Evaluation of investment options mitigating catastrophic losses under the impacts of climate change

Transcription

1 Chi Truong (Ausralia), Sefan Trück (Ausralia) Evaluaion of invesmen opions miigaing caasrophic losses under he impacs of climae change Absrac I is of significan concern ha climae change will exaggerae he frequency and severiy of exreme evens such as: floods, sorms, droughs and bushfires. As he value of properies under risk increases due o economic growh, also he probabiliy of caasrophic evens may be amplified by climae change impacs. Thus, here is a need for local governmens o inves in adapaion measures in order o reduce poenial losses from hese caasrophic evens. However, economic models ha help local governmens o evaluae hose invesmen projecs are currenly lacking. Two challenges are faced when evaluaing hese projecs. Firs, i is difficul o quanify he risk due o he lack of observaions on caasrophic evens a he local level. Second, invesmen coss are ofen lumpy and he invesmen decisions are irreversible, so ha he invesmen sraegy based on he ne presen value (NPV) crierion is no opimal. Under he uncerain growh of he sock of asses and he uncerain impacs of climae change, he opimal iming of invesmens ino adapaion sraegies ha reduce caasrophic risks is of major imporance. This paper presens a simple economic framework o quanify climae change risks and a real opion approach o illusrae he opimal iming of invesmen sraegies for local governmens. Keywords: real opion, caasrophes, climae change, adapaion. JEL Classificaion: Q51, Q54. Inroducion Concern over global warming consequences has inensified over he las wo decades as severe naural disasers become more frequen. Higher frequency of disasers is believed o be a direc consequence of global warming. Global warming raises he energy level wihin he climae sysem and makes caasrophic evens such as floods, sorms, droughs and bushfires more likely o happen. While climae change miigaion can help o rea he problem a is roo, miigaion iniiaives may ake a long ime o show heir impacs due o he ineria inheren in he global climae sysem. Even if subsanial emission reducion is commied, he global emperaure is going o increase before i sabilizes (IPCC, 27). The risks, relaed o caasrophic evens, are expeced o increase regardless of miigaion effors, making climae change adapaion essenial. Mos of adapaion decisions o miigae caasrophic losses require significan invesmen, he benefis of which scaer among various sakeholders and spread over a long ime horizon. To help policy makers make sound invesmen decisions, a horough analysis of he coss and benefis of differen adapaion sraegies is needed. This is no a simple ask, requiring he assessmen of all he impacs of he projec and hen aaching moneary values o hese impacs. Impac assessmen ofen requires muli-disciplinary approaches and impac moneizaion someimes requires complex modeling when markes for some producs of he projec do no exis. A large number of sudies have focused on Chi Truong, Sefan Trück, analysing he cos and benefis of adapaion projecs, if he projec is o be invesed immediaely (Brouwer and van Ek, 24; Suarez e al., 25; Michael, 27; Kirshen e al., 28; Symes e al., 29a). In hese sudies, afer he presen values of expeced coss and expeced benefis of he projec have been found, hey are aggregaed o give an expeced ne presen value (ENPV). As a general decision rule, he projec is invesed if he ENPV is posiive and no, oherwise. The ENPV crierion, however, ignores an imporan aspec of invesmen. By evaluaing he projec based on an immediae invesmen decision, he possibiliy ha he projec invesmen can be deferred o a fuure ime is no considered. Such analysis ignores he opimal iming of invesmens and akes away he flexibiliy o defer he invesmen decision and reconsider i a anoher ime. For an adapaion projec, his flexibiliy is imporan for wo reasons. Firs, because caasrophic risks increase over ime and he value a risk may be expeced o increase over ime, by delaying he invesmen, he capial cos of invesmen in iniial years, when he benefis of he projec are low, can be avoided. Second, because significan uncerainy is inheren in climae change projecions, deferring invesmen o fuure periods gives he invesor an opporuniy o revise he esimaion of he projec values based on new informaion on climae change. If he impacs of climae change are no significan, he projec is no invesed and he expensive invesmen cos is avoided. Oherwise, he projec is invesed and only he benefi of he projec over he deferral period is los. Therefore, he invesmen flexibiliy helps he invesor o avoid he downside risk (o he value of he projec) and benefi from he upside risk.

