Enhancing accuracy in streamflow prediction under climate change scenarios based on an integrated machine learning–metaheuristic optimization approach

Climate change is a crucial issue in the modern era, primarily due to the increase in greenhouse gas emissions from fossil fuel consumption (IPCC 2021). The impact on water resources is considered one of the effects of climate change. This impact varies in intensity and duration in each distinct region due to the severity of climate change (Mikova & Msafiri 2019). Understanding climate variability and its behavior in future periods, as well as the effects on different basins, especially on water resources, is particularly important in macro-level planning and strategies (Shrestha et al. 2021). Climate change and global warming have led to the expansion and persistence of droughts (Aryal et al. 2019).

This change causes an uneven distribution of precipitation and affects water resources (Ercan et al. 2020). Examining climate changes and their impact on streamflow can pave the way for adopting strategic policies for future water resource management. Realistic planning cannot be made regarding water resource utilization without considering the fact that the climate is changing. Streamflow is one of the key components in sustainable development; therefore, predicting the quantity and trend of changes in streamflow is vital in water resource management. Streamflow, the intensity of floods, and droughts are all influenced by temperature and precipitation, which are among the most important climatic elements (Wang et al. 2020). In this regard, studying the effects of climate change on the incoming flow to the salt marsh of the Qazvin Plain and its impact on the wetland and ecosystem of the region is particularly important and has not been previously investigated. Climate models have been developed as effective tools for climate simulations in past and future periods. However, most of these models disregard social and economic components. Therefore, the sixth phase of the Coupled Model Intercomparison Project (CMIP6) continues the evolution pattern and compatibility features of previous CMIP phases. It includes newly organized scenarios of global climate modeling designed to understand various weather mechanisms (Eyring et al. 2016). The models available in CMIP6 generally have higher resolution along with improved dynamic processes, and they apply shared social and economic emission scenarios SSP (shared socioeconomic pathways)/RCP (representative concentration pathways) for simulating future climate changes (O'Neill et al. 2016). The outputs of the models reported in CMIP6 under new scenarios depict pathways of common SSP and RCP. These CMIP6 scenarios, which include five main subgroups, focus on quantitative indicators such as population, urbanization, regional and inter-regional economic development, generalized scenarios (impacts, adaptability, and vulnerability reduction), energy programs, and land use changes. Among these scenarios are SSP1-19, SSP1-26, SSP2-45, SSP3-70, SSP4-34, SSP4-60, SSP5-34, and SSP5-85 (Riahi et al. 2017). In applications involving data or images with low resolution, such as those from general circulation models (GCMs), downscaling is employed. This process converts data or images with lower accuracy or resolution to higher accuracy or resolution. The technique is used in data science, image processing, climate modeling, and other fields. Sharma et al. (2024a) utilized a Fourier-transform-based fusion method to enhance the spatial resolution of the PAN (potential available network) and TIR (thermal infrared) bands of Landsat-9 land surface temperature (LST) images from 100 to 15 m. Comparing the downscaled LST with actual on-site measurements showed a root mean square error (RMSE) of 0.18 m³/s and a correlation of 0.93. In a study by Punyawansiri & Kwanyuen (2020) conducted in Phitsanulok Province, Thailand, the Long Ashton Research Station Weather Generator (LARSWG) model was used for downscaling data from CMIP Phase 5. Results indicated that the downscaled data using the LARSWG model exhibited a very high level of accuracy when compared with observational data.

One study that utilized CMIP6 models is the research by Hersi et al. (2023), where they investigated the future climate of Maniouni City in Tanzania using CMIP6 models. According to the results of SSP5-85 and SSP1-26 scenarios, the precipitation is reduced by 13.8%–4.5%, while the average minimum temperature increases by 2.8 °C and the average maximum temperature increases by 4.5 °C.

