Sensitivity based attribution of flood risk

Transcription

1 Senstvty based attrbuton of flood rsk Attrbuton du rsque d'nondaton basé sur la sensblté Jm Hall, Rchard Dawson, Lnda Speght, Slobodan Djordjevć, Dragan Savć and Jorge Leandro School of Cvl Engneerng and Geoscence, Newcastle Unversty Casse Buldng, Newcastle upon Tyne, NE1 7RU, Unted Kngdom JBA Consultng - Engneers & Scentsts Magna House, South Street, Atherstone, CV9 1DF, Unted Kngdom Centre for Water Systems, Unversty of Exeter Harrson Buldng, North Park Road, Exeter, EX4 4QF, Unted Kngdom RESUME Cet artcle présente l exploraton de nouvelles méthodes d attrbuton des rsques d nondaton à l ade d un modèle ntégré synthétque de réseaux de dranage en mleu urban. La seule approche permettant de trater le vaste nombre de varable d un système urban consste en une smplfcaton hérarchque du système. L attrbuton de rsques est analysée à pluseurs nveaux pour dentfer les composants responsables du rsque d nondaton. L attrbuton basée sur la sensblté répartt le rsque entre les varables nfluençant le rsque total. Cette approche utlse des moyennes statstques pour analyser les dégâts dus à une sére d événements, dégâts basés sur la modélsaton hydraulque détermnste de l nondaton de rues. Deux exemples d attrbuton de rsques basés sur les ndces de sensbltés sont présentés. ABSTRACT A synthetc ntegrated urban dranage system s used n ths paper to explore alternatve methods for flood rsk attrbuton. The only feasble approach to tacklng the problem of huge number of varables n urban systems s by herarchcal smplfcaton of the system, wth the attrbuton analyss beng appled at several levels, to dentfy the system components responsble for flood rsk. Senstvty-based attrbuton apportons rsk between the varables that nfluence the total rsk. In ths approach, statstcal means are used to analyse damage from a seres of events, based on determnstc hydraulc modellng of street floodng. Two examples of rsk attrbuton based on senstvty ndces are shown. KEYWORDS Flood damage, ntegrated flood rsk management, rsk attrbuton, urban floodng NOVATECH

2 1 INTRODUCTION Integrated Flood Rsk Management (IFRM) explctly recognses the nterrelatonshps between all sources of floodng, rsk management measures, ther analyss, costs and effectveness, wthn changng socal, economc and envronmental contexts. The man sources of floodng nclude pluval runoff that leads to sewers backng up and hgh surface flows, fluval floodng caused by hgh rver flows, coastal storm surges and perhaps also groundwater floods. A gven flood event could be caused by a sngle source, or several sources actng n combnaton. The UK s Department for Envronment Food and Rural Affars (DEFRA) has dentfed IFRM as a key strategc am (DEFRA et al., 2005). Lkewse, ntatves such as the Water Framework Drectve, Integrated Coastal Zone Management and proposed EU Floods Drectve are drvng the need for joned-up thnkng across Europe. In order to demonstrate the techncal feasblty of IFRM a necessary methodologcal advancement s the development of core concepts for a framework for unfed systems-based flood rsk analyss. After ths ntroducton, we shall present these concepts and present n greater detal a key aspect of these concepts: a methodology for attrbutng rsk between flood sources, management nfrastructure and stakeholders. Implementaton of ths approach on a synthetc system wll be shown. 2 SYSTEMS-BASED RISK ANALYSIS The core prncples of an ntegrated systems-based flood rsk analyss are now defned as (Hall et al., 2006): 1) Rsk s a common currency. To enable nter-organsatonal communcaton of flood rsk nformaton, the frst step s that t s measured usng a common metrc. Rsk estmates provde the common currency whch can be used to compare rsks from dfferent sources on a common bass. In a stuaton where there are several organsatons responsble for rsk management we wsh to be able to dsaggregate the total rsk and attrbute t to dfferent components n the system. 2) Rsk s a mult-dmensonal measure and should be a broad measure of all losses (and gans) ncludng socal, envronmental and economc. 3) Spatal and temporal profles of ths mult-dmensonal measure of rsk need to be constructed to support long term plannng. 4) Attrbuton of rsk. The contrbuton towards rsk from dfferent floodng sources and components of floodng pathways, ncludng nfrastructure components, s crtcal nformaton to support rsk-based decson-makng: a) Rsk ownershp. There are several organsatons wth a role n flood rsk management. We wsh to know, n broad terms, what proporton of the rsk each s responsble for. b) Estmaton of capacty to reduce rsk. Ideally, rsk should be owned by organsatons wth the greatest capacty to manage t. Capacty to reduce flood rsk s related to the potental to change the characterstcs of the floodng system. c) Asset management. An organsaton wth responsblty for management of flood defence or dranage nfrastructure should ratonally nvest resources so that they maxmse mpact n terms of rsk reducton. Wthn a specfed set of system components t s therefore necessary to dentfy those components that contrbute most to rsk and compare potental measures to reduce rsk wth the cost of mplementng those measures n order to develop an optmum nterventon strategy. A secondary problem s to target montorng strateges so that resources are nvested n data acquston that makes the greatest contrbuton to reducng uncertanty. 124 NOVATECH 2007

