced. Besides mathematical and statistical models, which relies on mathematics, understanding of basic equations relevant to the phenomena being modeled and number crunching, there are also physical models where modelers will have to built scaled physical models to study the process of interest, such as flow separation in a hydraulic structure, scouring effect in a stilling basin downstream of a spillway, efficiency of a bifurcation structure in splitting flow etc. Physical modelling is presented in sections on hydraulic, geotechnical and structural modelling. Modelling in practice usually involves the use of computer software due to the complexity of computations. This manual examines some the software popularly used by engineers in hydrological, hydraulic, geotechnical and structural modelling.

CHAPTER 2 HYDROLOGICAL AND HYDRAULIC MODELS


March 2009 2-i

Table of Contents

Table of contents .................................................................................................................... 2-i

List of Tables ......................................................................................................................... 2-ii

List of Figures ........................................................................................................................ 2-ii

2.1 INTRODUCTION ....................................................................................................... 2-1

2.2 EVENT BASED AND CONTINUOUS SIMULATION OF RAINFALL-RUNOFF ........................ 2-2

2.2.1 Institute of Hydrology, UKs Lumped Model ................................................... 2-3

2.2.2 Sugawaras Tank Model ............................................................................... 2-5

2.2.3 Time Series Modelling ................................................................................. 2-9

2.3 HYDRAULIC MODELS ............................................................................................. 2-16

2.3.1 Specific Energy ......................................................................................... 2-16

2.3.2 Modelling Various Types of Open Channel Flow ........................................... 2-19

2.4 PHYSICAL MODELS ................................................................................................ 2-28

2.4.1 Purposes and Objectives of Physical Modelling ............................................ 2-28

2.4.2 Theoretical Consideration .......................................................................... 2-29

2.4.3 Gravitational Forces and Froude Number .................................................... 2-30

2.4.4 Natural or Undistorted and Distorted Model ................................................. 2-31

2.4.5 Fixed and Mobile Bed Model ...................................................................... 2-32

2.4.6 Models Limitations and Selections .............................................................. 2-34

2.4.7 Model Example: Sri Johor Pond .................................................................. 2-37

2.5 OVERVIEW OF AVAILABLE SOFTWARE .................................................................... 2-40

2.5.1 Hydrological Models .................................................................................. 2-40

2.5.2 Hydraulic Models ...................................................................................... 2-41

2.5.3 Fluvial Hydraulic Models ............................................................................ 2-45

2.6 PUBLIC DOMAIN OR COMMERCIAL SOFTWARE ......................................................... 2-50

2.7 MODELLING PROCESSES ......................................................................................... 2-51

2.7.1 Data Collection ........................................................................................ 2-51

2.7.2 Calibration ............................................................................................... 2-51

2.7.2 Verification .............................................................................................. 2-52

REFERENCES ....................................................................................................................... 2-52


2-ii March 2009

List of Tables

Table Description Page

2.1 4-hourly Effective Rainfall Hyetograph 2-11

2.2 Derivation of the DRH by Convolution Process 2-12

2.3 Summary of Model Scales 2-38

List of Figures Figure Description Page

2.1 A Simple Catchment Model 2-1

2.2 Configuration of a Distributed Catchment Model 2-2

2.3 Institute of Hydrology, UKs Lumped Model 2-4

2.4 Generated Daily Inflows in Bukit Merah Reservoir 2-5

2.5 A Basic Tank Model Configured for Sg Kelantan by Sugawara (1981) 2-6

2.6 The Tank Configurations for a Sub-basin and for a Channel Reach for the Modified Tank Model 2-7

2.7 Sub-Basins and Channel Reaches of the Modified Tank Model for Sg Kelantan and Tabulation of Model Parameters 2-7

2.8 Tank model Simulation Results for the 1992 and 1994 Floods 2-8

2.9 Unit Hydrograph (UH) as a Function that Transform Effective Rainfall to a Direct Runoff Hydrograph (DRH) 2-10

2.10 4-hour UH for 1 cm Effective Rain and Tabulated UH Ordinates 2-11

2.11 Convolution of UH of Figure 2.10 with Effective Rain (ER) Hyetograph of Table 2.2 2-13

2.12 A Typical Three-Layer Feed Forward ANN 2-14

2.13 Logsig Transfer Function 2-14

2.14 Energy along a Streamline in an Open Channel Flow 2-17

2.15 Specific Energy 2-17

2.16 Depth-Discharge Curve for Constant E 2-18

2.17 Specific Energy Diagram 2-19

2.18 Steady Flow versus Unsteady Flow Hydrographs at a Location 2-20


March 2009 2-iii

Figure Description Page

2.19 Uniform Flow 2-20

2.20 Non-Uniform Flow 2-21

2.21 A Commonly Encountered UF, GVF and RVF Flow Condition 2-21

2.22 Classification of GVF Slopes 2-22

2.23 Categorising Initial Depth 2-22

2.24 The Classification and Shapes of Various GVF Water Surface Profiles 2-23

2.25 Transitions Encountered in Open Channel Flow Analyses 2-24

2.26 Sg Linggi Flood Profiles Output by the Hec-RAS Software 2-25

2.27 Gridded Computational x-t (Distance-Time) Plane for Finite Difference Computation of the Saint Venant Equation 2-26

2.28 Lane Relationship on River Scouring and Deposition 2-27

2.29 Configuration of Bifurcation Structure to be Modelled 2-38

2.30 Photos of Scaled Physical Model of Flow Bifurcation Structure 2-39

2.31 Recommendations Resulting from Physical Model Study 2-40

2.32 The Algorithm and Flow Line of FLUVIAL 12 Model 2-47

2.33 Changes in Cross Sectional Area of a River Reach 2-49

2.34 Flow Diagram for HEC 6 2-50


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March 2009 2-1

2 HYDROLOGICAL AND HYDRAULIC MODELS

2.1 INTRODUCTION Hydrological Models are models that simulates part of the hydrological cycle. Hydrological processes are complex and attempts have been made to represent the processes in a simplified manner and these simplified representations of a catchment are models of the catchment.

