Introduction

Precipitation is one of the most significant water resources to sustain the hydrological cycle. Therefore, its precise and reliable prediction is necessary for water resources planning and management in many sectors (e.g., agriculture and industry). Consequently, more accurate precipitation prediction plays a major role to minimize the damages and losses of extreme events such as drought and floods. Numerous models are used to predict climatic variables, especially precipitation and temperature, which are commonly grouped into two groups: dynamical and statistical approaches (Doblas-Reyes et al. 2013; Navid and Niloy 2018; Schepen et al. 2012). Dynamical models make predictions using multiple equations that represent the fluid behavior in the atmosphere–ocean-land, such as general circulation models (GCM). In statistical models, prediction is based on the relationships between the target predictor variable and atmosphere–ocean-land data including time series models (Islam and Imteaz 2020), multivariate regressions (Nalley et al. 2019; Qian and Xu 2020; Hu et al. 2020), and methods based on artificial intelligence like the artificial neural network (Doblas-Reyes et al. 2013; Woldemeskel et al. 2014; Canchala et al. 2020; Helali et al. 2021a). Statistical models are relatively flexible in model construction and can improve the prediction accuracy depending on the length of the statistical period and the type of available data, although they are unstable to dynamical models (Kim et al. 2020). The applications of machine learning models, especially artificial intelligence models in modeling natural phenomena, have been reported by several studies (Choubin et al. 2014; Modaresi et al. 2018a; Helali et al. 2021a). Studies have shown that using different statistical models such as regression and artificial intelligence methods as well as large-scale teleconnection indices can better predict climate variables such as precipitation (Hartman et al. 2016; Kim et al. 2020; Helali et al. 2021a), runoff (Lee et al. 2020), evapotranspiration (Asadi Oskouei and Helali 2021), and crop yield (Gonsamo et al. 2016; Heino et al. 2020).

Teleconnection indices (e.g., El Niño Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO)) are determined by the large-scale climate variables with repetitive and periodic patterns (annually or decadal returning period) to explain the effect of climate anomalies of a distant phenomenon on regional climate conditions (Gholami Rostam et al. 2020). Synoptic and dynamic analysis of precipitation anomalies also demonstrated the role of westward displacement (sea to land) and eastward (land to sea) components of Saudi Arabia’s high-pressure system (Helali et al. 2021c). Besides, the correlation between the teleconnection indices and climatic and hydrological variables has been extensively studied throughout the world (Gong and Wang 1999; Mekanik et al. 2013; Yang et al. 2019; Helali et al. 2020; Ahmadi et al. 2019). These indices were exploited by the researchers to measure hydrological sensitivity to climate change (Modaresi et al. 2018a; Kingston et al. 2006; Loboda et al. 2006) and in water resources planning due to their effect on climate changes and their impact on improving accuracy and time lag predictions (Dariane et al. 2019; Helali et al. 2021a). Pourasghar et al. (2012) revealed that changes in the annual precipitation of the southern part of Iran were mainly influenced by ENSO and Indian Ocean Dipole (IOD) indices so that in the negative phase of IOD, the anomalous moisture flux is directed towards the north. As a result, it decreases the moisture injection from the south, while fluctuations in late winter and early spring precipitation are strongly affected by changes in the Mediterranean Sea. Choubin et al. (2014) represented that teleconnection indices would explain up to 81% of the variance in Bakhtegan-Maharloo basin droughts, and those indices could better predict the drought using the neuro-fuzzy model rather than the regression model. Kinouchi et al. (2018) used teleconnection indices in two basins in Thailand and predicted seasonal precipitation using the multilinear regression (MLR) model and highlighted that equatorial SOI (EQ-SOI) and indices related to sea surface temperature (SST) could be used to quantify seasonal precipitation in the positive phase of EQ-SOI. Moreover, it is found that the LSSVM hybrid model was able to more accurately predict monthly precipitation of the Yangtze River basin by using teleconnection indices as predictor variables (Tao et al. 2017). Dariane et al. (2019) concluded that Pacific Decadal Oscillation (PDO), TNI, and NINO3 were the most important indices in long-term precipitation prediction using a genetic algorithm in some meteorological stations in Iran. Dehghani et al. (2020) demonstrated that seasonal precipitation had the highest correlation with Southern Oscillation Index (SOI), NAO, and PDO in Iran’s basins. The authors stated that those teleconnection indices could be used as predictor variables at the basin scale, as well. Kim et al. (2020) showed that teleconnection indices could more satisfactorily forecast the seasonal precipitation of most seasons in the Han basin of South Korea using a multivariate regression model. However, it failed to predict the summer precipitation accurately. Using teleconnection indices, Qian and Xu (2020) studied the autumn precipitation in the Yangtze River basin of China using Bayesian linear regression (BLR) and multilinear regression methods (MLR) and showed that the BLR method had more satisfactory results than the MLR method and can be used in planning water resource management of this basin. Based on a synoptic-dynamic analysis, Helali et al. (2021c) showed that the seasonal and annual rainfall anomalies in Iran basins at different intensities of the ENSO were more than the different phases of ENSO.

