Temporal change of extreme precipitation intensity–duration–frequency relationships in Thailand

Due to climate change, many research studies have derived the updated extreme precipitation intensity–duration–frequency relationship (IDF curve) from forecasted sub-hourly rainfall intensity time series, which is one of the most important tools for the planning and designing of hydraulic infrastructures. In this study, the IDF curves (1990–2016) of the six regions and procedures are used in accordance with those of the Royal Irrigation Department (RID)’s study (1950–1988). Each set of IDF relationships consists of 81 intensity values which are the combination of nine durations and nine return periods. The intensity ratios of this study and RID are compared. A greater-than-1 ratio indicates extreme intensity increment from the past to the present. Considering 81 ratios for each region, the number of greater-than-1 ratios for the North, Northeast, Central, East, West, and South regions are 8, 2, 31, 34, 6, and 7, respectively. These ratio numbers are far below 81 which means that the majority of extreme rainfall intensities do not increase from the past to the present. The study found that using accurate historical sub-hourly rainfall time series to create a set of IDF curves would be more reliable than using forecasted rainfall modeling.


INTRODUCTION
Expected rainfall intensity is required and used in the planning and design of engineering and environmental infrastructures in that it is termed the design storm (Balbastre-Soldevila et al. 2019;Cook et al. 2020). The appropriate design storm must be neither too large nor too small. When too large, the concerned infrastructure will be unnecessarily overdesigned and expensive, while when too small it will risk the damage caused by flood or heavy rain. A suitable design storm can be estimated from the relationship of extreme rainfall intensity, its duration, and frequency of occurrence. Generally, the shorter duration of the storm, the heavier the rainfall. Also, the heavier the storm, the less frequently it occurs. The imperative tool for planners and engineers to choose the appropriate design storm is, therefore, an accurate maximum rainfall intensity-duration-frequency (IDF) relationship (Mirhosseini et al. 2012;Sun et al. 2019). It is actually the relationship of the maximum rainfall intensity (or depth) at a specific duration and a specific return period. It can be in the form of the table of maximum intensity values at several durations and return periods or a set of curves of maximum intensity as a function of duration at several return periods, a so-called IDF curve. A return period is an average length of time that a specified, or higher, rainfall intensity occurs at a particular place with a specified duration. researchers recently have tried to use the reliable past data to predict future extreme events (Shepherd et al. 2018;Woo & Johnson 2018;Sillmann et al. 2021; and references therein). However, they are still not accurate and precise enough. This study attempts to derive new sets of IDF curves for all regions of Thailand (data periods: 1990-2016) and compares them to those of the original Royal Irrigation Department  using exactly the same methodology. The number of stations and their record lengths may not be the same for each pair of corresponding regions but average values will be used for comparison.
The aim of the study is, therefore, to compare the IDF relationships of the current study to those of the national standard in Bumpenkit (1999) to quantify the change of extreme rainfall intensities of the two periods to determine the acceptability of the official IDF curves.

STUDY AREA
Thailand is a part of mainland Southeast Asia situated between 97. 1-106.0 E and 5.4-20.6 N and surrounded by Myanmar, Laos, Cambodia, and Malaysia. It is divided into six regions, namely Northern, Northeastern, Central, Western, Eastern, and Southern (Figure 1(a)). A series of mountain ranges run in the north-south direction extending from the Northern region passing the Western to the Southern one, these mountain ranges are on the west and border Thailand with Myanmar ( Figure 1(b)). The trans-boundary Mekong River that runs along the eastern boundary divides Thailand from Lao and Cambodia. The Northeast region is a plateau with the Mekong on to the east. The Central region is a lowland receiving flood flow from the North and draining to the Gulf of Thailand. The Central normally includes the western and eastern regions; however, since their precipitation characteristics are different, we separate them for the purposes of this study. The Southern region of Thailand is a peninsula extending southward from the Central region to Malaysia with the Gulf of Thailand (of Pacific Ocean) on the east and Andaman Sea (of Indian Ocean) on the west. (Figure 1(b)).
The climate characteristics of Thailand are governed by the dynamics of the Intertropical Convergence Zone (ITCZ), a low atmospheric pressure band occurring from the combination of the solar radiation intensity and the inclination of the earth axis. During a few months at the beginning of the year, the ITCZ is located far below Malaysia; therefore, Thailand is without rainfall. The ITCZ moves rapidly northward to the western, central, and eastern parts in May and slowly moving to the north passing the Central, Northeastern, and Northern departing the northern boundary in mid-July. During the period of the ITCZ passing, it induces humidity from the Indian Ocean and the Gulf of Thailand, as southwest monsoon, to the upper part of the country. After a few weeks, the ITCZ comes back from China to the northern part of Thailand again, leaving the country's upper part to the south in mid-October. From July to October, the humidity from the southwest monsoon from the Indian Ocean plus the tropical cyclone from the South China Sea and the Pacific Ocean moves to Thailand's upper part creating heavy rainfall. After departing the upper part, the ITCZ moves across the peninsula from October to the New Year causing heavy rain in the Southern region. Accordingly, precipitation patterns of Thailand can be separated into two main regions: the upper and lower parts. The upper includes the Northern, Western, Northeastern, Central, and Eastern regions, whereas the lower is the Southern region. The lower part consists of two seasons, that is, the dry season from January to April and the rainy season from May to December. The upper part has three seasons: summer from February to April, rainy season from May to October, and cool season from November to January. The rainy season can also be separated into two periods by a drought spell: the former rainy season from May to July and the latter rainy season with a higher peak from August to October.

