Abstract

Modelling of runoff is a significant practice in water resources engineering. Therefore, discovering consistent and advanced methods for prediction of runoff is crucial for hydrologic processes. Here, a narrative integrated intelligence model attached with PSR (phase space reconstruction) is anticipated to estimate runoff for five watersheds of Balangir, Odisha, India. Monthly monsoon precipitation, temperature, humidity data of five watersheds over 28 years (1990–2017) are employed and validated. Here, the proposed model is an integration of support vector machine (SVM) with firefly algorithm (FFA) and PSR. Various indices such as NSE (Nash–Sutcliffe), RMSE (root mean square error) and WI (Willmott's index) are used to find the performance of the model. The developed PSR-SVM-FFA model demonstrates pre-eminent WI value ranging from 0.97 to 0.98 while the SVM and SVM-FFA models encompass 0.92 to 0.93 and 0.94 to 0.95, respectively. Also, an assessment of data from the suggested model is schemed and validated. The proposed PSR-SVM-FFA model gives better accuracy results and error limiting up to 2–3%.

Highlights

  • The most relevant techniques are used for performing the output of rainfall-runoff process at a single outlet. The advances gained from a modelling point of view are considered and discussed.

  • The models developed using three techniques are support vector machine (SVM), support vector machine with firefly algorithm (SVM-FFA) and support vector machine and firefly algorithm with Phase space reconstruction (PSR-SVM-FFA) in the study.

  • The study is different from previous studies by including and comparing two new techniques, SVM-FFA and PSR-SVM-FFA, while past research has used hybridization of SVM for predicting runoff in a watershed.

  • Interaction of all techniques along with five different models is presented.

  • The model proposed reasonably predicts the runoff at a single outlet and improves the method of measuring runoff without the detailed study for all sub-outlets of the watershed.

INTRODUCTION

Improvement in water resources is essential for balancing water demand around the globe. Due to the complex nature and uncertainty in water parameters, traditional methods like statistical method, Dickens formula (1865), Ryves formula (1984), and Khosla formula (1960) are insufficient to understand the cycle of rainfall-runoff (Das 2009). Innovative computational algorithms and their application to water resources engineering are necessary to understand the behaviour of the water cycle in the context of climate change. Computational algorithms in view of modern techniques like FFA, SVM and PSR are important for engineering applications. Attempts have also been made to apply these techniques to water resources engineering (Tayfur 2014).

