SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO560 Economic losses from US hurricanes consisen wih an influence from climae change Francisco Esrada 1,, W.J. Wouer Bozen, Richard S.J. Tol 3,,4,5 1 Cenro de Ciencias de la Amósfera, Universidad Nacional Auónoma de México, Ciudad Universiaria, Circuio Exerior, Mexico, DF, Mexico, Insiue for Environmenal Sudies, VU Universiy, Amserdam, Neherlands, 3 Deparmen of Economics, Universiy of Sussex, Falmer, Unied Kingdom, 4 Deparmen of Spaial Economics, VU Universiy, Amserdam, The Neherlands, 5 Tinbergen Insiue, Amserdam, The Neherlands Supplemenary Informaion Table of conens S1.1. Effecs of he sandard normalizaion procedure on he rending behavior of he economic coss of exreme evens. S1.. Differences in he rae of growh of exposed wealh and he normalizaion variables. S1..1. Differences in raes of growh caused by misidenificaion of he normalizaion variables. S1... Geographic and secor heerogeneiy of growh in exposed wealh and aggregaed proxy variables of wealh. S1..3. Effecs of ime evolving vulnerabiliy on he normalizaion procedure. S1..4. Simulaion experimens for illusraing he poenial failures of he normalizaion procedure when invesigaing he presence of a climae change signal on disaser losses. S. A modificaion of he sandard normalizaion procedure o esimae he presence of a climae change signal in disaser losses. S3. Invesigaing he exisence of a climae change signal in he hurricane damage in he Unied Saes during he period S3.1. Socioeconomic and climae daa sources. S3.. Normalizaion per even using disaggregaed populaion daa and real wealh per capia. S3.3. Sensiiviy analysis. S Number and inensiy of sorms and hurricanes in he Alanic basin. S3.3.. Landfalling sorms and hurricanes in he US. S Join esimaion of he normalizaion and he damage funcions for he hurricane losses in he US S Single-sep esimaion of he effecs of socioeconomic variables and climae relaed variables. S General findings and conclusions. NATURE GEOSCIENCE 1

2 S1.1. Effecs of he sandard normalizaion procedure on he rending behavior of he economic coss of exreme evens Invesigaing he exisence of a climae change signal in observed ime series of disaser damage is complicaed by he presence of confounding facors ha can also impar nonsaionary behavior o hese ime series. This problem, which may be bes described as a signal exracion issue, has been commonly addressed by scaling he observed damages wih he variables ha represen changes in exposure o disasers. These exposure changes are he resul of socioeconomic change. The nonsaionary behavior of disaser damages caused by hese variables could oherwise be misakenly aribued o facors associaed wih climae change. Increases in wealh and populaion in areas prone o suffer he impacs of exreme weaher evens have been idenified as wo prominen drivers ha cause effecs on disaser damages ha can confound wih climae change impacs 1 3. The effecs of increasing populaion and wealh on he economic coss of hurricane and sorm damages need o be properly conrolled for in order o invesigae he poenial influence of climae change on hese damages 4. The usually applied normalizaion procedure scales he inflaion-adjused value of he ime series of losses by an indicaor of wealh and/or populaion change,5. Thus, his normalizaion inends o show losses as if all disasers occurred over he same exposed asses a a single poin in ime 1,3. The normalizaion procedure is used for wo differen purposes. The firs is o re-express losses in a way ha he magniude of losses is measured in erms relaive o local populaion and wealh. The second is o invesigae o which exen he rend in losses can be explained by socieal change and hen o invesigae if here is a residual rend ha could be relaed o climae change 6. The usefulness and adequacy of he normalizaion procedure for he firs purpose is unquesionable, as i consiss in simply rescaling losses according o socioeconomic variables of ineres. This rescaling can give a firs order proxy for welfare losses. However, for he second purpose, which is he mos relevan one in erms of climae policy 6, he usefulness of he normalizaion procedure is quesionable because he underlying assumpions may no hold. In paricular, i imposes a proporional causal relaionship beween socieal change and losses which is hen i is used o derend losses o isolae a poenial climae change signal. The alernaive proposed in his paper is o esimae hese relaions using a saisical model, insead of re-expressing losses as a proporion of socioeconomic variables by assuming cerain relaions. In his secion we show ha he sandard normalizaion procedure commonly used in he lieraure is likely o inadverenly inroduce rends in he normalized damages as well as o incorrecly disor or cancel a poenial climae change signal. The sandard normalizaion procedure is shown o be appropriae only under very srong assumpions abou he idenificaion of he normalizaion variables as well as changes in exposure and vulnerabiliy. We use a simple mahemaical model o illusrae he resriciveness of he commonly used normalizaion approach. The normalized damages ND adjused by he socioeconomic variable y can be described as:

