Introduction

The climate change phenomenon and impacts of climatic variables (i.e., temperature and precipitation) have been one of the main elements in the prediction of changes in hydrological systems, which due to the importance of groundwater resources management and predicting the level of quantitative changes in future years, the development of a comprehensive model for estimating such objectives is always felt.

To predict climate parameters, different methods have been examined by researchers which have led to providing models for predicting climate change. In a general division, climate change prediction models can be classified into two main categories: (1) physical models, (2) statistical models.

Physical models have a function commensurate with the main components of each region in predicting climate parameters for future years. The main weakness of physical models is that they cannot be used directly for regional or point forecasts. Physical models need to be downscaled to improve their predictions at local scales by applying regional components to them. Downscaling is actually the process of moving from large-scale predictors to local-scale ones.

In general, downscaling methods are divided into two main categories: (1) dynamic method, (2) statistical method, in which various researchers have conducted various researches. Also to evaluate and predict groundwater level, various models have been presented on the basis of the various methods, which are mentioned on a case-by-case basis in the following.

In order to predict climate parameters and also evaluate the impact of climate change on the performance of groundwater resources, researchers and scholars have conducted various studies based on the use of different statistical methods and models (IPCC 2007) examined global warming and how increasing atmospheric CO2 concentrations cause climate sensitivity. He showed that water vapor, CO2 and other rare atmospheric gases are all effective absorbers of infrared radiation. These gases absorb long-wave radiation emitting from the earth's surface and re-emit radiation and increase the earth's surface temperature. He calculated that doubling the concentration of CO2 in the atmosphere would increase global temperatures by 3–4 °C.

Zarghami et al. (2011) utilized the observations acquired from six synoptic stations in East Azerbaijan Province to study climate change and its effects on runoff in three basins. In this research, the large-scale HadCM3 model has been downscaled by the LARS-WG model under scenarios A1B, B1 and A2 for the periods leading up to 2020, 2050 and 2100. The results showed that according to Scenario A2, an average temperature increase of about 2.3 °C and a decrease in annual rainfall of about 3% are expected to happen in the middle of the twenty-first century. These changes alter the region's climate from semi-arid to arid, based on the De Martonne index. Also in this study, to investigate the effect of these changes on runoff, an artificial network model has been used, which shows the reduction of runoff in the three studied basins.

Koohi Kouhi and Sanaei Nejad (2014), with the aim of providing a perspective on the future status of temperature and precipitation limit events using the outputs of the HadCM3 model and also the SDSM model, managed to average downscaling and limit indices of two variables including the maximum temperature daily rainfall within the Kashfroud Basin. The data used to evaluate the model included large-scale atmospheric variables obtained from the daily reanalyzing data of NCEP (1961–2001) and the regional mean precipitation and maximum temperature of this basin during the statistical period of 1969–2001 and 1972–2000, respectively. The results showed that the average maximum temperature during the next three periods increased significantly compared to the base period and the average monthly precipitation decreased compared to the base period.

Crossman et al. (2013), by combining the HBV and INCA-P models and using downscaled statistical data obtained from the CGCM3 model for two scenarios A1b and A2, evaluated the effects of climate change on the hydrology and water quality of the Black River, a tributary of Lake Simcoe, Canada, for the period of 2000–2100. Both scenarios predicted the highest rainfall during the winter and the highest temperature increase during the summer. Under both scenarios, more rainfall and higher temperatures in winter caused the snow to melt earlier in the spring. Also, increasing the temperature in summer reduces the flow. Despite the differences between the two scenarios, both showed an increase in total phosphorus loads entering Lake Simcoe in the twenty-first century, especially during the winter. In summer, due to the decrease of flow, despite the slow rate of increase in total phosphorus, the amount of this substance exceeded the allowable limit, which caused the phenomenon of nutrition in the river. Due to the long residence time of Lake Simcoe, an increase in the input load at any time can have a negative impact on ecological conditions, nutrient conditions, oxygen levels and fish populations.