In many typical catchment models, the catchment is represented as storage and rainfall falling on the catchment goes into this storage. Water is lost from this storage via evaporation, infiltration and outflows. In a typical application of catchment models, the parameter of interest is usually the outflow or discharge from the catchment. Simple equations are used to compute outflow from this storage. Such models are also called rainfall-runoff models (see figure 2.1).

R

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I I

Catchment and hydrological processes

Model representation of hydrological processes

R: Rainfall E : Evaporation

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E E

Figure 2.1 A Simple Catchment Model

With powerful computing tools made possible by computers, a more complex catchment model can be configured. The additional model features that are usually adopted are:

Further differentiation of storage into: surface storage and groundwater storage. Outflow from surface storage comes out fast (rapid runoff) whilst outflow from groundwater storage comes out slowly. Rainfall enters surface storage first and water gets into groundwater storage via infiltration. Some models even differentiate groundwater into primary and secondary groundwater storages.

Dividing the catchment into interlinking subcatchments. The model is now a distributed catchment model as opposed to a single lumped catchment model (see Fig 2.2). This allows the modeller the flexibility to consider parameter and input variations from one sub-catchments to another, such as:

Rainfall variation in meteorological input Infiltration variation in soil type Catchment lag time variation in terrain

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March 2009 2-3

Another area of simulation where soil moisture accounting plays an important role is the long term daily flow simulation carried out for water resources studies. The Thornwaite and Mather Water Balance Model described in DIDs Water Resources Publication No 6 (WRP6) is an example of a daily continuous soil moisture accounting model. The lumped catchment model of Blackie and Eeles adopted in the HYRROM software of UKs Institute of Hydrology is another example of a daily runoff simulation model using continuous soil moisture accounting. Two soil-moisture accounting model namely the lumped model of the Institute of Hydrology, UK and Sugawaras Tank Model are described below. 2.2.1 Institute of Hydrology, UKs Lumped Model The lumped model described by Blackie, J.R. and Eeles, C.W.O.: Lumped Catchment Models, Chapter 11 Hydrological Forecasting Edited by M.G. Anderson and T.P. Burt, John Wiley & Sons Ltd, 1985, is a continuous soil moisture accounting model and is suitable for simulation of daily rainfall-runoff. This model had been used in several studies i.e. to simulate several years of daily runoff for irrigation water resources simulation studies. Unlike many flood simulation models which caters for catchment sub-division and variation in catchment parameters and catchment rainfall, the model is a lumped model and simplifies this aspect of catchment modelling. But to cater for long term and continuous flow simulation it has a detailed soil moisture accounting component. The model formulation is simple and a schematic of the model is shown in Figure 2.3. This model defines four storages:

a) Interception storage CS b) Surface detention storage RSTOR c) Soil moisture storage (DCT-DC) d) Ground water storage GS

Input into the model is rainfall (RAIN). This goes into the interception storage whereby which has a maximum storage SS. Water is lost through this storage by evaporation ES where

ES = FS.EO (2.1) where EO is the potential evapotranspiration FS is a factor to convert EO to evaporation ES

Rain in excess of the interception storage becomes ERAIN (or the effective rain) and this is split into two amounts

1. ROFF which flows to the surface detention storage RSTOR and 2. ERAIN which goes into the soil moisture storage to reduce soil moisture deficit DC

Flow is routed through the surface storage RSTOR to obtain outflow from surface storage, RO and the equation is given by: RO = RK.RSTORRX (2.2) RK an RX are coefficient and exponent of surface storage routing equations.


2-4 March 2009

Figure 2.3 Institute of Hydrology, UKs Lumped Model

In the soil moisture storage, water is lost via transpiration EC and if soil moisture storage is greater than field capacity (i.e if DCDC>DCS GPR is routed through GS to yield the groundwater flow using the equation GRO = (GS/GSU)GSP (2.4)


March 2009 2-5

Both RO and GRO are then lagged by delay time RDEL and GDEL respectively before being added to form the catchment runoff. Figure 2.4 shows sample result from a daily runoff modelling study. The long term daily inflows (about 30-years) obtained from the modelling effort are useful for water resources study which in this case involves the study of water resources of Bukit Merah Reservoir. The parameters of the model configured for Bukit Merah Reservoir catchment are as shown in Figure 2.3

Figure 2.4 Generated Daily Inflows in Bukit Merah Reservoir

2.2.2 Sugawaras Tank Model Modelling for flood forecasting would be considered the most demanding rainfall-runoff modelling effort. The reliability of the model in simulating the catchment runoff can be compared with observed data immediately.

One of the models adopted for flood forecasting is Sugawaras Tank Model. The model was used for real-time forecasting of floods at Guillemard Bridge, Sg Kelantan. Sugawaras Tank Model can be configured in many ways and one of the model configuration is as shown in Fig 2.5 below. The Sg Kelantan Tank Model comprises 3 tanks. One for the surface flow, a second tank for the interflow and outflows from both tanks is routed through a third tank to simulate river routing process. Rainfall R enters the first tank. First tank storage must rise above H1 before any outflow occurs (conceptually H1 is the interception storage). Water is lost from the first tank via evaporation EV and infiltration INFIL1, storage higer than H1 will result in surface flow Q2 and Q1 if rain so heavy raises the storage to above H2. The second tank receives water from INFIL1 and the second tank storage must be in excess of H3 before interflow Q3 occurs. INFIL2 represents deep percolation. A constant base flow is included. Flows Q1, Q2, Q3 and baseflow feeds into the third tank and the routed flow represents the simulated flow at the catchment outlet and in the case of the Kelantan Flood Forecasting model, the outlet is at Guillemard Bridge.


