# Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}value of 0.85 and 0.74 during the training and testing period, respectively.

## 1. Introduction

^{2}[16,17]. Hydropower projects generating more than 30,000 MW are planned on the Indus River for the future. Therefore, estimation of sediment yields for reaches in the Upper Indus Basin (UIB) is important for the design and operation of existing and new water infrastructures.

#### Background

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The geographical location of the Gilgit basin is between latitude 35°55′35 N and 36°52′20″ N and longitude 72°26′04″ E and 74°18′25 E. The elevation of catchment ranges from 1454–7048 m a.s.l. Table S2 in supplementary materials shows the key features of the Gilgit basin. About 10% of the total catchment area is covered with glaciers and lies above an elevation of 5000 m. During the winter season, approximately 87% of the catchment area is covered with snow cover which reduces to 11% during the ablation period in summer. The mean annual discharge and suspended sediment concentrations (SSC) of the Gilgit basin are 291 m

^{3}/sec and 448 mg/L, respectively. The ablation period starts in July after seasonal snow melts. The melting of the glacier is slow and continues until the month of October. Then, the accumulation period of snow starts at the end of October. The Gilgit basin receives 75% of its rainfall starting from the mid of spring (April) to the end of summer (October). The mean annual basin rainfall from grid data in the Gilgit basin is approximately 670 mm. The mean monthly basin average temperature for the Gilgit basin ranges from −19.8 to 7.20 °C.

#### 2.2. Application of Temperature-Index Snow Model for Snow Cover Estimates

_{RS}(°C), daily maximum temperature (°C), and daily minimum temperature (°C) separate the snow and liquid rainfall as:

_{p}proportionate to temperature difference is calculated as:

_{RS}is used to define the type of precipitation into rain/snow and the threshold temperature T

_{SM}for the snow melt process which depends on numerous factors like the boundary layer condition of atmosphere, temperature, and air humidity, etc.

_{snow}(mm/day) are estimated as:

_{snow}(mm/day °C) is the degree day factor for snow melts, T

_{mean}(°C) is the mean daily air temperature, and T

_{SM}(°C) is the threshold temperature.

#### 2.3. Artificial Neural Networks (ANN)

_{1}and N

_{0}are the number of input and output neurons, respectively.

#### 2.4. Adaptive Neuro-Fuzzy Logic Inference System (ANFIS)

_{1}and x

_{2}with target values of z. Here, input of discharge and snow cover can be supposed as x

_{1}and x

_{2}with output z as sediment yield for a particular time t. Then, in Sugeno’s fuzzy logic structures, typical rule sets with two IF/THEN rules are expressed as:

_{i}, q

_{i}, and r

_{i}are parameters corresponding to Rule 1, Rule 2… Rule n.

_{i}, c

_{i}, N

_{i}} are the parameter sets for x

_{1}input in ith node. These parameters change the shape of the bell function in the range of 0–1.

^{th}rule to the sum of all rules:

_{ic}, v, and x are the number of clusters, number of data points, degree belongs to ith data point of Cith clusters data points, and input data sets. The p (p > 1) entitles to the fuzzifier exponent. In ANFIS-FCM, w

_{ic}is calculated as:

#### 2.5. Multivariate Adaptive Regression Splines (MARS)

#### 2.6. Sediment Rating Curve (SRC)

^{3}/day) is discharge, SSL (tons/day) both in log transformation form, and a and b are the constants that depend on the characteristics of a river and its catchments.

#### 2.7. Performance Measurement Metrics for Model Evaluation

^{2}):

_{io}is the observed sediment, S

_{is}is the simulated sediments, and $\overline{{S}_{is}}$ is the mean of the simulated sediments.

_{po}is the observed peak value of SSY, S

_{ps}is the simulated peak value of SSY.

