# Algal Bloom Prediction Using Extreme Learning Machine Models at Artificial Weirs in the Nakdong River, Korea

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}, which is equivalent to approximately 20% of the country’s area. The Nakdong River has eight weirs which were built in sequence starting in 2012. In particular, four of these weirs (Gangjeong-Goryeong weir, Dalseong weir, Hapcheon-Changnyeong weir, and Changnyeong-Haman weir) in the mid-lower Nakdong River region experience harmful algal blooms every summer, causing many problems for agricultural, residential, and commercial water supplies. Harmful algal blooms refer to toxic, hypoxia-generating cyanobacterial bloom genera controlled by the synergistic effects of nutrients (nitrogen and phosphorus), light, temperature, water residence, and biotic interactions [25]. Since the construction of the weirs, the public and the government have been interested in managing algal blooms. Figure 1 shows the locations of the four weirs on the Nakdong River in South Korea and the watershed area.

## 3. Extreme Learning Machine

#### 3.1. Architecture and Learning Method for ELM

**w**

_{i}and b

_{i}are the weight and bias between input layer and hidden layer, respectively. The output weights β are parameters to be estimated.

- (Step 1) Randomly assign hidden node parameters $({w}_{i},{b}_{i}),i=1,2,\cdots ,N$
- (Step 2) Calculate the hidden layer output matrix $\mathrm{H}=\left[\begin{array}{c}h({x}_{1})\\ \vdots \\ h({x}_{N})\end{array}\right]$
- (Step 3) Calculate the output weights β using a least squares estimate (LSE):$$\beta ={\mathrm{H}}^{*}\mathrm{T}$$$$\beta ={({\mathrm{H}}^{\mathrm{T}}\mathrm{H})}^{-1}{\mathrm{H}}^{\mathrm{T}}\mathrm{T}$$

#### 3.2. Model Application

^{2}. Water quality data with chlorophyll-a concentration were collected weekly and the weekly data were used for algal bloom prediction. Chlorophyll-a concentration was used data from 7 days prior.

^{2}) and root-mean-square error (RMSE) between the observed and predicted values. These indicators are defined as follows:

## 4. Results and Discussion

#### 4.1. Experimental Results

^{2}= 0.61 for training and 0.47 for testing, and RMSE of 8.6 μg/L for training and 14.5 μg/L for testing. The prediction results in Dalseong weir show R

^{2}= 0.55 for training and 0.44 for testing, and RMSE of 12.6 for training and 13.5 for testing. The ELM model shows better performance in Gangjeong-Goryeong weir than in Dalseong weir. The prediction results in Hapcheon-Changnyeong weir show R

^{2}= 0.38 for training and 0.41 for testing, and RMSE of 15.3 for training and 13.1 for testing. The prediction results in Changnyeong-Haman weir show R

^{2}= 0.29 for training and 0.36 for testing, and RMSE of 16.6 for training and 12.4 for testing. The Akaike information criterion (AIC) was developed for comparing models, based on information theory [31]. AIC applied to Gangjeong-Goryeong weir has a value of 371.2 for training and 452.2 for testing, and 444.6 for training and 455.8 for testing in Dalseong weir. The AIC value in Hapcheon-Changnyeong weir is 461.3 for training and 436.1 for testing data sets, and 469.0 for training and 421.9 for testing data sets in Changnyeong-Haman weir. The predictive power of the ELM model was found to be better in upstream weirs than in downstream weirs. This is because the downstream Nakdong River has more algal blooming factors, such as tributaries, water intakes, and dam discharge, which are difficult to control and manage.

^{2}= 0.71 (0.61) for training and 0.45 (0.47) for testing, RMSE = 6.8 (8.6) for training and 13.8 (14.5) for testing, and AIC = 333.8 (371.2) for training and 452.2 (446.2) for testing in Gangjeong-Goryeong weir. The ELM2 (ELM1) model showed better performance with R

^{2}= 0.76 (0.55) for training and 0.45 (0.44) for testing, RMSE = 8.9 (12.6) for training and 13.4 (13.5) for testing, and AIC = 388.1 (444.6) for training and 456.9 (455.8) for testing in Dalsone weir. Table 4 and Figure 8 show the results from the ELM2 model in Gangjeong-Goryeong weir and Dalseong weir.

