Introduction

The environmental changes have an impact on water resources that are likely to affect the irrigation system, hydropower, and several other aspects of life in many developed and developing countries (Aalinejad et al. 2016; Kawase et al. 2016; Zhao et al. 2016). These changes are putting stress on management of available water resources to increase the agricultural productivity, boost the economy, and ensure food security (Molden et al. 2016; Sofaer et al. 2016). Proper management of water resources is highly dependent on accurate streamflow prediction, which is a challenging process because of its nonlinear and multidimensional dynamics (Oyerinde et al. 2016; Woldemeskel et al. 2016; Veraart et al. 2017; Ghumman et al. 2017; Rauf and Ghumman 2018). Various modeling techniques have been used for stream flow prediction, e.g., distributed physically based models, lumped conceptual models, stochastic models, and black box models. Although the physically based models use the physical processes involved in the rainfall-runoff modeling, their successful use is limited mainly because of some difficulties in measuring parameters involved and complexity of the governing equations (Yousuf et al. 2017). There are problems in the use of time-series stochastic models due to non-stationary behavior and nonlinearity in the data distributions. Therefore, artificial neural network (ANN), support vector regression (SVR), and adaptive neuro fuzzy inference system (ANFIS) models are gaining importance in the prediction of the hydrologic phenomenon and stream flow forecasting (Kyada and Kumar 2015; Alfarisy and Mahmudy 2016; Kovačević et al. 2018). ANNs are flexible models with respect to the combination of input variables. These models can efficiently treat the nonlinearity of the system and are equally effective in accurate rainfall and streamflow simulations (Goyal et al. 2014; Wang et al. 2017a, b; Adnan et al. 2017a, b; AlOtabi et al. 2018). Shamim et al. 2016, Rauf et al. 2016, and Rauf and Ghumman 2018 have used ANN models to simulate monthly stream flow for high altitude catchments in Pakistan. Flood events have also been predicted using SVR models (Kisi 2015; Ghorbani et al. 2016). However, data-driven models have several types based on the techniques used for input selection, training process, and optimization of various parameters/weights.

Selection of an appropriate type of data-driven models for a given situation is a challenging task (Ali et al. 2017; Zaini et al. 2018; Mishra et al. 2018; Londhe and Gavraskar 2018). This paper has compared the performance of a few of such techniques out of ANN and SVR to facilitate the engineers and scientists in choosing a comparatively accurate streamflow prediction model. Data-driven models are normally trained for a specific data and may have applications limited to a specific site. Hence, there is still a space to work with such models and explore various aspects related to these models. The impact of using various record lengths and data sets need to be studied further, which may definitely be useful for engineers and researchers working in this field of specialization. This is the first time these techniques have been used for streamflow forecasting from the Upper Indus River Basin (UIRB). To predict the monthly stream flow, the measured monthly precipitation (P), temperature (T), and stream flow (Q) with various time (t in months) lags (Pt, Pt-1, Pt-2, Pt-3, Pt-4, Pt-5, Tt, Tt-1, Tt-2, Tt-3, Tt-4, Tt-5, and Qt-1, Qt-2, Qt-3, Qt-4, Qt-5.) were taken as input variable for streamflow (Qt + 1) as output variable. An important step of this modeling was to identify the best input combination. The model has high complexity when there are a large number of inputs (Bray and Han 2004). Hence, an efficient technique is required to choose the best combination of inputs.

In the present paper, the ability of correlation coefficient analysis (CCA) and genetic algorithm (GA) has been investigated to select the best input combination for ANN and SVR models.

In addition to correlation between input and output with respect to time lag, there may be as well a variety of input combination with respect to the main input variables (temperature, precipitation, evaporation, river stage, streamflow, etc.). Some of the past studies in this regards include the research of Dhamge et al. (2012), Jajarmizadeh et al. (2015), Imen et al. (2015), Rauf et al. (2016), Wang et al. (2017a, b), and Adnan et al. (2017a, b). The literature provided by these studies shows that development of input combination with respect to time on the basis of three variables precipitation, temperature, and streamflow has rarely been reported. Researchers commonly used the precipitation and streamflow together and few used streamflow as a single input parameter. Dhamge et al. (2012) for example has used rainfall and runoff depth as input variable. Jajarmizadeh et al. (2015) has used precipitation, temperature, and streamflow as input variables. Aichouri et al. (2015), Rauf et al. (2016), and Wang et al. (2017a, b) have used precipitation and streamflow as input variable. Seyam et al. (2017) has used precipitation and water level as input variable. Tayyab et al. (2016), Mehr and Kahya (2017), Yaseen et al. (2017), and Adnan et al. (2017a, b) have used single variable streamflow as input.

