JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION Vol. 44, No. 2

AMERICAN WATER RESOURCES ASSOCIATION

April 2008

ANALYSIS OF EXTREME SUMMER RAINFALL USING CLIMATE TELECONNECTIONS AND TYPHOON CHARACTERISTICS IN SOUTH KOREA1

Hyun-Han Kwon, Abedalrazq F. Khalil, and Tobias Siegfried2

ABSTRACT: It is now widely acknowledged that climate variability modulates the frequency of extreme hydrological events. Traditional methodologies for hydrologic frequency analysis are not devised to account for variation in the exogenous teleconnections. Flood frequency analysis is further plagued by the assumptions of stationary in the causal structure as well as ergodicity. Here, we propose a dynamical hierarchical Bayesian analysis to account for exogenous forcing that govern the summer season rainfall. The precursors for Korean summer rainfall at different frequencies are identified utilizing wavelet and independent component analyses. The sea surface temperatures, the ensemble of rainfall predictions by General Circulation Model, in addition to the typhoon attributes were found to have direct correlation with extreme rainfall events and were used as inputs to the logistic regression model. The model parameters are estimated using Markov Chain Monte Carlo and the resulting posterior distributions associated with individual inputs are analyzed to advance our understanding of the spatiotemporal impact of the teleconnections. Eight rainfall stations throughout Korea are considered in this analysis. We demonstrate that the probability of occurrence of extreme events could be successfully projected at a 90% rate of correct classification of extreme events.

(KEY TERMS: extreme summer rainfall; hierarchical Bayesian model; logistic regression; climate information.) Kwon, Hyun-Han, Abedalrazq F. Khalil, and Tobias Siegfried, 2008. Analysis of Extreme Summer Rainfall Using Climate Teleconnections and Typhoon Characteristics in South Korea. Journal of the American Water Resources Association (JAWRA) 44(2):436-448. DOI: 10.1111/j.1752-1688.2008.00173.x

INTRODUCTION

The climate is dynamic and continuously changing and the signature of these changes is evident on the hydrologic cycle and the associated rainfall patterns (Knox, 1984, 1993). El Nin˜o-Southern Oscillation (ENSO) as a surrogate of climate change has been extensively investigated with respect to different places and multiple hydrologic variables

(Ropelewski and Halpert, 1986, 1987; Halpert and Ropelewski, 1992; Piechota and Dracup, 1996). It is also now widely acknowledged that climate variability modifies hydrological frequency (Jain and Lall, 2000, 2001; Franks and Kuczera, 2002; Milly et al., 2002; Pizaro and Lall, 2002). Porparto and Ridolfi (1998) studied changes in flood frequency over paleo-timescales and demonstrated that estimated flood exceedance probability can increase quite rapidly with time. Hirschboeck, 1988 and Knox, 1993

1 Paper No. JAWRA-07-0001-P of the Journal of the American Water Resources Association (JAWRA). Received January 9, 2007; accepted August 14, 2007. ª 2008 American Water Resources Association. Discussions are open until October 1, 2008. 2 Respectively (Kwon), Senior Researcher, Water Resources Research Division, Korea Institute of Construction Technology, Daehwa-Dong, Ilsan-Gu, Goyang-Si, Gyeonggi-Do, South Korea 411-712; and (Khalil, Siegfried) Postdoctoral Research Scientists, Department of Earth and Environmental Engineering, Columbia University, New York, New York 10027 (E-Mail ⁄ Kwon: [email protected]).

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found that large floods at a given site may be related to large scale atmospheric circulation anomalies and studied the use of mixture models for estimating flood frequency. There is considerable evidence of regime-like or quasi-periodic climate behavior and of systematic trends in key climate variables over the last century and longer (NRC, 1998). As an example, climatic regime shifts that may result in long-term variability in flood risk are the Pacific decadal oscillation and the Northern Atlantic oscillation which both exhibit low frequency variability (Olsen et al., 1999). In recent decades, extreme weather events seem to be growing in frequency (Katz and Brown, 1992; Karl et al., 1995; Easterling et al., 2000). Frequency and intensity of climate- and water-related disasters are increasing worldwide, especially for hydrological extremes, causing a serious threat to the economic development of many regions. Associated economic losses are increasing comprehensively as a result of weather-related disasters, such as heavy storms, floods and droughts. This increase is partly due to economic growth and the increasing world population that inhabits exposed areas, but it is also believed that changes in the climate are responsible for the increasing impacts and losses. In particular water resources are vulnerable to changes in climate, compounding changes in water use of a growing population that is demanding more and more water per capita as part of its development. It is nowadays widely recognized that the frequency of a specific hydrologic variable should not be treated independent of climate variability (Olsen et al., 1999; Sankarasubramanian and Lall, 2003). For instance, warmer waters of the western tropical Pacific in conjunction with sea surface temperatures (SSTs) increases towards the central and eastern Pacific caused by global warming, increase cyclone occurrence and the associated threats. During the monsoon season in the Korean peninsula, these storms cause large local rains by providing constant water vapor into Korean peninsula. Traditional hydrological frequency analyses, however, are not able to take into account the increased impacts of climate variability to systematically inform on or estimate the extreme rainfall frequency (Sankarasubramanian and Lall, 2003). However, from the perspective of the development of a comprehensive water resources management strategy, a proper understanding of these extreme events is crucial because the latter often are catalysts for changes in water management by exposing vulnerabilities of existing management schemes. The objective of the study was to develop statistical seasonal rainfall models which allow for the JOURNAL

