The prediction of precipitation changes in the Aji-Chay watershed using CMIP6 models and the wavelet neural network

The climate system has been disturbed by greenhouse gas-induced climate shifts, emphasizing the need to investigate how climate change affects hydrological elements, particularly precipitation. To forecast forthcoming rainfall changes crucial for water resources, this study has employed CMIP6 models and wavelet neural network (WNN) to predict rainfall variations in the Aji-Chay watershed from 2065 to 2025. Climate change is causing concerning alterations in precipitation patterns, which are vital components of the Earth's hydrological cycle and essential for human activities like agriculture (Sun et al. 2006). These changes, including increased frequency and intensity of droughts, disrupt the intricate link between precipitation intensity and frequency. This disruption further impacts human activities, particularly in vulnerable regions like the Aji-Chay watershed. Climate change is expected to exacerbate these problems in the Aji-Chay watershed, making analysis and prediction of future precipitation trends crucial for informed decision-making. Climate change has led to observable changes in both the quantity and patterns of rainfall. The exacerbation of drought due to climate change is a global phenomenon. It is predicted that this trend will lead to substantial alterations in climate, spatio-temporal patterns, and hydrometeorological factors, such as precipitation. Therefore, the evaluation of global climate models (GCMs) and the detection of uncertainties and biases in the simulation of climate models are important steps toward understanding their application and potential for climate impact assessment studies (Raghavan et al. 2018; Zazulie et al. 2018; Rivera & Arnould 2019). The exacerbation of drought due to climate change is a global phenomenon. It is predicted that this trend will lead to substantial alterations in climate, spatio-temporal patterns, and hydrometeorological factors, such as precipitation. Accurate climate models are vital for understanding the impact of climate change on precipitation. Accurate climate models are vital for understanding the impact of climate change on precipitation. Previous studies have explored these impacts, however, limitations exist due to the use of older models and a lack of investigation under specific scenarios. Hessar & Ghazavi (2015) analyzed time series models and artificial neural networks in the field of climate scenarios. Yaghoubi et al. 2017 conducted a research to evaluate the effects of climate change between 2016 and 2099 on the runoff of the Gavharud watershed, considering the uncertainty. They analyzed meteorological data generated by the Hadley Center Coupled Model, version 3 (HadCM3) and the general circulation model under the A2 climate change scenario. Pour (2016) examined the effects of climate change on temperature, precipitation, and variations in the flow of the Qareh Soo River in the Qareh Soo watershed located in the Kermanshah province, one of the vital sub-basins of the Karkeh watershed.