As mentioned, climate change leads to changes in the amount and pattern of precipitation, affecting streamflow. Hydrologists also attempt to predict streamflow for various purposes, such as flood control, irrigation, water supply, water quality, recreation, and hydropower (Annayat et al. 2021). While many theoretical and physical models have been used to predict hydrological components, fuzzy inference system models are considered practical tools that can assist hydrologists in conditions where hydrological data are limited (Jimmy et al. 2021). The use of an adaptive neuro-fuzzy inference system (ANFIS) for hydrological time-series modeling in the Bitrani River in India showed that this model outperformed artificial neural network (ANN) models and time-series models (autoregressive moving-average, ARMA) and preserved the statistical features of observational time-series Nayak et al. (2004). In a study conducted in the Dikho River basin in India, river flow was predicted using the ANFIS model. The ANFIS model was also combined with the particle swarm optimization (PSO) algorithm to enhance prediction accuracy. Results comparing the hybrid ANFIS–PSO model with the regular ANFIS and ARIMA12 models indicated a higher accuracy of the ANFIS–PSO model in river flow prediction (Nath et al. 2020). Another study investigated the accuracy of the hybrid ANFIS models combined with optimization algorithms, including ICA (independent component analysis), BBO (biogeography-based optimization), TLBO (teaching–learning-based optimization), and IWO (invasive weed optimization), to predict daily reference evapotranspiration values. The results showed that among the hybrid models, ANFIS–ICA was considered superior with R = 0.99, RMSE = 0.5 m³/s, and Nash–Sutcliffe efficiency (NSE) = 0.98 (Zeinolabedini Rezaabad et al. 2020). In a different study on the Barak River basin in India, the integration of the ANFIS model with the PSO metaheuristic algorithm for monthly streamflow prediction using precipitation, temperature, humidity, and infiltration as input variables demonstrated that the ANFIS–PSO model with RMSE = 5.887 m³/s, mean absolute error (MAE) = 4.978 m³/s, R² = 0.9668, and NSE = 0.961 outperformed with more reliability and higher accuracy compared with the ANFIS and ANN models. The findings of this research illustrated that the combined ANFIS model with the PSO optimization algorithm is a reliable modeling approach for predicting monthly river flow (Samanataray & Sahoo 2021). In another study, changes in streamflow patterns in the Hunza basin, Pakistan, were investigated using ANN, recurrent neural network (RNN), and ANFIS methods. The results indicate that ANN outperforms RNN and ANFIS (Khan et al. 2023). Additionally, in a different study on the Karkheh watershed, the prediction of peak flow for different return periods was examined using random forest (RF), ANFIS, the M5 algorithm, and the multivariate regression model (MRM). The results suggest the data-driven models, particularly RF, perform better compared with the MRM method (Esmaeili-Gisavandani et al. 2023). In another study conducted in the Katar watershed, Ethiopia, the performance of the Hydrologic Engineering Center Hydrologic Modeling System, Soil and Water Assessment Tool (SWAT), feedforward neural network (FFNN), ANFIS, support vector regression (SVM), and multilinear regression was evaluated in rainfall–runoff-sediment modeling. The results indicate that the ANFIS model performs better than the other individual models for rainfall–runoff-sediment modeling. Furthermore, the combination of artificial intelligence models and physics-based models leads to improved performance (Gelete et al. 2023).

While the ANFIS model and its combination with optimization algorithms have been used in various fields, including simulating streamflow, they have not been utilized to investigate the effects of climate change on inflow to the Qazvin Salt Lake using the CMIP6 sixth-generation climate model ensemble models. Therefore, given the importance of the Qazvin Salt Lake and the wetland within it, the aim of this study is to evaluate climate change trends using four models (MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4) from the CMIP6 CMIP's sixth-generation model set, under the SSP1-26, SSP3-70, and SSP5-85 scenarios for the time periods (2026–2050), (2051–2075), and (2076–2100) in the Qazvin Salt Lake region. Consequently, the changes in streamflow to the salt marsh of the Qazvin Plain will be assessed using ANFIS methods and their combination with metaheuristic optimization algorithms such as PSO and GA under climate change conditions.

In this study, the average values of precipitation, minimum temperature, and maximum temperature from 56 weather stations in the Qazvin Plain were used as inputs for the runoff simulation models and for the hydrological station of Pole Shahabbasi as streamflow to the salt marsh of the Qazvin Plain using the Thiessen method. Additionally, climate change data from CMIP6 were obtained from the ESGF (Earth System Grid Federation) portal at https://esgf-node.ipsl.upmc.fr/projects/cmip6-ipsl/ (Hempel et al. 2013). The files available in this source are in NetCDF format for a global scale. The models used include MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4 considering the SSP1-26, SSP3-70, SSP5-85 scenarios, with available precipitation, maximum temperature, and minimum temperature data for these models. The scenarios were selected due to the investigation of climatic (rainfall and temperature) and hydrological (runoff) variables in the conditions of minimum, average, and maximum radiative forcing in the future. Based on this, four models (MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4) that have SSP1-26, SSP3-70, and SSP5-85 considered in the base of the ESGF database were selected.