3 1 ND D y where y h x f y (1) D are he inflaion adjused damages, f represens he poenial economic loss (i.e., acual vulnerable wealh) o a paricular exreme weaher even, y represens he chosen proxy scaling variable (e.g. a measure of wealh), x is he relevan weaher variable which is poenially influenced by climae change, and h is a general damage funcion i. The common finding repored in he lieraure is ha here is no longer a rend in ND, leading o he conclusion ha here is no real effec of climae change on damages or ha a leas his effec is no ye deecable. Neverheless, i should be sressed ha hese findings are condiional on he adequacy of he f y normalizaion procedure and in paricular on he raio (i.e., he normalized poenial loss). y The criical issue resides in wheher he funcion y f y y y f preserves he acual rae of growh of y. acually measures if he growh of f y is "acceleraing" or "deceleraing" in comparison o ha of y. As an example, consider per capia GDP. If per capia GDP shows a posiive rend r hen GDP is acceleraing wih respec o populaion. In general, if y e w and f y e grow a some raes r and yields: w w and hus D f y hx e hx, hen he normalizaion procedure ND y w r 1r h x e hx e hx f y () where 1 can be inerpreed as he difference in growh raes beween poenial economic f y and y. These mismaches can be caused by changes in vulnerabiliy and exposure ha are no capured by y as well as by he possible lack of a correc idenificaion of he relevan variables driving he poenial economic losses ii, and he absence of long enough daa records wih an appropriae geographic resoluion, among ohers. In general, f y is a complex funcion no only of y, bu also of several facors including exposure, vulnerabiliy and adapaion (which are no refleced by y ) 7. Therefore, he growh raes f y and y may show emporal and/or permanen mismaches ha can lead o a wide variey of nonsaionary behaviors ha may incorrecly cancel a poenial climae change signal as well as produce a rend ha migh misakenly be aribued o losses and he scaling variable due o mismaches beween he raes of growh of i Equaion (1) is used for illusraing purposes. Noe ha i could be easily exended o more han one scaling variable (e.g., wealh and populaion), as well as for a summary of losses from differen evens and locaions. ii This is likely o pose a problem in pracice because he relevance of he normalizaion variables is ofen no esed, and some of he poenial loss drivers may be unobservable or unmeasured, such as changes in physical vulnerabiliy of exposed buildings. 3

4 his phenomenon. Only in he special case of 1 for 1,.., n, no nonsaionary behavior will inadverenly be inroduced o ND. Tha is, he sandard normalizaion procedure requires vulnerabiliy o remain consan and ha changes in exposure are solely deermined by he normalizaion variables chosen. S1.. Differences in he rae of growh of exposed wealh and he normalizaion variables. S1..1. Differences in raes of growh caused by misidenificaion of he normalizaion variables. One criical problem of he normalizaion procedure is ha i relies solely on he judicious selecion of normalizaion variables, while formal esing of heir adequacy or significance is no applied. This complicaes he correc specificaion of he normalizaion procedure and precludes o invesigae if he adjusmen is correc or if he daa was under- or over-adjused. Therefore rends could have been incorrecly induced by he normalizaion procedure. To illusrae his possibiliy, consider he inflaion adjused daa series on hurricane damage in he Unied Saes for he period The lieraure proposes as normalizaion mulipliers he naional level of real wealh per capia RWPC and populaion P, in he affeced coasal couny i a ime. These variables are expressed as he raio of heir 005 values and heir values in he year when he even ook place 3. Fig. S1 shows he absolue losses (panel A), he losses normalized by boh RWPC and P, (panel B), he losses normalized by RWPC (panel C) and he losses normalized i by P i, (panel D). Each of hese panels show large differences regarding he size of he damages per even and imply a very differen evoluion of losses during he period. The normalizaion in panel B), which is he one ha has been used in he lieraure, provides a much lager scaling of he evens occurring a he beginning of he 0h cenury, making some of hem considerably larger han hose occurring in he record season of 005. This normalizaion has lead o he conclusion ha no climae change signal is presen in hurricane losses 3. The obvious problem is deermining which, if any, of he normalizaions in panels B), C) and D) correcly adjuss he losses o reflec changes in exposure. In he sandard normalizaion procedure here is no possibiliy o address his problem in a formal and objecive manner, and he final decision relies solely on he subjecive judgmen of he researcher. Furhermore, as discussed in S, he sandard normalizaion procedure assigns he same weigh o all normalizaion variables (i.e., imposes a join resricion on he scaling coefficiens o be equal o one). Consequenly, even if he selecion of normalizaion variables is correc, hey are likely o be over- or underrepresened in he adjused losses. Equaion () helps o explain he differences in he normalized losses in Fig. S1. When boh RWPC and P, are used for normalizing he losses, he raes of growh of hese variables are i P added r RWPC y r e. This leads o a much larger adjusmen facor when compared wih panels C) and D) in Fig. S1. Under he sandard normalizaion procedure here is no formal way o discriminae among hese normalizaion opions. Even sligh differences in he raes of growh beween he chosen normalizaion variables and he poenial losses can lead o incorrecly inducing or cancelling rends in he normalized losses. Fig. S uses equaion () o illusrae how he effecs of a 10% difference in he raes of growh ( 1. 1, 0. 9 ) produce a rend ha i 4

5 could be wrongly aribued o changes in climae variables or in vulnerabiliy, even hough boh of hem are held consan. In pracice, is an unobservable variable and no ess are conduced o evaluae he significance of he chosen normalizaion variables. Furhermore, noe ha r and are likely o vary wih ime as a funcion of several facors, such as he level of wealh, saving and invesmen raes, populaion concenraion, urbanizaion, he raio of angible/inangible wealh, as well as wih oher imporan drivers, such as axes and fiscal incenives, among ohers. If and r are allowed o vary wih ime, a variey of nonsaionary behavior (no only rends) can arise afer applying he sandard normalizaion procedure due o emporal and permanen mismaches in hese raes of growh. Furhermore, since he normalizaion procedure is based on comparing growh raes, oher problems may arise when choosing he appropriae scaling variables. I has been noed ha GDP may no be an adequae measure of wealh given ha GDP is a flow and wealh is a sock 8. Bu his widely used proxy for wealh 1 can lead o even more deceiving resuls: as is implied by economic growh heory, high raes of growh in GDP may indeed correspond o low levels of wealh 9. As such, poorer economies are likely o show faser increases in f, while for richer economies growh in y han y y would be deceleraing wih respec o f y. Tha is, he normalizaion procedure could produce he exac opposie scaling ha was inended o, and induce negaive/posiive rends ha will disor he analysis. In his case, even hough GDP is clearly a driver of exposed wealh, is rae of growh can be seen as ransformed by a funcion f GDP, leading o a very differen emporal evoluion han ha of GDP. In he nex subsecions some special cases are examined where mismaches in he growh raes of he poenial economic losses and he normalizing variables can occur, namely geographic and secor heerogeneiy and ime evolving vulnerabiliy. S1... Geographic and secor heerogeneiy of growh in exposed wealh and aggregaed proxy variables of wealh. As has been discussed previously in he lieraure, noably Neumayer and Barhel 5, some shorcomings of he normalizaion procedure arise because i assumes a homogeneous geographical disribuion of he raes of growh of he poenial losses and of he seleced normalizaion variables. This is a special case of equaion (), which can be expressed as: ND i, f yi, i, 1r h x e hx y (5) i, i, and n ND ND i i1, 5