Literature review shows a case relationship between teleconnection indices and climatic variables, especially precipitation, and therefore, it cannot be used operationally in the comprehensive and regional management of precipitation and water resources (Ruigar and Golian 2015; Kinouchi et al. 2018; Kim et al. 2020). On the other hand, the correlation between teleconnection indices and precipitation has been studied on a station and point scale, with sometimes contradictory results in neighboring areas (Ghasemi and Khalili 2008; Ahmadi et al. 2019) due to the lack of disproportion of the spatial scales of teleconnection indices and studied stations. Moreover, most studies have investigated the correlation and prediction of precipitation with teleconnection indices in limited seasons (Dehghani et al. 2020; Qian and Xu 2020; Helali et al. 2021a). Using different forecasting models also showed that intelligent structure models are more efficient and accurate in precipitation forecasting (Kinouchi et al. 2018; Xiao 2019; Kim et al. 2020; Zhu et al. 2020). Machine learning models (MLMs) are widely applied to solve hydrological problems. The significance of MLMs is the ability to plot the input–output patterns without prior knowledge of the factors affecting the forecast parameters (Najah et al. 2011; Hipni et al. 2013; Ridwan et al. 2021). The MLMs, the most popular intelligent methods, learn from the patterns of input datasets (training data) to model and predict non-linear variables and solve complex problems in prediction of natural hazard and phenomena (Kalantar et al. 2021; Seydi et al. 2022). The ML algorithms accurately and rapidly model complex features and a large number of inputs. The outperformance of ML-based algorithms was reported in many applications (Kalantar et al. 2021). MLMs are artificial intelligence (AI) used to induce regularities and patterns, providing easier implementation with low computation cost, as well as fast training, validation, testing, and evaluation, with high performance and simplicity compared to physical models (Mekanik et al. 2013). The continuous advancement of MLMs over the last two decades confirmed their suitability for precipitation with an acceptable rate (Mosavi et al. 2017, 2018). Anochi et al. (2021) evaluated the different machine learning models for precipitation prediction over South America. The results showed that the machine learning models could produce predictions for different climate seasons with minimum errors of 2 mm in most of the continent in comparison to satellite-observed precipitation patterns. Helali et al. (2021a) emphasized that the MLP model was more accurate than the MLR model in predicting spring rainfall in Iran’s basins. Helali et al. (2021b) analyzed the last spring frost (LSF) and chilling (LSC) considering the ENSO in Iran. Their results highlighted that the probability and occurrence date of the LSF and LSC (with different base and critical temperatures in ENSO phases) were correlated by precedence and latency in the whole period.

Considering the climate and also the importance of seasonal precipitation in an arid and semi-arid region, this study tried to comprehensively analyze the significance and correlation between teleconnection indices and seasonal precipitation in basins and sub-basins of Iran to select the most appropriate predictor variable using 4 simulating models (i.e., generalized regression neural network (GRNN), multi-layer perceptron (MLP), least squares support vector machine (LSSVM), and multilinear regression (MLR)). Then, the efficiency of statistical and intelligent models in seasonal precipitation simulation using teleconnection indices (as predictor variables) was analyzed and evaluated by the coefficient of determination (R2), root mean square error (RMSE), mean bias error (MBE), and scatter index (SI) statistic tests.

Data and methodology

Study area

Iran is in arid and semi-arid part of the world, a country in Western Asia with mean annual precipitation of less than one-third of the global average (Salehi et al. 2019; Biabanaki et al. 2013). Iran is divided into 6 main basins and 30 sub-basins covering various climates (Fig. 1). The areas with a lower density of the stations are located in hot deserts, having almost no precipitation. From 1987 to 2015, the maximum (i.e., Talesh sub-basin) and minimum (Hamoon-Hirmand sub-basin) mean annual precipitations were 1253.6 mm and 82.3 mm, respectively. The monthly precipitation data was recorded by the Islamic Republic of Iran Meteorological Organization (IRIMO) and the Ministry of Energy. A total number of 717 stations (117 synoptic stations and 600 rain gage stations) were selected out of 2300 available stations in terms of sufficient statistical length (1987–2015) and continuous data with no gaps. The homogeneity of the dataset was examined against the run-test (Helali et al. 2020), and the amount of seasonal precipitation (autumn, winter, and spring) was determined per sub-basin using the Thiessen method (Table 1). The summer precipitation was excluded due to very limited or no precipitation in the arid and semi-arid climate of the region. According to studies by Masoudian (2005) and Masoudian and Ataei (2005) in Iran, precipitation mainly occurs in the autumn, winter, and spring seasons, while the summer precipitations are limited to some parts of Iran. Moreover, the spring starts in April and ends in June. The autumn begins in October and ends in December, and the winter arrives in January and ends in March. The characteristics (i.e., area, number of stations in each basin and sub-basin, mean autumn, winter, spring, annual precipitation, and the average altitude) of each sub-basin are shown in Table 1. Due to low precipitation in the arid zone, the summer precipitation was omitted from the modeling. The teleconnection indices for this study are listed in Table 2. The teleconnection data set were downloaded from the National Oceanic and Atmospheric Administration (NOAA) website (http://www.cpc.ncep.noaa.gov/data/teledoc/teleindcalc.shtml).

Fig. 1
figure 1

Geographical location of Iran’s basins, sub-basins, and stations (the numbers of 1, 2, 3, 4, 5, and 6 are the main basins including the Caspian Sea, Persian Gulf-Oman Sea, Urmia Lake, Central Plateau, East Boundary, and Qara Qom, respectively.)

