Estimation of regional intensity–duration–frequency relationships of extreme rainfall by simple scaling in Thailand

As a tropical and monsoonal climate country, Thailand is subjected to flooding every year of various degrees and locations. The rainy season spans 6 months from May to October, with the first half dominated by convective rain and the second by tropical cyclones. The rainfall characteristics of the first half are therefore heavy but short-lived, while those of the second are milder but for longer periods. Both flash floods and river floods can occur in Thailand. For example, in 2011, the country's flood claimed 681 lives and caused USD 46.5 billion in damage (Poaponskorn & Meethom 2013). Recently, in 2022, both flash and river floods had cumulative humanitarian impacts on the Thai people. Much of the flooding was exacerbated by major dams being pushed to their capacities, which resulted in raised river levels downstream through the urgent release of water (IFRC 2023). Flood preventions all over the country therefore urgently need to be revised and improved with updated information.

The intensity–duration–frequency (IDF) relationship is a basic tool for flood prevention and other water resource management tasks. It is used to calculate maximum rainfall intensity at a specified rainfall duration and return period. The IDF relationship is normally presented in a graphical form, called an IDF curve, with rainfall intensity on the X-axis and duration on the Y-axis, with a series of return periods. An IDF curve is created from an automatic rainfall record spanning at least 30 years. The maximum annual series of rainfall intensities, extracted from the records for each duration, are related to return periods using probability theory such as Extreme Value Type 1 (EV1). The number of automatic recorders in the whole country is not as large as that of daily recorders, therefore by using the scaling property, we can convert daily IDF relationships to sub-daily ones.

The IDF curves were long studied and established in Thailand, but they were only applied to a small portion of the nation. As a result, Mustonen (1969) first suggested 14 curves: 5 for the Northeast; 2 for the Northern, Central, Eastern, and Southern regions; including 1 for the Western region. The Royal Irrigation Department (RID), Thailand's primary institution in charge of irrigation and drainage, released a complete analysis of IDF curves for all 59 curves, with 20 curves for the North, 10 for the Northeast, 5, 8, 4, and 12 curves, respectively, for the Central, East, West, and South (Bumpenkit 1999). In addition to the developed equations for rainfall intensity, Rittima et al. (2013) updated the IDF curve for rainfall durations of 0.25, 0.50, 0.75, 1, 2, 3, 6, and 12 h, covering 19 provinces and 11 catchment areas. The IDF curves under climate change uncertainty for the Bangkok area were created by Shrestha et al. (2017). Utilizing the Long Ashton Research Station Weather Generator (LARS-WG), a stochastic weather generator, and the rainfall disaggregation tool Hyetos, they investigated a methodology based on the spatial downscaling-temporal disaggregation method (DDM) to develop future IDFs. Additionally, Yamoat et al. (2022) developed IDF curves for six regions of Thailand, i.e., the Northern, Northeastern, Central, Western, Eastern, and Southern regions. They 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. However, these IDF curves can be used in a regionally averaged way. If we could find the specific IDF curve for ungauged sites, that would be excellent.

The ability of these techniques to estimate the IDF characteristics for ungauged sites is constrained. They could not transfer the IDF features from gauged sites to other sites. This is due to the fact that at sites where rainfall records are not available or the data sample is small, the ‘Simple Scaling’ method should be used. Here are some examples. Nhat et al. (2008) developed the regional IDF curves based on scaling properties for the Yado River catchment in Japan. Bara et al. (2009) approximated the IDF curves of extreme rainfall by using simple scaling in Slovakia. Chang & Hiong (2013) estimated the sub-daily IDF curves in Singapore using simple scaling. Galiatsatou & Iliadis (2022) studied the IDF curves at ungauged sites in a changing climate for sustainable stormwater networks in the village of Fourni, which is in the northeastern part of the island of Crete in Greece. Casas-Castillo et al. (2022) presented a simple scaling analysis of rainfall in Andalusia (Spain) under different precipitation regimes. Yuksek et al. (2022) created the regional IDF curves with the emphasis of Eastern Black Sea basin in Turkey. In summary, the results of these studies showed the good performance of the regional IDF curves.