In the present paper, a comparison has been made for the results of stream flow simulation from three input types with respect to the main input variables: (a) temperature, precipitation, and stream flow; (b) temperature and precipitation; and (c) stream flow only. The past data regarding monthly temperature, precipitation, and stream flow for UIRB were used. The total length of data collected is 30 years, i.e., from 1984 to 2014.

Study Area

The Indus River Basin comprises a total area of about 970,000 km2. However, the area selected for this study covers only Upper Indus Basin (UIB). It contains the catchment contributing to the upper part of the River Indus up to the Tarbela Reservoir, covering a basin area of about 175, 000 km2. UIB is surrounded by the world mightiest three mountain ranges that are the Karakoram, the Himalayan, and the Hindukush. This is expanded over the north-eastern and north-western part of Pakistan. The climate of the UIB is based on interaction between monsoon and westerlies (Lutz et al. 2016). UIB is a region undergoing a slightly increasing trend of snow cover in the southern (Western Himalayas) and northern (Central Karakoram) parts. Stream flow from the UIB is a combination of snow and glacier melt. The stream flow from rainfall is contributed from southern part, but snow and glacier melt are dominant in the northern part of the catchment (Tahir et al. 2015). The snow-fed sub-catchment of the Astore (sub-basin of UIB) was selected for the stream flow analysis. Astore catchment is located in the region of Gilgit-Baltistan and is about 120 km long having area of 5092 km2. The Astore basin was selected because it has an important geographical location (southern foothills of the Western Himalayas. The Indus River has some tributaries originating from these mountains The Astore River is one of the major tributaries of UIB region and any change in its flow into river Indus will have a considerable impact on the outflow of River Indus at Tarbela Reservoir. Figure 1 shows the location of Tarbela Dam at Indus River in Pakistan. The Astore River contributes an average annual flow of 228.8 m3/s to river Indus at Doyian. The Astore River stream flow is influenced by the winter rainfall at lower elevations which combines with the winter snowfall forced by Westerlies (Tahir et al. 2015). The data for this study were collected from the Astore hydro-climatic station, located at 35° 22′ N, 74° 51′ E with an elevation of 2394 m with respect to mean sea level and the Doyain river gauging station at 35° 45′ N, 74° 30′ E with an elevation of 1460.

Fig. 1
figure 1

Upper Indus Basin (UIB) and Astore catchment

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Methodology

The overall methodology is given in Fig. 2. Data regarding temperature, precipitation, and stream flow of upper Indus River was collected from 1984 to 2014. Three types of ANN models based on Broyden-Fletcher-Goldfarb-Shannon (BFGS), conjugate gradient (CG), and back propagation (BP) algorithms were used to simulate stream flow.

