# Simulation of Titicaca Lake Water Level Fluctuations Using Hybrid Machine Learning Technique Integrated with Grey Wolf Optimizer Algorithm

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## Abstract

**:**

^{2}= 0.96).

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}at an elevation of 3810 m a.m.s.l, with a mean depth of 105 m. The outlet is still at 3807 m a.m.s.l. [28].

#### 2.2. Data Used

#### 2.3. Preprocessing Methods

#### 2.3.1. Principal Component Analysis (PCA)

#### 2.3.2. Random Forest (RF)

#### 2.3.3. Relief (RL)

#### 2.4. Predictor Methods

#### 2.4.1. Support Vector Regression

#### 2.4.2. Grey Wolf Optimizer

#### 2.4.3. Hybrid SVR-GWO Model

#### 2.5. Performance Indexes

## 3. Results and Discussion

#### 3.1. Implementation of the Preprocessing Methods

#### 3.2. Performances of the SVR and SVR-GWO Models

^{2}. The SVR-GWO model in the testing period and in the best scenario (with input of L (t − 1), L (t − 2), L (t − 3), L (t − 4)) with the RMSE = 0.087 m, MAE = 0.066 m, and R

^{2}= 0.967 outperformed the ordinary SVR model (with input of L (t − 1), L (t − 2), L (t − 3), L (t − 4), L (t − 5)) with the RMSE = 0.1 m, MAE = 0.082 m, and R

^{2}= 0.961.

^{2}value of SVR predictions were about 0.95 & 0.96 and approved the high capability of this model in lake water level prediction; which is in line with the results of the current research, despite the lakes being located in two completely different areas. To evaluate the positive effect of merging SVR with GWO, there are no studies about lake water level prediction. However, in other areas such as monthly streamflow forecasting, this was a successful and efficient combination; so that in hybrid forms of SVR, the GWO was superior in competition with the algorithms such as Particle Swarm Optimization (PSO), Multi-Verse Optimization (MVO) and Shuffled Complex Evolution (SCE) [43].