Bachelet et al. (2016) used the MICROC5, CCSM4 and CANESM2 climate models, from the CMIP5 model set under the rcp4.5 and rcp 8.5 scenarios to predict temperature and precipitation in the deserts of Southern California. Based on the downscaled results of these three models, the temperature in this area is expected to increase, especially in summer. The rainfall trend in these three models shows an increase in winter and a decrease in other seasons.

Pumo et al. (2016) used the downscaled results of the CMIP5 climate models to predict the flow status of several seasonal Mediterranean rivers. The results of forecasting the flow rate of these rivers under the rcp4.5 and rcp 8.5 scenarios show a decreasing trend, which is greater under the rcp8.5 scenario.

Cousino et al. (2015) examined the effects of climate change on runoff, sediment load and nutrient load in the Maomi River Basin in the USA. In this area, the main cause of nutrient load entry into Lake Erie is agricultural activities known as non-point pollutants. In this study, to predict the future climate situation, four models from the CMIP5 model set under rcp2.6, rcp4.5, rcp6, rcp8.5 scenarios were used. Based on the climate results, all scenarios predict an increase in temperature and rainfall by 2100, in which the increase in rainfall in winter is higher than other seasons. Despite the prediction of increased rainfall, flowrate decreased due to the increase of evaporation in all scenarios. On a seasonal scale, the highest decrease was predicted in summer and the lowest decrease in spring. Sediment load and nutrient load entering the lake in all four scenarios showed a decreasing trend due to the decrease in runoff.

Farzaneh et al. (2011) studied the runoff produced in the Behesht Abad Basin of Northern Karun within a period from 2040 to 2069. To this end, first, using climate scenarios of the coupled 3D model of ocean–atmosphere, the general circulation of the atmosphere and the base period of 1961–1990, they selected the representative model of the region and then, considering the synoptic station of Shahrekord, the steps of statistical regression downscaling of the output of the representative AOGCM model were performed.

The results showed that the final HadCM3 model shows a 49% decrease in total average rainfall and a 30% increase in minimum temperature and a 10% increase in maximum temperature in the future, which will reduce runoff and change the region's climate from semi-arid to arid.

Barret et al. (2013) examined the uncertainty in the estimation of groundwater recharge in future periods in Eastern Canada. In this research, seven downscale climatic scenarios have been selected from diffusion scenarios and GCM methods and the combination of downscaling models has been produced and the recharge of the future period has been estimated by the HELP3 model for the period of 2046–2065. The outcomes of the research revealed that the forecasted recharge is more sensitive to changes in downscaling approaches and the GCM model. The average annual recharge variation varied from 58% increase to 6% decrease compared to the base period of 1961–2000. Due to the wide range of acquired numbers, probabilistic methods have been proposed to improve the results.

ToufanTabrizi (2009) through an experiment examined the effects of climate change on fresh groundwater resources in coastal regions. In this research, the interaction area between saline and fresh water in Deyr and Kangan aquifers located in Bushehr Province was simulated using the MODFLOW and MT3DMS models and future impacts of climate change were investigated under scenarios A1, A2, B1 in the HadCM model. The results showed that the highest saline intrusion toward freshwater was about 390 m and occurred under scenario A2. The lowest saline intrusion toward freshwater was about 230 m.

Ghazavi and Ebrahimi (2019) in a study examined the effects of climate change on groundwater resources in Ilam Province. They utilized the SRES scenarios and HadCM3 model to predict climate change in a period from 2015 to 2030 and also the MODFLOW model for modeling groundwater resources. The results of this study indicate changes in temperature and precipitation between 2015 and 2030 and also the resulting changes in the groundwater aquifer based on the prediction of climate change.

Lee et al. (2019) have conducted studies on the rate of change of groundwater level based on changes in climatic parameters in the Javam River Basin in South Korea. In this research, HadGEM3 model based on Rcp scenarios has been used to investigate and predict climatic parameters of temperature and precipitation. Also, the SWAT model has been used for hydrological modeling and prediction of related parameters. In this study, the rate of change in groundwater resources has been evaluated based on the established SWAT model.