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Table 1 The Information and characteristics of main basins and sub-basins
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Table 2 Lists of teleconnection indices for the proposed study area (Ahmadi et al. 2019; Helali et al. 2020)
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Selection of simulation indices

Dealing with large-scale datasets emphasizes the use of time-effective methods. Moreover, the optimization of the predictive variables will reduce the volume of data leading to higher and faster performance. The Pearson correlation method and correlation matrix were used to measure the relationship between 40 teleconnection indices and precipitation to determine and prioritize the most influential indices in the study area. Equation (1) explains the Pearson correlation coefficient (Salahi et al. 2017):

$$r=\frac{\sum_{i=1}^{n}\left({x}_{i}-\overline{x }\right)\left({y}_{i}-\overline{y }\right)}{\sqrt{{\left({x}_{i}-\overline{x }\right)}^{2}{\left({y}_{i}-\overline{y }\right)}^{2}}}$$
(1)

where xi denotes the independent (observation) and yi is the dependent variables (simulation), and \(\overline{x}\) and \(\overline{y}\) are the mean of independent and dependent variables, respectively. The r value ranges from 1 to − 1 representing perfect positive correlation to perfect negative correlation. Then, the percentage significant teleconnection indices (PST) were estimated based on p-value of ± 0.374 from the regression per basin and sub-basin. In this method, the datasets including the indices with a 1–6 months lag times and 40 indices with 240 variables were fed into the model by the correlation matrix and a stepwise procedure. This study aimed to investigate the effect of teleconnection indices on the seasonal precipitation of Iran basins and sub-basins. Considering the frequency and spatial distribution of the meteorological stations, an attempt was made to examine the correlations with time lags of 1 to 6 months (Helali et al. 2020, 2021c). Also, due to the importance of seasonal precipitation in the agricultural sector and forecasting crop yields, increasing the time lag by more than 6 months will associate with more uncertainty. That allowed us to define the significance of the relationship between predictive indices and the precipitation’s occurrences. First, all 40 indices with 6-month time lags were used to determine seasonal large-scale teleconnection indices per sub-basin. Second, the 3 indices with the highest coefficient of determination (R2) were fed into the models by a stepwise method (Table 4). Therefore, three variables with the highest coefficient of determination (R2) were selected as the most influential indices for the seasonal precipitation (three seasons) of each sub-basin.

Simulation models

Machine learning (ML) methods are considered advanced and intelligent methods with a higher ability for non‐linear data modeling and learning schemes for simulation (Ahmadi et al. 2020). The simulation model in ML techniques includes two phases of training and testing the model capability (Seyedzadeh et al. 2020). Therefore, four ML models including least squares support vector machine (LSSVM), two types of the artificial neural networks (i.e., the generalized regression neural network (GRNN), multi-layer perceptron (MLP)), and multilinear regression (MLR) were exploited to model seasonal precipitation per sub-basin. Defining the most important predictive indices, 70% of the data were randomly divided as the training samples and the remains as testing samples, and the corresponding pixels of the predictive indices were fed into the four machine learning (ML) algorithms. For each model, three seasonal outputs resulting from 30 iterations were generated. MATLAB software and programming (version 9.0, R2016a) was used to implement the GRNN, MLP, LSSVM, and MLR models. The descriptions of the models are provided below.

Generalized regression neural network

In ML family algorithms, artificial neural networks (ANN) try to simulate the biological neural networks’ structures or tasks similar to human brain information processing (Duan et al. 2013; Seyedzadeh et al. 2020). In ANN, the neurons as the processor elements include two factors, namely the weight and activation function. The input variables are weighted after being mapped to neurons, and the outcome is used as input to the activation function to create the final output. Equipped with the radial basis function (RBF) and probabilistic structure, GRNN is a type of neural network model that simulates the dependent variables in a regression function problem. Therefore, it does not experience the local minima problem, which is common in other neural networks (Cigizoglu 2005). GRNN, as a three-layer neural network, has many neurons in input and output layers equivalent to input and output vector dimensions, respectively. In contrast with the artificial neural network (ANN) in the middle layer, the number of neurons is defined by observed data for model calibration and testing (Araghinejad 2014; Modaresi et al. 2018a). The applied function (in the middle layer of this neural network) assigns a normal (Gaussian) function as Eq. (2).

$$f\left({X}_{r}.t\right)={e}^{-{\left[I\left(t\right)\right]}^{2}}$$
$$I\left(t\right)=\Vert {X}_{r}-{X}_{t}\Vert \times \frac{0.8326}{h}$$
(2)
$$t=1.2.\dots .n$$

where \(\left\| {X_{r} - X_{t} } \right\|\) measures Euclidean distance between real-time vector (Xr) and the observed vector of predictors related to the tth neuron (Xt). The constant of 0.8326 applies an optimization for spread parameter and h denotes the spread parameter presenting the spread of a radial basis function and adjusting the function for the best fit. The spread value is commonly 1.0. The larger values result in the smoother function approximation and the smaller ones lead to closely fitness. However, the spread value should be defined by users in the range of h > 0.

The model’s output (Yr) (forecasted seasonal precipitation) for the vector of (Xr) is determined according to a kernel function of the normal performance outputs [f (Xr,t)] as Eq. (3) (Modaresi et al. 2018a):

$${Y}_{r}=\frac{1}{\sum_{t=1}^{n}f\left({X}_{r}.t\right)}\sum_{t=1}^{n}\left[f\left({X}_{r}.t\right)\times {T}_{t}\right]$$
(3)

Multilayer perceptron

MLP is a common type of ANN with feed-forward network class including at least three layers, namely input, hidden, and output layer (Gholami Rostam et al. 2020). Several neurons in the hidden layer are determined based on weight and bias using the minimum RMSE in order to optimize the model performance (Widiasari et al. 2018). The functions used in the middle and output layers of the neurons perform the linear and sigmoid functions, respectively, presented in Eqs. 4 and 5 (Araghinejad 2014; Modaresi et al. 2018a):

$$f\left(x\right)=x$$
(4)
$$f\left(x\right)=\frac{1}{1+{e}^{-\alpha x}} \alpha >0$$
(5)

In each neuron, the weight (w) and bias (b) are calculated for inputs of the neurons as (wjxj + bj) where j = 1, 2… m. The optimum values are determined by the model calibration. To train and calibrate the neural network, a Feed Forward Back Propagation (FFBP) algorithm (Araghinejad 2014) is applied until the best forecasts are achieved, where the error function in Eq. 6 is minimized for the iterations (epochs):

$$E=\frac{1}{nc}\sum_{i=1}^{nc}{e}_{i}^{2}$$
(6)

where E denotes the error function; ei calculates the error of the model simulation for ith training pair data and nc is the number of training pairs.