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classification of extreme events and continual updates of the estimates of the frequency of these extreme events and the probability of extreme rainfall occurrence by focusing on potential climatic predictors and by developing a Hierarchical Bayesian logistic regression model of seasonal rainfall in South Korea. As a case study, climate variability in South Korea is studied. The results of our study have the potential to improve water resource management in this region by supporting management decisions which help to decrease vulnerability to droughts, floods, and other crises related to climate variability. The procedure used to assess low-frequency variability in Korea rainfall and its relationship to SST variation and estimate extreme rainfall occurrence probability with selected predictors is displayed in Figure 1. Wavelet transform analysis is used to characterize low frequency variability of rainfall with SSTs and a hierarchical Bayesian logistic regression model is employed to estimate extreme rainfall occurrence probability by considering the climate predictors such as SSTs, typhoon characteristics and GCM predictions. In the following, ‘‘Methodology’’ describes the dataset used to illustrate the method. Furthermore, the relevant theoretical aspects of hierarchical Bayesian model are introduced. An overview of the interconnections between seasonal rainfall and climate information is provided in ‘‘Korean Peninsula Case Study’’. ‘‘Statistical Model for Seasonal Rainfall’’ demonstrates the applicability of the proposed hierarchical Bayesian logistic model to eight rainfall

FIGURE 1. Procedure Used to Assess Low-Frequency Variability in Korea Rainfall and Its Relationship to Sea Surface Temperature Variation and Estimate Extreme Rainfall Occurrence Probability With Selected Predictors.

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spectrum in Fourier space, at a given N points, using a discrete Fourier transform (xn) as (Torrence and Compo, 1998).

x^j ¼ METHODOLOGY

Wavelet Transform Based Independent Component Analysis It is becoming increasingly accepted that a change in the variance of a distribution will have a larger effect on the frequency of extremes than a change in the mean (Katz and Brown, 1992; Meehl et al., 2000). Wavelet transform based independent component analysis (WICA) can be used to investigate changes in the variance of a distribution and to identify both temporal and spatial aspects between rainfalls at multiple locations. The Wavelet transform, which was originally proposed in the early 1900s (Chui, 1992), provides the ability to identify frequency components as well as their variation in time. Wavelet methods have become popular for geophysical time series analysis over the past ten years. We briefly summarize the wavelet transform analysis as presented by (Torrence and Compo, 1998). The term wavelets refers to sets of function of the form /b,a(t) = |a|)1 ⁄ 2/((t ) b) ⁄ a) (i.e., sets of function formed by dilation and translation of a single function /(t)) called as the mother wavelet. The continuous wavelet transform of a real time series x(t) is defined by (Chui, 1992)

1=2

Xðb; aÞ ¼ jaj

Z

þ1

xðtÞu ððt  bÞ=aÞdt;

ð1Þ

1

where X(b,a) is a wavelet spectrum, /(t) is a wavelet function, the (*) denotes the complex conjugate, b is the translation (shift) parameter and a, a „ 0, is the scale parameter. By localizing the wavelet function at t ) b = 0 and then by computing the coefficients X(b,a) we can explore the behaviour of x(t) near t = b. A variety of wavelet functions have been proposed (Foufoula-Georgiou and Kumar, 1995; Torrence and Compo, 1998). Here, we have used the Morlet wave2 let, defined as uðtÞ ¼ p1=4 eix0 t et =2 ;where x0 is a frequency. To estimate the continuous wavelet transform, an N times convolution of the function shown in Equation (1) is done for each scale, where N is the number of points in the time series (Kaiser, 1994). Numerically, we are able to estimate wavelet power JAWRA

