Evaluation of typhoon-induced rainfall using nonparametric Monte Carlo simulation and locally...

HYDROLOGICAL PROCESSESHydrol. Process. 25, 1765–1777 (2011)Published online 30 December 2010 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.7934

Evaluation of typhoon-induced rainfall using nonparametricMonte Carlo simulation and locally weighted polynomial

regression

Tae-Suk Oh,1 Young-Il Moon2* and Hyun-Han Kwon3

1 Global Civil Business Development Team, SK Engineering & Construction, SK Soonhwa B/D #66, Soonhwa-dong, Jung-gu, Seoul 100-130, SouthKorea

2 Department of Civil Engineering, University of Seoul, 13 Siripdae-gil, Dongdaenun-gu, Seoul 130-743, South Korea3 Department of Civil Engineering, Chonbuk National University, 664-14 1Ga, Deokjin-Dong, Jeonju-City, Jeonbuk, 561-756, South Korea

Abstract:

Typhoons in Korea are the major causes of natural disasters in the Korean peninsula. In this study, rainfall generatedby typhoons was quantitatively analysed using various statistical methods. First, the frequency analysis of rainfall inducedby typhoons was carried out to calculate the design rainfall. Second, the frequency analysis of simulated rainfall derived bynonparametric Monte Carlo simulation (NMCS) was performed to evaluate the uncertainty of rainfall caused by typhoons.Third, the regression relationship between the physical characteristic factors of typhoons and rainfall was established bylocally weighted polynomial regression (LWPR), and the characteristic factors of typhoons were simulated. The simulatedcharacteristic factors were then used to estimate rainfall and to calculate the design rainfall by typhoons. Comparative analysesof design rainfalls as estimated using various statistical methods were performed. The LWPR showed good performance interms of reproducing typhoon characteristics. Therefore, the combined NMCS and LWPR method suggested in this study canbe used as a supplementary technique for assessing extreme rainfall with climate change and reflected variability. Copyright 2010 John Wiley & Sons, Ltd.

KEY WORDS typhoon events; nonparametric Monte Carlo simulation; locally weighted polynomial regression

Received 12 April 2010; Accepted 11 October 2010

INTRODUCTION

Tropical depressions irregularly affect Korea and causenatural disasters with their strong winds and heavy rains.Depending on their regional origins, tropical depressionsare called by different names such as typhoons, hurri-canes, cyclones, and willy-willies. The tropical depres-sions affecting the Korean peninsula—which is locatedin East Asia—are called as typhoons.

The Korea Meteorological Administration (KMA)defines the ‘typhoons that affected the Korean penin-sula’ as those from the equatorial region and whosecentres reach 32–40°N and 120–138 °E. Therefore, thetypical track of typhoons affecting the Korean peninsulais defined as a typhoon approaching with a range of about32–40°N and 120–138 °E. Typhoons move beyond 40°N;they are extinguished at around 110–150 °E.

An annual average of 3Ð18 typhoons occurred in Koreafrom 1961 to 2005. The maximum daily rainfall driven bytyphoon was 870Ð5 mm, which was recorded in Gangne-ung in 2002 during typhoon Rusa. The rainfall in Gangne-ung at the time was unusual considering the fact that theannual average rainfall in Gangneung for 30 years from1976 to 2005 was 1457Ð6 mm. Seven of the 10 largest

* Correspondence to: Young-Il Moon, Department of Civil Engineering,University of Seoul, 13 Siripdae-gil, Dongdaemun-gu, Seoul 130-743.E-mail: [email protected]

daily rainfalls during typhoons affecting the Koreanpeninsula from 1904 to 2005 occurred in the beginningof 1990. Therefore, the magnitude of rainfalls caused bytyphoons in Korea is likely to intensify given the impactof climate change and abnormal weather caused by therecent global warming. As Korea is a peninsula, precip-itable water from typhoons is more likely to be suppliedwith greater amount of water vapour from warmer oceansconsidering the impact of global warming.

According to Knox (1984, 1993), the climate is chang-ing continuously. In particular, signature changes can beobserved on the hydrological cycle and associated rainfallpatterns. Porparto and Ridolfi (1998) studied the changesin flood frequency over paleo-timescales and demon-strated that the estimated flood exceedance probabilitycan increase quite rapidly over time.

