Application of geographic weighted regression to establish flood-damage functions reflecting spatial variation

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1 Applcato of geographc weghted regresso to establsh flood-damage fuctos reflectg spatal varato Lg-Fag Chag, Chu-Hug L ad Mg-Daw Su * Departmet of Boevrometal Systems Egeerg, Natoal Tawa Uversty Departmet of Boevrometal Systems Egeerg, Natoal Tawa Uversty, No., sec. 4, Roosevelt Rd. Tape, Tawa 67 Abstract Flood damage fuctos are ecessary to esure comprehesve flood-rsk maagemet. Ths study attempts to establsh a resdetal flood-damage fucto through tervewg the resdets lvg the rego where flood dsasters occur frequetly. Keelug Rver bas, ear Tape Metropolta Tawa was selected as study area. Flood damages are related to the flood depths, whch are the most commoly cosdered factor prevously publshed work. Ordary least squares (OLS regresso was used to costruct the flood-damage fucto at the begg. Aalytcal results dcate that flood depth s the sgfcat varable, but the spatal patter of the resduals shows that resduals ehbt spatal autocorrelato. The Geographcally Weghted Regresso (GWR Model was the appled to modfy the tradtoal regresso model, whch caot capture spatal varatos, ad to reduce the problem of spatal autocorrelato. The R-square value was foud to crease from.5 to.4, ad the spatal autocorrelato the resduals was o loger evdet. A modfed OLS model wth a dummy varable to capture the spatal autocorrelato patter was also proposed for future applcatos. 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 depedet varable to modfy the tradtoal regresso model. Keywords: flood damage, flood depth, OLS, GWR, spatal autocorrelato Itroducto Floods are major dsasters worldwde that causes serous damage to agrculture, fsheres, housg ad frastructure ad mpact severely o soco-ecoomc actvtes. Rsk maagemet plays a very mportat role mtgatg these mpacts of flood dsasters. A complete flood-rsk maagemet ad mtgato framework comprses a hydrologcal module for chael dscharge calculato, a ecoomc module for damage estmato, ad a rsk aalyss process (Grgg, 985. Studes o hydrology ad hydraulcs have receved far more atteto tha those o flood-damage assessmets (Chag,. Ths study focuses o establshg resdetal flood-damage fuctos for flood-loss estmato that was cosdered to be oe of the most mportat aspects regoal flood-rsk maagemet (Grgg, 985. Flood-damage fuctos are tradtoally estmated by a emprcal flood depth-damage curve (Smth, 994. These curves ca be costructed through damage vestgatos after the dsaster (FIA, 97; Grgg ad Helweg, 975; Smth, 994; Lekutha ad Vogvsessomja, ; Su et al., 5; Theke et al., 5, or by sythess (Smth, 994; Chag, ; Chag ad Su, ; Kag, Su, ad Chag, 5. Although these two methods are dfferet the establshmet of the curve, they both assume that the flood depth s the oly factor the flood-damage fucto. Nevertheless, the flood depth may ot be suffcet for a household flooddamage fucto. McBea et al. (988 poted out that there were may factors besdes flood depth that could affect the flood damage, such as tme of year of floodgelocty ad sedmet load of floodwaters, durato of floodg as well as the warg tme, * To whom all correspodece should be addressed ; fa: ; e-mal: sumd@tu.edu.tw Receved 3 July 7; accepted revsed form 5 December 8. ad therefore, t s recommeded that the flood-damage fucto should be adjusted. Yag et al. (5 also oted that some meteorologcal, physographc ad huma factors such as rafall, terra ad flood-preveto measures could fluece the actual flood damages. Hece, the relatoshps betwee varous factors ad flood damages are ow wdely eamed. The most commo factor beg cosdered s the type of buldg Grgg, 974; FEMA, 977; McBea et al., 988; Smth, 994; Tawa Water Resource Agecy, 997; Chag, ; Kag, Su, ad Chag, 5; Theke et al., 5; Baro-suarez