## 4. Conclusions

^{2}) and visual displays (i.e., scatter plot, box plot, etc.). Comparing the results of six scenarios from the implementation of the SVR and SVR-GWO models showed that the performance of the RF pre-processing method was better than PCA and RF methods for finding the best input for predictor models. The results demonstrated that the meta-optimized hybrid model (SVR-GWO) enhanced the capability of the original SVR model for the reproduction of the monthly lake water level. The SVR-GWO model with inputs of L (t − 1), L (t − 2), L (t − 3), L (t − 4) was found to be the most suitable model for prediction LWL. The results of this study suggest that the Grey Wolf Optimizer algorithm is a useful add-on tool for enhancing the accuracy of forecasting SVR model to predict LWL. Also, this research provided evidence for the effectiveness of the hybrid model, which can be utilized and investigated in hydrology for forecasting time series data such as lake water level (LWL). The results show that the models can be used to represent a 1-month (ahead) prediction of the lake water level. This can be applicable for the agricultural, industrial, environmental and urban sectors and systems related to Titicaca Lake and their managers and planners, to inform about the lake’s water level status in the coming month.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Ebtehaj, I.; Bonakdari, H.; Gharabaghi, B. A reliable linear method for modeling lake level fluctuations. J. Hydrol.
**2019**, 570. [Google Scholar] [CrossRef] - Seo, Y.; Kim, S.; Kisi, O.; Singh, V.P. Daily water level forecasting using wavelet decomposition and artificial intelligence techniques. J. Hydrol.
**2015**, 520. [Google Scholar] [CrossRef] - Hu, T.; Mao, J.; Pan, S.; Dai, L.; Zhang, P.; Xu, D.; Dai, H. Water level management of lakes connected to regulated rivers: An integrated modeling and analytical methodology. J. Hydrol.
**2018**, 562. [Google Scholar] [CrossRef] - Ghorbani, M.A.; Deo, R.C.; Karimi, V.; Yaseen, Z.M.; Terzi, O. Implementation of a hybrid MLP-FFA model for water level prediction of Lake Egirdir, Turkey. Stoch. Environ. Res. Risk Assess.
**2018**, 32. [Google Scholar] [CrossRef] - Rajurkar, M.P.; Kothyari, U.C.; Chaube, U.C. Modeling of the daily rainfall-runoff relationship with artificial neural network. J. Hydrol.
**2004**, 285. [Google Scholar] [CrossRef] - Croke, B.F.W.; Andrews, F.; Jakeman, A.J.; Cuddy, S.M.; Luddy, A. IHACRES Classic Plus: A redesign of the IHACRES rainfall-runoff model. Environ. Model. Softw.
**2006**, 21. [Google Scholar] [CrossRef] - Bicknell, B.R.; Imhoff, J.C.; Kittle, J.L., Jr.; Donigan, A.S., Jr.; Johanson, R.C.; Barnwell, T.O. Hydrological Simulation Program-Fortran User’s Manual for Release 11; U.S. Environ. Prot. Agency: Washington, DC, USA, 1996.
- Arnold, J.G.; Srinivasan, R.; Muttiah, R.S.; Williams, J.R. Large area hydrologic modeling and assessment part I: Model development. J. Am. Water Resour. Assoc.
**1998**, 34. [Google Scholar] [CrossRef] - Privalsky, V.E. Modeling long term lake variations by physically based stochastic dynamic models. Stoch. Hydrol. Hydraul.
**1988**, 2. [Google Scholar] [CrossRef] - Mohammadi, B.; Mehdizadeh, S. Modeling daily reference evapotranspiration via a novel approach based on support vector regression coupled with whale optimization algorithm. Agric. Water Manag.
**2020**, 237. [Google Scholar] [CrossRef] - Misra, D.; Oommen, T.; Agarwal, A.; Mishra, S.K.; Thompson, A.M. Application and analysis of support vector machine based simulation for runoff and sediment yield. Biosyst. Eng.
