Understanding extreme precipitation scaling with temperature: insights from multi-spatiotemporal analysis in South Korea

With global warming, the intensification of extreme precipitation events is anticipated to follow an exponential growth pattern aligned with the Clausius–Clapeyron (CC) scaling rate (approximately 7% per degree Celsius). However, the regional-scale response of extreme precipitation shows significant variability, deviating from the expected CC rate. This deviation is likely caused by diverse weather patterns and local fluctuations in thermodynamic influences, resulting in differences across seasons and within the region of interest. In this study, we examine the spatial distribution of scaling relationships between extreme precipitation and temperature in South Korea, considering daily and sub-daily scales, both annually and seasonally. For a thorough analysis, we utilize multiple precipitation accumulation periods, temperatures, and different conditional quantiles. Our results reveal that, at the annual scale, most scaling patterns exhibit a peak-like structure, with significant variations in breakpoints observed across temperature variables and regions. However, the southern area presents a notable exception with a positive scaling pattern, particularly with the dew point temperature. At the seasonal scale, we observe more variability, with notable shifts occurring during the wet season across different temperatures and regions. Lastly, we explore the long-term historical changes in the peak value in extreme precipitation and find significant increases at high quantiles in the southern area of South Korea. It informs that the observed peak like pattern does not impose a potential upper limit for extreme precipitation. Overall, our findings emphasize the need for cautious interpretation of precipitation scaling within specific spatiotemporal contexts, which could provide a solid basis for better understanding future extreme precipitation events in a changing climate.


