Spatio-Temporal Extreme Value Modeling of Extreme Rainfall over the Korean Peninsula Incorporating Typhoon Influence

Abstract

This study models the spatiotemporal heterogeneity of extreme rainfall over the Korean Peninsula using the generalised additive extreme value models (EVGAM) to address the limitations of traditional stationary approaches under climate change. Analyzing 30 years of daily precipitation data (1995–2024), we conducted a comparative analysis between typhoon-inclusive and non-typhoon scenarios to isolate the meteorological drivers of extremes. The results revealed distinct covariate dependencies: while spatial location (latitude and longitude) governs rainfall variability in non-typhoon conditions, elevation emerged as the critical determinant for the scale parameter during typhoon events, highlighting the role of orographic effects. Furthermore, the shape parameter exhibited multi-decadal oscillations corresponding to climate variability indices. To ensure local accuracy, a dual fitting strategy was implemented, supplementing EVGAM with standalone generalized extreme value (GEV) estimation for stations exhibiting poor goodness-of-fit. The resulting 50-year and 100-year return level maps quantify regional risks, identifying the southern coast as a high-vulnerability zone driven by typhoons, while inland basins benefited from orographic shielding. This comprehensive framework provides a robust scientific basis for adaptive water resource management and infrastructure design.

1. Introduction

The accelerating trend of climate change globally over recent decades is identified as the primary cause for the increasing frequency and intensity of localized and extreme weather phenomena [1,2,3]. Amidst these changes, extreme rainfall events stand out as one of the most distinctly affected hydrological phenomena due to climate change, leading to immense socio-economic losses and severe impacts. Indeed, research indicating that approximately 95% of natural disasters occurring in South Korea are attributable to extreme precipitation events underscores this risk [4]. Extreme precipitation phenomena can no longer be viewed as unforeseeable anomalies; instead, they represent high-impact, probable events that are often recognized as predictable but neglected threats. This highlights a critical gap, as current systems are largely unable to cope with the drastic shifts in rainfall patterns induced by climate change [5].

The root of this problem lies in the limitations of traditional statistical and engineering methodologies used for predicting extreme rainfall. Conventional hydraulic design criteria are based on outdated concepts assuming uniform temporal and spatial variability of precipitation, rendering them inadequate to represent rapidly changing extreme rainfall events [6]. Furthermore, conventional statistical methods are criticized as fundamentally unsuitable for modeling extreme, rare, and seemingly unpredictable events [7]. Given that the maximum hourly precipitation has shown a clear increasing trend over the past 50 years [3], and recognizing that climate change is one of the most critical factors altering precipitation characteristics [8], a new scientific approach is urgently required to predict and account for uncertain future rainfall.

The Korean Peninsula is directly affected by these global shifts [9], with unpredictable and record-breaking extreme rainfall cases reported annually. A representative example is the downpour of 141.5 mm/h recorded in South Korea in 2022 (an 80-year record), which resulted in casualties and enormous economic losses [10]. Therefore, accurately understanding the changing spatiotemporal variability of extreme rainfall is essential for modifying water resource management strategies and the design standards for related infrastructure [11]. It is crucial to estimate the return periods of extreme phenomena and adjust structural designs to accommodate potential future changes [12].

Research on extreme precipitation events is a core topic in climate studies [13], and probabilistic models such as extreme value theory (EVT) have been employed [14,15,16,17]. EVT, a branch of statistics, is used to analyze and predict the likelihood and intensity of extremely rare weather phenomena. Ref. [18] demonstrated that heavy-tail distributions, commonly used in EVT, effectively describe extreme values of precipitation. EVT primarily utilizes two methods: the block maxima (BM) approach and the peak-over-threshold (POT) approach. Various studies have compared BM and POT for analyzing extreme rainfall [19,20,21,22]. However, POT is generally more computationally expensive than BM due to the difficulty in selecting an appropriate threshold [23].

Specifically, the generalized extreme value (GEV) distribution, utilizing block maxima, has proven effective for analyzing the maximum values of rainfall extremes [24]. Yet, existing GEV studies often suffer from the limitation of inadequately incorporating covariates [25,26]. Furthermore, the distribution of extreme rainfall varies regionally due to significant geographical and climatic variability [27,28]. This necessitates a spatiotemporal approach that considers broad regional characteristics beyond single-site analysis [29,30], as extreme events with wide spatial ranges pose greater challenges for risk management [31]. Therefore, a spatiotemporal approach, considering not only temporal patterns but also the spatial context, is indispensable for predicting localized heavy rainfall that triggers flood and inundation damages.

To capture such complex spatiotemporal contexts and non-linear relationships, generalized additive models (GAM) has been utilized across various fields [32,33,34,35,36,37]. GAM has been applied for the spatiotemporal prediction of large-scale air pollution [38,39] used GAM to spatiotemporally identify non-linear and interaction effects of adjacent regional factors. Ref. [40] reported the use of GAM to integrate geographical factors and optimize, while capturing complex, non-linear relationships. Furthermore, Ref. [41] demonstrated the utility of GAM in extreme value analysis by implementing the model to capture flexible relationships for point and interval estimation of conditional quantiles during the inference process of univariate and multivariate extremes. Ref. [42] used GAM for spatiotemporal modeling to predict sea-level rise, incorporating factors reflecting regional characteristics. Notably, Ref. [43] modeled spatiotemporal exceedances over a threshold for extreme rainfall data via a time series-based approach, estimating the shape and scale parameters of the extreme value distribution using the generalised additive extreme value models (EVGAM). EVGAM is an extended extreme value model that combines extreme value theory with the smooth functions of GAM [44].