Nazaripouya et al. (2016) using the comparison of HadCM3 model and Integrated Precipitation and Climate Model version 4 (IPCM4) under scenarios A2 and B1, the uncertainty of the effects of climate change on temperature, precipitation and runoff in the Ekbatan Dam watershed for the period of 2045–2065 evaluated. Jahanbakhsh Asl et al. (2016) utilized the statistical model of the Long Ashton Research Station–Climate Generator (LARS-WG) to examine the impacts of climate change on temperature and precipitation in the Urmia-Chai watershed under three scenarios (A1, B1, A1B) for the period 2011–2030. Azizabadi Farahani et al. (2017) initially estimated precipitation and temperature variables from 1983 to 2012 and Canadian Earth System Model, version 2 (CanESM2) model outputs under three Representative Concentration Pathway (RCP) scenarios (2.6, 4.5, 8.5) for the period 2019–2048. They used drought indices and a conditional return period approach. The study revealed diverse changes in monthly precipitation and temperature variables across different scenarios in the future period. For a drought event with a severity level of 10 lasting up to 6 months, the return period changed from 5 years in the base period to 21, 17, and 4 years under RCP 2.6, 4.5, and 8.5 scenarios, respectively. Mansouri et al. (2018) investigated inflow variations to the Karun 4 Dam for 2050–2021 using HadCM3 model outputs (B1, A2) from the fourth report and combined outputs (RCP 2.6, RCP 8.5) from the fifth report. Artificial neural networks were used for runoff estimation. Precipitation in studied stations increased by 15% (B1) and 5% (RCP 2.6) while decreasing by 8% (A2) and 6% (RCP 8.5) annually. Sadeghi & Deen Pjooh (2019) employed statistical downscaling with LARS-WG6 to predict precipitation in the Tabriz region for three future periods (2021–2040, 2041–2060, and 2061–2080) using RCP4.5 and RCP8.5 scenarios with the Max Planck Institute – Earth System Model, version MR (MPI-ESM-MR) model. The findings indicated an increase in winter precipitation for all periods in both scenarios, while spring and autumn precipitation is projected to decrease under the RCP8.5 scenario. Omidvar et al. (2019) assessed the simulation of climate change effects on the behavior of precipitation and temperature at the Synoptic Station of Sirjan in Kerman Province. Initially, the performance of an artificial neural network model for downscaling climate variables predicted by the CanESM2 general circulation model was tested. Salahi et al. (2019) conducted a study to examine the impact of climate change on the planting time and the growth period of rainfed wheat in the Ardabil region. To achieve this, they first assessed the occurrence of climate change in the region using statistical downscaling. They used output data from the CanESM2 model and the Statistical Downscaling Model (SDSM) software under the RCP 4.5 scenario. They simulated maximum temperature, minimum temperature, and precipitation parameters for the future period (2011–2040). Senatore et al. (2022) assessed the hydrological impact of climate change under RCP scenarios by combining multiple global and regional climate models and making corrections. In this study, they investigated model uncertainties using analysis of variance (ANOVA). Few studies have been conducted on the impacts of climate change on various sectors of the economy in northwest Iran, particularly in the Aji-Chay watershed, utilizing the latest CMIP6 models and updated Shared Socioeconomic Pathways (SSP) scenarios from the Intergovernmental Panel on Climate Change (IPCC). Comprehensive studies based on the latest data are crucial to fully understand the impacts of climate change and to develop informed long-term policies in areas such as agriculture, water resources management, and industry. Due to the location of the Aji-Chay watershed in a semi-arid and arid region, as well as the continuous exploitation of groundwater in this area, conducting comprehensive research is essential for climate change. The main objective of this study is to evaluate the changes in precipitation patterns under the influence of climate change using CMIP6 models and the SSP5.85 scenario. The Aji-Chay watershed encounters various challenges categorized into water resource issues (such as decreased rainfall, drought, water quality decline, and overexploitation of groundwater), agricultural concerns (like outdated methods and reduced efficiency in irrigation), pasture degradation, air pollution, among others. Addressing these challenges necessitates thorough planning and collaboration among all pertinent institutions. The innovation of this research is the use of the ANOVA method to demonstrate the uncertainty of rainfall prediction models. In most previous studies, traditional methods such as mean comparison or root mean square error (RMSE) have been used to evaluate the uncertainty of models, the analysis was conducted using the neural wavelet network method to examine the data from 2025 to 2065. The analysis was carried out using the neural wavelet network method to examine data from 2025 to 2065. To conduct this study, the most suitable model was selected to estimate precipitation variables using a variety of time series models. Historical rainfall data from 1961 to 2010 collected from synoptic stations in the Urmia, the Tabriz, and the Khoi was used to predict variable values for the following 18 years (2011–2029). This can help researchers and policymakers choose the appropriate model for rainfall prediction.