Introduction
Extreme precipitation presents a significant risk to our society as it is closely linked to various natural hazards such as floods, landslides, and mudslides, all of which pose substantial risks to human society (Luna et al 2011, Kirschbaum et al 2012, Ivancic and Shaw 2015, Garg and Mishra 2019).Additionally, extreme precipitation can result in reservoir and levee failures, leading to catastrophic damage downstream (Jasim et al 2017, Vicente-Serrano et al 2017).
Therefore, enhancing our understanding of changes in extreme precipitation is vital for bolstering the resilience of human society.To facilitate adaptation efforts, it is crucial to grasp the degree to which precipitation events are anticipated to intensify across various geographical and temporal scales (Schröer and Kirchengast 2018, Wang et al 2018, Wasko et al 2018, Pumo et al 2019, Gao et al 2020).
The intensity of extreme precipitation can be affected by changes in atmospheric temperatures.Warmer air has a higher capacity to hold water vapor compared to colder air, which leads to increased water availability during precipitation events.Consequently, higher temperatures contribute to the heightened potential for extreme precipitation (Westra et al 2014).This is further substantiated by the theoretical Clausius-Clapeyron (CC) scaling rate, which suggests that a 1 • C increase in temperature corresponds to an approximate 7% increase in the moisture-holding capacity of the atmosphere, assuming certain conditions (e.g.unchanged relative humidity in atmospheric circulation; Pall et al (2007), Allan and Soden (2008).The scaling rate, serving as a fundamental physical basis for comprehending the response of extreme precipitation in a warming climate, has been utilized as a benchmark to interpret changes in precipitation (O'Gorman 2015, Fischer andKnutti 2016).Furthermore, global circulation models and coupled oceanatmospheric models employ the scaling relation to simulate extreme precipitation (Kharin et al 2013, Allan et al 2020).
While some studies have highlighted the robustness of the scaling rate, particularly on a global scale (Westra et al 2014, Fischer andKnutti 2016), others have indicated that the relationship between extreme precipitation and temperature does not consistently conform to the CC scaling rate.This inconsistency is observed at regional scale, where deviations such as a super-CC scaling rate (defined as scaling rate above the CC scaling) (Lenderink et al 2017, Schröer and Kirchengast 2018), a sub-CC scaling rate (defined as scaling rate below the CC scaling) (Drobinski et al 2016, Wang et al 2018), and even a negative scaling rate (implying a decrease in extreme rainfall intensity with rising temperature) (Panthou et al 2014, Bui et al 2019).These various deviations in the CC scaling rate are attributed to various factors, including the choice of temperature variable (Panthou et al 2014, Bui et al 2019), variations in hydroclimatic regimes (Lenderink and Fowler 2017), storm types (Molnar et al 2015), and the influence of seasonality (Tabari 2021).Therefore, the regional level plays a crucial role in shaping the overall behavior of this interaction, as the spatial and temporal variability of contributions influences the diverse patterns and outcomes observed in the relationship between atmospheric temperature and extreme precipitation.
South Korea, with its geographical location and prevailing climatological system, is highly susceptible to climate extremes (Park et al 2011, Lah et al 2015, Ahn and Nayak 2022).Consequently, previous research has primarily focused on examining the shifts in extreme precipitation, investigating their interaction with large-scale circulations, and projecting the intensity of future extreme precipitation (Eum and Cannon 2017, Park and Min 2017, Kim et al 2018, 2023, Noh and Ahn 2021).Furthermore, a significant warming trend in South Korea has been observed since 2010 (Ahn 2022).Research conducted by Choi et al (2018) reveals that a majority of the monitored stations have witnessed temperature increases of approximately 0.48 • C-1.8 • C per decade over the past 50 years, surpassing the global trends observed across all land areas (0.28 • C per decade; Bardin et al 2020).The provided information underscores the importance of urgently addressing the understanding of extreme precipitation in relation to the warming climate in South Korea.Accordingly, some studies have examined the relationship between extreme precipitation and temperature (Park and Min 2017, Sim et al 2019, Qiu and Im 2021).
When analyzing the scaling rate of precipitation, it is crucial to account for the variability of weather patterns that affect precipitation intensity throughout the annual cycle, coinciding with the seasonal fluctuations in temperature.However, despite its importance, there has been limited attention given to exploring seasonal variations in scaling rates using spatially continuous datasets (Sengupta et al 2023B).In particular, the existing literature on South Korea's scaling relation is primarily focused on data from the warm season, as seen in Park and Min (2017) and Sim et al (2019).A recent study by Qiu and Im (2021) examined the dependence of precipitation scaling on temperature across the entire calendar year using high-resolution data.Nevertheless, this study did not extensively explore the spatiotemporal relationship between extreme precipitation and temperatures within different seasons or various precipitation accumulation periods.
Moreover, the prevailing approach in the previous studies is to estimate the scaling rate either for individual stations or grids (Sim et al 2019, Qiu andIm 2021).However, when considering detailed settings such as a narrow width of bins, relying solely on individual station data with a small sample size can introduce significant uncertainty (Li et al 2023).Another approach is to aggregate all the data into a single dataset, representing the entirety of South Korea, and then calculate the scaling rate (Park and Min 2017).While promising in addressing the issue posed by a small sample size, the approach may fail to consider the possible presence of varied precipitation scaling patterns within the regional area.Therefore, it is necessary to determine appropriate climatological regions and aggregate data within the defined region in order to increase the sample size and effectively address the aforementioned limitations.
In response to the above research needs, this study attempts to expand our comprehensive understanding of precipitation scaling in South Korea.This objective is accomplished through a comprehensive spatiotemporal analysis, investigating the historical temporal changes in extreme precipitation in relation to temperature variations across the country.To be specific, this study addresses the following research questions: (1) do we identify diverse patterns of precipitation scaling based on the defined climatological regions?(2) Does the precipitation scaling rate vary across different regions when taking seasonality into account?(3) Are there any temporal trends in the relationship between extreme precipitation and temperature when considering long-term historical data?