3 2.1 Formulaton of the rsk problem Consder a system whch s descrbed by a vector of loadng varables S and a vector of varables that descrbe the flood management nfrastructure system R. We wrte all of the basc varables as X = (S, R). The resstance varables R mght nclude the heght or other dmensons of dkes, the propertes that determne dke falure or the dmensons of the sewer system. Ther varaton mght be contnuous (e.g. a heght varable) or dscrete (e.g. a blocked or not blocked descrptor of a ppe. The varablty n the loadng and resstance s descrbed by a jont probablty dstrbuton ρ(x). We may often be able to assume that many of the varables n R are statstcally ndependent and we wll often assume that S and R are ndependent. There s a damage functon D(X) where the unts of D are (Brtsh Pound) or some other sutable measure of mpact. The rsk r assocated wth the system s therefore r = ρ( X) D( X) dx (1) 0 The rsk ntegral can be further extended to address antecedent condtons ether by ncludng antecedent varables n the loadng vector S, or, alternatvely, by extendng the analyss so that S s a functon of tme. At any pont n tme the damage s D(X); the rsk s the nstantaneous expected value of ths functon. A further attracton of the approach s that t can deal wth other varatons n the system state varables wth tme, for example due to deteroraton n the condton n the varables descrbng the system state or changes n the loadng due to clmate change or other envronmental changes. 2.2 Standards based attrbuton Consder an organsaton wth responsblty for urban dranage (hereafter a UDO), provdng a specfed level of servce to dscharge ranfall events up to return perod T s, although t s lkely that through degradaton etc. the system only conforms to T s <T s. Therefore, after a ranfall event, T > T s, the sewer and dranage capacty (even assumng no blockages) wll certanly be exceeded. A flood model can be used to estmate the damage D(T s ) and D(T) (by defnton D(T s ) = 0). Damage attrbutable to the UDO s D(T s )-D(T s ) and damage not attrbutable to the UDO s D(T)-D(T s ). Ths can be extended to gve the expected attrbuted damage over the dstrbuton of ranfall L: lt ( s ) Expected attrbuted damage for UDO = ρ( LDLdl ) ( ) (2) 0 where l(t s ) s the ranfall wth return perod T s. Ths may be extended further to consder the stuaton n whch due to blockage or some other sewer falure the damage s not D(T) but D(T F) where F ndcates some falure event n the sewer system attrbutable to the UDO. The damage not attrbutable to the water servce provder s stll D(T)-D(T s ), so the damage that s attrbutable to them s now D(T F)-D(T)+D(T s ). The expected attrbuted damage calculaton now requres a probablty dstrbuton over the varous possble blockage states F j : n 2 j = 1 j j 0 lt ( s ) Expected attrbuted damage = PF ( ) ρ( LDL ) ( F) ds ρ( LDLds ) ( ) (3) However, P(F) s notorously dffcult to estmate for sewer systems and so applcaton of Equaton 3 s lkely to be lmted. NOVATECH

