Using the Geographically Weighted Regression to. Modify the Residential Flood Damage Function

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1 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Usg the Geographcally Weghted Regresso to Modfy the Resdetal Flood Damage Fucto L.F Chag, ad M.D. Su Room, Water Maagemet ad Geographc Iformato Research Lab, Departmet of Boevrometal Systems Egeerg, Natoal Tawa Uversty, No., sec. 4, Rd. Roosevelt, Tape Cty, Tawa 67, PH (886) ; FAX (886) ; emal: kk@uplad.ae,tu.edu.tw Room, Water Maagemet ad Geographc Iformato Research Lab, Departmet of Boevrometal Systems Egeerg, Natoal Tawa Uversty, No., sec. 4, Rd. Roosevelt, Tape Cty, Tawa 67, PH (886) ; FAX (886) ; emal: sumd@tu.edu.tw Abstract. Flood damage fuctos are ecessary to esure comprehesve rsk maagemet. Ths study attempts to establsh a resdetal flood damage fucto ad explores resdets lvg the Keelug bas, where flood dsasters occur frequetly Tawa. Ordary least squares (OLS) method s used to costruct a flood damage fucto. Aalytcal results dcate that flood depth, s the sgfcat varable, but the resdual s o-statoary wth spatal. The Geographcally Weghted Regresso (GWR) model s appled to modfy the tradtoal regresso model, whch caot capture spatal varatos, ad to solve the spatal o-statoary. Aalytcal results demostrate sgfcat spatal varato the local parameter estmates for the varable flood depth ad tercept. Therefore, a dummy varable, Zoe, s added to the OLS model. The R-square value s foud to crease from.5 to.4, ad the resdual s spatally statoary. I cocluso, the resdetal flood damage s determed by flood depth ad zoe, ad the GWR model ot oly captures the spatal varatos of the affectg factors, but also helps to dscover the explaatory varable to modfy the tradtoal regresso model.

2 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Key words:flood damage flood depth OLS GWR o- statoary Itroducto Floods occur frequetly Tawa because of ts geographcal locato, clmate ad topography. Statstcal data from the Mstry of the Iteror show that Tawa had a average of 4.47 typhoos ad may storms aually from 958 to 4. These evets have caused serous damage to agrculture, fshery, hydrologc egeerg, houses, traffc facltes, electrc power, telecommucatos ad ecoomcal actvtes. Rsk maagemet plays a very mportat role mtgatg the effects flood dsasters, whch cause damage to property ad threate lves. A complete flood maagemet ad mtgato system comprses a hydrologcal module for chael dscharge calculato, a ecoomc module for damage estmato, ad a rsk aalyss process (Grgg, 985). Although may studes have bee performed hydrology ad hydraulcs, few focus o flood damage Tawa (Chag, ). Sce the level flood damage vares regoally, studes relatg to other parts of the world caot be appled drectly to Tawa. For those reasos, ths study plas to establsh the resdetal flood damage fuctos, ad the result ca be cosdered as the referece of regoal rsk maagemet. Flood damage fucto s tradtoally estmated by a Emprcal Depth-Damage Curve. The curve ca be costructed two ways (Kag et al., 5), from the vestgato of damage after the dsaster (TVA, 969; FIA, 97; Grgg ad Helweg, 975; Smth et al., 994;Su et al., 5), ad from Sythess (Chag, ; Chag ad Su, ; Kag et al., 5). I the sythess approach, data of the property tems, possessve rate, ad the heght of the arragemet of the furture are collected, ad the possble damage of each tem durg floodg at each depth s vestgated. These two methods are dfferet the way of establshg the curve, both assume that the flood depth s the oly factor the flood damage fucto. Nevertheless, the flood depth may ot be suffcet for cosderato by a household flood damage fucto. McBea et al. (988) poted out that there were may factors besdes flood depth could affect the flood damage, such as tme of year of floodg, velocty of floodwaters, durato of floodg, sedmet load ad warg tme, ad therefore recommeded adjustg the flood damage fucto should be adjusted. Yag L. et al. (5) also oted that some meteorologcal, physographc