The primary objective of this study is to comprehensively model and predict the inherent spatial heterogeneity and temporal trends of extreme rainfall phenomena over the Korean Peninsula. While traditional GEV models are limited by their static nature in reflecting spatiotemporal variability, EVGAM can effectively model the spatiotemporal variation of extreme rainfall data by utilizing covariate information. Accordingly, this study applies EVGAM to meticulously analyze the parameter changes of extreme rainfall over the Korean Peninsula. Additionally, a comparative analysis is conducted by distinguishing between the presence and absence of typhoon data to quantitatively assess the influence of typhoons on the distribution of extreme rainfall.

Finally, by calculating and spatially mapping the return levels, we quantitatively present the regional risk of extreme rainfall, thereby providing academic grounds for establishing policies to address extreme disasters under climate change. Section 2 details the theoretical background of GEV and EVGAM and the model construction process. Section 3 describes the rainfall data utilized in the study. Subsequently, Section 4 presents the results of spatiotemporal parameter analysis using EVGAM estimation and the mapping of return levels. Section 5 summarizes the study findings and provides academic implications.

2. Methodology

The objective of this study is to predict extreme rainfall phenomena over the Korean Peninsula by fully integrating their spatial and temporal characteristics. For this purpose, the annual maxima, extracted from daily precipitation data, served as the fundamental data for the extreme value analysis. We utilized the EVGAM, the extreme rainfall prediction model, which models the location ($\mu$), scale ($log\sigma$), and shape ($\xi$) parameters of the GEV distribution as a function of spatial and temporal covariates. Each GEV parameter was modeled using smoothing functions reflecting spatial covariates such as latitude, longitude, and elevation, as well as the year. This approach aims to enhance prediction accuracy by integrating not only the spatial heterogeneity of extreme rainfall but also its temporal change trend into the model.

Following the EVGAM model fitting, a goodness-of-fit (GOF) test was performed to evaluate the local performance of the model and to ultimately estimate the parameters for each site. The GOF of the estimated parameters was assessed using the Cramér–von Mises (CVM) test based on the GEV distribution assumption. The core of this procedure is a dual model fitting strategy. For sites determined to be unsuitable based on the CVM test results—i.e., regions where the EVGAM model alone was deemed insufficiently explanatory—the parameters were subsequently re-estimated by directly fitting a site-specific GEV model (without covariates) to the local data. This dual process allowed us to complement regions where the spatiotemporal EVGAM had low explanatory power and secured an optimized set of parameters tailored to regional characteristics. Finally, based on the secured GEV parameters, return levels were calculated across the entire Korean Peninsula at a 1 km grid resolution. This allowed us to visualize the extreme precipitation corresponding to the 50-year and 100-year return levels in map form, thereby completing a region-specific meteorological disaster risk map. The entire research procedure is summarized in the following Figure 1.

2.1. Generalized Extreme Value Distribution

EVT is a statistical field dedicated to the analysis of extreme phenomena, such as maximum or minimum values. Similar to the Central Limit Theorem for sample means, EVT deals with the limiting distribution of sample maxima or minima [45]. In this study, the BM approach was employed to model the extreme value distribution. This approach involves dividing the observed data into blocks of equal size, extracting the maximum (or minimum) value from each block, and fitting these values to an extreme value distribution. This limiting distribution is established to converge to one of three possible types: Gumbel, Fréchet, or Weibull [46]. Ref. [47] established the theoretical foundation of EVT, proving that block maxima extracted from the original data, after appropriate normalization, converge to one of these three types. The GEV distribution, originally introduced by  [48], unifies these three distributions into a single form.

The cumulative distribution function (CDF) of the GEV distribution for a random variable X is given by:

$$F(x;\mu ,\sigma ,\xi )=exp\left\{-{\left[1+\xi \left({\displaystyle \frac{x-\mu }{\sigma }}\right)\right]}_{+}^{-1/\xi }\right\},\mathrm{for}1+\xi \left({\displaystyle \frac{x-\mu }{\sigma }}\right)>0,$$

(1)

where $\mu$ is the location parameter that determines the center of the extreme values (a higher value indicates higher average extreme rainfall); $\sigma >0$ is the scale parameter, controlling the variability or spread of the distribution (a larger value indicates greater fluctuation in extreme rainfall); and $\xi$ is the shape parameter, which determines the tail behavior of the distribution.

The shape parameter $\xi$ corresponds to the three classical extreme value distributions:

• $\xi >0$: Fréchet distribution (heavy-tailed, unbounded upper limit).
• $\xi <0$: Weibull distribution (short-tailed, finite upper limit $x\le \mu -\sigma /\xi$).
• $\xi =0$: Gumbel distribution (light-tailed, limit of $\xi \to 0$ in Equation (1)).

