Introduction

Water high-satisfactory is a main condition of lifestyles because of its straight impact on anthropological health. Very satisfactory water can be damaged by geological structure, salinity, over-harvesting of groundwater, municipal and domestic wastewater to floor streams, in addition to crop drainage and a wide variety of chemical compounds. (Derakhshannia et al. 2020; Fatahi Nafchi et al. 2021; Ostad-Ali-Askari et al. 2017a; Golian et al. 2020; Ostad-Ali-Askari et al. 2018b; Tsakiris and Alexakis 2012). A variety of strategies and procedures are applied to assess and predict high water satisfaction. Also, most of the water software along with SWAT, QUAL2K and MIKE-eleven use excellent equipment to evaluate the high satisfactory currents. Time group evaluation is one of the useful strategies that can be implemented in modeling and predicting water satisfaction (Abdollahi et al. 2021; Nafchi et al. 2021, 2022; Fattahi Nafchi et al. 2022; Ostad-Ali-Askari et al. 2021a; Chang 1988). Time group examines are beneficial in expertise and studying the method of various phenomena. It is likewise beneficial in producing beyond observations forecasting the destiny values primarily Depend totally at the beyond memory (Madani 2021). Time group consists of a string of records over the years with an identical c program language period among all records. The c program language period may be described as daily, weekly, month-to-month in addition to every year time steps. Time group study is used in selection in many operating systems and hydrological tactics. Time group assessment in hydrology has the most significant purpose: 1. Understanding and transcribing random tools of a hydrological system and 2. Estimating fate standards for the system (Pirnazar et al. 2018; Salehi Hafshejani et al. 2019; Talebmorad et al. 2021; Javadinejad et al. 2018, 2019a, b, 2021; Ostad-Ali-Askar et al. 2018a, 2019, 2020a; Kumar 2021). One of the most important issues in applied hydrology is water quality. Because the main activities of hydrology in order to supply water for drinking, agriculture or industry, each of which in terms of quality must have certain quality characteristics and criteria, and if such water supply is not possible, these activities are practically ineffective (Eslamian et al. 2018a; Eslamian et al. 2018b; Talebmorad et al. 2020; Fan 2020). Today, water quality studies are becoming more widespread and include issues related to surface and groundwater pollution (Cheng 2021). Water quality modeling is used to simulate changes in pollutants in the environment (Stansfield 2001). Concentrations of pollutants in the environment may increase or decrease due to various mechanisms that the fate of pollutants depends on the result of interactions between the mass and their transport processes, all these changes are the subject of water quality modeling (McKerchar 1974). Models include equations, relationships, and observational evaluation data that are used to explain the behavior of natural systems under different conditions and can have the ability to provide the best management option given specific time conditions and economic conditions (Shayannejad et al. 2022; Ostad-Ali-Askari et al. 2017b, 2020b, 2021b, c; Ostad-Ali-Askari 2022a, b; Raeisi Vanani et al. 2017;  Pregun 2022). Madian River, which supplies water to Lorestan gardens in Ziwadar area of Poldakhtar city, Madian River is one of the important tributaries of Kashkan river, which originates from Kuhdasht city and several springs are drained along the water flow path. Due to the decrease in rainfall and the negative balance of the Kuhdasht plain, the flow of mares in the river has drastically decreased and the orchards of Ziodar figs have faced severe water shortages on the eve of the irrigation season. Ziwadar area of Poldakhtar city does not have the capacity to develop new gardens in the current situation (Nafsin 2021). Considering the damages that are left every year due to floods and inundation of rivers, the study and determination of the flood zone of rivers has been considered for a long time (Xue 2021). Various factors can be influential in determining the flood zone, including parameters related to the morphology of the river. Among the parameters related to morphology affecting the bed bottom of rivers, the form of rivers in terms of alluvial and mountainous has a geostructural form that will be different according to each state of the river flood zone (Schäfer, 2021).