This study utilized two sets of data. The initial set comprises daily precipitation records for the Aji-Chay watershed spanning from 1981 to 2021 AD (at least 40 years). These data served as foundational/historical information for assessment and modeling, sourced from the National Meteorological Organization. The second category includes climate scenario data from the Coupled Model Intercomparison Project Phase 6 (CMIP6) GCMs, which have been freely accessible to researchers since 2022 via the https://climate-scenarios.canada.caM website. In this study, these data have been evaluated as prediction data from 2022 to 2065 AD. The reason for selecting the SSP5-8.5 scenario in this study is the highest greenhouse gas emissions and increased utilization of fossil fuels, along with the adoption of resource-intensive energy technologies worldwide. In this research, historical predictions of the sixth assessment report models are compared with reconstructed data in a similar period, and models with acceptable statistical performance are considered for predicting precipitation changes in the study area. The model data used in this research for the study region have horizontal resolutions of 100 and 250km. Statistical downscaling techniques are applied to the chosen models. The study is divided into two time frames: a historical period (1975–2014) and a future period (2025–2065) focusing on the precipitation parameter. Furthermore, the Kendall rank correlation test is used to determine the concordance of observed and predicted precipitation trends. In addition, ANOVA is used for verifying the accuracy between observed precipitation and the models under the SSP5-8.5 scenario, and this test is conducted using the MATLAB software environment.

In this study, data from three CMIP6 climate models were initially acquired from the database at https://climate-scenarios.canada.ca (see Table 1). Subsequently, relevant information and model characteristics were extracted using ArcGIS 10.8 and are briefly summarized in Table 2. It is important to note that this research adopts a pessimistic scenario.

The selection of this model is based on its Equilibrium Climate Sensitivity (ECS), which measures the Earth's warming response to a doubling of carbon dioxide (CO₂) concentration in the atmosphere. ECS is a critical parameter in climatology, providing insights into how Earth reacts to changes in greenhouse gas concentrations (Gettelman et al. 2019: 46). The INM-CM4-8 model exhibits high sensitivity to ECS, with a range of ECS changes from 1.1 to 1.4. This range surpasses more than half of the ECS variation range observed in CMIP6 models (Tiedtke 1993: 3051). The model is characterized by a complex cloud system that includes various cloud types with distinct characteristics. The model's demonstration of ECS sensitivity to variations in cloud parameterization aids scientists in gaining a better understanding of the mechanisms governing cloud evolution (Volodin 2021: 5).

Overall, demonstrates a proficient ability to replicate global and regional precipitation patterns, encompassing areas with both intense rainfall and arid conditions (Reddy & Saravanan 2023: 47119). However, the simulation of intense and unforeseen rainfall continues to pose a challenge for all climate models, MRI-ESM2-0 included (Dione et al. 2023: 355).

The CanESM5 model is adept at simulating one of the essential climatic features, precipitation. This model is applied for forecasting climate patterns over the century and is also employed to create seasonal and decadal predictions. Serving as a predictive tool, it aids in formulating optimal strategies for water resource management and decisions related to watersheds (Swart et al. 2019: 4855).

The provided formula is utilized for examining variations in precipitation over time. It serves as a tool for comparing precipitation levels between two distinct time periods, enabling the investigation of precipitation changes over the designated duration (Gallé & Katzenberger 2023 : 14). In this expression, A_t signifies the precipitation amount during a future time interval, while A(t₁) denotes the precipitation value in the baseline period (t₁).

Trend analysis is conducted to examine the underlying trend in the time series of the studied variable since climate change can potentially alter the regime governing many hydrological variables (Sen 1968; Mohammadpour Khoie & Nasseri 2022). In this study, trend analysis is performed on both observational time series and the models under the SSP5.85 scenario.

The Mann–Kendall test is a non-parametric test used to determine the presence of a trend and was proposed by (Kendall & Stuart 1973). Since this method does not make assumptions about the distribution of input data, it has been widely used for detecting statistically significant positive or negative trends in hydrological and climatic variables (Gocic & Trajkovic 2013; Pirnia et al. 2019).

The steps for calculating the statistic of this test are as follows:

The final stage involves hypothesis testing. The null hypothesis suggests the absence of a trend and its randomness, indicated by non-statistically significant Z. This null hypothesis is upheld when −Z_a/2 < Z < Z_a/2, with Z_a/2 values representing standard normal deviations (Z-table). Conversely, the alternative hypothesis indicates the presence of a significant trend, with statistically significant Z. In this study, a significance level of α = 0.05 is used, making the Z-table value 1.96 (Gan 1998). In climate change studies, two general approaches have garnered attention: utilizing a single model (Teixeira et al. 2013) and combining outputs from multiple models (Tebaldi & Knutti 2007; Gohari et al. 2014; Majone et al. 2016; Zamani et al. 2017). In addition to addressing the uncertainty associated with GCM models and employing model ensembles, evaluating the performance of these models is crucial. Utilizing models with superior capabilities in simulating climate variables for a specific region can help reduce uncertainties further. This study focuses solely on uncertainties related to Atmosphere–Ocean General Circulation Model (AOGCM) models. The effectiveness of each AOGCM is assessed using the ANOVA method.