Larocque et al. (2019) conducted a study on simulation methods and parametric studies on groundwater changes based on changes in climatic parameters in Canada. The results of the evaluations made in this study, which comprehensively evaluated the methods of modeling changes of groundwater resources based on climate change in Canada, are: (1) Use a variety of climate models and diffusion scenarios. (2) Promote the use of integrated models if possible. (3) Investigating the effect of long-term climate change on groundwater resources at different scales. (4) Simulate the combined effects of climate change and other pressures. And (5) developing models that cover other parts of Eastern Canada as dictated by stakeholders and water managers.

Nourani et al. (2019) using discrete wavelet transform and nonparametric Mann–Kendall method managed to analyze and study the behavior and trend of rainfall and runoff time series in the Tampa Bay Basin, USA. Also in 2019, they carried out an investigation on the basin of Lake Urmia based on rainfall and runoff time series analysis on the basis of the wavelet transform.

Cao et al. (2011) in a study to investigate the degree of complexity used the multiscale entropy method for rainfall and runoff time series and observed that the results obtained at higher timescales are different from the results obtained at lower timescales.

Some of the other research carried out on this topic within recent years are: Poursaeid et al. (2020, 2021, 2022), Yosefvand and Shabanlou (2020), Malekzadeh et al. (2019a, b), Azizpour et al. (2021, 2022), Zeinali et al. (2020a, 2020b), Bayesteh and Azari (2021), Mazraeh et al. (2023), Rajabi and Shabanlou (2012, 2013), Gerami Moghadam et al. (2022), Fallahi et al., (2023), Mohammed et al. (2023), Azizi et al. (2023) and Amiri et al, (2023).

In the continuation of these studies, in this research, the evaluation and prediction of climatic parameters have been done using the SDSM downscaling model as well as based on the new Rcp greenhouse gas emission scenarios. Also to predict the groundwater level and evaluate the effects of predicted climatic parameters on quantitative parameters of groundwater resources, a model based on the use of the GMDH neural network has been defined and used. It should be noted that the present research is conducted in the form of a case study on the Sahneh Plain in Kermanshah Province, Iran.

Methodology

Study area

In this research, the study area of the Sahneh Plain aquifer in Kermanshah Province is considered. The geographical characteristics and location of this area are as follows:

Sahneh city with an area of about 1612 km2 occupies 6.2% of the area of Kermanshah Province. Sahneh city is located in the east of Kermanshah Province. The Sahneh Plain in the southern and eastern part of the city consists of alluvial lands and surrounding slopes, which has an area of about 170 km2. This plain starts from the heights of Bid-e-Sorkh and ends at the heights of Naal Shekan. Figure 1 shows the geographical location of Sahneh Plain along with the location of piezometers located in the area.

Fig. 1
figure 1

Location of study area in Iran

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The Gamasiab River is the main river in the region. The Gamasiab River with a length of 320 km and an average annual discharge of 2.5 m3/s is one of the largest rivers in Iran. The catchment area of this river is 3264 km2.

The study area of Sahneh-Bistoon Plain is geologically located on the border between the highlands of Zagros and Sanandaj-Sirjan. Figure 2 shows the geological and aquifer map of the area.

Fig. 2
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Geological map and aquifer location

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The average rainfall of the region is 564.39 mm per year, which in February with 96.27 mm has the highest rainfall per year and according to the De Martonne method, the region has a semi-arid climate.

SDSM model

This model establishes statistical relationships between large-scale data behaviors (predictors) and local data (predictable) based on multiple linear regression methods. These connections are made using station observed data and the outputs of general circulation models in the same observation period. It is assumed that these relationships will be true in the future; in other words, the basic assumption in the statistical downscaling is independent of the time of these relationships. Before performing the downscaling process with this model, the observed data and the data of the general circulation models are normalized according to their mean values and standard deviation in the desired period. This is because general circulation models cannot simulate the local climate as well as monitoring, so comparing the two before normalizing can lead to unreasonable correlations.

