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
- Gaume, E.; Bain, V.; Bernardara, P.; Newinger, O.; Barbuc, M.; Bateman, A.; Blaškovičová, L.; Blöschl, G.; Borga, M.; Dumitrescu, A.; et al. A compilation of data on European flash floods. J. Hydrol. 2009, 367, 70–78. [Google Scholar] [CrossRef]
- Barredo, J.I. Major flood disasters in Europe: 1950–2005. Nat. Hazards 2007, 42, 125–148. [Google Scholar] [CrossRef]
- Ding, J.; Haberlandt, U. Estimation of instantaneous peak flow from maximum mean daily flow by regionalization of catchment model parameters. Hydrol. Process. 2017, 31, 612–626. [Google Scholar] [CrossRef]
- Fuller, W.E. Flood flows. Trans. ASCE 1914, 77, 564–617. [Google Scholar]
- Silva, E.A. Estimativa Regional da Vazao Máxima Instantânea em Algumas Bacias Brasileiras. Master’s Thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil, 1997. [Google Scholar]
- Silva, E.A.; Tucci, C.E.M. Relaçao entre as vazoes máximas diárias e instantáneas. Rev. Bras. Recur. Hídr. 1998, 3, 133–151. [Google Scholar] [CrossRef]
- Taguas, E.V.; Ayuso, J.L.; Pena, A.; Yuan, Y.; Sanchez, M.C.; Giraldez, J.V.; Pérez, R. Testing the relationship between instantaneous peak flow and mean daily flow in a Mediterranean Area Southeast Spain. Catena 2008, 75, 129–137. [Google Scholar] [CrossRef]
- Jarvis, C.S. Floods in United States. In Water Supply Paper; US Geological Survey: Reston, VA, USA, 1936. [Google Scholar]
- Langbein, W.B. Peak discharge from daily records. Water Resour. Bull. 1944, 145. [Google Scholar]
- Linsley, R.K.; Kohler, M.A.; Paulhus, J.L.H. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1949. [Google Scholar]
- Sangal, B.P. Practical method of estimating peak flow. J. Hydraul. Eng. 1983, 109, 549–563. [Google Scholar] [CrossRef]
- Fill, H.D.; Steiner, A.A. Estimating instantaneous peak flow from mean daily flow data. J. Hydrol. Eng. 2003, 8, 365–369. [Google Scholar] [CrossRef]
- Centre for Public Works Studies and Experimentation (CEDEX). Mapa de Caudales Máximos. Memoria Técnica (In Spanish). 2011. Available online: http://www.mapama.gob.es/es/agua/temas/gestion-de-los-riesgos-de-inundacion/memoria_tecnica_v2_junio2011_tcm7–162773.pdf (accessed on 5 January 2017).
- Fathzadeh, A.; Jaydari, A.; Taghizadeh-Mehrjardi, R. Comparison of different methods for reconstruction of instantaneous peak flow data. Intell. Autom. Soft Comput. 2017, 23, 41–49. [Google Scholar] [CrossRef]
- Haykin, S. Neural Networks: A Comprehensive Foundation, 2nd ed.; Macmillan: New York, NY, USA, 1994; ISBN 81-7808-300-0. [Google Scholar]
- Ajmera, T.K.; Goyal, M.K. Development of stage-discharge rating curve using model tree and neural networks: An application to Peachtree Creek in Atlanta. Expert Syst. Appl. 2012, 39, 5702–5710. [Google Scholar] [CrossRef]
- Mustafa, M.R.; Isa, M.H.; Rezaur, R.B. Artificial neural networks modelling in water resources engineering: Infrastructure and applications. World Acad. Sci. Eng. Technol. 2012, 62, 341–349. [Google Scholar]
- Cheng, C.T.; Feng, Z.K.; Niu, W.J.; Liao, S.L. Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China. Water 2015, 7, 4477–4495. [Google Scholar] [CrossRef]
- Govindaraju, R.S. Artificial neural networks in hydrology. II: Hydrological applications. J. Hydrol. Eng. 2000, 5, 124–137. [Google Scholar] [CrossRef]
- Hamaamin, Y.A.; Nejadhashemi, A.P.; Zhang, Z.; Giri, S.; Woznicki, S.A. Bayesian Regression and Neuro-Fuzzy Methods Reliability Assessment for Estimating Streamflow. Water 2016, 8, 287. [Google Scholar] [CrossRef]
- Abraham, A.; Köppen, M.; Franke, K. Design and Application of Hybrid Intelligent Systems; IOS Press: Amsterdam, The Netherlands, 2003; ISBN 978-1-58603-394-1. [Google Scholar]
- Kim, J.; Kasabov, N. HyFIS: Adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Netw. 1999, 12, 1301–1319. [Google Scholar] [CrossRef]
- Emamgholizadeh, S.; Moslemi, K.; Karami, G. Prediction the groundwater level of Bastam Plain (Iran) by artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). Water Resour. Manag. 2014, 28, 5433–5446. [Google Scholar] [CrossRef]
- Dastorani, M.; Moghadamnia, A.; Piri, J.; Rico-Ramirez, M. Application of ANN and ANFIS models for reconstructing missing flow data. Environ. Monit. Assess. 2010, 166, 421–434. [Google Scholar] [CrossRef] [PubMed]
- Seckin, N. Modeling flood discharge at ungauged sites across Turkey using neuro-fuzzy and neural networks. J. Hydroinform. 2011, 13, 842–849. [Google Scholar] [CrossRef]
- Tu, J.V. Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes. J. Clin. Epidemiol. 1996, 49, 1225–1231. [Google Scholar] [CrossRef]