The formulas for the three types of distributions are as follows ($\mu$ and $\sigma >0$ are assumed):

$$\begin{array}{cc}\hfill \mathrm{Gumbel}\mathrm{distribution}(\xi =0):& F\left(x\right)=exp\left\{-exp\left[-\left({\displaystyle \frac{x-\mu }{\sigma }}\right)\right]\right\},\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill \mathrm{Fréchet}\mathrm{distribution}(\xi >0):& F\left(x\right)=exp\left\{-{\left({\displaystyle \frac{x-\mu }{\sigma }}\right)}^{-1/\xi }\right\},x>\mu ,\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill \mathrm{Weibull}\mathrm{distribution}(\xi <0):& F\left(x\right)=exp\left\{-{\left[-\left({\displaystyle \frac{x-\mu }{\sigma }}\right)\right]}^{-1/\xi }\right\},x<\mu -\sigma /\xi .\hfill \end{array}$$

(4)

The GEV parameters are typically estimated using the maximum likelihood estimation (MLE) method, which maximizes the log-likelihood function $\ell (\mu ,\sigma ,\xi )$. The log-likelihood function is defined as follows for $\xi \ne 0$ [49,50]:

$$\ell (\mu ,\sigma ,\xi )=-Nlog\sigma -\left(1+{\displaystyle \frac{1}{\xi }}\right)\sum _{i=1}^{N}log[1+\xi z_i]-\sum _{i=1}^N{[1+\xi z_i]}^{-1/\xi },$$

(5)

where N is the number of observations and $z_i=(x_i-\mu )/\sigma$ is the standardized observation. MLE is the standard estimation method for the BM approach due to its desirable properties such as efficiency, consistency, and asymptotic normality [51,52]. The GEV fitting in this study was performed using the fit.gev() function included in the “evd” package within the R 4.4.3 statistical environment [53].

2.2. Generalised Additive Extreme Value Models

The framework employed in this study is the EVGAM, as implemented by  [50]. The EVGAM extends the three parameters of the GEV distribution ($\mu ,\sigma ,\xi$) by modeling them as smooth functions of spatial covariates through a GAM. This addresses the structural limitation of traditional standalone GEV models, which assume linearity between spatio-temporal covariates and distribution parameters, often failing to capture non-linear variations caused by complex terrain or climate variability [54]. Furthermore, while simple GAMs handle non-linearity well, they typically assume an exponential family distribution, which is unsuitable for heavy-tailed extreme values. EVGAM retains the flexible structure of GAMs while explicitly setting the response variable distribution to GEV, thereby simultaneously addressing the distributional characteristics of extreme data and complex spatio-temporal non-linear patterns.

In this study, the GEV parameters are modeled as smooth functions of spatial covariates (e.g., latitude, longitude, and elevation) as follows:

$$\begin{array}{cc}\hfill \mathrm{location}\mathrm{parameter}:& \mu ={\beta }_{\mu ,0}+\sum _{j=1}^{J_{\mu }}{s}_{\mu ,j}\left(C_{\mu ,j}\right),\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill \mathrm{scale}\mathrm{parameter}:& log\sigma ={\beta }_{\sigma ,0}+\sum _{j=1}^{J_{\sigma }}{s}_{\sigma ,j}\left(C_{\sigma ,j}\right),\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill \mathrm{shape}\mathrm{parameter}:& \xi ={\beta }_{\xi ,0}+\sum _{j=1}^{J_{\xi }}{s}_{\xi ,j}\left(C_{\xi ,j}\right),\hfill \end{array}$$

(8)

where ${\beta }_{·,0}$ is the intercept, J is the number of covariates, and $s_{·,j}\left(C_{·,j}\right)$ is the smooth function for the j-th covariate C. Specifically, the scale parameter is modeled through a log transformation ($log\sigma$) to satisfy the mathematical constraint that $\sigma$ must always be positive [44]. This EVGAM structure effectively captures the spatial and environmental characteristics of extreme events by flexibly reflecting how the parameters change based on spatial factors [50,55].

It is important to note that the relationship between covariates and parameters is not restricted to be linear. Through the use of basis functions and penalized likelihood estimation, the model flexibly captures inherent non-linearities. Furthermore, EVGAM explicitly models interaction effects between covariates; for example, spatial dependence is captured using tensor product splines of longitude and latitude ($s(Lon,Lat)$), representing a 2-dimensional interaction surface rather than the sum of individual effects. Additionally, different parameters can be influenced by the same covariates through independent linear predictors.

The model’s parameters are estimated by maximizing the penalized log-likelihood function (${\ell }_p$). This function incorporates a penalty term into the standard log-likelihood to prevent excessive flexibility and the overfitting of the smooth functions. The objective function, the penalized log-likelihood ${\ell }_p\left(\mathit{\beta }\right)$, is defined as:

$${\ell }_p\left(\mathit{\beta }\right)=\ell \left(\mathit{\beta }\right)-{\displaystyle \frac{1}{2}}\sum _{j=1}^J{\lambda }_j{\mathit{\beta }}^T{\mathbf{S}}_j\mathit{\beta },$$

(9)

where $\ell \left(\mathit{\beta }\right)$ is the standard log-likelihood (Equation (5)) in terms of the coefficient vector $\mathit{\beta }$ for all smooth functions. The penalty term consists of the sum of the products of the j-th smoothing parameter ${\lambda }_j$ and the j-th penalty matrix ${\mathbf{S}}_j$. A larger ${\lambda }_j$ strongly suppresses curvature, reducing the effective degrees of freedom (EDF) and simplifying the function (to constant or linear), while a smaller ${\lambda }_j$ increases the EDF, generating a more complex curve. This process improves the model’s generalization performance by suppressing overfitting.

The smoothing parameters $\mathit{\lambda }={({\lambda }_1,\dots ,{\lambda }_J)}^T$ and the coefficient vector $\mathit{\beta }$ are interdependent. Therefore, EVGAM estimation follows a two-stage iterative procedure. First, with $\mathit{\lambda }$ fixed, $\mathit{\beta }$ is estimated by maximizing the penalized log-likelihood ${\ell }_p\left(\mathit{\beta }\right)$ using Laplace approximation. Second, $\mathit{\lambda }$ is updated by maximizing the marginal (restricted) likelihood ${\ell }_r\left(\mathit{\lambda }\right)$, which is obtained by integrating out $\mathit{\beta }$, using restricted maximum likelihood. This iterative procedure is detailed in  [56]. In this study, EVGAM fitting was performed using the evgam() function included in the “evgam” package within the R 4.4.3 statistical environment [50].