METHODS
The maximum rainfall IDF relationship (IDF curve) of a homogeneous region is always presented as a set of curves of maximum average intensity as a function of duration in that each curve has a fixed return period. To create the relationship, the data of annual maximum rainfall intensities at several corresponding durations of rain from several automatic rain gauges are required. For example, for 20 years of data from a rainfall station, there are 20 maximum intensity values for each of a number of durations, i.e., 15, 30, 45 min, 1 h, 2, 3, 6, 12, and 24 h in this study. An automatic rain gauge usually gives a time series of rainfall depths of a given temporal resolution, e.g. 15 min, which is common in Thailand, for each year. These rainfall depth time series are divided by the time resolution to obtain the time series of average rainfall intensities. The maximum average intensity of each year for each of the nine durations has to be evaluated. Let ξ 15 (t) be a time series of average rainfall intensities for the 15-min resolution from the beginning to the end of a year; therefore, the maximum average intensity, i(15), of the year is as follows: where t is the resolution time step. The time series of average rainfall intensities for the durations, d, other than 15 min, which are integer multiples, N, of the resolution, can be calculated from the following equation (Koutsoyiannis et al. 1998): where δ is the resolution duration which is 15 min in this study, the summation is from i ¼ 0 to N À 1, and N is an integer multiple of the resolution. Then the maximum intensity for durations other than 15 min can be evaluated from the time series ξ d (t) of a year as: The procedures described in Equations (1)-(3) are applied to the time series of average rainfall intensities of 15 min resolutions for all annual data sets. Then for each of the rainfall stations, there are nine sets of annual maximum rainfall intensity series, denoted by i 15 , i 30 , i 45 , …, i 24 for the durations of 15, 30, 45 min, …., 24 h, respectively.
Each set of annual maximum rainfall intensities was assumed to follow the distribution of the extreme value type I (EV I) or Gumbel distribution which is the popular one for extrapolating to higher return levels (Koutsoyiannis et al. 1998;da Silva et al. 2019). To model the EV I distribution, we need two parameters, namely location parameter, u, and scale parameter, β, which can be evaluated using the method of moment as follows (Chow et al. 1988): where μ and σ are the mean and standard deviations of the annual maximum intensity series. From the cumulative distribution function of the EV I model, for each fixed rain duration, the return level or corresponding intensity, i, can be evaluated from the following equation (Chow et al. 1988), where T is the return period. Equation (6) shows that only intensity and return period are the random variables excluding the duration. The first step in evaluating maximum intensity i(d,T ) involved collecting annual intensity maxima at nine rain durations of 0.25, 0.5, 0.75, 1, 2, 3, 6, 12, and 24 h from each of automatic rain gauge stations. There are several automatic stations scattered all over Thailand and we separated them into six geoclimatic regions, namely the North (N), Northeast (Ne), Central (C), West (W), East (E), and South (S). Each region has a number of maximum intensity data of varied length as shown in Table 1 which shows that the basic data of the two studies (RID and this study) were not identical. The average and standard deviation of each data set were calculated, and then they were spatially averaged for each region (see also Figure 2).
The average values of the mean and standard deviation of each region were used to estimate the spatially average location and scale parameters from Equations (4) and (5), respectively. At each of nine rain durations, we used Equation (6) to estimate the corresponding maximum intensities of the specified return periods of 2, 5, 10, 25, 50, 100, 200, 500, and 1,000 years for each region.

RESULTS AND DISCUSSION
The derivation results of IDF relationships of this study are presented and then they were shown against the study of RID. Lastly, the ratios of the corresponding maximum intensities of this study to those of the RID were presented and discussed.