In this study, the level of a has been considered significant at both 95% and 99% confidence levels. The values of a for both levels are 0.05 and 0.01, calculated as z95% = 1.96 and z99% = 2.57. Ultimately, if the above relationship holds, it indicates the presence of a trend and supports the alternative hypothesis H₁. Otherwise, the data under investigation do not exhibit a trend, and the null hypothesis H₀ is confirmed. Additionally, for the period 1980–2014, the trend slope (Q) of the variables in this study was calculated using the non-parametric Sen's slope method.

Given the large-scale nature of general circulation models, fine-scale downscaling is used. Downscaling involves establishing a relationship between large-scale weather predictors and predicted variables (usually temperature and precipitation) at a regional scale. As a weather generator, LARSWG can simulate daily weather parameters for any period based on a set of semi-empirical frameworks (Semenov & Barrow 1997). This model uses a histogram with 23 intervals to describe the distribution of wet and dry day lengths, daily precipitation, maximum temperature, and minimum temperature. The generated climate data are produced as random values from the corresponding semi-empirical distributions by selecting an interval and then selecting a value within that interval from a uniform distribution. In this study, the LARSWG8 model is used, and in the first step, the model is validated. Subsequently, statistical tests and comparison of graphs are used to verify the model's accuracy.

The QM method is a non-parametric bias correction technique that demonstrates strong capability in eliminating biases in the first and second statistical moments (mean and standard deviation) as well as in the frequency of wet days (Ajaaj et al. 2016). This method is based on the empirical cumulative distribution function (ECDF) and eliminates bias by replacing the predicted value with the observed value at the corresponding quantile.

During the validation process, in addition to extracting statistical parameters, the statistical features of the generated and observed climatic data, such as temperature, minimum temperature, and maximum temperature, were analyzed to determine the performance of the LARSWG model under investigation. The validation of LARSWG can be done using two methods. In the first method, the statistical data are divided into two equal parts; using the first part, climatic data are generated without any scenarios, and then the validation is done using the second part. In the second method, the performance of the data generated by LARSWG can be evaluated using statistics such as t-student, F-test, and Kolmogorov–Smirnov (K–S). In this study, the K–S test was used to validate the LARS model.

The K–S test is one of the key statistical tools used to validate the LARSWG climate simulation model. It evaluates the agreement between simulated and observed data. This test assesses the model's capability to reproduce the probabilistic distribution of climate variables (e.g., temperature, precipitation, or solar radiation).

The test compares two hypotheses:

H₀: The simulated and observed data come from the same statistical distribution.

H₁: The simulated and observed data come from different statistical distributions.

The K–S test statistic (D) is the maximum absolute difference between the cumulative distributions of the observed and simulated data.

If p-value > 0.05, H₀ is accepted, concluding that the simulated and observed data distributions are similar.

A_i, B_i are fuzzy sets, and f_i is the output in the fuzzy region defined by a fuzzy rule.

p_i, q_i, and r_i are design parameters that are determined during the training process.

In this study, fuzzy C-means clustering was utilized to develop the fuzzy inference system, specified with genfis3 in the MATLAB software.

In this study, two algorithms, PSO and GA, were used to optimize ANFIS for streamflow prediction, and these models were implemented in MATLAB^®. For this purpose, three variables, including precipitation, maximum temperature, and minimum temperature, were considered as inputs to the models. Given the standard learning methods in the ANFIS structure, there is a possibility of getting stuck in local optima. Therefore, combining optimization methods can help overcome this issue by random search.

In equations (6) and (7), V_i(t) is the velocity with which particle i moves. P_i(t + 1) is the updated position of the particle based on its current position P_i(t) and velocity V_i(t + 1). P_iBest and GBest are national and global optimal values. The r₁ and r₂ values (which range between 0 and 1) are random values that are regenerated for each velocity update, and c₁ and c₂ are learning-rate parameters; c₁, c₂, and w are coefficients provided by the user.

GA as a derivative-free stochastic method for optimization, is one of the most well-known, oldest and most widely used evolutionary algorithms in solving many engineering problems. It can be used to solve nonlinear, stochastic, and non-differentiable problems which may seem impossible using gradient-based methods (Mirjalili 2019). The number of population points for each iteration in GA is randomly generated, and the best point in the population requires the same optimal solution as the final result (Goldberg & Holland 1988). The basic steps of GA include three important components. The first component is to create an initial population using an individual named n who is randomly selected to form the first population. Entering the nth person and producing the output is the second component. Each of the outputs is evaluated based on the objective function known as the fitness function. The expected demand from each person to achieve the desired goal is determined by the assessment. From the most worthy person in the previous generation, a new generation is created. In the reproduction process, the selection of chromosomes from the current generation is done based on the fitness of each chromosome to produce the new generation using the ‘selection’ operator. Chromosomes with higher probability are selected for modification and use in the next generation. Finally, the crossover operator, which is a key operator in GA, is defined to generate child chromosomes from two different parent chromosomes. In fact, by using this operator, two new chromosomes are generated that have a higher fitness than the two input chromosomes (parents) (Yaseen et al. 2019).

