Application of Soft Computing Models with Input Vectors of Snow Cover Area in Addition to Hydro-Climatic Data to Predict the Sediment Loads
Abstract
:1. Introduction
Background
2. Materials and Methods
2.1. Study Area
2.2. Application of Temperature-Index Snow Model for Snow Cover Estimates
2.3. Artificial Neural Networks (ANN)
2.4. Adaptive Neuro-Fuzzy Logic Inference System (ANFIS)
2.5. Multivariate Adaptive Regression Splines (MARS)
2.6. Sediment Rating Curve (SRC)
2.7. Performance Measurement Metrics for Model Evaluation
2.8. Application of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, and MARS Models
- (a)
- FlowsS1 = SSCt = f (Qt, β1) + eiS2 = SSCt = f (Qt, Qt−1, β1, β2) + eiS3 = SSCt = f (Qt, Qt−1, Qt−2, β1, β2, β3) + eiS4 = SSCt = f (Qt, Qt−1, Qt−2, Qt−3, β1, β2, β3, β4) + eiS5 = SSCt = f (Qt, Qt−1, Qt−2, Qt−3, Qt−4, β1, β2, β3, β4, β5) + ei
- (b)
- Flows and snow cover areaS6 = SSCt = f (Qt, SCAt, β1, β6) + eiS7 = SSCt = f (Qt, SCAt, SCAt−1, β1, β6, β7) + eiS8 = SSCt = f (Qt, SCAt, SCAt−1, SCAt−2, β1, β6, β7, β8) + ei
- (c)
- Flow, snow cover area, and effective rainfallS9 = SSCt = f (Qt, Rt−1, SCAt, SCAt−4, β1, β9, β6, β10) + ei
- (d)
- Flow, snow cover area, temperature, and evapotranspirationS10 = SSCt = f (Qt, Tt−1, Evapt−1, SCAt, SCAt−4, β1, β11, β12, β6, β10) + ei
- (e)
- Average mean basin air temperatureS11 = SSCt = f (Tt, β13) + eiS12 = SSCt = f (Tt, Tt−1, β13, β11) + eiS13 = SSCt = f (Tt, Tt−1, Tt−2, β13, β11, β14) + eiS14 = SSCt = f (Tt, Tt−1, Tt−2, Tt−3, β13, β11, β14, β15) + eiS15 = SSCt = f (Tt, Tt−1, Tt−2, Tt−3, Tt−4, β13, β11, β14, β15, β16) + ei
3. Results and Discussion
3.1. Simulation of Snow Melts and Snow Cover Area
3.2. Comparison of the ANN, ANFIS-GP, ANFIS-SC, ANFIS-FCM, MARS, and SRC Models
3.3. Deveoplement of Multiple Linear Regression Equation
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Variable | Data Source | Period | Source |
---|---|---|---|
Q * | Daily mean discharge (m3/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] |
log Q (m3/day) | log SSY (tons/day) | SCA (fractions) | Tavg (°C) | P (mm) | Evap (mm/day) | |
---|---|---|---|---|---|---|
log Q (m3/day) | 1 | |||||
log SSY (tons/day) | 0.87 | 1 | ||||
SCA (fractions) | −0.85 | −0.74 | 1 | |||
Tavg. (°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 |
ksnow = 4.2 (mm/day/°C) | ||
---|---|---|
Calibration Period (2000–2007) | Validation Period (2008–2010) | |
R2 | 0.90 | 0.90 |
NSE | 0.72 | 0.70 |
RMSE | 0.15 | 0.15 |
Scenarios | Model Inputs | Neurons | Transfer Function | R2 | RMSE | NSE | ||||
---|---|---|---|---|---|---|---|---|---|---|
Input | Output | Training | Testing | Training | Testing | Training | Testing | |||
S1 | Qt | 3 | logsig | purelin | 0.76 | 0.81 | 0.48 | 0.42 | 0.76 | 0.8 |
S2 | Qt, Qt−1 | 3 | logsig | purelin | 0.77 | 0.79 | 0.48 | 0.44 | 0.77 | 0.79 |
S3 | Qt, Qt−1, Qt−2 | 5 | radbas | purlin | 0.78 | 0.79 | 0.46 | 0.45 | 0.78 | 0.79 |
S4 | Qt, Qt−1, Qt−2, Qt−3 | 5 | tansig | purelin | 0.80 | 0.80 | 0.44 | 0.47 | 0.80 | 0.79 |
S5 | Qt, Qt−1, Qt−2, Qt−3, Qt−4 | 7 | logsig | purelin | 0.81 | 0.80 | 0.43 | 0.44 | 0.81 | 0.80 |
S6 | Qt, SCAt | 5 | tansig | purelin | 0.79 | 0.82 | 0.45 | 0.44 | 0.79 | 0.81 |