**2009**, 103. [Google Scholar] [CrossRef] - Emamgholizadeh, S.; Demneh, R.K. A comparison of artificial intelligence models for the estimation of daily suspended sediment load: A case study on the telar and kasilian rivers in Iran. Water Sci. Technol. Water Supply
**2019**, 19. [Google Scholar] [CrossRef] [Green Version] - 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. [Google Scholar] [CrossRef] - Solomatine, D.P.; Xue, Y. M5 model trees and neural networks: Application to flood forecasting in the upper reach of the Huai River in China. J. Hydrol. Eng.
**2004**, 9. [Google Scholar] [CrossRef] - Emamgholizadeh, S.; Bahman, K.; Bateni, S.M.; Ghorbani, H.; Marofpoor, I.; Nielson, J.R. Estimation of soil dispersivity using soft computing approaches. Neural Comput. Appl.
**2017**, 28. [Google Scholar] [CrossRef] - Aghelpour, P.; Bahrami-Pichaghchi, H.; Kisi, O. Comparison of three different bio-inspired algorithms to improve ability of neuro fuzzy approach in prediction of agricultural drought, based on three different indexes. Comput. Electron. Agric.
**2020**, 170. [Google Scholar] [CrossRef] - Aghelpour, P.; Varshavian, V. Evaluation of stochastic and artificial intelligence models in modeling and predicting of river daily flow time series. Stoch. Environ. Res. Risk Assess.
**2020**, 34. [Google Scholar] [CrossRef] - Guan, Y.; Mohammadi, B.; Pham, Q.B.; Adarsh, S.; Balkhair, K.S.; Rahman, K.U.; Linh, N.T.T.; Tri, D.Q. A novel approach for predicting daily pan evaporation in the coastal regions of Iran using support vector regression coupled with krill herd algorithm model. Theor. Appl. Climatol.
**2020**, 142. [Google Scholar] [CrossRef] - Aghelpour, P.; Mohammadi, B.; Biazar, S.M. Long-term monthly average temperature forecasting in some climate types of Iran, using the models SARIMA, SVR, and SVR-FA. Theor. Appl. Climatol.
**2019**, 138. [Google Scholar] [CrossRef] - Buyukyildiz, M.; Tezel, G.; Yilmaz, V. Estimation of the change in lake water level by artificial intelligence methods. Water Resour. Manag.
**2014**, 28. [Google Scholar] [CrossRef] - Moazenzadeh, R.; Mohammadi, B.; Shamshirband, S.; Chau, K. Coupling a firefly algorithm with support vector regression to predict evaporation in northern Iran. Eng. Appl. Comput. Fluid Mech.
**2018**, 12, 584–597. [Google Scholar] [CrossRef] [Green Version] - Liu, Z.; Zhou, P.; Zhang, Y. A probabilistic wavelet-support vector regression model for streamflow forecasting with rainfall and climate information input. J. Hydrometeorol.
**2015**, 16. [Google Scholar] [CrossRef] - Niu, M.; Wang, Y.; Sun, S.; Li, Y. A novel hybrid decomposition-and-ensemble model based on CEEMD and GWO for short-term PM2.5 concentration forecasting. Atmos. Environ.
**2016**, 134. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey wolf optimizer. Adv. Eng. Softw.
**2014**, 69. [Google Scholar] [CrossRef] [Green Version] - Dehghani, M.; Seifi, A.; Riahi-Madvar, H. Novel forecasting models for immediate-short-term to long-term influent flow prediction by combining ANFIS and grey wolf optimization. J. Hydrol.
**2019**, 576. [Google Scholar] [CrossRef] - Zolá, R.P.; Bengtsson, L. Long-term and extreme water level variations of the shallow Lake Poopó, Bolivia. Hydrol. Sci. J.
**2006**, 51. [Google Scholar] [CrossRef] [Green Version] - Hastenrath, S.; Kutzbach, J. Late Pleistocene climate and water budget of the south American Altiplano. Quat. Res.
**1985**, 24. [Google Scholar] [CrossRef] - Zolá, R.P.; Bengtsson, L.; Berndtsson, R.; Martí-Cardona, B.; Satgé, F.; Timouk, F.; Bonnet, M.P.; Mollericon, L.; Gamarra, C.; Pasapera, J. Modelling Lake Titicaca’s daily and monthly evaporation. Hydrol. Earth Syst. Sci.