Tabari et al. (2012) employed the SVM, ANFIS (adaptive neuro-fuzzy inference system), MLR (multiple linear regression) method utilizing six climate data variables as inputs to estimate evapotranspiration at Nozheh station, Iran. Outcomes suggested that SVM and ANFIS models perform better with greater precision than those of regression and climate-based models. Baydaroglu & Kocak (2014) applied support vector regression (SVR) to envisage water loss using solar radiation, relative humidity, wind speed, evaporation and temperature as input. SVR helps in predicting evaporation effectively since it has a good generalization ability with greater determination coefficients of 83 and 97% for univariate and multivariate time series entrenching. Raghavendra & Deka (2014) in their review found that SVM is more suitable for prediction than other techniques pertinent to hydrology. Cha et al. (2014) projected the SVM-FFA model for more precise forecast of malaria incidences in the Jodhpur and Bikaner area. Performance of the projected hybrid model was compared with ANN, autoregressive moving average as well as SVM and results indicated that the proposed integrated model provides forecasts with better accuracy as compared to traditional methods. The FNN (feed forward neural network) technique was used for monthly stream flow forecasting for a period of 53 years in the United States by Vignesh et al. (2015). Obtained outcomes are valuable in identifying suitable model intricacy at discrete stations, arrangements across regions and sub-regions, interpolating and extrapolating data, and classifying catchments. SVM-FFA and SVM-wavelet were used to evaluate precipitation trends in 29 meteorological stations in Serbia from 1946 to 2012 by Gocic et al. (2016). Estimation and prediction outcomes of hybrid models were contrasted and results showed that the SVM-wavelet approach gives improved prediction accuracy and ability to generalize. Moghaddam et al. (2016) implemented SVM-FFA for predicting the exhaustion lifetime of polyethylene terephthalate (PET) reformed asphalt mixture taking PET percentages, stress levels and environmental temperatures as inputs. Prediction results by SVM-FFA were compared against ANN and genetic programming (GP) and it was found that the hybrid model performs better. Al-Shammari et al. (2016) projected a hybrid method integrating SVM with FFA for predicting daily dew point temperature (Tdew) for an Iranian city and performance of the hybrid model is compared to SVM, ANN and GP. They observed that SVM-FFA is certainly very efficient in predicting Tdew with better accuracy and consistency. Integrated PSR–ANN and ANN techniques were utilized to predict daily river flow on river gauging stations in the USA by Delafrouz et al. (2017). The outcomes of PSR–ANN, ANN and gene expression programming models were compared and it was found that the projected hybrid model gives the best prediction accuracy for daily river flow. Mehr et al. (2018) employed integration of FFA and SVM for rainfall forecasting on a monthly basis at Tabriz and Urmia stations, Iran. The effectiveness of the hybrid model was cross-checked with SVR and GP-based forecasting models and it was found that the SVM-FFA model performs well with promising accuracy in terms of rainfall forecasting. Ghose & Samantaray (2019) employed LRNN (layer recurrent NN), RBFN (radial basis function NN) and FFBPN (feed forward back propagation NN) to evaluate runoff as a loss function of evapotranspiration, temperature and precipitation. Outcomes revealed that performance of the LRNN model is best as compared to FFBPN and RBFN for predicting runoff in the watershed which helps in planning, designing and managing hydraulic structures in the neighbourhood of the watershed. Zaini et al. (2018) used an SVM model and also a hybridized SVM-PSO (particle swarm optimization) model to scheme daily stream flow at Upper Bertam watershed, Malaysia. Hybridized models SVM-PSO1 and SVM-PSO2 perform best in comparison to SVM1 and SVM2 at forecasting river flow 1–7 days ahead. Tao et al. (2018) used SVM and SVM-FFA to anticipate rainfall at Chhattisgarh. The proposed hybrid model significantly improved forecasting accuracy and can also be used for monthly rainfall forecasting in provincial areas of India. Gandomi et al. (2011) utilized FFA to solve mixed variable structural optimization problems and also the implications of FFA are thoroughly analysed in comparison with PSO, GA, simulated annealing for future research. Ji & Sun (2013) presented a method for multitasking multiple classes of SVM on the basis of minimizing regularization functions and found it to be best among other multitask learning methods. Shamshirband et al. (2015) proposed a hybrid SVM-FFA model for estimating monthly mean horizontal global solar radiation (HGSR). Performance of the hybrid model is evaluated by comparing it with ANN, GP and ARMA (autoregressive moving average) models and results revealed that the projected hybrid model performs best.

Several researchers have found different individual algorithms for predicting runoff. Some have also developed optimization methods and least integrated methods to predict runoff. Thus, an attempt has been made to think about the hybrid model via integral algorithms. The objective of this research is to compare results of the SVM-FFA, PSR-SVM-FFA model with the SVM and empirical models to tune up the magnitude of runoff for controlling flood in the region. Basically, it is applicable for efficient planning and management of water resources such as flood control and management of a watershed.

STUDY AREA

Balangir district is located in the west part of Odisha, India, with an area of 5,165 km2, as shown in Figure 1. It lies between the latitudes of 20°59′00″ and longitudes of 83°32′22″. It has an average elevation of 115 metres (377 feet). The watershed is located towards the mid-north edge of Balangir district. Five gauging stations, Loisinga, Balangir, Tushura, Saintala and Patnagarh, are considered in the present research.

Figure 1

Schematic diagram of the proposed watershed.

Figure 1

Schematic diagram of the proposed watershed.

Figure 2

Graphical description of SVM model.

Figure 2

Graphical description of SVM model.

Physical and statistical characteristics of the gauging stations are described in Table 1. Here, prediction of runoff is assessed by taking the dataset from 1990 to 2017. Mean monthly precipitation and temperature data for the monsoon months (May to October) from the period 1990–2017, spanning over 28 years, are obtained from IMD (India Meteorological Department) Bhubaneswar. Runoff data are collected from the soil conservation office, Bolangir. Here, the runoff data are computed using Khosla's empirical equation to understand the coherence between developed empirical data and observed data collected from that department.