Least square support vector machine

As a supervised learning mechanism, the support vector machine (SVM) uses structural risk minimization notion to minimize the model error (Dibike et al. 2001; Ghosh et al. 2019), whereas other methods (e.g., ANN) apply the empirical risk minimization principles (Seyedzadeh et al. 2020; Modaresi and Araghinejad 2014). The least square support vector machine (LSSVM) approach (Suykens and Osipov 2008) exploits linear equations in simulation algorithm and leads to higher performance by using effective kernel function (Modaresi et al. 2018b; Seyedzadeh et al. 2020). In the LSSVM method, a nonlinear mapping of ϕ in the trait space for Xt ∈ Rm as the input data and Y(Xt) ∈ R as the output data is calculated as follows (Suykens et al. 2002):

$$Y\left({X}_{t}\right)={w}^{T}.\phi \left({X}_{t}\right)+b$$
(7)

where w and b denote the weights and biases values of the regression function, respectively, calculated by minimization of the following function:

$$\underset{w.b.{e}_{i}}{\mathrm{min}}j\left(w.e\right)=\frac{1}{2}{w}^{T}w+\frac{\gamma }{2}\sum\nolimits_{t=1}^{n}{e}_{t}^{2}$$
$$S.T:{w}^{T}\phi \left({X}_{t}\right)+b+{e}^{t}$$
(8)
$$t=1.2.\dots .n$$

where e is the error, and gamma (γ) are the regularization parameters in the model to control the flatness of approximation function, and the optimum values are determined by users.

Multilinear regression

The regression model reliability can decline if a few variables are chosen. In this work, in order to establish the forecast models for the seasonal observations, a regression equation using three independent variables was formulated (Kim et al. 2020). For this study, the datasets from the past 28 years were used to estimate the forecast models for each season. The regression equation with three independent variables was determined as follows:

$$Y={\alpha }_{0}+{\alpha }_{1}{X}_{1}+{\alpha }_{2}{X}_{2}+{\alpha }_{3}{X}_{3}+\varepsilon$$
(9)

where Y is the response (monthly precipitation); α0, α1, α2, and α3 determine the regression coefficients. In addition, X1, X2, and X3 are the most correlated teleconnection indices (predictors); and ε is the model’s residual.

Evaluation indices of models

To evaluate the accuracy of the simulation models and define the level of performances, the coefficient of determination (Behar et al. 2015; Houshyar et al. 2018), RMSE (Ma and Iqbal 1984; Willmott and Matsuura 2006; Heydari Tasheh Kabood et al. 2020), MBE (Ma and Iqbal 1984), and Scatter Index (SI) (Li et al. 2013; Seyedzadeh et al. 2020) were used by the following equations:

$${R}^{2}={\left[\frac{\sum_{i=1}^{n}\left({O}_{i}-\overline{O }\right)\left({M}_{i}-\overline{M }\right)}{\sqrt{\sum_{i=1}^{n}{\left({O}_{i}-\overline{O }\right)}^{2}{\left({M}_{i}-\overline{M }\right)}^{2}}}\right]}^{2}$$
(10)
$$RMSE=\sqrt{\frac{\sum_{i=1}^{n}{\left({O}_{i}-{M}_{i}\right)}^{2}}{n}}$$
(11)
$$MBE=\frac{\sum_{i=1}^{n}\left({M}_{i}-{O}_{i}\right)}{n}$$
(12)
$$SI=\frac{RMSE}{\overline{O} }$$
(13)

In the above equations, M is the modeled data, O is the observational, n denotes the time series number, and \(\overline{O }\) represents the mean. Based on the above statistics, the perfect models are defined by R2 values of 1 and RMSE and MBE values of zero. The efficiency of SI statistics in modeling and forecasting is classified in below (Li et al. 2013):

$$if\begin{Bmatrix}SI<0.1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;Exellent\\0.1<SI<0.2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;Good\\0.2<SI<0.3\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;Fair\\SI>0.3\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;Poor\end{Bmatrix}$$
(14)

Result

Structural of machine learning models

The structural characteristics and schematic views of the GRNN, MLP, LSSVM, and MLR models are shown in Table 3 and Fig. 2. Due to different results of training and testing in implementation of intelligent models, the average output of 10 consecutive executions for each model was reported as the final result of the models. To obtain the best accuracy, training of the GRNN, MLP, LSSVM, and MLR models was stopped after 50,000, 50,000, 50,000, and 1000 iterations, respectively.

Table 3 Characteristic of machine learning models study in the training and testing phases
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Fig. 2
figure 2

A schematic of the flowchart used for the machine learning models

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Optimal GRNN and MLP architectures were chosen through trial and error approach, which generally stopped after 1000 epochs. LSSVM gets the advantage of the applying equality constraints (in exchange for traditional inequality constraints of SVM) and implements the sum of squared regression errors in the training process. For the MLR model parameter selection, the iterative process continues until an acceptable level of error is obtained. The dataset was divided into the training set (70% of the dataset) used for developing the ANN model and estimating the model parameters, and the testing dataset (30% of the dataset) to evaluate the accuracy of the predictive variables.