#### 2.8. Application of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, and MARS Models

_{1}–S

_{15}by testing the accuracy of the network using minimum RMSE and maximum values of R

^{2}and NSE as performance criteria. The input scenarios developed in this study for predictions of sediment yields are listed here:

- (a)
- FlowsS
_{1}= SSC_{t}= f (Q_{t}, β_{1}) + e_{i}S_{2}= SSC_{t}= f (Q_{t}, Q_{t−1}, β_{1,}β_{2}) + e_{i}S_{3}= SSC_{t}= f (Q_{t}, Q_{t−1}, Q_{t−2}, β_{1,}β_{2,}β_{3}) + e_{i}S_{4}= SSC_{t}= f (Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, β_{1}, β_{2}, β_{3}, β_{4}) + e_{i}S_{5}= SSC_{t}= f (Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4}, β_{1}, β_{2}, β_{3}, β_{4,}β_{5}) + e_{i} - (b)
- Flows and snow cover areaS
_{6}= SSC_{t}= f (Q_{t}, SCA_{t}, β_{1}, β_{6}) + e_{i}S_{7}= SSC_{t}= f (Q_{t}, SCA_{t}, SCA_{t−1}, β_{1}, β_{6}, β_{7}) + e_{i}S_{8}= SSC_{t}= f (Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2}, β_{1}, β_{6}, β_{7}, β_{8}) + e_{i} - (c)
- Flow, snow cover area, and effective rainfallS
_{9}= SSC_{t}= f (Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4}, β_{1}, β_{9}, β_{6}, β_{10}) + e_{i} - (d)
- Flow, snow cover area, temperature, and evapotranspirationS
_{10}= SSC_{t}= f (Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4}, β_{1}, β_{11}, β_{12}, β_{6}, β_{10}) + e_{i} - (e)
- Average mean basin air temperatureS
_{11}= SSC_{t}= f (T_{t}, β_{13}) + e_{i}S_{12}= SSC_{t}= f (T_{t}, T_{t−1}, β_{13}, β_{11}) + e_{i}S_{13}= SSC_{t}= f (T_{t}, T_{t−1}, T_{t−2}, β_{13}, β_{11}, β_{14}) + e_{i}S_{14}= SSC_{t}= f (T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, β_{13}, β_{11}, β_{14}, β_{15}) + e_{i}S_{15}= SSC_{t}= f (T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4}, β_{13}, β_{11}, β_{14,}β_{15}, β_{16}) + e_{i}

## 3. Results and Discussion

#### 3.1. Simulation of Snow Melts and Snow Cover Area

_{snow}= 4.2 (mm/day/°C) for the Gilgit basin. The literature review [49,50,83,84,85,86] for the regional case studies shows that the value of K

_{snow}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 k

_{snow}= 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 K

_{snow}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.

^{2}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 R

^{2}, 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.

^{2}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.

^{2}during testing of the network for all input combinations.

#### 3.2. Comparison of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC Models

_{10}scenarios with model inputs of Q

_{t}, T

_{t−1}, Evapt

_{−1}, SCA

_{t}, and SCA

_{t−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 S

_{10}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 S

_{7}scenarios consisting of inputs of Qt, SCA

_{t}, and SCA

_{t−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.

_{10}involving the inputs of Q

_{t}, T

_{t−1}, Evap

_{t−1}, SCA

_{t}, and SCA

_{t−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 S

_{10}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 S

_{10}scenarios having inputs of Q

_{t}, T

_{t−1}, Evap

_{t−1}, SCA

_{t}, and SCA

_{t−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.

_{10}involving the inputs of Q

_{t}, T

_{t−1}, Evap

_{t−1}, SCA

_{t}, and SCA

_{t−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 S

_{10}scenario.

^{2}during the testing phase. The ANN has improved the results of the scatter plot of the R

^{2}value to up to 0.82 in comparison to the rating curve R

^{2}value of 0.71 during the testing period.

^{3}/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 R

^{2}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 R

^{2}value of 0.76 is better than the rating curve with an R

^{2}value of 0.71.

^{2}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 R

^{2}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.

#### 3.3. Deveoplement of Multiple Linear Regression Equation

_{1}= ANN model outputs of sediment load in log form (tons/day), x

_{2}= ANFIS-GP model outputs of sediment load in log form (tons/day), x

_{3}= ANFIS-SC model outputs of sediment load in log form (tons/day), x

_{4}= ANFIS-FCM model outputs of sediment load in log form (tons/day), x

_{5}= MARS model outputs of sediment load in log form (tons/day), and x

_{6}= SRC model outputs of sediment load in log form (tons/day). Figure 8 shows the results of the multiple linear regression Equation (23) during the training and testing periods.

## 4. Conclusions

^{2}when using the ANN model during the testing phase for the Gilgit River basin. It was concluded that the estimated snow cover area on land use maps and spatially distributed climatic information can improve the prediction of sediment yields when using data-based models.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Graphical presentations of (

**a**) mean basin temperature (T), discharges at Gilgit gauge (Q), and suspended sediment concentrations (SSC) at Gilgit gauge, (

**b**) mean basin snow covered area (SCA), mean basin rainfall (R), and mean basin evapotranspiration (Evap) for the Gilgit basin during period 1981–2010.