Table 1

Physical and statistical characteristics of five stations in Balangir, Odisha, India

Station nameDrainage area (km2)LatitudeLongitudeElevation (m)Mean rainfall (mm)Min.–Max. rainfall (mm)
Loisinga 317.6 20.86N 83.50E 162 91.22 7.83–158.8 
Balangir 386.98 20.7N 83.5E 115 87.82 7.93–157.29 
Deogaon 432.01 20.71N 83.49E 148 93.69 7.28–155.26 
Saintala 454.43 20.26N 83.20E 182 87.795 7.45–159.56 
Patnagarh 591.45 20.72N 83.15E 243 87.23 7.89–151.34 
Station nameDrainage area (km2)LatitudeLongitudeElevation (m)Mean rainfall (mm)Min.–Max. rainfall (mm)
Loisinga 317.6 20.86N 83.50E 162 91.22 7.83–158.8 
Balangir 386.98 20.7N 83.5E 115 87.82 7.93–157.29 
Deogaon 432.01 20.71N 83.49E 148 93.69 7.28–155.26 
Saintala 454.43 20.26N 83.20E 182 87.795 7.45–159.56 
Patnagarh 591.45 20.72N 83.15E 243 87.23 7.89–151.34 

METHODOLOGY

Khosla formula

Khosla considered precipitation, discharge and temperature data for different catchments in India and the USA to arrive at a pragmatic connection as follows in Equation (1). It is circuitously anchored in the water-balance perception and mean monthly temperature to replicate losses due to evapotranspiration:
formula
(1)
formula
where is monthly runoff, is monthly rainfall, is monthly losses and is mean monthly temperature of the catchment.

Support vector machine model

A technique with statistical learning theory and promising empirical results for recognition of pattern with high dimension data to avoid error with decision boundary using training in terms of support vector is known as a support vector machine (Cortes & Vapnik 1995).

A graphical description of the SVM model is shown in Figure 2. The principles of SVM include statistical learning known as structural risk minimization, which affords a higher boundary for generalization error of a classifier (R) concerning training error (Re), model complexity (h) and number of training examples (N) to evaluate probability of error and is defined as (Chen et al. 2018; Thanh & Kappas 2018; Wang et al. 2018a):
formula
(2)
where is monotonic increasing function of the model complexity.
This is enviable when designing a linear classifier which maximizes margins of their decision boundaries to minimize error. In this regard, SVM is an effective linear classifier which searches a hyper plane with the largest margin called the maximal marginal classifier. The decision boundary of the linear classifier is:
formula
(3)
The training phase of SVM involves estimation of constraints weight (w), bias (b) of decision boundary from the training data set. Parameters are preferred with the below conditions:
formula
formula
(4)
The objective function is the Lagrangian multiplier and denoted as:
formula
(5)
The linear programming is to be utilized through Karush–Kuhn–Tucker (KKT) conditions and the KKT condition is:
formula
formula
(6)

Integration of SVM with FFA model fitness

The FFA is a natural algorithm based on the blinking manners of fireflies (Yang 2009; Abd-Elazim & Ali 2018; Lieu et al. 2018; Wang et al. 2018b, 2018c). Since the complex nature of fireflies induces global communication among swarming particles, effective multi-objective optimization is necessary to recognize the multifaceted algorithm of FFA. In this algorithm, fireflies use flashing light to search for mates, to attract potential prey for protection from their predators. In order to achieve efficient optimal solutions, flashing light intensity induces fireflies to a more attractive position associated with objective function of the problem.

There are some components in FFA, such as distance, attractiveness and movement.

Euclidian distance

Euclidian distance is the distance between two fireflies i and j at locations ui and uj, defined as Euclidean distance (rij) applying Equation (7), where ui,k is the kth factor of spatial coordinate ui of ith firefly and d is dimension number:
formula
(7)

Attractiveness

Attractiveness task of a firefly is revealed in Equation (8):
formula
(8)

Movement

Progress of firefly i is towards an extra striking firefly j and is specified by Equation (9):
formula
(9)
where is the current position of firefly, is active for allowing a firefly's attractiveness to light intensity and is applied for random movement of a firefly.

The settings of firefly algorithm (FA) parameters: (light absorption coefficient) = 1.0, (randomization parameter) = 0.3, (attractiveness value) = 1.0 and random number generator consistently disseminated in space [0, 1] = 0.2. A flowchart of the SVM-FFA model is shown in Figure 3.