2 In his paper, we provide a framework o compue he opimal iming of adapaion sraegies, aking ino accoun invesmen flexibiliy under deerminisic assumpions abou he growh of he value a risk and he impacs of climae change on he probabiliy ha caasrophic evens occur. The paper is srucured as follows. In Secion 1, previous sudies on climae change adapaion will be reviewed. In Secion 2, he modeling framework is oulined and applied for he exemplary case of an adapaion measure o bushfire risk in Kuringai council, NSW, Ausralia. The las Secion concludes he paper. 1. Lieraure review Climae change adapaion involves a wide range of invesmen decisions. For example, infrasrucure upgrade or replacemen, land use planning as well as coasline and flood defense projecs are highly researched opics (Hallegae, 29). In mos adapaion sudies, climae change impacs are carefully esimaed, while invesmen choices are analysed, based on he simple ENPV crierion. To provide a predicion of climae change, adapaion sudies ofen assume a cerain global emission scenario o generae a global emission rae. The emission rae is hen used as an inpu o a general circulaion model (GCM) o provide forecass on he fuure global climae (Kirshen e al., 28, Ermolieva and Sergienko, 28, Jones e al., 27). The climae projecions generaed by GCMs and he economic scenarios for he examined region are hen combined o examine he opimal adapaion sraegies. In some sudies, insead of assuming an exogenous global emission rae, an inegraed assessmen model (IAM) is used o generae global emission raes (Kuik e al., 26). Alhough, adapaion may aler he emission rae a he global level when many regions are considered, as poined ou by Kuik e al. (26), no sudy so far has incorporaed he feedback from adapaion scenarios on emission raes. Once he global climae projecions have been obained, he correlaion beween he global weaher and he local weaher can be used o generae local climae projecions. Regarding invesmen analysis a he local level, mos adapaion sudies adop a saic framework, ignoring he flexibiliy of invesmen decisions (Wes e al., 21; Brouwer and van Ek, 24; Suarez e al., 25; Kousky e al., 26; Michael, 27; Kirshen e al., 28). The majoriy of hese sudies use insurance models o provide deailed modeling of caasrophic risk a he local level. Suarez e al. (25) evaluae he produciviy loss in he Boson merololian area due o lack of ransporaion in flood evens caused by climae change. An empirical flood insurance model is used ogeher wih a se of developmen assumpions regarding spaial paerns of populaion, economic aciviies and developmen paerns for he fuure years o esimae he flood cos in he case of no climae change. The impacs of climae change on he sea level and on he local weaher are evaluaed using a global climae model (GCM). The cos, imposed by climae change, is hen he difference beween he flood cos in he climae change scenario and he flood cos in he no climae change scenario. Suarez e al. (25) found ha he flood cos is significanly increased by climae change. However, no adapaion is considered in heir sudy. Kirshen e al. (28) evaluae adapaion sraegies o reduce he loss from increased sorm surge flooding in meropolian Boson. Sea levels are assumed o rise a a consan rae, which increases sorm surge heighs and resuls in more severe propery damage. Examined adapaion sraegies include no adapaion, propery floodproofing, building coasal proecion srucures such as seawalls and rereaing inland. They found ha i is opimal o use expensive srucural proecion in areas ha are highly developed and less srucural approaches such as: floodproofing and limiing or removing developmen in less developed or environmenal sensiive areas. Alhough i is claimed o be a unique sudy ha considers various adapaion acions, hese acions are evaluaed separaely. The sraegies are considered using he ENPV crierion, ignoring he value of he opion o delay he invesmen. Symes e al. (29b) examine land rerea sraegies in Souh Eas Queensland o avoid losses from sorm surges. Using an empirical insurance model and he assumpion ha he sea level will rise by.3m by 25, hey esimae he waer level for he whole region when he highes sorm surge occurs. The resuls are used o divide he region ino high risk and low risk areas wih high risk areas being he ones in which he highes waer level is above 1 m. Brouwer and van Ek (24) invesigae he increased risk due o he expeced impac of climae change and he increasing economic value of he proeced properies. They evaluae he benefis and coss of a floodplain resoraion (i.e., widening and deepening floodplain) sraegy o increase he resilience of waer sysems o reduce he risks and damages associaed wih flooding in he Neherlands. I is argued ha floodplain resoraion provides environmenal benefis in erms of creaing new wildlife habias, recreaional ameniies in addiion o reducing flooding risk. Brouwer and van Ek use a combinaion of modelling and exper judgemen mehods o evaluae he expeced consequences of proecion 99