**Figure 3.**Time series plot between the MODIS-observed snow cover fractions and temp-index snow model-simulated snow cover fractions during calibration (2000–2007) and validation periods (2008–2010).

**Figure 5.**Plot of the best performance measures for predictions of SSY using the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC models during the testing phase for the Gilgit basin.

**Figure 6.**Plot of the best performance measures for predictions of SSY using the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC models during the testing phase for the Gilgit basin.

**Figure 7.**Overall comparison of the performance measures of coefficient of determination (R

^{2}), Nash–Sutcliffe efficiency model performance coefficient (NSE), and root-mean-square error (RMSE) with different input variable scenarios during the testing phase from all models.

**Figure 8.**Plot of the observed vs. predicted SSY using multiple linear regression equation during the training and testing phases for the Gilgit gauging station.

Variable | Data Source | Period | Source |
---|---|---|---|

Q * | Daily mean discharge (m^{3}/sec) | Daily, 1981–2010 | Water and Power Development Authority (WAPDA), Pakistan |

SSC * | Suspended sediment concentration (mg/L) | Intermittent days per week 1981–2010 | Water and Power Development Authority (WAPDA), Pakistan |

SCF | Snow cover fractions ranging (0–1) extracted from MODIS satellite data | Weekly, basin avg. 2000–2010 | https://nsidc.org/data/MOD10A2 |

T | Daily mean, maximum & minimum air temperature (°C) on a 5 × 5 km grid | Daily, basin avg. 1981–2010 | HI-AWARE project [47,48] |

P | Daily mean rainfall (mm/day) on a 5 × 5 km grid | Daily, basin avg. 1981–2010 | HI-AWARE project [47,48] |

Evap | Daily mean Evapotranspiration (mm/day) on a 5 × 5 km grid | Daily, basin avg. 1981–2010 | HI-AWARE project [47,48] |

**Table 2.**Relationship of Gilgit basin input variables determined by using the Pearson’s correlation coefficient. Log Q: logarithm of water discharges at Gilgit gauge; Log SSY: logarithm of sediment yields at Gilgit gauge; SCA: basin average snow cover area: T

_{avg}: averaged basin mean temperature; P: basin-averaged effective rainfall; Evap: basin averaged evapotranspiration.

log Q (m ^{3}/day) | log SSY (tons/day) | SCA (fractions) | T_{avg}(°C) | P (mm) | Evap (mm/day) | |
---|---|---|---|---|---|---|

log Q (m^{3}/day) | 1 | |||||

log SSY (tons/day) | 0.87 | 1 | ||||

SCA (fractions) | −0.85 | −0.74 | 1 | |||

T_{avg.} (°C) | 0.87 | 0.79 | −0.88 | 1 | ||

P (mm) | 0.16 | 0.15 | 0.09 | 0.1 | 1 | |

Evap. (mm/day) | 0.86 | 0.81 | −0.82 | 0.93 | 0.06 | 1 |

**Table 3.**Results of performance measurement statistics during calibration (2000–2007) and validation (2008–2010) periods of the temperature-index snow model for simulations of snow melt and snow cover fractions.

k_{snow} = 4.2 (mm/day/°C) | ||
---|---|---|

Calibration Period (2000–2007) | Validation Period (2008–2010) | |

R^{2} | 0.90 | 0.90 |

NSE | 0.72 | 0.70 |

RMSE | 0.15 | 0.15 |

**Table 4.**Training and testing statistics of the ANN model employing the Levenberg-Marquardt algorithm using different input combinations for the Gilgit basin.