4 2.3 Senstvty based attrbuton An ntutve measure of nfluence or senstvty s the extent to whch varaton n a factor of nterest (or a set of factors) has on a system performance, n our case flood rsk r. Ths s the classcal senstvty analyss problem to whch there are a number of solutons. However, relatng senstvty analyss to rsk attrbuton s, n general, not straghtforward. If each of the loadng varables (e.g. fluval flows, ranfall) were the unequvocally responsblty of a partcular agent, then senstvty analyss would provde a bass for defnton of rsk ownershp. Rsk ownershp could be dsaggregated on the bass of senstvty to the relevant loadng varable. However, ranfall runoff, for example, s dealt wth n sewer and hghway dranage systems as well as urban water courses. Hence t s necessary to consder the varables R that defne system performance. Evdently, ths s also necessary to make asset management prortsaton decsons. Rsks arse because of phenomena whose future state s not known wth certanty. If the magntude of a gven load on a system was known wth certanty then decsonmakng would be easy. We would take measures to reduce the predcted damage f t was economcal to do so and otherwse we would not. In other words we would know future losses precsely and the noton of rsk, whch s assocated wth phenomena that are only predcable n probablstc terms, would be redundant. Because, n fact, the future s uncertan we construct the concept of rsk and desgn measures to reduce rsk.e. to reduce the expected damage due to some uncertan hazards. Varance-based methods seek to attrbute rsk to system varables on the bass of the amount that those varables contrbute to uncertanty and hence to rsk. Consder a model of the form Y = g(x 1,, X k ). The senstvty ndex I represents the fractonal contrbuton of a gven factor X to the varance n a gven output Y. In order to calculate the senstvty ndces the total varance V n the model output Y s apportoned to all the nput factors X as (Sobol, 1993): V = V + V + V V (4) j jl k < j < j< l where V = ( = ) V E Y X x (5) (, ) ( = ) V = = = j V E Y X x X j xj V V j (6) V E Y X x s referred to as the Varance of the Condtonal Expectaton (VCE) and s the varance over all values of x n the expectaton of Y gven that X has a fxed value x. Ths s an ntutve measure of the senstvty of Y to a factor X, as t measures the amount by whch E( Y X = x ) vares wth the value of x, whle all the effects of the X j s, j, are averaged. The frst order (or man effect ) senstvty ndex S for factor X s therefore defned as: I V V = Also of nterest s the nfluence of factor X when actng n combnaton wth other factors. There are 2 k -1 of such nteractons, so t s usually mpractcal to estmate the effect of all of them. A more practcal approach s to estmate the k total senstvty ndces, I T, where (Homma and Saltell 1996): V E( Y X = ~ x~ I = 1 T VY ( ) 126 NOVATECH 2007 (7) (8)

5 where X ~ denotes all of the factors other than X. The total senstvty ndex therefore represents the average varance that would reman as long as X stays unknown. The total senstvty ndces provde an ndcator of nteractons wthn the model. For example, factors wth small frst order ndces but hgh total senstvty ndces affect the model output Y manly through nteractons the presence of such factors s ndcatve of redundancy n the model parametersaton. In the case of flood rsk analyss, the output quantty of nterest s the damage D. The probablty densty functon of the annual damage estmate, f D (d): fd( d) = Id( D( X)) D( X) ρ( X) dx (9) where I d ( ) s the ndcator functon. Recall that rsk r s the mean of D.e. r = ρ( X) D( X) dx (10) 0 The varance s 2 Var( d) = ρ( X ) D( X r ) dx (11) 0 The varance-based senstvty analyss descrbed above s appled to ths functon. 3 IMPLEMENTATION The rsk attrbuton methodology s mplemented n the frst nstance on a realstc (but not real) system shown n Fgure. Upstream of the urban area s a rural catchment of 50km 2. Runoff from rural catchment s dscharged nto the rver that s the recpent for runoff from urban area. The area of the urban catchment s 1.5km 2, wth 4.6km of storm sewer ppes (mnor dranage system, wth three outlets to the rver) and 3.3km of streets/roads wth assumed wde trapezodal cross-secton (major dranage system, wth one outlet lnk ). Interacton between mnor and major system can take place through vrual wers that lnk manholes to surface network nodes. Fgure 1 Urban flood system (catchment boundary covers area of 1.2km by 1.25km) NOVATECH