3 measures. Non-moneary benefis are moneised, using resuls from saed preference sudies. They found ha he ENPV of floodplain resoraion is posiive and he invesmen is desirable, bu cauioned ha he exac size and value of he prediced impacs of he sraegy is highly uncerain. In summary, saic sudies no aking ino accoun he opimal iming of invesmens ino adapaion sraegies seem o dominae he lieraure. Using empirical insurance models, hese sudies can provide quie accurae forecass for he near fuure. These sudies, however, ignore he value of he opion o delay he invesmen. For adapaion sraegies ha involve a long ime horizon, ignoring he opion value, may resul in significan losses or subopimal invesmen decisions. 2. Modeling framework In his Secion, we will provide a framework for he analysis of climae change adapaion opions wih respec o risk from caasrophic evens and finding he opimal adapaion sraegy. In a firs sep we sugges an approach for quanifying poenial losses from exreme evens like sorms, droughs or bushfires ha migh be furher increased in frequency and severiy due o climae change impacs. We recommend he use of he so-called loss disribuion approach (LDA) ha is quie popular in he financial indusry for modeling insurance claims and losses, arising from operaional risks in he banking indusry (see Klugman e al., 1998; or Bank of Inernaional Selemen, 21). The LDA involves he esimaion of an adequae frequency and severiy disribuion for he considered exreme evens. The aggregae loss disribuion for he hazard is hen compued by combining hese wo disribuions such ha expeced annual loss and he loss a any arbirary confidence level can be compued. In he second sep, using he calculaed figures of he aggregae loss disribuion for each year in combinaion wih cos esimaes for adapaion sraegies i is hen possible o apply he real opion heory o compue he opimal sraegy The loss disribuion approach. The LDA is a saisical approach for generaing an aggregae loss disribuion. To compue he probabiliy disribuion of he aggregae loss over a one year ime horizon, we need o esimae he probabiliy disribuion funcion of he single even loss and is frequency. For a naural or climae-impac relaed hazard, his means ha we have o deermine a probabiliy disribuion for he number of evens per ime period as well as a severiy disribuion for poenial losses from he evens. Then i is possible o compue he cumulaive losses for each ime period. Generally, a sochasic process S, is assumed describing he cumulaive caasrophic losses faced over he ime inerval [, ]. The process S, is modeled by a compound Poisson process of he form: N iid... S X, X ~ F, (1) k k k where F denoes he disribuion funcion for he severiy of he losses, N denoes a homogenous Poisson process wih inensiy, and N is assumed o be independen from X. The compound Poisson process in equaion (1) has parameers ha do no change hrough ime. In conras, in considering poenial losses under climae change scenarios, i is more realisic o assume ha he frequency and severiy disribuion may change coninuously hrough ime. To apply he LDA o he climae change adapaion problem, we use T compound Poisson processes, each represening he aggregae loss occuring in one ime period, where T is he lifeime of he projec. Le and F be he parameers of he compound Poisson process in period. A propery of he compound process in equaion (1) is ha he expeced aggregae loss, ES ( ), is equal o he produc of he expeced number of evens and he expeced individual loss: ES ( ) EN ( ) EX ( ) EX ( ). (2) 2.2. Invesmen model. In his Secion, we consider an adapaion projec ha reduces he probabiliy of he propery a risk being damaged when a caasrophic even occurs. As in many previous sudies (Wes e al., 21; Brouwer and van Ek, 24; Suarez e al., 25; Michael, 27; Zhu e al., 27; Kirshen e al., 28), we assume ha he invesor is risk neural. This assumpion is reasonable for invesmen projecs, funded by governmen, since caasrophic risks in differen regions are independen and he governmen can pool hese risks such ha only he expeced values are relevan (Kousky e al., 26). Suppose ha he projec reduces he probabiliy of he propery a risk being damaged when a caasrophic even occurs by a proporion k. Wih he projec in place, he number of damaging evens in period follows a Poisson process wih inensiy k, and he expeced benefi of he projec in period is k E( X ). We assume ha he invesmen decision can be deferred forever, bu once he projec is invesed, a k 1