N1 1X xn expð2pijn=NÞ; N n¼0

ð2Þ

where j = 0,…,N ) 1 is the frequency index. In the continuous limit, the Fourier transform of a function ^ ðaxÞ. By the convolution theorem, /(t ⁄ a) is given by u the wavelet transform is the inverse Fourier transform of the product

Xn ðaÞ ¼

N1 X

^  ðaxj Þ expðixj ndt Þ x^j u

ð3Þ

j¼0

Information in the wavelet power spectrum can be interpreted at each time and scale. Torrence and Compo, 1998 suggested two ways. One is time-integrated variance of energy coefficients at every scale to construct global wavelet power and another one is scale integrated variance of energy coefficients over time to compute the scale averaged wavelet power (SAWP) as N1 1X X2n ðaÞ ¼ jXn ðaÞj2 N n¼0

dj dt X2n ðtÞ ¼ Cd

j2 X jXn ðaj Þj2 j¼j1

aj

ð4Þ

ð5Þ

The Cd is a reconstruction coefficient and is a constant for each wavelet function. j1 and j2 are scales over which the averaging takes place. dj and dt are the scale averaging coefficient, sampling period respectively. The general procedure used to investigate the space and time variability of Korean rainfall and its relation to the variation of the Pacific and Indian Ocean SSTs using WICA is illustrated in Figure 2. The first step in the analysis is to explore the climate modes that influence specific low frequency aspects of the rainfall using wavelet analysis to capture the time varying low frequency structure and independent component analysis (ICA) to identify the spatial modes of variation of the low frequency signals for multiple locations in Korea. The WICA approach was initiated and employed for assessing Everglades National Park area rainfall variability in Southern Florida with SSTs by Kwon et al., 2006. Please refer to Kwon et al., 2006 for the detailed procedure. Wavelet power at a given frequency and time may provide a way to relate 438

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FIGURE 2. Procedure Used to Assess Low-Frequency Variability in Korea Rainfall and Its Relationship to Sea Surface Temperature Variation.

evolving quasi-oscillatory phenomena, such as traveling waves and their attenuation in space and time. In addition to energy or power at individual scales, power over a range of scales, the SAWP, which represents the mean variance of wavelet coefficients over a range of scales may also be used. As SAWP is a time series of average variance in a certain band, SAWP can be used or both, to examine the modulation of one-time series by another and to assess the modulation of one frequency by another within the same time series (Torrence and Compo, 1998). Having obtained the SAWP and individual scale power, wavelet energy based ICA can be used to extract the coherent modes of spatial and temporal variability of the SAWP as well as the individual scale power. ICA (Hyvarinen et al., 2001), seeks to find a rotation of the data matrix that leads to components that are independent in the sense that their mutual information is minimum, as opposed to principal component analysis where only linear independence is assured after. JOURNAL

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Hierarchical Bayesian Logistic Multiple Regression A hierarchical Bayesian-based logistic regression model is proposed to incorporate nonstationarity using time-dependent climate predictors. The objective of Bayesian inference is to compute the posterior distribution of the desired variables, in this case the parameters of occurrence probability of extreme events. The posterior distribution p(h|x) is given by the Bayes’ Theorem as follow:

pðhjxÞ¼

pðhÞpðxjhÞ pðhÞpðxjhÞ ¼R / pðhÞpðxjhÞ; pðxÞ H pðhÞpðxjhÞdh ð6Þ

where h is the vector of parameters of the distribution to be fitted, Q is the space parameter, p(h|x) is the likelihood function, x is the vector of observations and p(h) is the prior distribution. 439

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A Bayesian hierarchical logistic regression model was used to estimate the effects of the predictor variables. Logistic regression is a type of predictive model that can be used when the response variable is a categorical variable with two categories. Let y = (y1,…yn) be a vector of dichotomous observations (yi 2 {0, 1}). Here, a 10% exceedance threshold is used for classifying rainfall. The following relationship between the success probability pi = Pr(yi = 1) and explanatory variables contained in matrices X is assumed  LogitðpiÞ ¼ log

pi 1  pi

 ¼ b1 X1i þ    þ bk Xki ;