Recently, extreme weather events seem to havebecome increasingly frequent (Katz and Brown, 1992;Karl et al., 1995; Easterling et al., 2000). In fact, thefrequency and intensity of water-related disasters areincreasing worldwide.

The frequency of a specific hydrologic variable shouldnot be treated independently of climate variability (Olsenet al., 1999). For example, the warmer waters of thewestern tropical Pacific increase towards the central andeastern Pacific due to global warming and trigger cycloneoccurrence and associated threats. During the summer

Copyright 2010 John Wiley & Sons, Ltd.

1766 T-S OH, Y-IL MOON AND H-H KWON

Figure 1. Flowchart of analysis procedure

season in the Korean peninsula, these typhoons causelarge local rains by bringing constant water vapour intothe Korean peninsula. Note, however, that traditionalhydrological frequency analyses are not able to take intoaccount the increased impacts of climate variability forthe systematic reporting or estimation of extreme rainfallfrequency (Sankarasubramanian and Lall, 2003).

In the United States, the empirical simulation technique(EST)—which considers the errors and uncertainty inaddition to the average frequency value of a correspond-ing frequency—was developed to assess the tropicalstorms (Scheffner et al., 1996, 1999). An improvementfrom simple frequency analysis, EST is a nondetermin-istic technique that can simultaneously consider typhoonevents and environmental changes caused by typhoons.With its multiparameter structure, the technique performsthe simulation of multiple life-cycle sequences; it can beused to evaluate casualties, property damage, tidal wavescaused by the passage of storms, and coastal erosion.Scheffner et al. (1996) elaborated on the theory and appli-cation of EST and assessed the risk of tidal waves inthe coast of Delaware during storms through time seriesstatistical simulation and by explaining the relationshipbetween hydrological events and frequencies with non-deterministic multiparameters.

In this study, various statistical methods were used forthe quantitative evaluation of rainfall caused by typhoons

that make their landfall on the Korean peninsula, andcause considerable damage as well as to analyse uncer-tainty. This study sought to develop statistical typhoonrainfall models that allow for the classification of extremeevents and continual updates of the estimates of thefrequency of these extreme events, and probability ofextreme rainfall occurrence by focussing on typhoonevents.

METHOD OF ANALYSIS

In this study, the characteristics of rainfalls caused bytyphoons were mainly analysed. First, the frequency anal-ysis of rainfalls caused by typhoons was performed tocalculate the design rainfall. Second, more details onthe design rainfalls induced by typhoons were evalu-ated by the nonparametric simulation technique. Third,the regression relationship between the physical charac-teristic factors of typhoons and rainfalls was establishedby locally weighted polynomials, with the rainfalls seriesconditioned on the physical characteristic factors gener-ated to estimate the design rainfalls. Finally, a compara-tive analysis of the different values of the design rainfallas calculated by different techniques was performed. Theoverall procedure of this study is illustrated in Figure 1.

A main innovation of the proposed approach is tocombine nonparametric Monte Carlo simulation (NMCS)

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. 25, 1765–1777 (2011)

STATISTICAL ANALYSIS OF TYPHOON EVENTS 1767

and locally weighted polynomial regression (LWPR)technique in simulating rainfall extremes induced bytyphoons while the EST techniques utilized a simplelinear regression technique. The existing problems of theEST techniques are excessive overestimation given theabnormal extremes. The overestimation is mostly affectedby using the linear regression for extrapolation of thequantile values. This problem can be improved by thelocal polynomial regression technique approach that ismore stable solution in generating the rainfall extremesfor extrapolation of the quantile values.

Rainfall frequency analysis

In general, the following steps are taken to estimatethe design rainfall through the rainfall frequency anal-ysis. First, the annual maxima or annual exceedance isextracted from the observed rainfall data at target sta-tions, and the stationary of the extreme data is examined;second, basis statistics such as mean, standard deviation,and skewness are computed to get an insight of extremeevents; third, the probability distribution type for rainfallfrequency analysis is chosen, with probability distribu-tion types categorized as normal family, gamma fam-ily, extreme value family, and Wakeby family dependingon the distribution group; fourth, parameters associatedwith distribution are estimated by the moments method,maximum likelihood method, and probability weightedmoments method; fifth, the selected probability distri-bution type is fitted to the data, and design rainfall isestimated by the quantile function.