Fig. 2
figure 2

Step-wise methodology

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Artificial Neural Networks

ANN models are used to execute problems having high complexities. Many investigations have proven that ANN is a proficient technique for modeling nonlinear relationships between inputs and desired outputs in hydrologic time-series analyses (Humphrey et al. 2016; Aziz et al. 2017; Yazdani and Zolfaghari 2017). A general architecture and flow chart of ANN is shown in Fig. 3a, b. ANN consists of several “layers” of neurons, input layer having nodes representing various input variables, the hidden layer with many hidden nodes, and an output layer (Fig. 3a). Application of ANN to stream flow simulation requires selection of best variables, functions and weights, and optimization techniques, which could generate stream flow. Optimization techniques require an objective function based on errors between the simulated and measured stream flows. The values of parameters of model are changed every time in optimization process to find a solution such that the objective function achieves the minimum possible value (usually called global minimum). There are several techniques to change the parameters of model in every iteration and search the minimum value of objective function. Derivatives of objective function and constraints are used in some optimization techniques whereas others do not require derivatives and constraints. In stream flow prediction models, the algorithms that are faster in execution and robust in nature can be used for standard numerical optimization, e.g., conjugate gradient (CG), Quasi-Newton (QN), and Levenberg–Marquardt (Beale 1972; Fletcher 1987). The QN method has shown successful performance in several studies (Martınez 2000; Byrd et al. 2016; Leong et al. 2011). The method was developed by Broyden, Fletcher, Goldfarb, and Shanno (BFGS). The BFGS algorithm needs more computing in each repetition and also requires larger storage than CG method. It is an effective training function for smaller networks. Another method called the back propagation (BP) algorithm is common to train ANN. It is considered one of the simplest and most commonly used methods for optimization in ANN (Ganin et al. 2016; Wang et al. 2017a, b; Pellakuri and Rao 2016). In this study, the results of stream flow prediction for UIB by all the three training algorithms, i.e., the BFGS, CG, and BP have been compared.

Fig. 3
figure 3

a ANN architecture and flow chart. (b) Methodology for predicting the best output using the best input combination for ANN

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An efficient technique is required to select the best combination of input with respect to time lag. CCA and GA (Rauf and Ghumman 2018; Ganin et al. 2016; Wang et al. 2017a, b; Pellakuri and Rao 2016) were used to select the best input combination. The input data of the model were taken as the observed monthly rainfall, temperature, and stream flow for UIB. Four possible combinations C1, C2, C3, and C4 were selected by CCA and one by GA regarding time lag of input variables with respect to the corresponding output value of stream flow. The measured stream flow data for the same river were used as the target in the ANN model calibration and validation. Data from1985–2004 was used for the calibration/ training and learning of ANN and 2005 to 2014 for validation.

Support Vector Regression

SVR is an artificial intelligent-based supervised learning model. It is a two-layered network. The weights are nonlinear in the first layer and linear in the second (Bray and Han 2004). SVR can be applied to regression problems (Smola 1996; Kecman 2001). A general structure and flow chart of SVR model is shown in Fig. 4a, b. The basic mathematical function used in SVR is given by Eq. (1) (Lafdani et al. 2013)

$$ y=f(x)=\left[\sum \limits_{i=1}^N{\alpha}_iK\left({x}_i,x\right)\right]-b $$
(1)
Fig. 4
figure 4

a Structure of SVR model. b The methodology of selecting the best output from the best input combination for SVR modeling

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In Eq. (1), K is the kernel function, N is the number of training data points, xi represents vectors used in the training process, x is an independent vector, and αi and b are the parameters derived by the objective function maximization. There are four types of commonly used kernels, namely linear kernel, polynomial kernel, RBF kernel, and sigmoid kernel. Additional details may be seen from (Schölkopf and Smola 2002).

Several codes for SVR are available. The one used in this study is known as LIBSVM (Chang and Lin 2011), supported by the National Science Council of Taiwan. The modeling of SVR was done using MATLAB R2013a.

Genetic Algorithm

GA follows genetic principals by creating various combinations of inputs. The best one with respect to reducing the error in output and complexity of ANN and SVR models is obtained. GA can perform a global search. It consists of an iterative process for a constant-size population of individuals (inputs and weights). The GA is capable of effectively exploring large search spaces, which can be used with ANN for determining the number of hidden nodes and hidden layers, select relevant feature subsets and the learning rate. It initializes and optimizes the network connection weights of ANN. Further details can be seen from (Arena et al. 1992; Blanco et al. 2000). The Win Gamma Software was used in this study to run GA. From the available options in the Winn Gamma Software, GA was used for the identification of better input combination. The default values given in the software for various variables were considered for this study. The GA simulations developed 100 possible input combinations of which 10 best combinations were selected on the basis of least gamma (Ʈ) and standard error (SE) values. One best combination was selected out of these combinations for analysis with lowest Gamma value.

Gamma value (Ʈ)

The gamma Ʈ is the estimate of that part of the variance of the output which cannot be accounted for by a smooth data model. The gamma is actually the vertical intercept of the regression line (Evans and Jones 2002).

