COASTAL ZONE RISK IN THE NETHERLANDS

Transcription

1 COASTAL ZONE RISK IN THE NETHERLANDS Prof J.K.Vrijling, dr ir P. van Gldr, ir J. Litjns - van Loon INTRODUCTION It is wll known that a major part of th Nthrlands lis blow sa lvl. An intricat systm of sa dfncs protcts th country from flooding with an xplicitly dfind crtainty. Th sa dfncs along th North Sa ar partly formd by duns. Ths duns howvr hav two functions; dfnding Holland against flooding by storm surgs and providing spac for natur, rcration, tourism and housing. Th first function is wll studid, but th consqunc of th first for th scond drw only attntion in th last yars. During storm surgs th duns will b rodd ovr som distanc and th proprty locatd in this zon will b undrmind and lost. As th width of this rodd zon is limitd to 5 to mtrs, th popl living thr can fl to th saf hintrland and no casualtis ar xpctd. At som placs spcially at th location of sasid rsort town, th duns ar covrd with rstaurants, hotls, apartmnt buildings, tc. and th rlatd roads and walkways. Now th qustion is to what dgr th proprty should b protctd by th govrnmnt against th rosiv forcs of th sa. Two principls could b followd hr: quity or fficincy. Th first principl would rquir th sam safty for th inhabitants of th duns as for th popl bhind th duns. Although this is not xactly comparabl as xplaind abov, proponnts of this principl would lik to prohibit activitis with fixd assts saward of a safty contour of -4 pr yar. Such a policy would howvr xclud a vry attractiv zon of th safront from conomic activity. This sms conomically infficint bcaus th rat of rturn on invstmnt in this zon is highr than th probability of losing it. Thrfor th scond principl is rsarchd furthr in this papr and th qustion is answrd up to which lvl of probability (contour) th govrnmnt should prohibit fixd invstmnt if th rasoning is limitd to matrial damag and conomic fficincy. Starting with th distribution of th invstd valu as a function of th distanc from th high watr lin and using th probability of xcdanc of a crtain distanc by rosion, th risk can b calculatd as a function of th distanc. Aftr som mathmatical manipulation th risk can also b dpictd in a frquncy-damag curv, a FD-curv similar to th wll known FN-curv (th FN-curv plots th probability of xcdanc against th numbr of casualtis). Finally it is attmptd to find an Dlft Univrsity of Tchnology, Faculty of Civil Enginring and Goscincs, Hydraulic Enginring Division, P.O. Box 548, 6 GA Dlft, Th Nthrlands, Fax: , j.k.vrijling@ct.tudlft.nl, p.vangldr@ct.tudlft.nl Ministry of Transport, Public Works and Watr Managmnt, DWW, P.O. Box 544, 6 GA Dlft, Th Nthrlands, J.Litjns-vLoon@DWW.RWS.MinVnW.NL

2 conomic optimum by quating th cost of bach nourishmnt with th rduction of proprty risk du to dun rosion. DUNE EROSION DURING STORM SURGES caus th windfild of th cyclon is th moving forc bhind th wav growth and th wind stup in th North Sa, th significant wav hight and th storm surg lvl at th Dutch coast show considrabl dpndancy. This dpndancy is nhancd by wav braking in th shallow coastal ara whr th watr dpth is govrnd by th bottom topography and th storm surg lvl. Thrfor th rosion ε(hw) of th coastal duns during storm surgs can b rasonably wll dscribd as a function of th watr lvl HW alon. A simpl approximation, that nabls furthr mathmatical analysis, is givn by: nγ ε ( HW) = HW P h dun n th bach slop P th dun foot γ a calibration factor h dun th dun hight at position P ( ) In which: () From Eqn. (), an xprssion of HW as a function of ε can b drivd: εhdun HW( ε) = + P nγ Using this xprssion on can transform th high watr probability distribution into probability distribution of th dun rosion F ε (x). Givn an xponntial distribution for HW with location A and scal B (Van Dantzig, 956), th distribution function for ε is givn by: F ( x) = ε c = hdun nγ x( AP)/ c B/ c A graph of this probability distribution in th form of its complmnt, th probability of xcdanc lin, is givn blow. () (3) Fig.. Probability of xcdanc of th rosion