Study area and dataset
Situated in the southern part of the Korean Peninsula, South Korea experiences a variety of atmospheric systems.In winter, the region is influenced by the influx of cold air masses from expanding Siberian high-pressure zones, while during summer, warm air masses from the North Pacific high-pressure system prevail, leading to contrasting weather patterns (Kim and Jain 2011, Noh and Ahn 2021).These diverse atmospheric contributions result in hot and humid summers and cold and dry winters in the country.Specifically, the Changma season, which lasts for approximately 1 month in summer, brings about over half of the annual precipitation (approximately 1110 mm) due to a lingering stationary front across the Korean Peninsula.In contrast, winter precipitation accounts for less than 10% of the total annual precipitation (Lee and Ahn 2021).Moreover, the country's significant variations in elevation have notable effects on the intensity and distribution of precipitation (Houze Jr 2012).For example, the eastern and northern mountainous regions, including the Taebaek Mountain range, contribute to reduced precipitation along the northeastern coast (Kim and Lee 2006).Taken together, the substantial spatiotemporal climatological variability in South Korea, especially in terms of extreme precipitation intensity, serves as the motivation for this study, which aims to investigate the scaling rate of precipitation at the seasonal scale.
We use temperature, precipitation, and relative humidity obtained from 88 stations within the Automated Synoptic Observing System (ASOS) database, which is provided by the Korean Meteorological Administration (KMA; see figure 1).Of the 103 available stations, 15 were removed since their record had less than 10 years of continuous sub-daily data spanning a period of 23 years .It is important to note that the ASOS database offers sub-daily data from the year 2000 onwards.Furthermore, to examine long-term temporal changes in the relationship between extreme precipitation and temperature, this study obtains daily (i.e.1440 min) data from the same stations, covering a span of 63 years .The quality of the selected stations was assessed using both basic and extended checks in accordance with the guidelines outlined by the World Meteorological Organization (WMO) guide (WMO 2010), and implemented by the (KMA 2016).The acquired dataset also possesses a high temporal resolution, enabling us to obtain minute-level records for precipitation.Subsequently, the estimation of dew point temperature is carried out for each station utilizing the widely recognized Magnus formula (Buck 1981).

Methods
This study analyzes the precipitation scaling with respect to three temperature variables (T j ): maximum temperature (T max ), minimum temperature (T min ), and dew point temperature (T dew ).The scaling focuses on the maximum precipitation (P i ) over the four following accumulation periods, i = 10, 60, 180, and 1440 min.The cumulative precipitations are calculated by aggregating data within mobile windows ranging from 10 to 1440 min, starting from 00:00 and ending at 23:59.As an example, we can have 8 values obtained by aggregating data over 180 min (equivalent to 3 h) within specific time intervals, including periods such as 00:00-02:59, 03:00-05:59, and so forth, up to 21:00-23:59.Additionally, we have 24 values obtained by aggregating data over 60 min (equivalent to 1 h) within time intervals like 00:00-00:59, 01:00-01:59, and 23:00-23:59.The cumulative precipitations over the four accumulation periods are analyzed based on the annual and seasonal samples.For the seasonal analysis, the wet season is defined as the period from June to September, during which precipitation is concentrated across the country.In contrast, the other months are considered as dry seasons.To minimize internal variability caused by temperature diurnal fluctuations, even during precipitation events daily mean values are employed for the three temperature variables (Westra et al 2013).

Determining of sub-regions
This study performs a regional-based scaling analysis by using spatially pooled data.In order to achieve this, we classify stations with comparable precipitation characteristics into the same region.Given the distinct annual cycle of precipitation over the study area, the gamma distribution is adopted to characterize the variability of precipitation for each month across stations.The methodology employed in the Standardized Precipitation Index (Edwards 1997) serves as the basis in this process.To be specific, two maximum precipitations from two different accumulation periods (i.e. 60 and 1440 min) are fitted to a gamma distribution.This process yields two parameters, namely shape and scale, for each month and accumulation period.Consequently, this study obtain a total of 48 (= 2 × 2 × 12) parameters for each station.
Next, the obtained parameters are employed as inputs to the principal component analysis (PCA), which is utilized to reduce dimensionality.PCA is beneficial in situations where the dimensionality of the data is excessively high to impede direct distance calculations (Jolliffe and Cadima 2016).The principal components (PCs), which represent the new variables obtained through PCA (see figure S1), are utilized for further analysis.Additionally, the normalized latitude and longitude of each station, obtained by subtracting the means and dividing by the standard deviations, are also included.The normalization process is employed to ensure that all input equally contributes to the subsequent procedure.
Finally, this study utilizes the K-mean clustering algorithm (MacQueen et al 1967) which is a divisive unsupervised learning algorithm designed to aggregate data over similar stations.While employing the Bayesian information criterion (BIC) as a criterion for determining the number of sub-regions (S) and aiming to select the most parsimonious model, we perform the K-mean algorithm by minimizing the following objective function: where ∥Y η − C υ 2 ∥ is squared Euclidean distance between the ηth station and υth regional center in multidimensional space of data attributes.M is the total number of stations and V is the number of subregions.

