Estimating IDF curves under changing climate conditions for different climate regions

The human-induced change in the natural balance of the atmosphere, which is one of the climate components, is an important issue for the future of the world. The disruption of the balance of temperature and precipitation leads to flooding events that cause loss of life and property in some regions, while, on the other hand, extreme temperature increases lead to drought. Due to the wide range of areas affected by global climate change, studies are usually conducted in detail on the impact areas. For example, studies can be classified as those related to global climate models and scenarios (Durand et al. 2009; Maraun et al. 2010; Vrac et al. 2012; Gogien et al. 2023), the effects of climate change on glaciers (Gan et al. 2015; Du et al. 2022), droughts (Zhao et al. 2023; Zhou et al. 2023), rainfall (Paeth et al. 2011; Soubeyroux et al. 2015; Garba & Abdourahamane 2023), and so on.

Intensity–duration–frequency (IDF) curves are curves that show the intensity of precipitation at various rainfall durations according to recurrence periods. IDF curves are frequently used in the design of urban drainage systems, bridges, culverts, and other water structures. These curves are generally created with observed data. However, due to global climate change, they do not include possible precipitation changes; in other words, IDF curves have a static nature. Assuming that the past situation will occur in the future, this approach may cause any water structure project to experience capacity problems due to possible precipitation changes in the future. Therefore, taking into account the impact of climate change in determining IDF curves will be useful in evaluating alternative options to take precautions against capacity problems that existing and newly constructed water structure systems may face.

IDF curves can be obtained by frequency analysis if local precipitation records are available. Annual maximum values for each selected precipitation period are extracted from the observed historical data, and frequency analysis is applied to them. In frequency analysis, the Extreme Value Type I distribution is mostly used. After the IDF curves are determined, one of the first steps in any hydrological design project is determining the design precipitation intensity from these IDF curves for a selected precipitation duration and return period (Chow et al. 1988).

Although the forecast uncertainty is much higher than the temperature data, global climate models also make simulations of global precipitation until the end of the century under various scenarios. For example, MPI-ESM HR model simulations predict that with increasing temperatures, the water cycle will accelerate, global average precipitation amounts will increase, and along with changes in precipitation distribution, precipitation will increase in some ocean and land regions and decrease in others (URL 1). To obtain IDF curves from the future precipitation forecasts of climate models, shorter-term precipitation data should be obtained from precipitation data in the form of daily outputs by using one of the following precipitation data disaggregation methods.

Apart from the global climate models that model climate dynamics on a physical basis, various artificial intelligence methods are also used for shorter-term (hourly, several days, or monthly) forecasts of precipitation amounts. Khan & Maity (2020) predicted precipitation heights up to 5 days in advance using a hybrid deep learning method consisting of a combination of convolutional neural network and multi-layer perceptron (Conv1D-MLP). It has been stated that the hybrid model gives more successful results than Multi-Layered Perceptron (deep MLP) and support vector regression, another machine learning method. Azad et al. (2019) showed that the binary hybrid models created by combining five different optimization techniques (genetic algorithm [GA], ant colony optimization for the continuous domain [ACO_R], particle swarm optimization, and differential evolution) with the adaptive neuro-fuzzy inference system can improve monthly precipitation height estimations.

Chhetri et al. (2020) compared the performance of six models (linear regression, multi-layer perceptron [MLP], convolutional neural network, long short-term memory [LSTM], gated recurrent unit [GRU], bidirectional long short-term memory [BLSTM], and BLSTM-GRU combination) in estimating normalized monthly precipitation depths. They stated that the BLSTM-GRU combination out of these six models outperformed the other models and gave the lowest mean square error.