Figure 3

Descriptive flowchart of SVM-FFA model.

Figure 3

Descriptive flowchart of SVM-FFA model.

Objective function

F (Y), Y=(Y1, Y2, Y3, ………..,Yk)Z

Fireflies' initialization, Yj(j=1,2,3,4,………….m)

Concentration of light Lj at Yj, f(Yj)

Light preoccupation coefficient β

While z<maximum generation do

  For j=1:m all m fireflies do

    For i=1:i all m fireflies do

      If Li>Lj then

Transfer firefly j towards i in k dimension

      End if

Attractiveness diverges with distance r through exp[-βr]

Calculate high result and update intensity of light

      End for

    End for

Evaluate best value

End while

Final result and conception

Integration of PSR coupled with SVM-FFA model

Illustration of hybrid extravagance model is demonstrated in Figure 4. The models involve the subsequent modelling process (Dutta et al. 2018; Fan et al. 2018; Hajiloo et al. 2018; Sun & Wang 2018).

  • (i)

    First phase, optimal τ and m is established to accomplish MIF and FFN approaches for embattled index phase space reconstruction. In this manner, phase space will converge from input aspects and abstract critical dynamics of chaotic time series.

  • (ii)

    Second phase, input matrix is assembled rooted in several dimensions Xt, Xt−τ, Xt−2τ, …, Xt−(m−1)τ by considering optimal τ and m, for targeted value Xt+1. According to the PSR technique, an input matrix is proposed (Sivakumar et al. 2001).

  • (iii)

    Third phase, the hybrid SVM-FFA model is fed by the produced matrix using phase space signal.

Figure 4

Graphical representation of hybrid PSR-SVM-FFA.

Figure 4

Graphical representation of hybrid PSR-SVM-FFA.

Objective function

For univariate time signal , PSR is
formula
where, N is time series, is lag and is embedding dimension for X1.
For multivariate time series,
formula
PSR computes the reconstruction for each time series:
formula
  • s: measurement number.

Delay estimation

For delay, PSR allows average mutual information (AMI).

For reconstruction, time delay is first local lowest AMI.
formula

Τ = 1 [for max. lag].

Embedding dimension (ED) estimation

ED for PSR is appraised utilizing the false nearest neighbour (FNN) algorithm. For I point at d dimension, points Xri and adjacent point Xr*I in reconstructed phase space {Xri}, i = 1:N, are false neighbours if > distance threshold where, is distance metric, d is smallest value; <per cent false neighbours and is ratio of FNN points to total PSR quantity.

Processing and preparation of data

Humidity, temperature and monthly average rainfall are composed of data from the meteorological department of India for a season of monsoon months (May to October) for 1990–2017. Data from 1990 to 2009 are employed for training and from 2010 to 2017 are considered for testing the model. Daily data are transformed into monthly data, which finally helps in training and testing the model. Subsequent runoff arrangements are employed as input (Table 2).

Table 2

Input constraints for SVM, SVM-FFA model

InputModel name (SVM)Model name (SVM-FFA)
 SVM1 SVMI-FFA 
 SVM2 SVM2-FFA 
 SVM3 SVM3-FFA 
 SVM4 SVM4-FFA 
 SVM5 SVM5-FFA 
InputModel name (SVM)Model name (SVM-FFA)
 SVM1 SVMI-FFA 
 SVM2 SVM2-FFA 
 SVM3 SVM3-FFA 
 SVM4 SVM4-FFA 
 SVM5 SVM5-FFA 

where, is one-month lag runoff, is two-month lag runoff, is three-month lag runoff, is four-month lag runoff and is five-month lag runoff.

Model performance evaluation

The indicators NSE, RMSE and WI are used to assess the performance of model efficiency. The formulae can be articulated as:
formula
(10)
formula
(11)
formula
(12)
where, Oi and Pi are observed and predicted ith runoff and is mean of observed runoff.

RESULTS AND DISCUSSION

Runoff is estimated by using the Khosla formula for five watersheds in the monsoon period (May–October) for 1990–2017. A graphical representation of mean monthly runoff is presented in Figure 5.

Figure 5

Estimated mean monthly runoff of monsoon season for proposed watershed.

Figure 5

Estimated mean monthly runoff of monsoon season for proposed watershed.