Percentage of significant teleconnection indices

The analysis of the PST is presented in Fig. 3 and the significant levels of correlation (in terms of sub-basin and season) are illustrated in Fig. 4. Considering the lag time of 1–6 months, the PST with autumn precipitation in basin 1 (CS) was between 17.5 and 35.0% (maximum amount in the time lag of 1–3 months). While in basin 2, PST were estimated between 12.5 and 45.0% (maximum values in 1–3 month time lag), basin 3 (UL) between 5.0 and 37.5% (maximum values in 1–3 month time lag), basin 4 (CP) from 10.0 to 42.5% (maximum values in 1–4-month time lag), basin 5 (EB) between 5.0 and 42.5% (maximum values in 1–4 months lag times), and finally in basin 6 (QQ), it was recorded between 5.0 and 32.5% (maximum values at 6-, 3-, 2-, and 1-month time lags). Therefore, in most of the main basins, the PST had the highest values with autumn precipitation in 1–4 month time lags (Fig. 3A). According to the results, MEI, NINOs, SSTs, POI, SOI, and TPI (teleconnection indices) exhibited the most significant correlation with autumn precipitation basins in the abovementioned time lags. In addition, MEI, NINOs, SST, and TPI indices had positive correlations, whereas POI, SOI, TNA, WPSST, and CSST showed negative correlations (Fig. 4A).

Fig. 3
figure 3

The percentage of significant teleconnection (PST) between teleconnection indices and seasonal precipitation of Iran’s basins and sub-basins with delays of 1–6 months (lag time 1 to 6)

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Fig. 4
figure 4

The diagrams of (positive/negative) significant correlations (Pearson correlation) of indices affecting seasonal precipitation; A, B, and C stand for autumn, winter, and spring, respectively, in sub-basins in one- to 3-month time lags of autumn and spring precipitation (lag 3 to lag 1) and in 4- to 6-month time lags of winter precipitation (lag 6 to lag 4). Black dotted line indicates the most important teleconnection indices

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Likewise, the PST with winter precipitation (in time lags of 4–6 months) had the highest value in most of the basins (Fig. 3B). Therefore, the PST of winter precipitation was observed in some basins and was limited to NAO2, PDO, TNA-TSA, AO, CSST, NCP, and MSST indices (Fig. 3B). The correlation between winter precipitation and NAO2, NCP, PDO, and TNA-TSA was positive, while its correlation with CSST, MSST, TSA, WPSST, EA, AO, and POL was negative (Fig. 4B).

Moreover, the highest PST in spring precipitation occurred in 1–4-month time lags in most of the basins (Fig. 3C). Consequently, SST, NINOs, MEI, NPI, PNA, POI, SOI, TNI, TPI, and TNIi indices showed significant correlation with some basins in the 1–3-month time lags. The correlation with MEI, NINOs, SSTs, PNA, TNA, TPI, and TNIi was positive, while the negative correlation was observed with CSST, NPI, POI, SOI, TNI, and WPSST (Fig. 4C).

The Pearson correlation results highlighted that the teleconnection indices with higher significant changes in most of the basins became dependent on the season and time lags (Fig. 4). The autumn precipitation had the highest PST correlations in the 6- and 5-month lag time of TNA (57% of sub-basins), the 4- and 3-month time lags of SOI (50% and 73% of sub-basins), the 2-month time lag of NINO 3.4 (77% of sub-basins), and 1-month time lag of NINO 4 (70% of sub-basins). It was observed that the pattern and PST correlations of teleconnection indices with winter precipitation changed in order to obtain a significant correlation between PDO, NAO2, MSST, TSA, SOI, and POL indices and a higher number of basins (i.e., 40%, 30%, 60%, 47%, 20%, and 40% of the basins, respectively) in 6-, 5-, 4-, 3-, 2-, and 1-month time lags. An examination of spring precipitation and its relationship with teleconnection indices indicated that NINO 4 index had a significant correlation with higher percentage of basins in time lags of 6, 5, and 2 months (50% of sub-basins), SOI in 6, 4, and 3 months (50–53% of sub-basins), SST4 in 6, 5, and 2 months (50% of sub-basins), POI in 1 month (57% of sub-basins), and WPSST in 3 and 1 month (50% of sub-basins). Finally, the most significant independent predictors (in terms of time lag and teleconnection indices pattern) are calculated and listed in Table 4. Those indices were considered as the optimum inputs or main teleconnection variables for the different models reducing the volume of computation in seasonal precipitation simulation in Iran’s sub-basins.

Table 4 The most significant teleconnection indices for seasonal precipitation at main and sub-basin of Iran
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Accuracy assessment and evaluation of the models

The accuracy assessment results of the models in seasonal precipitation simulation (based on teleconnection indices) are summarized for autumn, winter, and spring precipitation in Tables 5, 6, and 7, respectively. In autumn precipitation, the changes of R2 values in CS, PG, UL, CP, EB, and QQ main basins were recorded between 0.47 and 0.94, 0.48 and 0.95, 0.74 and 0.90, 0.37 and 0.90, 0.45 and 0.95, and 0.35 and 0.84, respectively. Similarly, the RMSE ranged between 6.9 and 90.1 mm in CS, 11.1 and 58.1 mm in PG, 16.1 and 24.2 mm in UL, 5.3 and 62.5 mm in CP, 3.3 and 15.0 mm in EB, and 6.9 and 14.9 mm in QQ. Based on MBE statistics in CS, PG, UL, CP, EB, and QQ main basins, the MLP, LSSVM, GRNN, GRNN, LSSVM, and MLR models had minimum values of MBE and there was no sign of overestimation or underestimation of the models in different sub-basins with specific teleconnection indices. A closer examination of the obtained results revealed that the best model based on R2 and RMSE statistics in most of the sub-basins was the LSSVM model followed by the MLP. The rate of changes in the coefficient of determination in the LSSVM model was equal to 0.82–0.94, 0.86–0.95, 0.90, 0.82–0.90, 0.93–0.95, and 0.84 in CS, PG, UL, CP, EB, and QQ basins, respectively, and the corresponding RMSE values of 6.9–56.2, 11.1–28.2, 16.1, 5.3–29.6, 3.3–5.4, and 6.9 mm.