Standard Error

This is the usual goodness of fit applied to the regression line. If this number is close to zero, one has more confidence in the value of the gamma as an estimate of the noise variance on the given output. The standard error (SE) is defined as (Krause et al. 2005; Lafdani et al. 2013).

$$ \mathrm{SE}=\sigma /\surd n $$
(2)

where σ is the standard deviation of the population and n is the size (number of observations) of the sample.

The comparatively lower values of Ʈ and SE indicate that the given combination will produce lower complexity in modeling with better predicted results of stream flow.

Correlation Coefficient Analysis

A correlation coefficient is a number that quantifies the statistical relationships between two or more variables. Here, this relationship has been determined between the 17 input parameters (PPT, temp, and streamflow) and one output streamflow. The correlation coefficient analysis was performed using statistical tool available in MS Excel for the purpose. The correlated values classified as most effective correlation values (> 50% correlation) and least effective correlation values (< 50% correlation). Positive correlation indicates that for any two variables say Pt-1 and Qt + 1, both the variables increase and decrease together, whereas a negative correlation coefficient means that, an increase in Pt-1 is associated with a decrease in Qt + 1. Correlation coefficients have values always between − 1 and 1. The value − 1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation. The most effective parameters were found to be Pt-3, Tt, Tt-1, Tt-5, and Qt-1 while Pt-2, Pt-4, Pt-5, Tt-4, Qt-2, and Qt-4 comes out as the least effective parameters. The input parameters having most effective correlation with the output were considered for the development of the input combinations. Four different input combinations were developed on this criterion. Similarly, the input combinations were developed for other two input types having two variables as precipitation and temperature and single variable streamflow only.

Model Performance Evaluation

There are a number of statistical parameters to measure the performance of the models (Burnham 2002). The most widely used parameters were adopted in this study (Krause et al. 2005; Lafdani et al. 2013; Shamim et al. 2016; Rauf et al. 2016).

  1. 1.

    Root mean square errors (RSME)

    $$ \mathrm{RMSE}=\sqrt{\sum_{i=1}^n\frac{{\left({Q}_i^p-{Q}_i^o\right)}^2}{n}} $$
    (3)
  2. 2.

    Mean bias error (MBE)

    $$ \mathrm{MBE}={\sum}_{i=1}^n\frac{\left({Q}_i^p-{Q}_i^o\right)}{n} $$
    (4)
  3. 3.

    The correlation between actual and predicted values (R2):

    $$ {R}^2=1-\frac{\left({Q}_i^o-{Q}_i^p\right)}{\left({Q}_i^o-{Q}_{avg}\right)} $$
    (5)
  4. 4.

    Nash–Sutcliffe model efficiency coefficient (NSE)

    $$ \mathrm{NSE}=1-\frac{\sum_{\mathrm{i}=1}^{\mathrm{n}}{\left({Q}_i^o-{Q}_i^p\right)}^2}{\sum_{\mathrm{i}=1}^{\mathrm{n}}{\left({Q}_i^o-{Q}_{avg}\right)}^2} $$
    (6)

In the above equations, \( {Q}_i^p \) represents the predicted value of streamflow, \( {Q}_{\mathrm{i}}^{\mathrm{o}} \) represents the observed values of stream flow, Qavg is the average of observed stream flow, and n represents the total number of input samples.

