In recent old ages, inundation flood theoretical accounts become of import progressively in both inundation prediction and harm appraisal as it provides the footing for the determination devising of inundation hazard direction. Such theoretical accounts are chiefly used to imitate inundation flood extent and deepnesss at different subdivisions of the studied inundation rivers. With their aid, hydrologists are able to analyze and analyze the hydrologic systems of inundations good.

This undertaking was initiated to further understand the inundation theoretical account Lisflood-FP planetary clime alteration and predict the future strength of precipitation and temperature in Singapore. This will let applied scientists and other professionals to estimate the strength of the hereafter conditions and behavior necessary plants to forestall unwanted event like deluging, from go oning.

## Background

Floods are the most destructive and repeating natural catastrophes all over the universe and a broad scope of the universe population and their belongings is at the hazard of deluging. Therefore, one of the important undertakings in quantifying the harm appraisal of the inundation events is that finding the dependable anticipation of possible extent and H2O deepness of inundation flood. In General, inundation flood postulations are used to serve the decision-making in design urban planning in future. The rule of postulation are derived from individual realization of numerical hydraulic theoretical accounts and applied on a forward-modeling model ( BatesandDe Roo, 2000 ) . Despite standardization surveies are afoot to find a individual parametric quantity set that optimises the theoretical account tantrum to some observed informations, the assurance degree of the predicted consequences becomes a major job for determination shapers.

If the uncertainness is considered in footings of input parametric quantities ( e.g. geographical information, hydrological informations, fluid mechanicss parametric quantities, and boundary conditions ) , merely a little part of a typical issue might be regarded as certain or deterministic. The remainder necessarily contains uncertainness that arises from the complexness of the system, deficiency of cognition or human-induced mistakes.

In old surveies, the uncertainness beginnings associated with the inundation flood patterning have been generalised into three classs, such as input informations, fluid mechanicss parametric quantities and theoretical account constructions ( Bales and Wagner, 2009 ) . Different uncertainness techniques ( e.g. Generalized Likelihood Uncertainty Estimation ) have been applied into the inundation flood patterning to measure the uncertainness derived from one or multiple factors. However, limited surveies have been farther discussed the sensitiveness of uncertainness beginnings like raggedness coefficients. Furthermore, the uncertainness analysis methods applied in old surveies relied heal

## Objective and Scope

This study is a write up on the research of Final Year Project, Flood Inundation Modeling under stochastic uncertainness, had been carried on by the writer for the last 10 months. The aim of this undertaking is to consistently analyze and analyze the impact or effects of uncertainnesss associated with parametric quantity of roughness coefficient in inundation flood mold, which is Lisflood-FP Modeling. The predicted informations can be used for the postulation of future inundation flood and harm appraisal under hazard analysis.

In this study, the following preliminary survey plants will be covered.

To reexamine the unidimensional ( 1-D ) and planar ( 2-D ) hydraulic theoretical accounts for flood flood mold, and to reexamine the uncertainness beginnings associated with the inundation flood patterning procedure and the available uncertainness analysis methods.

To carry on a Monte Carlo simulation to measure the extension of uncertainness associated with raggedness coefficients to the consequences of flood flood mold, in footings of H2O deepnesss and flood extent.

The range of this undertaking includes a comprehensive literature reappraisal on inundation flood patterning procedure and acknowledgment of the uncertainness effects from assorted beginnings. On the footing of literature reappraisal, the impact of the uncertainness of raggedness coefficients is to be analysed a conjectural survey instance. A decision will be made harmonizing to the preliminary information analysis and the thoughts for hereafters work will be shaped.

## Methodology ( GLUE )

Annual studies of companies and information from public sphere were reviewed extensively to place current GHG emanations decrease steps that are adopted by transporting companies. Academic research documents and studies from bureaus such as IMO, DNV and World Shipping Council ( WSC ) were examined to garner information on the possible and effectivity of the steps and to place critical issues. Primary research was conducted through a two-pronged attack of studies and interviews. Survey inquiries were designed in conformity to the aim of this survey and the questionnaires were posted to container liner transportation companies, both with and without offices in Singapore. A little figure of study responses were anticipated and hence the studies were used to capture land information. The interviews with governmental bureau, categorization societies and selected transportation companies serve as the 2nd pillar of the primary information aggregation in this survey.

## Report Structure

Figure 1. Report structureThis study includes 5 chapters as shown in Mistake: Reference beginning non found. A list of abbreviations and a glossary are

besides included.