Since the future rainfall prediction data obtained from global climate models are in the form of daily total rainfall, it is necessary to convert the daily rainfall data into hourly (1, 2, 6, 12, and 24 h) and minute-based (5, 10, 15, and 30 min) rainfall data in order to create IDF curves. In other words, the daily rainfall data need to be disaggregated. Various methods and codes are used to disaggregate the rainfall data. For instance, the Hyetos computer program used for this purpose disaggregates daily rainfall data into shorter-duration rainfall data (Tayşi & Özger 2022) by using various statistical parameters calculated from hourly daily rainfall data (such as maximum rainfall, mean rainfall, standard deviation, etc.). However, this program requires hourly rainfall data for disaggregation, whereas the outputs of climate models are daily, which requires an extra effort to convert them into hourly data.

In their study, Knoesen & Smithers (2009) used the ratio method to disaggregate daily precipitation data for the South Africa region into standard duration rainfall data. In this method, a ratio is obtained for each duration from observed data, and these ratios are applied to future precipitation data through various models to perform the disaggregation process. Srivastav et al. (2014) developed the equidistance quantile matching method to disaggregate precipitation data. Only maximum precipitation data are used in this method; hence, all available data need to be in its maximum form. Since IDF curves are also generated with maximum precipitation data, the outputs of the method can be directly used to create IDF data without the need for any external processing. As this method is more result-oriented, it can be considered more useful than other disaggregation methods.

Although no novel methods are given in this work, there are few studies in the literature that investigate the impact of climate change on the analysis and design of infrastructure-related engineering structures. Therefore, this study aims to investigate the effects of climate change on the IDF curves of three provinces (Muğla: Mediterranean climate, Ordu: Black Sea climate, and Diyarbakır: Continental climate) located in different climate regions of Turkey. To achieve this, IDF curves obtained from the precipitation data predicted by the GFDL-ESM2M, MPI-MR-ESM, and HadGEM-ES climate models under the RCP4.5 and RCP8.5 scenarios for the years 2023–2098 were compared with the IDF curves obtained from observed data.

Statistical data on temperature and precipitation for selected cities are given in Table 1. Table 2 contains information on station, altitude, and coordinate data for the selected cities.

All data used in the study were obtained from the Turkish State Meteorological Service (TSMS). HadGEM-ES, GFDL-ESM2M, and MPI-ESM-MR models were selected as global climate models. The reason for this is that TSMS has expressed that these models are the ones that best overlap with Turkey's climate dynamics among global climate models. The spatial resolution of the climate models, which is between 112.5 and 220 km, was converted to 20-km-resolution model data through the RegCEM4.3.4 projection by the TSMS. Therefore, in this study, 20-km-resolution model data were used. RCP4.5 and RCP8.5 scenarios were chosen because these scenarios have been found to be suitable for studies on climate models in many studies in the literature (Zhou et al. 2020; Bhasuru et al. 2022; Hall et al. 2022). Here, RCP4.5 represents a medium-risk situation, and RCP8.5 represents the most dangerous situation. As the data set, observed data for the years 1971–2000 in the provinces and historical data from climate models for the same period were used.

in these equations represents the maximum values of the observed data, j represents the duration, and represents the maximum data of the historical data set of global climate models. a₁ and b₁ represent the coefficients of the linear equation.

• 5.
  Based on the equidistance quantile matching method, a linear functional relationship is established between the cumulative distribution function of global climate models' future rainfall prediction and the cumulative distribution function of the models' historical data sets.

  

  (9)

  

  (10)

In these equations, represents the maximum data of the historical data set of the global models and represents the 24-h maximum precipitation data of the global climate models. a₂ and b₂ represent the coefficients of the linear equation.

• 6.
  At this step, the equations obtained in steps 8 and 10 are combined to obtain the following equation:

  

  (11)

In this equation, represents disaggregated standard duration global model data and represents the global model 24-h maximum. Other parameters are as defined above.

Finally, precipitation data are obtained by return periods using the values found and the Gumbel distribution, and IDF curves are drawn (Srivastav et al. 2014). Although the equidistance quantile matching method has been explained in detail by Srivastav et al. (2014), its demonstration on a sample application will contribute to a better understanding of the method. An example application of the method is given in the Supplementary Material.