6 where 1 is he difference in growh raes beween poenial economic losses and he scaling i, variable, and i, represens he fracion of he mismach due o differences in he raes of growh of he local and aggregae scaling variable in he i-h affeced localiy ( i 1,..., n ). To illusrae he effec on he normalizaion procedure of mismaches beween he local and aggregae scaling variables, we use sae level and local income growh raes in Florida, U.S. obained from he Bureau of Economic Analysis of he US Deparmen of Commerce (hp://bea.gov/iable/). For his example 0 and i, varies for he i counies, bu i is consan in ime, such ha y r f i, i, 1 y e. Fig. S3a shows he raio of he local and sae level proprieors' income. While he annual average compound growh rae of sae level proprieors' income for Florida over he period is 5.88%, large differences exis among is counies, ranging from 1.38% o 9.13%. Even when imposing 0 he normalizaion procedure produces a variey of posiive/negaive ime rends ha inroduce a nonsaionary behavior on ND i,. Given ha i, is in mos cases unknown due o he lack of adequae spaial resoluion of he daa, hese rends would be aribued o h x or o changes in vulnerabiliy when in fac he rending behavior is an arifac creaed by he normalizaion procedure. In addiion, if i, is allowed o vary wih ime, a wide variey of nonsaionary behaviors can be inroduced o he normalized wealh and, herefore, o normalized losses due o differences in local and sae level economic developmen over ime. f yi, Fig. S3b shows similar resuls for he raio of he couny and sae level per capia y personal income. Figs. S4a and S4b show ha posiive and negaive rends can also be inadverenly inroduced o he normalized losses due o differences in he raes of growh of he differen secors in he affeced counies. These figures show he proprieors' personal income a he couny level for he farm (Fig. S4a) and nonfarm (Fig. S4b) secors normalized by he sae level proprieors' personal income. These figures sugges ha if he proporion of damages is larger in he farm f yi, secor, hen he raio will likely inroduce a negaive rend o he normalized losses. y S1..3. Effecs of ime evolving vulnerabiliy on he normalizaion procedure. Some effors have been carried ou o ry o creae vulnerabiliy indices based on observed daa 10. However, his approach is problemaic since i presupposes ha he sandard normalizaion procedure is correc and no affeced by a ime evolving vulnerabiliy. The sandard normalizaion procedure ignores vulnerabiliy and does no include any correcion o ake ino accoun changes in his variable. Equaion (1) implicily assumes ha vulnerabiliy remains 6

7 consan over ime and ha i does no vary wih changes in exposure. A re-expression of equaion () ha allows o make vulnerabiliy explici is as follows: ND y v w r v 1r h x e hx e hx f y (6) where v acs as scaling facor and represens he effec of vulnerabiliy over he rae of growh of he poenial economic losses. Larger mismaches wih he growh rae of he normalizaion variable occur if v 1. While i is uncerain how much reducion/increase in vulnerabiliy has occurred, i is very unlikely ha he implici assumpion of consan vulnerabiliy 11,1 (i.e., v is sricly equal o 1) underpinning he sandard normalizaion procedure holds. For example, in he USA building codes o flood-proof newly buil srucures have srenghened over ime in response o severe flood evens 13. The Federal Emergency Managemen Agency (FEMA) imposes minimum building codes on communiies in he USA ha choose o paricipae in he Naional Flood Insurance Program (NFIP) ha was founded in For example, hese regulaions require new consrucions in flood-prone areas o be elevaed o he expeced waer level ha can be caused by a flood ha occurs on average once in 100 years. More buildings have become subjec o hese building requiremens over ime when new communiies joined he NFIP, and minimum building codes have become sricer as well 13. Moreover, several US saes and ciies have sared o adop flood-resisan building code regulaions ha go beyond minimum NFIP building code requiremens 14. Changes in adapaion have been also inferred from observed damage daa from around he world 10,1 (S). Resuls in S provide addiional evidence of adapaion processes affecing he vulnerabiliy of US properies o landfalling hurricanes and sorms. To illusrae he effecs of a ime varying vulnerabiliy consider he example of he proprieor's income in Walon, Florida. For his example, he normalizaion was carried ou using he sae level proprieor's income and i is assumed ha 0 in equaion (5). When he sandard normalizaion procedure is applied and vulnerabiliy is assumed o be consan and equal o one, hen due o he differences in he raes of growh of sae and couny f y level in he proprieor's income, he resuling normalized poenial losses conain a y posiive rend induced by he normalizaion procedure (Fig. S5). Neverheless, when vulnerabiliy is no fixed ( v 1), resuls can be quie differen. If in realiy for he period vulnerabiliy decreased as v (i.e., imposing a oal reducion in he rae of growh of he poenial economic losses of 0% by year 011), hen incorrecly a negaive rend f y in normalized losses would be found insead (Fig. S5). y Disasers are he produc of a mixure of socioeconomic and geophysical processes for which he observed economic losses associaed wih hem are jus paricular realizaions. Differen levels of vulnerabiliy and exposure would have led o very differen coss for he same geophysical even. 7