Scenarios | Model Inputs | Neurons | Transfer Function | R^{2} | RMSE | NSE | ||||
---|---|---|---|---|---|---|---|---|---|---|

Input | Output | Training | Testing | Training | Testing | Training | Testing | |||

S_{1} | Q_{t} | 3 | logsig | purelin | 0.76 | 0.81 | 0.48 | 0.42 | 0.76 | 0.8 |

S_{2} | Q_{t}, Q_{t−1} | 3 | logsig | purelin | 0.77 | 0.79 | 0.48 | 0.44 | 0.77 | 0.79 |

S_{3} | Q_{t}, Q_{t−1}, Q_{t−2} | 5 | radbas | purlin | 0.78 | 0.79 | 0.46 | 0.45 | 0.78 | 0.79 |

S_{4} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 5 | tansig | purelin | 0.80 | 0.80 | 0.44 | 0.47 | 0.80 | 0.79 |

S_{5} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4} | 7 | logsig | purelin | 0.81 | 0.80 | 0.43 | 0.44 | 0.81 | 0.80 |

S_{6} | Q_{t}, SCA_{t} | 5 | tansig | purelin | 0.79 | 0.82 | 0.45 | 0.44 | 0.79 | 0.81 |

S_{7} | Q_{t}, SCA_{t}, SCA_{t−1} | 7 | tansig | tansig | 0.80 | 0.80 | 0.44 | 0.43 | 0.80 | 0.8 |

S_{8} | Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2} | 8 | tansig | tansig | 0.80 | 0.81 | 0.44 | 0.43 | 0.80 | 0.81 |

S_{9} | Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4} | 7 | logsig | purelin | 0.80 | 0.82 | 0.44 | 0.42 | 0.80 | 0.82 |

S_{10} | Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4} | 5 | radbas | tansig | 0.81 | 0.82 | 0.42 | 0.43 | 0.81 | 0.81 |

S_{11} | T_{t} | 3 | logsig | purelin | 0.69 | 0.73 | 0.55 | 0.50 | 0.69 | 0.73 |

S_{12} | T_{t}, T_{t−1} | 3 | logsig | tansig | 0.69 | 0.74 | 0.54 | 0.51 | 0.69 | 0.73 |

S_{13} | T_{t}, T_{t−1}, T_{t−2} | 6 | tansig | tansig | 0.74 | 0.73 | 0.51 | 0.51 | 0.74 | 0.72 |

S_{14} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3} | 8 | tansig | tansig | 0.75 | 0.74 | 0.49 | 0.51 | 0.75 | 0.74 |

S_{15} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4} | 7 | radbas | tansig | 0.74 | 0.76 | 0.49 | 0.51 | 0.74 | 0.76 |

**Table 5.**Training and testing statistics of the AFIS1 grid partition (GP) model employing different input combinations for the Gilgit basin.

Scenarios | Model Inputs | Membership Functions | No of Functions | R^{2} | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||||

S_{1} | Q_{t} | pimf | 4 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{2} | Q_{t}, Q_{t−1} | pimf | 2 | 0.78 | 0.78 | 0.46 | 0.47 | 0.78 | 0.78 |

S_{3} | Q_{t}, Q_{t−1}, Q_{t−2} | gauss2mf | 2 | 0.79 | 0.77 | 0.45 | 0.49 | 0.79 | 0.77 |

S_{4} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | gbellmf | 2 | 0.81 | 0.75 | 0.43 | 0.50 | 0.81 | 0.75 |

S_{5} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4} | trimf | 2 | 0.81 | 0.71 | 0.43 | 0.53 | 0.81 | 0.69 |

S_{6} | Q_{t}, SCA_{t} | trimf | 2 | 0.79 | 0.77 | 0.45 | 0.45 | 0.79 | 0.77 |

S_{7} | Q_{t}, SCA_{t}, SCA_{t−1} | trimf | 2 | 0.79 | 0.78 | 0.44 | 0.47 | 0.79 | 0.78 |

S_{8} | Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2} | trimf | 2 | 0.82 | 0.76 | 0.42 | 0.47 | 0.82 | 0.75 |

S_{9} | Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4} | trimf | 2 | 0.82 | 0.76 | 0.41 | 0.49 | 0.82 | 0.76 |

S_{10} | Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4} | trimf | 2 | 0.85 | 0.72 | 0.38 | 0.52 | 0.85 | 0.72 |

S_{11} | T_{t} | psigmf | 2 | 0.70 | 0.70 | 0.55 | 0.52 | 0.70 | 0.70 |

S_{12} | T_{t}, T_{t−1} | pimf | 2 | 0.71 | 0.71 | 0.54 | 0.51 | 0.71 | 0.71 |

S_{13} | T_{t}, T_{t−1}, T_{t−2} | trimf | 2 | 0.71 | 0.73 | 0.52 | 0.52 | 0.71 | 0.73 |

S_{14} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3} | trapmf | 2 | 0.72 | 0.72 | 0.51 | 0.53 | 0.72 | 0.72 |

S_{15} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4} | trimf | 2 | 0.77 | 0.60 | 0.46 | 0.65 | 0.77 | 0.59 |

**Table 6.**Training and testing statistics of the AFIS2 subtractive clustering (SC) model employing different input combinations for the Gilgit basin.