After assessing the trends in precipitation changes at the Aji-Chay station during a future time period, in order to ensure the accuracy of the models under examination and to identify variations in mean precipitation values during that period, a one-way ANOVA was employed, and the relevant hypotheses were tested. However, as ANOVA assumes equal variances between groups, the Levene test for variance equality was conducted as well. Furthermore, to compare means between two time periods with unknown population variances, an independent samples t-test was utilized. This test essentially conducts multiple independent sample t-tests with a shared error level. As mentioned earlier, it determines whether there are significant pairwise differences among the models under examination.

The objectives of ANOVA include testing for statistical differences in the means of a continuous variable among two or more groups, assessing statistical differences in the means of a continuous variable within two or more time intervals, and examining statistical differences in the means of a continuous variable among two or more treatments (Javankhah Amiri & Khatami 2005: 13). In its simplest form, ANOVA offers a statistical test that assesses the equality of means among different groups without specifying which groups differ from one another. Therefore, the Tukey test was used to identify distinct groups.

In this test, comparisons between means are made against a fixed value, irrespective of the specific means under examination. Statistical significance between two means is established when their difference surpasses the predetermined constant value. The response variable needs to be quantitative and measured on a relative interval scale, while the independent variable must be qualitative, with at least two levels or categories. The distribution of the quantitative variable within each level of the qualitative variable (groups or treatments) should be normal. Homogeneity among the variables should also be ensured, and this can be assessed using tests such as the Hartley and Levene tests (which evaluate the independence of one sample selection from other selections) (Rezai & Shoberiri 2015).

The assumptions for the Tukey test are as follows:

• 1.

  Independence: Populations I and j should be independent of each other.

• 2.

  Equal variances: The variances of both populations should be equal (Amiri & Karami 2012: 505).

Artificial neural networks are a well-known evolutionary model inspired by the neural networks found in the human body (Kothari & Gharde 2015; Tahani et al. 2016). This model can identify and simulate relationships between input and output variables. Artificial neural networks are a suitable model for simulating both linear and non-linear relationships, which is why they have been considered as a suitable simulation model in a wide range of environmental studies (Wang et al. 2006; Kothari & Gharde 2015; Noori & Kalin 2016; Prasad et al. 2017).

The integration of wavelet and artificial neural network introduces a groundbreaking paradigm within artificial intelligence, recognized as the WNN. This model emerges as a feasible substitute for recurrent neural networks (RNNs), demonstrating the ability to effectively employ any desired non-linear function. The governing algorithm of this network encompasses two fundamental processes: the self-organization of the network and error reduction. In the initial stage, the network's structure is delineated by employing the wavelet as an activation function. Through this iterative procedure, network parameters are adjusted, maintaining the network's framework and advancing to the next phases. In the following stage, the network estimator addresses simulation inaccuracies by utilizing algorithms embedded within the neural network design. Each hidden layer unit, which integrates a wavelet as its activation function and a time square window, adjusts its parameters by following optimization principles. This inherent flexibility enables the wavelet to function similarly to a behavior function. Through this transformative process, the original signal can be decomposed into its constituent basis signals.

In which X_i and Y_i represent the ith observed and simulated data, respectively, and are the overall means of Y_i and X_i in the population, and n is the total number of samples evaluated (Panahi & Khormabad 1398: 148). A smaller value for statistical metrics such as RMSE, Mean Bias Error (MBE), and MAE being closer to zero is better. The values of R² and R range from zero to one, and the closer they are to one, the better the data fit (Ahmadi et al. 1398: 278).