This study consists of 6 chapters shown in Figure 1.1. Chapter 1 is a brief debut of background and range of this survey. Chapter 2 reviews the hydraulic theoretical accounts used for flood flood mold, the associated uncertainness beginnings and the uncertainness analysis methods. In Chapter 3, a 2-D hydraulic theoretical account is established for a survey instance adapted from a existent universe river system, where the theoretical account constellation and simulation consequences are introduced. Chapter 4 and Chapter 5 discuss the effects of the uncertainness of the raggedness coefficients on inundation flood patterning. In Chapter 6, a sum-up is made and the thoughts for future surveies are presented.

## Chapter 2 LITERATURE REVIEWS

The information acquired through assorted literature reappraisals are discussed in this chapter to understand the background of inundations and inundation jeopardies, every bit good as the importance of inundation flood patterning. On the other manus, the 1-D/2-D hydrodynamic theoretical accounts for imitating both channel and flood plain flows were reviewed severally. Subsequently, an overview of this chapter is provided.

## 2.1 Introduction

2.1.1 Floods

Throughout the long human history, inundations are the most often happening natural hydrological phenomena, which consist of the hereafters such as H2O deepness, flow speed, and temporal and spacial kineticss. The regular-magnitude inundations occur every twelvemonth at the expected watercourse flow scope. It is good to supply fertilise dirt with foods, transport big measures of deposit and sedimentation on the flood plain, and clean-up a river with any dead contaminates. However, some inundations become catastrophes due to the utmost events, which happen all of a sudden without any warning, such as storm, dam interruption, storm rush and tsunami. As a consequence, their important impacts cause imponderable harm on human society and ecosystems, peculiarly in footings of life loss and belongings harm.

Flood can be defined as H2O organic structure rises to overrun the lands where is non usually submerged with the position of deluging wave promotion ( Ward, 1978 ) . This definition includes two chief inundation types, viz. river inundations and costal inundations. River inundations are largely originating from overly or long-drawn-out rainfall, therefore the river discharge flow transcending the watercourse channels capacity and dominating the Bankss and embankments. Particularly in urban country, inundations may besides take topographic point at the sewerage drains when the heavy storms H2O surcharged in and overflow the drains. In add-on, some natural or man-induced calamity could ensue in the H2O degree is risen up all of a sudden and so overrun the river bank or dike.

The grounds why the costal inundations appear are normally originated from the terrible cyclonal conditions systems in footings of a combination of high tides, elevated sea degree and storm rushs with big moving ridges. The flood at coastal countries may consequences from the overflowing as the H2O degree exceeds the crest degree of defence, or from the overtopping as the moving ridges run up and interrupt over the defence, or defence construction failure itself ( Reeve and Burgess, 1994 ) . Furthermore, tsunami can do long ocean moving ridges due to the great temblor and ensuing in coastal inundations.

2.1.2 The inundation jeopardy

Flood jeopardy is defined that those inundations generate pop-up menaces to the life and belongingss of human existences at the flood-prone countries where adult male had encroached into. The hazard degree is validated by a combination of physical exposure and human exposure to the inundation flood procedure.

Floods have been regarded as the top of the most destructive jeopardies from everlasting. In China, inundations account for approximately 1/3 of all the natural calamities and responsible for 30 % of the overall economic losingss ( Cheng, 2009 ) . Furthermore, some south-east Asiatic states are flood-prone countries, such as Indonesia, Thailand, and Myanmar, which are bearing the catastrophes from the frequent river and coastal inundations. In 2004, the mega-quake, which exceeds magnitude of 9.0, induced a series of destructive tsunamis with the highest moving ridge of 30 metres along the seashores surrounding the Indian Ocean. There were over 230,000 victims lost their lives in around 14 states. Hence, Indonesia was the hardest hit, followed by Sri Lanka, India, and Thailand ( Paris et al. , 2007 ) . Furthermore, the tropical cyclone ‘Nargis ‘ happened on 2nd May, 2008 attacked the Southwest Coast of Myanmar. There were 24 million people been affected and about 50,000 to 100,000 people been killed ( Kenneth, 2008 ) .

However, deluging is non merely the critical issue in Asiatic, but besides in the full universe. In 1927, the United States met the most annihilating implosion therapy of the Mississippi River in American history. The levee system was broken out and submerged 27,000 km2. Because of 1000000s of population life along the Mississippi River, it led over 400 million US dollars in loss and 246 human deceases ( Barry, 1998 ) . In Europe, Netherlands had affected by the critical river inundations in the past old ages since the most countries are below the sea degree. The worst inundation catastrophe happened in 1953 killed 1,835 people, covered about 200,000 hectares of land, destroyed 3,000 household houses and 200 farms, and drowned 47,000 caputs of cowss ( Lamb and Knud, 1991 ) .

The facts mentioned above proven that the planetary implosion therapy direction is progressively critical to protect 1000000s of world-wide population from the terrible menace. However, because of the high costs and built-in uncertainnesss, it is impossible and unsustainable to construct up the absolute inundation protection system, but it can be managed to cut down the jeopardy to lives and belongings by the most cost-efficient steps. Therefore, inundation flood theoretical accounts become the most utile predictive tools which are used to measure and analyze the inundation jeopardies, every bit good as to better and extenuate the inundation hazard direction.