The performances of the SVM model with different inputs for the five proposed watersheds are presented in Table 3. Three evaluating parameters, NSE, RMSE and WI, are estimated for both testing and training phases as explained below.

Table 3

Results of SVM model for runoff prediction

PositionsModelTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir SVMI 0.513 91.93 0.841 0.486 88.93 0.849 
SVM2 0.548 87.17 0.857 0.509 85.48 0.864 
SVM3 0.597 84.86 0.874 0.552 81.39 0.881 
SVM4 0.642 80.05 0.869 0.601 77.91 0.886 
SVM5 0.681 76.98 0.935 0.653 73.92 0.942 
Loisinga SVMI 0.497 93.78 0.826 0.451 91.95 0.845 
SVM2 0.518 89.42 0.831 0.486 88.12 0.857 
SVM3 0.561 85.18 0.862 0.537 83.85 0.884 
SVM4 0.598 77.04 0.886 0.552 75.93 0.905 
SVM5 0.636 72.73 0.919 0.601 70.21 0.925 
Patnagarh SVMI 0.505 92.75 0.818 0.478 90.68 0.832 
SVM2 0.531 88.51 0.835 0.507 85.08 0.856 
SVM3 0.574 84.94 0.862 0.541 80.59 0.881 
SVM4 0.605 81.62 0.881 0.576 78.38 0.907 
SVM5 0.648 76.83 0.927 0.613 73.41 0.931 
Saintala SVMI 0.527 92.85 0.795 0.485 90.03 0.821 
SVM2 0.551 88.22 0.829 0.517 86.62 0.857 
SVM3 0.605 83.94 0.857 0.554 81.79 0.882 
SVM4 0.663 79.05 0.874 0.617 75.91 0.914 
SVM5 0.692 73.82 0.938 0.658 69.73 0.947 
Deogaon SVMI 0.518 92.65 0.805 0.496 90.52 0.831 
SVM2 0.547 88.91 0.826 0.501 86.01 0.852 
SVM3 0.582 85.57 0.853 0.549 82.59 0.886 
SVM4 0.621 81.48 0.882 0.584 78.71 0.918 
SVM5 0.683 77.73 0.945 0.648 74.05 0.953 
PositionsModelTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir SVMI 0.513 91.93 0.841 0.486 88.93 0.849 
SVM2 0.548 87.17 0.857 0.509 85.48 0.864 
SVM3 0.597 84.86 0.874 0.552 81.39 0.881 
SVM4 0.642 80.05 0.869 0.601 77.91 0.886 
SVM5 0.681 76.98 0.935 0.653 73.92 0.942 
Loisinga SVMI 0.497 93.78 0.826 0.451 91.95 0.845 
SVM2 0.518 89.42 0.831 0.486 88.12 0.857 
SVM3 0.561 85.18 0.862 0.537 83.85 0.884 
SVM4 0.598 77.04 0.886 0.552 75.93 0.905 
SVM5 0.636 72.73 0.919 0.601 70.21 0.925 
Patnagarh SVMI 0.505 92.75 0.818 0.478 90.68 0.832 
SVM2 0.531 88.51 0.835 0.507 85.08 0.856 
SVM3 0.574 84.94 0.862 0.541 80.59 0.881 
SVM4 0.605 81.62 0.881 0.576 78.38 0.907 
SVM5 0.648 76.83 0.927 0.613 73.41 0.931 
Saintala SVMI 0.527 92.85 0.795 0.485 90.03 0.821 
SVM2 0.551 88.22 0.829 0.517 86.62 0.857 
SVM3 0.605 83.94 0.857 0.554 81.79 0.882 
SVM4 0.663 79.05 0.874 0.617 75.91 0.914 
SVM5 0.692 73.82 0.938 0.658 69.73 0.947 
Deogaon SVMI 0.518 92.65 0.805 0.496 90.52 0.831 
SVM2 0.547 88.91 0.826 0.501 86.01 0.852 
SVM3 0.582 85.57 0.853 0.549 82.59 0.886 
SVM4 0.621 81.48 0.882 0.584 78.71 0.918 
SVM5 0.683 77.73 0.945 0.648 74.05 0.953 

Bold font indicates best value of model performance.

