Estimation of Instantaneous Peak Flow Using Machine-Learning Models and Empirical Formula in Peninsular Spain
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data
2.2. Empirical Formulas
2.2.1. Fuller
2.2.2. CEDEX Regionalization of Fuller´s Formula
2.2.3. Sangal
2.2.4. Fill and Steiner
2.3. Artificial Neural Network (ANN)
2.4. Adaptive Neuro-Fuzzy Inference System (ANFIS)
2.5. Evaluation Criteria
3. Results and Discussion
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Name | Code | Area (km2) | Altitude (m) | R-B Index | Köppen Classification | Flow Availability (Years) |
---|---|---|---|---|---|---|
Trevias | TRE | 411 | 35 | 0.24 | Cfb | 43 |
Begonte | BEG | 843 | 395 | 0.24 | Csb | 43 |
Coterillo | COT | 485 | 16 | 0.47 | Cfb | 40 |
Andoain | AND | 765 | 38 | 0.39 | Cfb | 43 |
Priego | PRI | 345 | 818 | 0.12 | Csb | 46 |
Bolulla | BOL | 30 | 120 | 0.17 | Bsk | 38 |
Gargüera | GAR | 97 | 380 | 0.29 | Csa | 40 |
Cuernacabras | CUE | 120 | 305 | 0.31 | Csa | 40 |
Jubera | JUB | 196 | 892 | 0.10 | Csb | 62 |
Tramacastilla | TRA | 95 | 1278 | 0.10 | Csb | 48 |
Belmontejo | BEL | 187 | 830 | 0.08 | Csa | 42 |
Peralejo de las Truchas | PER | 410 | 1143 | 0.16 | Csb | 68 |
Riaza | RIA | 36 | 1139 | 0.16 | Csb | 70 |
Pitarque | PIT | 279 | 990 | 0.09 | Cfb | 45 |
River Basin District | Formula |
---|---|
Miño-Sil and Galicia Costa | IPF = MMDF × (1 + 1.81 × A−0.23) |
Cantábrico and País Vasco | IPF = MMDF × (1 + 3.1 × A−0.26) |
Duero | IPF = MMDF × (1 + 1.78 × A−0.29) |
Tajo | IPF = MMDF × (1 + 5.01 × A−0.38) |
Guadiana and Guadalquivir (Zone 1) | IPF = MMDF × (1 + 35.89 × A−0.72) |
Guadiana and Guadalquivir (Zone 2) | IPF = MMDF × (1 + 112.82 × A−0.7) |
Guadiana and Guadalquivir (Zone 3) | IPF = MMDF × (1 + 11.56 × A−0.42) |
Jucar | IPF = MMDF × (1 + 20.87 × A−0.51) |
Segura | IPF = MMDF × (1 + 145.85 × A−0.75) |
Ebro (Zone 1) | IPF = MMDF × (1 + 2.49 × A−0.36) |
Ebro (Zone 2) | IPF = MMDF × (1 + 3.39 × A−0.29) |
Ebro (Zone 3) | IPF = MMDF × (1 + 37.73 × A−0.55) |
Basin Code | R2 | RMSE (m3/s) | ||||||
---|---|---|---|---|---|---|---|---|
Fuller | CEDEX | Sangal | Fill Steiner | Fuller | CEDEX | Sangal | Fill Steiner | |
TRE | 0.85 | 0.85 | 0.82 | 0.80 | 93.68 | 76.09 | 82.16 | 99.27 |
BEG | 0.89 | 0.89 | 0.87 | 0.88 | 56.35 | 59.53 | 78.09 | 58.63 |
COT | 0.70 | 0.70 | 0.68 | 0.68 | 159.65 | 126.11 | 137.51 | 167.11 |
AND | 0.54 | 0.54 | 0.61 | 0.62 | 184.61 | 174.11 | 158.67 | 177.70 |
PRI | 0.90 | 0.90 | 0.89 | 0.89 | 9.94 | 11.04 | 10.39 | 11.67 |
BOL | 0.92 | 0.92 | 0.94 | 0.94 | 6.92 | 16.28 | 8.17 | 9.26 |
GAR | 0.71 | 0.71 | 0.69 | 0.70 | 12.10 | 11.20 | 14.11 | 15.70 |
CUE | 0.65 | 0.65 | 0.66 | 0.65 | 30.93 | 28.23 | 33.50 | 35.97 |
JUB | 0.30 | 0.30 | 0.29 | 0.28 | 14.15 | 13.97 | 14.14 | 14.50 |
TRA | 0.81 | 0.81 | 0.84 | 0.83 | 3.34 | 6.38 | 3.96 | 4.77 |
BEL | 0.44 | 0.44 | 0.43 | 0.41 | 7.63 | 6.79 | 7.53 | 7.80 |