3 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE ad huma factors such as rafall, terra ad draage could fluece the actual flood damage. Hece, the relatoshps betwee varous factors ad flood damage are ow wdely examed. The most commo factor beg cosdered s the buldg type (Grgg, 974; FEMA, 977; McBea et al., 988; Smth, 994; Tawa Water Resource Agecy, 997; Chag, ; Kag et al., 5). Other factors clude area of ma floor, famly come (McBea et al., 988), flood warg system (Wd et al., 999; Davd, ), flood warg lead tme(peg-rowsell et al., ), experece of floodg (McPherso, 977; McBea et al., 988; Wd 999; Krasovskaa, ), the preparato before dsaster(peg-rowsell et al., ), durato of floodg (McBea et al., 988 ; Torterotot et al. 99; Hubert et al., 996), velocty of floodwaters(chm Hll, 974; Black, 975; Smth, 994; Beck et al., ), umber of people(mcbea et al., 988 ; Shaw, 5) ad the locato of household(chag, ; Shaw, 5). Sce the flood damage s affected by may factors, some recetly proposed multple regresso models for establshg the flood damage fucto corporate all such factors(shaw, 5). Although ths approach ca corporate all factors as the predctors ad rase the R-square value, t also creases the dffculty of predctor s data collecto whe predctg the damage. Ths model s a global multple regresso method, ad assumes that the regresso coeffcet s costat across the study rego (Platt, 4). I other words, t does ot cosder the spatal varato, so the resduals from the global model ofte exhbt spatal autocorrelato (Fothergham et al., ). It volates the assumpto of lear regresso. Thus, the am of ths study s to establsh the flood damage fucto for oe household by usg the smallest possble umbers of explaed varables, whle also cosderg the spatal varato ad solvg the resdual wth spatal autocorrelato problems.

4 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Ths study frst establshes the appled theoretcal equatos. Data sources are the dscussed, ad the studed areas are troduced. Fally, results are dscussed ad coclusos are draw. Method The frst step establshg the flood damage fucto for oe household by usg the smallest umbers of explaed varables, cosderg the spatal varato ad the solvg the resdual wth spatal autocorrelato problems, are to determe the factors causg flood damage. May flood damage factors exst as descrbed above, but the characterstcs of flood damage vary amog regos. Based o case studes Tawa, Shaw (5) corporated factors cludg flood depth, udatg tme, buldg type, structure, the umbers of floors, presece of a basemet, area, umber of people ad rego. He demostrated that the flood depth s the major factor affectg flood damage fuctos. Grgg (996) oted that eve wthout cosderg other factors, the flood depth damage curve was stll approprate for estmatg the flood damage. Therefore, ths study determes the flood damage factor accordg to the flood depth, whch s the most commoly cosdered factor prevous works. Ths study frst apples the OLS for global regresso to establsh the flood damage fucto. The Mora s I value s the used to proceed wth the test of spatal resduals to check whether the resduals have spatal autocorrelato. If the resduals have spatal autocorrelato, the the GWR s appled ad the test the sgfcace of the spatal varablty the rego. If the coeffcet exhbts sgfcat spatal varato, the spatal groupg s performed; the dummy varable s added to the orgal global regresso model, ad fally the result s modfed. The theoretcal models used ths study are troduced as follows. Global Regresso Model A global regresso model, calculated usg OLS, s adopted to establsh the flood damage fucto. Sce flood damage creases wth flood depth, the followg S-curve model was costructed: y = e ( β + β / x) + ε ()

5 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE where, y s the damage(nt dollar), x s the depth(cm), β β are the regresso coeffcets, ε s the resdual Formula () s the atural logarthm of formula () l y = β + β + ε x () where, y s the flood damage(nt dollar) x s the flood depth(cm) ε s the resdual The, β β ca estmated by smple lear regresso model. A basc assumpto fttg such a model s that the observatos are depedet of oe aother. A secod assumpto s that the structure of the model remas costat over the study area. That s, the estmated parameters have o local varatos. Resdual spatal autocorrelato testg After establshg the regresso model, the spatal autocorrelato coeffcet, Mora s I, s computed to detect spatal autocorrelato the resduals. Accordg to the defto of the researchers (Baley & Gatrell, 995), Mora s I value ca be dcated as I = = j= j w w, j, j (y y)(y j= j y) (y y) (3) where s the umber of pots or cells, y m s the value zoe m, ybar s the mea of attrbute y, ad w j s the spatal proxmty of pot ad j. We ofte use the verse of the dstace betwee pot ad j. Ths assumers that attrbute values of pots follow the frst law of geography. Wth the verse of the dstace, we gve smaller weghts to pots that are far apart ad lager weghts to pots that are closer together. For example, w j ca defed as /d j, where d j s the dstace betwee pot ad j. The expected value of Mora s I (.e. the value that would be obtaed f there