Among the five models, the SVM5 model shows the best result with WI 0.935 and 0.942 for training and testing period, respectively, while ,, are considered as input parameters for Balangir watershed. For the remaining watersheds, model SVM5 gives best WI value for both phases out of five simulations. In the case of the Loisinga watershed, the pre-eminent WI values for training and testing periods are 0.919 and 0.925 for model SVM5. For the training phase at Patnagarh, Saintala and Deogaon watersheds, principal WI values are 0.927, 0.938 and 0.945, respectively. The result for the SVM-FFA model based on NSE, RMSE and WI for testing and training periods is given in Table 4.

Table 4

Outcomes of SVM-FFA model for runoff prediction

PositionsModelTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir SVMI-FFA 0.694 89.71 0.846 0.673 86.48 0.859 
SVM2-FFA 0.717 86.04 0.862 0.698 82.71 0.864 
SVM3-FFA 0.759 80.54 0.899 0.736 79.03 0.903 
SVM4-FFA 0.782 76.82 0.926 0.758 75.66 0.941 
SVM5-FFA 0.815 74.34 0.965 0.791 70.72 0.971 
Loisinga SVMI-FFA 0.681 90.55 0.835 0.662 90.55 0.841 
SVM2-FFA 0.708 86.81 0.847 0.689 86.27 0.865 
SVM3-FFA 0.746 82.59 0.892 0.716 80.91 0.901 
SVM4-FFA 0.772 76.68 0.926 0.751 73.78 0.937 
SVM5-FFA 0.807 70.39 0.958 0.783 68.49 0.961 
Patnagarh SVMI-FFA 0.679 91.84 0.818 0.649 88.81 0.825 
SVM2-FFA 0.692 87.96 0.858 0.662 83.96 0.864 
SVM3-FFA 0.737 83.68 0.885 0.709 78.78 0.899 
SVM4-FFA 0.769 78.17 0.929 0.726 75.93 0.937 
SVM5-FFA 0.791 74.09 0.953 0.754 70.07 0.962 
Saintala SVMI-FFA 0.688 90.38 0.825 0.648 88.81 0.836 
SVM2-FFA 0.711 86.17 0.859 0.672 84.35 0.868 
SVM3-FFA 0.745 81.04 0.907 0.705 79.16 0.913 
SVM4-FFA 0.781 77.91 0.924 0.751 73.49 0.935 
SVM5-FFA 0.813 70.55 0.955 0.793 67.88 0.966 
Deogaon SVMI-FFA 0.693 90.01 0.848 0.654 89.28 0.855 
SVM2-FFA 0.713 85.63 0.869 0.689 84.96 0.885 
SVM3-FFA 0.759 83.86 0.914 0.723 80.81 0.929 
SVM4-FFA 0.792 79.47 0.939 0.751 76.67 0,946 
SVM5-FFA 0.828 74.28 0.961 0.779 70.11 0.974 
PositionsModelTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir SVMI-FFA 0.694 89.71 0.846 0.673 86.48 0.859 
SVM2-FFA 0.717 86.04 0.862 0.698 82.71 0.864 
SVM3-FFA 0.759 80.54 0.899 0.736 79.03 0.903 
SVM4-FFA 0.782 76.82 0.926 0.758 75.66 0.941 
SVM5-FFA 0.815 74.34 0.965 0.791 70.72 0.971 
Loisinga SVMI-FFA 0.681 90.55 0.835 0.662 90.55 0.841 
SVM2-FFA 0.708 86.81 0.847 0.689 86.27 0.865 
SVM3-FFA 0.746 82.59 0.892 0.716 80.91 0.901 
SVM4-FFA 0.772 76.68 0.926 0.751 73.78 0.937 
SVM5-FFA 0.807 70.39 0.958 0.783 68.49 0.961 
Patnagarh SVMI-FFA 0.679 91.84 0.818 0.649 88.81 0.825 
SVM2-FFA 0.692 87.96 0.858 0.662 83.96 0.864 
SVM3-FFA 0.737 83.68 0.885 0.709 78.78 0.899 
SVM4-FFA 0.769 78.17 0.929 0.726 75.93 0.937 
SVM5-FFA 0.791 74.09 0.953 0.754 70.07 0.962 
Saintala SVMI-FFA 0.688 90.38 0.825 0.648 88.81 0.836 
SVM2-FFA 0.711 86.17 0.859 0.672 84.35 0.868 
SVM3-FFA 0.745 81.04 0.907 0.705 79.16 0.913 
SVM4-FFA 0.781 77.91 0.924 0.751 73.49 0.935 
SVM5-FFA 0.813 70.55 0.955 0.793 67.88 0.966 
Deogaon SVMI-FFA 0.693 90.01 0.848 0.654 89.28 0.855 
SVM2-FFA 0.713 85.63 0.869 0.689 84.96 0.885 
SVM3-FFA 0.759 83.86 0.914 0.723 80.81 0.929 
SVM4-FFA 0.792 79.47 0.939 0.751 76.67 0,946 
SVM5-FFA 0.828 74.28 0.961 0.779 70.11 0.974 