Precipitation scaling rate
In the existing literature, various methods have been proposed for analyzing precipitation scaling.These methods include the binning method (Herath et al 2018, Ali et al 2021), quantile regression (Wasko and Sharma 2014, Ghausi and Ghosh 2020), and fitting a generalized extreme value distribution to normalized extreme precipitation (Zhang et al 2017).In this study, the binning method is adopted, which has demonstrated robust results in previous research (Blenkinsop et al 2015, Ali and Mishra 2017, Wasko et al 2018, Hosseini-Moghari et al 2022).
Rain days are first defined as those with precipitation intensity exceeding 0.1 mm d −1 at a specific station.Also, this study excludes snow type of precipitation events based on the information provided by KMA due to its potential to cause significant deviations in precipitation scaling (Chen et al 2022).Based on the two criteria above, the annual or seasonal data for the rain days are identified.From this dataset, the corresponding daily temperature values are extracted to initiate the binning method.Following the studies of Herath et al (2018) and Sengupta et al (2023A), the precipitation data is partitioned and distributed across 30 equal-frequency temperature bins that correspond to the specific station.The motivation for employing equal frequency binning is to ensure that all bins contain an equal number of data values.This approach prevents potential imbalances in the highest and lowest temperature bins, considering the general normal distribution of temperature.By using equal frequency binning, the dataset is evenly distributed across the temperature range, allowing for a more representative analysis.Additionally, the use of equal-width bins may result in the disregarding of empty bins, which can introduce a distortion in the relationship between precipitation and temperature.In particular, we use the method of 3-bin moving window averaging to smooth the results similar to the approach described by Wang et al (2017).We consider the median temperature as the representative temperature for each bin, and subsequently estimate the three specific quantiles (i.e. the 90th, 95th, and 99th quantiles) for precipitation intensity through the binning process.

Features of peak structure in sub-regions
In this study, our primary focus is on the scaling rate, the peak value of extreme precipitation (P pk i ) and the temperature breakpoint (T bk j ) as the unique features of the extreme precipitation scaling.In certain regions, the scaling rate can exhibit deviations, either increasing to a super-CC scaling rate or decreasing to a sub-CC scaling rate.To investigate these deviations, we develop the following linear segmented model: where, ψ bk j represents the multiple temperature breakpoints and I (•) is the indicator function equal to one if the condition is true.
To develop the linear segmented model, we conduct tests with zero and one breakpoint.Similar to the clustering analysis, we use the BIC as a criterion to determine the model formulation.The modeling is implemented by using the segmented package in the R programming language (Muggeo et al 2008).For readers who are interested, a more comprehensive explanation of the theoretical background can be found in Muggeo et al (2014).
Afterwards, the lower slope (β 1 ) and its p-value are then employed to determine the scaling rates and significance of the fit.This is because the slope dominates the primary segment of the precipitationtemperature pairs.The scaling rate (α) is calculated using the following relation (Ali et al 2018, Sengupta et al 2023A): Based on the estimated α, this study classifies scaling rates into four following variants: the CClike scaling (5% • C −1 %-9% • C −1 ), the super-CC scaling (greater than 9% • C −1 ), the sub-CC scaling (0% • C −1 -5% • C −1 ), and the negative-CC scaling (less than 0% • C −1 ) (Chen et al 2022).
Finally, this study investigates the temporal change of P pk 1440 during the period of 63 years (1960-2022) using the method of temporal moving window.The window width is set at 3 years, with a step size of 3 years.To be specific, we obtain 21 values of time series by manipulating daily data across consecutive periods such as 1960-1962, 1963-1965, 1966-1968, and so on, up until 2020-2022.The time series are employed to assess the significance of monotonic trends by the nonparametric Mann-Kendall trend analysis (Mann 1945, Kendall 1955).In this study, a significance level of 0.05 is specifically adopted.