Scenarios | Model Inputs | Radii | R^{2} | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | |||

S_{1} | Q_{t} | 0.50 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{2} | Q_{t}, Q_{t−1} | 0.70 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{3} | Q_{t}, Q_{t−1}, Q_{t−2} | 0.70 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{4} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 0.70 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{5} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4} | 0.80 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{6} | Q_{t}, SCA_{t} | 0.60 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{7} | Q_{t}, SCA_{t}, SCA_{t−1} | 0.80 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{8} | Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2} | 0.70 | 0.79 | 0.77 | 0.44 | 0.48 | 0.79 | 0.77 |

S_{9} | Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4} | 0.60 | 0.79 | 0.78 | 0.45 | 0.47 | 0.79 | 0.78 |

S_{10} | Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4} | 0.90 | 0.80 | 0.79 | 0.43 | 0.46 | 0.80 | 0.79 |

S_{11} | T_{t} | 0.50 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |

S_{12} | T_{t}, T_{t−1} | 0.60 | 0.71 | 0.70 | 0.52 | 0.55 | 0.71 | 0.70 |

S_{13} | T_{t}, T_{t−1}, T_{t−2} | 0.80 | 0.72 | 0.72 | 0.51 | 0.53 | 0.72 | 0.72 |

S_{14} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3} | 0.80 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |

S_{15} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4} | 0.70 | 0.72 | 0.73 | 0.51 | 0.52 | 0.72 | 0.73 |

**Table 7.**Training and testing statistics of the AFIS3 FCM clustering model employing different input combinations for the Gilgit basin.

Scenarios | Model Inputs | No of Clusters | R^{2} | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | |||

S_{1} | Q_{t} | 2 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{2} | Q_{t}, Q_{t−1} | 4 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |

S_{3} | Q_{t}, Q_{t−1}, Q_{t−2} | 2 | 0.77 | 0.78 | 0.46 | 0.47 | 0.78 | 0.78 |

S_{4} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 2 | 0.77 | 0.78 | 0.46 | 0.48 | 0.77 | 0.78 |

S_{5} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4} | 2 | 0.77 | 0.78 | 0.46 | 0.48 | 0.77 | 0.77 |

S_{6} | Q_{t}, SCA_{t} | 2 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{7} | Q_{t}, SCA_{t}, SCA_{t−1} | 2 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |

S_{8} | Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2} | 2 | 0.78 | 0.77 | 0.45 | 0.48 | 0.80 | 0.78 |

S_{9} | Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4} | 2 | 0.79 | 0.78 | 0.44 | 0.47 | 0.79 | 0.78 |

S_{10} | Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4} | 2 | 0.80 | 0.78 | 0.43 | 0.47 | 0.80 | 0.78 |

S_{11} | T_{t} | 3 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |

S_{12} | T_{t}, T_{t−1} | 2 | 0.71 | 0.70 | 0.53 | 0.55 | 0.71 | 0.70 |

S_{13} | T_{t}, T_{t−1}, T_{t−2} | 4 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |

S_{14} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3} | 6 | 0.76 | 0.72 | 0.48 | 0.53 | 0.76 | 0.72 |

S_{15} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4} | 2 | 0.72 | 0.70 | 0.51 | 0.55 | 0.72 | 0.70 |

**Table 8.**Training and testing statistics of the MARS model employing different input combinations for the Gilgit basin.

Scenarios | Model Inputs | Basis Function | R^{2} | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | |||

S_{1} | Q_{t} | 5 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |

S_{2} | Q_{t}, Q_{t−1} | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |

S_{3} | Q_{t}, Q_{t−1}, Q_{t−2} | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |

S_{4} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |

S_{5} | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, Q_{t−4} | 15 | 0.78 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |

S_{6} | Q_{t}, SCA_{t} | 15 | 0.77 | 0.78 | 0.46 | 0.48 | 0.78 | 0.77 |

S_{7} | Q_{t}, SCA_{t}, SCA_{t−1} | 20 | 0.77 | 0.77 | 0.46 | 0.48 | 0.77 | 0.77 |