ð7Þ

where Xi is the ith rows of the known design matrices X, and b is a vector of regression parameters which is following a Gaussian distribution bk  Nðgbk ; rk Þ. Similarly, the hyper-parameters gbk and rk are also assigned to a conjugate distribution. Here we assume that gb  Nð0:0; rrk Þ. Restricting this parameter to a zero-mean process is a analogous to introducing regularization to the parameter estimation. The hierarchical Bayesian structure also requires that rk and rrk follow a distribution. Here, we assume them to follow a half-Cauchy distribution. A half-Cauchy prior distribution is an example of a weakly informative prior distribution that is assigned to the variance. A half-Cauchy is a special case of the conditionally conjugate folded-noncentral-t family of variance prior distributions. This setting gives a much sharper inference, using the partial pooling that comes with fitting a hierarchical model (Gelman, 2006). A graphical representation of the model structure is shown in Figure 3. The posterior distribution of each parameter and hyper-parameter result from the maximization of the model likelihood. Analytical integration of this term is not feasible. A variety of inference techniques have been employed (Seltzer et al., 1996; Gyftodimos and Flach, 2004; Chen et al., 2005) and we have chosen to apply the Gibbs sampler, which is an effective Markov Chain Monte Carlo (MCMC) method for simulating the posterior probability distribution of the data field conditional on the current choice of parameters (Gelman et al., 1995; Tsionas, 2001; Hue et al., 2002; Gelman et al., 2003; Godsill et al., 2001; Ridgeway and Madigan, 2003; Tucker and Liu, 2003; Chen et al., 2005). The use of the Gibbs sampler, as discussed in the context of hierarchical Bayesian models enables a simple sampling-based solution to such problems (Gilks et al., 1995). The steps to set the logistic regression model as a generalized multiple linear model are defined as followed:

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FIGURE 3. A Directed Acyclic Graph of the Hierarchical Bayesian Multiple Regression Model. Dotted arrows represent stochastic relationships, solid arrows represent deterministic relationships, and circles represent variables and data. Large square plates represent loops.

1. Let us say that an exceedance probability is 0.1. Then, we can identify from the cumulative distribution function of y, a corresponding threshold y*, such that the JJAS seasonal rainfall is exceeded on average with exceedance probability pexc, i.e., E[p(y > y*)] = 0.1, i.e., the 90th percentile of the rainfall. 2. Given the assumption that y is an independent and identically distributed random variable, it is reasonable to consider the binomial process m (m = 1 if y > y*, 0 else). If pexc is 0.1 and the sample size for y is almost 50, then there will be five cases where m = 1, and 45 cases for which m = 0 (Figure 4a). Now, if we consider a logistic regression of m on X (e.g., the SSTs, the GCM precipitation, and the characteristics of the typhoon), one can estimate the conditional probability E[p(m|X)]. If E[p(m|X)] is greater than or equal to the 0.5, then we expect an extreme event (i.e., on average one expects an exceedance of the threshold y* corresponding to pexc). 3. The link function is a logit link which is defined by Equation (7). And then E[p(m|X)] has an S-shaped function (see Figure 4b). This process will be applied to the 1958 to 2001 data for major eight rainfall series in Korea, yt, and the potential predictors, Xt. We consider a candidate level for the exceedance probability 0.1, corresponding to the events with return periods of 1 in 10 years. From the empirical cumulative distribution function of y, we identify the corresponding thresholds for

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temperature. During the rainy season from June to September, Korea receives about 70% of its annual precipitation of 1,283 mm. About 18% of the total annual precipitation falls during the dry season from October to March. Annually, two to three of the approximately 28 typhoons occurring in the vicinity of the northwestern Pacific Ocean influence the Korean peninsula directly or indirectly. When a typhoon is located north of 20N and west of 140E, it is expected to influence the Korean peninsula. It has been reported that East Asia including Korea is not only experiencing regional warming but also precipitation anomalies (Chung and Yoon, 2000; Qian and Zhu, 2001; Chung et al., 2004). For example, a prolonged period of heavy rain and flooding and severe damage occurred in southeastern Korea for more than 10 days in 2002. Furthermore during the 3 month period JJA in 2003, a prolonged period of rain days occurred and the total number of rainy days exceeded 60 days. The total amount of rainfall in this summer was more than twice of an average year. In addition, a typhoon passing through southeast Korea on September 12 produced heavy rainfall. This resulted in a record breaking damage by winds and flood in South Korea (Chung et al., 2005). Over time, water resources management in Korea has generally become more complicated by the unprecedented frequency in extreme hydrologic events and the need for adaptive water resources management accounting for climate change has become apparent.

FIGURE 4. Example of Logistic Regression With (a) Categorized Rainfall With 10% Exceedance Probability Threshold and (b) S-Shape Cumulative Density Function of 10% Exceedance Events Given X Predictors.

each station. These thresholds are then used to construct the binary series mt that represent exceedance of the 1 in 10 year thresholds.