2.1.3 The Importance of inundation flood patterning

From the positions of physical procedures and anthropogenetic influence, the flood plain is a dynamic flow environment. Since it is much hard to manage the confliction between maximizing benefit-over-cost ratio and understating the human impact, the application of flood patterning becomes the most likely moderate attack for flood direction scheme. Actually, the concluding aim of inundation flood surveies could be minimise susceptibleness and exposure to loss in both economic system and human lives facets ( Parker, 1995 ) . Therefore, it is necessary to utilize flood flood theoretical accounts to imitate and foretell the possible impacts of flood plain development.

The rule of inundation flood theoretical accounts is to let the upstream inundation flow to dispatch straight to the downstream inundation extent. Those theoretical accounts become much valuable and helpful inundation predictive tools which are able to use in different existent and practical scenarios for analysis. In comparing with those traditional statistical theoretical accounts, which are harmonizing to all the numerical informations observations of past inundation events, the largest advantages of physically-based flood theoretical accounts are their capableness of spacial and temporal variables in footings of discharge, H2O degree, speed, flow continuance and flood extent, on the processive inundation events. Meanwhile, they besides support the hydro-system operation, inundation warning, hazard quantification and determination devising for the design and planning of inundation extenuation steps.

Besides, the inundation hazard maps are able to be determined on the footing of the inundation flood patterning consequences. They are inactive planar maps bespeaking the inundation chance with inundation deepness and extents, which is normally generated through flood uncertainness quantification techniques, i.e. Monte Carlo Simulation. They are widely adopted by authorities and insurance company to define countries of land at high hazard and steer the investing and exigency response schemes.

## 2.2 LISFLOOD-FP – Flood Inundation Model

A inundation flood theoretical account is an intergraded inundation simulation model-chain which includes an appraisal of stochastic rainfall, a simulation of rainfall-runoff and an flood theoretical account of inundation development ( McMillan and Brasington, 2008 ) . For stochastic rainfall appraisal of certain catchment, harmonizing to the available precipitation records, a long man-made rainfall series could be created. Hereafter, these series are applied into a rainfall-runoff theoretical account to bring forth the corresponding discharge appraisal series. And the appraisals of discharge are imported into a 2-D hydrodynamic theoretical account, which utilizes high-resolution lift informations to enable urban flood plain mold at the smallest graduated tables and paves the manner for extra faculties for exposure and harm appraisal. Finally, the inundation flood theoretical account is expected to run within a proved uncertainness appraisal model and later to compare with the real-world scenarios for theoretical account standardization and let expressed uncertainnesss analysis.

LISFLOOD-FP theoretical account is one of the most popular inundation flood theoretical accounts all over the universe ( Bates and De Roo, 2000 ) . It is a conjugate 1D/2D hydraulic theoretical account on the footing of a raster grid. LISFLOOD-FP theoretical account treats the implosion therapy as an intelligent volume-filling procedure from the position of hydraulic rules by incarnating the cardinal physical impressions of mass preservation and hydraulic connectivity.

2.2.1Principles of LISFLOOD-FP Model

2.2.1.1Model Structure and Concepts

The basic constituents of the LISFLOOD-FP theoretical account is a raster Digital Elevation Model ( DEM ) ( Bates and De Roo, 2000 ) of declaration and truth sufi¬?cient to place surface raggedness for both the channel ( location and incline ) and those elements of the i¬‚oodplain topography ( butchs, embankments, depressions and former channels ) considered necessary to i¬‚ood flood anticipation.

A i¬‚ood consists of a big, low amplitude moving ridge propagating down vale ( Bates and De Roo, 2000 ) . When the bankful i¬‚ow deepness is reached, H2O Michigans to be contained merely in the chief river channel and H2O spills onto next shallow gradient i¬‚oodplains. These i¬‚oodplains act either as impermanent shops for this H2O or extra paths for i¬‚ow conveyance.

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Figure 1 Conceptual theoretical account of the LISFLOOD-FP inundation flood theoretical account ( Wilson, 2003a ; 2003b )

2.2.1.2 Premises for LISFLOOD-FP Model

In order to plan a physical theoretical account imitating the inundation development and to merely the numerical calculation, the premises are stated as followerss:

The flow within channel can be represented by the kinematic moving ridge estimates.

The channel is assumed to be so broad and shallow that the wetted margin is approximated by the channel breadth.

The inundation flow can be bit by bit varied.

Both In-channel and Out-of-channel implosion therapy flow are treated as raster grids by utilizing a series of storage discretised cells.