2-6 March 2009

Figure 2.5 A Basic Tank Model Configured for Sg Kelantan by Sugawara (1981)

The parameters initially configured for Sg Kelantan is presented in Figure 2.5 above. The original Tank model configured for Sg Kelantan is a lumped model. Towards the end of 90s, the Kelantan Tank Model was modified. The Tank configuration is as shown in Figure 2.6. This configuration is for a sub-basin and a channel reach. Availability of more powerful and cheaper computers allows DID to configure Sg Kelantan model as distributed model. The Sg Kelantan basin is divided into four sub-basins, B1 to B4 and the sub-basins are linked by channel reaches C1 to C3. A schematic of the Modified Tank Model for Sg Kelantan and the model parameters are presented in figures 2.7 and 2.8.


March 2009 2-7

Figure 2.6 The Tank Configurations for a Sub-basin and for a Channel Reach for the Modified Tank Model

Figure 2.7 Sub-Basins and Channel Reaches of the Modified Tank Model for Sg Kelantan and Tabulation of Model Parameters


2-8 March 2009

02468

1012141618

v-91

ec-91

ec-91 n-9

2an

-92

Stag

e (m

)

0

10

20

30

40

50

60

70

Rain

fall

(mm

)

15-No 1-D 15-

D 1-Ja

8-J

Avg Rainfall OLVL4 LVL4

02468

101214161820

15-Oc

t-92

1-Nov

-92

15-No

v-92

1-Dec-

92

13-De

c-92

Stag

e (m

)

0102030405060708090100

Rain

fall

(mm

)

Avg Rainfall OLVL4 LVL4

02468

101214161820

1-Nov

-94

15-No

v-94

1-Dec-

94

15-De

c-94

24-De

c-94

Stag

e (m

)

05101520253035404550

Rain

fall

(mm

)Avg Rainfall OLVL4 LVL4

Figure 2.8 Tank model Simulation Results for the 1992 and 1994 Floods


March 2009 2-9

2.2.3 Time Series Modelling Whilst hydrological models described thus far are models which attempt to simulate the physical hydrological processes such as the various storages and flows in the hydrological cycle, there is another way to generate runoff data based purely on statistics of historical data. Such analyses are also called time-series analyses. A hydrological time series is a set of hydrological observations such as rainfall, evaporation and river discharges that are arranged chronologically. Ideally, long series of data can be derived from actual observations but this is usually not the case and studies are sometimes carried out using synthetic time series in particular rainfall and streamflow series. Synthetic flow series are generally adopted in many studies for reservoir sizing, for determining the reliability of water supply and for reservoir operation studies. Natural hydrological processes are either stochastic or combination of deterministic and stochastic processes. Inflow and rainfall processes often exhibits marked seasonal variability, superposed with random deviations from the seasonal variation. Therefore, in a typical time-series analysis, the historical time series data is taken and attempt is made to break down the data into the deterministic component and the stochastic component. The deterministic component of a monthly flow for instance would be the seasonal cycle of monthly flows. Such models do not place emphasis of the physical processes. The catchment is considered a system that transform the system input (rainfall) to yield system output (runoff) and there is no necessity to understand the physical processes that transform rainfall to runoff and therefore such models are also known as black box models. The transformation function (the mathematical or statistical function that transforms the rainfall input to runoff output) is determined using using mathematical and statistical calibration. Examples of such models are:

o Simple and multiple regression, o transfer functions, o neural networks and o stochastic models

Regression Model The most simple relationship between two variables (e.g. yearly runoff, Y versus yearly rainfall, X) is a linear regression equation of the form:

Y=a+bX (2.5) where a, b are equation constants or regression coefficients. Multiple regression is a straightforward extension of simple linear regression. It is used for correlating one variable with many variables, for example yearly runoff, Y as a function of yearly rainfall, X1 and yearly evaporation, X2. Y=a+bX1+cX2 (2.6)

where a, b and c are equation constants or regression coefficients. Regression equations that have higher degree polynomials

Y=a+bX13+cX2 (2.7)


2-10 March 2009

The regression coefficients are usually chosen to minimize the sum of squares of error e Minimize e2 (2.8)

Where e = difference between observed Y, Yi and predicted values of Y, Yi Regression methods are conceptually simple and have been applied to infill data series. Although attempts have been made to improve the reliability and accuracy of hydrological data collection, there are still data gaps (periods of missing data) in DIDs hydrological records. Regression methods are often be used to infill the missing records, the missing monthly and yearly rainfall or discharge data.

Transfer or Transformation Functions

Transfer or transformation function seeks to convert rainfall series to runoff series. In many applications, it is the runoff data that is of main interest. Runoff data is more difficult to collect and more difficult to extrapolate to the point of interest. In DID, rainfall records extends to the 1940s while streamflow records began during the 1960s. In terms of numbers, there are more rainfall stations than streamflow stations. One way of generating runoff data from rainfall data (apart from the other conceptual models such as the Tank Model and Lumped Catchment Model described in previous sections) is the unit hydrograph method.

The unit hydrograph method is an application of the convolution integral procedure and is an example of a black-box transfer or transformation function (see Figure 2.9)

Transfer or transformation

function

Effective rainfall

hyetograph

Direct runoff Hydrograph

Figure 2.9 Unit Hydrograph(UH) as a Function that Transform Effective Rainfall to a Direct Runoff Hydrograph (DRH)

The unit hydrograph (UH) method defines for a catchment, a t-duration unit hydrograph. The t-duration UH describes the runoff distribution due to a unit effective rainfall input over a duration t. Figure 2.10 shows a 4-hour unit hydrograph due to a unit effective rainfall of 1 cm.