6 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE were o spatal patter to data) s E () I = (4) ( ) wth values of I larger tha ths dcatg postve spatal autocorrelato (smlar values cluster together) ad the values below ths dcatg atve spatal autocorrelato (smlar values are dspersed ). Uder ths assumpto, the varace of I s gve by Var () I [( 3 + 3) S S + 3S ] k ( ) [ S S + 6S ] () I = E (5) ( )( )( 3) S where S = w j S S = j ( w j + w j ) = = j= ( w j. + w. ) = = k = = j= ( y y) ( y y) 4 The dstrbuto of I s asymptotcally ormal uder assumpto radomzato. The stadardzed Z scores ca be calculated as I E(I) Z(I) = (6) S E(I) S E(I) = SQRT[ w j + 3( w j ) ( ( )( w j ) j j j j w j ) (7) The ull hypothess s radomly dstrbuted. If Z(I) >.96 or Z(I) <.96, the the resdual s statstcally sgfcat wth a statstcal sgfcace level of 5%. The resdual patter s clustered whe Z(I) >.96. Coversely, the resdual patter s dspersed whe Z(I) <.96. Alteratvely, f.96 < Z(I) <.96, the the resdual patters ot statstcally sgfcatly dfferet from a radom patter, eve f t looks somewhat clustered or vsually dspersed.

7 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE GWR Model If the resdual has spatal autocorrelato, the GWR ca be utlzed to modfy ad solve the problem (Brusdo et al., a,b Fothergham et al., a,b 998 Platt, 4). The modfcato of Formula () s l y Where y = β (u, v ) + β(u, v ) + ε (8) x s the flood damage of pot x s the flood depth of pot ( u, v ) deotes the coordates of the th pot space β (u, v ), β(u, v ) s a realzato of the cotuous fucto at pot I ε s the resdual of pot u, v ) ( I smple lear regresso model, a parameter s estmated for the relatoshp betwee each depedet varable ad depedet by OLS ad the relatoshp s assumed to be costat across the study area. The estmator for t s β = (X X) T X T Y (9) The GWR model recogzes that spatal varatos relatoshps mght exst. The GWR estmator s β = (X WX) T X T WY () Where X s the matrx of the depedet varable s observato value, whch s the matrx of x ( u x ( u X = x ( u, v ), v ), v ) β s the matrx of the regresso coeffcet, whch s the matrx of

8 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE β (u, v) β (u, v ) β =.. β (u, v ) β(u, v) β (u, v ).. β (u, v ) W s a matrx whose off-dagoal elemets are zero ad whose dagoal elemets deote the geographcal weghtg of observed data for pot. That s w W = (u, v ).. w (u, v ) w.. (u, v ) The weghtg of each observed data s w j (u, v ) exp( d j / h) = () dj s the Eucldea dstace betwee observed data ad j h s the costat value of badwdth *The badwdth may be ether suppled by the user, or estmated usg a techque such as crossvaldato. The parameter estmated wth GWR s the plotted oto the map to determe the parameter varato wth the rego. Smlarly, the stadard error ca be plotted oto the map to derve ts varato over space. Fally, the Mote Carlo test s employed to determe whether ay of the local parameter estmates are sgfcatly o-statoary. If the test result s sgfcat, the the parameter varatos are due to chace. Modfed global regresso model GWR aalyss ca ot oly modfy the resduals of tradtoal regresso wth spatal autocorrelato, but also cosder the spatal varato. Nevertheless, the result of GWR ca obta th regressos more complcated tha tradtoal global regresso. Therefore, the result of the GWR model s adopted to modfy the tradtoal