Flow between storage cells can be calculated utilizing analytical uniform flow expressions, i.e. the Saint-Venant and Manning equations.

There is no exchange of impulse between chief channel and flood plain flows, merely mass is exchanged.

2.2.2 In-Channel Flow

The hydraulic theoretical accounts consist of two chief procedures, stand foring the flow within the channel ( In-channel Flow ) and flux on the flood plain ( Out-of-channel Flow ) . But we ignore the effects at the channel-i¬‚oodplain interface development of intense shear beds leads to a strongly disruptive and 3-dimensional i¬‚ow i¬?eld. In this undertaking, one of the aims is to quantify the uncertainness associated with the flood procedure.

In-channel Flow is defined that the channel flow is below bankful deepness. Therefore, the flow procedure is represented by utilizing a classical unidimensional hydraulic everyday attack ( 1-D attack ) , which is described in footings of a simplification of the full unidimensional St. Venant equation system ( Knight and Shiono, 1996 ) , which leads to a kinematic moving ridge estimate obtained by extinguishing local acceleration, convective acceleration and force per unit area footings in the impulse equation.

2.2.2.1 Saint-Venant Equations

Due to simpleness of calculation and easiness of parameterization, the unidimensional ( 1-D ) Saint-Venant equations have been the most widely adopted attack for unsteady unfastened channel flow. The partial differential Saint-Venant equations comprise the continuity and impulse equations under the undermentioned premises ( Chow et al. 1988 ) :

Flow is 1-D, and deepness and speed vary merely in the longitudinal way of the channel.

Velocity is changeless, and the H2O surface is horizontal across, any subdivision perpendicular to the longitudinal axis.

Flow varies bit by bit along the channel so that hydrostatic force per unit area prevails and perpendicular accelerations can be neglected.

The longitudinal axis of the channel is approximated as a consecutive line.

The bottom incline of the channel is little and the channel bed is fixed. The effects of scour and deposition are negligible.

Resistance coefficients for steady unvarying turbulent flow are applicable so that relationships ( e.g. Manning ‘s equation ) can be used to depict opposition effects.

The fluid is incompressible and changeless denseness throughout the flow.

Therefore, the continuity equation states that the alteration in discharge with distance downstream ( ) , and the alteration in the cross-sectional country of flow over clip ( ) are in balance. Therefore, the sidelong influx ( ) to or from the channel and flood plain can be expressed as ( Wilson, 2004 ) .

( 2.1 )

where Q is the volumetric discharge in channel [ L3/T ] , x is the longitudinal distance along the channel [ L ] , T is clip interval [ T ] , A is the cross-sectional country of flow [ L2 ] and Q is the sidelong influx from other beginnings per unit length along channel [ L2/T ] .

The impulse equation states that entire applied forces is equal to the rate of impulse alteration in each unit of flow, plus the net escape of impulse ( Chow et al. 1988 ) . For this undertaking, the full dynamic wave equations can be simplified in footings of kinematic moving ridge theoretical account. The premises are that local acceleration, convective acceleration and force per unit area footings are ignored, and the flow gravitative forces are equal to the frictional opposition force. The impulse equation can be written as:

( 2.2 )

where is the down-slope of the bed [ – ] and is the incline of clash [ – ]

Roughness coefficients are defined as the opposition to deluge flows in channels and flood plains. To present Manning ‘s raggedness ( n ) , the Manning Equation is chosen. Therefore, the clash incline in the impulse equation can be described as:

( 2.3 )

where R is hydraulic radius [ L ] . Substituting the hydraulic radius, the impulse equation can be written as:

( 2.4 )

where N is the Manning ‘s coefficient of clash and PA is the wetted margin of the flow [ L ] .

However, for the Equation ( 2.4 ) , there are some restrictions such as merely sing the down gradient hydraulic features, and pretermiting the backwater effects and daze moving ridges.

2.2.2.2 Numeric Solution

The 1-D Saint-Venant Equations are discretized utilizing numerical methods of a finite difference estimate ( Chow, 1988 ) . Stream flow and transverse subdivision values are calculated with a simple additive strategy that uses a backward-difference method to deduce the finite difference equations. Therefore, they are combined to obtain the undermentioned equations:

( 2.5 )

where Q is the volumetric discharge in channel [ L3/T ] , x is the longitudinal distance along the channel [ L ] , T is clip interval [ T ] , Q is the sidelong influx from other beginnings per unit length along channel [ L2/T ] , and is the geometry and frication factor of channel which is written as:

( 2.6 )

where is the Manning clash coefficient [ T/ L1/3 ] , is the channel breadth [ L ] , and is the channel incline.

