Development of intensity–duration–frequency relationships in Khon Kaen City, Thailand under changing climate using GCMs and a simple scaling method

Hydrological characteristics of urban areas have dramatically changed because of rapid urbanization and climate change increasing the risk of urban flooding. Designing stormwater infrastructure for metropolitan areas and comprehending rainfall patterns need the use of intensity–duration–frequency (IDF) curves (Martel et al. 2021). However, conventional IDF curves may no longer be accurate due to changing climatic conditions and the complexities of urban development. To overcome this difficulty, it is necessary to incorporate cutting-edge climate projections into the creation of IDF curves. Future climate conditions are forecasted using the most recent generation of climate models as represented by the Coupled Model Intercomparison Project Phase 6 (CMIP6). Therefore, updating IDF curves to reflect the changing rainfall characteristics is predominant to effective urban flood management and resilient urban infrastructure (Kourtis et al. 2023).

CMIP6 models from the sixth report of the Intergovernmental Panel on Climate Change (IPCC) combine representative concentration pathways (RCPs) with shared socioeconomic pathways (SSPs) to create more reasonable future scenarios (Crévolin et al. 2023). Additionally, CMIP6 endeavours to tackle the concerns identified by CMIP5 such as improving the representation of changes in land use, improving the estimation of radiative and aerosol forcings, as well as reducing systematic errors in process simulations (Eyring et al. 2016). Over Southeast Asia, CMIP6 models have been found to replicate precipitation more accurately than their previous versions (Khadka et al. 2022). Similar to this, Nooni et al. (2023) reported that the majority of CMIP6 global climate models (GCMs) precisely reproduced the spatial variation of precipitation over Africa and the Arabian Peninsula. Additionally, Crévolin et al. (2023) found that simulations of CMIP6 in extreme precipitation are closer to the observed datasets than CMIP5 for almost all 30 Canadian cities. To enhance the accuracy of GCM rainfall prediction at regional and local scales, several downscaling tools are available such as Long Ashton Research Station Weather Generator (Semenov & Brooks 1999), hybrid Regional Climate Model–Statistical Downscaling Model scaling (Wilby et al. 2023) and stacking ensemble machine learning (Anaraki et al. 2023) and scaled distribution mapping (Switanek et al. 2017).

In engineering applications, the necessity arises for the use of sub-daily rainfall data to generate IDF curves. Nevertheless, the data typically available from measurement stations and future climate models are mainly detailed on a daily temporal scale. This poses a challenge for the formation of IDF curves, which are essential for designing hydraulic structures and improving flood management for maximum efficiency (Kourtis et al. 2023). Sophisticated statistical and hydrological approaches become more important for updating IDF curves. These approaches effectively bridge the gap between the available daily data and the need for shorter-duration data. In a study conducted by Alzahrani et al. (2023), various temporal disaggregation methods were compared. These methods consisted of the multiplicative random cascade model, the Hurst–Kolmogorov process, the K-nearest techniques and the Fahad–Ousmane method. The analysis was based on sub-daily simulations using observed daily rainfall data obtained from the South Nation watershed in Canada. The findings of their study suggested that the Fahad–Ousmane method characterised by its simplicity and the steady-state stochastic disaggregation model can yield superior results when compared to more complex alternatives. Adib & Rad (2019) applied a radial base function–artificial neural network to extract climate data using the HadCM3 model. This was done to prepare rainfall data for a 30-year period (2021–2050) based on A1B, B1 and A2 scenarios. Subsequently, the selected network was used to generate IDF curves for the Baghmalek watershed in southwestern Iran. Crévolin et al. (2023) applied the quantile–quantile downscaling approach to estimate extreme rainfall values at fine spatiotemporal scales in Canadian cities. Additionally, an alternative simple temporal disaggregation approach introduced by Gupta & Waymire (1990) and widely adopted internationally is known as the simple scaling method. For instance, Maity & Maity (2022) formulated a new set of IDF curves incorporating the influence of climate change impacts across India. This was achieved by integrating the simple scaling method with the generalised extreme value distribution. Similar to this, examples of the use of the simple scaling method for temporal disaggregation can be found in diverse geographical contexts such as Slovakia (Bara et al. 2010), Japan (Nhat et al. 2008), Iran (Soltani et al. 2017) and Thailand (Yamoat et al. 2023).