Evaluating scaling relationship in sub-regions
Figure 2 presents the Bayesian Information Criterion (BIC) for the k-means clustering fit with S = 2, …, 16 regions, aiming to explore the appropriate number of sub-regions.Similar results are observed when using the Akaike Information Criterion (AIC) (see figure S2 in the supporting information).As the number of regions increases, the penalized likelihood metrics consistently decrease until reaching approximately 8 sub-regions.This indicates that a large number of sub-regions may be necessary to effectively explain the characteristics in maximum precipitation, which is likely due to the heterogeneity in the study area.However, this study choose five sub-regions as a manageable number for diagnostic analysis (see figure 1), as it captures most of the improvements in terms of the BIC and AIC metrics.
Figure 3 presents the scaling relationship between the four maximum precipitations (P i ) and three temperatures (T min , T max , and T dew ) at the annual scale based on the defined sub-regions.In this analysis, we focus on the 99th quantiles, which represent the widely used measure for this type of application.Several insights emerge from this figure.First, the scaling rate generally intensifies with a rise in low temperatures and exhibits a moderate decrease at high temperatures.To be specific, the Northwestern (NW) and eastern-coastal (EC) regions experience a peak like pattern across all temperatures, which is a characteristic pattern of the scaling rate over the entire South Korea, as addressed in Park and Min (2017).However, in the Southern (SO) and southern-coastal (SC) regions, a positive pattern is observed particularly with T dew , where precipitation increases with an increase in temperature.Next, in many cases, the scaling relationship follows a CC-like scaling behavior before the T bk j .However, super-CC scaling can often be observed at relatively high temperatures (e.g.18 • C < T j < T bk j ).The super-CC scaling is especially observed for sub-daily precipitation in the NW and EC regions, irrespective of the temperature variables.Lastly, the breakpoints across temperatures substantially vary over the defined sub-regions.For example, while both the NW and EC show a peak like pattern for T dew , their respective breakpoints occur at approximately 21.0 • C and 17.8 • C. In particular, the breakpoints in the EC region are significantly lower (18.3 • C and 21.5 • C for T min and T max ) compared to those observed in the other regions.Overall, while a similar scaling pattern is observed for the four accumulation precipitations at each temperature, diverse patterns of precipitation scaling are identified at sub-regional scales.These findings provide further support for the necessity of investigating scaling patterns in sub-regional areas across the study area.

Exploring season-wise variations in the scaling pattern
We then examine the relationship between extreme precipitation and temperature at the seasonal scales.Again, we use five sub-regions to explore the scaling relationship.Figure 4 shows the scaling relationship between the four maximum precipitations P i and T max while figures S3 and S4 represent the scaling relationship with T min and T dew , respectively.During the dry season, a positive relationship is generally observed across all three temperature variables, subregions, and quantiles.However, there is a notable shift in the wet season, wherein the relationship varies according to the temperature variables, accumulation periods and sub-regions.To be specific, a significant negative relationship is observed for T max , such as a monotonic decrease observed for P 1440 in the NW, EC, and SC regions.On the other hand, a positive relationship is observed for T dew , particularly with a short-duration precipitation such as P 10 and P 60 in many sub-regions.Furthermore, in the CE and SO regions, there is an evident peak structure observed for the relationship between P 1440 and T min .
Based on the findings presented above, this study classifies the regional characteristics of the scaling rates by considering different seasons and temperatures (see figure 5).In this analysis, we place our main emphasis on the 99th quantiles of P 1440 , which, once again, serve as the widely accepted measure for this specific application.In the dry season, the scaling rates of T min and T dew generally show a CClike scaling over the country, aligning well with the theoretical CC scaling rate.On the other hand, the scaling rate of T max exhibits a decreasing trend in space from south to north while it shows a super-CC scaling in the SC region.In the wet season, the scaling rates for temperature exhibit more diversity.For example, the scaling rate of T dew shows a CC-like scaling in the western area (e.g.NW region) whereas a more intensive rate is observed in the eastern area (e.g.EC and CE regions).Also, extreme precipitation on T max demonstrates negative scaling in the NW, EC, and CE regions, whereas a super-CC scaling is observed in the southern area (i.e.SO and SC regions).
The scaling relationship may be influenced by multiple attribution factors.First, as addressed in Ji and Ahn (2023), South Korea experiences a prevalence of storm events originating from the south.This southward orientation results in a substantial influx of moisture from the southern sea.Consequently, the SC region often demonstrates a super-CC scaling in many cases.Furthermore, during the wet season, the EC region may experience insufficient moisture supply due to orographic effects.It may result in a negative-CC scaling trend.Lastly, the decrease of extreme precipitation with high maximum temperature approximately greater than 25 • C, in many subregions during the wet season is affected by changes in relative humidity.Figure 6 represents the dependence of relative humidity on T min and T max for the events of extreme precipitation in the dry and wet seasons.In the dry season, the relative humidity during precipitation events monotonically increases with increasing temperature.To be specific, extreme precipitation falls in extremely saturated conditions (e.g. more than 96%) when T min and T max are greater than 10 • C and 15 • C, respectively.However, the pattern is different during the wet season.While relative humidity remains high when T min reaches significantly high values, it starts to decrease once T max exceeds approximately 25 • C. The observed decreases in relative humidity with increasing maximum temperature may elucidate the presence of the peak structures (see figure 3) and the decrease of extreme precipitation during high temperature conditions.