Meanwhile, the finite difference equation can be set up in order to cipher the measure Qi, J at each node ( one, J ) , where I represents the infinite and j the clip:

( 2.7 )

( 2.8 )

in order to make a additive equation, the value of Q in the look of Equation ( 2.5 ) is found by averaging the undermentioned values:

( 2.9 )

Note: All Equations variables refer to the definitions in Figure 2

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Figure 2 Finite difference box for the additive kinematic moving ridge equation

2.2.3. Channel Discretisation by Mesh Generation

In order to carry on the kinematic moving ridge simulation, the flow sphere is spatially discretised into distinct elements or grid cells to stand for the arbitrary modling country by numerical mesh coevals procedure. It starts at the inflow point of each grid cell with index of the way to the following downstream cell. With the aid of Airborne Laser Altimetry ( LiDAR ) and Stereo Air-photogrammetry, the high-resolution DEM grid cells are able to incorporate topographic informations, such as channel width, bed incline, manning clash coefi¬?cient and bankful deepness. Therefore, the numerical solution can be approximative obtained with the advantage of high-performance digital computing machines and high numerical stableness. In this undertaking, the regular high declaration rectangular grids mesh coevals is adopted. However, despite that the mesh declaration in the part is increased, it resulted in less smooth of clash coefficients. This is because the polygonal country over which the assorted clash parts were averaged was reduced.

2.2.4 Out-of-Channel Flow

Out-of-Channel flow ( i.e. Floodplain Flow ) is defined that H2O is transferred from the channel to the next overlying flood plain countries when bankful deepness is exceeded by inundation. However, the 1-D attack is non suited to imitate the flood plain flows due to its incapableness of capturing speed fluctuations and free surface across the channel. Therefore, flood plain flows can be likewise described in footings of classical continuity and impulse equations, discretized over a grid of square cells, which allows the theoretical account to stand for two-dimensional dynamic flow on the flood plain. Therefore, we assume that each cell is treated as a storage volume and the alteration in cell volume over clip is hence equal to the i¬‚uxes into and out of it during the clip measure ( See Figure 3, Wilson, 2003a ; 2003b ) .

( 2.10 )

where is the volume fluctuation [ L3 ] of each cell during clip [ T ] , and, , and are the volumetric flow rate [ L3/T ] severally coming from the up, the down, the left and the right next cells of the grid.

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Figure 3 Flows between cells on the flood plain with LISFLOOD-FP

( Wilson, 2003a ; 2003b )

Flow between two cells is assumed to be merely a map of the free surface height difference between these cells, therefore the undermentioned discretisation of continuity Equation ( 2.1 ) ( See Figure 4 & A ; 5 )

( 2.11 )

( 2.12 )

( 2.13 )

where A is the H2O free surface height [ L ] at the cell node ( one, J ) , and are the cell dimensions [ L ] , A is the effectual grid graduated table Manning ‘s clash coefficient for the flood plain, andA andA describe the volumetric flow rates [ L3/T ] between the flood plain cell node ( one, J ) .

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Figure 4 Discretization strategy for flood plain grid

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Figure 5 Floodplain Flows between Two Cells

The flow deepness, A hflow, represents the deepness through which H2O can flux between two cells, and is defined as the difference between the highest H2O free surface in the two cells and the highest bed lift ( this definition has been found to give reasonable consequences for both wetting cells and for flows associating flood plain and channel cells ) .

## 2.3 Uncertainty in deluging flood mold

It is the cardinal factor to cut down or forestall the degree of inundation jeopardies that guaranting anticipation accurately of the inundation flood country and supplying dependable information of hazard. In general, the consequence produced by inundation theoretical accounts is merely a individual deterministic anticipation for the peak flow of the inundation. However, the assurance degree of the end product consequences would be affected by the uncertainness of input informations in footings of extremum flow, the topographic informations, and the theoretical account parametric quantities. As a consequence, the uncertainness associated with the inundation flood mold is rarely quantified, It most likely because that the beginnings of uncertainness are non wholly accomplished and deficiency of available informations to analyze uncertainness.

Uncertainty analysis of LISFLOOD-FP mold has been studied in recent old ages. From those studies, the beginnings of uncertainness can be summarised into three major catalogues in footings of theoretical account informations inputs, fluid mechanicss parametric quantities and theoretical account constructions.

2.3.1Model informations inputs

2.3.1.1 Hydrologic and meteoric informations

One of the most dominant input parametric quantities is the design flow, which comes from flood frequence analysis and provides the boundary status. However, the uncertainness of steamflow is built-in since it is derived from the stage-discharge evaluation curves on the footing of inundation records, particularly for the high-return-period flow events. In drumhead, there are four types of uncertainnesss associated with the hydrograph of steamflows, viz. ( 1 ) watershed features ; ( 2 ) storm precipitation kineticss ; ( 3 ) infiltration and ( 4 ) ancestor conditions. However, the storm precipitation kineticss has the largest impact on the anticipation. Furthermore, the overall anticipation of hydrologic theoretical accounts could be increase due to uncertainty-added by missing of apprehension of the spacial and temporal variableness in precipitation, evapotranspiration, and infiltration.