Unit

hydrograph


March 2009 2-11

Time (hours)

Direct runoff (m3/s)

Time (hours)


0 0.0 10 12.0 1 0.6 11 8.0 2 2.0 12 5.0 3 8.0 13 3.0 4 15.0 14 2.0 5 18.0 15 1.5 6 19.0 16 1.0 7 18.6 17 0.8 8 17.5 18 0.5 9 15.0 19 0.2

Figure 2.10 4-hour UH for 1 cm Effective Rain and Tabulated UH Ordinates

Application of UH to rainfall-runoff modelling involves convoluting the effective rainfall hyetograph with the unit hydrograph in accordance with the principle of proportionality and superposition to compute component runoff hydrographs and adding the component hydrographs to derive the final direct runoff hydrograph(DRH) The following example illustrates the concept of using the UH Method for rainfall-runoff modelling. The 4-hour UH of a catchment is as given in Figure 2.10. The objective is to derive the resulting DRH given a 4-hourly interval effective rainfall hyetograph as shown in Table 2.1.

Table 2.1 4-hourly Effective Rainfall Hyetograph

Time (hrs) 0 4 8 12 16 20 Effective Rain, ER (cm) 0 1 4 3 1 2

Note that as the UH is a 4-hour UH, the effective rainfall hyetographs applied has to be presented in the form of a 4-hourly interval hyetographs. Table 2.2 shows the computations involved in deriving the DRH. The computation process is known as convolution and is very similar to the process involved in time-area method. Figure 2.11 shows the convolution process graphically.


2-12 March 2009

Table 2.2 Derivation of the DRH by Convolution Process

Time (hour

s)


Effective Rain,

ER (cm)

Runoff generated by each 4-hour effective rain (ER) (m3/s)

Convoluted

Hydrograph (m3/s)

1 cm 4 cm 3 cm 1 cm 2 cm

0 0.0 0.0 0.0

1 0.6

1

0.6 0.6

2 2.0 2.0 2.0

3 8.0 8.0 8.0

4 15.0 15.0 0.0 15.0

5 18.0

4

18.0 2.4 20.4

6 19.0 19.0 8.0 27.0

7 18.6 18.6 32.0 50.6

8 17.5 17.5 60.0 0.0 77.5

9 15.0

3

15.0 72.0 1.8 88.8

10 12.0 12.0 76.0 6.0 94.0

11 8.0 8.0 74.4 24.0 106.4

12 5.0 5.0 70.0 45.0 0.0 120.0

13 3.0

1

3.0 60.0 54.0 0.6 117.6

14 2.0 2.0 48.0 57.0 2.0 109.0

15 1.5 1.5 32.0 55.8 8.0 97.3

16 1.0 1.0 20.0 52.5 15.0 0.0 88.5

17 0.8

2

0.8 12.0 45.0 18.0 1.2 77.0

18 0.5 0.5 8.0 36.0 19.0 4.0 67.5

19 0.2 0.2 6.0 24.0 18.6 16.0 64.8

20 0.0 0.0 4.0 15.0 17.5 30.0 66.5

21 3.2 9.0 15.0 36.0 63.2

22 2.0 6.0 12.0 38.0 58.0

23 0.8 4.5 8.0 37.2 50.5

24 0.0 3.0 5.0 35.0 43.0

25 2.4 3.0 30.0 35.4

26 1.5 2.0 24.0 27.5

27 0.6 1.5 16.0 18.1

28 0.0 1.0 10.0 11.0

29 0.8 6.0 6.8

30 0.5 4.0 4.5

31 0.2 3.0 3.2

32 0.0 2.0 2.0

33 1.6 1.6

34 1.0 1.0

35 0.4 0.4

36 0.0 0.0


March 2009 2-13

0

2

4

6

8

10

12

14

16

18

200.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0 4 8 12 16 20 24 28 32 36

Rai

nfal

l (cm

)

Run

off (

m3/

s)

Time (hours)Rain 1cm ER4 cm ER 3 cm ER1 cm ER 2 cm ERConvoluted Hydrograph

Figure 2.11 Convolution of UH of Figure 2.10 with Effective Rain (ER) Hyetograph

of Table 2.2 Artificial Neural Network (ANN)

Artificial Neural Networks (ANNs) are basically computing systems similar to biological neural networks. They are characterized by three components: Nodes Weights (connection strength) An activation (transfer) function

In an ANN, there are layers and at each layer there are nodes. A commonly used ANN is the three-layer feed-forward ANN. A typical three-layer feed-forward ANN, consists of a layer of input nodes, a single layer of hidden nodes, and a layer of output nodes, as shown in Figure 2.12. In the figure, i, j, k denote nodes inner layer, hidden layer and output layer, respectively. w is the weight of the nodes. Subscripts specify the connections between the nodes. For example, wij is the weight between nodes i and j. The term "feed-forward" means that a node connection only exists from a node in the input layer to other nodes in the hidden layer or from a node in the hidden layer to nodes in the output layer; and the nodes within a layer are not interconnected to each other.


2-14 March 2009

i

j

k

wij

wjk

Input Layer Hidden Layer Output Layer

Figure 2.12 A Typical Three-Layer Feed Forward ANN Each node in the input layer receives an input variable and passes it to the nodes in the hidden layer. In addition, a bias node, which is also a weight with a fixed input, 1.0, is usually added to the input layer and to the hidden layer. The nodes in the hidden layer and in the output layer are nonlinear nodes meaning the weights multiplied by inputs.

Activation function determines the response of a node to the total input it receives. The most commonly u ed sigmoid function given as, s

y=fx= 11+ exp-x

(2.9)

Sigmoid functions are used to bound the outputs of the weighted sum of all the incoming inputs x. Whatever the output of x becomes, the result will be limited to [0, 1] interval by sigmoid function in a nonlinear manner. Since, it is easy to take derivative of sigmoid function; it is more popular than any other functions. A log sig transfer functions is given Figure 2.13

Figure 2.13 Logsig Transfer Function

The process of fitting the network to the experimental data is called training. It consist of adjusting the weight associated with each connection (synapse) between neurons. Training and testing concept is similar to the idea of calibration, an integral part of most hydraulic modelling studies. The available data set is generally grouped into two parts, one for training and the other for testing.