^{2}= 0.44 (0.38) for training and 0.43 (0.41) for testing, RMSE of 14.6 (15.3) for training and 13.1 (13.1) for testing, and AIC of 455.8 (461.3) for training and 437.5 (436.1) for testing in Hapcheon-Changnyeong weir. The ELM2 (ELM1) model showed better performance with R

^{2}= 0.32 (0.29) for training and 0.46 (0.36) for testing, RMSE = 16.3 (16.6) for training and 11.4 (12.4) for testing, and AIC = 468.3 (469.0) for training and 410.5 (421.9) for testing in Changnyeong-Haman weir. The ELM2 results from both downstream weirs were similar to the ELM1 model (Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13). This is because the downstream Nakdong River has more algal blooming factors such as tributaries, water intakes, and dam discharge, which are difficult to control and manage. Thus, these algal blooming factors need to be applied to the ELM2 model for more accurate prediction. On the other hand, upstream chlorophyll-a concentration can be a good indicator to predict algal blooms in upstream weirs. Moreover, we compared with the well-known conventional neural network with BP (Back-Propagation) in Table 5. Here, the learning rate was 0.001 and the number of epochs was 1000. In the case of Gangjeong-Goryeong weir, the RMSE values for training and testing set were 9.27 and 15.73, respectively. We also obtained RMSE values of 11.44 and 14.12 for training and testing data in Dalseong weir, respectively. In Hapcheon-Changnyeong weir, the RMSE values for training and testing are 14.69 and 13.43, respectively. We also obtained RMSE values of 16.68 and 11.35 for training and testing in Changnyeong-Haman weir, respectively. Also, we compared with multiple LR (Linear Regression) in Table 5. In the case of Gangjeong-Goryeong weir, the RMSE values for training and testing set were 11.3 and 17.5, respectively. We also obtained RMSE values of 15.3 and 20.7 for training and testing data in Dalseong weir, respectively. In Hapcheon-Changnyeong weir, the RMSE values for training and testing are 14.7 and 13.9, respectively. We also obtained RMSE values of 16.9 and 14.0 for training and testing in Changnyeong-Haman weir, respectively.

^{2}improved by 16.4% for training and −4.3% for testing, and RMSE improved by 20.9% for training and 4.8% for testing. The prediction results for Dalseong weir show that R

^{2}improved by 38.2% for training and 2.3% for testing, and RMSE improved by 29.4% for training and 0.7% for testing. The prediction results for Hapcheon-Changnyeong weir show that R

^{2}improved by 15.8% for training and 4.9% for testing, and RMSE improved by 4.6% for training and 0.0% for testing. The prediction results for Changnyeong-Haman weir show that R

^{2}improved by 10.3% for training and 27.8% for testing, and RMSE improved by 1.8% for training and 8.1% for testing. Figure 13 shows a performance comparison between the ELM1 and ELM2 model results in all four weirs.

#### 4.2. ELM Performance Discussion

- -
- ELM consists of a simple tuning-free three-step algorithm.
- -
- The learning speed of ELM is extremely fast.
- -
- The hidden node parameters are independent of training data. Although hidden nodes are important, they need not be tuned.
- -
- ELM could generate the hidden node parameters before using the training data.
- -
- ELM can be effectively applied to most real-world problems such as compression, feature learning, clustering, regression and classification.

## 5. Conclusions

^{2}and lower RMSE values for training and testing datasets in the upstream weirs. The ELM2 model also showed better performance with higher R

^{2}and lower RMSE values for training and testing datasets in the downstream weirs. However, the results from downstream weirs showed similar performance as the previous ELM1 model. This is because the downstream Nakdong River has more diverse algal blooming factors such as tributaries, water intakes, and dam discharge, which are difficult to control and manage.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Weekly total nitrogen, total phosphorus, and chlorophyll-a data at the Gangjeong-Goryeong weir from 2013 to 2016 (n = 201).

**Figure 3.**Weekly total nitrogen, total phosphorus, and chlorophyll-a data at Dalseong weir from 2013 to 2016 (n = 205).

**Figure 5.**Diagram for ELM model (ELM2). AT: air temperature; RF: rainfall; SR: solar radiation; TN: total nitrogen; TP: total phosphorus; NP: ratio of total nitrogen over total phosphorus; Chla: chlorophyll-a concentration; Chla_u: upstream chlorophyll-a concentration.

**Figure 6.**Performance of ELM as a function of the number of hidden nodes. (

**a**) Gangjeong-Goryeong weir and (

**b**) Dalseong weir.

**Figure 7.**Training and testing results from the ELM1 model for chlorophyll-a prediction. (

**a**) Training results and (

**b**) testing results.

**Figure 8.**Training and testing results from the ELM2 model for chlorophyll-a prediction. (

**a**) Training results and (

**b**) testing results.

**Figure 9.**Performance of the ELM1 and ELM2 models in Gangjeong-Goryeong weir. (

**a**) ELM1 model and (

**b**) ELM2 model.

**Figure 10.**Performance of the ELM1 and ELM2 models in Dalseong weir. (

**a**) ELM1 model and (

**b**) ELM2 model.

**Figure 11.**Performance of the ELM1 and ELM2 models in Hapcheon-Changnyeong weir. (

**a**) ELM1 model and (

**b**) ELM2 model.

**Figure 12.**Performance of the ELM1 and ELM2 models in Changnyeong-Haman weir. (

**a**) ELM1 model and (

**b**) ELM2 model.

**Figure 13.**Comparison between the ELM1 and ELM2 model results for chlorophyll-a prediction in all four weirs. (

**a**) Training results and (

**b**) testing results. GG: Gangjeong-Goryeong weir; D: Dalseong weir; HC: Hapcheon-Changnyeong weir; CH: Changnyeong-Haman weir.