Table 5 Comparison of statistical evaluation indices of the models (R2, RMSE, and MBE of autumn precipitation using four models in basins and sub-basins of Iran)
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Table 6 Comparison of statistical evaluation indices of the models (R2, RMSE, and MBE of winter precipitation using four models in basins and sub-basins of Iran)
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Table 7 Comparison of statistical evaluation indices of the models (R2, RMSE, and MBE of spring precipitation using four models in basins and sub-basins of Iran)
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According to the MBE statistics for winter precipitation (Table 5), it was determined that the minimum errors in CS, PG, UL, CP, EB, and QQ basins were obtained by GRNN, MLR, GRNN, MLR, LSSVM, and GRNN models, respectively. The analysis of the models based on R2 and RMSE statistics confirmed the superiority of the LSSVM model in most of the basins and sub-basins followed by MLP model. Based on R2, the best models were CS, PG, UL, CP, EB, and QQ.

The calculated values of R2, RMSE, and MBE between the simulations and observations for spring precipitation using different models are presented in Table 6. Considering the MBE statistics, the lowest errors in CS, PG, UL, CP, EB, and QQ basins were acquired by MLP, MLP, MLR, LSSVM, MLR, and MLP models, respectively. The analysis of models’ performances based on R2 and RMSE statistics revealed that the LSSVM model (in most of the basins and sub-basins) outperformed other models followed by the MLP model. Accordingly, the rate of change in the R2 of the best models in CS, PG, UL, CP, EB, and QQ basins were between 0.83–0.92, 0.82–0.94, 0.89, 0.86–0.93, 0.85–0.93, and 0.84, respectively, with the corresponding RMSE values between 6.4–26.6, 19.2–45.3, 7.8, 10.7–35, 13.2–15.0, and 14.4 mm.

Efficiency evaluation of the models

The models’ efficiency based on the scatter index (SI) is shown in Fig. 5 for autumn (first column), winter (second column), and spring (third column). The SI illustrated that the LSSVM model had a good performance in most of the sub-basins in autumn: in basin 1 (CS), the ranges of change in the SI in GRNN, MLP, LSSVM, and MLR models were 0.12–0.27, 0.10–0.18, 0.06–0.14, and 0.14–0.19, respectively (excellent to good); in basin 2 (PG), the LSSVM model had good to fair performance (excluding the KAM and SBL sub-basins); and other models had fair to poor performance. Also in basin 3 (UL), LSSVM model showed good performance and other models ranked as fair. In basin 4 (CP), LSSVM model had good performance in CTD and STL sub-basins (0.19 and 0.16) and fair performance in ABS, GKH, LUD, and SKD sub-basins (with the values of 0.25, 0.22, 0.28, and 0.25, respectively), and MLP model had fair performance in some limited sub-basins. In basin 5 (EB), only LSSVM model performed well in KHD sub-basin (0.17), whereas it had fair performance (0.29) in HAH. The MLR model had fair performance in KHD sub-basin (0.29). In basin 6 (QQ), the MLP, LSSVM, and MLR models showed fair to good performance (0.23, 0.15, and 0.16, respectively). According to these results, the efficiency of all 4 models in modeling and predicting autumn precipitation was good only in the CS basin, while in other sub-basins, the LSSVM model showed good and MLP appeared fair (Fig. 5, first column).

Fig. 5
figure 5

Qualitative values of the scatter index (SI) in different machine learning models in autumn, winter and spring precipitation in all basins

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The analysis of winter precipitation forecast based on the SI showed excellent to good efficiencies using LSSVM and MLP models (Fig. 4, second column). In general, the efficiency of teleconnection indices in winter precipitation simulation was good by using LSSVM and MLP models, while it was poor by using GRNN and MLR models (Fig. 5, second column).

The results of different models efficiency in spring precipitation simulation are presented in Fig. 5 (third column). In basin 1 (CS), the rates of change of SI in GRNN, MLP, LSSVM, and MLR models were excellent to good; in basin 2 (PG), the models had poor performance in most of the sub-basins (the performance of all 4 models was good to fair except in GKR, KRK, and WSB sub-basins); in basin 3 (UL), MLP and LSSVM models had good performance and GRNN and MLR models had fair performance; in basin 4 (CP), LSSVM and MLP models had good to fair performance and GRNN and MLR models exhibited poor performance; in basin 5 (EB), the LSSVM model had fair performance (in two sub-basins of HAH and KHD) and other models had poor performance; in basin 6 (QQ), LSSVM and MLP models had good performance and MLR and GRNN models were fair. A general review of the results shows that the simulation performance of the 4 models was good to fair only in CS basin, while in other basins and sub-basins, only LSSVM and MLP models showed fair and rarely good performance (Fig. 5, third column).