Results and discussion

Input Combinations

Various input combinations assessed by GA for the input type having all three parameters are shown in Table 1. Figure 5 illustrates Ʈ and SE variations. It is observed that the 10101110100110100 (nine inputs as Pt, Pt-2, Pt-4, Pt-5, Tt, Tt-2, Tt-5, Qt-1, Qt-3 for single output Qt + 1) was the best combination of given input variables and was selected for analysis on basis of least gamma and SE value. It shows that precipitation and temperature within a time lag of running month (t) and five previous months(t−5) have an impact on stream flow Qt + 1, whereas only two previous values of stream flow (Qt-1, Qt-3) are linked to Qt + 1. According to Slater and Villarini (2017), the variability of precipitation is key parameter for high stream flows. The temperature is driving factor for streamflow predictions in seasons and catchment areas having notable snowmelt. The stream flow of UIB contains glacier melt components, flow from rain, and a groundwater component. So the selected input combination is logical and understandable. The correlation values among various input variables and output in case of CCA are shown in Fig. 6. Here, the negative (−ve) values of correlation show that such an input values will give decreasing values of output Q. Hence, the input variables, Pt-3, Tt, Tt-1, Tt-5, and Qt-1, correlate highly to the output parameter (Qt + 1). Considering the most correlating input parameters predicted by CCA, four input combinations (given in Table 2) were used in ANN and SVR modeling. It is worth mentioning that some percentage of subjectivity is involved in selecting the input combinations on the basis of CCA.

Table 1 Ten selected input combinations on basis of lowest gamma (Ʈ) and standard error (SE) values developed by GA simulations
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Fig. 5
figure 5

Gamma and SE of the data corresponding to input combinations

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Fig. 6
figure 6

Correlation between different input variables and streamflow (Qt + 1)

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Table 2 Input combinations developed by CCA
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Results of Stream Flows Modeling

ANN models

The R2, RMSE, NSE, and MBE for various-ANN models from different input combinations for all the three parameters (P, T, and Q) developed by GA and CCA are given in Figs. 7, 8, and 9 and Table 3. Comparison of observed and predicted stream flow for the testing phase of various ANN models is represented by Figs. 10 and 11. Italic values in Table 3 represent the best values of indices. It is observed that hardly any model has best values of all the four indices. One model has the best R2 value whereas the other has lowest RMSE. One has the highest NSE and other has the best value of MBE. For example, BFGS-ANN model based on input combination of CCA-C3 has highest R2 (Fig. 7) whereas the same model based on GA has the lowest value of RMSE. A similar situation can be seen from other figures. Hence, selection/rejection of the best possible model should not be based on a single evaluating index. However, the indices in these figures show that all input combinations produced acceptable accuracy which demonstrates the high-efficiency selecting algorithms CCA and GA and the ANN models. However, the input combination determined through CCA can be marked as comparatively better than that of GA because its performance both in training and testing phase is better. The best ANN model with respect to overall performance is the BFGS algorithm. The accuracy depends upon the choice of input and the optimization method used in ANN. As the efficiency of optimization method increases, it brings higher accuracy in the simulated stream flow. It is proven that the combination of CCA/GA and efficient optimization technique BFGS improves the performance of ANN model significant. Similarly, the ANN models were developed using input combinations for two variables (P and T) and single variable. The results are given in Tables 4 and 5.

Fig. 7
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Errors and correlation coefficient (BFGS-ANN model)

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Fig. 8
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Errors and correlation coefficient (CG-ANN model)

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Fig. 9
figure 9

Errors and correlation coefficient (BP-ANN model)

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Table 3 Values of Indices for the best input combination predicted for ANN modeling based on the GA/CCA
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Fig. 10
figure 10

Scatter plot of observed and predicted stream flow by best ANN models for testing data sets

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Fig. 11
figure 11

Comparison of the observed Vs predicted stream flow by ANN models using GA and CCA

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Table 4 Values of indices for the best input combination (only P and T) predicted for ANN modeling based on the GA/CCA
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Table 5 Values of indices for the best input combination (only streamflow) predicted for ANN modeling with GA/CCA
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SVR Models

Results obtained by using four selected kernels in SVR model based on the input combination selected by GA are compared to that of CCA in Figs. 12, 13, 14, and 15. The best combinations determined for the different selected SVR kernel models are given in Table 6. The SVR with RBF kernel shows the best results with minimum RMSE = 1.0 and maximum R2 = 0.811 in case of combination of nine inputs for single output. The performance of the SVR-RBF kernel with input combination C2 from CCA was good in the training phase, while in the testing phase, the input combination C4 showed the best results with the lowest RMSE. The curves of predicted stream flows (Qt + 1) versus observed stream flows from Epsilon-SVR models for the testing phase are shown in Figs. 16 and 17. Similarly, the SVR models were developed using input combinations for two variables (P and T) and single variable (only Q). The results are given in Tables 7 and 8.