8 Such differences in levels can, among ohers, arise due o differen shares of economic secors, differen proporions in ime of y ha become increases in poenial economic losses for he differen localiies affeced and echnological changes. The limiaions of he sandard normalizaion mehod discussed above preclude is correc specificaion and, in consequence, his procedure canno guaranee ha no rend will be inroduced or aken away by is applicaion. Therefore, when rying o uncover he exisence of a climae change signal in disaser losses, he sandard normalizaion procedure could lead o resuls almos as misleading as assuming ha he increases in wealh and populaion have no effec on disaser losses. S1..4. Simulaion experimens for illusraing he poenial failures of he normalizaion procedure when invesigaing he presence of a climae change signal on disaser losses. This subsecion provides simulaion examples o illusrae he combined effecs of he differences in growh raes beween f y and y, and ime-dependen vulnerabiliy when invesigaing he exisence of a climae change signal afer he sandard normalizaion procedure has been applied. The general simulaion model is se up as follows: hx D f y (7) y h x f ND (8) y h x (9) v w y e f (10) r y e (11) v v (1) where chosen o be 3% plus a normally disribued noise of N 0,0.01 ~ exp, c b, w is he growh rae of he poenial economic losses, which is, v is a uniform random variable U p, q and he rae of growh of he normalizaion variable is r 4.5%. In all cases he simulaion experimens consised of 1,000 realizaions and he ime horizon was chosen o be 100 years. For he firs simulaion experimen, vulnerabiliy was held fixed ( v 0 ), and was chosen o represen a saionary climae ( b 0, ). The goal of his simulaion is o illusrae ha even under he assumpion of a saionary climae, he normalizaion procedure can lead o differen rending behaviors depending on he differences in he raes w and r. Given ha he rue value of w is unknown, in pracice wha is observed afer he normalizaion of losses is he 8

9 resuling nonsaionary/saionary behavior, a resul ha is commonly inerpreed as indicaing effecs on losses of climae change, adapaion and/or changes in vulnerabiliy. Table S1 shows he percenage of significan posiive/negaive rends in he realizaions of he damage funcion, losses and normalized losses iii. The slopes and he corresponding -saisics values were obained from he regression Z u, where Z represens eiher h x, D or ND. As expeced from a saionary climae, he percenage of significan rends in h x is 5.4%, which is very close o he number of rejecions of he null hypohesis ( 0 ) ha are expeced o occur by chance. This is no he case of he un-normalized losses of which 99.% have posiive significan rends. These rends are caused by he growh in he poenial economic losses, which is wha he normalizaion procedure aims o correc. Neverheless, afer he normalizaion procedure has been applied, he percenage of he adjused losses ha show a significan negaive rend is 75.9% of he realizaions. These rends are an arifac caused by he differences in he raes of growh of he normalizaion variable y and he poenial economic losses f y. This rend is likely o be erroneously aribued o some geophysical or socioeconomic facors (e.g., climae change, or adapaion measures) oher han an unobservable mismach of he growh raes of f. y and The second simulaion experimen allows for a nonsaionary climae where he rend in he damage funcion is defined by (Fig. S6). As is shown in he Table S, in all cases he un-normalized losses D have a significan posiive rend, while he normalized losses obscured he climae change signal conained in h x abou 64% of he simulaions for which a posiive significan rend was originally deeced and he normalizaion incorrecly induced a significan negaive rend in 11.% of hem. Since in realiy he rue informaion abou he generaing processes of h x, D and ND is lacking, he mismach beween significan rends in h x and he lack hereof in ND could be erroneously inerpreed as he absence of a climae change signal in disaser losses, while in fac climae change has increased damage. The hird simulaion experimen also allows for a nonsaionary climae ( ) bu inroduces a ime-decreasing vulnerabiliy deermined by equaion 1 and v ~ U 0,0.. Tha is, for his experimen a reducion in vulnerabiliy causes an up o 0% decrease in he rae of growh of he poenial economic losses over he simulaed 100-year period. As shown in Table 3, given ha he normalizaion procedure assumes ha vulnerabiliy remains consan in ime (more precisely i ignores i, implying v 1 in equaion 8), he final effec is ha an even smaller number of imes he exising climae change rend in he damage funcion will sill be deecable in he normalized losses and, in abou 14.3% of he cases, his procedure will impar a negaive rend o hem. In general, hese simulaion experimens sugges ha when invesigaing he exisence of a climae change signal in disaser losses he curren normalizaion pracice could lead o resuls y iii Saisical significance is evaluaed a he 5% level. 9