4 new projec will be invesed whenever he old one is fully depreciaed. These are sandard assumpions in real opion sudies (Dixi and Pindyck, 1994). Then, invesmen provides a cash flow of k E( X ) for each period from he ime i is invesed o he infiniy and he invesmen cos is he presen value of a flow of invesmen cos per projec ha occurs every T years. Specifically, he invesmen cos can be calculaed as follows. Le I T be he esimaed invesmen cos for a projec ha lass T years and A be he annuiy of he invesmen cos, i.e: T 1 A A 1 A... A I, T T 1 r (1 r) 1 where words: 1 A I T 1 T 1 is he discoun facor. In oher 1 r 1. Then, he invesmen cos over he infinie ime horizon is: I A(1 r) / r. (3) The invesmen problem is hen o find he invesmen ime so ha he ENPV of he invesmen is maximised: r max e k E( X ) I, (4) where I is calculaed using in he equaion (3) Empirical resuls Baseline analysis. The model is applied o he case of bushfire managemen in Ku-ring-gai Council Local area (in New Souh Wales, Ausralia), where residenial properies are in close proximiy o bushfire risk areas. Assume ha as an adapaion sraegy, he risk of house damage could be reduced by consrucing a fire rail ha breaks wild fire ransiion and allows more ime for fire brigades o respond bushfires. To invesigae he reducion of he risk for residenial properies, exper opinions could be used o calibrae he parameers of he loss disribuions before and afer implemening his adapaion measure. Under a changed climae wih a endency o have hoer emperaures, he frequency of bushfires is likely o increase. The esimaion of he bushfire frequency disribuion is based on he assumpion ha he sock of greenhouse gases will significanly increase over he nex decades and coninue his increasing rend unil he year 21, when i sabilises a a consan level. In order o quanify he frequency disribuion, we apply an exper guess saing ha for he considered Ku-ring-gai area i is expeced ha he frequency of bushfires will approximaely double unil 25. Based on hese forecass, we furher make he assumpion ha he inensiy of bushfires,, is assumed o increase linearly unil he ime when he climae sysem sabilises, i.e., he year 21. Wih he inensiy in year 21, esimaed by he exper o be.2, he bushfire inensiy is esimaed o increase o a level of.4 by 25. Wih a coninuing linear increase of he inensiy unil 21, we assume ha he inensiy reaches a level of.65 by 21 and remains a ha level for subsequen years (Table 1). We acknowledge ha he choice of he frequency parameer for our case sudy is raher based on an exper esimae han a climae model, however, given he difficulies of such models wih respec o downscaling predicions o he local scale, we consider our approach sill as a feasible alernaive. Differen from bushfire frequency, bushfire severiy in fuure years depend on he physical srengh of bushfires and he value of he risk-prone properies. Alhough he weaher under a changed climae may make bushfires more fierce, he fuel load can be expeced o be lower due o more frequen bushfires. Therefore, we assume ha he physical srengh of bushfires in he fuure will be same as he curren level. In conras, he value of he risk-prone properies depends on he number of addiional houses in he region and he fuure coss of reconsrucing houses afer a fire occurs. The census daa for Kuring-gai indicaes ha he number of houses in his area has reached a sable level and in fuure years, i is unlikely ha new houses will be consruced (Hazvi and Oo, 28). The number of damaged houses, when a fire occurs, is herefore assumed o be consan in he fuure years and equal o 3 houses as esimaed by he exper for year 21. For he fuure coss of house reconsrucion, we use he esimaion by ABCB (28) for he year 21 consrucion cos and calculaing he real growh rae of house consrucion by subracing he inflaion rae from he nominal growh rae of consrucion esimaed cos using he price index of maerials used in house building for NSW over he period of (ABS, 21). The consrucion cos is esimaed o increase a a rae of.1% per year from he level of $32, per house in 21. The discoun rae is assumed o be he social discoun rae since he considered projec is invesed by he public secor. I is assumed o be 1% (see Gollier (28) for he discussion on social discoun rae under climae change). 11