Fig. 12
figure 12

Errors and correlation coefficient (SVR–linear kernel model)

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Fig. 13
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Errors and correlation coefficient (SVR–polynomial kernel model)

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Fig. 14
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Errors and correlation coefficient (Epsilon–SVR–RBF kernel model)

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Fig. 15
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Errors and correlation coefficient (SVR—Sigmoid kernel model)

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Table 6 The best input combinations for SVR models
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Fig. 16
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Scatter plot of observed and predicted discharge by Epsilon-SVR models

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Fig. 17
figure 17

Comparison of the observed and predicted stream flow by SVR models using GA and CCA

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Table 7 Values of indices for the best input combination (only P and T) predicted for SVR modeling based on the GA/CCA
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Table 8 Values of indices for the best input combination (only Q) predicted for SVR modeling based on the GA/CCA
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Comparison of SVR and ANN Models

The performance of the SVR and ANN models is compared in Table 9 and Figs. 18 and 19. The performance of BFGS-based ANN model is better than SVR (RBF kernel) model. The R2 is 0.846, 0.811 and RMSE is 0.616 and 1.0 respectively for the two models. Furthermore, BFGS-ANN and SVR (RBF kernel) models have the best NSE values, 0.846 and 0.800 respectively.

Table 9 Comparison of ANN and SVR models using three variables (P, T, and Q), two variables (P and T) and one variable (Q only) as input combinations
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Fig. 18
figure 18

Comparison between SVR and ANN models for prediction of future discharge

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Fig. 19
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ANN and SVR models with the best input (simulated and observed stream flow)

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Future Stream Flow Predictions

Figures 20 and 21 show the future precipitation and stream flow predicted by the ANN model. It is evident from the figures that the precipitation and stream flow are almost of the same pattern, indicating that the stream flow is depending on the precipitation in the region and any change in precipitation due to climatic variability will have an effect on stream flow of river Indus The figures show that precipitation is decreasing from 2015 to 2045, while in the same period, the stream flow is being increased. This might be due to high snowmelt caused by the rising temperature during the said period. In the mid-twenty-first century, the precipitation is seen to be increasing, which is causing an increase in the stream flow during the period. The figures show the alarming picture at the end of the century that both precipitation and stream flow are decreasing till the start of the twenty-second century.

Fig. 20
figure 20

Future precipitation predicted by the ANN model

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Fig. 21
figure 21

Future stream flows predicted by the ANN method

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Summary, Conclusion, and Recommendations

In this study, two types of data-driven techniques, ANN and SVR were applied to develop models for predicting stream flow in the UIB. The GA and CCA were used to predict the best input combination for stream flow forecasting. The performance of three different ANN and four SVR models was compared using four statistical parameters (R2, RMSE, MBE, and NSE). Determination of the best input combination for nonlinear systems like streamflow is a complex and challenging process. Hence, the aim of this study was to determine the most effective combination of input variables to be used for data-driven modeling, like ANN and SVR, for short-term streamflow forecasting.

The SVR-RBF kernel with input combination identified by CCA had better performance than the other three SVR models (linear, polynomial, and Sigmoid kernel) both in the training and testing phase. The results also showed that BPNN models had better performance than BFGS-ANN and CG-ANN that of in the training phase while in the testing phase, BFGS-ANN and CG-ANN models showed the better results than BPNN models for input combination identified by CCA. In brief, the BFGS-ANN model and SVR model (RBF kernel) produced the best performance in streamflow forecasting. The performance of input combination identified by the CCA is better than that of GA. The input combination, “Pt-3, Tt, Tt-1 Tt-2, Tt-5, Qt-1, Qt-5,” showed the best results for BFGS-ANN model.

The input combinations developed for three variables (P, T, and Q) show comparatively better results than that from the input combinations developed using two variables (P and T) and single variable (Q only).

To improve the study further, we recommend that the results obtained from GA test be compared against other input selection methods, e.g., principal component analysis and fuzzy system, to predict streamflow through ANN and SVR models with higher reliability. The results obtained in this study are for the monthly data inputs and can be improved if daily data are used for the purpose.