Figure 3 illustrates a notable decrease in precipitation during the study period, particularly in February. This decrease is significantly larger than the historical average variability for the region, indicating a deviation from expected seasonal patterns. For instance, the average February precipitation for the baseline period (1981–2010) was 38.54 mm. However, in February 2024, the observed precipitation was only 35.24 mm, representing an 8.59% decrease. This decline is statistically significant, with a 99% confidence level, suggesting that it is unlikely to be due to natural variability alone. This observed deviation from historical trends aligns with concerns about the impact of climate change on regional precipitation patterns. Global warming is expected to lead to increased aridity in some regions, and the observed decrease in February precipitation could be an early manifestation of this trend.

To further investigate this possibility, future research should focus on analyzing long-term precipitation data and comparing the data with climate model projections for the region. This will help to determine whether the observed decrease is part of a long-term trend and whether it can be attributed to climate change. As seen in Figures 5 and 6, the downward trend of rainfall in July and August during the study period is clearly visible. This is in line with predictions about the effect of global warming on rainfall patterns.

Furthermore, a twofold decreasing trend is noticeable in June during the observational period and in the CanESM5 model for the future period (2025–2065) under the SSP5.85 scenario, indicating the presence of a drought trend in the region. On the other hand, the CanESM5 model simulates an increase in average rainfall during March and April compared to the baseline period. These increases are predicted to be 1.90 and 2.035 mm for March and April, respectively. The observed trends imply potential alterations in the seasonal weather patterns of the study region. This could impact the amount and characteristics of precipitation throughout the year, potentially as a result of global warming. These results align with the research conducted by Azizi-Ebrahim et al. (2023) and provides strong evidence of the impact of climate change on rainfall patterns in the study area. Both the INM-CM4 and MRI-ESM2 climate models project a decrease in April precipitation exceeding 1% for the near future under the SSP5.85 scenario. MRI-ESM2 predicts a more substantial decline of 1.98 mm (13.76%), whereas INM-CM4 suggests a decrease of 2.035 mm (7.08%). Compared to historical data (baseline period), future projections using the SSP5.85 scenario in the studied climate models suggest varying decreases in precipitation across the study area for the 2025–2065 period. These projected changes range from a slight decrease of 0.146 mm to a more substantial decline exceeding 2.127 mm.

First, we defined a historical period (baseline) to serve as a reference point. Then, we compared the precipitation levels during this period with those expected in the future. This comparison forms the basis for our key findings. A statistical technique called ANOVA was used to assess the uncertainties associated with the climate models employed in this study. Our analysis revealed a statistically significant decline of 3.37% in monthly precipitation across the watershed area during the observation period. This decrease is considered significant with a confidence level of 95%. Notably, the CanESM5 model projects an even steeper decline of 3.916% in watershed precipitation with 95% confidence, highlighting the potential severity of these future changes.

Interestingly, the INM-CM4-8 and MRI-ESM2-0 models exhibited a higher level of confidence in their projections compared to historical data (baseline period) at a 95% confidence level. This suggests lower uncertainty in their predictions. However, the CanESM5 model stood out with the highest level of confidence when forecasting precipitation under scenario 5.85 for the study period (2025–2065). These findings highlight the exceptional ability of the CanESM5 model to simulate precipitation patterns within the watershed area (refer to Table 4 for details).

Table 4

Summary of factorial analysis of variance

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The CanESM5 model predicts slightly more rainfall (−5.91 mm) for the future compared to that observed in the past (−5.05 mm). This difference might be because real-world rainfall data mainly reflect geographic aspects such as latitude and altitude. The CanESM5 model, however, is more complex and considers additional factors such as ocean currents, air circulation patterns, and even climate change. Interestingly, the similarity between the observed baseline rainfall and the CanESM5's projection for the future might be attributed to their shared utilization of geographical factors to simulate rainfall. These factors include latitude, altitude, and distance to the ocean, all of which can significantly impact precipitation levels.