6 Ppes are desgned so that, at low rver flows (.e. at free outflow from all outlets), sewer system can handle surface runoff from 1 n 10 year storms wth surchargng but wthout the hydraulc head reachng the terran level. At more ntense storms, mnor system capacty becomes nsuffcent and pluval floodng takes place. On the other hand, assumng zero runoff from urban area, fluval floodng occurs at rver flows exceedng the 1 n 100 year flow rate. The urban area s susceptble to combned pluval/fluval floodng when backwater nfluence from the rver may reduce the capacty of the sewer system. Propertes (or damage ponts) are assumed to be spaced at 20m ntervals along the roads. Fgure 2 shows steps requred to generate estmates of flood rsk, descrbed below: 1) Ranfall boundary condtons are defned as a seres of 50% summer profle storms (Butler and Daves, 2004) for return perods of 1 to 1000 years and duratons between 15mn and 24h. 2) The ranfall s propagated through a hydrologcal model ARNO (Todn, 1996) to gve the upstream rver flow rates for the hydrodynamc model. 3) The ranfall and rver flow are used as nputs to the coupled surface/sub-surface hydrodynamc model, SIPSON (Djordjevć et al., 2005). 4) Maxmum flood depths obtaned by the hydrodynamc model are ntegrated over functons descrbng depth-damage relatonshps for propertes (Pennng-Rowsell et al. 2003) to calculated the flood damage, D, for a gven event. 5) The flood rsk, expressed n terms of expected annual damage, s calculated usng Equaton (1). 6) The senstvty-based analyss s subsequently appled usng Equaton (10). Calculate ranfall nputs Catchment ranfall Urban ranfall Hydrologcal model Rver flows Depthdamage curves Hydrodynamc surface/ subsurface model Flood depths Flood damages Rsk analyss and attrbuton Fgure 2 Model lnkages for ntegrated flood rsk assessment In addton to varyng loadng parameters (ranfall duraton, peak ntensty and rver flows), the followng nfrastructure parameters were vared: 1) Ppe sze (unform dstrbuton, range -40% to +50% of the desgned dameters). 2) Percentage of mpermeable area (normal dstrbuton, range 30% to 90%). 3) Rver bottom wdth (beta dstrbuton, range 1.5m to 11m). 128 NOVATECH 2007

7 Based on senstvty ndces, the pe chart n Fgure 3 shows the total contrbuton of each varable to rsk. As s evdent, duraton, peak ranfall and ppe sze are the most mportant loadng varables. Rver wdth has no effect on flood rsk and the nfluence of peak flow and mpermeable area s generally nsgnfcant. It should be noted that the obtaned fgures are very much case-specfc and therefore should not be consdered to have any general relevance. Instead, they should be taken as an llustraton of the proposed methodology. Impermeable area 2% change n ppe sze 19% rver wdth 0% duraton 41% peak ran 31% peakflow 7% Fgure 3 Total senstvty ndces The nfluence of sewer blockages was analysed. Senstvty ndces were calculated for ndvdual ppes (assumng ther blockage) to dentfy whch ones contrbute most to the flood rsk. As expected (see Fgure 4), blockage of the lowest of the three outlets (ppe ) contrbutes most to flood rsk. Somewhat surprsngly, blockage of the mddle outlet (ppe ) would contrbute nsgnfcantly to flood rsk. Other nvestgatons made n ths study ncluded combnatons of blocked ppes and analyss of the effect of clmate change assumng dfferent scenaros (Speght, 2006). Fgure 4 Total senstvty to blockages n the sewer system NOVATECH