9 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE regresso model three steps. Frst, plot the hstogram of parameters wth sgfcat varato over space, ad observe the dstrbuto of each parameter. Next, perform spatal groupg based o the spatal dstrbuto of each parameter. Fally, corporate dummy varables to the orgal regresso model. Determe the ma varable by stepwse regresso, ad elmate the sgfcat varable. The model s thus modfed as follows: m = l y β β β GP + β + GP + ε x = x where () y s the flood damage(nt dollar) x s the flood depth (cm) GP s the dummy varable m s the umbers of spatal groupg β β β are the regresso coeffcets, ε s the resdual. The modfed regresso model ca ot oly cosder the spatal varato of each parameter, but ca also avod resduals wth spatal autocorrelato ad too may regresso equatos. Data Collecto ad Studed Area To establsh the flood damage fucto for oe household a resdetal area, the bas of the Keelug Rver, where flood dsasters occur frequetly, was selected as the studed area. The data of questoares from the flood damage caused by Nar Typhoo were collected. Households wth prevous flood experece were explored. The vestgated areas cluded Xzh Cty, Qdu Dstrct, Nagag Dstrct, Nehu Dstrct, SogSha Dstrct, Sy Dstrct ad Da-a Dstrct (as show Fgure ). The questoare cluded questos o dsaster scale (the flood depth ad udated tme), level of damage (the damage of household furture, decorato, ad vehcles etc.), basc household formato (the characterstcs of the buldg lke umbers of floors ad area) ad the rsk percepto factors (the flood experece, rsk formato, scale of the rsk, fluece of mass meda, whether oe s wllg to take the rsk or ot, whether the rsk s cotrollable or ot, fear of

10 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE the rsk). A total of 3 completed questoares were receved. All data were geocoded to the map. Fgure. Geographc dstrbuto of study area Tawa Result Global regresso model The regresso result of Formula () s show Table. The coeffcet of determato R =.5, the regresso coeffcet of tercept ad flood depth were sgfcatly dfferet from zero (at.5 level). Fgure plots the resduals versus the predctor values. Because the pots appear to scatter radomly about the le the mea of the resduals, all fudametal assumptos are correct. Itally, the resdual was mapped to determe whether the resduals had spatal autocorrelato (as show Fgure 3). The fgure reveals that the resdual spatal patter was vsually clustered, so Mora s I test was employed to test whether the resduals had spatal autocorrelato. The testg result demostrates that the Mora s I =.68, ad (Z(I) = 4.936>.96), mplyg that the resduals had spatal autocorrelato, volatg the assumpto of lear regresso. Therefore, GWR was appled to modfy the model.

11 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Table. Global regresso parameter estmates(=3) Parameter Estmate Std Estmate Std Err T P-Value Itercept /X Fgure. Global model resdual plot GWR Model The GWR model result dcates that R creased from.5 (OLS) to.6 (GWR), demostratg that GWR provdes a better explaatory ablty tha OLS. Fgure 4 ad 5 show the hstogram ad map of the tercept term from the GWR model. Fgure 4 reveals that the values of the tercept ca be dvded to three groups, hgh, medum ad low. Fgure 5 depcts the spatal dstrbuto of these three groups. The groups wth hgh values were located o the ortheast area. The groups wth medum values were located o the mddle area. The groups wth low values were located o the wester area. These fdgs dcate that the spatal patter was clustered sgfcatly. The tercept term dcates that floodg leads to fudametal flood damage. Fudametal flood damage s rsg gradually from West to Northeast, accordg to the spatal dstrbuto of the tercept. Fgure 6 dsplays the hstogram of the verse of flood depth varable-form GWR model, dcatg that the coeffcets ca be dvded to hgh ad low. Fgure 7 depcts the regresso coeffcets of the verse flood depth varable. The fgure shows that the groups wth hgh values were located o the medum ad wester areas, ad the groups wth low values were located o the ortheast area. These fdgs dcate that the spatal patter was also clustered sgfcatly.

12 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Mora s I =.68 Fgure 3. Global model resdual surface Fgure 4. Hstogram of the Itercept term from GWR model

13 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Fgure 5. Map of the Itercept term from GWR model Fgure 6: Hstogram of the regresso coeffcets of the verse of flood depth varable from GWR model