2.3. Return Level

The T-year return level ($R_T$) refers to the extreme event magnitude that is expected to be exceeded, on average, once during a return period of T years [57]. Using the GEV parameters ($\mu ,\sigma ,\xi$) estimated through EVGAM, the T-year return level $R_T$ is calculated as follows:

$$R_T=\mu -{\displaystyle \frac{\sigma }{\xi }}\left[1-{\left\{-log\left(1-{\displaystyle \frac{1}{T}}\right)\right\}}^{-\xi }\right],\mathrm{for}\xi \ne 0.$$

(10)

For $\xi =0$, the formula simplifies to $R_T=\mu -\sigma log\left\{-log\left(1-1/T\right)\right\}$. This formula allows EVGAM to effectively predict spatially varying return levels. In this study, extreme rainfall events were analyzed for return periods of $T=50$ years and $T=100$ years.

2.4. Model Selection

A stepwise model selection procedure based on backward elimination was applied for the optimization of the EVGAM. This process starts by setting the initial model formulas (${\mathcal{F}}_{\mathrm{init}}$) for the three extreme value parameters ($\mu$, $log\sigma$, and $\xi$) and a significance level of $\alpha =0.05$. It then iteratively removes smooth terms that exceed the significance level (i.e., non-significant terms) by checking the p-values of the smooth terms within the currently fitted model. This procedure is repeated until all remaining smooth terms are statistically significant ($p\le \alpha$).

The detailed backward elimination optimization algorithm is presented in Algorithm 1.

Algorithm 1 Stepwise Backward Elimination for EVGAM Optimization.

Require:  Extreme Value Distribution Parameters $\theta \in \{\mu ,log\sigma ,\xi \}$, Initial Model Formula ${\mathcal{F}}_{\mathrm{init}}$, Significance Level $\alpha =0.05$ Ensure:  Optimized Model Formula ${\mathcal{F}}_{\mathrm{final}}$  1: ${\mathcal{F}}_{\mathrm{current}}\leftarrow {\mathcal{F}}_{\mathrm{init}}$                                 ▹ Initialize the current model formula  2: loop  3:     $\mathrm{Fit}\mathrm{model}{M}_{\mathrm{current}}\mathrm{using}{\mathcal{F}}_{\mathrm{current}}$                       ▹ Fit the EVGAM using the current formula  4:     $\mathcal{S}\leftarrow \left\{\mathrm{Smooth}\mathrm{terms}\mathrm{in}{M}_{\mathrm{current}}\right\}$                    ▹ Set of all smooth terms in the current model  5:     if $\mathcal{S}=Ø$ then  6:         break                                   ▹ No more smooth terms to evaluate  7:     end if  8:     $\mathcal{P}\leftarrow \{p\text{-}\mathrm{value}\mathrm{of}s\mid s\in \mathcal{S}\}$                           ▹ Calculate the p-value for each smooth term  9:     $p_{\max }\leftarrow max\left(\mathcal{P}\right)$                                          ▹ Find the largest p-value 10:     if $p_{\max }\le \alpha$ then 11:         break                           ▹ All remaining smooth terms are statistically significant 12:     else 13:         $s_{\mathrm{remove}}\leftarrow \mathrm{Smooth}\mathrm{term}\mathrm{corresponding}\mathrm{to}{p}_{\max }$        ▹ Identify the most insignificant smooth term for removal 14:         ${\mathcal{F}}_{\mathrm{current}}\leftarrow {\mathcal{F}}_{\mathrm{current}}\setminus \left\{s_{\mathrm{remove}}\right\}$                      ▹ Remove the term from the current model formula 15:     end if 16: end loop 17: ${\mathcal{F}}_{\mathrm{final}}\leftarrow {\mathcal{F}}_{\mathrm{current}}$                                ▹ Set the final optimized model formula 18: return  ${\mathcal{F}}_{\mathrm{final}}$

2.5. Goodness-of-Fit Test

To evaluate how well the GEV distribution-based EVGAM model explains extreme rainfall at each observation station, a GOF test was performed. This evaluation was conducted by combining the leave-one-out cross-validation (LOOCV) procedure with the CVM test.

The LOOCV procedure is a resampling-based validation method. It involves fitting the model using data from $N-1$ stations (excluding one) and then predicting the value at the excluded station. This process is repeated for all N stations. The difference between the predicted distribution and the actual observed values obtained through this process is then used to calculate the CVM test statistic, which assesses the localized distribution fit.

The CVM statistic, proposed by [58], evaluates the overall distribution GOF by integrating the squared difference between the empirical cumulative distribution function ($F_N\left(x\right)$) of the sample and the theoretical cumulative distribution function ($F\left(x\right)$) being compared, with respect to the theoretical distribution $F\left(x\right)$. The CVM statistic $W^2$ is defined as:

$$W^2=N{\int }_{-\infty }^{\infty }{[F_N\left(x\right)-F\left(x\right)]}^{2}dF\left(x\right).$$

(11)

Compared to the traditional Kolmogorov–Smirnov test, the CVM test has the advantage of being more sensitive to the GOF across the entire distribution, rather than just at the point of maximum deviation [58]. In this study, the localized GOF of the model was determined by evaluating the p-value of the CVM test against a significance level of $\alpha =0.05$.