Nonparametric Monte Carlo simulation

Monte Carlo simulation is a technique that generatesrandom variates based on the assumption that eventswhich can occur in the future are statistically similar toevents which have occurred in the past. The simulationtechnique is a widely used technique for estimating theapproximate solutions of various mathematical problemsthrough the repeated statistical sampling of the enteredvalues (Fishman, 1996) and for extending a large quan-tity of data from probability distribution types or carryingout research on complex statistical behaviours (Hamm,2002). In this study, the kernel density function esti-mator (Breiman et al., 1977; Moon and Lall, 1994) isused to estimate the probability distribution of variatesin performing nonparametric simulation on the rainfalldata. Determining the probability distribution of vari-ates requires selecting the appropriate kernel function(Epanechnikov, 1969) and determining the appropriatebandwidth. The Gaussian kernel function tends to yieldsmall quantiles owing to excessively rapid convergencein the case of extrapolation. In contrast, the thickness ofthe tail of the Cauchy kernel function leads to very largequantiles generated by simulations because of continu-ous divergence when extrapolation is performed. Further-more, the modified Cauchy kernel function (Cha et al.,2006), i.e. the tail of the Cauchy kernel function thatwas revised to estimate extreme events better, was used

in this study. To determine the bandwidth, the conceptof plug-in method as proposed by Sheather (1986) andSheather and Jones (1991) was applied. Equation (1) isthe expression of the modified Cauchy kernel function,and Equation (2), the regular expression of the Sheatherand Jones plug-in method.

F�x� D 8

�3p

5��1 C x^2/5�^2��1�

h D R�K�

nR(fg�h�

) (∫xzK�x�dx

)z �2�

where R�K� D ∫K2�x�dx and

∫x2K D ∫

x2K�x�dx.The variable kernel density function (Lall et al., 1993;

Moon and Lall, 1994) was used to estimate the proba-bility density function and to determine the quantiles bygenerating random numbers (0, 1). Therefore, quantilesmatching the occurrence probability of the correspondingvariates were estimated by the cumulative kernel densityfunction obtained by performing the integral of the kerneldensity function (Falk, 1985) to carry out NMCS.

Locally weighted polynomial regression

The regression relationship between the physical char-acteristics of typhoons and rainfall was established byLWPR. In this section, a brief explanation of LWPR isprovided; for a more detailed explanation of the LWPRalgorithm including a description of the statistical for-mulas, refer Lall et al. (2006). Linear regression con-siders the case wherein function f�.� is linear in x,i.e. f�x� D xb, where b is the M-vector of coefficientsthat do not depend on x. Statistical software is readilyavailable to perform these computations. Consequently,these methods have widespread use. Nonlinear relation-ships between x and y are considered in this frame-work through prior transforms applied to x and/or y. Forinstance, the components of x may include polynomialterms (1,v,v2,. . .) in original variable v. Cleveland (1979);Cleveland and Devlin (1988), and Cleveland et al. (1988)pioneered this idea into a statistical methodology for thelocal approximation of functions from data. In recentstudies (Lejeune, 1985; Muller, 1987; Fan and Gijbels,1992; Hastie and Loader, 1993; Loader, 1999), thesemethods have been recognized as very useful general-izations of kernel regression (weighted moving averages;Lall et al., 2006). The material presented here buildsdirectly on the method of Cleveland and Devlin (1988)and the developments in Lall et al. (1996). For a generalbackground on the methods, refer to the recent mono-graph by Wand and Jones (1995).

The LWPR at each point of estimate xŁl , l D 1 . . . np

given (n ð M) data matrix X and (n ð 1) response vectory was obtained through the solution to the weighted leastsquares problem

ˇminl �y1 � Zlˇl�

TW1�yl � Zlˇl� �3�

where subscript l recognizes that the associated elementis connected with the point of estimate xŁ

l , ˇl denotes



the estimates of the coefficients of the terms in the basisdefined by Zl, a matrix formed by augmenting X withcolumns that represent the polynomial expansion of Xto degree p (including cross product terms, if desired);Wl is a k ð k diagonal weight matrix with elements

wii,l D K�ui,l�/k∑

jD1K�uj,l�, where ui,l D di,l/dk,l. di,l is

the distance from xŁl to xi using an appropriate metric,

and K�.� is a weight function. We have implemented abisquare kernel (K�u� D 15/16�1 � u2�2). The latter wasrecommended by Scott (1992) because of its smoothnessproperties. Matrices Yl and Zl were defined over the knearest neighbourhood of xŁ