The purpose of training is to determine the set of connection weights that cause the ANN to estimate outputs within the given tolerance limits to target values. The data set reserved for training is used for this purpose.


March 2009 2-15

This grouping of the complete data to be employed for training should contain sufficient patterns so that the network can learn the underlying relationship between input and output variables adequately. That is why the training part generally consists of most of the data available. In the literature, there is no specific rule while grouping total data into training and test divisions. It became standard for some years to train artificial neural networks by a method called Backpropagation. Backpropagation models, in a feedforward architecture, contain three components. They are an input layer, an output layer and at least one hidden layer. In backpropagation algorithm there are two main steps. The first step is a forward pass, which is also called as activation phase. In that step, inputs are processed to reach the output layer through the network. After the error is computed, a second step starts backward through the network, which is also called as error backpropagation. During the training phase, an error value, usually mean square error (MSE) is calculated between the desired output and the actual output. The MSE is then propagated backwards to the input layer and the connection weights between the layers are readjusted. After the weights have been adjusted and the hidden layer nodes have generated an output result, the error value is again re-determined. If the error has not reached, which is usually defined by a particular iteration number, the error will then again be propagated backwards to the input layer. This procedure continues until the model has finally reached to the predetermined tolerance limit. The weights in backpropagation algorithm are adjusted according to the direction in which the performance function, in this study MSE, decreases rapidly. Although the function decreases most rapidly along the steepest descent direction (negative of the gradient), it may not produce the fastest convergence. A search is performed along conjugate directions, which produces generally faster convergence than steepest descent directions The number of input, output, and hidden layer nodes depend upon the problem being studied. If the number of nodes in the hidden layer is small, the network may not have sufficient degrees of freedom to learn the process correctly. If the number is too high, the training will take a long time and the network may sometimes overfit the data. Stochastic Models Stochastic models are used in hydrology for time series data generation often for water resources simulation studies. The performance of a proposed water resources system, often involving a combination of direct river extraction, dam storage and perhaps diversions from another catchment is assessed by simulating the flows and storages in the proposed system using long term hydrological time series. However, in many cases, the observed records are short. In Malaysia, many areas do have about 20 years of streamflow records available. Based on statistics of available time series records which are often too short or fragmented to be useful, stochastic models are applied to generate longer hydrological time series with statistics that preserved the statistics of the available time series. There are a number of commonly used stochastic models such as the autoregressive (AR) and the Periodic Autoregressive (PAR) models The objective of stochastic models is to generate hydrological time series, which preserve the statistical properties of the original data at more than one time level (typically annual and seasonal). For instance, generated monthly inflows must reproduce the basic statistics (e.g., mean, standard deviation and skewness coefficient) of observed monthly flow data. Further, they should represent adequately the statistics of the annual historical series. The autoregressive model assumes that there is persistence in successive hydrological values e.g. rainy days occurs in a stretch or dry weather persists for many days. Therefore a simple approach to predicting river flow is to correlate it with flows 1 day before (lagged by 1 day).


2-16 March 2009

An example of a simple first order AR model for predicting flow xt is as follows: Xt=Xm+ k Xt-k-Xm + e (2.10)

Where xm = mean x: xt-k = the k time step lag time Q:

k = the lag k serial correlation coefficient and e = a random error term

The serial correlation coefficient is given by:

t,t-1=

t,t-1

12 t-1

2 (2.11)

Where t = (xt xm) and t-k = (xt-k xm)

where k = 0, 1, 2, is the time lag. The zero lag coefficient r0 is equal to one, and higher lag coefficients generally damp towards small values with increasing lag. The autocorrelation coefficients can be plotted versus lag in a plot known as a correlogram.

Besides flows and rainfall, the AR model is also used to model residual errors in flood forecasts. For example, adjustments to flood forecasts made using the DIDs Tank Model for Sg Kelantan is adjusted using the AR Model of the residual errors.

The Thomas-Fiering model has been widely used for data generation and forecasting of hydrologic variables. Thomas and Fierings (1962) early model and its periodic autoregressive (PAR) and moving average (MA) extensions generate monthly or seasonal flow directly. An example of a Thomas-Fiering Model for predicting inflow qt to the reservoirs is as follows:

qt=t+t-1,t tt-1

(qt-1-t-1)+tt1-t-1,t

2 (2.12)

where , and are the estimated lag-one autocorrelation, mean and standard deviation associated with the inflows to the reservoirs. 2.3 HYDRAULIC MODELS

The other popularly used models in DID are hydraulic models, in particular open channel flow (OCF) models. Important in the understanding of hydraulics of open channel flow are specific energy concepts and the various types of open channel flow such as uniform flow versus non-uniform flow, steady flow versus unsteady flow. 2.3.1 Specific Energy Understanding energy concepts is useful in explaining many open channel flow phenomena. The total energy content of a unit volume of fluid is usually expressed in the form of Bernoullis Equation: H = z + d + V2/2g which comprises elevation, pressure, and velocity heads respectively (see Figure 2.14)


March 2009 2-17

Figure 2.14 Energy along a Streamline in an Open Channel Flow

Consider the streamline at the flow surface (see Figure 2.15). z is the elevation of the bottom streamline, flow depth is y, the elevation of the surface streamline is z + y. At the flow surface gauge pressure is zero, so Bernoulli's Equation for this streamline is z + y + V2/2g = C. For the bottom streamline, the gauge pressure p = y and p/ = y. Bernoulli's equation is z + y + V2/2g = C. C, the energy per unit weight, has the same value at any depth. y + V2/2g is called the specific energy E, and is the energy per unit weight with reference to the stream bed.