S7 | Qt, SCAt, SCAt−1 | 7 | tansig | tansig | 0.80 | 0.80 | 0.44 | 0.43 | 0.80 | 0.8 |
S8 | Qt, SCAt, SCAt−1, SCAt−2 | 8 | tansig | tansig | 0.80 | 0.81 | 0.44 | 0.43 | 0.80 | 0.81 |
S9 | Qt, Rt−1, SCAt, SCAt−4 | 7 | logsig | purelin | 0.80 | 0.82 | 0.44 | 0.42 | 0.80 | 0.82 |
S10 | Qt, Tt−1, Evapt−1, SCAt, SCAt−4 | 5 | radbas | tansig | 0.81 | 0.82 | 0.42 | 0.43 | 0.81 | 0.81 |
S11 | Tt | 3 | logsig | purelin | 0.69 | 0.73 | 0.55 | 0.50 | 0.69 | 0.73 |
S12 | Tt, Tt−1 | 3 | logsig | tansig | 0.69 | 0.74 | 0.54 | 0.51 | 0.69 | 0.73 |
S13 | Tt, Tt−1, Tt−2 | 6 | tansig | tansig | 0.74 | 0.73 | 0.51 | 0.51 | 0.74 | 0.72 |
S14 | Tt, Tt−1, Tt−2, Tt−3 | 8 | tansig | tansig | 0.75 | 0.74 | 0.49 | 0.51 | 0.75 | 0.74 |
S15 | Tt, Tt−1, Tt−2, Tt−3, Tt−4 | 7 | radbas | tansig | 0.74 | 0.76 | 0.49 | 0.51 | 0.74 | 0.76 |
Scenarios | Model Inputs | Membership Functions | No of Functions | R2 | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | ||||
S1 | Qt | pimf | 4 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S2 | Qt, Qt−1 | pimf | 2 | 0.78 | 0.78 | 0.46 | 0.47 | 0.78 | 0.78 |
S3 | Qt, Qt−1, Qt−2 | gauss2mf | 2 | 0.79 | 0.77 | 0.45 | 0.49 | 0.79 | 0.77 |
S4 | Qt, Qt−1, Qt−2, Qt−3 | gbellmf | 2 | 0.81 | 0.75 | 0.43 | 0.50 | 0.81 | 0.75 |
S5 | Qt, Qt−1, Qt−2, Qt−3, Qt−4 | trimf | 2 | 0.81 | 0.71 | 0.43 | 0.53 | 0.81 | 0.69 |
S6 | Qt, SCAt | trimf | 2 | 0.79 | 0.77 | 0.45 | 0.45 | 0.79 | 0.77 |
S7 | Qt, SCAt, SCAt−1 | trimf | 2 | 0.79 | 0.78 | 0.44 | 0.47 | 0.79 | 0.78 |
S8 | Qt, SCAt, SCAt−1, SCAt−2 | trimf | 2 | 0.82 | 0.76 | 0.42 | 0.47 | 0.82 | 0.75 |
S9 | Qt, Rt−1, SCAt, SCAt−4 | trimf | 2 | 0.82 | 0.76 | 0.41 | 0.49 | 0.82 | 0.76 |
S10 | Qt, Tt−1, Evapt−1, SCAt, SCAt−4 | trimf | 2 | 0.85 | 0.72 | 0.38 | 0.52 | 0.85 | 0.72 |
S11 | Tt | psigmf | 2 | 0.70 | 0.70 | 0.55 | 0.52 | 0.70 | 0.70 |
S12 | Tt, Tt−1 | pimf | 2 | 0.71 | 0.71 | 0.54 | 0.51 | 0.71 | 0.71 |
S13 | Tt, Tt−1, Tt−2 | trimf | 2 | 0.71 | 0.73 | 0.52 | 0.52 | 0.71 | 0.73 |
S14 | Tt, Tt−1, Tt−2, Tt−3 | trapmf | 2 | 0.72 | 0.72 | 0.51 | 0.53 | 0.72 | 0.72 |
S15 | Tt, Tt−1, Tt−2, Tt−3, Tt−4 | trimf | 2 | 0.77 | 0.60 | 0.46 | 0.65 | 0.77 | 0.59 |
Scenarios | Model Inputs | Radii | R2 | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | |||
S1 | Qt | 0.50 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S2 | Qt, Qt−1 | 0.70 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S3 | Qt, Qt−1, Qt−2 | 0.70 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S4 | Qt, Qt−1, Qt−2, Qt−3 | 0.70 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S5 | Qt, Qt−1, Qt−2, Qt−3, Qt−4 | 0.80 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S6 | Qt, SCAt | 0.60 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S7 | Qt, SCAt, SCAt−1 | 0.80 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S8 | Qt, SCAt, SCAt−1, SCAt−2 | 0.70 | 0.79 | 0.77 | 0.44 | 0.48 | 0.79 | 0.77 |
S9 | Qt, Rt−1, SCAt, SCAt−4 | 0.60 | 0.79 | 0.78 | 0.45 | 0.47 | 0.79 | 0.78 |
S10 | Qt, Tt−1, Evapt−1, SCAt, SCAt−4 | 0.90 | 0.80 | 0.79 | 0.43 | 0.46 | 0.80 | 0.79 |
S11 | Tt | 0.50 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |
S12 | Tt, Tt−1 | 0.60 | 0.71 | 0.70 | 0.52 | 0.55 | 0.71 | 0.70 |
S13 | Tt, Tt−1, Tt−2 | 0.80 | 0.72 | 0.72 | 0.51 | 0.53 | 0.72 | 0.72 |
S14 | Tt, Tt−1, Tt−2, Tt−3 | 0.80 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |
S15 | Tt, Tt−1, Tt−2, Tt−3, Tt−4 | 0.70 | 0.72 | 0.73 | 0.51 | 0.52 | 0.72 | 0.73 |
Scenarios | Model Inputs | No of Clusters | R2 | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | |||
S1 | Qt | 2 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S2 | Qt, Qt−1 | 4 | 0.77 | 0.78 | 0.46 | 0.47 | 0.77 | 0.78 |
S3 | Qt, Qt−1, Qt−2 | 2 | 0.77 | 0.78 | 0.46 | 0.47 | 0.78 | 0.78 |
S4 | Qt, Qt−1, Qt−2, Qt−3 | 2 | 0.77 | 0.78 | 0.46 | 0.48 | 0.77 | 0.78 |
S5 | Qt, Qt−1, Qt−2, Qt−3, Qt−4 | 2 | 0.77 | 0.78 | 0.46 | 0.48 | 0.77 | 0.77 |
S6 | Qt, SCAt | 2 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S7 | Qt, SCAt, SCAt−1 | 2 | 0.78 | 0.78 | 0.45 | 0.47 | 0.78 | 0.78 |
S8 | Qt, SCAt, SCAt−1, SCAt−2 | 2 | 0.78 | 0.77 | 0.45 | 0.48 | 0.80 | 0.78 |
S9 | Qt, Rt−1, SCAt, SCAt−4 | 2 | 0.79 | 0.78 | 0.44 | 0.47 | 0.79 | 0.78 |
S10 | Qt, Tt−1, Evapt−1, SCAt, SCAt−4 | 2 | 0.80 | 0.78 | 0.43 | 0.47 | 0.80 | 0.78 |
S11 | Tt | 3 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |
S12 | Tt, Tt−1 | 2 | 0.71 | 0.70 | 0.53 | 0.55 | 0.71 | 0.70 |
S13 | Tt, Tt−1, Tt−2 | 4 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |
S14 | Tt, Tt−1, Tt−2, Tt−3 | 6 | 0.76 | 0.72 | 0.48 | 0.53 | 0.76 | 0.72 |
S15 | Tt, Tt−1, Tt−2, Tt−3, Tt−4 | 2 | 0.72 | 0.70 | 0.51 | 0.55 | 0.72 | 0.70 |
Scenarios | Model Inputs | Basis Function | R2 | RMSE | NSE | |||
---|---|---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | |||
S1 | Qt | 5 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |
S2 | Qt, Qt−1 | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |
S3 | Qt, Qt−1, Qt−2 | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |
S4 | Qt, Qt−1, Qt−2, Qt−3 | 15 | 0.77 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |
S5 | Qt, Qt−1, Qt−2, Qt−3, Qt−4 | 15 | 0.78 | 0.78 | 0.47 | 0.47 | 0.77 | 0.78 |
S6 | Qt, SCAt | 15 | 0.77 | 0.78 | 0.46 | 0.48 | 0.78 | 0.77 |
S7 | Qt, SCAt, SCAt−1 | 20 | 0.77 | 0.77 | 0.46 | 0.48 | 0.77 | 0.77 |
S8 | Qt, SCAt, SCAt−1, SCAt−2 | 15 | 0.77 | 0.77 | 0.46 | 0.48 | 0.77 | 0.77 |
S9 | Qt, Rt−1, SCAt, SCAt−4 | 25 | 0.78 | 0.77 | 0.45 | 0.48 | 0.78 | 0.77 |
S10 | Qt, Tt−1, Evapt−1, SCAt, SCAt−4 | 10 | 0.79 | 0.79 | 0.45 | 0.46 | 0.79 | 0.79 |
S11 | Tt | 20 | 0.69 | 0.70 | 0.54 | 0.55 | 0.69 | 0.70 |
S12 | Tt, Tt−1 | 15 | 0.70 | 0.70 | 0.53 | 0.55 | 0.70 | 0.70 |
S13 | Tt, Tt−1, Tt−2 | 10 | 0.71 | 0.71 | 0.52 | 0.55 | 0.71 | 0.70 |
S14 | Tt, Tt−1, Tt−2, Tt−3 | 10 | 0.72 | 0.71 | 0.52 | 0.54 | 0.72 | 0.71 |
S15 | Tt, Tt−1, Tt−2, Tt−3, Tt−4 | 20 | 0.72 | 0.71 | 0.51 | 0.54 | 0.72 | 0.71 |
Models | Training Period | Testing Period | ||||
---|---|---|---|---|---|---|
R2 | RMSE | NSE | R2 | 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 |
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) |
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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
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 StyleHussan, 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