l . Singular value decomposi-tion (SVD) using the algorithms from Press et al. (1989)was used to solve the linear estimation problem resultingfrom Equation (3). A variety of estimators of predictivemean square error P� Of� (PMSE) have been proposed inliterature. A suitable measure of predictive variability isthe PMSE, which, for predictor Oy0 of y0, is E[� Oy0 � y0�2]where E denotes the expectation. The problem lies incombining data so that PMSE will be minimized. Cleve-land and Devlin (1988) considered Mallows’ Cp in theirwork on local polynomial regression. Li (1985) discussedthe related theoretical foundations and other measuressuch as ordinary and generalized cross validation (GCV),finite prediction error, Information Criterion of Akaike(AIC), and Bayesian Information Criterion (BIC). TheGCV statistic proposed by Craven and Wahba (1979) isparticularly noteworthy as it has performed well (Hardle,1984, 1989) in practical applications. It is defined as

GCV( Of

)D MSE� Of�

[n�1tr�I � H�]2 �4�

Lall et al. (1996) introduced the use of a local GCV(LGCV) score that uses data directly from the localregression at the point of estimate. In this case, errorsei,l are the residues of the model fitted over the k nearestneighbours of point xŁ

l , and Wi is the correspondingweight matrix. The trace of matrix H in this case is simplyd0, the number of coefficients fitted. The LGCV score isthen given as

LGCVl� Of� D eT1 w1e1

�k � n0p/k�2 �5�

The appropriate values of k and p can then be obtainedas those that minimize the LGCV score for the localregression. The LGCVl value also provides insight intothe local predictive error variance. Such approach toparameter selection is particularly useful when making afew estimates from a large data set. According to Stuartand Ord (1991), the confidence intervals can be computedby estimating S2

el as the variance of the local error of eachestimate Of�x1�.

DATA

Given the maximum wind speed at the centre of thestorm, the World Meteorological Organization (WMO)

Figure 2. Yearly occurrence of typhoons

Figure 3. Monthly typhoon occurrences

provides the following categories of tropical depressionsthat occur in the equatorial region: tropical depression,tropical storm, severe tropical storm, and typhoon. InKorea, typhoons are defined as storms with maximumwind speed of 17 m/s at the storm centre. The typi-cal track of typhoons affecting the Korean peninsulais defined as a typhoon approaching with a rangeof about 32–40°N and 120–138 °E (KMA). Typhoonsmove beyond 40°N; they are extinguished at around110–150 °E. Figure 2 illustrates the 143 typhoons thatstruck Korea from 1961 to 2005 and the typhoons thatoccurred in the equatorial region of the western partof the North Pacific Ocean. The correlation coefficientbetween the number of typhoons that hit Korea and thetotal number of typhoons was about 0Ð12; note, however,that the correlation coefficient was not statically signifi-cant at the 5% level. Figure 3 illustrates the comparisonof the monthly frequency of typhoons that occurred in



Figure 4. Trajectory of typhoon Rusa

the equatorial region from 1961 to 2005 and typhoonsthat affected Korea.

Figures 2 and 3 show that a total of 1222 typhoonsoccurred in the equatorial region of the Pacific Oceanfrom 1961 to 2005. The annual average was 27Ð16typhoons, and the standard deviation was 4Ð90. The rangeof number of typhoons per year was from 16 to 45. Atotal of 143 out of 1222 typhoons hit Korea. The annualaverage was 3Ð18 typhoons, and the maximum number oftyphoons that occurred a year was six in the beginning ofthe year 1976. First, we will start to explain how to derivethe rainfall associated with typhoons. The hourly rainfallseries was mainly used to determine the design rainfall.Typhoon Rusa was utilized to understand the procedurebetter. The track of Rusa is presented in Figure 4. Thesolid line indicates the path of Rusa, whereas the box onthe map is the area affected by Rusa.