3. Research Data

This study utilizes long-term daily precipitation data from the Korea Meteorological Administration’s (KMA) automated synoptic observing system (ASOS) to analyze extreme rainfall events. Spanning 30 years (1995–2024), these daily precipitation data are used to construct a dataset optimized for extreme value analysis.

To thoroughly investigate the influence of typhoons on extreme rainfall characteristics, a consolidated database distinguishing typhoon events was constructed. For the identification of “typhoon-affected days,” we relied on the official historical typhoon records provided by the KMA. The KMA designates the specific temporal scope (start and end dates) for each typhoon event that directly or indirectly affected the Korean Peninsula. In this study, any daily precipitation observed during these designated periods was classified as typhoon-induced rainfall. Based on this classification, the present study performs a comparative analysis under two distinct scenarios:

• Scenario 1 (Typhoon): This scenario utilizes the complete 30-year daily precipitation time series, incorporating both non-typhoon and typhoon-induced rainfall events.
• Scenario 2 (Non-typhoon): This scenario utilizes a filtered dataset where data corresponding to the KMA-designated typhoon dates have been excluded to isolate non-typhoon meteorological characteristics.

The analysis was restricted to 63 target observation stations located in the inland region of the Korean Peninsula. This restriction was imposed to ensure homogeneity and focus on inland extreme rainfall characteristics, as island areas influenced by a maritime climate exhibit distinctly different meteorological properties from inland regions [59,60]. The spatial distribution of the 63 selected stations is presented in Figure 2.

4. Results and Discussion

To meticulously analyze the spatiotemporal characteristics of extreme rainfall events over the Korean Peninsula, precipitation data were modeled using the EVGAM. Specifically, for the comparative analysis of typhoon influence on the extreme rainfall distribution, two independent EVGAMs were fitted to two distinct datasets: the full precipitation data (typhoon-inclusive) and the data excluding typhoon-induced rainfall (non-typhoon).

The initial EVGAM model structure adhered to the GEV distribution, incorporating geographic location (latitude, longitude), elevation, and temporal trend (Year) as potential covariates for all three parameters: location ($\mu$), scale ($log\sigma$), and shape ($\xi$). Longitude (Lon) and latitude (Lat) were applied as a two-dimensional smooth function to capture spatial nonlinearity, whereas elevation (Elev) and year were set as one-dimensional smooth functions. Subsequently, a stepwise model selection algorithm based on backward elimination was employed to select the final model, retaining only the statistically significant covariates. The composition of the final selected model is detailed in

Table 1. EVGAM covariate selection results using model selection algorithm.

Case	Model	Parameter		Estimate (S.E.)/EDF	t/${\mathit{\chi }}^2$	p-Value
Typhoon (Raw Data)	Initial	Location	Intercept	110.81 (1.03)	107.29	<0.001
			Lon, Lat	18.59	131.27	<0.001
			Elev	1.02	0.01	0.938
			Year	4.51	48.58	<0.001
		Log Scale	Intercept	3.65 (0.02)	173.97	<0.001
			Lon, Lat	2.00	1.68	0.431
			Elev	1.01	5.98	0.015
			Year	1.00	0.00	0.966
		Shape	Intercept	0.12 (0.02)	5.84	<0.001
			Lon, Lat	2.01	0.02	0.988
			Elev	1.00	0.00	0.988
			Year	7.85	15.00	0.097
	Selected	Location	Intercept	110.8 (1.05)	105.61	<0.001
			Lon, Lat	14.81	126.21	<0.001
			Year	1.02	17.57	<0.001
		Log Scale	Intercept	3.67 (0.02)	178.76	<0.001
			Elev	2.01	14.03	0.001
		Shape	Intercept	0.11 (0.02)	5.65	<0.001
			Year	4.62	16.44	0.004
Non-Typhoon	Initial	Location	Intercept	99.62 (0.92)	108.31	<0.001
			Lon, Lat	14.23	141.17	<0.001
			Elev	1.01	0.09	0.768
			Year	7.78	297.57	<0.001
		Log Scale	Intercept	3.52 (0.02)	170.18	<0.001
			Lon, Lat	2.00	28.68	<0.001
			Elev	1.00	6.47	0.011
			Year	1.00	0.00	0.957
		Shape	Intercept	0.14 (0.02)	6.62	<0.001
			Lon, Lat	2.00	1.22	0.544
			Elev	1.00	0.48	0.488
			Year	2.09	3.71	0.186
	Selected	Location	Intercept	98.75 (0.96)	102.55	<0.001
			Lon, Lat	6.71	101.69	<0.001
			Year	1.15	69.14	<0.001
		Log Scale	Intercept	3.56 (0.02)	169.74	<0.001
			Lon, Lat	4.67	37.85	<0.001
		Shape	Intercept	0.11 (0.02)	5.44	<0.001
			Year	7.28	32.18	<0.001

.

The final selected models revealed distinct characteristics: for the typhoon-inclusive EVGAM, elevation was selected as a significant covariate for the scale parameter ($log\sigma$); however, under the non-typhoon condition, the spatial location (latitude and longitude) was selected for the scale parameter. In the EVGAM framework, the scale parameter ($log\sigma$) represents the variability of the extreme rainfall amount. This suggests that the variability of extreme rainfall under non-typhoon conditions is governed by the broader regional and climatic characteristics of the Korean Peninsula, which is reflected by the inclusion of the basic regional pattern (latitude and longitude) in the scale parameter. Conversely, the inclusion of typhoons indicates that the dominant factor determining the variability shifts to a topographic characteristic, namely elevation. This implies a physical mechanism where the magnitude difference of typhoon-induced extreme rainfall is drastically amplified by changes in elevation, thereby significantly influencing its variability. The characteristics of the selected covariates for each parameter were subsequently analyzed in detail.