Figure 2.15 Specific Energy

For a rectangular channel of width b, area of flow A = by and Q = AV, therefore E = y + Q2/2gA2. E = y + q2/2gy2, expressing E as a function of q(discharge per unit width) and the depth y, or q = y[2g(E - y)], expressing q as a function of E and y.


2-18 March 2009

Figure 2.16 Depth-Discharge Curve for Constant E

The curve of q as a function of y for a constant specific energy E is plotted (see Figure 2.16). From this curve note that q has a maximum value qm (the critical flow). The depth when q=qm is the critical depth yc and yc can be found by differentiating q with respect to y and setting the derivative equal to zero. The result is yc = 2E/3. The critical flow qm = (gyc3) i and critical velocity Vc = qc/yc. When y > yc, the velocity of flow V < Vc : flow is subcritical. When y < yc, V > Vc: flow is supercritical. For a discharge q, flow can be in either subcritical or super critical region (e.g. when q/qm =0.6 flow can exist in a sub critical or b supercritical status see Figure 2.16) This diagram explains the behavior of flow when there is a constriction in the channel. If the flow is constricted such that q/qm increases from 0.6 to 0.8 (i.e. from line ac to line bd in Figure 2.16), the flow depth decreases when flow is subcritical, while in supercritical flow the depth increases. y/yc of a rectangular channel, for a constant discharge q can be plotted as a function of E (see Figure 2.17). The critical depth yc = (q2/g)1/3. If x = y/yc, then E/yc = x + 1/2x2. Critical depth corresponds to y/yc = 1, for which E/yc = 3/2. At point a flow is subcritical. Line segment hf represents y/yc, while line segment fa represents the kinetic energy V2/2gyc. Note that the specific energy E is a minimum at the critical depth Yc. This minimum value depends on the discharge q. If there is a hump in the bed of the channel, specific energy will drop from E1 to E2. The reduction in specifiv energy = height of the hump. If the flow is subcritical, we see that depth of flow, y will decrease slightly from point a to point b. If the flow is supercritical, y will increase slightly from point d to point e. Note the similar response during a lateral constriction. If the hump is high enough, the flow may become critical at c. The specific energy cannot decrease further, and any further raising of the hump will result in an increase in upstream flow level. This phenomena is also known as choking.


March 2009 2-19

Figure 2.17 Specific Energy Diagram

2.3.2 Modelling Various Types of Open Channel Flow The physics governing open channel flow hydraulic computations are well established and the problem is usually the problem of configuring a representative hydraulic model and simplifying the computation and the data requirements. However, the processes in erosion and sedimentation aspect of hydraulic computation or fluvial hydraulics are too complicated to formulate and hence the reliance on empirical equations in the area of erosion and sedimentation and moveable bed hydraulics. Hydraulic computations and hence models can be classified as follows:

Steady flow versus unsteady flow

Steady flow would be flows that are not changing with time. Example of flow conditions that can be assumed steady would be flow in an irrigation canal system and the normal flow and low flow in rivers or drains. A flood flow is essentially unsteady flow but simplifying the analysis to a steady peak discharge flow greatly reduces the computational effort and therefore this simplified analysis is often applied. But it depends on the situation being studied. If the interest is in designing the size of channel to cope with a flood then applying a steady state flood flow at peak discharge in the hydraulic analyses would yield conservative results in terms of flood levels and required channel size.

Unsteady flow computations would be important in the design of storage ponds, tidal control gates and pumps where the variation in discharge with time cannot be ignored. (See figure 2.18).


2-20 March 2009

Steady Flow of 9.5m3/s

Unsteady Flow Hydrograph Rising to a Peak Flow of 9.5m3/s

0

2

4

6

8

10

12

1 6 11 16 21

Discharge

Q(m

3/s)

Time(hrs)

0

2

4

6

8

10

12

1 6 11 16 21

Discharge

Q(m

3/s)

Time(hrs)

Figure 2.18 Steady Flow versus Unsteady Flow Hydrographs at a Location

Uniform flow (UF) versus non-uniform flow (NUF) Uniform flow (UF) occurs when the flow values and flow sections do not vary with distance. (See figure 2.19). An example of uniform flow would be flow in a channel of the same size, same roughness and same slope and flow rate is the same all along the channel. If the assumption is uniform and steady flow then Mannings Equation can be applied and this is the simplest open channel flow computation. Again flow in a regular section irrigation canal and normal and low flow in regular section drains can be considered uniform flow.

Figure 2.19 Uniform Flow

Isometric View Longitudinal Section

(No change in cross-section, slope or flow condition results in a condition that can be

approximated using uniform flow equations)

If there is change in the channel flow section due to presence of a bridge or culvert or there is a weir or an irrigation regulator structure then flow becomes non-uniform at the area in the vicinity of the changing flow sections. (See figure 2.20). In natural rivers the flow is not uniform because natural channel sections are not uniform and vary from place to place. Backwater profiles due to weirs, culverts and constriction can be computed using the standard step method or the direct step method. A software designed to handle non-uniform steady flow analyses is Hec-RAS.


March 2009 2-21

NUF

UF

Non-uniform flow flow occurs if changes in flow conditions occur such as presence of a weir,

change in channel slope, cross-section, roughness, discharge,etc.

Figure 2.20 Non-Uniform Flow

Gradually varied flow (GVF) versus rapidly varied flow (RVF)

Most non-uniform flow encountered in design and analyses are gradually varied flow in the sense that the surface water profile varies gradually and therefore the equation valid for such flows are simplified. Usually the flow becomes rapidly varied at hydraulic jumps and at drawdowns just upstream of an overflow weir and there are hydraulic jump equations and weir overflow equation to handle such situations. A typical situation where uniform flow (UF), gradually varied flow (GVF) and rapidly varied flow occurs is shown in figure 2.21.

