3.1. Simulation of Snow Melts and Snow Cover Area
The results of the calibrated temperature-index snow melt model are shown in Table 3
. The model was calibrated and validated to simulate the snow cover by using the degree day factor for the snow model. Table 3
shows the value of the degree day factor ksnow
= 4.2 (mm/day/°C) for the Gilgit basin. The literature review [49
] for the regional case studies shows that the value of Ksnow
ranges from 3–7 (mm/day/°C) in the Upper Indus Basin (UIB). Thus, during calibration and validation of the temperature-index snow model for this study, the value of ksnow
= 4.2 (mm/day/°C) lies within the range of the values of previous studies carried out for snow melt runoff modeling in the UIB. The difference between the Ksnow
value in the current study and that of previous studies is probably due to the use of different resolutions of input datasets, lengths of calibration datasets, threshold temperatures for separating rainfall and snow, threshold temperatures for snow melts, and characteristics of the catchment.
also shows the performance measurement statistics for the snow model during the calibration and validation periods. The value of R2
is found at 0.90 between the MODIS-observed snow covered area and model simulated snow cover area both during the calibration and validation periods. The performance evaluation criteria using the three criteria of R2
, NSE, and RMSE show that goodness of fit between the model and observed MODIS snow cover maps is more than 70% which is satisfactory in estimation of both the snow melts and snow cover area. Figure 3
also shows the time series plot between model snow cover area and MODIS-observed snow cover area during the calibration (2000–2007) and validation (2008–2010) period, respectively.
For application of the ANN model, the transfer functions logsig, purelin, tansig, and radbas were used in the hidden layers. The network was trained by using 16 combinations of four transfer functions for input and output layers. The optimum number of neurons was determined ranging from 3–8 in single hidden layers for overall input scenarios giving best results at the end. Table 4
shows the results of various input combinations using ANN model. For the ANFIS-GP, ANFIS-SC, and ANFIS-FCM models, the hybrid algorithm was used in this study.
For the ANFIS-GP model application, the gaussmf, gauss2mf, trimf, trapmf, gbellmf, pimf, dsigmf, and psigmf membership functions were used. In ANFIS-GP, the type of membership functions and number of member functions are important for training the network. Table 5
shows the results of all scenarios using the ANFIS-GP model with optimal number and type of membership functions. The optimal number of functions ranges between 2 and 4 for all scenarios.
For application of the ANFIS-SC model, the network is trained with an optimal range of the radius of clusters which give a minimum value of RMSE and highest values of R2 and NSE. The optimal value of the cluster radius represents the influence of the cluster radius on the dataset clusters. If the cluster radius is small, then there are numerous small cluster datasets.
On the other hand, a large value of the cluster radius means that there are a few large cluster datasets for training the network. During training of the network, the hit-and-trial method was used to find out the optimum value of the cluster radius with the smallest value of RMSE for all scenarios during the testing period. Table 6
shows the results of the ANFIS-SC model for all scenarios. It was found that the optimal range of the cluster radius is from 0.5–0.9 for all scenarios.
For application of the ANFIS-FCM model, the various numbers of clusters were used to train and test the network for all scenarios. Table 7
shows the results of the ANFIS-FCM model for all input combinations. The optimal number of clusters ranges between 2 and 6 for this study with the lowest value of RMSE and highest value of R2
during testing of the network for all input combinations.
For application of the MARS model, the controlling parameters generally include the maximum basis functions, maximum interaction, speed factor, minimum number of observations between knots, penalty of variable, and degree of freedom. However, for this study, the hit-and-trial method was used to train the model with an optimal number of maximum basis functions ranging from 5 to 25 for all input scenarios with the remaining parameters being default values in the model. Table 8
shows the results of the MARS model for various input scenarios used in this study.
For application of the sediment rating curve (SRC) model, the power law function was used to train the model with 70% of the datasets after transformation of flows and sediment yields into logarithm form.
After training of SRC with 70% of the data sets, the model was tested with 30% of the remaining data. Figure 4
shows the plot of the sediment rating curve using the power law functions. Table 9
also shows the results of training and testing of the sediment rating curve (SRC) model and compares its model performance statistics with other models used for predictions of sediment yields used in this study.