Applied time-series analysis

ARIMA modes can reproduce the main statistical traits of a hydrological time group (autoregressive, incorporated, transferring average). ARIMA modes were used to observe river runoff and discharge (Kurunç et al. 2005), lake water area (Sheng and Chen 2011), sediment production (Hanh et al. 2010) and first water-rate (Ahmad et al. 2001; Lehmann & Rode 2001; Faruk 2010; Durdu 2010; Khalil Arya and Zhang 2015). Automated correlation modes have been used in several studies of flow analysis (Thomas and Fiering 1962). McKarchar and Delleur (1974) took the first step in using time groups in hydrology using self-regulated integrated moving averages. They applied seasonal modeling correctly to examine the seasonal properties of flow components. Time group modeling is in determining and predicting the sample of month-to-month flow and management of green combined water resources (Jalal Kamali 2006). It is widely used for predicted hydrological variables that include rainfall and discharge in addition to floods. (Komornık et al. 2006; Damle and Yalcin 2007). Many investigations have centered on water first-rate components, a Brief evaluation of that is referred to as follow. Many studies have focused on first-class water components, a brief evaluation of which is as follows.

Applied time series analysis on surface water quality

Hirsch et al. (1982) developed new strategies for examining month-to-month micro-water information for uniform traits. Temporal adjustments in micro-water components including pH, alkalinity, general phosphorus and nitrate concentration were also investigated using the Niagara Information Group. (El-Shaarawi et al. 1983). Yu et al. (1993) analyzed the micro-water data of Arkansas, Verdigris, and Neosho floors in addition to the Walnut River Basin to examine traits in 17 main materials using four unique nonparametric strategies. High circulatory states and leaky data from Plynlimon, Mid Wales were investigated using the Kendall Seasonal Test (Robson & Neil 1996). Gangyan et al. (2002) investigated the temporal sediment load traits of the Yangtze River the use of the turning factor test, Kendall’s rank correlation test. Gangyan et al. (2002) using the spin factor test, studied the temporal sediment load characteristics of the Yangtze and River the Kendall rank correlation test. Jassby et al. (2003) in Lake Tahoe, USA developed an advanced timeline version for Secchi intensity. Panda et al. (2011) studied sediment load traits of a tropical river basin in India.

Applied time series analysis on groundwater quality

Time group assessment has been performed in the best groundwater modeling in separate areas. Chang (1988) proposed a modeling approach consisting of examining the homogeneity of records and selecting a first-class version for use by the water loss group to use a random process. One study considered the best groundwater settings due to human exercise, using time group assessments of the best water records correctly from 1964 to 1965. Loftis (1996) reviewed global agricultural and urban surveys, supply factors, and unsafe groundwater near and local groundwater at best around the world, including a few snapshots. Lee and Lee (2003) evaluated and quantified the potential for groundwater depletion in the Seoul Business District, Korea. Various studies have been conducted on the water temperature time group (Kim et al. 2005) best performed the time group assessment to investigate the impact of tides on groundwater in the coastal region of Korea. Also, temporal variability of turbidity, dissolved oxygen, conductivity, temperature and fluorescence with decreasing Mekong River as the use of time group assessment was examined. (Irvine et al. 2011). The best water modeling plays an important role in the best water control and conservation. (Singh et al. 2004; Chenini and Khemiri 2009; Fang et al. 2010; Su et al. 2011; Prasad et al. 2014; Seth et al. 2013; Parmar and Bhardwaj 2014). The use of time group study in aquatic assets shows the performance and efficiency of this method due to the random nature of hydrological processes. It examines the ambitions to use this technique in the best water study. In the gift review, the best components of the Madian river water at Baraftab station have been examined. The technique and survey area are presented in the next section.

Materials and methods

The study area

The study site is located in west of Iran in the Kuhdasht region. Figure 1 shows the study site in Iran. This river station is located at 47°48ʹE and 33°18ʹN minutes north. The area of the basin is about 1108 square kilometers, which is located in the Kashkan basin of Karkheh basin. The time sequence of 9 components of water quality such as TDS, EC, HCO3-, Cl-, SO42-, Ca2 + , Mg2 + , Na + and SAR of the Baraftab station in Madian river was measured in this research (Figs. 1, 3 and 6).