Based on the final selected model, the temporal and spatial changes in the estimate of $\mu$, which represents the mean magnitude of extreme rainfall, were analyzed over time (per decade) and space (longitude and latitude) using the selected covariates (longitude, latitude, and year) for the location parameter ($\mu$) (Figure 3 and Figure 4).

The results from the typhoon-inclusive EVGAM (Figure 3) show clear spatial heterogeneity. Estimates of the location parameter ($\mu$) appear relatively high in the southern coastal and northern regions, and low in the inland areas. This pattern suggests that these regions, which concentrate the main typhoon paths, are exposed to the highest mean magnitude of extreme rainfall under typhoon conditions.

Comparing these results with the non-typhoon condition model (Figure 4) clearly reveals the difference in the mechanisms driving extreme rainfall. Under the non-typhoon condition, the $\mu$ value remained high in the northern region, but the estimate for the southern coastal region was significantly lower than in the typhoon-inclusive scenario. Statistically, this suggests that the magnitude of extreme rainfall in the southern coastal region is strongly dominated by the influence of typhoons rather than non-typhoon factors.

Notably, both models consistently exhibited a long-term temporal decreasing trend in the location parameter across most regions over the analysis period (1995–2024). While this finding appears to contrast with the global consensus of intensifying extremes, it is consistent with the specific multidecadal variability observed in the Korean Peninsula. The starting period of this study (mid-1990s) coincides with a documented regime shift characterized by a significant increase in summer rainfall and daily maximum precipitation [61,62,63]. Consequently, the analysis begins from a high-magnitude baseline. Furthermore, recent studies indicate a complex shift in rainfall regimes during the 2010s. While annual mean precipitation and the frequency of heavy rainfall events have generally increased, the magnitude of the annual maximum rainfall decreased or stagnated compared to the peak levels of the 2000s [64,65]. This recent decline has been observed in both regional studies, such as the decrease in sub-hourly extreme rainfall in Seoul [6], and broader national assessments [66,67]. Additionally, ref. [68] suggested that polarizing rain types and increasing early summer droughts may contribute to these variations. Thus, the observed decreasing trend in $\mu$ reflects the transition from an exceptionally wet period in the late 1990s and 2000s to a relatively moderate phase in the recent decade, rather than a contradiction to long-term climate change signals.

The analysis then shifted to the scale parameter ($log\sigma$), which quantifies the variability of extreme rainfall. As established during the model selection phase, this parameter’s governing covariate differs significantly between the two models: Elevation was selected for the typhoon-inclusive model, while spatial location (longitude and latitude) was selected for the non-typhoon model.

When examining the spatial distribution of the $log\sigma$ estimates in the typhoon-inclusive model (Figure 5a), a distinct pattern emerges: the estimates are consistently higher in coastal areas and lower in high-altitude regions. This trend suggests that the largest variability (variance) in extreme rainfall magnitude occurs near the coastline. According to [69], coastal regions serve as the primary interface for moisture influx from the ocean; the abundance of water vapor significantly enhances thermodynamic instability, thereby increasing the uncertainty and variability of precipitation.

Conversely, in high-altitude regions, the physical dynamics shift toward orographic effects. Ref. [70] notes that as air masses encounter mountainous terrain, they are forced to ascend (orographic lifting). This mechanism tends to concentrate rainfall within specific, narrower topographic zones. Because the location of this precipitation is highly constrained and governed by the fixed geography of the terrain, the resulting rainfall patterns exhibit less temporal and spatial randomness. Consequently, the variability (scale parameter $log\sigma$) is consistently lower compared to the dynamic, moisture-dominated instability observed in coastal areas.

In contrast, the scale parameter in the non-typhoon model (Figure 5b) exhibited relatively high values in the northwestern region. This spatial distribution implies that, in the absence of typhoons, the increased deviation in extreme rainfall magnitude in the northwest is primarily attributable to non-typhoon meteorological systems, such as the Stationary Front and Localized Convective Storms [71]. These systems act as the dominant non-typhoon factors contributing to the large variability in that specific geographic area.

Finally, we analyzed the shape parameter ($\xi$), for which Year was selected as the sole covariate, indicating that the extreme value index and the tail characteristics of the rainfall distribution are changing over time. As illustrated in Figure 6, the $\xi$ estimates from the typhoon-inclusive model show a marked fluctuation with an approximate 20-year period. This long-period variability exhibits a multi-decadal pattern consistent with the time scales of long-term climate oscillations, such as the Pacific Decadal Oscillation (PDO) [72]. Conversely, the $\xi$ estimates for the non-typhoon model display a variability pattern with an approximate 10-year period. This shorter cycle visually resembles the decadal variability characteristic of the El Niño-Southern Oscillation (ENSO), suggesting a potential link to the extremity of non-typhoon related extreme rainfall [73]. Therefore, while not a direct statistical confirmation of causality, this temporal analysis of $\xi$ highlights that the probability distribution of extreme rainfall exhibits non-stationary behaviors that warrant future investigation regarding their association with global climate dynamics.

To estimate the regional GEV parameters across all 63 ASOS stations using the final selected EVGAM covariate structure, we employed the LOOCV procedure. This methodology ensures objectivity and stability by training the EVGAM on data from $n-1$ stations and then estimating the GEV parameters for the left-out station.