2.3.1.2 Topographic informations

The topographic informations is including both land surface digital lift theoretical account ( DEM ) and river bed plumbing. It is one of the dominant factors to foretell the inundation flood country accurately. It does non merely act upon the hydrologic patterning procedure, but besides the function H2O surface lifts. First, the extraction of watershed features ( e.g. incline, watercourses and watershed boundaries ) from DEM is affected by its declaration, taking to varied discharge values estimated from the hydrologic theoretical account. Second, the declaration of DEM and the truth of plumbing affect the cross subdivisions extracted for 1-D channel flow simulation and the interpolated meshes ( or grids ) for 2-D overland flow simulation. Third, Bales and Wagner ( 2009 ) investigated the Tar River basin and revealed that high-quality topographic informations, along with the appropriate application of hydraulic theoretical accounts are likely the most of import factors impacting the horizontal extent and perpendicular H2O surface lifts of inundation flood maps.

2.3.2 Model constructions

The inundation flood theoretical accounts are besides sensitive to the channel geometry in footings of cross subdivisions figure, cross-sectional spacing in between, finite-element mesh quality and hydraulic constructions. Additionally, the type of theoretical account ( 1-D, 2-D or coupled ) used in imitating the river hydrokineticss besides brings uncertainness to the overall consequences. The geometry representation of channel is more critical to 2-D and ( 3-D ) theoretical accounts since the lift is defined at each mesh node distributed throughout the channel and flood plains. Furthermore, the mesh coevals schemes will impact 2- and 3-D theoretical accounts non merely in the anticipation of flood country, but besides the computational clip ( Horritt et al. 2006 ) .

2.3.3 Fluid mechanicss parametric quantities

Hydraulic theoretical accounts ( e.g. 1-D, 2-D or coupled ) used to imitate the river hydrokineticss and H2O surface lift in flood plain are sensitive to a set of theoretical account parametric quantities. Clash values ( Maning ‘s roughness coefficient, N ) , accounting for effects of variable cross subdivisions, non-uniform incline, flora and constructions at the sub-grid graduated table, have a important impact on hydraulic simulations ( Merwade et al. , 2008 ) .

Maning ‘s roughness coefficient ( n ) , which is normally assigned by utilizing standard look-up tabular arraies for different substrate types, can run from 0.035 to 0.065 in the chief channel, and 0.080 to 0.150 in the flood plains ( Chow et al. 1988 ) . Distributed informations throughout the flood plain are rarely available as a footing for gauging clash values for the theoretical account sphere. Many of the uncertainnesss in hydraulic theoretical accounts are lumped in the Manning ‘s n value, such that the theoretical accounts can be calibrated through adjusting such a parametric quantity. The difference in magnitude and altering channel conditions will do the “ optimum ” set of parametric quantities to be found in a somewhat different country of the parametric quantity infinite for each different inundation event.

Wohl ( 1998 ) analysed the uncertainness of Manning ‘s n relation to a normally used step-backwater theoretical account for channel ranges in five canon rivers. The consequences indicated that the uncertainnesss in discharge appraisal ensuing from the raggedness coefficients in step-backwater mold of paleo-floods were comparable to or lower than those associated with other methods of indirectly estimation inundation discharges. Pappenberger et Al. ( 2005 ) analysed the uncertainness caused by Maning ‘s N ( scope from 0.001 to 0.9 ) in the unsteady flow constituent of the 1-D theoretical account HEC-RAS. The consequences showed that many parametric quantity sets could execute every bit good even with utmost values. However, this was dependent on the theoretical account part and boundary conditions. Pappenberger et Al. ( 2007 ) employed a fuzzy set attack for graduating inundation flood theoretical accounts under the uncertainnesss of raggedness and cross-section. The raggedness of channel has been identified as more sensitive than the standard divergence of the cross-section.

## 2.4 Integrated mold and uncertainness analysis model

Flood hazard maps are critical to assist pull off the hazard of flood, which are generated based on good apprehension of the uncertainness associated with the assorted variables involved in inundation flood mold. A consecutive procedure is usually adopted, where hydrologic analysis starts foremost, and so hydraulic analysis and geospatial processing will follow.

Merwade et Al. ( 2008 ) proposed a conceptual model that could link informations, theoretical accounts and uncertainness analysis techniques to bring forth probabilistic inundation flood maps. This model was called floodplain patterning information system ( FMIS ) , supplying a workflow sequence where points such as terrain description, type of simulation theoretical account and parametric quantities of the system, can be changed to analyze the comparative consequence of the single variables on the overall system ( Figure 2.5 ) . Basically, in such a model, each point ( e.g. informations and parametric quantities ) affected by uncertainness was assigned a chance distribution and the consecutive work flow was run for indiscriminately generated inputs that could give the end product as a chance distribution map.