3 This probability of xcdanc lin givs th position of th lins paralll to th coastlin with a probability of p=/n to b xcdd. Th position x p of such a lin or contour, that is dtrmind by th p-quantil of dun rosion can b analytically dtrmind from P(ε > x p ) = p and is givn by: A E A map showing th layout of th sasid rsort with th /, /5 and / lins is a suitabl lmnt in th communication btwn th authoritis and th citizns in th final dcision making procss. ECONOMIC VALUE IN THE COASTAL ZONE In th Dutch sa sid rsorts lik Schvningn and Noordwijk considrabl invstmnt is don to dvlop tourism. Evrywhr th structur of th dvlopmnt diffrs. Somtims a boulvard strtchs along th coast on top of th duns in front of th gusthouss, in othr cass th proprtis ar dirctly at th sa front (Carvalho and Colho 998). Th distribution of th conomic valu in th coastal zon is paramtrizd as a function of th distanc from th coastlin by th valu dnsity function f v (x), whr th intgral of f v (x) ovr th coastal zon is th total valu of th proprty. Practical xprinc for Schvningn and Noordwijk shows that th valu dnsity is bst modlld by a multi-uniform distribution or a histogram as givn by: For Schvningn thr zons wr ndd, as shown hr, for Noordwijk a singl zon appard to b sufficint. It should b notd that this form of f v (x) could b th rsult of conomic facts as wll as of th rlativ crudnss of th proprty tax valuation that forms th basis of th data. 4 4 xp = ( AE BE ln p) A P B = BE = c c V if x X V if X < x X fv( x) = V if X < x X othrwis 3 3 (4) (5) f v ( x) 4 6 x 6 Fig.. Th valu dnsity function for Schvningn in Dfl/m THE RISK IN THE COASTAL ZONE Th risk at position x is dscribd by th product of th probability that th rosion during a storm xcds x and th valu of th invstmnt at x: Risc( x) = ( F ( x)) f ( x) v 3

4 Th coastal risk profil Risc(x) rsults thus practically spaking from th multiplication of th graph of th rosion xcdanc lin and th valu dnsity function. A graph of Risc(x) is dpictd hr. (6). Risc( x). 4 6 x, x 6 Fig. 3. Coastal risk profil Th xpctd valu of th damag pr m is qual to th intgral: X3 TotalRisk( a) = Risc( x) dx a (7) For Schvningn th ordr of magnitud of th total risk for th coastal zon amounts to 5 Dfl/m. y. In th fild of risk communication th FN-curv is oftn usd (Vrijling, ). This curv dpicts on a doubl logarithmic scal th frquncy of an accidnt against th numbr of fatalitis. caus nobody is xpctd to loos his lif in cas of a storm surg th FN-curv is of lssr importanc hr. It might howvr b hlpful to hav a Frquncy-Damag Curv, a FD-curv, that plots th frquncy of th storm surg against th siz of th damag. Earlir th distanc x was xprssd as a function of th p-quantil of th rosion. Th cumulativ distribution of th invstmnt F v (x) can b found by intgrating th valu dnsity function f v (x). Now th FD-curv can b found by liminating of x from th cumulativ valu distribution F v (x) using th p-quantil of th rosion givn by x(p). This rsults in th following FD-curv: p FD ( p ) Fig. 4. FD-curv A practical chck with a thortical basis is that th ara undr th FD-curv is qual to th xpctd valu of th damag. This valu was calculatd arlir as th total risk. 4