KOREAN PENINSULA CASE STUDY

Background Information South Korea is located in the moderately humid zone of medium latitude. It has a distinct seasonal climate which is largely influenced by dry, cold continental air masses during the winter and humid, warm air masses from the ocean during the summer. Temperature varies widely between summer and winter, and there is great regional diversity. The distribution of precipitation is more varied than that of JOURNAL

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Data In this case study, we use data on historical rainfall, characteristics of typhoons, global SST and GCM precipitation forecasts. For rainfall, we use monthly rainfall data which are assessed at the main eight weather stations in South Korea. A map of the study area is presented in Figure 5. Monthly rainfall data from 1958-2001 were available. For the purpose of this study, we focus on the wet season rainfall (JuneSeptember, JJAS) which is dominated by summer monsoon and typhoons. For SST, we use the 1856present monthly anomaly, 5 · 5 gridded product of Alexey Kaplan for the same period. Anomalies are based on the 1951-1980 time period (Kaplan et al., 1998). The global monthly SST data were transformed to seasonal SST in the same way as for rainfall. We account explicitly for the typhoons that hit South Korea using historical data (1958-2001) on their characteristics, including the number of typhoons in each month irrespective of their class, the total number of typhoons and low pressure storms as well as their duration. ECMWF forecasts within the DEMETER project are used as GCM precipitation forecasts 441

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FIGURE 5. Study Area and Main Rainfall Stations in South Korea.

(Palmer et al., 2004). The data available to us were nine ensemble members for 180 days.

Climate Characterization for Summer Rainfall in Korea Two well-defined rainfall peaks are existed in midJune and early September (Ho et al., 2003). The first rainfall peak occurs over a period of 30-40 days in June through July at all points of South Korea, with only minor time lags at different stations. This period accounts for more than 50% of annual precipitation at most stations. A second peak of rainfall is observed in early September when the monsoon front retreats to the south. The latter usually occurs with a typhoon (Chung and Yoon, 2000). Normally, cyclonic storms originate in the east Philippines, move toward the north and around Taiwan and shift direction mostly northeastward. The most common period for cyclonic storms in Korea is July through August. Although the number of storms is much less frequent in June and September, it seems that the typhoon in these months gives the strength to the monsoon, which may generate large local rainfall event. An important objective of this study was to examine a possibility of classification of the extreme rainfall events given relevant predictors. With regard to the latter, we explore the preceding seasonal SST and the predicted precipitation from GCM for the period from June to September. Converse to that and in the case of typhoon characteristics, concurrent data were used. Although the typhoon data are not preceding data, this study takes into account the typhoon as JAWRA

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potential predictors because it has an important role to generate heavy rainfall in summer season. Moreover, typhoon characteristics are usually predicted prior the official onset of the season and we intend to utilize these predictions to enhance the model performance with respect to the prediction of the likelihood of extreme rainfall events. Typhoon projections when combined with the prevailing states of Koran rainfall teleconnections further informs the decisionmakers of exposure to typhoons and enable early engagement of risk management schemes. The proposed model could use the information on the current prevailing conditions and the predicted hurricane count to estimate the occurrence probability of interest. A 95% confidence limit for the wavelet amplitude corresponding to a null hypothesis of red noise was applied in the wavelet analysis. Significant peaks with a period of 2-8 years are evident in the wavelet power spectrum and the global power spectrum in most of the stations, indicating the presence of the inter-annual variation throughout the last several years. We have initially considered the 2-year to 8-year frequency band on the basis of the global SWAP, as this feature is indicated consistently, and can be identified at almost all times with the degrees of freedom available. This study explored the interdecadal variability in the amplitude (power) associated with the 2-year to 8-year band of rainfall for summer season and identified inter-decadal patterns of modulation of the rainfall variability in the interannual band. The JJAS (June-September) season’s leading two wavelet independent components (WIC) retained 71% of eigenvalues. The temporal variation in the two WIC of the SAWP (and in all the eight individual series) seems to be interdecadal and interannual modes and WIC-2 appears to have an increasing trend (Figure 6). The correlation of the two WIC

FIGURE 6. The Two WICs of JJAS Seasonal Rainfall From Eight Stations. They retained 71% of eigenvalues. These WICs indicate interannual and decadal variability in the JJAS season.