In contrast, the WNN model predicts a 5.92% increase in future rainfall for this region, contradicting the CanESM5 model's prediction. This difference in forecasts might be due to the way each model simulates climate. CanESM5 is a global model that utilizes complex equations to represent various climate processes on a large scale. Conversely, the WNN model focuses on a specific region and utilizes an artificial neural network, which is a type of machine learning, to simulate climate processes. In simpler terms, CanESM5 learns from global weather data, while WNN learns from data specific to this region.

Table 5 presents the results of a statistical test (Tukey test) comparing rainfall data from historical observations (1987–2020) with predictions from future models (2025–2065) for the study area. The test results are significant, indicating their reliability at a 95% confidence level. According to the table, only the CanESM5 model shows acceptable variation in rainfall predictions for March and April compared to historical data (observational period). These indicate that the CanESM5 model's predictions for these months are statistically similar to past observations. Furthermore, when comparing the simulation results of the CanESM5 model under the SSP5-8.5 scenario for the period 2025–2065 to the period 1987–2020, these results are consistently validated at a monthly scale. The performance of the INM-CM4-8 and MRI-ESM2-0 models is considered acceptable; however, their performance in replicating the frequency distribution of the observational period is weaker. Despite this, their performance in evaluating the impacts of climate change on averages at all time scales remains adequate. Consequently, the evaluation results for the INM-CM4-8 and MRI-ESM2-0 models are considered less reliable.

Table 5

Partial output of the interaction effect of precipitation from the observational period relative to the study models of the future period in Tukey HSD test

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Neural networks require careful preparation of rainfall data for accurate predictions. The recommended approach involves cleaning the historical data by removing outliers and standardizing it for consistency. These preprocessed data are then divided into two sets: training data and testing data. The training data help the neural network learn patterns between past and future precipitation. Finally, the unseen testing data are used to evaluate the model's accuracy in predicting future rainfall.

The results of these predictions are provided in Table 6. It is evident from this table that the performance and accuracy of the models, obtained through the MIR wavelet decomposition, have improved due to their similarity to the rainfall signal and its inherent complexity. The high accuracy achieved by the neural network-wavelet model can be attributed not only to the preprocessing and wavelet-based segmentation of sub-signals but also to the amplification of the relative weight of each sub-signal's influence through the decomposition process.

Table 7 illustrates the precipitation change predictions for the upcoming decade at the Aji-Chay station. This table is divided into two sections. The first section presents forecasts from the CMIP6 models analyzed during the baseline period over the past three decades (1975–2014). In the MRI-ESM2 model, the annual precipitation amounted to 337.57 mm; in the CanESM5 model, it was 290.61 mm, and in the INM-CM4 model, it reached 344.42 mm. For the subsequent four decades (2025–2065), the projected annual precipitation is 313.11 mm in the MRI-ESM2 model, 274.14 mm in the CanESM5 model, and 316.14 mm in the INM-CM4 model. This pattern indicates a decreasing trend in precipitation over these four decades compared to the previous three decades. In the next decade (2025–2035), this trend, observed across all CMIP6 models under the SSP5.85 scenario, shows a reduction of more than 5%. Specifically, this reduction is equivalent to 5.0%. Consequently, it implies an anticipation of an average annual precipitation decrease of more than 5% at the Aji-Chay station in the next decade.

Table 7

Average annual rainfall predicted by different models over the next two decades at Tabriz Synoptic Station

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In the upcoming decade (2025–2065), the projected precipitation amount for the Aji-Chay station is 322.23 mm, as indicated in the first section of the table. The recorded precipitation for this station in the preceding decade (1981–2020) was 304.22 mm. Consequently, based on the findings of the examined CMIP6 models, the estimated percentage decrease in precipitation for the next decade at the Aji-Chay station is approximately 5%.

The second section provides the forecasts generated by the WNN.

For the upcoming decade (2025–2035), the projected value for the WNN is 5.04%. This figure indicates an expected average annual precipitation increase of about 5.04% at the Aji-Chay station in the next decade.