**2019**, 23. [Google Scholar] [CrossRef] [Green Version] - Choubin, B.; Malekian, A. Combined gamma and M-test-based ANN and ARIMA models for groundwater fluctuation forecasting in semiarid regions. Environ. Earth Sci.
**2017**, 76. [Google Scholar] [CrossRef] - Hinton, G.E.; Salakhutdinov, R.R. Reducing the dimensionality of data with neural networks. Science
**2006**, 313. [Google Scholar] [CrossRef] [Green Version] - Cutler, D.R.; Edwards, T.C.; Beard, K.H.; Cutler, A.; Hess, K.T.; Gibson, J.; Lawler, J.J. Random forests for classification in ecology. Ecology
**2007**, 88. [Google Scholar] [CrossRef] - Díaz-Uriarte, R.; de Andrés, S.A. Gene selection and classification of microarray data using random forest. BMC Bioinform.
**2006**, 7. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kira, K.; Rendell, L.A. Feature selection problem: Traditional methods and a new algorithm. In Proceedings of the Tenth National Conference on Artificial Intelligence, San Jose, CA, USA, 12–16 July 1992. [Google Scholar]
- Faris, H.; Aljarah, I.; Al-Betar, M.A.; Mirjalili, S. Grey wolf optimizer: A review of recent variants and applications. Neural Comput. Appl.
**2018**, 30. [Google Scholar] [CrossRef] - Mirjalili, S.; Saremi, S.; Mirjalili, S.M.; Coelho, L.D.S. Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization. Expert Syst. Appl.
**2016**, 47. [Google Scholar] [CrossRef] - Mohammadi, B.; Ahmadi, F.; Mehdizadeh, S.; Guan, Y.; Pham, Q.B.; Linh, N.T.T.; Tri, D.Q. Developing novel robust models to improve the accuracy of daily streamflow modeling. Water Resour. Manag.
**2020**, 34. [Google Scholar] [CrossRef] - Mehdizadeh, S.; Mohammadi, B.; Pham, Q.B.; Khoi, D.N.; Linh, N.T.T. Implementing novel hybrid models to improve indirect measurement of the daily soil temperature: Elman neural network coupled with gravitational search algorithm and ant colony optimization. Meas. J. Int. Meas. Confed.
**2020**, 165. [Google Scholar] [CrossRef] - Mohammadi, B.; Aghashariatmadari, Z. Estimation of solar radiation using neighboring stations through hybrid support vector regression boosted by Krill Herd algorithm. Arab. J. Geosci.
**2020**, 13. [Google Scholar] [CrossRef] - Mohammadi, B.; Linh, N.T.T.; Pham, Q.B.; Ahmed, A.N.; Vojteková, J.; Guan, Y.; Abba, S.I.; El-Shafie, A. Adaptive neuro-fuzzy inference system coupled with shuffled frog leaping algorithm for predicting river streamflow time series. Hydrol. Sci. J.
**2020**, 65. [Google Scholar] [CrossRef] - Vaheddoost, B.; Guan, Y.; Mohammadi, B. Application of hybrid ANN-whale optimization model in evaluation of the field capacity and the permanent wilting point of the soils. Environ. Sci. Pollut. Res.
**2020**, 27. [Google Scholar] [CrossRef] - Moazenzadeh, R.; Mohammadi, B. Assessment of bio-inspired metaheuristic optimisation algorithms for estimating soil temperature. Geoderma
**2019**, 353. [Google Scholar] [CrossRef] - Li, B.; Yang, G.; Wan, R.; Dai, X.; Zhang, Y. Comparison of random forests and other statistical methods for the prediction of lake water level: A case study of the Poyang Lake in China. Hydrol. Res.
**2016**, 47. [Google Scholar] [CrossRef] [Green Version] - Tikhamarine, Y.; Souag-Gamane, D.; Kisi, O. A new intelligent method for monthly streamflow prediction: Hybrid wavelet support vector regression based on grey wolf optimizer (WSVR–GWO). Arab. J. Geosci.
**2019**, 12. [Google Scholar] [CrossRef] - Aghelpour, P.; Guan, Y.; Bahrami-Pichaghchi, H.; Mohammadi, B.; Kisi, O.; Zhang, D. Using the MODIS Sensor for Snow Cover Modeling and the Assessment of Drought Effects on Snow Cover in a Mountainous Area. Remote Sens.
**2020**, 12, 3437. [Google Scholar] [CrossRef]