5 Table 1. Esimaed values of parameers Parameers Value Curren damage risk, 21.2 Damage risk in year 21, Expeced number of houses damaged per even 3 Curren consrucion cos per house $32, Real growh rae of consrucion cos.1%/year Risk reducion proporion by projec, k 2% Lifeime of he projec, T Invesmen cos per projec 5 years $1.5 million Projec mainenance cos $5, Real ineres rae 1% The model in equaion (4) is solved using an Excel spreadshee. The ENPVs of he projec (dependen on he ime when he invesmen is made) in he base case is depiced in Figure 1. As shown, he maximal value of he invesmen projec is achieved if he projec is invesed in 58 years ime, even hough invesing immediaely would give a posiive ENPV. The difference beween he ENPV when invesmen ime is opimised and he curren ENPV of he projec is he value of invesmen flexibiliy. For he invesigaed base case, his value is nearly 5% of he rue value of he projec such ha immediae invesmen, despie a posiive ENPV would resul in a subopimal oucome in comparison o he poenial economic benefi of he adapaion sraegy under he opimal invesmen ime. ENPV (housands dollars) 3, 2,5 2, 1,5 1, 5 Opimal invesmen ime Fig. 1. Opimal invesmen ime for baseline case Sensiiviy analysis. To examine he robusness of he empirical resuls, we carry ou sensiiviy analysis on he discoun rae, he invesmen cos, he growh rae of he value a risk, and he growh rae of caasrophic risk. 1. Discoun raes. The debae on a choice beween a social discoun rae and a marke discoun rae is ye o be seled in he lieraure (Kuik e al., 26). In he case of using a marke discoun rae, he discoun rae will be significanly higher han in he base case scenario. Under a higher discoun rae, he capial cos, avoided by deferring he invesmen, increases. As a resul, he value of flexibiliy and waiing ime increase as illusraed in Figure 2a. This resul holds as long as he discoun rae does no increase excessively and drive he curren ENPV of he projec below zero. When he curren ENPV of he projec becomes negaive, he flexibiliy value is equal o he value of he projec when invesmen ime is opimised. The resuls, when he discoun rae is increased o 3%, are shown in Figure 2a. The ENPV of he projec is negaive if i is invesed immediaely, bu posiive if invesmen is deferred by 68 years. Using he ENPV crierion would urn down valuable projecs. However, he value los, due o he usage of he ENPV crierion, is lower when he discoun rae is higher. 2. Invesmen coss. The impacs of he iniial invesmen coss are similar o he impacs of he discoun rae. As he invesmen coss decrease, also he capial cos avoided by invesmen delay decreases. Therefore, he benefi of delaying he invesmen decreases and he waiing ime is shorened. As shown in Figure 2b, when he invesmen cos is reduced by one hird, he waiing ime is reduced from 58 years o 44 years. Noe ha, under he given scenario, when he invesmen cos is reduced o a sufficienly low level (e.g., $5,), i is opimal o inves in he projec immediaely insead of posponing he invesmen o a laer poin in ime. 3. Growh rae of value a risk. We examine he impacs of an increase in he growh rae of he value a risk in our example he expeced number of houses ha will be damaged imes he reconsrucion cos per house by increasing he growh rae of he consrucion cos from.1% o 1%. Wih a higher growh of he value a risk, he annual benefi of he projec in a laer period is higher. The cos of waing increases and he value of invesmen flexibiliy and he waiing ime are decreased, as shown in Figure 2c. 4. Growh rae of caasrophic risk. Modeling resuls, when he growh rae of caasrophic risk is doubled, is presened in Figure 2d. Alhough he role of caasrophic risk and he role of consrucion cos are he same, he role of he growh rae of risk is differen from ha of consrucion cos. The former is assumed o sabilised in year 21, while he laer is no. However, he impacs of a higher growh rae of risk esimaed by he model are he same as ha of he growh rae of he value a risk. Wih a higher growh rae of risk, he invesmen flexibiliy value and he waiing ime are reduced. 12