et al., 7. Other factors clude floor area, famly come(mcbea et al., 988; Lekutha ad Vogvsessomja,, flood-warg system (Wd et al., 999; Davd, ; Du Plesss,, flood-warg lead tme Peg-Rowsell et al., ; Theke et al., 5, eperece 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, Kauark-lete ad Roche 99; Hubert, Deutsch, ad Desbordes, 996; Lekutha ad Vogvsessomja, ; Theke et al., 5; Baro-suarez et al., 7elocty of floodwaters (CHM Hll, 974; Black, 975; Smth, 994; Beck et al.,, persos per household (McBea et al., 988; Shaw, Huag ad Ho, 5 ad the locato of the household Chag, ; Shaw, Huag ad Ho, 5. Sce flood damage s affected by may factors, some multple regresso models to corporate such factors were also proposed (Shaw, Huag ad Ho, 5. Although ths approach ca corporate more factors as the predctors ad mprove the statstcal sgfcace of the fttg model, t also creases the dffculty of data collecto of predctors whe predctg the damage the future. Global multple regresso methods were used most of these studes, ad the regresso coeffcets were assumed costat across the study rego (Platt, 4. I other words, the spatal varato was ot cosdered, so the global model resduals may ehbt spatal autocorrelato Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le 9

2 (Fothergham, Brusdo ad Charlto, ; Zhag, Gove ad Heath, 4; 5; Kupfer ad Farrs, 7. Thus, the am of ths study s to establsh the flood-damage fucto for oe household by usg the smallest possble umber of depedet varables, whle also cosderg the spatal varato ad solvg the problem of spatal autocorrelato resduals. Method The frst step s to determe the factors affectg flood damages. May flood-damage factors est as descrbed above, but the characterstcs of flood damage vary amog regos. Shaw et al. (5 corporated flood depth, udato tme, buldg ad structure types, the umbers of floors, presece of a basemet, floor area, persos per household ad rego hs study, ad the flood depth whch was foud to be the major factor of flood-damage fuctos that study. Some other studes eve show that wthout cosderg other factors, the flood depth aloe was stll approprate for estmatg the flood damages (Grgg, 996. Based o the formato preseted prevously publshed work, the flood depth was chose as the prcple factor for assessg the flood damages. The ordary least squares (OLS for global regresso was used tally to establsh the flood-damage fucto ths study. After the model was cofrmed through all the eeded statstcal tests, the Mora s I (Fothergham et al., statstcs were the used to eame f there were ay spatal autocorrelatos resduals. If spatal autocorrelatos amog resdual were preset, the the Geographcally Weghted Regresso (GWR Model was appled to solve the problem. Global regresso model Frst a global regresso model, formulated usg OLS regresso, was adopted ths study to establsh the flood-damage fucto. Sce flood damage creases wth flood depth, the followg S-curve model was costructed: y = e ( β + β / y s the flood damage (NT dollar s the depth (cm β, β are the regresso coeffcets ε s the resdual By takg the atural logarthm of Eq. ( t becomes: l y = β + β ε s the resdual Through ths trasformato, β, β ca be estmated by a 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. The establshed model was subjected to all ecessary statstcal tests cludg coeffcets sgfcace, model goodess of ft ad resduals patter eamato. Resdual spatal autocorrelato test After the regresso model s cofrmed wth all eeded statstcal tests, Mora s I test was used to detect ay estg spatal ( ( autocorrelato amog the resduals. Accordg to Baley ad Gatrell (995, Mora s Ide ca be epressed as: I = w, j (y y j j= s the umber of pots or cells y m s the value zoe m y s the mea of attrbute y w j s the spatal promty of pot ad j The verse of the dstace betwee pots ad j s ofte used to represet the spatal promty, ad