FMIS is able to find: ( 1 ) the impact of single input parametric quantities on the overall discrepancy of the theoretical account end product ( e.g. inundation flood extent ) ; ( 2 ) the uncertainness zone at assorted assurance degrees ; ( 3 ) theoretical account parametric quantities that bear the cardinal uncertainnesss and ( 4 ) the factors ( e.g. precipitation variableness, terrain and hydraulic constructions ) that are important for accurate designation of the inundation flood country. FMIS will non merely turn to the extension of uncertainness derived from theoretical account inputs and parametric quantities to the theoretical account end product, but besides assess the comparative importance of input uncertainnesss on the mold end product.

Figure 2.5 Integrated mold and uncertainness analysis model ( after Merwade et al. , 2008 )

## 2.5 Methodology of Uncertainty Analysis

The inundation flood theoretical account is, by definition, an estimate to world. Inherently, the issue associated with the mold is the assurance that the decision-maker can set in the consequences from a theoretical account. How safe and dependable the consequences from a theoretical account are will impact the determinations to be made. Imperfect cognition about the processs and informations generates uncertainness in calculating inundations which has been discussed above. Historically, chance theory ( Ross, 1995 ) and fuzzed set theory ( Zadeh, 1965 ) have been the primary tools for stand foring uncertainness in mathematical theoretical accounts.

The appraisal of uncertainness in deluging flood mold requires the extension of different beginnings of uncertainness through the theoretical account. Propagation of distributions ( e.g. Monte Carlo Simulation ) and minutes ( e.g. First-Order Second Moment ) are the two typical extension methods. The former one provides the estimations of chance or possibility ( i.e. fuzzed distribution ) of the theoretical account end products and the latter one offers the ratings of the distribution minutes ( e.g. mean and standard divergence ) of the theoretical account consequences.

Previously, a assortment of methodological analysiss have been reported for the intervention of uncertainness in inundation prediction, such as the Generalized Likelihood Uncertainty Estimation ( GLUE ) by Beven and Binley ( 1992 ) , Bayesian Forecasting System ( BFS ) by Krzysztofowicz ( 1999 ) and Fuzzy Extension Principle ( FEP ) by Maskey et Al. ( 2004 ) . A elaborate reappraisal of the major types of methods is given in the undermentioned subdivisions.

2.5.1 Monte Carlo Simulation

Monte Carlo Simulation ( MCS ) utilizes multiple ratings with indiscriminately selected theoretical account input and repeats the executings of numerical theoretical accounts to see the full scope of input factors and their possible interactions with regard to pattern end products. Each executing of the theoretical account produces a sample end product. The end product samples can so be examined statistically and the distributions of the anticipations can be determined.

MCS typically consists of the undermentioned stairss ( Saltelli et al. , 2000a, B ) : ( 1 ) definition of theoretical account variables ( input factors, Xi ) used for the analysis ; ( 2 ) choice of scope and the Probability Distribution Function ( PDF ) for each Eleven ; ( 3 ) coevals of samples based on the PDF information ( trying ) ; ( 4 ) rating of the theoretical account end product for each input sample ; ( 5 ) statistical analysis on all the obtained theoretical account end products ( i.e. coevals of end product distribution information ) and ( 6 ) sensitiveness analysis.

MCS has the undermentioned advantages: ( 1 ) the ability to manage uncertainness and variableness associated with the theoretical account parametric quantities ; ( 2 ) the ability of being applied in a deterministic mold construction and ( 3 ) flexibleness with regard to the types of chance distributions that can be used to qualify theoretical account inputs.

2.5.2 Generalized likeliness uncertainness appraisal

The Generalized Likelihood Uncertainty Estimation ( GLUE ) is a statistical method for quantifying the uncertainness of theoretical account anticipations. It recognizes the equality or near-equivalence of different sets of parametric quantities in the standardization of the theoretical accounts. It is based on a big figure of tallies of a given theoretical account with different sets of parametric quantity values, generated from specified parametric quantity distributions indiscriminately. Each set of parametric quantity values is assigned a likeliness of being a simulator of the system through comparing the predicted responses with ascertained 1s. The term likeliness is used in a really general sense, as a fuzzy, belief or possibility step of how good the theoretical account conforms to the ascertained behaviour of the system.