First, temporal and spatial information such as timeof genesis and typhoon tracks were gathered. In addition,auxiliary climate state variables such as sea-level pressureand typhoon category were prepared. Second, typhoonRusa’s duration in Korea was identified. Typhoon Rusawas active from 22 August 2002, 6 : 00 hours to 3September 2002, 18 : 00 hours. On the basis of the def-inition of ‘typhoons that affect Korea (typhoons located

within 32–40°N and 120–138 °E)’ as established byKMA, the typhoon duration in the range was found tohave lasted for 36 h from 30 August 2002, 22 : 00 hoursto 1 September 2002, 9 : 00 hours. Third, hourly rainfalldata during the 36 h as measured by eight rainfall stationswere collected. Fourth, the maximum hourly rainfall dataof successive durations (1, 3, 6, 9, 12, 15, 18, and 24 h)during the period the typhoon was affecting Korea wereextracted. Fifth, the spatial information on typhoon tracksand climate information associated with typhoon such assea-level pressure and sea-level temperature when maxi-mum rainfall occurred were collected. The data used herewere provided by KMA. Extended reconstructed Sea Sur-face Temperature(SST) version 2 operated by NationalOceanic and Atmospheric Administration(NOAA) (Smithet al., 2003, 2004) was mainly used, with the gridded SSTdata near the typhoon’s centre finally extracted. Rainfalldata associated with typhoon and physical characteristicsof the typhoon were collected from 143 typhoon eventsobserved from 1961 to 2005. Finally, a total of 45 rain-fall events were obtained from among the 145 typhoonevents that hit the Korean peninsula. Annual maximumseries from the rainfall events was constructed from therainfall events caused by typhoons. Moreover, this studyselected only one rainfall event for each of the durationfrom each typhoon event as one of its limitations. Table Ishows the specifications of rainfall stations for analysis.Table II shows the physical characteristics of typhoonsand associated 24-h rainfall in Seoul (ID 108).

ANALYSIS OF RAINFALLS CAUSEDBY TYPHOONS

As mentioned earlier, rainfall events from eight stationscaused by typhoons that affected Korea were further anal-ysed. Frequency analysis was carried out to analyse 45annual maximum series. In addition, NMCS (200 yearsð 1000 times) was applied to estimate design rainfalls,and associated uncertainties were derived from the simu-lations. General frequency analysis was used to comparewith the proposed NMCS.

Frequency analysis

Frequency analysis was performed using hourly maxi-mum rainfall data. A total of 45 typhoon-induced rainfall

Table I. Specifications of rainfall stations that collected data on the analysis targets

Rainfall station Northlatitude (N)

Eastlongitude (E)

Height abovesea level (m)

Height aboveground (m)

Observationfor first year

105 Gangneung 37°450 128°540 26Ð5 0Ð5 1961108 Seoul 37°340 126°580 86Ð0 0Ð5 1961112 Incheon 37°280 126°380 68Ð9 0Ð5 1961143 Daegu 35°530 128°370 57Ð6 0Ð6 1961156 Gwangju 35°100 126°540 70Ð5 0Ð6 1961159 Busan 35°060 129°020 69Ð2 0Ð6 1961165 Mokpo 34°490 126°230 37Ð4 0Ð6 1961184 Jeju 33°310 126°320 20Ð0 0Ð5 1961



Table II. Typhoon characteristics at the time of maximum 24-hrainfall at station 108

Typhoonnumber

Latitude Longitude Centralpressure

Sea surfacetemperature

Rainfall

6123 34Ð3 126Ð4 999Ð2 21Ð9 25Ð26209 36Ð7 126Ð2 980Ð9 24Ð1 50Ð26210 38Ð3 125Ð9 986Ð4 23Ð9 22Ð86305 36Ð7 126Ð5 1001Ð0 23Ð0 27Ð30205 36Ð5 127Ð5 984Ð3 22Ð5 62Ð50215 36Ð4 128Ð0 980Ð0 24Ð2 55Ð00407 34Ð6 125Ð3 985Ð1 23Ð8 71Ð50415 36Ð3 131Ð1 970Ð8 25Ð6 52Ð0

Figure 5. Results of the frequency analysis for the typhoon-induced 24-hmaximum rainfall

events from 1961 to 2005 were selected for further anal-ysis. In carrying out frequency analysis, the momentmethod, maximum likelihood method, and probabilityweighted moments method were initially considered asmethods of estimating the parameters of the selectedprobability distribution. No significant differences werefound among parameters computed by the three dif-ferent methods. The chi-square goodness-of-fit methodwas used in conjunction with the Kolmogorov–Smirnovmethod and the Cramer Von Mises method at the signifi-cant level of 5%. There were eight plausible distributionsbased on the goodness-of-fit tests used. Finally, the use ofthe Gumbel distribution with two parameters was decidedfor further analyses. Rainfall frequency analysis was per-formed for the annual maximum series of eight differentdurations (1, 3, 6, 9, 12, 15, 18, and 24 h). The resultsof rainfall frequency analysis for 24-h duration are illus-trated in Figure 5. Seoul, Gwangju, Mokpo, and Daegushow relatively similar pattern of design rainfall, whereasGangneung, Jeju, and Busan were much bigger than otherstations. In particular, Gangneung is the biggest one dueto typhoon Rusa in 2002.