14 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Fgure 7. Map of the Iverse of Flood Depth term form GWR model The regresso coeffcets of the verse of flood depth varable dcate the chage of the flood damage per flood depth. A greater value dcates a greater chage flood damage wth creasg flood depth. The spatal dstrbuto of the coeffcets reveals that the value creased gradually from Northeast to West. The resdual of the GWR was mapped to detfy ay relatoshp betwee resdual ad spatal autocorrelato (as show Fgure 8). The spatal patter of resdual s ot clustered over space vsual. Further Mora s I was calculated to test whether the resduals had spatal autocorrelato. Accordg to the test result, I =.4 ( Z(I) =.6<.96 ), demostratg that the resdual wth spatal autocorrelato was already modfed. Mote Carlo smulato was the used to determe whether each regresso coeffcet was spatally o-statoary (Table ). Smulato results show that the regresso coeffcets of Itercept ad /X had sgfcat spatal varato at the % level, meag the two varables, Itercept ad /X, spatally affect the flood damage. Ths fdg mples that the regresso coeffcets were ot costat the study rego. Therefore, the GWR model s well suted to modfyg the tradtoal regresso model. Modfed global regresso model The costat values Fg. 5 were splt to hgh, medum ad low, ad the

15 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE verse flood depth s regresso coeffcets Fg. 7 were dvded to hgh ad low respectvely. I Table 3, * deotes data, ad N/A represets o-data. Aalytcal results show that all of the data could be dvded to three groups. These three groups were the mapped, revealg that these three groups were spatally clustered (as show Fgure 9). Therefore, spatal groupg was utlzed to modfy the orgal tradtoal model (OLS). Mora s I =.4 Fgure 8. Resduals from GWR model Table. Results of Mote Carlo test for spatal o-statoary a (=3) P-Value Itercept.*** /X.*** a Tests f regresso coeffcets chage over space a way that s ulkely to occur at radom *** = sgfcat at.% level ** = sgfcat at % level * = sgfcat at 5% level

16 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Table 3. The Dstrbuto of GWR s Regresso Coeffcet Values Parameter Itercept Low Mddle Hgh Low N/A N/A *Group3 Hgh *Group *Group N/A * deotes data ad N/A deotes o-data Group3 Group Group Zoe 3 Zoe Zoe Fgure 9. The Spatal Clusterg The orgal tradtoal model (OLS) was modfed accordg to the groupg result by addg two dummy varables, GP ad GP. The dummy varable GP = whe the locato of household was wth the Zoe, ad GP = otherwse. The dummy varable GP = whe the household was wth Zoe, ad GP = otherwse. The ull hypothess s that the regresso coeffcets of the costat ad verse of the flood depth wll ot chage wth dfferet areas The alteratve hypothess s that the regresso coeffcets of the costat ad

17 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE verse of the flood depth wll chage wth dfferet areas Therefore, the equato ca be modfed as the follows. l y = β + β + β GP + β3 GP + β 4 GP + β5 GP + ε (3) x x x Where y s the flood damage x s the flood depth GP = whe the locato of household was wth the Zoe GP = otherwse GP = whe the household was wth Zoe GP = otherwse β β β β 3 β 4 β 5 are the regresso coeffcets, ε s the resdual. Stepwse regresso was frst adopted to determe the ma varable. The calculato result reveals that oly ad GP were sgfcat, meag that the x equato could be chaged as l y = β + β + β GP + ε (4) x Equato (4) dcates that f the household was located Zoe, where GP =, the the equato could be preseted as l y = (β + β ) + β + ε (5) x Whe the household was ot located Zoe, where GP =, the the equato could be preseted as l y = β + β + ε (6) x Table 4 presets the result of the modfed regresso model The focusg o the ma varables ad proceeds wth regresso aalyss. The regresso coeffcets were statstcally sgfcat at a statstcal sgfcace level of 5%. The coeffcet of determato R of the modfed model creased from.5 (OLS) to.6 (modfed OLS). Ths result was smlar to that of the GWR model.

18 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Table 4. Result of modfed global a regresso model (=3) Parameter Estmate Std Estmate Std Err T P-Value Itercept /X GP a The average regresso result of the whole studed area To test f for spatal autocorrelato, the resdual of the modfed OLS was mapped to the map, ad the Mora s I value was obtaed (as show Fg. ). Test results demostrate that the Mora s I =.33, ad (Z(I) =.3<.96), dcatg that the spatal patter of resdual was radom. Therefore, the modfed OLS dd ot volate the assumpto of lear regresso. Mora s I =.33 Fgure. Resdual spatal dstrbuto from modfed regresso model Dscusso Fgure llustrates the result of the global regresso equato, whch demostrates that the damage varato was greatest at low depths. The average total damage was $5, per household. Substtutg the aalytcal result of modfed global regresso to Equatos