Investigating temporal changes in the peak value of extreme precipitation
Lastly, we investigate the long-term temporal changes in the relationship between extreme precipitation and temperature over 5 sub-regions in South Korea to support the claim that extreme precipitation intensifies in response to increasing temperatures.
To accomplish this, we analyze the temporal change of P pk 1440 over the 63 year historical period, focusing on the 90th, 95th and 99th quantiles of precipitation (see figure 7).In this analysis, T max is employed to identify the peak since a peak like structure is exhibited for P 1440 over all sub-regions (see figure 3).
Results indicate that the temporal change of P pk 1440 varies based on the interest quantiles and sub-regions.Higher quantiles have generally experienced a significant increase over the 63 year historical period.Specifically, the 95th quantile of extreme precipitation exhibits a significant upward trend in the SC region, while the 99th quantiles of P pk 1440 have significantly increased in the NW, SO, and SC regions.It is worth mentioning that our analysis, as depicted in figure 3, prominently reveals a peak-like structure in these areas.These results imply that the peak like pattern does not impose a potential upper limit for extreme precipitation.Furthermore, in the other regions (i.e.EC and CE regions), no significant temporal trends are observed in P pk 1440 .This information informs that the historical trends exhibit some degree of spatial heterogeneity.For comparison purposes, we additionally aggregate all the data into a single dataset and then examine the temporal change of P pk 1440 focusing on the entirety of South Korea (see figure S5 in the supplement).The analysis shows a noteworthy upward trend in all considered quantiles of P pk 1440 , underscoring the potential for misleading outcomes if sub-regions are not considered in assessing temporal shifts in extreme precipitation.This informs the necessity of our investigation, which takes into account diverse precipitation scaling patterns within multi-spatiotemporal frames.