In the GLUE process, all the simulations with a likeliness step significantly greater than zero are retained for consideration. Rescaling of the likeliness values ( such that the amount of all the likeliness values peers to 1 ) yields a distribution map for the parametric quantity sets. Such likelihood steps may be combined and updated utilizing Bayesian theorem. The new likelinesss can so be used as burdening maps to gauge the uncertainness associated with theoretical account anticipations. As more ascertained informations become available, farther updating of the likeliness map may be carried out so that the uncertainness estimates bit by bit become refined over clip. The demands of the GLUE process are listed as follows ( Beven and Binley, 1992 ) :

A formal definition of a likelihood step or a set of likeliness steps.

An appropriate definition of the initial scope of distribution of parametric quantity values to be considered for a peculiar theoretical account construction.

A process for utilizing likelihood weights in uncertainness appraisal.

A process for updating likeliness weights recursively as new informations become available.

A process for measuring uncertainness such that the value of extra informations can be assessed.

The GLUE process requires that the sampling ranges be specified first for all parametric quantities to be considered. The scopes can ab initio be broad every bit long as it is considered executable by physical statement or experience. Second, a methodological analysis for trying the parametric quantity infinite is required. In most of the GLUE applications, this has been done by MCS, utilizing unvarying random trying across the specified parametric quantity ranges. Third, the process requires a formal definition of the likeliness step to be used and the standards for credence or rejection of the theoretical accounts, which is normally a subjective pick. There may besides be more than one nonsubjective map calculated from different types of informations, and it will so be necessary to stipulate how these should be combined.

Typically, continuously distributed step ( e.g. H2O deepness or discharge ) is used to specify the likeliness weights. However, in flood flood mold, binary form informations ( afloat or non-inundated ) normally are obtained in the signifier of a map ( 2-D in infinite but zero-dimensional in clip ) and are of involvement because the modeller wishes to foretell spatially distributed measure and estimation distributed uncertainnesss. Assorted likeliness steps are defined as planetary theoretical account public presentation steps for binary categorization informations in historical surveies based on the matrix listed in Table 2.2, where a value of 1 is assigned to the presence of a measure in either informations ( D ) or theoretical account ( M ) and a value of 0 to its absence ( Aronica et al. , 2002 ) .

To set up likeliness steps in measuring public presentation of i¬‚ood extent maps predicted by the theoretical account against the ascertained i¬‚ood extent map, an nonsubjective map of the likeliness step is shown below ( Bates and de Roo, 2000 ) :

F & lt ; 1 & gt ; ( 3.1 )

where is the ascertained country of flood, and is the sculptural country of flood.

In consequence, the statistic determines the ratio between the figure of grid cells classified right as being either dry or wet and the figure of cells classified falsely, Eq. 11 can be reformulated as

F & lt ; 2 & gt ; ( 3.2 )

where obtains a value of 1 for cells classified as afloat both in observed and modeled informations, and obtains a value of 1 for cells observed as dry but predicted to be wet, and obtains a value of 1 cells observed as moisture but classified as prohibitionist.

Hence, the likeliness step by comparing of the modelled end products with the ascertained information is more straightforward to cipher.

## Chapter 3 METHODOLOGY AND CASE STUDY

This chapter consists of 3 parts. The first portion on methodological analysis high spots the study and interview processs. The study and interview consequences obtained are presented in portion two and three, severally.

## 3.2 Survey consequences

## Study Area – River Thames, UK

The trial site is located on the upper Thames in Oxfordshire, UK, where the river has a bankful discharge of 40 m3s-1 and drains a catchment of 1000 km2. A short ( c. 5 kilometer along channel ) trial range has been identified, bounded upstream by a gauged weir at Buscot ( which provides the theoretical account boundary status ) , and with moderately well-confined flows at the downstream terminal. The theoretical account topography was parameterized with a 50 m declaration stereophotogrammetric DEM ( 76 x 48 cells ) with a perpendicular truth of +/-25 centimeter, and channel information obtained from large-scale UK Environment Agency maps and studies.

In December 1992 a 1-in-5 twelvemonth inundation event occurred, with a peak discharge of 76 m3s-1, ensuing in considerable floodplain flood along the range. The inundation event coincided with an flyover of the ERS-1 remote feeling orbiter, which acquired a SAR ( man-made aperture radio detection and ranging ) image of the inundation. This provided a map of flood extent with boundaries accurate to +/-50 m ( Horritt and Bates, 2001 ) about 20 H after the hydrograph extremum, but with discharge still high at 73 m3s-1. The wideness of the hydrograph, along with the short length of the range, means that a dynamic theoretical account was unneeded, and steady province simulations were alternatively used with discharge matching to the flow at the clip of the SAR flyover. An initial sensitiveness analysis indicated that the Thames theoretical account was sensitive to friction values and the clash values for the standardization procedure were distributed indiscriminately and uniformly between 0.01 m1/3s-1 and 0.05 m1/3s-1 for the channel, and 0.02 m1/3s-1 and 0.10 m1/3s-1 for the flood plain.