w j ca be defed as /d j, where d j s the dstace betwee pot ad j. Ths assumes that attrbute values of pots follow the frst law of geography. Wth the verse of the dstace, smaller weghts are gve to pots that are farer apart ad larger oes to pots that are closer together. The epected value of Mora s I whe there are o spatal patter the data set s: E Whe the resultg Mora s I value s larger tha the epected value, t dcates postve spatal autocorrelato where smlar values cluster together. O the other had, whe the de value s below the epected value, t shows egatve spatal autocorrelato where smlar values are more dspersed. Uder ths assumpto, the I varace s gve by: Var ( I S (3 (4 E( I (5 The dstrbuto of I s asymptotcally ormal uder the assumpto of radom dstrbuto. The stadardsed Z scores ca be calculated as: ( I = = = j= w, j = ( (y y(y j y [( S S + 3S ] k[ ( S S + 6S ] w j = j S S ( w j + w j = = j= ( w j. + w. = = k = = j= ( y y ( y y I E(I Z(I = S E(I 4 ( ( ( The ull hypothess s set as the resduals radomly dstrbuted spatal sese. If.96 < Z(I <.96, the the ull hypothess ca ot be rejected wth a statstcal sgfcace level of 5%, ad we may coclude that the resdual patters are ot of sgfcat statstcal dfferece from a radom patter. Otherwse, 3 S wj + 3( wj ( w = SQRT ( ( w j j j j SE( I j j (6 (7 Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le

3 the resdual patter wll be clustered as Z (I >.96 ad wll be dspersed whe Z(I <.96. GWR model If the resdual has spatal autocorrelato, the GWR ca be utlsed to modfy the OLS regresso to solve the problem (Brusdo et al., 996; Fothergham et al., 998; ; ; Platt, 4; Zhag et al., 4; 5; Kupfer ad Farrs, 7. If the spatally vared characterstcs flood damages are take to accout, Eq.( ca be modfed as: l y = β (u + β (u y s the flood damage of pot s the flood depth of pot u s the coordates of the th pot space b (u, b (u s the realsato of the cotuous fucto at pot e s the resdual of pot (u I a smple lear regresso model, a sgle set of parameters s estmated for the relatoshp betwee each depedet ad depedet varables by OLS ad the relatoshp s assumed to be costat across the study area. It ca be estmated as follows: β = (X X T X T Y The GWR model recogses that spatal varatos relatoshps mght est. So the estmate GWR becomes: T T β = (X WX X WY ( X s the matr of the depedet varable s observato value, whch s the matr of : ( u ( u X = ( u b s the matr of the regresso coeffcet, whch s the matr of : β (u, v β (u β =.. β (u W s a matr whose off-dagoal elemets are zero; the dagoal elemets deote the geographcal weghtg of observed data for pot. That s: w W = The weghtg of each observed data s: w (u.. β(u, v β (u.. β (u w.. (u j (u = ep( d j / h w.. (u (8 (9 ( d j s the Eucldea dstace betwee observed data ad j h s the costat value of badwdth The badwdth h may be ether suppled by the user, or estmated by usg a techque such as cross-valdato. The parameter estmated wth GWR s the plotted oto the map to determe the parameter estmated to ehbt sgfcat spatal autocorrelato. GWR aalyss ot oly ca modfy the problem of spatal autocorrelato the resduals from OLS regresso, but also ca take to accout the spatal varato of flood-damage characterstcs. Data collecto ad study area To establsh the flood-damage fucto for oe household a resdetal area, the Keelug Rver bas ear Tape Metropolta Tawa, where flood dsasters occur frequetly, was selected as the study area. Feld survey data of the flood damages caused by Nar Typhoo were collected. The vestgated areas are show Fg. (et page, ad clude Xzh Cty, ad towshps of Qdu, Nagag, Nehu, SogSha, Sy ad Da-a. The flood-damage surveys cluded such tems as the basc household formato (the characterstcs of the buldg lke the umbers of floors ad floor area, persos per household, come levels, etc., flood depth ad udato tme, level of damage (the damage