UF GVF RVF GVF UF

Figure 2.21 A Commonly Encountered UF, GVF and RVF Flow Condition

The shape of a GVF is governed by the flow conditions with respect to the bed slope, So which is classified based on the normal flow depth Yo and critical depth Yc and critical slope Sc. (See figure 2.22).

Bed slope S0 bed slope is classified as follows: Steep : yo < yc or so>sc Critical : yo = yc or so= sc Mild : yo > yc or so< sc Horizontal : S0 = 0 Adverse : S0 < 0


2-22 March 2009

Figure 2.22 Classification of GVF Slopes

The zone where the initial flow depth occurs (see figure 2.23): Zone 1 : y > yo

The space above both critical and normal depth Zone 2 : yo < y < yc

The region between the normal and critical depth Zone 3 : y < yc

The zone above the bed but below both critical and normal depth

Figure 2.23 Categorising Initial Depth Many hydraulic texts gives the various shapes of the surface water profiles of open channel flows classifying the curves as M1, M2 or M3 with M signifying mild slope and the numeric after M the initial depth zone and S1,S2,S3 for steep slope profiles and so on. The shapes of the various water surface profiles are as shown in figure 2.24.

Yc

Yn

Critical Depth

Normal Depth

Bed Level

Zone 3

Zone 2

Zone 1

Steep

Critical Mild

S

CM

AH

Horizontal Adverse


March 2009 2-23

Figure 2.24 The Classification and Shapes of Various GVF Water Surface Profiles As mentioned above, it is common practice to reduce an open channel flow (OCF) problem to the simplest possible to allow for easy analyses and to avoid being lost in complex analyses thereby losing the main focus of the design process. The simplest OCF condition would be uniform flow whereby Mannings equation can be applied. However, in reality it is not possible to reduce all OCF to uniform flow. There are drops, weirs, sluice gates, etc and the flow in the vicinity of these structures will undergo a transition phase where the flow is essentially a GVF. The transitions can be easily determined if one can classify the curves according to the slope and the initial flow condition. Examples of transitions regularly encountered are presented in figure 2.25.


2-24 March 2009

Figure 2.25 Transitions Encountered in Open Channel Flow Analyses

The above approach towards an open channel flow problem is effective when analyzing urban drainage and irrigation conveyance problems where channel are for most part regular and the assumption of uniform flow is justified. Computations are simple and can be handled with simple spreadsheet programs such as MSExcel. When modelling natural rivers and streams the flow condition become very non-uniform then the complexity of the computations becomes too difficult to handle and most would rely on specially written softwares to handle the computations. Hec-RAS a river analysis software developed by the US Army Corps of Engineers would be one of the most popular software used. One of the outputs of Hec-RAs Analyses is Flood profiles and Figure 2.26 shows the flood profiles obtained for Sg Linggi.


March 2009 2-25

Figure 2.26 Sg Linggi Flood Profiles Output by the Hec-RAS Software

One dimensional unsteady flow, two dimensional, quasi-two dimensional flow

Flow confined within rivers are considered one-dimensional flows whereas flows that overspills the flood plain and moves downstream via pathways other than the river is essentially two dimensional. One dimensional flow, steady and uniform would be the easiest to compute (Mannings Equation can be applied). One dimensional but non-uniform flow would require backwater computations which are more complicated but there are available softwares such as Hec-RAS which can easily handle this type of flows. When flow becomes unsteady then the computational and modelling effort becomes more complicated. In a very hydrodynamic flow condition such as flow affected by tides in a river with very mild gradient then the full 1-dimensional hydrodynamic equation which is the Saint Venant Equation would apply.

The St Venant Equation comprises the momentum equation given by:

Qt

+ (Q2/A)

x+gA( h

x-So+Sf)=0 (2.13)

And the continuity Equation given by:

Qx

+ At

=0 (2.14)

This equation contains partial differential terms and cannot be solved analytically. The solution of the St Venant Equation requires a numerical formulation that approximates the Equation. A popular numerical method adopted for solving the St Venants Equation is the finite difference method. However there are various finite difference schemes that could be formulated. In the finite difference method, computations are carried out over a gridded x-t plane, x being the incremental distance along the stream and t the time step (see Figure 2.27)


2-26 March 2009

Computation progresses from one timeline to the next

0 0

Figure 2.27 Gridded Computational x-t (Distance-Time) Plane for

Finite Difference Computation of the Saint Venant Equation The gridded computation plane comprises incremental time lines (horizontal lines) starting with time line 0 where the initial conditions are known at every points along time line 0. The finite difference representation of the Saint Venant Equation presents the spatial and temporal derivatives in terms of unknown variables in the current time line 1 and known variables in the preceding time line 0. The finite difference equations are solved for time line 1 and computation moves towards the next time line 2 and so on. The finite difference scheme could be explicit or implicit. In the explicit scheme, the unknown values are solved sequentially for each distance point from one point to the next along a time line. In an implicit scheme, the unknown values of each distance point along a time line are expressed as unknown values of previous and next distance points and the unknown values are solved simultaneously. The equations of explicit schemes are easier to write and solve but has more instability and accuracy problems while the implicit scheme equations are more complex to handle and would require more computational power. Detail presentation of the various explicit and implicit finite difference schemes can be obtained from Chow et. Al. (1988) The EXTRAN software of EPA uses the explicit finite difference scheme. The implicit finite difference scheme is more stable and accurate but its formulation and solution is complex and computationally it requires solution of large matrices and hence more demand on computer memory and time. MIKE 11, Hec-RAS uses the implicit finite difference scheme in solving th St Venants equation. Models that cater for 1-dimensional unsteady flow are Mike 11, InfoWorks RS, Hec-RAS and EXTRAN.