Here five different models are used to estimate NSE, RMSE and WI value for five projected watersheds. When , , is used as input scenario, WI value provides the best result. Considering Balangir, the best values for WI are 0.965 and 0.971 for the training and testing periods, respectively. For the training phase, the WI values for Loisinga, Patnagarh, Saintala, Deogaon watershed are 0.958, 0.953, 0.955, 0.961, respectively. Similarly, the WI values of the testing phase are 0.968, 0.962, 0.966 and 0.974 for Loisinga, Patnagarh, Saintala and Deogaon watershed, respectively. Results of the PSR-SVM-FFA model for both testing and training phases are presented in Table 5.

Table 5

Optimal parameters of τ, m for proposed watersheds and results of PSR-SVM-FFA model for runoff prediction

PositionsOptimal parameters of τ, m for PSRTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir (m=14, τ=50.905 43.74 0.984 0.874 42.27 0.985 
Loisinga (m=14, τ=50.938 39.18 0.970 0.908 37.96 0.967 
Patnagarh (m=14, τ=50.912 40.38 0.971 0.893 39.08 0.974 
Saintala (m=14, τ=50.897 37.66 0.972 0.869 36.11 0.976 
Deogaon (m=14, τ=50.923 41.82 0.982 0.897 40.35 0.988 
PositionsOptimal parameters of τ, m for PSRTraining period
Testing period
NSERMSEWINSERMSEWI
Balangir (m=14, τ=50.905 43.74 0.984 0.874 42.27 0.985 
Loisinga (m=14, τ=50.938 39.18 0.970 0.908 37.96 0.967 
Patnagarh (m=14, τ=50.912 40.38 0.971 0.893 39.08 0.974 
Saintala (m=14, τ=50.897 37.66 0.972 0.869 36.11 0.976 
Deogaon (m=14, τ=50.923 41.82 0.982 0.897 40.35 0.988 

Assessment of results for recommended model

A comparison between the PSR-SVM-FFA, SVM-FFA and SVM models for testing of all projected watersheds is presented in Figures 68. The pre-eminent WI values for SVM, SVM-FFA and PSR-SVM-FFA models are 0.935, 0.965 and 0.984, correspondingly, for Balangir watershed. Similarly, for Loisinga station, the paramount WI value is 0.919, 0.958 and 0.9702 for SVM, SVM-FFA and PSR-SVM-FFA models, respectively. Patnagarh, Saintala and Deogaon illustrate values for the SVM model of 0.9276, 0.9386 and 0.9459, respectively, during the testing phase. For the SVM-FFA model, the excellent values of WI are 0.953, 0.955 and 0.961 with respect to Patnagarh, Saintala and Deogaon. Similarly, the best values of the PSR-SVM-FFA model are 0.971, 0.972 and 0.982 for Patnagarh, Saintala and Deogaon, respectively.

Figure 6

Best fit lines by SVM model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 6

Best fit lines by SVM model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 7

Best fit lines by SVM-FFA model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 7

Best fit lines by SVM-FFA model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 8

Best fit lines by PSR-SVM-FFA model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 8

Best fit lines by PSR-SVM-FFA model at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