To understand whether the equidistance quantile matching method used to reduce daily rainfall data for climate models to shorter-term rainfall data is suitable for updating IDF curves, observed historical data sets from 1971 to 2000 and the historical data of climate models from the same period were used. In the study, the daily maximum historical rainfall data of the global climate models used were converted to 5-, 10-, 15-, and 30-min and 1-, 2-, 6-, and 12-h maximum rainfall data using the quantile matching method described above. The model historical data converted to minute and hourly durations were compared with the observed historical data.

Global climate models are developed based on similar physical theories, but due to differences in land use and the parameters used for land, ocean, and atmosphere, the local performance of these models can vary significantly. Therefore, some global climate models can better simulate the climate of a specific region than other models. However, there is no physical background as to why some models are successful in certain regions or why they are not successful in other regions (Iqbal et al. 2020). Perhaps it would be helpful to follow this approach. Since it is not possible to validate global climate models with future prediction data, historical data can be split into two parts. The first part can be used to calibrate the quantile matching method, while the second part can be used for validation. In this way, it is possible to determine which model better represents the regional climate. Then, all historical data can be used in model calibration, and the relatively reliable prediction of selected models can be ensured for future predictions.

As seen in Figure 5, it is possible to make similar inferences for Ordu province as for Diyarbakir province. However, the increase in precipitation intensity estimated by the HadGEM-ES model for 5–15 min and a 5- to 10-year period is slightly higher for Ordu province, around 25%.

It can also be said that HadGEM-ES model estimates are more compatible with floods seen in Ordu province in recent years. In other words, the predictions of other models for the decrease in precipitation intensity are less consistent with regional conditions.

Considering the floods that have occurred in the regions studied in recent years, it can be said that the HadGEM-ES model is more in line with the observed situation.

As Liew et al. (2014) stated, since it is not possible to confirm future climate change with a direct method, present-climate simulations of these models should be evaluated to have more confidence in the future predictions of climate models. For this, historical data from climate models should be compared with observed data. The regional climate model (WRF) used by Liew et al. (2014) consistently underestimated the IDF curves of Jakarta, Singapore, and Kuala Lumpur stations by 38–45%. This difference was considered the bias of the model, and the model outputs were corrected with a ‘delta’ factor. They also used this delta factor in the future predictions of the model. For the Jakarta station, it is estimated that the precipitation intensity, which corresponds to precipitation with a return period of T = 50 years and a duration of t = 24 h, will increase by approximately 200% by the end of the century. They also predicted that precipitation, which now has a return period of T = 50 years and a duration of t = 24 h, may occur more frequently by the end of the century, decreasing to about 1 in 5 years. Therefore, they stated that the current drainage system will not be able to handle future extreme precipitation events (Liew et al. 2014). Instead of a ‘delta’ correction, a linear relationship is created between the distribution parameters of the historical data of climate models and the distribution parameters of the observed data in our study, minimizing any biases that may exist in the model outputs at this stage. The future prediction data from climate models are then disaggregated using these distribution characteristics, and future IDF curves are generated. As a result, there is no way to validate the models' future forecasts, and the model's credibility must be restricted by its ability to predict historical data.

Climate models may predict precipitation heights for a region inconsistently, depending on the model or collection of models employed. Guo et al. (2017) used a regional climate model named PRECIS to simulate the climate of China between 1950 and 2099, with boundary conditions determined by the four-element HadCM-3 and ECHAM5 global models. When the model's historical data are compared to observed precipitation data, the PRECIS model is found to overestimate the observed data. It has been discovered that the models' predictions for the future diverge in several locations. While HadCM-3 models anticipated an increase in future precipitation heights in some areas, ECHAM5 forecasted a reduction. However, the overall trend in precipitation from the beginning to the middle of the century was clearly upward.