to household furture, teror decoratos, ad vehcles, etc. ad the rsk-percepto factors (eperece of flood, rsk formato, fear of the rsk, wllgess to take the rsk, ad the fluece of mass meda. A total of 3 completed questoares were collected. All data were geocoded for spatal aalyss ad plottg oto a map. Results Global regresso model The regresso result of Eq. ( s show Table. The coeffcet of determato R s.5 ad the estmates for both parameters are sgfcatly dfferet from zero at.5 sgfcace level. Whle the resduals plot s show as Fg. (et page. From the fgure, the resduals seem to be fluctuatg radomly aroud zero, dcatg a good ft for a lear model. The resduals were the mapped, as show Fg. 3, to determe f there s ay estg spatal autocorrelato. Obvous clusterg patter was observed the fgure. Mora s I test was the employed to test the estece of spatal autocorrelato ad the result was the followg:.68 wth Z(I = >.96. Ths mples that the resduals had sgfcat spatal autocorrelato ad t volates the assumptos for lear regresso. Therefore, the GWR as descrbed above was appled to modfy the model. GWR model The applcato of GWR model mproved the R creased from.5 as OLS regresso to.6, demostratg that GWR TABLE Global regresso parameter estmates (s3 Parameter Estmate Std estmate Std Err T P-Value Itercept /X Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le

4 Fgure Geographc dstrbuto of study area Tawa Fgure Global model resdual plot Fgure 4 Hstogram of the tercept from GWR model Fgure 3 Global model resdual surface provdes a better terpretg ablty tha OLS. As show Fg. 4, the hstogram of tercept estmates dsplays three obvous groups. Fgure 5 depcts the spatal dstrbuto of these three groups. The tercept term Eq. ( ca be terpreted as the basc or fed floodg damage due to from cleag ad restorato. There s a sgfcat clustered patter dcatg that basc flood damages crease gradually from west to ortheast corer the study rego. Fgure 6 also shows that there are two groupgs of the estmates for the parameter of versed flood depth the GWR model. Fgure 7 shows that the hgh value group was located the cetral ad wester parts, ad the group wth low values was Fgure 5 Map of the tercept from GWR model located the ortheast corer. These parameter estmates dcate the chage of the flood damages wth the flood depths, ad are creased gradually from ortheast to west the study area. The resduals of the GWR were the mapped, as show Fg. 8, to eame f there ests ay patter or spatal auto- Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le

5 Group Group Group3 Zoe 3 Zoe Zoe Fgure 6 Hstogram of the regresso coeffcets of the verse of flood-depth varable from GWR model Fgure 9 The spatal clusterg TABLE Results of Mote Carlo test for spatal o-statoary a (s3 P-Value Itercept.*** /X.*** a Tests f regresso coeffcets chage over space a way that s ulkely to occur at radom *** s sgfcat at.% level ** s sgfcat at % level * s sgfcat at 5% level Fgure 7 Map of the verse of flood-depth from GWR model TABLE 3 The dstrbuto of GWR s regresso coeffcet values Low Mddle Hgh Low N/A N/A Group3 Hgh Group Group N/A N/A deotes o-data Modfed global regresso model Fgure 8 Resduals from GWR model correlato. The Mora s I was calculated as.4 wth Z(I=.6 <.96, demostratg that the spatal autocorrelato problem OLS was already corrected. Although the GWR cured the spatal autocorrelato problem resduals, the model s of lttle use term of future applcatos. The GWR geerates regresso coeffcets for each sample pots. These estmates are oly good for those specfc locatos ad ca ot be used for further estmato at locatos other tha those of the sample stes. Therefore, the GWR model results were more closely eamed ths study to develop further kowledge for later use modfyg the tradtoal OLS regresso model. Sce groupg patters were show Fg. 4 ad 6 of the estmates for both parameters, these estmates were summarsed Table 3. All the sample pots ca be categorsed to three groups as show Table 3. By ocular observato, the map Fg. 9 shows strog spatally clusterg tedeces. The orgal OLS was the modfed accordg to the groupg result by addg two dummy varables, GP ad GP. The dummy varable GP s for data zoe ad s otherwse. The dummy varable GP s for data Zoe ad s otherwse. The orgal OLS regresso model was the modfed as follows: Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le 3