In Equations (8)–(13), Q_O represents observed flow values, Q_P represents predicted flow values, is the mean of observed flow, is the mean of predicted flow, σQ_O is the standard deviation of observed flow, and σQ_P is the standard deviation of predicted flow. The current study investigates the effects of climate change under the scenarios of the Sixth Assessment Report on streamflow changes in climate change conditions using fuzzy logic inference system models and their combination with PSO and GA algorithms.

To determine the best model, the performances of the MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4 models were assessed against observational data using two metrics, the coefficient of determination (R²) and RMSE, for minimum temperature, and maximum temperature parameters, as well as for precipitation. The evaluation included RMSE and corrected RMSE errors for precipitation (Table 1). Based on the results, the GFDL-ESM4 model exhibits the lowest error in predicting precipitation as well as minimum and maximum temperatures.

Using the Site Analysis functionality of the LARSWG8 model and two datasets containing daily observational values and geographical information of the study station, both validation and verification of the model were conducted simultaneously. To validate the performance of LARSWG8 during the validation process, statistical tests such as the K–S test were employed. Additionally, the p-value was computed, indicating the lack of significant difference between the observed and predicted data, as shown in Table 2.

In Table 3, the results of the Mann–Kendall test and Sen's slope estimator are provided. The Mann–Kendall test results indicate the presence of a trend at the 95% significance level for cells marked with one asterisk (i.e., non-significant trend) and at the 99% significance level for cells marked with three asterisks (i.e., significant trend).

Based on the results from the GFDL-ESM4 model, precipitation is estimated to decrease by approximately 1 mm for the SSP5-85 scenario and increase by around 0.7 mm for the SSP3-70 and SSP1-26 scenarios during the years 2026–2100. The average maximum temperature is projected to increase by 2.4 °C for the SSP5-85 scenario, 2 °C for the SSP3-70 scenario, and 1.6 °C for the SSP1-26 scenario. Furthermore, the minimum temperature is expected to increase by 1.6 °C for the SSP5-85 scenario, 1.5 °C for the SSP3-70 scenario, and 1.2 °C for the SSP1-26 scenario. These findings are illustrated in Figures 5–7, respectively.

Among the examined models for predicting streamflow, the ANFIS model with input variables of precipitation, minimum temperature, and maximum temperature, combined with the PSO algorithm, demonstrated the best performance based on correlation coefficient, RMSE (cubic metres per second), Nash–Sutcliffe coefficient, and Kling–Gupta efficiency values (0.97, 0.91, 0.19, and 0.98 during the training period and 0.95, 0.83, 0.2, and 0.97 during the testing period). Therefore, this model will be utilized for river flow estimation during the climate change period. Additionally, Sharma et al. 2024b, who employed the geostatistical interpolation method of kriging combined with the PSO algorithm to enhance and optimize thermal images, demonstrated that integrating the PSO algorithm with the kriging method significantly improved the overall quality of the images. This combination created a powerful tool for efficient and precise spatial enhancement of thermal images.

As depicted in Figure 9, in all three scenarios (SSP5-85, SSP3-70, and SSP1-26), there is a reduction in streamflow during the future period (2026–2100) under climate change conditions, with the crisis being more severe in the first four months of the year. Furthermore, the analysis of results indicates that SSP3-70 scenarios generally estimate higher streamflow. In the ANFIS–PSO model, the highest rate of increase in streamflow occurs in the first month, while the highest rate of decrease in streamflow is observed in the eighth and ninth months of the year.

The analysis of precipitation trends, as well as minimum and maximum temperatures, indicated that significant changes during the baseline period mostly occurred in the first six months of the year, suggesting a stronger manifestation of climate change during these months. The results revealed that precipitation levels decrease in wet seasons while temperatures rise, which subsequently impacts runoff reduction.

Examining precipitation and temperature conditions in the future under climate change scenarios indicated that in the Qazvin Plain, precipitation decreased under the SSP5-85 scenario but increased under the SSP3-70 and SSP1-26 scenarios. Meanwhile, temperature showed the highest increase under SSP5-85 and the lowest under SSP1-26. Nasirabadi et al. (2024) reported that in the Karaj Dam basin, precipitation decreased by 0.05%–11.15% in most scenarios, and temperature increased by 1.51–2.91 °C across all GCM models and their scenarios.