19 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE (5) (6) yelds the the flood damage fuctos for households s located ad outsde Zoe, respectvely. Whe the household s located Zoe, the flood damage fucto s: l y = ε (7) x Whe the household s outsde Zoe, the flood damage fucto s: l y = x Where + ε y s the flood damage x s the flood depth (8) ε s the resdual Equatos (7) ad (8) dcate that the flood damage fucto costat of a household located Zoe s lower tha that of a household located the other Zoes. Ths result shows the houses located outsde Zoe would suffer greater fudametal satary damage tha houses Zoe whe flood occurs. Mappg the results of Equatos (5) ad (6) to the plot of flood damage versus flood depth (as dsplayed Fg. ) dcates that the flood damage Zoe would be smaller tha that the other areas. The low water depth s taget slopes outsde Zoe would be greater tha those wth Zoe, meag the damage s most varable outsde Zoe. 6 5 loss(nt$) depth(cm) Fgure. The Curve of Flood Depth Damage

20 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE Fgure demostrates that the total flood damage wth flood depths other areas of cm 33cm would be approxmately $8,. Sce Zoe dd ot have hgh water depth s data ths torretal ra, the total flood damage at a flood depth of 5 cm would be approxmately $6,. The results of ths global regresso were represeted as a chart of flood damage versus flood depth, ad the compared wth those of Fg. The result of the global regresso s average total household damage was approxmately $5,, whch s betwee the $6, 8, estmated by the modfed regresso model, because the global regresso model dd ot cosder the spatal varato, makg the dffereces betwee areas udetectable. Fgure. Flood Depth-Damage Curve of Zoe ad Other rego Furthermore, the damage fucto results of ths study were compared wth those estmated by Shaw et al.(5), who utlzed the followg damage fucto: l(tloss)= l(depth)+.739(pre) 6.5(INS).7 (OWN) +.44 (BUILD) (.63) (.39)*** (.64) (-3.9)*** (-.39) (.97) (EXP) +.845(EXP)+.69(EXP3).5(LIVY) +. (IC) +.38 (PEO) Where (.66)* (.) (.) (-.86)* (.5) (.97)

21 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE TLOSS s Total losses of physcal property curred by a household DEPTH PRE INS OWN BUILD IC PEO EXP EXP EXP3 LIVY s Iudato from the flood (cm) Dummy= f adoptg preparedess agast floods Dummy= f purchasg flood surace for the house or car Dummy= f havg the owershp of the house Dummy= f a sgle house; Dummy= f a apartmet Household come (thousads of NT dollars) The umber of people the household Dummy= f havg oe floodg experece the past Dummy= f havg two floodg expereces the past Dummy= f havg three or more floodg expereces the past Years of lvg the area The total flood damage of oe floor estmated by Shaw et al. (5), was approxmately $43,4, whch s also betwee $6, ad $8, as estmated by the proposed modfed regresso model. For comparso, Kag et al. (5) calculated the total flood damage for oe household as approxmately $,, ad Chag () whch the total flood damage for oe household was approxmately $8,. The preset study produced lower a estmate tha the above studes, probably because t defed flood damage dfferetly from the others, ad also cosdered the resdets preparedess ad the actos mmedately after floodg. Damage ca be classfed to three ma types: captal restorato of affected households; replacemet, whch ew captal s utlzed to replace the damaged captal, ad drectly provdg the affected captal wth the orgal servces. Ths study adopts the flood damage defto of Kag et al. (5): d = w + m( x, y, z ) where d deotes the Flood damage to captal; w deotes the value of servces that caot be provded after damage to captal from the day of flood to the day of restorato; x deotes the value of servces that caot be provded after damage to captal from the day of restorato; y deotes the cost of restorato or replacemet followg ths restorato, ad z deotes the value of servces provded after damage. Kag et al. (5) ad Chag () assumed that all damaged captal was replaced wth ew captal. Addtoally, both adopted the Sythess approach, whch