6 l y = β + β + β GP + β3 GP + β 4 GP + β5 GP + β3 GP + β 4 GP + β5 GP ( y s the flood damage s the flood depth GP s whe sample s zoe ad s otherwse GP s whe sample s zoe ad s otherwse b, b, b, b 3, b 4, b 5 are the regresso coeffcets e s the resdual. TABLE 4 Result of modfed global a regresso model (s3 Parametemate Est- Std Std Err T P-value estmate Itercept /X GP a The average regresso result of the etre study area Stepwse regresso was adopted to determe the ma varables. The results revealed that oly / ad GP were sgfcat ad the model could be modfed as: l y = β + β + β GP (3 Table 4 shows the results of the modfed OLS regresso model. The regresso estmates were all statstcally sgfcat at a statstcal sgfcace level of 5%. The coeffcet of determato R also creased from.5 (OLS to.6 (modfed OLS, smlar to that of the GWR model. To test f the resduals ehbt spatal autocorrelato, the resduals of the modfed OLS were mapped to the map as show Fg. ad the Mora s I value was obtaed. The Mora s I s.33 wth Z(I=.3 <.96 dcatg a radom patter the spatal dstrbuto of resduals. The modfed OLS has successfully corrected the spatal autocorrelato problem of resduals the orgal OLS model. The resultg flood-damage fuctos from OLS ad Modfed OLS models are show as Fg.. The damage fuctos share the same patters ad tred for both models. Houses located outsde zoe would suffer from bgger flood damages tha those zoe whe floodg occurs. From the fgure, the mamum flood damage per household s NT$5 for OLS ad appromately NT$6 for Zoe ad NT$8 for area other tha Zoe the modfed OLS model. The modfed OLS model shows better results tha the global OLS model by dstgushg the dffereces floodg damage characterstcs betwee areas. Coclusos Although flood-damage curves are used commoly for flood rsk assessmets, most of the curretly used flood-damage curves fal Fgure Resdual spatal dstrbuto from modfed regresso model to capture spatal varatos regoal floodg damages. The paper proposed a approach that ot oly uses the smallest umbers of eplaed varables to establsh the flood-damage fuctos for sgle household, but also solves the problem tradtoal regresso models for overlookg the spatal varatos floodg loss characterstcs. The troducto of the GWR model mproved the coeffcet of determato from.5 the orgal OLS to.6. The GWR model corrects the spatal autocorrelato problems resduals, but t also has some drawbacks. It produces a dfferet set of estmates for the regresso parameters at each sample pots. Ths makes ts applcato for estmatg the flood loss at locatos other tha those at the Fgure The resultg flood damage fuctos from OLS ad modfed OLS models 4 Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le

7 sample pots dffcult. A modfed OLS model was the proposed ths study by trudg dummy varables dfferetatg regos wth dfferet floodg loss characterstcs. Ths modfed OLS model ot oly corrects the spatal autocorrelato problem resduals but ca also be used for future applcatos regoal flood-damage assessmets. Ackowledgmet The authors would lke to thak the Natoal Scece Coucl, Tawa for ts facal support uder Cotract No. NSC_93-65-Z--35 ad most especally thaks to Dr. Shaw for hs provso of data collected uder Cotract No. NCDR_95-T3. Referece BAILEY TC ad GATRELL AC (995 Iteractve Spatal Data Aalyss. Wley, New York. BARO-SUAREZ JE, DIAZ-DELGADO C, ESTELLER-ALBERICH MV ad CALDERON G (7 Ecoomc flood loss estmato curves for Meca rural ad resdetal areas. Part : Methodology proposal. Igeera Hdraulca E Meco 3 ( 9-. 