Predictive variables provide information about the large-scale state of the atmosphere, while predictable variables specify the state of the atmosphere on a point/local scale. The statistical downscaling process in the SDSM model is performed in the following steps: (a) data quality control: preliminary evaluation of downscaling capability by predictor/large-scale variables. At this stage, predictive data are evaluated from the point of view, the number of data, maximum data, minimum data and suspicious and missing data. (b) Screening variables: The relationship between monitoring data (predictable) and large-scale data (predictor) has different strengths and weaknesses. At this stage, the main goal is to determine the strongest relationship between predictors and predictables. At this stage, 3 main issues have been evaluated: seasonal correlation, partial correlation and distribution chart. (c) Calibration: The large-scale variables introduced in the previous steps are used to determine multivariate linear correlation relationships. The timescale of statistical models designed at this stage can be monthly, seasonal or annual. The standard variance and standard error of the model are specified. In other words, in this stage, annual, seasonal and monthly statistical models are made developed based on multiple equations and using predictive and daily predictive data. (d) Data Generation: At this stage, several series of current climate conditions are created using observational forecasters. It can be evaluated immediately after the statistical model is designed. The SDSM random component can help us produce different series of simulated data (up to 100 series) that have the same statistical characteristics; however, the daily values of each series are different. (e) Analysis of observed and downscaled data: In this stage, the following analysis is performed on the monitored and downscaled data. It should be noted that these analyses are performed on annual, monthly and daily scales. (f) Scenario Generation: At this stage, daily data of the predictable variables for upcoming decades are generated using the downscaled equations created in the calibration stage and general circulation model data. The general circulation model predictors should be normalized to a reference period and available for all variables used in the calibration stage.

The algorithm and procedure for predicting climatic parameters of temperature and precipitation are shown in the flowchart of Fig. 3.

Fig. 3
figure 3

Flowchart of prediction procedure of climate parameters in SDSM model (Wilby and Dawson 2007)

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Data of climate parameters prediction model

In this study, the first step is to predict climatic parameters of temperature and precipitation for a period from 2020 to 2060 based on Rcp greenhouse gas emission scenarios. In this regard, using the SDSM downscaling model, climatic parameters are predicted based on three scenarios: Rcp2.6, Rcp4.5, Rcp8.5.

Two basic datasets are needed to create the SDSM model. The first set is the time history of the measured data (i.e., daily data) from the synoptic stations of the Sahneh Plain region, where the station position and the characteristics of the observational data are described in Table 1.

Table 1 Characteristics of synoptic station and observed data
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The second dataset is the NCEP model data (large-scale predictive data) that initially must be obtained to implement downscaling. These data are obtained from the website of climate data (https://climate-scenarios.canada.ca/?page=bccaqv2-data) based on the selection of the study area location. The specifications and range of predictive data acquisition are shown in Fig. 4.

Fig. 4
figure 4

Region for obtaining large-scale climatic data

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In this research, four climatic parameters are modeled based on predictive (large-scale) climatic data and observed data as follows:

• Climatic parameters modeled in the SDSM model:

  1. 1.

    Daily maximum temperature: T_max

  2. 2.

    Minimum daily temperature: T_min

  3. 3.

    Daily average temperature: T_mean

  4. 4.

    Daily precipitation: P

Prior to develop the SDSM model and predict climate parameters, pre-processing is performed on the measured data of the Pol-e-Chehr station (Gamasiab river). The purpose of this pre-processing is to control the number of unmeasured data (Missing data) and data with incorrect values (Outlier Data) whose report is based on the codes created in the MATLAB software as described in Table 2.

Table 2 Results of pre-processing on observed data
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In the pre-processing stage of the observed data, graph outputs are presented annually based on four considered parameters for a period from 1987 to 2017 (see Figs. 5, 6, 7, 8).