The linear scale plot of actual versus predicted monthly runoff for proposed model of projected area is shown in Figure 9. Results illustrate that estimated peak runoff is 141.208 mm, 142.313 mm and 149.272 mm for SVM, SVM-FFA and PSR-SVM-FFA against actual peak 157.22 mm for the Balangir watershed. The approximated peak runoffs are 126.4107 mm, 147.091 mm and 154.655 mm for SVM, SVM-FFA and PSR-SVM-FFA adjacent to the actual peak 158.8 mm for Loisinga division. For Patnagarh gauging station, tangible runoff is 150.43 mm aligned with predicted runoff of 136.032 mm, 141.329 mm and 145.744 mm for SVM, SVM-FFA and PSR-SVM-FFA, respectively. Correspondingly, for Saintala watershed, the observed maximum runoff is 156.34 mm associated with estimated runoff of 151.728 mm, 147.522 mm and 144.911 mm for PSR-SVM-FFA, SVM-FFA and SVM, respectively. Similarly, evaluated peak runoffs are 149.322 mm, 141.591 mm and 140.376 mm, for PSR-SVM-FFA, SVM-FFA and SVM models with respect to genuine runoff of 154.23 mm for Deogaon watershed.

Figure 9

Variation of measured runoff and predicted runoff at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Figure 9

Variation of measured runoff and predicted runoff at (a) Balangir, (b) Loisinga, (c) Patnagarh, (d) Saintala and (e) Deogaon watersheds during training phase.

Comparison of best results

The SVM, SVM-FFA and PSR-SVM-FFA models are used to evaluate the performance of NSE, RMSE and WI indictors for five gauging watersheds. Assessments of performance indicators are specified in Table 6, which illustrates the efficiency of each model. Evaluating runoff is important and so the methods used here are significant for demonstrating runoff information. Therefore, calculation of RMSE, WI and NSE values are essential for predicting runoff. It is apparent that the PSR-SVM-FFA model is executed well, comparably to SVM-FFA and SVM. Accuracy of models is evaluated and assessed.

Table 6

Performance indices of different models for runoff forecasting

StationsSVM
SVM-FFA
PSR-SVM-FFA
NSERMSEWINSERMSEWINSERMSEWI
Balangir 0.653 73.92 0.942 0.791 70.72 0.971 0.874 42.27 0.985 
Loisinga 0.601 70.21 0.925 0.783 68.49 0.961 0.908 37.96 0.967 
Patnagarh 0.613 73.41 0.931 0.754 70.07 0.962 0.893 39.08 0.974 
Saintala 0.658 69.73 0.947 0.793 67.88 0.966 0.869 36.11 0.976 
Deogaon 0.648 74.05 0.953 0.779 70.11 0.974 0.897 40.35 0.988 
StationsSVM
SVM-FFA
PSR-SVM-FFA
NSERMSEWINSERMSEWINSERMSEWI
Balangir 0.653 73.92 0.942 0.791 70.72 0.971 0.874 42.27 0.985 
Loisinga 0.601 70.21 0.925 0.783 68.49 0.961 0.908 37.96 0.967 
Patnagarh 0.613 73.41 0.931 0.754 70.07 0.962 0.893 39.08 0.974 
Saintala 0.658 69.73 0.947 0.793 67.88 0.966 0.869 36.11 0.976 
Deogaon 0.648 74.05 0.953 0.779 70.11 0.974 0.897 40.35 0.988 

Assessment of each model is demonstrated in Figure 10 in terms of linear bar scheme.

Figure 10

Comparison of performance index for proposed watershed.

Figure 10

Comparison of performance index for proposed watershed.

CONCLUSIONS

The efficiency of SVM, SVM-FFA and PSR-SVM-FFA approaches is explored for runoff prediction. Five gauging stations in Bolangir district, India are used for execution over a period of 28 years. The performance accuracy of PSR-SVM-FFA models is demonstrated in contrast to SVM-FFA and SVM models. It is appraised with various statistical indicators, WI, NSE and RMSE parameters, to reveal the projected PSR-SVM-FFA model is superior to SVM-FFA and SVM. It is observed that there is a significant improvement in the performance of the selected hybrid model for predicting the accuracy of each watershed. It is observed that the development of PSR coupled with the hybrid SVM-FFA model is superior to SVM models because of comprehensive withdrawal of input arrangements to produce targeted values. The PSR-SVM-FFA model is established to be a suitable model for runoff forecasting in arid watersheds. The research carried out over five gauge watersheds will help in the widespread good performance of non-gauging arid watersheds to predict runoff in similar conditions. Also, the present research findings can be used for irrigation and water resources engineering to design hydraulic structures regarding agriculture.

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