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pool that dominate the spatial relationship of rainfall over East Asia. Rectangular zones that encompassed these regions were specified as follows: Indian SST (5S-10N to 40E-90E); Pacific SST (10S-10N to 120E-150E). The MAM values for the SST were spatially averaged over the selected box. The raw correlation coefficient without wavelet filtering between SST indices and eight rainfall stations vary over 0.10-0.50. The JJAS precipitation forecast is considered as potential predictor. The correlations coefficient with rainfall varies over 0.06-0.43. It seems to have predictability by considering the difficulties of prediction of rainfall in summer season due to various types of severe weather condition such as typhoon, local convection, and orographic effects. Table 1 lists the correlation coefficients of the spatially averaged indices with JJAS rainfall (significance at the 95% confidence level or higher is shown in bold type). Also shown in Table 1 are the relationships between JJAS rainfall and the typhoon indices. The overall relationship is not high, but the episodic influences of typhoon on summer rainfall can play a significant role in classifying extreme events.

STATISTICAL MODEL FOR SEASONAL RAINFALL

FIGURE 7. Correlation Analysis Between JJAS Rainfall WICs and Global MAM SST, Contour Plot of Correlation of Rainfall WIC-1 With (a) Previous Seasonal SST(MAM), WIC-2 With (b) Previous Seasonal SST(MAM).

with SSTs in the preceding March-April-May (MAM) season is illustrated in Figure 7. WIC-1 appears to be correlated with SST in the Indian Ocean, while WIC-2 once again correlated with SST in the Indian Ocean and with the tropical western Pacific. The spatial correlation pattern indicates that the Indian Ocean and tropical western Pacific Ocean dynamics induce development of the strong interannual variability of rainfall in Korea. The results from our analysis agrees with the one from Lee et al., 2005 in determining low-frequency teleconnections. Potential predictors were identified from the SST dataset according to regions where the correlations were strong and consistent with expectations based on results of precipitation studies (see Figure 7) (Lee et al., 2005). In a study of Indian and Pacific SST and East Asia rainfall modes, Yang and Lau, 2004 found an ENSO-like mode in the Pacific SST and a secondary mode in the east Indian-western Pacific warm JOURNAL

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By means of the proposed model, we estimate the probability that rainfall will exceed the 10% exceedance threshold given the stated predictors. The logistic regression model (introduced in ‘‘Methodology’’) is useful to model discrete responses. Events greater than the 90th percentile are referred to as extreme events. This threshold, which corresponds to 1-in-10-year event, was estimated from an empirical cumulative distribution function for each of the stations in the study area. We used the data extended over 1958-2001 and we assumed that the maximum seasonal rainfall in June-September season is independent and identically distributed. The logistic regression models are solved simultaneously in a Bayesian framework. Noninformative priors are assumed for each of the parameters bk, and their optimal values are selected through a maximization of the posterior likelihood associated with the logistic regression models. A MCMC procedure is used. In particular, the Gibbs sampling approach to MCMC (Gilks et al., 1995) has been used in this study. We chose to run three chains simultaneously searching for optimal parameters. The evolution of each chain was monitored to check for convergence to a common value. Selection of the 443

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TABLE 1. Correlation Matrix Between JJAS Rainfall and Predictors. No. of Storms in Each Month

Station Seoul Incheon Busan Mokpo Daegu Gangreung Jeju Ulsan

No. of Storms

Duration of Storms

6

7

8

9

Typhoon

Low Pressure

Typhoon

Low Pressure

Sea Surface Indian SST

Temperature Pacific SST

GCM Demeter

)0.03 0.00 0.03 0.38 )0.14 )0.14 0.20 )0.14

)0.06 0.10 0.11 )0.17 0.02 )0.08 )0.26 0.02

)0.10 )0.18 0.21 0.02 0.11 0.11 0.31 0.11

0.19 0.00 0.08 0.18 0.18 0.08 )0.02 0.18

0.00 0.05 0.36 )0.12 0.36 0.00 0.12 0.36

0.02 )0.05 0.05 0.29 )0.01 0.05 0.05 )0.06

0.02 0.13 0.24 )0.16 0.24 )0.01 0.24 0.24

0.21 )0.03 0.23 0.32 0.14 0.30 0.23 0.13

0.40 0.51 0.17 0.29 0.51 0.36 0.01 0.31

0.22 0.18 0.18 0.40 0.28 0.23 0.30 0.10

0.38 0.39 0.10 0.43 0.28 0.33 0.07 0.06

Note: Bold Significant at 5% and 10%.