March 2009 2-27

However, if the slope of the river is steep then a diffusion wave equation may be applicable. This would greatly simplify the computation effort. In a two dimensional model the model complexity and computation effort is even greater. There are models such as Mike 21 and InfoWork RS that can handle 2 dimensional unsteady flow modelling and of course given the complexity of the model, the data requirements such as the survey of the terrain, the roughness would be substantial. To take care of overflows into flood plain, quasi 2D flow modelling is often adopted. MIKE11 and InfoWorksRS have been configured as quasi-2D flow models in an attempt to get a more representative flow modelling. In coastal hydraulics 2-Dimensional and even 3-dimensional flows may have to be considered.

Fixed bed model versus moveable bed models In many open channel analyse, the assumption is that the river channel section geometry is fixed. Hence they are call fixed bed model. In actual flow condition especially during a flood, the river scours and silts up dynamically as the flood flow passes through the section. Hence the need to look at moveable bed models.

Alluvial rivers/channels have been primarily self-regulating and adjust their characteristics in response to any change or perturbation in the environment for millennium. Such changes as a result of perennial or flood discharges or human activities encroaching the river domain distort the natural quasi-equilibrium of a river; therefore, in the process of restoring the equilibrium, the river will adjust to the new conditions by changing its slope, roughness, bed-material size (non cohesive), cross sectional shape, or meandering pattern as depicted in the Lane relationship as shown below (see Figure 2.28)

QS Qd (2.15)

Q = water or flow discharge rate S = energy slope Qs = sediment discharge rate ds = sediment size

Figure 2.28 Lane Relationship on River Scouring and Deposition

Within the limited scope of the constraints, any change in one of the above characteristics may adjust the other variables as the river attempts to strike a balance between its ability to transport sediment while maintaining the equilibrium or sediment balance.

The design engineers interest in the fluvial responses is generally focused on the ability to predict how the river flow and the water surface/level will change in both short and long terms if the existing stable or equilibrium situations of the river system or network are disturbed.


2-28 March 2009

Examples of these types of disturbances are, building a control structure across the river width, river training works, channelisation, and dam construction in the headwater region of the watershed. Modelling technique is commonly used to address the effect of the sediment imbalance mechanisms in a riverine system. On the other hand, physical modelling will be much more expensive to carry out notwithstanding the inability to confident overcome the scaling effects when reducing the nature to a simple in house model. The basic description of water and sediment interaction and flow in a riverine system comprises of four essential components, (1) conservation of water, (2) conservation of momentum, (3) conservation of sediment and (4) sediment transport relationships. These are expressed in the forms of mathematical equations in the form of partial differential equations (PDEs). Analytical solutions to the PDEs are generally not found for most of the initial and boundary conditions. Simplification of the models is generally acceptable in light of the scarcity of hydrologic, hydraulics, geometrical, and sediment information. Quasi-steady state solutions are generally obtained after some assumptions and simplifications. 2.4 PHYSICAL MODELS Physical model is a prediction device or tool or representation that a full size (prototype) phenomenon in hydraulic engineering is reproduced at a smaller scale normally in a controlled laboratory setting. The application of physical models in hydraulic design is rather common nowadays primarily with increased sophistications and precisions in measuring techniques and instrumentations. It is an undeniable fact that almost all major hydraulic structure designs in Malaysia, such as reservoir spillways, intake structures, river control structures, harbours, jetties, detention ponds, etc have been design with the aids of commissioned physical model studies/undertakings in tandem. It is used as a compliment to mathematical modelling tools which are almost indispensable design aids and tools in engineering practices in Malaysia. 2.4.1 Purposes and Objectives of Physical Modelling The purpose of a physical model study is to verify the nature of the flow and to predict performance of the structure if they are built to a full scale or prototype. Hydraulic phenomena in nature are too complex in configuration to be described and represented by even rigorous and sophisticated mathematical techniques and formulae, lest to say the confident detailed design of the hydraulic structure. It is also used to model the local effects of the structures on the river environments. The raison dtre of the physical models is to obtain sufficient and optimal information necessary to fulfill the objective for an efficient and satisfactory engineering design. Therefore, they are carried out to increase or lend confidence in design. Furthermore, they are also used to diagnose and solve problems with the existing hydraulic structures and equipments. Testing and commission of a physically scaled model can always eliminate or reduce design uncertainties arising from local effects and/or site-specific conditions, untried arrangements, structures of unprecedented magnitude, and complicated natural flow conditions. Studies of such nature can also assist both planners and designers on minimize the risk of costly repairs or inefficient operation in later years of operation. Projects that require millions to be invested must be optimally designed for specific purposes and at the same they must be bringing both tangible and intangible benefits to the investors as well.


March 2009 2-29

In addition to this, model studies are also often required by hydraulic equipment suppliers such as pumps, valves, fittings, etc in order to verify good inflow conditions for optimal performance. The physical model study in river engineering and management includes major spillways and stilling basins, hydropower/water supply/irrigation intakes, drop structures, gates, intakes, sedimentation, and river navigation, to mention a few. Most of the time both physical and numerical modelling techniques are carried out in tandem for verification and validation of the hydraulic design purposes. 2.4.2 Theoretical Consideration In a physical model, the flow characteristics are deemed similar to the proto type if the model exhibits similarity in (1) geometry, (2) motion, and (3) force or dynamics. These similitudes form the basis of reducing or scaling the proto type to model in hydraulic engineering practices (Chanson, 1999). Geometrical similarity:

Length:Lx-lplm

-dpdm

-HpHm

(2.16) Geometrical properties such as length, area, and volume are parameters that are derived from geometrical similitude. Kinematic similarity:

Velocity: Vx-VpVm

-(V1)p(V1)m

-(V2)p(V2)m

(2.17)

Dynamic similarity:

Force: Fx-F1pF1m

-F2pF2m

volume 7_engineering modelling

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