The primary aim of this study is to investigate the scaling property of observed annual maximum (AM) rainfall series across durations ranging from 3 to 24 h at 3-h intervals, and to develop present and future IDF curves. The development of future IDF curves is dependent on the extraction of scaling properties from historically observed rainfall data and the climate projections provided by the CMIP6 models. This constitutes a novel contribution of this study. By incorporating the most recent climate model outputs into the IDF curve generation process, this study seeks to develop a more reliable and adaptable tool for urban planners and engineers. The intention is to ensure that the changing precipitation patterns brought through climate change are appropriately taken into consideration during the design and evaluation of stormwater infrastructure. Ultimately, this study aims to provide a comprehensive and up-to-date framework for integrating urban flood management techniques with the changing climatic conditions, thereby enhancing the sustainability and resilience of urban regions.

The ground-based rainfall observation is located at the Khon Kaen meteorological station in Khon Kaen City, Thailand. The station is 187 m above mean sea level and is situated at latitude 16°27′40″ north and longitude 102°47′23″ east. The observed 3-hourly and daily rainfall datasets available cover the period from 1991 to 2022. They were collected from the Thai Meteorological Department. To construct IDF curves, AM rainfall series for various durations are required. Therefore, AM rainfall series over moving windows of 3-, 6-, 9-, 12-, 15-, 18-, 21- and 24-h durations were derived from the observed datasets.

GCM outputs of CMIP6 are crucial tools for deriving future climate data. Due to their coarse spatial resolutions, GCM outputs often require a downscaling process to make them applicable to the regional and basin scales. Along with the coarse resolution, systematic errors because of various factors such as incomplete representation of physical processes and the inherent limitations of the models must be reduced through bias-correction techniques (Fang et al. 2015). Therefore, in this study, the downscaled and bias-corrected outputs of 15 CMIP6 GCMs collected from the Hydro-Informatics Institute (HII) in Thailand were employed. Statistics regarding the annual rainfall data of these 15 CMIP6 GCMs from 1991 to 2014 are presented in Table 1. These downscaled and bias-corrected outputs of the 15 CMIP6 GCMs were derived using observed rainfall data from 1,150 ground-based stations across Thailand and the scaled distribution mapping method (Switanek et al. 2017). Simulated rainfall outputs were accessible on a daily basis and at a resolution of 5 km. For this investigation, future simulated rainfall data spanning from 2023 and 2050 under four climate change scenarios, namely SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5, were considered for the analysis of future IDF curves.

SSP1-2.6, which is SSP1 + RCP2.6, represents an optimistic path towards sustainability and climate action with a low level of greenhouse gas emission. SSP2-4.5, which is SSP2 + RCP4.5, represents a future characterised by moderate population growth, intermediate levels of economic development and efforts to mitigate climate change. SSP3-7.0, which is SSP3 + RCP7.0, is considered a realistic worst-case scenario characterised by regional rivalry and limited global cooperation. SSP5-8.5, which is SSP5 + RCP8.5, represents a future with high population growth, high energy demand and limited climate change mitigation efforts (IPCC 2023). In this study, these scenarios were chosen because they capture a range of future climate conditions enabling a more comprehensive assessment of potential changes in design storm frequencies under diverse climate scenarios.

In addition, the evaluation of the bias-corrected CMIP6 GCM rainfall data was executed by appraising a specific statistical index, the correlation coefficient (r). This coefficient was computed from the comparison between the monthly mean rainfall series observed and those that had undergone correction. Afterwards, the bias-corrected CMIP6 GCM rainfall data that exhibited the higher r value were identified as the most suitable CMIP6 GCM and were consequently chosen for subsequent analyses.

Frequency analysis of rainfall is important for understanding the variability of rainfall. In this study, the AM rainfall series for 3-, 6-, 9-, 12-, 15-, 18-, 21- and 24-h durations were fitted to four probability distributions, namely, Gumbel or Extreme Value Type-I (EV1), Log-Pearson Type-III (LP3), Pearson Type-III (P3) and Generalised Pareto (GP). The distribution fitting was performed by using the Bulleting 17B method implemented in the Hydrologic Engineering Center's Statistical Software Package.

After the computation of KS and Chi-squared statistics, they were compared with the critical values at the significant level of 0.05 as per the KS and Chi-squared statistical tables. If the KS and Chi-squared statistics were less than or equal to the critical values, the distribution is considered appropriate for frequency analysis. Subsequently, the four probability distributions were ranked according to the KS and Chi-squared statistics. The lower these statistics, the more suitable the probability distribution is considered for the AM rainfall series. Finally, the best-fit distribution was chosen based on this ranking and was then used for the scaling analysis and IDF generation.