Fig. 5
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Maximum temperature parameter based on observed data of Pol-e-Chehr synoptic station

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Fig. 6
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Minimum temperature parameter based on observational data of Pol-e-Chehr synoptic station

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Fig. 7
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Average temperature parameter based on observational data of Pol-e-Chehr synoptic station

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Fig. 8
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Precipitation temperature parameter based on observational data of Pol-e-Chehr synoptic station

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Greenhouse gas emission scenario

Any change in the concentration of greenhouse gases in the Earth's atmosphere causes a change in the balance between the components of the Earth's climate system. But how much of these gases will enter the Earth's atmosphere by human societies in the future, and consequently what will happen to the Earth's climate system, is not certain. Therefore, it is presented in a completely uncertain way and under different scenarios. In its fifth assessment report (AR5_Fifth Assessment Report), the Intergovernmental Panel on Climate Change used the new RCP scenarios to represent the trajectories of different concentrations of greenhouse gas emissions. The new emission scenarios have four key trajectories named RCP6.5, RCP4.5, RCP2.6 and RCP8.5, which are named based on their radiation emission in 2100 [6,7].

In this study, three new greenhouse gas scenarios (Rcp2.6, Rcp4.5, Rcp8.5) are used to predict climatic parameters.

Groundwater level evaluation and prediction model

In this study, in order to evaluate and predict the quantitative changes of groundwater resources based on climatic parameters, a model based on the use of artificial neural network method is developed. According to various studies, the use of artificial neural networks to obtain relationships between different parameters has been very efficient. This is important in predicting models and creating relationships between parameters that do not have a clear relationship between themselves and leads to impressive results.

Artificial neural networks take a series of observed data as inputs and, after judgment processing based on training, determine the relationship between inputs and outputs.

Neural networks can be used mainly in predicting time series and examining the relationship between them, but in some cases, neural networks have limitations such as the need for high input data to train the neural network and the lack of providing enough information about relationships between input and output parameters. Based on it and due to the weaknesses of neural network algorithms in predicting and presenting the desired model, the group method of data handling (GMDH) was created.

The GMDH neural network algorithm was developed in 1966 by Ivakhnenko as an extensive high-order polynomial. In designing the basis of GMDH neural networks, the aim was to prevent growth and divergence and also to link the shape of the network structure to one or more numerical parameters so that by changing them, the structure of the neural network would change. This neural network builds a self-regulatory model that establishes and presents relationships with output data based on primary input data. The basis of this algorithm is based on creating polynomials as described in Eq. (1). In this algorithm, initial data are divided into two categories: training and verification. The general procedure of this algorithm is on the basis that input data are initially given to the GMDH network. In this step, a combination of initial data is created and sent to the first layer. Then, inputs of this layer are sent to the next layer as a combination of classified data. This procedure continues until the results of layer n + 1 are better than layer n. If this event is reversed (layer n + 1 results are not better than layer n based on the convergence test) the layer creation cycle stops.

$$\hat{y} = a_{0} + \sum\limits_{i = 1}^{m} {a_{i} x_{i} } + \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{m} {a_{ij} x_{i} x_{j} } + \sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{m} {\sum\limits_{k = 1}^{m} {a_{ijk} x_{i} x_{j} x_{k} + \cdots } } } }$$
(1)

In fact, the main purpose in this algorithm is to find the coefficients a in the polynomial of Eq. (1). In this algorithm, if we consider X as the inputs of the algorithm and Y as the output, the schematic of the algorithm is in the form of Fig. 9.

Fig. 9
figure 9

Schematic of GMDH artificial neural network

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The numerical data group classification method (GMDH) is one of the neural network models that is used in identifying, predicting and classifying data. GMDH is a network statistical training technology that is the result of cybernetic research including self-organizing systems, control theory and information, and computer science. GMDH is a regular process to overcome the statistical weaknesses of the neural network. In fact, the main purpose of the GMDH network is to build a function in a network based on the quadratic transfer function. The effective input variables, the number of layers and neurons in the hidden layers and the optimal structure of the model are determined automatically. GMDH is widely used for modeling complex systems and predicting multivariate processes.

In the present study, due to the relationship between the average groundwater level in the Sahneh plain area (based on piezometric groundwater level data) and climatic data (temperature and precipitation), which included four main parameters (i.e., T_max, Tmin, T_mean, P), the GMDH neural network is designed based on the provided description.