Design rainfall by NMCS

Nonparametric kernel density estimation has beenwidely used in the water resources field, and sev-eral promising nonparametric approaches to estimate theprobability density function of hydrologic variables havebeen introduced (Moon et al., 1993; Moon and Lall,1994; Kwon et al., 2006). The NMCS approach is appliedto 45 rainfall events induced by typhoons. The quantileestimation method applied in this study was the kernelquantile function estimator, with the bandwidth selectioncriterion proposed by Moon and Lall (1994). The quan-tile of each variable was generated numerically from thecumulative kernel density function corresponding to therandom number. Given the simulated data, design rainfallwas derived through Gumbel distribution. Figure 6 illus-trates the design rainfall computed by frequency analysisbased on the simulation results (200 years ð 1000 times).Although design rainfalls for all the duration series wereestimated, only 24-h duration events for eight stationswere shown due to limited paper space.

The proposed NMCS technique was found to have thecapability to reproduce the distribution of extreme events;design rainfall estimated by observation was located atthe centre of the uncertainty bound based on simulationensembles. The derived uncertainty in Gangneung stationshowed large variation at high return levels compared toother stations. The results seemed to reflect the unusualevent caused by typhoon Rusa.

EVALUATION OF TYPHOON-INDUCED RAINFALLTHAT CONSIDERS THE METEOROLOGICAL

FACTOR

Characterizing the spatial information on typhoons is cru-cial in deriving typhoon-induced rainfall. In this regard,the spatial information and physical characteristics oftyphoons such as track coordinate (latitude, longitude),pressure, and sea surface temperature at the centres oftyphoons were initially regarded as input variables inthe polynomial regression framework; hourly maximumrainfall caused by typhoon events was used as the depen-dent variable. The regression relationship between theindependent variables and the dependent variable wasestablished by locally weighted polynomial. First, inde-pendent variables in the model were generated by NMCS.Second, design rainfall was derived using the simulatedinput variables as inputs in the locally weighted polyno-mial model. Finally, the Gumbel distribution was appliedto the simulated rainfall series for the design rainfallestimation.

Simulation of typhoon characteristics

The physical characteristics of typhoons such as lati-tude, longitude, pressure, and sea surface temperature atthe centres of typhoons were simulated by Nonparamet-ric Monte Carlo (NMC). First, typhoon-induced maxi-mum rainfall events were considered, with the typhoonfeatures on that day vis-a-vis extreme rainfall extracted.



(a) Station 105 (b) Station 108

(c) Station 112 (d) Station 143

(e) Station 156 (f) Station 159

(g) Station 165 (f) Station 184

Figure 6. Rainfall frequency analysis from the NMCS for each station

A total of 45 feature vectors for each station were finallyprepared for further analysis. Figure 7 details the proba-bility density function derived by the simulated typhooncharacteristics, where the solid line indicates the derivedkernel density function based on the observed typhooncharacteristics; the red histogram represents the relative

frequency using the number of class intervals proposedby Sturges (1926). The multimodality of the distribu-tion of typhoon properties such as spatial information(latitude and longitude) and sea-level pressure is oftena strong indication that the distribution of the variablein the population is not a Gaussian distribution. In this



(a) Typhoon latitude (b) Typhoon longitude

(c) Central pressure (d) Sea surface temperature

Figure 7. Simulation of the physical characteristics of typhoons using NMCS

regard, it showed the advantages of NMC, i.e. its effec-tive description of multimodal distribution in simulatingthe variables.