Gumbel distribution parameters
Two parameters of Gumbel distribution, namely location parameter, u, and scale parameter, β, were evaluated from the means and the standard deviations of the annual maximum intensity series of each of the durations and regions. The mean values of the maximum rainfall intensity for each of the regions and each of durations are illustrated in Table 2 in    (Table 3). Since the β parameters vary directly with the standard deviation, its minima are the same as the minimum spreading values of σ (Tables 3 and 4). The maximum values of u parameter follow the same pattern as those of the mean values (Tables 2 and 5).

IDF relationship comparison
In this subsection, we present IDF relationships from our study for all regions in Table 6 for the benefit of those who would like to use them for determining rough design storms or further research. We also add a set of IDF relationships from the RID study (Bumpenkit 1999) for the Central region only in Table 7. The reason for presenting only a single set of IDF relationships of RID is because one can determine the rest from the ratios in the next subsection. For a brief overview, the study presents only a single set of IDF curves of our study for the Central region in Figure 3. However, Figures 4-6 compare the Central region curves of this study to those of RID's study for the return periods of 2, 5, 10, 25, 50, 100, 200, 500 and 1,000 years.   They describe that the maximum intensity values from our study are all lower than those from RID for a 2-year return period; nonetheless, only a few for a 100-year return period at a higher duration are as shown in Figure 7.