Results and discussion

The results of this study are presented in two main sections (1—results of predicting climatic parameters for the period of 2021–2060, 2—results of establishing a groundwater level forecasting model of Sahneh Plain based on the GMDH neural network).

Prediction of climate parameters

The procedure for predicting climatic parameters based on the SDSM model is discussed in detail in Sect. 3.2. The following are the results of forecasting four climatic parameters, i.e., T_max, T_min, T_mean, P for the two datasets of Dataset1 presented in Sect. 3.1, in a period from 2020 to 2060.

In order to verify and validate the model created for each of the climatic parameters, 80% of the total data are used as model calibration data (modeling) and 20% of them are used as verification data, which their results are presented below (Fig. 10). The results presented in this section indicate the actual amount of data (measured data) and the predicted values of the generated model.

Fig. 10
figure 10

Validation of SDSM model in predicting four climatic parameters of the research

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Figure 10 shows the verification of the SDSM model created for predicting climatic parameters. According to the bar graphs that show the mean values of four climatic parameters (i.e., maximum temperature, minimum temperature, average temperature and precipitation) based on the model forecast (Red graphs) as well as observed data (green graphs), it is clear that the created model has a high accuracy in predicting climatic parameters. In order to quantitatively evaluate the performance of the model, the amount of computational error between the results of the prediction model and the observed data has been evaluated based on three statistical tests whose results are shown in Table 3. The statistical tests to evaluate the error rate are:

Table 3 Results of statistical tests in the validation climate parameters prediction model
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Root-mean-square error (RMSE)

$${\text{RMSE}} = \sqrt {\frac{{\sum\nolimits_{i = 1}^{n} {\left( {y_{i} - \hat{y}_{i} } \right)^{2} } }}{n}}$$
(2)

Mean square error (MSE)

$${\text{MSE}} = \frac{{\sum\nolimits_{i = 1}^{n} {\left( {y_{i} - \hat{y}_{i} } \right)^{2} } }}{n}$$
(3)

Mean absolute error (MAE)

$${\text{MAE}} = \frac{{\sum\nolimits_{i = 1}^{n} {\left| {y_{i} - \hat{y}_{i} } \right|} }}{n}$$
(4)

Table 3 presents the results of the statistical tests on the performance of the predicted model. Based on the results, it is clear that the model has high accuracy in predicting climatic parameters. Also, the predicted values for the maximum temperature parameter (i.e., T_Max) have the highest accuracy, but for predicting the precipitation parameter (i.e., P) are less accurate. The results obtained from the prediction of four climatic parameters (annual average of each parameter) based on 3 scenarios (i.e., Rcp2.6, Rcp4.5, Rcp8.5) for the period from 2021 to 2060 are presented in Figs. 10 and 11.

Fig. 11
figure 11

Prediction of annual average of maximum and minimum temperatures based on three Rcp scenarios

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According to the results presented in the diagrams in Fig. 10, it is clear that the annual average maximum temperature (T_Max) predicted for the period from 2021 to 2060 based on the Rcp2.6 scenario has lower values than the two scenarios Rcp4.5, Rcp8.5. Also, the annual average minimum temperature (T_Min) predicted based on the Rcp2.6 scenario has lower values.

The results presented in the diagrams in Fig. 11 show the mean annual predicted average temperature and also the mean annual rainfall in the period of 2021–2060 based on the Rcp scenarios. According to the results, it is found that the predicted rate of mean temperature change (T_Mean) is based on the pattern of maximum and minimum temperature changes. Therefore, the minimum and maximum values are predicted in the Rcp2.6 and Rcp8 scenarios, respectively. Considering different greenhouse gas emissions in each of scenarios Rcp4.5, Rcp2.6 and Rcp8.5, the change rate of the obtained predictions has a reasonable trend. To examine the influence of different Rcp scenarios on the values of the predicted average temperature, a comparison between the predicted values based on the three scenarios is illustrated in the graphs of Fig. 12.