In the practice of the simple scaling method, the EV1 distribution is typically applied (Bara et al. 2010; Yamoat et al. 2023); however, in this study, the simple scaling method was used with the distribution that was determined to be most suitable during the evaluation based on the KS and Chi-squared tests. Consequently, the AM rainfall intensity series spanning various durations (3, 6, 9, 12, 15, 18, 21 and 24 h) were fitted with the selected distribution. The corresponding distribution parameters were determined by using the method of moments. IDF curves were constructed through this conventional frequency analysis procedure using the selected distribution. Simultaneously, additional IDF curves were derived by means of the simple scaling of the 24-h AM rainfall intensity series. To assess the effectiveness and suitability of the simple scaling method, an observation of the scaling behaviour was conducted, and a comparative analysis among these IDF curves was carried out.

In the previous section, current IDF curves were produced using the simple scaling method. For the formulation of IDF curves under the projected scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5), the 24-h AM rainfall series from 2023 to 2050 were extracted from the bias-corrected rainfall data of CMIP6 GCM, which was determined to be most suitable based on the observed rainfall data. These 24-h AM rainfall series were fitted to the selected distribution. Following this, the 24-h AM rainfall series of various return periods (2, 5, 10, 25, 50 and 100 years) were disaggregated into durations of 3, 6, 9, 12, 15, 18, 21 and 24 h using the simple scaling method. As a result, future IDF curves for the four projected scenarios were generated.

The AM rainfall series for 3-, 6-, 9-, 12-, 15-, 18-, 21- and 24-h durations extracted from the Khon Kaen meteorological station were subjected to testing with four probability distributions. These probability distributions were evaluated based on the KS and Chi-squared tests for goodness of fit. A summary of the ranking of the probability distributions, according to the goodness-of-fit tests, is presented in Table 2. As observed, LP3 was identified as the best fit for the AM rainfall series across nearly all rainfall durations. Consequently, the LP3 distribution was selected for further investigation.

The findings of this study may be somewhat limited by the simulated rainfall of GCMs as the selection of GCMs was grounded on the monthly analysis between the observed rainfall data and the bias-corrected rainfall data of the GCMs. Despite the GCM being deemed suitable for simulating monthly rainfall, it may fall short in accurately representing extreme daily rainfall events. These findings underscore the importance of considering the uncertainties of GCMs in predicting daily rainfall. Therefore, it is recommended to consider multiple GCMs to establish the upper and lower boundaries of the results. Moreover, future research could investigate downscaling and bias-correction methods for modelling and predicting extreme rainfall events under climate change conditions.

In the pursuit of developing comprehension of rainfall characteristics within the context of climate change, this study has adopted a comprehensive approach consisting of data analysis, statistical methodologies and climate modelling. The investigation mainly focused on the analysis of AM rainfall series with a particular emphasis on disaggregating 24-h AM rainfall data recorded at the Khon Kaen meteorological station spanning from 1991 to 2022. The application of the simple scaling method yielded valuable insights into the temporal distribution of rainfall intensities. An inherent advantage of this method lies in its capability to estimate design values of rainfall intensities across various durations using the often readily available daily rainfall data. However, this study is limited by the unavailability of highly detailed temporal rainfall series (i.e., 0.25, 0.50, 0.75, 1 and 2 h). As a result, the developed IDF curves are applicable for durations ranging from 3 to 24 h. Our study revealed new insights regarding the application of the simple scaling method. The results from this method are sensitive to the sample size, the range of rainfall durations and the chosen probability distribution.

Furthermore, our work went beyond the boundaries of historical data. We applied the simple scaling method to bias-corrected rainfall data obtained from CMIP6 GCMs, thereby projecting future IDF curves under four distinct scenarios: SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5. The results of these projections revealed crucial insights into the potential impacts of different climate pathways on rainfall patterns. In conclusion, our study significantly contributes to the field of water resources engineering and climate adaptation. We propose a new methodological framework for generating IDF relationships under climate change conditions. This framework encompasses the selection of GCMs and probability distribution along with the application of the simple scaling method. The IDF curves developed can be essential for sustainable water resource management and infrastructure planning in the changing climate of Khon Kaen City. Our future research in this direction will focus on enhancing confidence in the development of IDF curves. This includes investigating the applicability of GCMs for simulating extreme daily rainfall events. Future work is also needed to improve temporal scaling methods for estimating sub-daily extreme rainfalls.

This study is supported by the Research and Graduate Studies as well as the Sustainable Infrastructure Research and Development Center, Faculty of Engineering, Khon Kaen University. We are also deeply grateful to the Thai Meteorological Department and HII in Thailand for their invaluable contributions in providing the essential meteorological datasets. In addition, we extend our thanks to the anonymous reviewers and the editorial team.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.