TABLE 2. Posterior Median Estimates and Credible Intervals for Selected Parameters From Hierarchical Bayesian Logistic Model for Each Station. Station Seoul

Incheon

Busan

Mokpo

Daegu

Gangreung

Jeju

Ulsan

Node Beta[l] Beta[2] Beta[3] Beta[4] Beta[l] Beta[2] Beta[3] Beta[4] Beta[5] Beta[l] Beta[2] Beta[3] Beta[4] Beta[l] Beta[2] Beta[3] Beta[4] Beta[l] Beta[2] Beta[3] Beta[4] Beta[l] Beta[2] Beta[3] Beta[4] Beta[5] Beta[l] Beta[2] Beta[3] Beta[4] Beta[5] Beta[l] Beta[2] Beta[3]

(tropical depression duration) (Indian SST) (GCM precipitation) (no. of storm, July) (no. of storm, August) (Indian SST) (GCM precipitation) (total no. of typhoon) (Pacific SST) (GCM precipitation (tropical depression duration) (Pacific SST) (GCM precipitation) (no. of typhoon) (Indian SST) (GCM precipitation) (no. of storm, June) (no. of storm, August) (Indian SST) (GCM precipitation) (no. of storm, June) (no. of storm, August) (no. of typhoon) (GCM precipitation) (total no. of typhoon) (Indian SST)

Mean

SD

MC error

% 2.50%

Median

97.50% %

Misclass

)4.62 1.66 2.89 1.83 )8.28 4.56 )3.22 2.00 3.39 )4.19 1.83 1.02 0.82 )9.54 3.29 1.56 4.87 )5.82 2.04 2.38 2.64 )5.14 )4.88 2.97 2.71 2.42 )7.37 2.43 2.71 1.53 2.47 )3.80 1.78 1.37

1.52 0.75 1.39 0.91 3.29 2.31 1.68 1.19 1.69 1.24 0.79 0.69 0.77 3.49 1.52 1.31 2.13 2.01 0.94 1.27 1.25 1.78 3.13 1.42 1.29 1.29 2.95 1.39 1.44 1.10 1.16 1.10 0.98 0.76

0.05 0.02 0.04 0.03 0.21 0.15 0.10 0.06 0.10 0.04 0.02 0.02 0.02 0.17 0.07 0.03 0.10 0.08 0.03 0.04 0.05 0.07 0.08 0.05 0.04 0.04 0.16 0.07 0.07 0.05 0.05 0.03 0.02 0.02

)8.19 0.34 0.65 0.26 )16.30 1.06 )7.14 0.05 0.84 )7.03 0.48 )0.23 )0.57 )17.51 0.80 )0.75 1.52 )10.48 0.47 0.42 0.58 )9.44 )12.39 0.63 0.65 0.29 )14.63 0.27 0.58 )0.40 0.55 )6.42 0.30 0.05

)4.42 1.59 2.72 1.75 )7.74 4.24 )3.02 1.86 3.15 )4.02 1.76 0.98 0.79 )9.10 3.10 1.46 4.59 )5.55 1.94 2.19 2.50 )4.84 )4.29 2.81 2.56 2.28 )6.82 2.22 2.48 1.47 2.33 )3.64 1.60 1.29

)2.25 3.35 6.08 3.82 )3.42 9.98 )0.59 4.71 7.43 )2.24 3.57 2.51 2.47 )4.07 6.72 4.45 9.71 )2.75 4.17 5.41 5.47 )2.56 )0.42 6.16 5.64 5.32 )3.20 5.77 6.19 3.98 5.27 )2.07 4.14 3.03

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The optimal significant predictors from a set of independent variables are selected by the stepwise regression method for each station. Table 2 summarizes the results from the Bayesian model. Values are 444

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E[p(m|X)] is greater than or equal to 0.5, then we expect an extreme event (i.e., on average we expect an exceedance of the threshold y* corresponding to pexc).

DISCUSSION AND CONCLUSION

FIGURE 8. Kernel Density Estimates of the Parameters (regression coefficients) From Hierarchical Bayesian Logistic Regression Model for Jeju Station.