10 which are almos as misleading as if no correcion was applied for he increasing wealh and populaion. The exisence of unobserved variables precludes he possibiliy of verifying he validiy of he normalizaion and no firm conclusion abou he exisence of a climae change can in fac be drawn, alhough his has been common pracice 1. Evidenly, depending on he values chosen for he raes of growh r and w as well as he evoluion of he climae variable and vulnerabiliy, differen rends and percenages of significance can arise. This simulaion experimen shows ha only in very special cases, he sandard normalizaion procedure can be successfully applied wihou inadverenly inroducing or aking away rends in he normalized losses. Even if he normalizaion variables are chosen correcly, i is quie likely ha hey will provide a poor represenaion of he acual growh in he poenial economic losses. If his is he case, he normalizaion procedure would impar a nonsaionary behavior o ND ha could blur any climae change signal or creae a false one. This is furher complicaed by he effecs of vulnerabiliy and adapaion which are largely deermined by socioeconomic facors and mosly unobservable, bu can hardly be considered o remain consan over ime. S. A modificaion of he sandard normalizaion procedure o esimae he presence of a climae change signal in disaser losses. Observed losses from disasers represen a mixure of differen socioeconomic and geophysical processes ha are inherenly random, uncerain and in some cases unobservable. As shown in he previous secions, he sandard normalizaion procedure which consiss of scaling he observed losses by some wealh and/or populaion proxy variables is only adequae under very resricive condiions. In his secion a regression-based normalizaion procedure is presened which provides a way o es he significance of he chosen normalizaion variables, o esimae he coefficiens for scaling he rae of growh of he normalizaion variables and o es for he significance of climae variables ha may be considered as direc or indirec drivers of he observed losses. The main purpose of he sandard normalizaion procedure is o remove he effecs of socioeconomic variables on he observed losses in order o es for he presence of a poenial climae change signal. In his subsecion we show ha he normalized losses obained by means of he sandard normalizaion procedure are equivalen o he residuals of a regression wih disaser damage as dependen variable and he socioeconomic drivers as explanaory variables and wih parameers ha are resriced o be equal o uniy. I is imporan o undersand why regression can be used as a ool for conducing he normalizaion of damages. A propery of regression residuals is ha hey are orhogonal o he fied values of he dependen variable as well as o he explanaory variables. For his reason, regressing a dependen variable agains some desired explanaory variables is used o filer he dependen variable from effecs of he explanaory variables. In his case, he purpose of he regression is no o idenify relaionships beween variables per se, bu o properly remove he effecs of he explanaory variables on a ime series of ineres. Regression has been widely used for removing he effecs of variables ha could obscure subsequen analyses. Derending is he mos common example: he dependen variables are regressed agains a linear, nonlinear ime 10

11 rend or even sochasic rends. The residuals of hese regression (he error erms) become he variable of ineres and are used for a wide variey of analyses, such as sudying cycles, seasonaliy or oher ime-series properies of he dependen variable 15, as well as for residualbased saisical ess 15,16, among many ohers). Regression is also commonly used for removing no only he effecs of rends bu also of auocorrelaion, i.e. ime dependence (e.g., hrough ARMA prewhiening filers), he effecs of oher explanaory variables over he dependen variable 18,19, cycles, seasonaliy, as well as inhomogeneiies and disconinuiies in a se of observaions due for example o changes in wheher saions characerisics and heir locaion 0, o name a few. Consider he basic scheme of he sandard normalizaion procedure: D ND (13) y which is mahemaically equivalen o ln ND lnd lny (13') where he naural logarihm of he normalized damages ln ND is he residual of subracing he naural logarihm of he normalizaion variable ln from he observed damages ln. Noe ha by rearranging he erms in 13' and recognizing he sochasic naure of he variables in his equaion, 13' is an esimable regression: ln D lny lnnd where ln ND and, are he regression coefficiens and error erm, respecively and is he slope coefficien Under his approach, he proporionaliy assumpion becomes empirically esable (i.e. wheher 1) as well as he relevance of y as a normalizaion variable. More generally, equaion (1) can be expressed as: y D ND y h x y f (14) g g y y e is a power funcion and 1 in he sandard normalizaion procedure. Noe ha when 1 he rae of growh of he normalizaion variable is scaled. This coefficien r where can be esimaed using he observed daa o preven he mismach in he growh raes of f y and y. ND in equaions (1) and (14) is equivalen o he exponenial of ln( D ) ln( ) (15) y from: 11

12 when he resricion 1 is imposed. The validiy of his resricion can be empirically esed and a more appropriae value for can be esimaed. Moreover, he saisical significance of y can be evaluaed, providing an objecive crierion for selecing he relevan normalizaion variables. will conain he variabiliy and nonsaionary signals ha are no explained by he scaling variable y. Noe ha he proposed regression-based approach encompasses he sandard normalizaion procedure, as he laer is a special case of he former. In S1..4 some of he effecs of omiing changes in vulnerabiliy (or adapaion) are described and i is illusraed how he sandard normalizaion procedure can produce misleading resuls. Alhough he regression-based mehod proposed here is also sensiive o he misspecificaion of how vulnerabiliy evolves over ime, i consiues a significan improvemen compared o he sandard normalizaion procedure. The omission of a measure of how vulnerabiliy has evolved represens an omied variable problem (see S3.3.4). However in his case i is omied because his variable is largely unobserved or unmeasured (alhough o a cerain degree i can be represened by he evoluion of wealh and populaion). The effecs of omiing vulnerabiliy on parameer esimaes in he regression-based normalizaion are: If wealh and/or populaion is posiively correlaed wih vulnerabiliy, hen he coefficien of wealh and/or populaion would be biased upwards. Tha is, par of he effec of increases in vulnerabiliy is capured by he upwards bias in he coefficien of wealh and/or populaion. If wealh and/or populaion is negaively correlaed wih vulnerabiliy, hen he coefficien of wealh and/or populaion would be biased downwards. These wo effecs assume ha increases in losses are posiively relaed o increases in vulnerabiliy (which could be expeced). Par of he effecs of he omied variable (vulnerabiliy or adapaion) will be refleced by he elasiciy esimaes 4,7,1. As such, even if he effecs of changes in vulnerabiliy may no be compleely aken ino accoun by he regression-based approach, i is less rigid han he sandard normalizaion procedure which assumes uniary elasiciies. Furhermore, if vulnerabiliy and adapaion daa become available, hen such daa can be direcly included in he proposed normalizaion regression. An implici assumpion in equaion (15) is ha he parameers of his regression are sable hroughou he sample. Abrup and significan changes in vulnerabiliy could lead o changes in how losses and socioeconomic drivers are relaed and he regression parameers would likely show srucural changes. In his case, he parameer values would no be valid for he whole sample and he srucural changes would need o be modeled in regression (15). In his paper, a es 1 is used o es for he exisence of such srucural breaks (see S3..). Invesigaing he exisence of a poenial climae change signal in ND is usually done by esing for a linear rend by means of a normal linear regression and ignoring ha losses are usually highly skewed and non-normally disribued. Srong deviaions from he normaliy assumpion can render hypohesis esing on he esimaed coefficiens invalid. Alernaive approaches like 1