PER | 0.92 | 0.92 | 0.90 | 0.91 | 17.44 | 20.13 | 19.49 | 16.80 |
RIA | 0.72 | 0.72 | 0.72 | 0.71 | 4.41 | 3.39 | 3.27 | 3.33 |
PIT | 0.87 | 0.87 | 0.82 | 0.85 | 4.48 | 16.57 | 2.80 | 2.27 |
Basin Code | Data Set | ANN | ANFIS | Best Empirical Formula | ||||
---|---|---|---|---|---|---|---|---|
R2 | RMSE | R2 | RMSE | R2 | RMSE | Formula | ||
TRE | Training | 0.92 | 55.3 | 0.92 | 54.81 | 0.86 | 78.94 | CEDEX |
Test | 0.66 | 52.95 | 0.67 | 47.8 | 0.53 | 62.55 | ||
BEG | Training | 0.7 | 90.69 | 0.92 | 47.86 | 0.88 | 58.38 | Fuller |
Test | 0.83 | 72.03 | 0.87 | 59.31 | 0.95 | 47.07 | ||
COT | Training | 0.77 | 117.19 | 0.79 | 107.49 | 0.69 | 134.55 | CEDEX |
Test | 0.82 | 70.04 | 0.82 | 68.8 | 0.91 | 84.26 | ||
AND | Training | 0.46 | 170.75 | 0.5 | 163.13 | 0.53 | 159.13 | Sangal |
Test | 0.75 | 172.29 | 0.79 | 188.6 | 0.83 | 156.92 | ||
PRI | Training | 0.89 | 9.75 | 0.91 | 9 | 0.88 | 10.26 | Fuller |
Test | 0.98 | 5.62 | 0.98 | 4.8 | 0.96 | 8.52 | ||
BOL | Training | 0.97 | 4.6 | 0.99 | 1.7 | 0.95 | 7.48 | Fuller |
Test | 0.78 | 3.27 | 0.77 | 4.5 | 0.72 | 4.09 | ||
GAR | Training | 0.82 | 8.62 | 0.94 | 5.06 | 0.71 | 11.29 | CEDEX |
Test | 0.75 | 10.36 | 0.85 | 8.46 | 0.72 | 10.72 | ||
CUE | Training | 0.85 | 12.26 | 0.9 | 10.24 | 0.75 | 17.34 | CEDEX |
Test | 0.79 | 44.92 | 0.77 | 41.38 | 0.85 | 52.07 | ||
JUB | Training | 0.39 | 10.31 | 0.41 | 10.12 | 0.32 | 11.1 | CEDEX |
Test | 0.5 | 20.27 | 0.59 | 19.51 | 0.48 | 21.38 | ||
TRA | Training | 0.83 | 2.88 | 0.84 | 2.76 | 0.82 | 3.38 | Fuller |
Test | 0.83 | 2.66 | 0.8 | 2.7 | 0.83 | 3.15 | ||
BEL | Training | 0.49 | 6.44 | 0.6 | 5.61 | 0.47 | 7.12 | CEDEX |
Test | 0.84 | 6.23 | 0.77 | 7.21 | 0.8 | 7.99 | ||
PER | Training | 0.91 | 16.87 | 0.93 | 14.33 | 0.9 | 17.64 | Fill-Steiner |
Test | 0.96 | 7. 39 | 0.98 | 5.44 | 0.92 | 9.28 | ||
RIA | Training | 0.73 | 3.27 | 0.75 | 3.11 | 0.71 | 3.5 | Sangal |
Test | 0.88 | 1.64 | 0.86 | 2.33 | 0.88 | 2.11 | ||
PIT | Training | 0.8 | 2.29 | 0.86 | 2.13 | 0.79 | 2.25 | Fill-Steiner |
Test | 0.92 | 2.2 | 0.97 | 0.82 | 0.97 | 2.07 |
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Jimeno-Sáez, P.; Senent-Aparicio, J.; Pérez-Sánchez, J.; Pulido-Velazquez, D.; Cecilia, J.M. Estimation of Instantaneous Peak Flow Using Machine-Learning Models and Empirical Formula in Peninsular Spain. Water 2017, 9, 347. https://doi.org/10.3390/w9050347
Jimeno-Sáez P, Senent-Aparicio J, Pérez-Sánchez J, Pulido-Velazquez D, Cecilia JM. Estimation of Instantaneous Peak Flow Using Machine-Learning Models and Empirical Formula in Peninsular Spain. Water. 2017; 9(5):347. https://doi.org/10.3390/w9050347
Chicago/Turabian StyleJimeno-Sáez, Patricia, Javier Senent-Aparicio, Julio Pérez-Sánchez, David Pulido-Velazquez, and José María Cecilia. 2017. "Estimation of Instantaneous Peak Flow Using Machine-Learning Models and Empirical Formula in Peninsular Spain" Water 9, no. 5: 347. https://doi.org/10.3390/w9050347