3.2. Comparison of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC Models
The results of the training and validation of the various scenarios are shown in Table 4
, Table 5
, Table 6
, Table 7
, Table 8
and Table 9
for the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC models for predictions of the sediment yields for the Gilgit basin. In Table 4
, the ANN shows the best performance of S10
scenarios with model inputs of Qt
, and SCAt−4
. In the ANN, the model parameters having radbas and tansig as input and output transfer functions along with five numbers of neurons performed best with S10
input scenarios during the training and validation phases. Table 5
shows the results of the ANFIS-GP for all input scenarios. Here, the ANFIS-GP shows the best performance of the model with S7
scenarios consisting of inputs of Qt, SCAt
, and SCAt−1
. The ANFIS-GP model performs best with model parameters consisting of triangular (trimf) membership functions along with two numbers of membership functions (MFs). The results of the ANFIS-SC model are shown in Table 6
From Table 6
, the input scenario S10
involving the inputs of Qt
, and SCAt−4
gives the best performance of the ANFIS-SC model. The ANFIS-SC uses the model parameters having the value of a cluster radius of 0.90 to perform best with S10
input combinations. Table 7
shows the results of input scenarios by using the ANFIS-FCM model. It is evident that the best performance of the ANFIS-FCM model, too, was obtained with S10
scenarios having inputs of Qt
, and SCAt−4
. In the ANFIS-FCM model, the best network was developed by using the model parameter having two numbers of clusters with S10 input scenario.
represents the results of the MARS model used in this study for prediction of the sediment yield of the Gilgit River basin. As shown in Table 8
, again the input scenario S10
involving the inputs of Qt
, and SCAt−4
developed the best-performing network in the MARS model. The MARS model performed best with its basis function (BF) parameter having the value of 10 with the S10
shows the overall results of the best networks of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, and MARS models compared with the sediment rating curve performance for the Gilgit basin. Table 8
shows that the ANN model performs better than all other models with the least values of the RMSE errors of 0.42 and 0.43 during the training and testing phase.
Similarly, Figure 5
shows the scatter plot between the observed and predicted SSY by using ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC during the testing phase for overall best input scenarios. From the scatter plot graphs, it can be observed that the ANN-based model has the least scatters with the highest value of R2
during the testing phase. The ANN has improved the results of the scatter plot of the R2
value to up to 0.82 in comparison to the rating curve R2
value of 0.71 during the testing period.
shows the annual time series variation graphs of the observed and estimated SSY by using the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC models with best- performed input combinations. This Figure 6
also includes the one detailed graph derived from the main time series plot to compare all model performances during the peak annual suspended sediment yields (SSY) period of the year 2005.
It is illustrated in Figure 6
that during the peak SSY period of the year 2005, the estimated SSY of the models ANN, MARS, and ANFIS-FCM are relatively closer to the observed SSY than those of the other models. However, the models ANFIS-GP and ANFIS-SC significantly underestimated the SSY during this peak year period of 2005. Similarly, the SRC model significantly overestimated the SSY during that period.
shows an overall comparison of different input variable scenarios developed from flows Q (m3
/day), snow cover area SCA (fractions), effective mean basin rainfall R (mm/day), mean basin average temperatures T (°C/day), and mean basin evapotranspiration Evap (mm/day) for predictions of SSY during the testing period in the Gilgit basin. The model performance of R2
was improved up to the value of 0.82 by introducing the combinations of the snow cover area along with flows, effective rainfall, temperatures, and evapotranspiration. The input combinations consisting of only the mean basin average temperature T perform less than other combinations consisting of flows, snow covers, effective rainfall etc. However, the mean basin average temperature T variable scenarios’ performance with an R2
value of 0.76 is better than the rating curve with an R2
value of 0.71.
Rajaee et al. [22
] applied artificial neural networks (ANNs), neuro-fuzzy (NF), multiple linear regression (MLR), and sediment rating curve (SRC) for prediction of suspended sediment concentrations (SSC) for Little Black River and Salt River in United states of America (USA). For example, in Little Black River gauging station, the value of R2
was 0.69 for NF model, while it was 0.45, 0.25, and 0.23 for ANN, MLR, and SRC models respectively. In the present study, the value of R2
ranges from 0.78–0.82 using ANN and ANFIS models. It suggests that the soft computing models could be successfully applied for daily prediction sediment yields.
The mean values of SSY and relative accuracies of the ANFIS-GP, ANFIS-SC, ANFIS-SC, ANFIS-FCM, MARS, and SRC models at Gilgit gauging station are shown in Table 10
. The ANN model predicted the means of the peak sediment fluxes to be 6613 (tons/day) and 5186 (tons/day), while the ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC models resulted in less accurate outcomes. However, Table 10
also shows that the ANFIS-FCM model with a relative accuracy of 81.31% has a superior accuracy in predicting the peak values of sediment yields compared to the ANN (80.17%), ANFIS-GP (78.45%), ANFIS-SC (75.49%), MARS (80.16%), and SRC (66.33%) models.