Comparison of training and testing periods

An analysis of the mean and time series of seasonal precipitation modeled (simulations) and observed (observations) in the training and testing phases in sub-basins is plotted in Fig. 6 and Fig. 7. Clearly, there was no difference between the seasonal precipitation simulations and observations in the training phase, but in the testing phase, a slight difference was observed. The precipitation in the selected sub-basins, namely CS, PG, UL, CP, EB, and QQ, reached the values of 78.0, 12.3, 16.9, 19.3, 2.9, and 2.5 mm in autumn, respectively, the values of 4.5, 26.5, 8.1, 5.1, 4.3, and 9.3 mm in winter, and 15.8, 9.0, 0.4, 2.9, 0.5, and the values of 1.2 mm in spring. Therefore, in the selected sub-basins of each basin, modeling and precipitation forecasting were based on teleconnection indices and the models with minor errors were used in the training and testing phase. According to the previous section and the SI, the use of intelligent models (i.e., ML), especially LSSVM and MLP, might lead to higher efficiency in seasonal precipitation simulation in the main basins and sub-basin scale.

Fig. 6
figure 6

Comparison between the simulations and observations in the training and testing phases in selected sub-basins of each basin (series 1 to 20 of training and series 21 to 28 of test phase)

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Fig. 7
figure 7

Modeled and observation data in the training and testing periods in selected sub-basins on a bisector diagram

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Examination of the time series results of the observed and modeled data in selected sub-basins showed an appropriate distribution of all machine learning models around the bisector axis. The distribution of the observed and modeled data in the training phase in the LSSVM and MLP were better than the GRNN and MLR models, while in the test phase, the distribution of the MLP and GRNN were more robust (Fig. 7).

The results showed that the RMSE value of the LSSVM model had the lowest value in the autumn season in the training phase, but in the testing phase, the RMSE values of the MLP and GRN models were less than the MLR and LSSVM models. Also, the amount of RMSE values of the CTD, LUD, DJD, HAJ, SKD, HAM, HAH, KHD, and QRQ sub-basins did not substantially differ from each other (Fig. 8). The RMSE in winter rainfall in the training phase in the LSSVM and MLP models were less than the GRNN and MLR models, and also the difference between all models in the ARZ and ATR sub-basins had the lowest value. However, in the testing phase, the RMSE values of the MLP and GRNN models had the lowest value. Therefore, it can be said the MLP and GRNN models had better accuracy than LSSVM and MLR models (Fig. 8). The results in the spring showed that the RMSE in the LSSVM model had the lowest value in the training phase in most sub-basins, but in the testing, the RMSE of the MLP and GRNN were lower and had better performance (Fig. 8).

Fig. 8
figure 8

The RMSE values in train and test steps of machine learning models study in the different seasons

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Discussion

Seasonal precipitation simulation is one of the challenging subjects for climatologists and water resource specialists to provide efficient and practical solutions, forecasting, and modeling. In this regard, using dynamic models is one of the answers to solve this problem. Due to a large amount of data, the complexity of the components of the climate system, and the short period of the simulation, statistical models are suggested (Doblas-Reyes et al. 2013; Rodwell and Palmer 2014; Qian and Xu 2020; Kim et al. 2020). Teleconnection indices as influential climate factors affect different parts of the world. Therefore, their correlations with climate variables and exploiting them as predictors were also confirmed (Ruigar and Golian 2015; Xiao 2019; Zhu et al. 2020). As mentioned before in similar studies, the relationship between teleconnection indices and precipitation was a case of point relationship using limited or linear models for forecasting. However, the teleconnection indices occur on a large scale and their correlation and impacts on precipitation should be correspondingly examined with the proper spatial scale of the teleconnection indices patterns (Goudarzi et al. 2017). To fill the existing gaps, the correlation between teleconnection indices and seasonal precipitation was expanded from a station or point perspective to the basin perspective and then the entire basins and sub-basins of Iran. In addition, an attempt was made to evaluate the different predictive models’ performance.

Preliminary results of the study evaluated that the highest PST was between teleconnection indices and autumn (1–4 months lag times), winter (4–6 months lag times), and spring (1–4 months lag times). In other words, seasonal precipitation of Iran’s main and sub-basins were predicted by 1–4 months lag times before the occurrence, which was in agreement with the results of Helali et al. (2020) study analyzing the correlation of autumn precipitation in basin level in Iran. The significance and pattern of indices also varied based on the sub-basin and time lags, which was not in agreement with the results of previous studies. The current study was conducted in the sub-basin level showing the highest PST correlation between the following: (a) autumn precipitation and AO, SOI, SSTs, AMO, SCN, Nino 3.4, PDO, PNA, TNA, WP, and TSA indices; (b) winter precipitation and EAWR, SSTs, NAO, PNA, POL, PDO, SCN, TNA, and TSA indices; and (c) spring precipitation and SST, PNA, Nino, NAO, NPI, POL, PNA, NPI, and NCP indices. In Helali et al. (2020) study, it was found that the indices related to ENSO, SST, TNA, PDO, and AMO had the highest correlation with basin precipitation, which is consistent with the results of this research. According to Ahmadi et al. (2019), ENSO, AMO, and AO were the most related teleconnection indices affecting precipitation in Iran’s climatic regions. Moreover, Dehghani et al. (2020) concluded that SOI, NAO, and PDO indices were the most significant indices, whereas the current study showed that the type of teleconnection indices varied according to the season and sub-basin.