A subsequent GOF test was conducted to verify that the estimated GEV parameters adequately describe the extreme rainfall distribution at each location. The test results revealed that the GEV distribution was deemed unsuitable for 8 stations in the typhoon-inclusive model (Geoje, Namhae, Mokpo, Sancheong, Andong, Yeongdeok, Uiseong, and Tongyeong). Conversely, the non-typhoon model showed unsuitable results for 9 stations (Geoje, Namhae, Mokpo, Busan, Andong, Yeongdeok, Uiseong, Jangheung, and Changwon) (Figure 7). This outcome suggests that while the EVGAM, with its spatiotemporal covariates, successfully models the extreme rainfall distribution across most of the stations, the specific localized characteristics or outlier behavior of extreme rainfall at these particular coastal and inland stations may lead to a deviation from the GEV distribution’s assumptions or fall outside the EVGAM’s predictive capability.

For the stations identified as having an unsuitable GOF for the EVGAM model, a Standalone GEV Fitting was performed using only the local extreme rainfall data. The resulting parameters are presented separately in

Table 2. Parameter estimation results from standalone GEV fitting for stations inadequate in the GOF test.

	Station	Location	Scale	Shape	${\mathit{w}}^2$	p-Value
Typhoon (Raw Data)	Andong	88.821	26.068	−0.040	0.064	0.793
	Geoje	154.881	37.585	0.377	0.043	0.922
	Mokpo	94.778	28.190	−0.015	0.036	0.956
	⋮	⋮	⋮	⋮	⋮	⋮
	Tongyeong	125.861	30.184	0.119	0.025	0.991
	Uiseong	80.269	29.681	−0.051	0.120	0.496
	Yeongdeok	86.937	27.884	0.461	0.027	0.987
Non-Typhoon	Andong	77.456	24.601	0.031	0.043	0.922
	Busan	114.783	37.953	0.285	0.042	0.925
	Changwon	117.503	43.987	0.178	0.037	0.950
	⋮	⋮	⋮	⋮	⋮	⋮
	Uiseong	73.775	27.960	−0.150	0.064	0.796
	Yeongdeok	74.020	18.286	0.313	0.023	0.994
	Jangheung	121.329	46.368	−0.213	0.055	0.849

.

We then analyzed the Model Bias by assessing the difference between the newly estimated Standalone GEV parameters and the EVGAM-based parameters ($\mathrm{Difference}=\mathrm{EVGAM}\mathrm{parameter}-\mathrm{GEV}\mathrm{parameter}$).

In the typhoon-inclusive model, the location parameter ($\mu$) showed a negative bias (${\mu }_{\mathrm{EVGAM}}<{\mu }_{\mathrm{GEV}}$) at Geoje, Namhae, and Sancheong, indicating that the EVGAM underestimated the mean magnitude of extreme rainfall at these sites. Conversely, a positive bias (${\mu }_{\mathrm{EVGAM}}>{\mu }_{\mathrm{GEV}}$) was observed for Mokpo, Andong, Yeongdeok, Uiseong, and Tongyeong, suggesting an overestimation. The bias directionality for the scale parameter ($log\sigma$) consistently matched that of the location parameter, except at the Geoje station.

For the non-typhoon model, the location parameter exhibited a negative bias at Geoje, Namhae, Busan, Jangheung, and Changwon, and a positive bias at Mokpo, Andong, Yeongdeok, and Uiseong. Notably, the scale parameter bias directionality aligned with the location parameter bias at all non-conforming stations.

Analyzing the shape parameter bias ($\xi$) in the typhoon-inclusive model revealed a negative difference (${\xi }_{\mathrm{EVGAM}}<{\xi }_{\mathrm{GEV}}$) at Geoje, Yeongdeok, and Tongyeong, which suggests the model underestimated the extreme risk (tail heaviness) at these locations. A positive difference was observed at the remaining stations. Similarly, in the non-typhoon model, a negative bias was found at Geoje, Namhae, Busan, Yeongdeok, and Changwon, with a positive bias at the rest.

This systematic analysis of parameter bias strongly suggests that the spatiotemporal smoothing inherent in the EVGAM is not adequately capturing the localized extreme rainfall characteristics of these non-conforming stations. This outcome implies that the extreme rainfall behavior at these locations is significantly influenced by local factors (e.g., micro-topographic effects, localized convective systems) that are not accounted for as covariates within the current model structure.

Using the final fitted EVGAM parameter estimates, 50-year and 100-year return levels were calculated to generate extreme precipitation risk maps for the Korean Peninsula. These estimates were applied to a 1km grid across the entire peninsula to capture high-resolution spatial variability.

Figure 8 and Figure 9 illustrate the resulting spatial distributions, distinguished by the inclusion of typhoon events. Figure 8 presents the return levels calculated including typhoon events. The high degree of spatial detail and elevated intensities observed in Figure 8, particularly for the 100-year return levels (Figure 8b), reflect the significant contribution of typhoons to extreme precipitation variability. In contrast, Figure 9 illustrates the return levels excluding typhoon events. This exclusion results in a smoother spatial distribution, highlighting broad-scale climatological trends driven by non-typhoon systems (e.g., Changma fronts). Comparing Figure 8 with Figure 9 clearly demonstrates that the inclusion of typhoons leads to higher risk estimates and more complex local variations, distinct from the smoother background climatology seen in the non-typhoon scenario.

For observational stations where the EVGAM parameter estimates were deemed unsuitable, a different approach was employed. In these cases, parameters were estimated using a standalone GEV model to ensure local accuracy. Based on these independent parameter estimates, the 50-year and 100-year return levels were calculated for each respective station.