Fig. 1
figure 1

The site of the investigation zone

Full size image

Methodology

The perception and knowledge of ARIMA modeling was confirmed in the characteristic survey. (Pankratz 1983; Vandaele 1983; Box and Jenkins 1976). The history of this method is temporarily provided. Autoregression (AR) modes suppose the values of the Depend variable, Zt, as the regression property of the previous values, Zt − 1, Zt − 2 … Zt − n. An AR version of order 1 (i.e., AR version (1)) is defined as an Eq. 1:

$$Z_{t} = \Phi_{1} Z_{t - 1} + \alpha_{t} \left( 1 \right)$$
(1)

where Zt and Zt-1 show the mismatch from the mean, Φ1 is the first-order AR coefficient and defines the effect of the unit extrusion on Zt-1 on Zt, and αt is white noise.

The αt principles are usually chosen and expected to be neutral with zero proposed cost and normal variance cost. The cost of variance for a fixed, high-quality Zt version is limited (Vandaele 1983) and |Φ1| to meet these conditions must be much less than 1. Higher order AR modes are possible, just like multiple regressions; for this case, the absolute cost of each AR coefficient must be much less than 1. Moving Average (MA) modes cover the beyond random fluctuations to capture the time sequence.: An MA version of order 1 (ie MA version (1)) may be expressed as an Eq. 2:

$$Z_{t} = \alpha_{t} - \theta_{1} \alpha_{t - 1}$$
(2)

where θ1 is the MA coefficient and random shocks (white sound) (αt) are usually distributed and neutrally expected to change at the proposed zero cost and fixed cost. Values greater than 1 indicate that similar descriptions inside the transverse have a greater effect on Zt than recent new observations that are not always plausible in a hydrological time group. A higher order of MA modes is possible. Similar to AR version coefficients, the absolute cost of each MA coefficient must be much less than 1. Because saving a time group is so important, modeling it may be possible to use a hybrid version (ARMA) instead of a regular AR or MA version from time to time. Also, showing a time group with ARMA version (1,1) is more economical than evaluating with AR version (3), as this version requires fewer component estimates. Mixing modes is possible due to the fact that they are theoretically represented as natural modes AR or MA with infinite order. (Vandaele 1983). A hybrid version can provide more flexibility in explaining the consequences of interaction between processes. (Salas et al. 1980). The primary purpose of time group assessment is to identify seasonal styles and/or trends over time. Most of the time, the hydrological time group shows an everyday seasonal sample that may be removed by standardizing the records for the offer and the seasonal standard. Information and modeling of the form of correlation with within the time group is also another goal of time group analysis. Basic areas with ARIMA modeling include: (1) version identification, (2) estimating version orders, and (3) version validation using routine testing. The impacts are prepared with inside the subsequent section. Rivers are one of the most important dynamic ecosystems and awareness of temporal and spatial changes in river water quality is very important. Madian River, which supplies water to the famous black fig orchards of Lorestan in Ziwadar area of Poldakhtar city, added: Madian River, one of the important tributaries of Kashkan River, originates from Koohdasht city and several springs are drained along it. Due to the decrease in rainfall and the negative balance of Koohdasht plain, the flow of mares in the river has drastically decreased and ziodar fig orchards have faced severe water shortages on the eve of the irrigation season. The flow of Madian in the river has decreased by 73% compared to the same period of the previous year and has decreased by 95% compared to the average long-term statistics (about 61 years) (Kim 2021).

Results and discussion

In this view, 9 excellent components of water are examined. With a delay, the records became a finite table time group. In the second a degree MINITAB 14 changes to apply in this view to examine that group nine times. The ACF and PACF of time group have been plotted at the second one degree. The ACF and PACF time groups are plotted quadratically. After specifying the ACF and PACF whenever a group considers the order of the version first. Then four values were applied to study the effects of group technology and the recommended modes and 35 record-time groups were generated. Depending on the four values, a pleasant version is considered for each time a group of 35 records and those modes are applied to predict the five time group values. These four values were R2, AIC, RMSE and VE% (Karamouz and Araghinejad 2015). The cost of AIC is estimated through the Eq. 3:

$${\text{AIC}} = \left( {n \times {\text{ Ln }}\left( {\sigma^{2} } \right) + 2 \times \left( {p + \, q} \right)} \right)$$
(3)

where σ is the same old fault of the remains. n is the design size. p and p represent AR and MA, respectively. The VE% fee is also programmed using the Eq. 4:

$${\text{VE }}\% = \frac{{\mathop \sum \nolimits_{t = 1}^{n} \left| {\frac{{y_{t} - \hat{y}_{t} }}{{y_{t} }}} \right|}}{n}$$
(4)

where yt and ŷt represent the values created and assumed, respectively, and n is the size of the outline. In predicting the next level, the best water components are finished. The consequences are confirmed by the inside of the next fig. Pre-defined metrics (AIC, RMSE, and VE%) were applied at this level to represent the performance of each form in predicting the cost of records. Figure 2 shows the uniform time group of the best water records for the TDS component and the predicted values for five consecutive years. The TDS standard group shows that this component has an extraordinary mode, which has been removed and verified with kilometers as shown in Table 1 (Fig. 2). The results show that the form is able to model the time set well. However, there is an increasing style for source values for five consecutive years that is not consistently indistinguishable from the predicted years. For an additional component, since the miles are from Fig. 3, the EC time group examines an increasing mode that has been omitted in the second level. Then the use of a good version was predicted for five years. Table 2 also shows the results of the model selection and fine-tuning (Fig. 4). The projected values for five consecutive years are also specified in this figure. Similar to the previous components, HCO3- examines the increasing gradient and modeling is done after removing the mode. Table 3 shows the modeling implications for this component. The uniform Cl-time group is provided in Fig. 5. The predicted values of this component are also confirmed in this figure. The implications show that the selected version, confirmed in Table 4, is able to model the group well. Figure 6 proves the old group similar to SO42-. SO42 group modeling became a skill in a reliable group without removing fashion. The projected values are also confirmed in this figure for five years. The consequences of the era and good competition are shown in Table 5. Also, the same old Ca2 + group is prepared in Fig. 7, and the predicted values of this component are specified on this figure. The implications of Table 6 show that the selected version created in Table 6 is able to model the group well. Figure 8 shows the same old group of Mg2 + .Fig. 8 shows that the group observes a growing fashion. Modeling of the Mg2 + group was performed after removing the fashion, which is also provided in this figure. Table 7 shows that the selected form can model the group well.

Fig. 2
figure 2

Unchanging time classification of TDS and the forecast values for 5 years

Full size image
Table 1 The consequences of TDS group, order (1,3)
Full size table
Fig. 3
figure 3

Unchanging time arrangements of EC and the projected values for 5 years

Full size image
Table 2 The consequences of EC group, order (1,1)
Full size table
Fig. 4
figure 4

Unchanging period classification of HCO3.− and the forecast values for 5 years

Full size image
Table 3 The consequences of HCO3.− group, order (1,2)
Full size table
Fig. 5
figure 5

Uniform time classification of Cl− and the assessed values for 5 years

Full size image
Table 4 The consequences of Cl− group, order (1, 2)
Full size table
Fig. 6
figure 6

Uniform time arrangement of SO42− and the assessed values for 5 years

Full size image
Table 5 The consequences of SO42− group, order (1, 1)
Full size table
Fig. 7
figure 7

Unchanging time arrangement of Ca2 + and the foretold values for 5 years

Full size image
Table 6 The consequences of Ca2+ group, order (1,1)
Full size table
Fig. 8
figure 8

Unchanging period categorizations of Mg2 + and the forecast values for 5 years

Full size image
Table 7 The consequences of Mg2+ group, order (1,1)
Full size table

Figure 9 specifies over-all group of Na + . The figure shows that the group is done in a downward fashion. The modeling for the Na + group became final after the mod was removed, which is fine-tuned in this figure. The characteristics show that the selected form, created in Table 8, is able to accurately model the group. Finally, Fig. 10 proves the total SAR group. SAR group modeling was performed after removing the mode, which is also prepared in this figure. Table 9 shows that the selected form is able to modeling the group well.