A detailed analysis revealed that the highest PST correlations of teleconnection indices with autumn precipitation in 6, 5, 4, 3, 2, and 1-month time lags belonged to TNA, TNA, SOI, SOI, NINO 3.4, and NINO 4, respectively. Likewise, winter precipitation was correlated with PDO, NAO2, MSST, TSA, SOI, and POL indices, and spring precipitation was correlated with NINO 4 (in 6-, 5-, and 2-month lags), SOI (in 6-, 4-, and 3-month lags), SST4 (in 6-, 5-, and 2-month lags), POI (in 1-month lag), and WPSST (in 3- and 1-month delays). Most studies in Iran represented that teleconnection indices mainly affect autumn precipitation and partially influence winter and spring precipitation in a good correlation with some of these patterns such as the West Mediterranean Oscillation (WeMo) and Scandinavian Pattern (SP) (Ghasemi and Khalili 2008; Ghasemi 2019). While the current study showed that in addition to autumn precipitation, an appropriate and significant correlation was found between teleconnection indices and winter (NAO2, PDO, AO, CSST, MSST indices in different time lags) and spring (NINOs, SSTs, SOI, TNIi, TPI, POI, and MEI in different time lags) precipitation. Hence, it is concluded that those indices are significant predictor variables. Synoptic and dynamic analysis of the relationship between autumn precipitation in Iran’s sub-basins and teleconnection indices showed that these precipitations were partially related to the MJO index at first, which was the stimulus of ENSO phase initiators and regional indices such as NAO and AO had the same effect as ENSO through the large atmospheric bridge mechanism. In fact, regional indices are a medium for measuring the impact of global indices such as ENSO, PDO, and AMO on Iran’s climate, but in general, the impact of ENSO in Iran precipitation is more evident, especially in autumn (Nazemosadat and Cordery 2000; Helali et al. 2020, 2021c).

The analysis of the ML models uncovered that LSSVM and MLP models had better performance than GRNN and MLR models in autumn, winter, and spring in most of the sub-basins of Iran between 1987 and 2015. However, the regression method (Nalley et al. 2019; Qian and Xu 2020; Kim et al. 2020), fuzzy and neural network (Karamouz et al. 2006; Choubin et al. 2014; Canchala et al. 2020; Gholami Rostam et al. 2020), and genetic algorithm method (Dariane et al. 2019) proved to be the best-known models in previous research. In essence, the efficiency of LSSVM (in most of the sub-basins) and MLP (in some of the sub-basins) was good by higher seasonal forecast accuracy in comparison with GRNN and MLR models during all times. The results of this study were consistent with other studies that proposed the LSSVM model as the best model with the lower error (Tao et al. 2017; Seyedzadeh et al. 2020). The results show that although in the training phase, the RMSE of LSSVM and MLP models were less than other models; in the testing phase, the RMSE of MLP and GRNN mostly represented the lowest values. Therefore, it is better than the MLP and GRNN to be used in forecasting and seasonal precipitation modeling seasonal precipitation. The advantages of this study were the analysis of the correlation between teleconnection indices and SP in all basins and sub-basins of Iran (spatial balance between the teleconnection indices and the study area), precipitation forecast of all seasons (unlike other studies conducted in a specific season), and using different models and evaluation of their efficiency in the seasonal precipitation forecast. This study showed the efficiency of teleconnection indices in seasonal precipitation simulation in Iran’s sub-basins and suggested the appropriate models for such complex variables, to be deployed in water resource management on a larger scale as sub-basins.

Conclusion

Due to the importance of water resource management on a regional scale and the impact of large-scale teleconnection indices on it, this study attempted to model and simulate the precipitation of different main and sub-basins of Iran using ML models with different architectures. In summary, seasonal precipitation in Iran was correlated with teleconnection indices, and in most cases, their significance was higher in autumn and spring than in winter. The dynamic and synoptic analysis of these phenomena might contribute to that and more investigation is necessary for future studies. The highest PST correlation was with autumn (in 1- to 4-month lag), winter (in 4- to 6-month lag), and spring (in 1- to 4-month lag) precipitation. The most important indices affecting autumn precipitation were MEI, NINOs, SSTs, POI, SOI, and TPI. Similarly, the winter precipitation was mainly affected by NAO2, PDO, TNA-TSA, AO, CSST, NCP, and MSST. SSTs, NINOs, MEI, NPI, PNA, POI, SOI, TNI, TPI, and TNIi influenced spring precipitation, as well. These time lags were due to the distance of these indices with the climate and especially the precipitation of the study area. The analysis reflected that autumn precipitation was positively correlated with MEI, NINOs, SSTs, and TPI, and it was negatively correlated with POI, SOI, TNA, WPSST, and CSST. Winter precipitation was correlated positively with NAO2, NCP, PDO, and TNA-TSA and it was negatively affected by CSST, MSST, TSA, WPSST, EA, AO, and POL. Spring precipitation showed a positive correlation with MEI, NINOs, SST, PNA, TNA, TPI, and TNIi and a negative correlation with CSST, NPI, POI, SOI, TNI, and WPSST. Therefore, teleconnection indices had the potential to simulate the seasonal precipitation of the basin and sub-basins of Iran. The seasonal precipitation forecast was more accurate by using MLP followed by the GRNN model in most basins, but in general, in sub-basins with geographical and climatic diversity, most of the models’ accuracies decreased. The results of this study demonstrate the efficiency of teleconnection indices as precipitation predictor variables in Iranian sub-basins. The reason for the various results by machine learning models in different sub-basins can be the climatic characteristics and the topographic diversity of each sub-basin. It is recommended to test other algorithms to tackle the geographical and climatic diversity of such study areas. Elimination of the microclimate effect in the region restricted our study; from the basin perspective, we could no longer assess the impact of the teleconnection indices on the precipitation of a particular station in the region, but we considered the spatial fit of the teleconnection indices within the basin. Therefore, the future study will explore some other robust algorithms or integration of the above-applied ML models that consider the spatial fit of teleconnection patterns with precipitation and the microclimate effects. Moreover, it seems helpful to examine those limited stations with summer precipitation to investigate the relationship between the teleconnection indices and precipitation from seasonal and basin points of view.