22 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE does ot cosder the resdets preparedess ad the mmedate actos to agast the flood damage. Both factors ca cause the over-estmato of damage values. Cocluso The proposed approach ot oly uses the smallest umbers of explaed varables to establsh the flood damage fuctos for oe household, but also solves the problem tradtoal regresso models, whch caot cosder spatal varato. Addtoally, the proposed method modfes the resdual wth spatal autocorrelato. I the coeffcet of determato equato, R =.5 the orgal OLS. The GWR equato ot oly cosders the spatal varato, but also ca creases the coeffcet of determato.6. However, the proposed method has some lmtatos: because the characterstc of GWR equato s ts th data pots have th regressos, oly flood damage of those th coordates ca be forecast, ad the use of space s rratoal. Cosequetly, ths study apples the result of GWR cosderg the spatal varato to proceed wth the spatal clusterg, ad adopts dummy varables to modfy the orgal OLS equato. Ths approach ot oly modfes the problem of the orgal OLS, whch caot cosder the spatal varato, but also rases the modfed coeffcet of determato to.6. Ths study ot oly fds a quattatve equato to descrbe the depedet varable, flood damage, as a fucto of the depedet varable, flood depth, but also cosders the spatal varato. The fal aalyzg results dcate that the flood damage to a household ut s maly a factor of the flood depth ad ts located Zoe. That s, the rego should be cosdered wth respect to the effect of the fucto coeffcet. Ackowledgmet The authors would lke to thak the Natoal Scece Coucl of the Republc of Cha, Tawa for facally supportg ths research uder Cotract No. NSC_93-65-Z--35. Referece BAILEY TC ad GATRELL AC (995) Iteractve spatal data aalyss. Wley, New York BECK J, METZGER R, HINGRAY B, ad Must A. () Flood rsk assessmet based o securty defct aalyss. Paper preseted at the 7th Geeral Assembly of the Europea Geophyscal Socety, Geophyscal Research, Nce Frace, 6 Aprl

23 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE BLACK RD (975) Flood proofg rural structures: a project ages report, pesylvaa. Fal Report prepared for the Uted States Departmet of Commerce, Ecoomc Developmet Admstrato. Natoal Techcal Iformato Servce, Sprgfeld, VA, USA, May 975 BRUNSDON C, FOTHERINGHAM AS, ad CHARLTON ME (996) Geographcally weghted regresso: a method for explorg spatal o-statoarty. Geographcal Aalyss 8(4):8-98 BRUNSDON C, FOTHERINGHAM AS, ad CHARLTON ME (998a) Spatal o-statoarty ad autoregressve models, Evromet ad Plag A 3(6): BRUNSDON C, FOTHERINGHAM AS, ad CHARLTON ME (998b) Geographcally weghted regresso - modelg spatal o-statoarty, Joural of the Royal Statstcal Socety, Seres D-The Statstca 47(3): CHANG LF () Flood damage estmato for resdetal area. Dssertato, Natoal Tawa Uversty ( Chese) CHANG LF, ad SU MD (). Applcato of spatal data to damage estmatos flood. Joural of Chese Agrcultural Egeerg 47():-8 ( Chese) CHM HILL (974) Potetal flood damages. Wllamette Rver System Departmet of the Army Portlad Dstrct, Corps of Egeers, Portlad, OR, USA DAVID TF () Flood-warg decso-support system for sacrameto, Calfora. Water Resources plag ad maagemet 7(4):54-6 DU PLESSIS LA (). A revew of effectve flood forecastg, warg ad respose system for applcato South Afrca. WATER SA 8 (): 9-37 APR FEMA (977) Reducg flood damage through buldg desg: a gude maual - elevated resdetal structures. F. E. M. Agecy, ed. FIA (97) Flood hazardfactors, depth-damage curves, elevato frequecy curves, stadard rate tables. U. S. Federal Isurace Admstrato. FOTHERINGHAM AS, BRUNSDON C, ad CHARLTON ME () Geographcally weghted regresso: the aalyss of spatally varyg relatoshps. Wley, Chchester FOTHERINGHAM AS, BRUNSDON C, ad CHARLTON ME () Quattatve geography. Sage, Lodo FOTHERINGHAM AS, BRUNSDON C, ad CHARLTON ME (998) Geographcally weghted regresso: a atural evoluto of the expaso method for spatal data aalyss. Evromet ad Plag A 3():95-97 FOTHERINGHAM AS, CHARLTON ME ad BRUNSDON C (997a) Two techques for explorg o-statoarty geographcal data. Geographcal Systems 4: 59-8.