13 Box-Cox ransformaions are required in such cases 3. Box-Cox ransformaions are widely used in he lieraure and provide a simple way o make daa approximaely normal. The Box-Cox ransformaion is a class of power ransformaions such ha: y * y 1 ln if 0 y if 0 where is commonly esimaed by maximizing he log-likelihood funcion or by minimizing he skewness coefficien. Furhermore, as is ofen discussed in he lieraure 4 6, hx is likely o be a nonlinear funcion of x (e.g. a power funcion). Therefore, invesigaing he exisence of a climae change signal should no be limied o linear rends, bu should allow for a variey of sysemaic behavior ha could be consisen wih i. In addiion, for he slope coefficien esimaes using unransformed daa, 95% confidence inervals based on block-boosrap echniques 7 are esimaed. The mehod for boosrapping regression coefficiens can be described as follows 8. Consider he residuals of a linear rend regression model: u ND cˆ bˆ * * A boosrap sample u is generaed by resampling wih replacemen he error erm u. Then u is * * used o calculae a boosrapped sample of he dependen variable ND cˆ b ˆ u. The linear * rend regression model is esimaed using ND as he dependen and he esimaed coefficiens * * ˆc and ˆb are saved. These seps are repeaed a large number of imes in order o obain an esimae of he disribuion of he regression parameers. For his paper we use 1,000 boosrap samples o calculae he 95% confidence inervals and sandard error esimaes of he slope parameer. When using he boosrap mehod, we consider a coefficien saisically significan if he 95% confidence inerval does no include zero. In case of auocorrelaed daa, he resampling wih replacemen is done using a number of observaions a a ime insead of jus one. For he esimaes presened here, a block-boosrap of 10 observaions was used iv. Oher mehods for modeling non-normal variables have been used in he lieraure, including exreme value models, quanile regression 9 and compound Poisson processes 30. S3. Invesigaing he exisence of a climae change signal in he hurricane damage in he Unied Saes during he period The exisence of a climae change signal in he economic losses from hurricane landfalls in he U.S. has been ruled ou by previous sudies 3, Here we es if his conclusion is robus o using he regression-based normalizaion procedure described in he previous secion. Moreover, iv Resuls are fairly robus o choosing longer block lenghs. 13

14 we examine if his conclusion sill holds when he loss daa is ransformed o be approximaely normally disribued before esing for he presence of a linear rend. S3.1. Socioeconomic and climae daa sources. All socioeconomic daa used here are aken from he Cener for Science and Technology Policy Research and cover he period (hp://sciencepolicy.colorado.edu/publicaions/special/normalized_hurricane_ damages.hml). The ime series of he inflaion adjused economic losses relaed o hurricane landfalls along he Unied Saes Gulf and Alanic coass ( D, ) correspond o he losses ha occurred in he couny i i in he year as a resul of a paricular hurricane. The normalizaion variables used are he coasal and naional populaion P i, and P, and naional real wealh per capia RWPC defined as he curren-cos ne sock of fixed asses and consumer durable goods produced each year adjused by inflaion and populaion a he naional level. The normalizaion variables are expressed as he raio of heir 005 values and heir values in he year ha he disaser ook place. This daabase also includes informaion abou he sorm/hurricane caegory associaed o he recorded damages. From his informaion we derive he annual number of landfalling hurricanes and sorms (NE), and he hurricane caegory (HC) where zero represens a ropical sorm. In he case of hurricanes wih differen caegories when affecing differen counies, he larges value was assigned. The daabase of landfalling hurricanes and sorms in he US from he Re-Analysis Projec NOAA 35,36 (hp:// is also analyzed. The reanalysis of landfalling hurricanes in he US is available for he period, while he reanalysis of landfalling sorms is limied o he periods and The revised HURDAT basin-wide daase on hurricanes and sorms 37 (hp:// is analyzed o provide a sensiiviy analysis of our resuls. The climae indices considered for his sudy are he Accumulaed Cyclonic Energy (ACE; hp://climexp.knmi.nl/daa/ialanic_annual_ace.da), he yearly number of hurricanes in he Alanic basin (Emanuel, hp://climexp.knmi.nl/daa/ica.da), he Alanic Mulidecadal Oscillaion (AMO; hp:// he Souhern Oscillaion Index (SOI; hp:// and he Pacific Decadal Oscillaion (PDO; hp://jisao.washingon.edu/pdo/pdo.laes) and global mean surface emperaure (G; NASA) which is used as a general index represening he evoluion of he observed warming during he 0h cenury. Wih he excepion of G, all hese climae variabiliy indices are commonly used in he lieraure for predicing he oal seasonal number of hurricanes 38, he probabiliy of hurricane landfall in he US 39 and heir desrucive poenial 40. Noe ha G has been recenly shown o be an imporan explanaory variable of Alanic Cyclone Aciviy measured by sorm surge saisics 41. In he same sudy i is argued ha projecions based on he relaionship of cyclonic aciviy in he Norh Alanic and G are preferable because he causal relaionship can be considered unidirecional, unlike wih oher regional variables. 14