Fig. 12
figure 12

Prediction of annual average of mean temperature and precipitation based on three Rcp scenarios

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By evaluating the results of the prediction of the mean annual precipitation in the period of 2021–2060 (Fig. 11), it is clear that the maximum rainfall values are predicted based on the Rcp4.5 scenario. In addition, the forecasts indicate the minimum rainfall values acquired by the Rcp2.6 scenario. For a more accurate assessment of the rainy and low rainfall future years, a comparison between the mean annual precipitation values based on the three Rcp scenarios is presented in the diagrams of Fig. 13.

Fig. 13
figure 13

Comparison between the results of the mean temperature prediction (T_Mean) based on three Rcp scenarios

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Results of groundwater level prediction

In this study, to establish a relationship between the average groundwater level in the Sahneh Plain area (7 wells for which groundwater level data are available) and climatic data (temperature and precipitation) which include 4 main parameters, i.e., T_max, Tmin, T_mean, P, the GMDH neural network is designed based on the description provided in Sect. 3.3.

In this neural network, 85% of the primary data are used as network training data and 15% of the data are used as testing data. The main parameters of the designed GMDH neural network are as follows:

  • The maximum number of neural network layers is equal to 100 layers

  • The maximum number of neurons created in each layer is considered to be 100

  • The alpha parameter, which is used as a criterion for calculating the convergence test, is equal to 0.6. The main purpose of selecting small values for the alpha parameter is to evaluate all possible states of communication between neural network inputs (i.e., 4 climatic parameters) to lead to the best performance model for predicting the groundwater level.

  • The inputs of the GMDH neural network are four climatic parameters of temperature and precipitation, and its output is the average monthly water level of 7 wells in the Sahneh Plain area.

The results of data analysis based on the GMDH neural network indicate the relationship between the input data X and the considered output Y.

The results of the model performance based on the parameters defined for the artificial neural network are presented below. According to the numerical model, the main performance criterion of the model is the accuracy of the groundwater level prediction based on the climatic parameters (i.e., maximum temperature, minimum temperature, average temperature and precipitation). In order to evaluate the created model, using the input observed data (four climatic parameters) and the output observed data (average groundwater level of Sahneh Plain) the model is verified and validated (Fig. 14).

Fig. 14
figure 14

Comparison between the results obtained from the mean annual precipitation prediction based on three Rcp scenarios

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The main data of the research are divided into two groups including 80% (train) and 20% (test), and the error between the values obtained by the model and the observed data is examined based on the statistical tests and mean evaluation and standard deviation of error.

Figures 15, 16 and 17 show the error rate and performance evaluation of the numerical model created based on three categories of data (1—training data, 2—test data, 3—all data). For more detailed examination, the MSE and RMSE statistical tests as well as the mean and standard deviation of error in the results of the model are calculated for the results obtained from the model and shown in the graphs. The results show that the use of the designed GMDH artificial neural network is very efficient studying and analyzing as well as achieving a relationship between the climatic parameters and groundwater level in the plain area and the created model establishes a relationship between the inputs and outputs of the model with high accuracy (Fig. 18).

Fig. 15
figure 15

Results obtained from model validation based on GMDH train data

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Fig. 16
figure 16

Results obtained from model validation based on GMDH test data

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Fig. 17
figure 17

Results obtained from model validation based on GMDH all data

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Fig. 18
figure 18

Results obtained from GMDH validation

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Prediction of groundwater level

According to the created numerical model verified and validated in Sect. 4.2, the groundwater level values are forecasted based on the climate data predicted for the period from 2021 to 2060 based on three scenarios of the greenhouse gas emission. The diagrams in Figs. 19, 20 and 21 show the results of the groundwater level prediction in the Sahneh Plain area based on the three Rcp scenarios.

Fig. 19
figure 19

Results obtained from the monthly prediction of groundwater level in the period of 2021–2060 based on the Rcp2.6 scenario

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Fig. 20
figure 20

Results obtained from the monthly prediction of groundwater level in the period of 2021–2060 based on the Rcp4.5 scenario

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Fig. 21
figure 21

Results obtained from the monthly prediction of groundwater level in the period of 2021–2060 based on the Rcp8.5 scenario

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In the graphs of Figures 19, 20 and 21, the monthly values of the average groundwater level in the Sahneh Plain are shown based on different Rcp scenarios for the period of 2021–2060. Based on the obtained results, it is determined that the average groundwater level in each of the scenarios and based on the values of the climatic parameters (T_Max, T_Min, T_Mean, P) predicted based on the used scenarios has different monthly values.