24 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE FOTHERINGHAM AS, CHARLTON ME ad BRUNSDON C (997b) Measurg spatal varatos relatoshps wth geographcally weghted regresso. I: Fscher MM ad Gets A. (eds.) Recet developmets spatal aalyss, spatal statstcs, Behavoral Modelg ad Neurocomputg. Sprger-Verlag, Lodo, Chapter 4 FOTHERINGHAM A.S., M.E. CHARLTON ad BRUNSDON C (996) The geography of parameter space: a vestgato to spatal o-statoarty. Iteratoal Joural of Geographc Iformato Systems : GRIGG NS ad HEIWEG OJ (974) Estmatg drect resdetal flood damage urba areas. Colorado State Uversty GRIGG NS (985) Water resources plag. McGraw-Hll, New York GRIGG NS ad HEIWEG OJ (975) State-of-the-art of estmatg flood damage urba areas. Water Resources Bullet (), GRIGG NS (996) Water Resources Maagemet. McGraw-Hll, New York HUBERT G, DEUTSCH JC, ad DESBORDES MC (996) Polcy decso support systems: modelg of rafall flood damages. I: PENNING-ROWSELL, E. (Ed.) Improvg flood hazard maagemet across Europe. Europea Uo Evromet Program, Cotract Number EV5V-CT93-96, EURO Flood II, Chapter 3 KANG JL, SU MD, ad CHANG LF (5) Loss fuctos ad framework for regoal flood damage estmato resdetal area. Joural of Mare Scece ad Techology 3(3) :93-99 KRASOVSKAIA I () Percepto of the rsk of floodg: the case of the 995 flood Norway. Hydrologcal Sceces Joural-Joural Des Sceces Hydrologques 46(6): MCBEAN EA, GORRIE J, FORTIN M, DING J, ad MOULTON R (988) Adjustmet factors for flood damage curves. Joural of Water Resources Plag ad Maagemet 4(6): MCPHERSON HJ ad SAARINEN TF (977) Flood pla dwellers percepto of flood hazard Tucso. Arzoa, Aals of Regoal Scece (): 5-4 PLATT RV (4) Global ad local aalyss of fragmetato a mouta rego of Colorado, Agrculture Ecosystems & Evromet (-3): 7-8 PENNING-ROWSELL EC, TUNSTALL SM, TAPSELL SM, ad PARKER DJ () The beefts of flood wargs: Real but elusve, ad poltcally sgfcat. Joural of the Chartered Isttuto of Water ad Evrometal Maagemet 4(): 7-4 SHAW DG, HUANG HH, ad HO MC (5) Modelg flood loss ad rsk percepto: the case of typhoo Nar Tape. Proceedgs of the Ffth Aual IIASA-DPRI Meetg o Itegrated Dsaster Rsk Maagemet: Iovatos Scece ad Polcy, Bejg, Cha,3-8 September 5

25 World Evrometal ad Water Resources Cogress 7: Restorg Our Natural Habtat 7 ASCE SMITH DI (994) Flood damage estmato - A revew of urba stage-damage curves ad loss fucto, Water SA (3):3-39 SU MD, KANG JL, CHANG LF, ad CHEN AS (5) A grd-based GIS approach to regoal flood damage assessmet. Joural of Mare Scece ad Techology 3(3): 84-9 TAIWAN WATER RESOURCE AGENCY (997) Natoal flood surace program plot study: A case studes ad for Tag-Dee-Yag area. Tawa project report, Tawa ( Chese). TORTEROTOT JP, KAUARK-LEITE LA, ad ROCHE PA (99) Aalyss of dvdual real tme resposes to floodg ad fluece o damage to households. Paper preseted at the 3rd Iteratoal Coferece o Floods ad Flood Maagemet, Florece, Italy, 4 6 November 99. WIND HG, NIEROP TM, DE BLOIS CJ, ad DE KOK JL (999) Aalyss of flood damages from the 993 ad 995 Meuse floods. Water Resources Research 35(): YANG L, ZUO C, ad WANG YG (5) A effectve two-stage eural etwork model ad ts applcato o flood loss predcto. Advaces I Neural Networks - Is 5, Pt 3, Proceedgs.Vol:3498, -6

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