8 4 DISCUSSION AND CONCLUSIONS Integrated flood rsk analyss requres that rsk s measured usng a common metrc. We have dentfed core prncples and dentfed two approaches to dsaggregatng the contrbuton to rsk from dfferent loadngs, system components and stakeholders. The standards-based attrbuton methodology does not requre sgnfcant computatonal resource, but because of the dffcultes assocated wth estmatng sewer falure probabltes s lmted n practse to rsk attrbuton of loadngs only (.e. the contrbuton towards the total rsk from urban ranfall and rver flow). The senstvty-based attrbuton methodology can be readly used to explore the contrbuton from specfc nfrastructure components (eg. flood defences, sewer network). However, dranage systems nvolve thousands of varables. The only feasble approach to tacklng ths problem s therefore by herarchcal smplfcaton of the system, wth the attrbuton analyss beng appled at several levels, from a very broad scale to dentfy the man nfluences on flood rsk, to a detaled scale for small well defned problems, to dentfy the components that are responsble for flood rsk. Approach to ntegrated flood rsk management presented n ths paper uses statstcal methods to analyse results of seres of smulatons made by determnstc full-dynamc flood model. Consequent flood damage s nterpreted usng spatal ntegraton of maxmum flood depths lnked to correspondng depth-damage curves. Asset management decsons based on senstvty-based attrbuton of flood rsk are clearly much sounder than those made upon standards-based analyss, whch are based on a sngle event (or a lmted number of events). Future research wll look at possbltes for mplementng rsk attrbuton methodology at a broader scale on real systems. In these studes, the mportance of other groups of elements such as pumps, storage or SUDS wll be analysed. Descrpton of damage wll be enhanced to nclude spatally varable housng densty and value (usng GIS), traffc dsrupton, health mpacts and other damages. 5 ACKNOWLEDGEMENTS The research upon whch ths paper s based s funded through the EPSRC Flood Rsk Management Research Consortum: (Work Packages 4.5 and 6.1): Grant GR/S76304/01. 6 REFERENCES Butler, D. and Daves, J. (2004), Urban Dranage, Spon Press, London. DEFRA (2005), Makng Space for Water: Frst Government response to the autumn 2004 consultaton exercse, DEFRA ( Djordjevć, S. Prodanovć, D. Maksmovć, C. Ivetć, M. Savć, D.A. (2005), SIPSON Smulaton of Interacton between Ppe flow and Surface Overland flow n Networks, Water Scence & Technology, IWA, 52(5), Hall, J., Dawson, R., Speght, L., Djordjevc, S., Savc, D. and Leandro, J. (2006). Attrbuton of flood rsk n urban areas, 7 th Int. Conf. on Hydronformatcs, Vol. I, Nce, Homma, T. and Saltell, A. Importance measures n global senstvty analyss of model output. Relablty Engneerng and Systems Safety, 1996, 52(1), Pennng-Rowsell, E.C., Johnson, C., Tunstall, S.M., Tapsell, S.M., Morrs, J., Chatterton, J.B., Coker, A. and Green, C. (2003) The Benefts of Flood and Coastal Defence: Technques and Data for Mddlesex Unversty Flood Hazard Research Centre. Speght, L. (2006) Analyss of the causes of flood rsk n urban areas, MSc thess, School of Cvl Engneerng and Geoscences, Newcastle Unversty, Newcastle-upon-Tyne. Sobol, I.M. (1993) Senstvty analyss for non-lnear mathematcal models, Mathematcal Modellng Computatonal Experment, 1, Todn, E. (1996), The ARNO ranfall-runoff model, Journal of Hydrology, 175, NOVATECH 2007