S_{8} | Q_{t}, SCA_{t}, SCA_{t−1}, SCA_{t−2} | 15 | 0.77 | 0.77 | 0.46 | 0.48 | 0.77 | 0.77 |

S_{9} | Q_{t}, R_{t−1}, SCA_{t}, SCA_{t−4} | 25 | 0.78 | 0.77 | 0.45 | 0.48 | 0.78 | 0.77 |

S_{10} | Q_{t}, T_{t−1}, Evap_{t−1}, SCA_{t}, SCA_{t−4} | 10 | 0.79 | 0.79 | 0.45 | 0.46 | 0.79 | 0.79 |

S_{11} | T_{t} | 20 | 0.69 | 0.70 | 0.54 | 0.55 | 0.69 | 0.70 |

S_{12} | T_{t}, T_{t−1} | 15 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |

S_{13} | T_{t}, T_{t−1}, T_{t−2} | 10 | 0.71 | 0.71 | 0.52 | 0.55 | 0.71 | 0.70 |

S_{14} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3} | 10 | 0.72 | 0.71 | 0.52 | 0.54 | 0.72 | 0.71 |

S_{15} | T_{t}, T_{t−1}, T_{t−2}, T_{t−3}, T_{t−4} | 20 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |

**Table 9.**Comparison of performance measurements by using the SRC, ANFIS-GP, ANFIS-SC, ANFIS-SC, ANFIS-FCM, and MARS models in predictions of sediment yields.

Models | Training Period | Testing Period | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | NSE | R^{2} | RMSE | NSE | |

SRC | 0.81 | 0.49 | 0.75 | 0.71 | 0.60 | 0.66 |

ANN | 0.81 | 0.42 | 0.81 | 0.82 | 0.43 | 0.81 |

ANFIS-GP | 0.79 | 0.44 | 0.79 | 0.78 | 0.47 | 0.78 |

ANFIS-SC | 0.80 | 0.43 | 0.80 | 0.79 | 0.46 | 0.79 |

ANFIS-FCM | 0.80 | 0.43 | 0.80 | 0.78 | 0.47 | 0.78 |

MARS | 0.79 | 0.45 | 0.79 | 0.79 | 0.46 | 0.79 |

**Table 10.**Comparison of the ANFIS-GP, ANFIS-SC, ANFIS-SC, ANFIS-FCM, MARS, and SRC models’ absolute sediment fluxes and relative accuracies (%age) for peak estimations of SSY for the Gilgit gauging station.

Year | Peaks > 3200 (tons/day) | ANN (tons/day) | ANFIS-GP (tons/day) | ANFIS-SC (tons/day) | ANFIS-FCM (tons/day) | MARS (tons/day) | SRC (tons/day) |
---|---|---|---|---|---|---|---|

1983 | 3901 | 3934 (99.15) | 3884 (99.56) | 3886 (99.62) | 3613 (92.62) | 3826 (98.07) | 4654 (80.69) |

1984 | 4955 | 3542 (71.48) | 4543 (91.68) | 3033 (61.21) | 3789 (76.46) | 3385 (68.31) | 4375 (88.29) |

1991 | 3256 | 3088 (94.84) | 2804 (86.11) | 3128 (96.06) | 3093 (94.99) | 3105 (95.36) | 4468 (62.77) |

2003 | 4057 | 2372 (58.46) | 2514 (61.96) | 2616 (64.48) | 2790 (68.77) | 2674 (65.91) | 4400 (91.54) |

2005 | 16,898 | 12,993 (76.89) | 8949 (52.95) | 9480 (56.10) | 12,458 (73.72) | 12,365 (73.17) | 32,385 (8.35) |

Mean(Relative Accuracy %) | 6613 | 5186(80.17) | 4539(78.45) | 4429(75.49) | 5149(81.31) | 5071(80.16) | 10,056(66.33) |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hussan, W.U.; Khurram Shahzad, M.; Seidel, F.; Nestmann, F.
Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads. *Water* **2020**, *12*, 1481.
https://doi.org/10.3390/w12051481

**AMA Style**

Hussan WU, Khurram Shahzad M, Seidel F, Nestmann F.
Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads. *Water*. 2020; 12(5):1481.
https://doi.org/10.3390/w12051481

**Chicago/Turabian Style**

Hussan, Waqas Ul, Muhammad Khurram Shahzad, Frank Seidel, and Franz Nestmann.
2020. "Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads" *Water* 12, no. 5: 1481.
https://doi.org/10.3390/w12051481