According to the predicted values of the average monthly groundwater level, it is determined that the highest and lowest groundwater levels are 1343 and 1326, respectively. In addition, the amount of groundwater level changes based on the predicted climatic parameters in each of the greenhouse gas emission scenarios indicates the impact of the Rcp scenarios on groundwater level changes.

Based on the results, it is clear that the trend of groundwater level changes compared to the years prior to the prediction period has a decreasing trend in all three scenarios, so that the maximum level values are always less than 1343 and on the other hand we have experienced a significant drop in water level in different years, which indicates a decrease in the groundwater level in the forecast years in Sahneh Plain. For a more accurate evaluation and comparison between the results obtained from the neural network model prediction using each of the climate change scenarios, the diagrams in Fig. 22 show the groundwater level changes for the years from 2021 to 2060 based on each of the Rcp scenarios.

Fig. 22
figure 22

Comparison of the results of groundwater level prediction in the period of 2021–2060 based on all 3 scenarios

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According to Fig. 22, it is clear that the minimum and maximum values of the groundwater are predicted in the Rcp2.6 and Rcp8.5 scenarios, respectively. In addition, the minimum groundwater level based on the Rcp2.6 and Rcp4.5 scenarios is forecasted to occur in 2056 and 2046, respectively.

Based on the outcomes acquired from each of the emission scenarios, it is specified that the minimum values of the groundwater level predicted in the Rcp8.5 scenario are greater than the two other ones.

By evaluating the results (Fig. 22) it is specified that the change trend of the groundwater level for the prediction years follows no regular path and has many fluctuations between 2021 and 2060 based on variations in climate parameters, but a general decreasing trend in the average groundwater level of the region compared to previous years has been observed and the maximum values of groundwater level more than 1343 in the region are not predicted in any of the scenarios.

Conclusion

In this study, to evaluate the effects of climate change and its impact on groundwater resources, a study based on the numerical method was implemented. In the first step, using the SDSM numerical model, the climatic parameters of the Sahneh Plain region were predicted for the period from 2021 to 2060. After predicting climatic parameters for the Sahneh Plain region, a model was created using the GMDH artificial neural network method. At this stage, based on part of the observed data, the groundwater level prediction model has been verified and validated. The results showed the high accuracy of the model in predicting the groundwater level. In the last stage, based on the climatic parameters predicted in each of the Rcp scenarios, the mean values of the groundwater level were predicted based on the model created for the years from 2021 to 2060. The predicted climatic parameters in the Sahneh Plain region included four parameters: maximum temperature T_Max, average temperature T_Mean, minimum temperature T_Min and precipitation P, which were predicted based on three Rcp scenarios for 2021–2060. The results of forecasting the climatic parameters showed that the maximum and minimum values of temperature were predicted in emission scenarios Rcp8.5 and scenario Rcp2.6, respectively. Also, the values of annual maximum precipitation were predicted in scenario Rcp4.5. The numerical model created to predict the average groundwater level in the Sahneh Plain area has been implemented based on the GMDH artificial neural network method. According to the verification and validation performed on this model, it was determined that the created numerical model had acceptable accuracy in predicting the groundwater level based on the climatic parameters. Based on the results obtained from the groundwater level prediction model, it was determined that the maximum annual average of the groundwater level in the Sahneh Plain area was 1343 and its minimum value was 1340, which according to the trend of groundwater level changes in previous years we have experienced a decrease in the groundwater level in this area. According to the results obtained from the groundwater level prediction, it was found that in all three scenarios from 2046 to 2056, the average annual groundwater level had its lowest values and we need preventive measures, proper management of water resources and serious attention in extracting groundwater resources during this period.