Neural network models are sensitive to input data, which can lead to variations in their outcomes. In this investigation, precipitation data from 1981 to 2020 were used to train the neural network model in the Aji-Chay watershed. Not all factors influencing precipitation changes in this watershed were accounted for in the analysis. Consequently, relying solely on the presented precipitation percentage values, the WNN (5.92%) and CanESM5 (5.40%) models demonstrate proximity to each other. This underscores the model's satisfactory performance in replicating the climate of the examined region. The study forecasts a significant reduction in precipitation for the Aji-Chay watershed under the SSP5.85 scenario. This decline in precipitation could have severe implications, such as diminishing agricultural productivity due to reduced rainfall, resulting in lower crop yields and an increase in food prices. The reduced precipitation also increases the risk of drought in the Aji-Chay watershed, which could potentially result in significant economic and environmental consequences.

Rainfall, a crucial element of the planet's water cycle, has a profound impact on human endeavors. The effects of rainfall are intricately linked to both its volume and characteristics, with alterations in precipitation amounts and patterns being significantly influenced by shifts in climate. This research aimed to forecast changes in precipitation within the Aji-Chay watershed between 2025 and 2065 by comparing models from the CMIP6 under the SSP5-8.5 scenario with a WNN. Furthermore, to evaluate the uncertainty related to CMIP6 models, an ANOVA was utilized. The results indicated that, in the models analyzed, there was a decrease in precipitation for the future period compared to the baseline period. The decrease ranged from −0.146 to more than −2.127 mm under the SSP5.85 scenario for the years 2025–2065. During the observational period, a statistically significant decreasing trend of 3.37% in monthly watershed precipitation was identified at a significance level of 0.05. The CanESM5 model highlighted this trend by predicting a decrease in precipitation in the watershed at a rate of 3.916. There is a 95% confidence level associated with this prediction. The accuracy evaluation of the CMIP6 models indicated that the CanESM2 model performed well in simulating precipitation in the study area, consistent with previous studies that identified it as the optimal model for the Aji-Chay watershed. Furthermore, the simulated precipitation using the hybrid WNN model at the Tabriz station for the period 2025–2065 was lower than that of the CanESM5 model. However, for the period 2025–2065, the simulated precipitation of the INM-CM4 and MRI-ESM2 models exceeded that of the CanESM5 model.

One of the limitations of this study is that it only measured changes in rainfall over time. Meanwhile, other factors such as changes in temperature, vegetation and land use can also affect changes in rainfall. This study did not consider these factors and can be proposed as a suggestion for future studies.

In general, the results of this study highlight several key findings. Firstly, it is evident that the precipitation parameters have been effectively downscaled by the fine-scale model. The modeling and downscaling capabilities of the past climate at the study station are generally well established. Furthermore, the results indicate that the downscaled data from CanESM5 closely match the actual climate parameters of the region. This suggests that these downscaled data can be employed to provide more accurate future climate projections at the station level. Utilizing statistical models in conjunction with these data can significantly contribute to enhanced resource management, particularly in the context of water resources.

Considering the non-stationary and non-linear characteristics of precipitation time series, the utilization of a WNN is essential for accurate prediction and simulation. The wavelet transformation separates the signal into high and low-frequency components, providing access to multi-scale signal features and significantly enhancing the accuracy of the model. Additionally, in the hybrid model, the accuracy of peak precipitation prediction, which holds great significance in precipitation modeling, is notably enhanced.

Another important point to consider is that an increase in the delay in the output signal can decrease the accuracy of predictions in the WNN model. The use of the Morlet wavelet has been shown to enhance the prediction accuracy of the model. ANOVA results show both homogeneity and non-homogeneity of precipitation indices, with the predicted precipitation demonstrating homogeneity at a 99% confidence level, indicating it is part of a statistical population. This highlights the high accuracy of the prediction method, which can be credited to the complex wavelet shape of the Morlet wavelet. By breaking down the signal into simpler wave components, the model can better model random data, resulting in improved prediction accuracy compared to traditional methods.

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

The authors declare there is no conflict.