Intensity ratios between this study and RID's values
It is always presumed that, due to climate change, the maximum rainfall intensity at a specific duration and the return period should progressively increase in accordance with time. Here we compare the rainfall intensities from two data sets: the older one from RID (1950RID ( -1998 to the more recent one in this study   (Table 1). These two data sets, even with some overlap, exhibit a range of time difference about 15-25 years. Therefore, the rainfall intensity values from this study should likely be higher than those from the RID study due to climate change. The rainfall intensity ratios of this study compared to the RID study are used to determine their change. If the ratio is higher than 1, it means the intensity is increasing as expected and vice versa. The intensity ratios of the North, Northeast, Central, East, West, and South are illustrated in Table 8, and the statistical summary of the intensity ratio is shown in Table 9. Each region comprises 81 ratios, as the combination of nine durations and nine return periods is taken into account. The ratios that are higher than 1.0 show the increase in rainfall intensity from the past to the present. The statistical summary in Table 9 shows that the highest number of the higher-than-1 ratio is in the East region for 34 ratios and the lowest in the  Northeast at 2 ratios. Considering the mean values of ratio and numbers of higher-than-1 ratio (Table 9), we can classify all regions into three groups, (1) Northeast, (Ne), (2) North, West, and South (NWS), and (3) Central and East (CE). The Northeast group (Ne) consists of a single region called the Khorat plateau. Its landscape is undulating terrain with a range of Phu Phan dividing the region into two basins, i.e., the Sakon Nakhon Basin in the North and the Khorat Basin in the South. A majority of the region drains its into the Mekong River. The second group consisting of the NWS is mountainous with mountain ranges lying along the north-south direction extending from southernmost to northernmost. The rainfall of the area derives mainly from the Southwest monsoon and it always causes flash floods and landslides. The last group, CE, is the combination of the Central lowland and the low hilly eastern part. Most of the drainage from this region goes to the Gulf of Thailand. The plateau, the Northeast group, has two greater-than-1 ratios at 0.25 h duration for 500-and 1,000-year return periods with the mean intensity value of 0.81 (Tables 8 and 9). The mountainous regions, the NWS, have the greater-than-1 ratios of 8, 6, and 7, with the mean intensity values of 0.89, 0.90, and 0.90 for the North, the West, and the South, respectively. The ratios for the  North and the South are only from the smallest duration, 0.25 h. The North has eight ratios at 5-, 10-, 25-, 50-, 100-, 500-, and 1,000-year return periods, while the South has seven ratios from 10-to 1,000-year return periods. The West region, which is located between the North and the South, has six ratios with five from the smallest duration of 0.25 h and the return periods between 50 and 1,000 years as well as one ratio from the next smallest duration of 0.5 h with return periods of 1,000 years.
The last groups, which are the Central and the East, have 31 and 34 ratios, respectively (Tables 8 and 9). For the Central region, the number of greater-than-1 ratios is four each from the 25-and 50-year return periods with the durations of 0.25, 0.5, 0.75, and 1 h; five ratios from the 100-year return period with the durations of 0.25-2 h; and six ratios each for the return periods of 200, 500, and 1,000 years with the durations of 0.25-3 h ( Table 8).
The East region has the largest number of 34 ratios with irregular distribution. There are nine ratios each of 0.25 and 0.5 h durations for all return periods, that is, one ratio of 2-year return period for 0.75 durations, 4 each of 3 and 12 h durations for 100-to 1,000-year return periods, and seven ratios of 6 h duration for 10-to 1,000-year return periods (Table 8). The analysis of the Eastern region in this study, however, was the least reliable because only three data sets were used.   For the practical planning and design of hydraulic infrastructures, we have to choose appropriate rainfall intensity from IDF curves by first considering rainfall duration and then return period. Rainfall duration is chosen from the size and shape of the watershed or from its time of concentration, while a small watershed normally gives a shorter duration (Chow et al. 1988). The choice of return period depends on the size of watershed and the risk of failure (Chow et al. 1988).
Extreme outflow discharge from a small watershed does not always cause serious damage compared to that from a large watershed. Table 8 shows that the greater-than-1 ratios mostly exist at short durations especially at higher return periods. At return periods of 500 and 1,000 years, the greater-than-1 ratios exist at 15 min for all groups. For lower return periods at 50, 100, and 200 years, the ratios exist at 15 min for all except group 1 (Ne). The planning and design of hydraulic structures of larger watersheds with longer rainfall durations and involving higher risk require longer return periods. Therefore, the findings presented in Table 8 imply the acceptability of the national standard IDF curves from RID for all of Thailand. However, for the last group, namely the East and the Central regions, at the return periods from 50 years onward, the planning and design of hydraulic structures should be conducted with care. Table 9 summarizes the number of greater-than-1 ratios for all regions which are classified into three groups, i.e., Ne, NWS, and CE. The first group, Ne, comprises only two greater-than-1 ratios from 81 ratios. The NWS group shows average greaterthan-1 ratios of 7.3. Regarding the CE group, its average number of greater-than-1 ratios is 34.5 from 81 ratios. These results suggest that Thailand's IDF curves that were derived from the accurate historical rainfall data can render reliable design storms. To confirm this finding, two independent studies of IDF curves of the same rainfall station in Bangkok, Thailand, were investigated. Weesakul et al. (2017) and Shrestha et al. (2017) studied future IDF curves from the same data set but with different methodology. The former assumed the annual maximum intensity series following Gumbel (EV 1) distribution, while the latter assumed the general extreme value (EV3) distribution. The former acquired the future precipitation time series during 2015-2039 from a global climate model using the GEM 2-ES model with the greenhouse gas scenario of RCP4.5, whereas  the latter derived the future ones during 2011-2030 from eight models with the scenario of SRA1B. The two scenarios are similar in the greenhouse gas of low to medium concentration. For bias correction, the former used the current data sets of 1990-2014, while the latter used those of 1981-2010. The values of extreme rainfall intensities in Table 10 were digitized from Weesakul et al. (2017) and Shrestha et al. (2017). The two studies used the same rainfall data set from the Sukhumvit area in Bangkok. The base periods (BP) and the forecast periods (FP) of the two studies are somewhat similar (Table 10). The significant difference between both studies is that the latter used eight global climatic models, while the former used only one to generate the future daily rainfall data sets. The results of the latter, therefore, should be more reliable. When considering the ratios of FP intensities to BP intensities, the former values are between 1.3 and 1.8 with the mean of 1.47 and the latter values are in the range of 1.0-1.3 averaging at 1.12. This implies that the more reliable method renders the closer of the future values to the base values, even though larger-than-1 ratios present in all of the results. All climatic models assume an increase in greenhouse gas which may trigger higher rainfall intensity in the future. We cannot predict the long-term rate of the greenhouse gas emission. The COVID-19 pandemic is one recent example that can temporarily reduce the emission rate. Some studies and attempts have been implemented to reduce and stabilize the emission rate such as the green new deal energy plan and the like ( Jacobson et al. 2019;Nielsen et al. 2020). This study, therefore, suggests that using an accurate historical data set could be favorable to that using lengthy synthesized future data set for generating the IDF relationships.

CONCLUSIONS
An accurate IDF curve is crucial for hydraulic infrastructure design. The accuracy of an IDF curve is not known beforehand because the historical set of precipitation data were used to predict the future rainfall information. Due to climate change, new IDF curves are expected to change as a result of increasing rainfall intensities. We have compared a set of past IDF curves (RID's study) with that of the recent ones (this study) and found that the majority of them did not increase as expected. Another shortcoming of this finding is the relatively small time-lapse of about 15-20 years between the two data sets from the RID study and this study.