estimates and statistics of the regression coefficients for predictors. It is found that the SSTs and the GCM precipitation are generally selected as a predictor for each station. The first parameter is Beta[1] with the regression intercept, and others are the regression coefficients denoted with Beta[2],… Beta[J + 1], where J is the number of predictors. Mean, standard deviation, and the 95% credible interval are based on a hierarchical Bayesian specification of a linear regression model where rainfall is governed by the predictors. It is found that the coefficients for the predictor variables are statistically significant given their uncertainties. One can also look into the validation of parameters with graphical presentation. As an example, the posterior distribution via hierarchical Bayesian inference relating to the parameter’s uncertainty for Jeju station is shown in Figure 8. The distribution of Beta[4] and Beta[5] show relatively tight uncertainty bounds compare to Beta[2] and Beta[3]. From the above related statistics, the numbers of typhoons and Pacific SST have a significant influence that is associated with a narrowly bounded distribution. This process is also applied to the other stations to validate parameters of model. Thus, the importance of degree of parameter can be interpreted as well as the validation can be examined by Bayesian inference. Given the proposed model, the miss-classification rate with observed rainfall across eight stations ranges from 2 to 9%. Finally, the predicted E[p(m|X)] from hierarchical Bayesian logistic regression with return periods of 1 in 10 years are illustrated in Figure 9. Here, If JOURNAL

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The first objective of this study was to develop a better understanding of the mechanisms determining the low frequency variability and to identify the relevant predictors which could be used in estimating the occurrence probability of extreme rainfall in South Korea. The second objective was to develop a statistical seasonal rainfall model so as to estimate occurrence probability of extreme summer rainfall. The results of this analysis demonstrated the existence of strong influences of Indian and Western Pacific Ocean on extreme rainfall in Korea. This evidence of teleconnection between Korea and conditions in the Indian and Pacific oceans, as parameterized by our indices of SSTs are consistent with the conclusions of East Asia rainfall studies (Yang and Lau, 2004; Lee et al., 2005). This study investigated the inter-decadal variability in the amplitude (power) associated with the 2-year to 8-year band of rainfall for summer season and identified inter-decadal patterns of modulation of the rainfall variability in the inter-annual band. Both temporal and spatial aspects of these modes were identified by WICA approach. The importance of the SST dynamics known from the previous studies (Latif et al., 1994; Nagai et al., 1995) could be confirmed with respect to modulation of interannual variability of rainfall associated with the Indian and Pacific Ocean large-scale SST modes. Our results have shown that the tropical western Pacific SST and Indian Ocean SST is important in modulating the interannual variability of Korea rainfall. This analysis enabled us to identify the SST zones that govern the physics of extreme rainfall events. Second, multiple hierarchical Bayesian logistic models were built to estimate the probability of occurrence of extreme events condition on the identified climatological precursors. Predictors such as the preceding season SST in the identified zones, the ensemble of precipitation predictions by GCM, and the characteristics of the typhoon were simultaneously utilized in estimating the occurrence probabilities. It was found that those predictors play an important role in the model in classifying extreme condition from historical data. Specifically, the proposed model based on indices of MAM SSTs in the Indian and Western Pacific oceans, an index of 445

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FIGURE 9. Predicted E[p(m|X)] From Hierarchical Bayesian Logistic Regression Evaluated for the Values of the Climate Indices and the 10-Year Return Period JJAS Rainfall of (a) Seoul, (b) Incheon, (c) Busan, (d) Mokpo, (e) Daegu, (f) Gangreung, (g) Jeju, (h) Ulsan. Red arrow indicates a misclassification event from the model. If E[p(m|X)] is greater than or equal to 0.5, then we expect an extreme event (i.e., on average we expect an exceedance of the threshold y* corresponding to pexc).

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GCM precipitation and typhoon allow us to estimate occurrence probability for the JJAS rainfall. The hierarchical Bayesian logistic model showed good performance in terms of classifying extreme events. The model indicates that the right classification rate is approximately over 90% in all stations. Changes in large-scale patterns of SST over the past century have been recognized to be inherently susceptible to climate change. (Cai and Whetton, 2001) identified that 43.6% of the total temporal variance in SST is attributed to global warming. This accentuates that to fully understand as well as predict changes of regional rainfall patterns, such as more frequent and more intense extreme events, quantifying the relative influences of the modes of natural climatological variability is very important. We note that SSTs in both Indian and Pacific Ocean show significant relevance in modulating the frequency analysis of extreme hydrological events over the Korean peninsula. The posterior distribution of the parameters associated with SST (see Table 2) suggests that the amount of information imbedded in these zones of the ocean could enhance our prediction models, increase the skill of modeling of climate change impact under different scenarios, and steer prudent ex ante risk management schemes. Therefore, we argue that the findings of this study could be of paramount importance to flood index insurance and mitigation programs. Moreover, quantification of changes in the risk associated with the extreme rainfall may provide value for reservoir managers and provide some impetus for managing flood dynamically in a manner that is consistent with its nonstationary nature.

ACKNOWLEDGMENT This work was partially supported by ‘‘Seed Money Project’’ of Korea Institute of Construction Technology, Korea.

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