5 OPTIMAL SAFETY LEVEL Now th qustion is to what frquncy or contour lin th proprty should b protctd by th govrnmnt against th rosiv forcs of th sa. Thr ar two principls that giv guidanc in problms rgarding th distribution of scars rsourcs i.. tax payrs mony: quity or fficincy. Th first principl would rquir th sam safty for all. Thus th inhabitants of th coastal zon on top of th duns should hav th sam safty lvl for thir proprty as th popl bhind th duns. Although both cass ar not xactly comparabl bcaus th popl bhind th duns run also th risk of drowning as xplaind abov, proponnts of this principl would lik to prohibit activitis with fixd assts saward of a safty contour of -4 pr yar. This would howvr xclud a vry attractiv zon of th safront from conomic activity. This sms conomically infficint bcaus th rat of rturn on invstmnt in this zon is highr than th probability of losing it. Thrfor th scond principl will b rsarchd furthr. Th qustion is answrd up to which lvl of probability (contour) th govrnmnt should prohibit fixd invstmnt if th rasoning is limitd to matrial damag and conomic fficincy. To answr th qustion to which rturn priod th dvlopmnt of proprty should b allowd a dcision problm has to b formulatd quating th cost of protction with th risk. Two altrnativ policis ar studid. Following th first calld rtrat th govrnmnt rducs th risk by rmoving th proprty from th sashor up to x o. Th total cost of this policy is th cost of rmoval and th prsnt valu of th rmaining risk. caus th prsnt valu of th risk is takn from t= to infinity th prsnt valu oprator bcoms /r whr r = th rat of intrst. X3 X3 TC( x ) = F ( x ) + / r f ( x) ( F ( x) dx = V x + / r V dx v v ε x x x A To find th optimal valu of x o th xprssion for th total cost must b diffrntiatd with rspct to x o. In this cas th drivativ of th intgral is qual to th intgrand with x o as argumnt: TC( x ) V = V + = x r With som clvr rarranging th optimal p-quantil for rtrat is found to qual th rat of intrst: x A (8) (9) opt x A p = = r () So if th ral rat of intrst is. -.4 pr annum th coastal zon should b vacatd up to th contour with a rturn priod of 5 to 5 yar. On should b awar that disagrmnt might aris btwn th ownr of a spcific proprty and th govrnmnt. If his proprty gnrats a rturn on invstmnt that xcds th rat of intrst (which is not unlikly) th ownr is inclind to opt for a rturn priod qual to th rciprok of his rat of rturn on invstmnt. Th govrnmnt should allow this on th condition that th ownr accpts all rsponsibility and givs up th right of compnsation. Th scond policy altrnativ is indicatd as attack. Following this policy th govrnmnt will incras th distanc from th first proprtis to th sa shor by a dun nourishmnt of N [m/m] If th dun hight is h dun th sand volum ndd is N. h dun [m 3 / m]. Th cost of nourishmnt is assumd to qual p s [Dfl/ m 3 ] lading to a cost pr running mtr of coast of N. h dun. p s [Dfl / m]. Th ffct of th nourishmnt is modlld as a saward shift of th contour ovr N [m]. Introducing ths changs th xprssion for th total cost consisting of th cost of nourishmnt n th prsnt valu of th risk bcoms 5

6 Aftr intgration of prsnt valu of th risk th total cost as a function of N bcoms approximatly: Diffrntiation with rspct to th dcision variabl N will lad to an optimum X3 TC( N) = N h p + / r f ( x) ( F ( x + N) dx = dun s v X3 = N h p + / r V dx dun Obsrving again that th xponntial function quals th probability that th rosion xcds th saward boundary of th invstmnt, on writs: Th rquird nourishmnt has to rduc th probability that th proprty is damagd to p opt and is qual to: (5) Th optimal probability of damag to th proprty is thus qual to th rat of intrst tims th cost of mtr nourishmnt pr m running coast dividd by th valu of th proprty pr m. On should chck if th scond zon of th valu dnsity function givs a mor stringnt rquirmnt in trms of nourishmnt. Th nourishmnt rquird by th scond zon bcoms: s ε ( x+ NA V TC( N) N hdun ps + ( ( x + N + ) r ( + N) A TC( N) V = hdun ps + = N r ( x+ N) A B h dun ps popt = = r V N = ( A B ln( p )) opt E E opt ( X+ N) A B h dun ps popt = = r V ( x+ NA () () (3) (4) (6) Nopt = ( AE BE ln( popt )) X (7) If this valu xcds th formr th optimal valu has to b rfind numrically bcaus th simpl approximation givs a rasonabl stimat but is only accurat for th first zon. CONCLUSIONS AND RECOMMENDATIONS Aftr a long priod whr most attntion wnt to th protction of th low lying aras of th Nthrlands, rcntly attntion is givn to th risk in th coastal zon. caus no casualtis hav to b fard only th probability of conomic damag to th sa sid dvlopmnts is studid. Th risk is rprsntd in nw ways, that ar thought to b hlpful in th public discussion. Firstly contour lins paralll to th coast ar givn for crtain spcifid probabilitis of damag to th proprty. Scondly th risk is rprsntd in a graph as a function Risc(x) of th distanc from th coastlin. Thirdly th xpctd valu of th damag, th Total Risk is calculatd as th ara undr th Risc(x) curv. Fourthly th damag is givn as a function of th probability in a Frquncy-Damag curv, a FD-curv. It can b provn that th ara undr th FD-curv is qual to th Total Risk (Vrijling and Van Gldr, 997). This provids a usful chck. Finally it is shown that 6