Conclusions
Over the past few years, South Korea has faced numerous extreme precipitation events, resulting in significant economic and social consequences (Ahn andNayak 2022, Kim et al 2023).Consequently, understanding the processes in determining extreme precipitation is crucial for enhanced weather forecasts and climate projections.This study explores the thermodynamic relationship between extreme daily, hourly, and sub-hourly precipitation and variations in three temperature variables: maximum temperature, minimum temperature, and dew point temperature.The investigation is conducted across an extensive network of 88 meteorological stations in South Korea.To be specific, our analysis focuses on understanding the regional scaling pattern, with a particular emphasis on the sub-daily relationship.This involves dividing the study area into five subregions using clustering analysis to better comprehend the spatial variations.Furthermore, we investigate the historical changes in the regional characteristics of daily precipitation scaling over a 63 year period .With a focus on our specific objectives, this study reveals the following distinct aspects of the scaling pattern over South Korea.
(1) We observe diverse statistics of the precipitation scaling patterns across the defined climatological regions.The Northwestern and Easterncoastal regions experience a peak like pattern across all temperatures, whereas a positive pattern is observed particularly with dew point temperature in southern area.Furthermore, we address the substantial variation in breakpoints across temperature variables and sub-regions.These findings emphasize the potential misunderstanding that may arise from aggregating data from different sub-regions, highlighting the need to consider specific regional characteristics.
(2) The consideration of seasonality reveals variations in the precipitation scaling rate.During the wet season, a notable shift is observed in which the relationship between precipitation and temperature variables varies across different sub-regions.For example, extreme precipitation demonstrates a negative scaling in the upper regions (e.g.NW region) when analyzed with respect to maximum temperature, while a super-CC scaling is observed in the southern area.On the other hand, during the dry season, a positive relationship is generally observed across all temperature variables and sub-regions.
(3) The historical changes in the peak precipitation also exhibit variability within the defined climatological regions.Notably, the 99th quantiles of the peak precipitation have shown significant increases in the NW, SO, and SC regions, whereas insignificant temporal trends are observed for all quantiles in EC and CE regions.This information may offer a historical basis to better understand and anticipate future extreme precipitation events.
Overall, our results demonstrate a unique relationship between extreme precipitation and temperature in South Korea.However, it is imperative to interpret these conclusions with careful consideration of the inherent limitations in this study.First, the meteorological stations are limited in their record length particularly for the sub-daily data.Although we increase the sample size by adopting the process in sub-regions, the limited record contribute to increase the uncertainty in the results of the binning method and linear segmented model.Next, extreme precipitation can be influenced by a variety of storm types, even within the same season (Schröer and Kirchengast 2018).However, this analysis is not considered in this work.Future research of this nature is crucial to determine the extent to which sub-regional scaling rates vary based on the prevailing precipitation-induced mechanisms, as seen in the study conducted by Magan et al (2020) and Park and Min (2017).Lastly, we investigate the influence of relative humidity on peak structure.However, it is important to note that dynamic factors, such as the increase in convective rain, the cooling effect of precipitation, and the reduction in the duration of wet events at high temperatures, also have an impact on the formation of peak structures.These dynamic factors require further exploration in future work.

Figure 1 .
Figure 1.Geographical distribution of the 88 meteorological stations used in this study.The colors assigned to the stations represent their corresponding sub-regions, namely Northwestern (NW), Eastern-coastal (EC), Central (CE), Southern (SO) and Southern-coastal (SC) regions.

Figure 2 .
Figure 2. The BIC for 2-16 sub-regions in the k-means clustering analysis.The BIC at five sub-regions is highlighted.

Figure 3 .
Figure 3.The relationship between extreme precipitation over four different accumulation periods (10, 60, 180, and 1440 min) and daily mean temperature variable, such as (left) minimum temperature, (middle) maximum temperature, and (right) dew point temperature in the 5 sub-regions including (a) Northwestern, (b) Eastern-coastal, (c) Central, (d) Southern, and (e) Southern-coastal regions.If a breakpoint for P1440 occurs during the development of the linear segmented model, the average estimated temperature breakpoint is presented along with its corresponding 95% credible interval.

Figure 5 .
Figure 5.The spatial distribution of the precipitation scaling with daily temperature variables, such as (left) minimum temperature, (middle) maximum temperature, and (right) dew point temperature over the dry and wet seasons.Each color represents a different scaling rate variant.

Figure 6 .
Figure 6.The relationship between daily relative humidity and (upper) daily minimum temperature and (lower) daily maximum temperature for the events of extreme precipitation.Solid (dotted) line represents the wet (dry) season.

Figure 7 .
Figure 7.The historical change of the peak value of extreme precipitation using the temporal moving window method for the period of 63 years (1960-2022) for the (a) Northwestern, (b) Eastern-coastal, (c) Central, (d) Southern, and (e) Southern-coastal regions.In each timeseries, the trend line is presented if the Mann-Kendall trend analysis yields a p-value < 0.05.