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 Geophys. Res. - 6 Aprl, Nce, Frace. 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 eplorg spatal o-statoarty. Geogr. Aal. 8 ( CHANG LF ( Flood Damage Estmato for Resdetal Area. M.Sc Thess, Natoal Tawa Uversty ( Chese. CHANG LF ad SU MD ( Applcato of spatal data to damage estmatos flood. J. Ch. Agrc. Eg. 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 Resour. Pla. Maage. 7 ( DU PLESSIS LA ( A revew of effectve flood forecastg, warg ad respose system for applcato South Afrca. Water SA 8 ( archve//aprl/375.pdf FEMA (977 Reducg Flood Damage through Buldg Desg: A Gude Maual Elevated Resdetal Structures. FEM Agecy (ed. FIA (97 Flood Hazard Factors, Depth-Damage Curves, Elevato Frequecy Curves, Stadard Rate Tables. US 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 epaso method for spatal data aalyss. Evro. Pla. A 3 ( GRIGG NS ad HEIWEG OJ (974 Estmatg Drect Resdetal Flood Damage Urba Areas. Colorado State Uversty, Colorado, USA. 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 Resour. Bull. ( 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: Peg-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. J. Mar. Sc. Techol. 3 ( KRASOVSKAIA I ( Percepto of the rsk of floodg: The case of the 995 flood Norway. Hydrol. Sc. J. Joural Des Sceces Hydrologques 46 ( KUPFER JA ad FARRIS CA (7 Icorporatg spatal o-statoarty of regresso coeffcets to predctve vegetato models. Ladscape Ecol. ( LEKUTHAI A ad VONGVISESSOMJAI S ( Itagble flood damage quatfcato. Water. Resour. Maage. 5 ( McBEAN EA, GORRIE J, FORTIN M, DING J, ad MOULTON R (988 Adjustmet factors for flood damage curves. J. Water Resour. Pla. Maage. 4 ( McPHERSON HJ ad SAARINEN TF (977 Flood pla dwellers percepto of flood hazard Tucso. Arzoa. A. Reg. Sc. ( 5-4. PLATT RV (4 Global ad local aalyss of fragmetato a mouta rego of Colorado. Agrc. Ecosyst. Evro. ( PENNING-ROWSELL EC, TUNSTALL SM, TAPSELL SM ad PARKER DJ ( The beefts of flood wargs: Real but elusve, ad poltcally sgfcat. J. Chart. Ist. Water Evro. Maage. 4 ( 7-4. SHAW DG, HUANG HH ad HO MC (5 Modelg flood loss ad rsk percepto: the case of typhoo Nar Tape. Proc. 5 th Au. IIASA-DPRI Meetg o Itegrated Dsaster Rsk Maagemet: Iovatos Scece ad Polcy. 3-8 September, Bejg, Cha. SMITH DI (994 Flood damage estmato A revew of urba stagedamage curves ad loss fucto. Water SA ( SU MD, KANG JL, CHANG LF ad CHEN AS (5 A grd-based GIS approach to regoal flood damage assessmet. J. Mar. Sc. Techol. 3 ( TAIWAN WATER RESOURCE AGENCY (997 Natoal Flood Isurace Program Plot Study: A Case Study for Tag-Dee-Yag area. Tawa project report, Tawa ( Chese. THIEKEN AH, MULLER M; KREIBICH H ad MERZ B (5 Flood damage ad fluecg factors: New sghts from the August flood Germay. Water. Resour. Res. 4 ( W43_ -6. TORTEROTOT JP, KAUARK-LEITE LA ad ROCHE PA (99 Aalyss of dvdual real-tme resposes to floodg ad fluece o damage to households. Proc. Paper preseted at the 3 rd It. Cof. o Floods ad Flood Maagemet. 4-6 November 99, Florece, Italy. WIND HG, NIEROP TM, DE BLOIS CJ ad DE KOK JL (999 Aalyss of flood damages from the 993 ad 995 Meuse floods. Water Resour. Res. 35 ( YANG L, ZUO C ad WANG YG (5 A effectve two-stage eural etwork model ad ts applcato o flood loss predcto. Proc. Advaces Neural Networks Is 5, Pt 3 Vol: ZHANG LJ, GOVE JH ad HEATH LS (5 Spatal resdual aalyss of s modellg techques. Ecol. Model. 86 ( ZHANG LJ, BI HQ, CHENG PF ad DAVIS CJ (4 Modellg spatal varato tree dameter-heght relatoshps. Forest Ecol. Maage. 89 ( Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le 5

8 6 Avalable o webste ISSN = Water SA Vol. 34 No. Aprl 8 ISSN = Water SA (o-le