7 th qustion to which contour dvlopmnt has to b allowd has to b answrd by conomic rasoning. If th govrnmnt, following th quity principl would protct th proprty on th duns to th sam lvl of frquncy as that bhind th duns, a safty lvl of -4 pr yar would b rquird. Economic rasoning shows howvr that th protction should b limitd to a frquncy lvl of th ordr of th rat of intrst i.. - to - pr yar. In ordr to find th optimum lvl of protction two stratgis wr valuatd. Following th first stratgy calld rtrat th govrnmnt should buy proprty until th probability that th most sawardly locatd proprty is damagd by dun rosion during a storm is rducd to th rat of intrst r. p = = r opt xa Th scond stratgy attack calls for dun nourishmnt to protct th proprty. Now th dun should b xtndd saward by nourishmnt until th probability that th proprty is damagd during a storm surg is limitd to th rat of intrst tims th cost of mtr nourishmnt dividd by th valu of mtr proprty. ( x+ N) A B h dun ps popt = = r V Th simpl rsults of this papr ar rachd undr assumptions that should b rlaxd. Firstly th main part of th Dutch coast rquirs rgular nourishmnt to kp it in a stabl position. This scular rosion procss and th priodic rstoration of th coastlin should b takn into account (Bakkr and Vrijling, 98). Also th ffct of climat chang and th consqunt sa lvl ris on th conclusions of th papr hav to b studid in futur (Vrijling and Van urdn, 99, and Jallow t al., 996). REFERENCES Bakkr, W.T. and Vrijling, J.K. 98, Probabilistic Dsign of Sa Dfncs, ICCE, Sydny, 4-59 Carvalho TMM, Colho COA, 998. Coastal risk prcption: a cas study in Aviro District, Portugal JOURNAL OF HAZARDOUS MATERIALS, 6 (-3): 63-7 AUG 998 Jallow BP, Barrow MKA, Lathrman SP, 996. Vulnrability of th coastal zon of Th Gambia to sa lvl ris and dvlopmnt of rspons stratgis and adaptation options, CLIMATE RESEARCH 6 (): FEB van Dantzig, D. 956, Economic Dcision Problms for Flood Prvntion, Economtrica 4, Nw Havn, Vrijling, J.K.,. Probabilistic dsign of watr dfns systms in Th Nthrlands, Rliability Enginring & Systm Safty, Volum 74, Issu 3, Dcmbr, Pags Vrijling, J.K. and van urdn, J.A. 99, Salvl ris: a probabilistic dsign problm, ICCE, Dlft, 6-7. Vrijling, J.K. and P.H.A.J.M. van Gldr, 997, Socital risk and th concpt of risk avrsion, Procdings of ESREL'97, Europan Safty and Rliability Confrnc, pp. 45-5, Prgamon,

8 COASTAL ZONE RISK IN THE NETHERLANDS Prof J.K.Vrijling, dr ir P. van Gldr, ir J. Litjns - van Loon Kywords: Safty Economics Coastal zon risk Dun rosion FN-Curvs Floods Dlft Univrsity of Tchnology, Faculty of Civil Enginring and Goscincs, Hydraulic Enginring Division, P.O. Box 548, 6 GA Dlft, Th Nthrlands, Fax: , j.k.vrijling@ct.tudlft.nl, p.vangldr@ct.tudlft.nl Ministry of Transport, Public Works and Watr Managmnt, DWW, P.O. Box 544, 6 GA Dlft, Th Nthrlands, J.Litjns-vLoon@DWW.RWS.MinVnW.NL 8