The purpose of the study is to investigate the scale variance (or scaling properties) of rainfall for the derivation of IDF relationships at ungauged sites. To determine the scaling behavior of statistical moments over various durations, the scaling properties of intense rainfall are explored in this study, along with the updating of IDF curves across the entire country of Thailand. Firstly, using the annual maximum rainfall intensity (AMRI) records for varying durations and return periods at the 37 selected stations spread all over Thailand, the scaling exponent for each gauge site and the space variation of the scale exponents were explored. The scale exponent and two statistical parameters of 24-h rainfall data can be used to construct the IDF relationships. Secondly, the IDF relationships at any location are constructed by interpolating these parameters from their contour maps. Finally, the regional scaling model's IDF relationships at the ungauged locations are investigated.

The aim of the study was to ascertain whether simple scaling could be used to represent regional IDF relationships for ungauged locations. According to the behavior of scaling relationships in statistical moments over various durations, the scaling properties of extreme rainfall were explored.

Similar scaling relationships were apparent in the data from the other gauges. This suggests that simple scaling may be appropriate in Thailand for the considered durations. Table 2 displays the findings of the scaling exponent factor H for the 37 stations in Thailand, with high coefficients of determination (R²) ranging from 0.97 to 1.0 for each station. The results indicate a strong validity of the simple scaling property of the extreme rainfall in time series.

As a result of the hilly terrain in the north and east of Thailand, and there are not many observatories there, it is better to have information on the surrounding areas from neighboring countries that the IDW method will be more accurate to generate IDF curves at these locations. However, the IDW method outperforms multi-quadric interpolation and traditional kriging (Ware 2005).

The regional scaling model can be applied at any site in the study region for storm duration d equal to 0.25, 0.5, 0.75, 1, 2, 3, 6, 12, and 24 h. For each storm duration d and return period T, the design storm I(d,T) can be evaluated as follows:

• (1)

  Estimate the local scale exponent (H) value for the site of interest by interpolating from the map in Figure 4.

• (2)

  Estimate the location and scale parameters (μ₂₄ and σ₂₄) of 24-h duration from Figures 5 and 6, respectively.

• (3)

  Calculate μ_d and σ_d of a specified duration, d, from Equations (8) and (9), respectively.

• (4)

  Calculate the extreme rainfall intensity of specified duration and return period from Equation (7).

Tables 3 and 4 show the RMSE and MRPE values that were obtained for nine return periods (2, 5, 10, 25, 50, 100, 200, 500, and 1,000 years) and nine durations (0.25, 0.5, 0.75, 1, 2, 3, 6, 12, and 24 h) for three stations. According to the validation results for all three stations, the regional scaling model performed well for Thailand, with a mean relative percentage error that was less than 20%. They performed just as well as the studies in Singapore (Chang & Hiong 2013), Japan (Nhat et al. 2008), Greece (Galiatsatou & Iliadis 2022), Spain (Casas-Castillo et al. 2022), and Turkey (Yuksek et al. 2022).

Chon Buri station is in the east, and Kamphaeng Phet station is in the north; both have hilly terrain and are poorly gauged (see Figure 1). The study of Erazo (2020), on rainfall intensity interpolations in poorly gauged and mountainous areas of Ecuador, shows that the IDW method is the most efficient way to represent both the spatial pattern of precipitation throughout Ecuador and the daily volumes of areal precipitation at the catchment scale (Erazo 2020). Since Thailand is also a tropical country with some hilly areas like Ecuador, we conclude that the three simple scale parameters of the interpolation for Thailand could be evaluated by the IDW interpolation technique.

Flooding is always a big problem in Thailand as a result of insufficient drainage systems for both urban and rural areas. To mitigate this problem, an accurate IDF relationship for the site must be used for hydraulic infrastructure design. Because continuous rain records in the country are significantly fewer in number than daily records, we used simple scale theory to calculate a scale exponent from each of the 37 AMS across the country. Regarding the 30-year records of daily rainfall, AMS of extreme daily rainfall intensity were extracted and used to obtain location and scale parameters. The interpolation values of the scale exponent and the parameters of location and scale were mapped and ready to be used. The IDF curves from three at-site records were used for validating the result. This showed that, by and large, the errors were less than 15%. The proposed maps can help generate an accurate IDF curve at any site in Thailand.

This research was funded by the College of Industrial Technology, King Mongkut's University of Technology North Bangkok (Grant No. Res-CIT0299/2022).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.