To visualize the spatial risk, the return levels calculated at each ASOS station were spatially interpolated to the 1 km grid using the inverse distance weighting (IDW) method. Figure 10 displays the spatial risk including typhoon events. The characteristic circular patterns and localized maxima, especially in the southeastern inland regions, effectively pinpoint hotspots driven by extreme typhoon rainfall recorded at specific stations. Conversely, Figure 11 depicts the return levels excluding typhoon events. While it still captures elevated potential along the eastern coast and southern regions, the distinct high-intensity hotspots seen in Figure 10 are less pronounced or absent. This comparison indicates that the most severe local risks identified in Figure 10 are largely driven by typhoon events.

Notably, regardless of the inclusion of typhoons, the Andong area (Gyeongsangbuk-do region) consistently maintained low return levels in both Figure 10 and Figure 11. This aligns with the region’s physical characteristics as a basin surrounded by mountain ranges. The result is a reduced risk due to the Orographic Shielding Effect, where incoming rain clouds or rainfall systems are blocked or significantly weakened by the surrounding topography.

The comparison between the two sets of maps reveals distinct characteristics in both modeling approach and data composition. The EVGAM-based maps (Figure 8 and Figure 9) provide a spatially continuous and texture-rich assessment, leveraging covariates to capture fine-scale topographic influences. In contrast, the IDW-interpolated maps (Figure 10 and Figure 11) offer a representation strongly anchored to specific observations, exhibiting “bullseye” patterns that preserve the exact extreme values at station locations.

Examining the spatial patterns in detail reveals that coastal areas exhibit uniformly higher return levels than inland regions, with the southern coast showing the maximum risk. This high vulnerability is attributed to the southern coast serving as a major entry path for typhoons, facilitating the most active and continuous supply of oceanic moisture. Notably, the eastern coastal region demonstrates high return levels in the typhoon-inclusive models (Figure 8 and Figure 10), but these estimates are significantly reduced in the non-typhoon models (Figure 9 and Figure 11). This striking difference suggests that the extreme rainfall risk on the east coast is heavily dependent on large-scale rainfall events caused by typhoons, rather than localized non-typhoon factors.

Given the complementary strengths of these approaches—the covariate-driven spatial detail of EVGAM and the observation-faithful locality of IDW—and the confirmed dominant role of typhoons in defining regional risks, the development of an ensemble model is suggested as a key direction for future research. This comprehensive risk map is essential for identifying regional heterogeneity in extreme rainfall vulnerability driven by climate change and provides a critical basis for formulating effective disaster prevention and adaptation policies.

5. Conclusions

This study successfully applied the EVGAM to comprehensively analyze the spatiotemporal heterogeneity of extreme rainfall events across the Korean Peninsula, particularly those amplified by climate change. By comparing scenarios with and without typhoon-induced rainfall, we quantitatively demonstrated the differential influence of large-scale meteorological phenomena (typhoons) versus non-typhoon mechanisms on the extreme rainfall distribution. The EVGAM effectively overcame the limitations of conventional static GEV models by integrating spatiotemporal covariates (latitude, longitude, elevation) and a temporal covariate (year) into the three GEV parameters ($\mu$, $log\sigma$, and $\xi$). The primary contributions and findings of this study are summarized as follows.

First, the model selection process provided critical meteorological insights into the variability of extreme rainfall. A key finding is the identification of distinct covariates for the scale parameter ($log\sigma$). Under non-typhoon conditions, variability was governed by spatial location (latitude and longitude), reflecting broad synoptic patterns. In contrast, for the typhoon-inclusive model, elevation was selected as the significant covariate. This statistically demonstrates that topographic characteristics significantly modulate the variability of extreme rainfall. Specifically, the results reflect the physical mechanism where variability is relatively lower in high-altitude regions due to the orographic locking of rainfall systems, whereas coastal areas exhibit higher variability driven by moisture instability.

Second, the physical interpretation of the EVGAM parameters revealed the non-stationary nature of rainfall extremes linked to climate oscillations.

• Location Parameter ($\mu$): Spatially, the typhoon-inclusive scenario showed the highest $\mu$ values along the southern coast and northern regions, aligning with primary typhoon tracks. The significantly lower $\mu$ values in the southern coast under the non-typhoon scenario statistically confirm that typhoon influence dominates the extreme rainfall magnitude in this area.
• Shape Parameter ($\xi$): Temporal analysis revealed distinct cycles associated with climate indices. The typhoon-inclusive model exhibited an approximate 20-year cycle linked to the PDO, while the non-typhoon model showed a shorter 10-year cycle suggesting an association with the ENSO.

Third, this study implemented a dual fitting strategy to minimize estimation uncertainty and enhance model robustness. While EVGAM effectively captures broad spatiotemporal trends, it may show limitations in representing localized anomalies at specific stations. By systematically identifying these stations via Goodness-of-Fit tests and applying a standalone GEV fitting, we complemented the global smoothing of EVGAM with site-specific optimization. This approach effectively bridged the gap between spatial generalization and local specificity, ensuring reliable parameter estimation across all analyzed stations.

Finally, the return level maps generated through this comprehensive framework elucidated the spatial risk distribution. The analysis confirmed that the most severe risks, particularly in the southern coastal region, are predominantly driven by typhoon events. Conversely, inland basins like the Andong area consistently exhibited reduced risk due to the Orographic Shielding Effect. These findings underscore the necessity of incorporating both spatiotemporal non-stationarity and the dual fitting approach into future hydraulic design and disaster management policies to address the evolving climate risks effectively.