Fig. 9
figure 9

Unchanging time arrangements of Na + and the foretold values for 5 years

Full size image
Table 8 The consequences of Na+ group, order (1, 2)
Full size table
Fig. 10
figure 10

Unchanging time arrangement of SAR and the foretold values for 5 years

Full size image
Table 9 The consequences of SAR group, order (1,2)
Full size table

The results of forecasting

Table 10 shows the forecast properties for the 9 components. Also, time group of HCO3-, Cl-, SO42 + , Ca + , Mg2 + , Na + , SAR, TDS and EC are specified in Fig. 11.

Table 10 Consequences of prediction the 5 years of components
Full size table
Fig. 11
figure 11

Time classification of foretold values for the last 5 years of water quality components

Full size image

The last five years of time group display the forecasted values for components.

Conclusion

In this study, 9 special water components of Madian River in Baraftab were considered. ARIMA modeling method is suitable for constructing and predicting components. SO42–, Na + and SAR show a depressing fashion, yet the extraordinarily diverse water properties, which show an increasing style. However, the use of a delay to the limited time group position of the light table was prepared for portraits. Examination of the set-time set also shows that there may be an unusual place-increasing style for all components for SO42–, Na + , and SAR. EC, Cl–, Ca2 + , Mg2 + and HCO3– show an increasing style which is a suggestion for worsening of super-monopolized water. The water that eventually enters through the streams is examined as one of the main reasons for the excellent deterioration of water depending on sectoral surveys (JCE 2005), sharp increase in relative population density, increase in artificial frameworks input, municipal wastewater discharge, and conservative pastoral sewage popularity through rivers, problematic international disturbance schemes, water dispersion, and drive dispersion. Crop waste and livestock are different causes of contaminating floor water. Similarly, a sudden increase in water is increasing due to a sharp increase in population within the plot, and green changes within the plot are critical except for additional ecological loss. In statistical analysis of water quality variables, determining the relationships between these variables is one of the important issues. In this study, focal correlation analysis and principal component analysis were used to find the relationships between variables and determine the main variables determining water quality, respectively. Cluster analysis method was also used to classify the studied stations. The results showed that there is a significant relationship between the two categories of physical and chemical variables of the river, which are mostly due to man-made resources. Also, the results of principal component analysis showed that the main variables determining the quality of river water are EC, temperature, SAR, SO4, pH and DO, which are often caused by industrial and human pollutants. The results of cluster analysis for classification of stations showed that they are in the same category in terms of similarity of water quality variables. Therefore, urban areas and human pollutants have had a significant impact on the classification of stations.

Water quality could be an around the world issue which influences human creatures lives on a very basic level. Water shortage is heightening in result of quality weakening. Diverse variables such as population increase, economic advancement and water contamination may well be considered as the roots of the issue. The think about and estimating of water quality is essential to avoid genuine water quality deteriorations in future. Distinctive strategies have been utilized to foresee and gauge the quality of water. It appears that the quality of water is falling apart based on an expanding drift for the larger part of parameters and needs genuine administrative activities. Water contamination is one of the foremost vital natural issues which the world faces. Widespread issue of water lack and shortage of secure and sound water require the examination of problem. Water contamination, from a neighborhood stream and bowl to territorial water pollution, from single to complex contamination, from surface water to groundwater, has been a genuine restriction to sustainable economic development. Water quality may well be influenced by saltiness, overdraw of ground water, urban and household wastewater entrance into surface streams as well as rural waste. The reason of most water quality and stream thinks about is to point out the data and necessary information to oversee water assets as well as their use, control and advancement. Time and cash are spared through these studies and future advancement of water assets becomes inexpensive. The most goals of water quality modeling may well be to: infer cause and impact connections, distinguish impacts of toxin sources, survey fundamental levels of observing, assess arranging and administration choices, center on additional observing and administration destinations and evaluate and assess future water quality conditions. Time arrangement examination is one of the valuable strategies which are connected in water quality modeling and determining.