**Figure 5.**Schematic view of predicting lake water lake by SVR and SVR-GWO by using data-driven techniques.

**Figure 8.**Scatter plot of the predicted lake water level from the SVR and SVR-GWO models versus the corresponding measurements for the testing stage.

**Figure 9.**Box plot of observed and predicted lake water level for the testing period of the SVR and SVR-GWO models in all scenarios.

**Figure 10.**Time series plot of observed and predicted LWL for the best SVR and SVR-GWO models for four years of 2013, 2014, 2015 and 2016.

**Figure 12.**The histogram of the predicted and the observed ratio of lake level in the testing period, the data comparison intervals were selected from 3807.6 m to 3810 m.

Dataset | Min (m) | Max (m) | Mean (m) | SD (m) | Skewness (m) | Kurtosis (m) | Confidence Level (95%) |
---|---|---|---|---|---|---|---|

Total | 3807.387 | 3811.277 | 3808.959 | 0.781 | 0.11 | −0.584 | 0.067 |

Training | 3807.387 | 3811.277 | 3809.059 | 0.834 | −0.101 | −0.743 | 0.082 |

Testing | 3807.717 | 3809.797 | 3808.658 | 0.483 | −0.054 | −0.701 | 0.083 |

Component | % of Variance | Cumulative % |
---|---|---|

1 | 84.98 | 84.98 |

2 | 8.05 | 93.03 |

3 | 5.24 | 98.27 |

4 | 1.05 | 99.32 |

5 | 0.38 | 99.7 |

6 | 0.18 | 99.88 |

7 | 0.05 | 99.93 |

8 | 0.03 | 99.96 |

9 | 0.01 | 99.97 |

10 | 0.01 | 99.98 |

11 | 0.01 | 99.99 |

12 | 0.01 | 100 |

**Table 3.**Scenarios defined according to the selected input variables by PCA, RF, and RL pre-processing methods.

No. | Preprocessing Method | Input Combinations | Model Designation | |
---|---|---|---|---|

SVR | SVR-GWO | |||

1 | Principal component analysis | PCA1 | SVR1 | SVR-GWO1 |

2 | Random forest | L (t − 1), L (t − 2), L (t − 3), L (t − 4) | SVR2 | SVR-GWO2 |

3 | Relief | L (t − 1), L (t − 2), L (t − 3), L (t − 4), L (t − 5) | SVR3 | SVR-GWO3 |

**Table 4.**Performance evaluation of the SVR and SVRGWO models by different pre-processing methods in train and test stages.

Partition | Models Name | RMSE (m) | MAE (m) | R^{2} |
---|---|---|---|---|

Train phase | SVR1 | 0.395 | 0.312 | 0.774 |

SVR2 | 0.11 | 0.082 | 0.982 | |

SVR3 | 0.108 | 0.08 | 0.983 | |

SVR-GWO1 | 0.304 | 0.208 | 0.877 | |

SVR-GWO2 | 0.084 | 0.06 | 0.989 | |

SVR-GWO3 | 0.079 | 0.052 | 0.99 | |

Test phase | SVR1 | 0.329 | 0.276 | 0.558 |

SVR2 | 0.101 | 0.084 | 0.96 | |

SVR3 | 0.1 | 0.082 | 0.961 | |

SVR-GWO1 | 0.27 | 0.223 | 0.727 | |

SVR-GWO2 | 0.087 | 0.066 | 0.967 | |

SVR-GWO3 | 0.089 | 0.064 | 0.966 |

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## Share and Cite

**MDPI and ACS Style**

Mohammadi, B.; Guan, Y.; Aghelpour, P.; Emamgholizadeh, S.; Pillco Zolá, R.; Zhang, D.
Simulation of Titicaca Lake Water Level Fluctuations Using Hybrid Machine Learning Technique Integrated with Grey Wolf Optimizer Algorithm. *Water* **2020**, *12*, 3015.
https://doi.org/10.3390/w12113015

**AMA Style**

Mohammadi B, Guan Y, Aghelpour P, Emamgholizadeh S, Pillco Zolá R, Zhang D.
Simulation of Titicaca Lake Water Level Fluctuations Using Hybrid Machine Learning Technique Integrated with Grey Wolf Optimizer Algorithm. *Water*. 2020; 12(11):3015.
https://doi.org/10.3390/w12113015

**Chicago/Turabian Style**

Mohammadi, Babak, Yiqing Guan, Pouya Aghelpour, Samad Emamgholizadeh, Ramiro Pillco Zolá, and Danrong Zhang.
2020. "Simulation of Titicaca Lake Water Level Fluctuations Using Hybrid Machine Learning Technique Integrated with Grey Wolf Optimizer Algorithm" *Water* 12, no. 11: 3015.
https://doi.org/10.3390/w12113015