15 ACE is defined as he sum of he squares of he maximum susained surface wind speed measured every six hours for all named sorms while hey are a leas ropical sorm srengh v. In conjuncion wih he oal number of named sorms, hurricanes, and major hurricanes, ACE is used o caegorize he Norh Alanic hurricane seasons. SOI is a measure of he El Niño/Souhern Oscillaion (ENSO) which is associaed o he hurricane aciviy in he Alanic, he landfall frequency of hurricanes in he U.S and he hurricane damages 45. The warm ENSO phase is associaed wih lower hurricane aciviy, landfall frequency and damages. The PDO represens a long-lived El Niño-like paern of Pacific climae variabiliy 46 and provides informaion for invesigaing he effecs of his phenomenon in he inerannual and mulidecadal imescales. As in he case of PDO, AMO has been shown o also affec he number of hurricanes, heir inensiy and landfall occurrence in he mulidecadal imescale 47. The warm phase of he AMO is associaed wih more acive ropical cyclone seasons and i is believed ha i can modulae he ENSO-hurricane aciviy relaionships. The resuls and conclusions presened in his paper are based on mehodological improvemens of previous analyses of rends in naural disaser losses. As such, we aim o keep our resuls comparable wih influenial published work on his heme. For his reason, we use he daase of Pielke 3 which is especially suiable because i was published in a peer reviewed journal and i consiues an emblemaic example in he hurricane losses and climae change lieraure as is refleced by he many imes i was cied (468 imes according o Google Scholar a he ime of wriing). The main drawback of his daase is ha he records end in 005. The ICAT damage esimaor offers an alernaive wih records unil 01. However, his daase shows significan differences wih ha of Pielke ha could impede a direc comparison of he sandard commonly used normalizaion procedure wih he normalizaion mehod we propose. These daases are differen no only in he periods hey cover ( agains ) bu also in erms of he number of sorms ha occur in he period and he magniude of he recorded losses. The ICAT damage esimaor daase is far less discussed in he lieraure (e.g., Google Scholar for "ica damage esimaor" only produces 5 resuls) which is why i is no used here. S3.. Normalizaion per even using disaggregaed populaion daa and real wealh per capia. In his subsecion he resuls of he sandard and he proposed regression-based normalizaion procedures are compared and he exisence of a climae change signal is invesigaed. The normalizaion procedure PL05 used in Pielke 3 can be described as follows: ND D * RWPC * P (16) i i i i where ND i are he normalized damages in 005 dollars. Noe ha ND i in equaion (16) is equivalen o he exponenial of y from he following regression: v hp:// 15

16 ln( D ) ln( P ) ln( RWPC ) (17) i i i when he resricion 1 is imposed. As an alernaive hese coefficiens can be esimaed and he validiy of his resricion can be empirically esed. Table S4 reveals ha P i is no significanly differen from zero a any convenional level while RWPC i is only significan a he 10% level. The esimaed elasiciies indicae ha while damages are proporional o RWPC i, he damages are far less han proporional o populaion P i and ha changes in populaion have no significan effec on damages. Analyzing global damage daa suggess ha urbanizaion and ciies have been developed wih effecively provided proecion agains disasers, indicaing ha significan adapaion effors have aken place in such areas 4,7,1. Previous sudies on global and US hurricane damages using regression models o esimae he elasiciies of damages o wealh and populaion variables repor coefficiens ha are also well below uniy 4,1. However, hese sudies did no explore he implicaions of hese resuls for he normalizaion echniques discussed here. As menioned in S, regression (17) assumes ha is esimaed parameers are sable. In order o check his assumpion, he CUSUM es 1 was applied and no evidence of srucural breaks was found. As expeced from he coefficien values in Table 1, he resricion of 1 is rejeced a he 1% level by means of a Wald es (es saisic value of 11.53) and i is ouside he 95% confidence ellipse of hese coefficiens (Fig. S7). Consequenly, he normalizaion procedure producing PL05 is incorrecly specified in he sense ha he imposed coefficien resricion does no hold and ha according o he -saisic P i is no relevan for normalizing D i. The resul is ha PL05 imposes a much larger scaling of he evens in he pas han wha is jusified by he daa, poenially cancelling any posiive rend ha could be associaed wih a climae change signal. As can be seen from Fig. S8, he normalized losses PL05 and he regression-based esimaes (REGN) imply a very differen evoluion of adjused hurricane losses during he period. Fig. S9 shows he normalized damages per year from 1900 o 005, which also show he weighing differences beween PL05 and REGN. Afer normalizing for changes in socioeconomic facors, generally he following linear regression is used o es for he exisence of a linear rend (i.e., es wheher or no b 0): ND c b (18) u where a posiive rend could poenially provide evidence of he presence of an effec of climae change on he economic coss of hurricane losses. As repored in he lieraure, he exisence of a significan linear rend is rejeced for PL05, bu a significan rend is found for REGN, even afer correcing he corresponding sandard errors for boh heeroskedasiciy and auocorrelaion (Table S5). According o his esimae he normalized hurricane losses have been increasing by 136 million dollars a year during he pas cenury (i.e., he losses are on average abou 14 billion dollars larger in 005 han if here was no rend). Noe ha if he desrucive hurricane loss year 005 is excluded, he rend is sill significan a he 1% level, bu he yearly esimae of losses decreases o abou 78 million dollars per year during he 0h cenury. If he linear rend in regression (18) is subsiued by G, he corresponding coefficien is significan a he 10% level 16