- Rezaei, H.; Rahmati, M.; Modarress, H. Application of ANFIS and MLR models for prediction of methane adsorption on X and Y faujasite zeolites: Effect of cations substitution. Neural Comput. Appl. 2015, 28, 301–312. [Google Scholar] [CrossRef]
- Bisht, D.; Mohan-Raju, M.; Joshi, M. Simulation of water table elevation fluctuation using fuzzy-logic and ANFIS. Comput. Model. New Technol. 2009, 13, 16–23. [Google Scholar]
- Guldal, V.; Tongal, H. Comparison of recurrent neural network, adaptive neuro-fuzzy inference system and stochastic models in Egirdir lake level forecasting. Water Resour. Manag. 2010, 24, 105–128. [Google Scholar] [CrossRef]
- Shabani, M.; Shabani, N. Application of artificial neural networks in instantaneous peak flow estimation for Kharestan Watershed, Iran. J. Resour. Ecol. 2012, 3, 379–383. [Google Scholar] [CrossRef]
- Dastorani, M.T.; Koochi, J.S.; Darani, H.S.; Talebi, A.; Rahimian, M.H. River instantaneous peak flow estimation using daily flow data and machine-learning-based models. J. Hydroinform. 2013, 15, 1089–1098. [Google Scholar] [CrossRef]
- Kottek, M.; Grieser, J.; Beck, C.; Rudolf, B.; Rubel, F. World Map of the Köppen-Geiger climate classification updated. Meteorol. Z. 2006, 15, 259–263. [Google Scholar] [CrossRef]
- Senent-Aparicio, J.; Pérez-Sánchez, J.; Bielsa-Artero, A.M. Asessment of Sustainability in Semiarid Mediterranean Basins: Case Study of the Segura Basin, Spain. Water Technol. Sci. 2016, 7, 67–84. [Google Scholar]
- Baker, D.B.; Richards, R.P.; Loftus, T.T.; Kramer, J.W. A new flashiness index: Characteristics and applications to Midwestern rivers and streams. J. Am. Water Resour. Assoc. 2004, 40, 503–522. [Google Scholar] [CrossRef]
- Holko, L.; Parajka, J.; Kostka, Z.; Škoda, P.; Blöschl, G. Flashiness of mountain streams in Slovakia and Austria. J. Hydrol. 2011, 405, 392–401. [Google Scholar] [CrossRef]
- Centre for Public Works Studies and Experimentation (CEDEX). Anuario de Aforos (In Spanish). Available online: http://ceh-flumen64.cedex.es/anuarioaforos/default.asp (accessed on 4 January 2017).
- Maier, R.H.; Jain, A.; Graeme, C.D.; Sudheer, K.P. Methods used for the development of neural networks for the prediction of water resource variables in river systems: Current status and future directions. Environ. Model. Softw. 2010, 25, 891–909. [Google Scholar] [CrossRef]
- Hasanpour Kashani, M.; Daneshfaraz, R.; Ghorbani, M.; Najafi, M.; Kisi, O. Comparison of different methods for developing a stage–discharge curve of the Kizilirmak River. J. Flood Risk Manag. 2015, 8, 71–86. [Google Scholar] [CrossRef]
- Govindaraju, R.S. Artificial neural networks in hydrology. I: Preliminary concepts. J. Hydrol. Eng. 2000, 5, 115–123. [Google Scholar] [CrossRef]
- Wang, J.; Shi, P.; Jiang, P.; Hu, J.; Qu, S.; Chen, X.; Chen, Y.; Dai, Y.; Xiao, Z. Application of BP Neural Network Algorithm in Traditional Hydrological Model for Flood Forecasting. Water 2017, 9, 48. [Google Scholar] [CrossRef]
- Meng, C.; Zhou, J.; Tayyab, M.; Zhu, S.; Zhang, H. Integrating Artificial Neural Networks into the VIC Model for Rainfall-Runoff Modeling. Water 2016, 8, 407. [Google Scholar] [CrossRef]
- Wolfs, V.; Willems, P. Development of discharge-stage curves affected by hysteresis using time varying models, model trees and neural networks. Environ. Model. Softw. 2014, 55, 107–119. [Google Scholar] [CrossRef]
- Levenberg, K. A Method for the Solution of Certain Problems in Least Squares. Appl. Math. 1944, 2, 164–168. [Google Scholar]
- Marquardt, D. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Appl. Math. 1963, 11, 431–441. [Google Scholar] [CrossRef]
- Nayak, P.C.; Sudheer, K.P.; Rangan, D.M.; Ramasastri, K.S. A neuro-fuzzy computing technique for modeling hydrological time series. J. Hydrol. 2004, 291, 52–66. [Google Scholar] [CrossRef]
- Takagi, T.; Sugeno, M. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Trans. Syst. Man Cybern. 1985, 15, 116–132. [Google Scholar] [CrossRef]
- Sugeno, M.; Kang, G.T. Structure identification of fuzzy model. Fuzzy Sets Syst. 1988, 28, 15–33. [Google Scholar] [CrossRef]
- Jang, J.S.R. ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 1993, 23, 665–685. [Google Scholar] [CrossRef]
- Moriasi, D.N.; Arnold, J.G.; Liew, M.W.; Binger, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 2007, 50, 885–890. [Google Scholar] [CrossRef]
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
APA StyleJimeno-Sáez, P., Senent-Aparicio, J., Pérez-Sánchez, J., Pulido-Velazquez, D., & Cecilia, J. M. (2017). Estimation of Instantaneous Peak Flow Using Machine-Learning Models and Empirical Formula in Peninsular Spain. Water, 9(5), 347. https://doi.org/10.3390/w9050347