**Figure 14.**RMSE curves obtained by training of ANFIS-FCM for four weirs (num. of rule = 2). (

**a**) Gangjeong-Goryeong weir; (

**b**) Dalseong weir; (

**c**) Hapcheon-Changnyeong weir; (

**d**) Changnyeong-Haman weir.

Variables | Gangjeong-Goryeong Weir | Dalseong Weir | Hapcheon-Changnyeong Weir | Changnyeong-Haman Weir |
---|---|---|---|---|

Chlorophyll-a (μg/L) | 19.0 (2.2–106.7) | 26.0 (2.7–104.1) | 23.2 (1.7–100.7) | 25.2 (2.9–123.3) |

Total Nitrogen (mg/L) | 2.605 (1.201–4.100) | 3.723 (1.814–6.433) | 3.397 (1.842–6.207) | 2.778 (1.249–5.483) |

Total Phosphorus (mg/L) | 0.048 (0.012–0.157) | 0.061 (0.017–0.163) | 0.058 (0.016–0.163) | 0.054 (0.015–0.174) |

Items | Variables | Source |
---|---|---|

Weather | Air temperature, Rainfall, Solar radiation | Korea Meteorological Administration (http://kma.go.kr) |

Water quality | Total Nitrogen, Total Phosphorus, N/P ratio, chlorophyll-a | Ministry of Environment, National Institute of Environmental Research (http://water.nier.go.kr) |

ELM1 Model | Gangjeong-Goryeong Weir | Dalseong Weir | Hapcheon-Changnyeong Weir | Changnyeong-Haman Weir | |
---|---|---|---|---|---|

R^{2} | Training | 0.61 | 0.55 | 0.38 | 0.29 |

Testing | 0.47 | 0.44 | 0.41 | 0.36 | |

RMSE | Training | 8.6 | 12.6 | 15.3 | 16.6 |

Testing | 14.5 | 13.5 | 13.1 | 12.4 | |

AIC | Training | 371.2 | 444.6 | 461.3 | 469.0 |

Testing | 452.2 | 455.8 | 436.1 | 421.9 |

ELM 2 Model | Gangjeong-Goryeong Weir | Dalseong Weir | Hapcheon-Changnyeong Weir | Changnyeong-Haman Weir | |
---|---|---|---|---|---|

R^{2} | Training | 0.71 | 0.76 | 0.44 | 0.32 |

Testing | 0.45 | 0.45 | 0.43 | 0.46 | |

RMSE | Training | 6.8 | 8.9 | 14.6 | 16.3 |

Testing | 13.8 | 13.4 | 13.1 | 11.4 | |

AIC | Training | 333.8 | 388.1 | 455.8 | 468.3 |

Testing | 446.2 | 456.9 | 437.5 | 410.5 |

Model | RMSE | Gangjeong-Goryeong Weir | Dalseong Weir | Hapcheon-Changnyeong Weir | Changnyeong-Haman Weir |
---|---|---|---|---|---|

ELM2 | Training | 6.8 | 8.9 | 14.6 | 16.3 |

Testing | 13.8 | 13.4 | 13.1 | 11.4 | |

Multiple LR | Training | 11.3 | 15.3 | 14.7 | 16.9 |

Testing | 17.5 | 20.7 | 13.9 | 14.0 | |

NN with BP | Training | 9.3 | 11.4 | 14.7 | 16.7 |

Testing | 15.7 | 14.1 | 13.4 | 11.4 | |

ANFIS-FCM (r = 2) | Training | 7.8 | 9.3 | 13.3 | 14.2 |

Testing | 16.7 | 13.2 | 15.1 | 13.0 | |

ANFIS-FCM (r = 3) | Training | 6.7 | 8.9 | 12.9 | 12.2 |

Testing | 29.9 | 16.8 | 15.2 | 14.6 |

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## Share and Cite

**MDPI and ACS Style**

Yi, H.-S.; Park, S.; An, K.-G.; Kwak, K.-C. Algal Bloom Prediction Using Extreme Learning Machine Models at Artificial Weirs in the Nakdong River, Korea. *Int. J. Environ. Res. Public Health* **2018**, *15*, 2078.
https://doi.org/10.3390/ijerph15102078

**AMA Style**

Yi H-S, Park S, An K-G, Kwak K-C. Algal Bloom Prediction Using Extreme Learning Machine Models at Artificial Weirs in the Nakdong River, Korea. *International Journal of Environmental Research and Public Health*. 2018; 15(10):2078.
https://doi.org/10.3390/ijerph15102078

**Chicago/Turabian Style**

Yi, Hye-Suk, Sangyoung Park, Kwang-Guk An, and Keun-Chang Kwak. 2018. "Algal Bloom Prediction Using Extreme Learning Machine Models at Artificial Weirs in the Nakdong River, Korea" *International Journal of Environmental Research and Public Health* 15, no. 10: 2078.
https://doi.org/10.3390/ijerph15102078