To update IDF curves under changing environmental conditions, Srivastav et al. (2014) introduced the equidistance quantile matching approach. Precipitation intensities were predicted to increase in all RCP scenarios (RCP-26, RCP-45, and RCP-85) in a study conducted for many Canadian locations. When compared to the corresponding quantile matching model, models without temporal downscaling were said to underestimate precipitation intensities. In the study, as the scenario deteriorated from RCP-26 to RCP-85, the model predicted an increase in precipitation intensity in the future. This circumstance is consistent with the outcomes of our investigation. However, because the study did not evaluate multiple climate models, it is not able to directly compare the conclusions produced with some of the findings in our study.

Lastly, the findings obtained in this study are similar to those obtained by Tayşi & Özger (2022), who studied the estimation of IDF curves for future periods under RCP4.5 and RCP8.5 scenarios using the HadGEM-ES model for Istanbul province. They reported that the HadGEM-ES model predicted an increase in precipitation intensity in Istanbul province in both scenarios. Gürkan et al. (2016) derived precipitation scenarios for 2023–2098 according to the GFDL-ESM2M model throughout Turkey in their study. According to the findings, rainfall is expected to decrease throughout Turkey. Although the findings of the two models in our study support this conclusion for Turkey as a whole, it may be possible to reach different results from the general trends when observations at a smaller scale are considered. Therefore, it is considered that the increase in extreme precipitation intensities predicted by the HadGEM-ES model is more reasonable, at least for the provinces examined in this study.

This study investigates the effect of climate change on extreme precipitation intensity. To do this, future IDF curves were estimated under two different conditions (RCP4.5 and RCP8.5) using various climate models (HadGEM-ES, GFDL-ESM2M, and MPI-ESM-MR).

Since climate models produce daily precipitation data for future predictions, reducing daily rainfall to hourly and sub-hourly rainfall is necessary to increase the temporal resolution of the generated predictions. Although there are various methods for this reduction, it has been observed that the equidistance quantile matching method used in this study is quite successful in performing this operation. The success of this method has been demonstrated through verification with historical data.

According to the findings obtained from the study, it is not possible to reach a general conclusion when the three models used are evaluated together. The HadGEM-ES model predicts increases of up to approximately 25%, depending on the scenario used, for future precipitation intensities for different provinces, while the GFDL-ESM2M and MPI-ESM-MR models predict decreases of up to approximately 50%. According to this result, different climate models may be able to make similar predictions on a global scale, but it shows that it is possible for them to make conflicting predictions on small local scales. This also indicates that care should be taken in selecting the model to be used for local-scale climate prediction.

The increase in extreme rainfall events observed in recent years in cities located in different climate regions studied within the scope of this study suggests an increase in rainfall intensities in the future as well. Accordingly, it seems that the HadGEM-ES model, which predicts an increase in rainfall intensities for certain rainfall durations and return periods, may be more suitable than the other two models in estimating future IDF curves for the examined cities. It should be noted that this conclusion involves a bit of speculation, as different climate models yield contradictory findings. Accordingly, an analysis using a larger number of global climate models and higher-resolution regional models can yield more quantitative results to confirm an increase, decrease, or both in future precipitation intensities for a given region in the country.

The current or future conditions of IDF curves are particularly important in evaluating the capacities of existing urban drainage systems or determining the capacities of new infrastructure systems to be designed. The increase in precipitation intensity predicted by the IDF curves indicates that there may be capacity deficiencies in the current systems, and therefore, local governments need to plan appropriate measures before these situations are experienced again. Therefore, it is quite important to accurately estimate the IDF curves when evaluating alternative measures to be taken against the negative effects of climate change, especially on urban drainage.

It can be considered useful for the relevant local governments to examine the capacity status of the existing systems by evaluating the approximate 25% increase in precipitation intensity predicted in the regions examined in this study as a scenario and to determine alternative solutions against capacity deficiencies, if any.

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

The authors declare there is no conflict.