Rainfall estimation using LWPR

The regression relationship between the physicalcharacteristics of the observed typhoons and observedextreme rainfall was established by LWPR. Given therelationship, the simulation was implemented 200 yearsð 1000 times to examine how the proposed modelcan provide a reasonable result. In this stage, numerousextreme rainfall series were generated using the simu-lated typhoon properties sampled through NMC. Optimalparameters k and p in the LWPR model were deter-mined by Equation (5). Finally, the return periods ofthe simulated rainfalls were estimated using the Gumbeldistribution in conjunction with the probability weightedmoment methods. All the eight durations at eight stationswere analysed, but the results for the 24-h duration ateach station were represented owing to space limitation.The rainfall frequency curve with confidence intervalderived by simulations is illustrated in Figure 8. As aresult of the simulation, the return periods from obser-vations mostly fell within the confidence limit of 95%(Figure 8). Although the return periods for station 105(Gangneung) and station 159 (Busan) indicated the valueof the quantile to deviate slightly from the median, theresults from the locally weighted polynomial approach

were not significantly different from those obtained bythe analysis of original data.

To investigate further the proposed model’s perfor-mance, we compared the location and scale parameters,i.e. whether the simulated extreme rainfall series did havea similar pattern in terms of the probability density func-tion. In comparing the parameters, NMCS and LWPRwere separately considered to understand the sensitivityof the model better. Figure 9 shows a box-whisker plotconstructed by 200 years ð 1000 times simulation. Asillustrated in Figure 9, the location and scale parameterwere reasonably reproduced by the proposed approach.On the basis of the results, LWPR was slightly better inreproducing the characteristics of the distribution. Again,the results confirmed that station 105 (Gangneung) waspoorly modelled. As mentioned earlier, typhoon Rusabrought heavy rains and flooding to the Gangneung area,even amounting to 36 in. (910 mm) in some areas. Thisseems to be one of the reasons for the model to producemore rainfall based on the proposed model.

Finally, design rainfall induced by typhoon was esti-mated using two different approaches. Design rainfallaccording to three different durations (1, 12, and 24 h)at each station is represented in Figure 10. LWPR inconjunction with NMCS showed better performance thanNMCS in terms of reproducing extreme characteristics.This implies that the LWPR model using typhoon char-acteristics as inputs has advantages in characterizingtyphoon-induced extreme rainfall.






(g) Station 165 (h) Station 184

Figure 8. Rainfall frequency analysis from the NMCS and LWPR for each station

CONCLUSION

In this study, rainfall events caused by typhoons wereanalysed using rigorous statistical methods. For rainfallevents caused by typhoons, only for those whose centreswere located in the zone that could affect the Korean

peninsula were chosen. In addition, hourly maximumrainfall events from each of the typhoon events duringthe period studied were grouped by duration for analysis.First, the observed rainfall was used to perform frequencyanalysis. Second, the results from the nonparametricsimulation were subjected to frequency analysis for






(g) Station 165 (h) Station 184

Figure 9. Box–Whisker plot to compare the model parameters of rainfall frequency analysis. ‘x’ indicates the location and scale parameter as obtainedfrom observation



(a) Comparison of probability rainfall at Location 105

(b) Comparison of probability rainfall at Location 108

(c) Comparison of probability rainfall at Location 112

(d) Comparison of probability rainfall at Location 143

Figure 10. Comparison of design rainfall according to the analysis methods

comparison. Third, the regression relationship betweenthe physical characteristics of typhoons and rainfall wasestablished by the locally weighted polynomial. After-wards, frequency analysis was carried out on rainfallestimates obtained by simulations of the physical charac-teristics to compute design rainfall.

The results of the frequency analysis on the resultsof simulations (200 years ð 1000 times) on rainfallscaused by typhoons were not significantly different from

those on observed data. In particular, the results of thefrequency analysis on original data were included in thescope of error from the simulation results. Moreover,the comparison of the estimated quantiles showed thatthe results of the locally weighted polynomial probablyproduced rainfall of similar size.

When compared, the scale and location parameters asestimated from the observed data and simulation datawere found to be slightly different. Note, however, that



(e) Comparison of probability rainfall at Location 156

(f) Comparison of probability rainfall at Location 159

(g) Comparison of probability rainfall at Location 165

(i) Comparison of probability rainfall at Location 184

Figure 10. (Continued )

simulated data were not found to distort observed datasystematically. Therefore, a combination of nonparamet-ric simulation and locally weighted polynomial could beproposed as an alternative method of evaluating rainfallcaused by typhoons.

The evaluation of rainfall estimated by the regressionrelationship between the physical characteristics andrainfall can be said to secure a certain degree of reli-ability. Moreover, the findings can be used for rainfall

evaluation using meteorological factors related to rain-fall because evaluating rainfall change caused by climatechange given the impact of global warming is difficultowing to the uncertainty of rainfall data.

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