17 (-saisic value of 1.89) and indicaes ha hurricane losses in he US would increase by abou 1 billion dollars per 1ºC increase in global emperaures. However, an imporan assumpion when esing for saisical significance of he coefficiens in regression (18) is normaliy, and in cases of srong deviaion from his assumpion he esimaed sandard errors and he significance ess can be severely affeced. To avoid his problem, we es for a rend on he Box-Cox ransformaions of PL05 and REGN. The Box-Cox parameer was esimaed boh by maximizing he log-likelihood funcion MLE MS ( ) and by minimizing he skewness coefficien ( ). Table S6 shows ha boh mehods lead o similar esimaes for PL05 and REGN. However, he Box-Cox ransformaions based on MS he esimaes no only produce daa ha is more close o a normal disribuion, bu hey also help in reducing is heeroskedasiciy. The resuls of esing for a ime rend in he Box-Cox ransformed normalized loss daa reveal a highly significan posiive rend in boh PL05 and REGN. Once he daa is ransformed o fulfill he normaliy assumpion of regression (18), i becomes clear ha he normalized losses have sysemaically increased since he beginning of he 0h cenury, irrespecive of wheher he sandard or he regression-based normalizaion procedures are used. These resuls sugges ha if a more appropriae regression mehod is applied o he (debaable) PL05 normalizaion, hen an opposie conclusion can be drawn as in Pielke 3 and a climae change signal in hurricane loss rends canno be ruled ou. However, hese sysemaic increases in losses should be carefully inerpreed since hey may be caused by facors oher han he effecs of climae change. Naural variabiliy, in paricular low frequency oscillaions, can be misaken for a rend if hese sysemaic movemens are no aken ino accoun. To provide a beer assessmen of he exisence of a poenial rend in hurricane losses, we presen several regression models ha use geophysical variables o explain he rend and variabiliy of he normalized losses. In all cases, he exponenial smoohed G ( G ; Hol-Winers mehod 48 ) is used as an index o represen he warming rend signal over he analyzed period. Noe ha similar resuls are obained when using he Hodrick-Presco filer 49 for exracing he rend. For modeling he variabiliy of losses, he variables lised in S3.1 were used and he bes combinaions of variables in erms of heir saisical adequacy and fi are repored in Table S8. To evaluae he saisical adequacy of he regression models a series of misspecificaion ess were applied (Tables S9, S10a-S10d). In all cases, excep for models 3e, 4c and 4e for PL05, G is found o be significan a he 5% or 10% levels, denoing ha he observed warming rend helps o explain he remaining rend in losses afer being correced by wealh and populaion. This finding holds irrespecive of he normalizaion procedure used and of he mehod for esimaing he Box-Cox parameer. The regressions coefficiens have an inuiive physical inerpreaion: a more acive hurricane season in he Alanic and higher accumulaed cyclonic energy are associaed wih larger economic losses. The ACE is a proxy measure of he desrucive poenial of he ropical cyclone season. The losses from hurricane landfall are inversely relaed o he PDO, in accordance wih wha has been previously repored in he lieraure regarding he ENSO effecs on hurricane damages in he US 45. The cold PDO phase is linked o he occurrence of a higher number of 17

18 hurricanes in he Alanic and o increases in he likelihood of landfalling hurricanes in he US Gulf and Alanic coass, and hus he hurricane relaed economic losses end o be larger. The bes regression models, in erms of saisical adequacy and fi, are 1b, 1c and b, c hose MLE MS REGN, respecively, which explain abou 40% of he esimaed for REGN and variance of he normalized losses. In addiion o he warming rend represened by G, hese models are complemened by aggregae measuremens of he hurricane season aciviy (NHUR) and he accumulaed energy of hurricanes during he season (ACE). Two common problems arise in mos of he oher models: heersokedasiciy and parameer or variance insabiliy 50. MS Resuls illusrae ha he Box-Cox ransformed daa based on he effecively help correcing MLE non-normaliy bu also heeroskedasiciy, an oucome ha is no achieved using. Parameer or variance insabiliy occurs in almos all models for PL05, while in mos of he models based on REGN his problem is no presen. These resuls sugges ha even hough he warming rend is sill deecable in PL05, he sandard normalizaion procedure has disored his rend by imposing a coefficien resricion ha, as menioned above, is no empirically valid. Table 3 in he main ex presens he esimaed increases in losses associaed o some of he bes models in Table S8. Noe ha he figures in Table 3 represen a small proporion of he oal losses from ropical cyclones in he US and of he losses associaed o he mos inense hurricanes. For example, he losses associaed o he residual rend represened by he models in Table 3, amoun o % up o 1% of he oal losses in 005. Despie is curren small magniude, he finding of a residual rend is imporan since i represens a sysemaic increase in ropical cyclones losses ha could be consisen wih climae change. I is also imporan o noe ha boh NHUR, ACE and NE have a rend ha can be represened eiher by a simple ime rend or G, suggesing ha hese variables hemselves could conain a warming signal (Tables S11, S1 and S13). In he case of NHUR and NE a log-linear and four differen coun daa regression models indicae he exisence of a rending behavior in hese variables. The Huber-Whie sandard errors are used since hey allow for conducing valid inference even when he disribuion is incorrecly specified and heeroskedasic. All models for NHUR and ACE indicae ha G, he warming rend, is highly significan and ha AMO and SOI can accoun respecively for he low frequency variabiliy oscillaions and par of he year o year variabiliy of he annual oal number of hurricanes. ACE also accouns for he low frequency oscillaions and, since i is closely relaed o NHUR, i is able o explain a larger par of he observed variabiliy. In all cases, he regression residuals do no show any remaining rending or oscillaory paern (Fig. S9). For ACE, he esimaes obained by linear normal MS regressions using boh he original daa and is Box-Cox ransformaion (based on ) are presened (Table S1). In boh cases here is evidence of a posiive rend which can be represened by a ime rend or by G. The low frequency oscillaory movemen in ACE is explained by AMO and PDO and indicaes ha periods of warm AMO and cold PDO phases are relaed wih periods of sronger hurricane seasons. As in he case of NHUR, he regression residuals for ACE do no show any remaining rend or low frequency variaion (Fig. S10). The finding of a rend in ACE is consisen wih resuls from previous publicaions 51. Trends in ropical cyclone frequency have been idenified in he Norh Alanic. Recen analysis indicaes ha hese rends are robus since he 1970s 5. However, here is low confidence 18