6 ENPV (housands dollars) ENPV (housands dollars) Opimal invesmen ime , -1,5 a. Impacs of a higher discoun rae Opimal invesmen ime 4, 3, 2, 1, b. Impacs of a lower invesmen cos ENPV (housands dollars) ENPV (housands dollars) Opimal invesmen ime 14, 12, 1, 8, 6, 4, 2, c. Impacs of a higher growh in VaR 1, 8, 6, 4, 2, Opimal invesmen ime d. Impacs of a higher growh in risk Fig. 2. Sensiiviy analysis resuls Conclusion In his paper, we have oulined a framework o quanify he risk of caasrophic evens and o evaluae opimal adapaion sraegy incorporaing he value of invesmen flexibiliy. The applicaion of he framework has been demonsraed for he case of bushfire managemen in he Ku-ring-gai area, NSW, Ausralia. For a sylized example, we have illusraed ha immediae invesmen ino an adapaion measure o climae change migh provide a posiive economic value, bu deferring he invesmen o a laer poin in ime can provide even a greaer economic benefi. A large number of previous sudies have focused on evaluaing wheher an adapaion projec creaes posiive values o he sociey, ignoring he value of flexibiliy in invesing. The resuls in his paper demonsrae ha in evaluaing References adapaion projecs, i is imporan no only o cover all he impacs of adapaion projecs, bu also o consider he choices an invesor has in erms of opimal iming of he adapaion sraegy. A limiaion of he framework oulined in his paper is ha no uncerainy has been considered. In realiy, he uncerainy relaing o he esimaion of coss and benefis of adapaion projecs is vas. Therefore, deferring he invesmen will enable he invesor o gain more accurae climae change impac assessmens. The value of informaion will enhance he value of invesmen flexibiliy and i is even more imporan o incorporae he value of invesmen flexibiliy in he cos benefi analysis. The exension of he framework o allow for uncerainy abou he growh of value a risk and he impacs of climae change on caasrophic risks is lef for fuure research. 1. Ausralian Building Codes Board (28). Impacs on housing affordabiliy, Available from URL: hp:// B17A1B2FB9AA&ypename &fieldname=filename. 2. Ausralian Bureau of Saisics (21) Producer price indexes, Ausralia, Canberra. 3. Brouwer, R. and van Ek, R. (24). Inegraed ecological, economic and social impac assessmen of alernaive flood conrol policies in he Neherlands, Ecological Economics, 5, pp Dixi, A.K. and Pindyck, R.S. (1994). Invesmen under uncerainy, Princeon Universiy Press, Princeon, New Jersey. 5. Gollier, C. (28). Discouning wih fa-ailed economic growh, Journal of Risk and Uncerainy, 37, pp Hallegae, S. (29). Sraegies o adap o an uncerain climae change, Global Environmenal Change-Human and Policy Dimensions, 19, pp Hazvi, E. and Oo, G. (28). Prices, rens and raional speculaive bubbles in he Sydney housing marke, Economic Record, 84, pp

7 8. IPCC (27). Climae change 27: he physical science basis, conribuion of working group i o he fourh assessmen repor of he inergovernmenal panel on climae change, Cambridge Universiy Press, Cambridge: New York. 9. Kirshen, P., Knee, K. and Ruh, M. (28). Climae change and coasal flooding in Mero Boson: impacs and adapaion sraegies, Climaic Change, 9, pp Kousky, C., Lumer, E.F.P. and Zeckhauser, R.J. (26). Privae Invesmen and Governmen Proecion, Journal of Risk and Uncerainy, 33, pp Kuik, O.J., Bucher, B., Caenacci, M., Karakaya, E. and Tol, R.S.J. (26). Mehodological aspecs of recen climae change damage cos sudies, Fridjof Nansen Insiue, Oslo and Research Uni for Susainabiliy and Global Change, Hamburg Universiy. 12. Michael, J.A. (27). Episodic flooding and he cos of sea-level rise, Ecological Economics, 63, pp Suarez, P., Anderson, W., Mahal, V. and Lakshmanan, T.R. (25). Impacs of flooding and climae change on urban ransporaion: a sysemwide performance assessmen of he Boson Mero area, Transporaion Research Par D-Transpor and Environmen, 1, pp Symes, D., Akbar, D., Gillen, M. and Smih, P. (29a). Land-use miigaion sraegies for sorm surge risk in Souh Eas Queensland, Ausralian Geographer, 4. pp Symes, D., Akbar, D., Gillen, M. and Smih, P. (29b). Land-Use Miigaion Sraegies for Sorm Surge Risk in Souh Eas Queensland, Ausralian Geographer, 4, pp Wes, J.J., Small, M.J. and Dowlaabadi, H. (21). Sorms, invesor decisions, and he economic impacs of sea level rise, Climaic Change, 48, pp Zhu, T.J., Lund, J.R., Jenkins, M.W., Marques, G.F. and Rizema, R.S. (27). Climae change, urbanizaion, and opimal long-erm floodplain proecion, Waer Resources Research,