Machine-learning models are recognized as efficient tools for simulating and predicting time series (Tikhamarine et al. 2019). Machine-learning-based approaches, such as ANFIS, exhibit less dependence on the quality and quantity of input data compared with statistical techniques while also outperforming statistical methods in estimating critical values (Kim et al. 2000). Since ANFIS relies on the performance of ANNs, which depend on the accuracy of their weight and bias estimation, utilizing metaheuristic algorithms to estimate ANN parameters can significantly enhance the speed and accuracy of river flow simulations (Nath et al. 2020).

In this study, the ANFIS model was used individually and in combination with the metaheuristic algorithms PSO and GA to predict river flow. The results demonstrated that the hybrid ANFIS–PSO model outperformed both the standalone ANFIS and the hybrid ANFIS–GA models. This finding highlights that incorporating metaheuristic algorithms into standalone models improves their accuracy, a conclusion supported by various studies such as Sammen et al. (2020), Bac et al. (2022) and Ehteram et al. (2022). The superiority of the ANFIS–PSO model lies in the minimal assumptions made by the PSO algorithm about the problem, which eliminates the likelihood of models being trapped in local minima (Elbedwehy et al. 2012). This is a significant advantage of PSO over GA in enhancing ANFIS performance. Nath et al. (2020) investigated runoff estimation using ANFIS and ANFIS–PSO models in northeastern India. Their results demonstrated that the PSO algorithm significantly enhanced the deficiencies of the ANFIS model.

The overall findings of this research indicated that climate change, under all scenarios, will lead to a reduction in river flow in the future. Consistent with these results, Abdissa & Chuko (2024) examined the impacts of climate change on water resources in the Walga–Darge basin and found that reduced precipitation and increased temperature will result in reduced runoff in future periods. However, contrary to these findings, Zakizadeh et al. (2021) studied the effects of climate change on runoff variations in the Darabad basin in northeastern Iran using the SWAT model and demonstrated that increased precipitation and temperature under climate change conditions will result in increased runoff in the future.

Yoosefdoost et al. (2022) investigated the effects of climate change on runoff into the Karaj Dam using CMIP5 models as input to data-mining algorithms, including ANNs, support vector machines (SVM), genetic expression programming (GEP), and the conceptual HYMOD (Hydrological Model). The results showed that the SVM model outperformed ANNs, GEP, and HYMOD by 3%%, 5, and 14%, respectively. The SVM model predicted a 25% decrease in mean runoff into the dam reservoir for the 2020–2040 period compared with the baseline period.

The findings of this study underscore the necessity of implementing sustainable management and adaptation strategies to protect future water resources in this basin. In this context, evaluating the performance of other streamflow simulation techniques, including statistical, machine-learning, and conceptual models, can provide further assurance to decision-makers. Additionally, beyond streamflow, assessing other hydrological components, particularly evapotranspiration and groundwater, can significantly enhance the understanding of the basin's water-resource status.

Considering the significant impact of climate change on precipitation, temperature, and streamflow, incorporating climate change effects into simulations and future designs is essential for appropriate water-resource planning. In this regard, the present study assessed the impact of climate change on precipitation, temperature, and consequently streamflow in the salt marsh of the Qazvin Plain. Four models from the CMIP Phase 6 dataset – namely MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4 – along with the three SSP1-26, SSP3-70, and SSP5-85 scenarios were utilized to investigate the trends of precipitation and temperature using the LARSWG8 model for the periods (2026–2050), (2051–2075), and (2076–2100). Based on the R² and RMSE error indices, the GFDL-ESM4 model demonstrated the lowest error in predicting precipitation and minimum and maximum temperatures.

Furthermore, in this study, the ANFIS models were combined with metaheuristic optimization algorithms, PSO, and GA to assess streamflow under historical and climate change conditions using four models (MPI-ESML-2HR, MIROC6, IPSL-CM6A-IL, and GFDL-ESM4) and three scenarios (SSP1-26, SSP3-70, and SSP5-85). The results indicated that the ANFIS model combined with the PSO algorithm (ANFIS–PSO), using precipitation, minimum temperature, and maximum temperature as input variables, outperformed the other models.

The authors would like to acknowledge the Imam Khomeini International University for pursuing this research.

The authors received no funds, or grants for the preparation of this manuscript.

S.H. and M.R.N. conceptualized the study, and wrote, reviewed, and edited the article. B.N. reviewed and edited the article.

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

The authors declare there is no conflict.