# Prediction of Water Level in Lakes by RNN-Based Deep Learning Algorithms to Preserve Sustainability in Changing Climate and Relationship to Microcystin

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study Area

^{2}and a reasonable depth of 30 m. It has a volume of about 1.3 billion m

^{3}. The greatest depth of the lake basin is 54 m, and its catchment area is 250 km

^{2}[36]. The Lake is surrounded by southern mountains and northern hills.

#### 2.2. Dataset Description

#### 2.3. Data Preprocessing

#### 2.4. Model Descriptions

_{t}is the forgotten variable, i

_{t}the input variable, and o

_{t}the output variable. X

_{t}indicates the values that the feature receives at t time, and h

_{t}

_{−1}is the output cell of the previous cell. Inside the LSTM cell, memory is indicated by c

_{t}

_{−1}. W is the weight matrix, and B is the term bias. The sigmoid function (σ), the hyperbolic tangent function (tanh), processes the X

_{t}variable and the h variable from the previous learning.

_{r}, U

_{r}, W

_{z}, U

_{z}, W

_{c}, U

_{c}represent the weight matrix.

_{n}= new state, in = input, h

_{n}

_{−1}= output of past state, h

_{n}

_{+1}= output of future state, and the ⊗ symbol represents the concatenation operation.

#### 2.5. Hyperparameters

#### 2.6. Evaluation Metrics

^{2}, or R as evaluation metrics to compare their algorithms with the base model or with other algorithms [20]. These metrics account for more than 50% of the evaluation metrics in the literature. On the other hand, there are less favorable evaluation metrics used by some researchers, including Nash–Sutcliffe Efficiency [42], accuracy [50], Mean Relative Error [20], and Percent Bias [51].

_{i}is the expected value for the dataset’s i

^{th}observation, Q

_{i}is the actual value for that observation, and “n” denotes sample size.

_{i}is the expected value for the dataset’s ith observation, Y

_{i}is the actual value for that observation, and “m” denotes sample size.

_{t}is the forecast value at time t and Y

_{t−n}is the value at the previous nth day

#### 2.7. Water Quality Indicator

## 3. Results

## 4. Discussion

## 5. Conclusions

- The results of the algorithms can be compared, and although there could be different but similar results, the algorithms can be used interchangeably.
- Overall, the GRU algorithm performs better than other gated RNN algorithms because it has a lower RMSE. However, it does not perform better in all time periods, so the algorithm needs to be replaced by another one to achieve better results for LWL prediction cases further in the future.
- Gated RNN-based algorithms appear to have higher RMSE results as the prediction horizon increases, indicating poorer performance in lower prediction time periods. A more accurate comparison is possible using the Naïve Method, and the percentage increase could provide a healthier result for comparing algorithm results with different prediction time periods. Although the prediction may differ from the actual values as the time period increases, the performance increase is much higher compared to the Naïve Benchmark, making it more attractive for use in LWL prediction cases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**One day (

**left side**) and 5 days (

**right side**) ahead prediction results. The vertical dashed lines indicate the train set-validation set-test set, respectively.

**Figure A2.**Ten days (

**left side**) and 20 days (

**right side**) ahead prediction results. The vertical dashed lines indicate the train set-validation set-test set, respectively.

**Figure A3.**Thirty days (

**left side**) and 45 days (

**right side**) ahead prediction results. The vertical dashed lines indicate the train set-validation set-test set, respectively.

**Figure A4.**Sixty days (

**left side**) and 120 days (

**right side**) ahead prediction results. The vertical dashed lines indicate the train set-validation set-test set, respectively.

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**Figure 2.**Time series plots of daily meteorological data, water withdrawals, and lake water level for Lake Sapanca from 11 October 2012 through 4 August 2023. (x-axis: data rows in sequence.)

**Figure 6.**Linear trend of microcystin concentration in the water column at different depths from surface to 20 m from 21 March 2019 to 12 April 2023. (x-axis: data rows in sequence, y-axis: microcystin concentration).

**Figure 7.**Spearman rank correlation between microcystin and meteorological parameters (** p < 0.01, * p < 0.05).

Inputs: | Output: |
---|---|

Maximum Temperature | LWL |

Minimum Temperature | |

Average Temperature | |

Precipitation | |

Withdrawal |

ANN | LSTM | GRU | Stacked LSTM | Bidirectional LSTM | |
---|---|---|---|---|---|

Neuron number | 128 | 128 | 64 | 128 | 32 |

Epoch | 250 | 100 | 100 | 100 | 50 |

Batch size | 64 | 128 | 128 | 128 | 128 |

Number of layers | 1 | 2 | 2 | 2 | 2 |

Prediction period | 45 | 60 | 60 | 60 | 60 |

**Table 3.**The performance of ANN and RNN-based algorithms for predicting lake water level with increasing time intervals, RMSE results. (Metric is based on m.)

Algorithm/Prediction Period | Naïve Method | ANN | LSTM | GRU | Stacked LSTM | Bidirectional LSTM |
---|---|---|---|---|---|---|

1 day | 0.0134 | 0.0131 | 0.0162 | 0.0134 | 0.0171 | 0.0156 |

5 days | 0.0484 | 0.0445 | 0.0514 | 0.0429 | 0.0494 | 0.0563 |

10 days | 0.0875 | 0.0815 | 0.0799 | 0.0732 | 0.0890 | 0.0875 |

20 days | 0.1551 | 0.1271 | 0.1227 | 0.1070 | 0.1289 | 0.1257 |

30 days | 0.2168 | 0.1540 | 0.1356 | 0.1316 | 0.1221 | 0.1226 |

45 days | 0.3139 | 0.1918 | 0.1775 | 0.1728 | 0.1769 | 0.1947 |

60 days | 0.4041 | 0.2627 | 0.1762 | 0.2203 | 0.1976 | 0.1985 |

120 days | 0.6973 | 0.4810 | 0.4586 | 0.3838 | 0.4275 | 0.3873 |

**Table 4.**Benchmark performance comparison of algorithms; figures indicate improvement in RMSE values over Naïve Method.

Algorithm/Prediction Period | ANN | LSTM | GRU | Stacked LSTM | Bidirectional LSTM |
---|---|---|---|---|---|

1 day | 2.26% | −18.92% | 0.00% | −24.26% | −15.17% |

5 days | 8.40% | −6.01% | 12.05% | −2.04% | −15.09% |

10 days | 7.10% | 9.08% | 17.80% | −1.70% | 0.00% |

20 days | 19.84% | 23.33% | 36.70% | 18.45% | 20.94% |

30 days | 33.87% | 46.08% | 48.91% | 55.89% | 55.51% |

45 days | 48.29% | 55.51% | 57.98% | 55.83% | 46.87% |

60 days | 42.41% | 78.55% | 58.87% | 68.64% | 68.24% |

120 days | 36.71% | 41.30% | 58.00% | 47.97% | 57.16% |

**Table 5.**The performance of ANN and RNN-based algorithms for predicting lake water level with increasing time intervals, MAPE results. (%).

Algorithm/Prediction Period | Naïve Method | ANN | LSTM | GRU | Stacked LSTM | Bidirectional LSTM |
---|---|---|---|---|---|---|

1 day | 0.03% | 0.09% | 0.17% | 0.37% | 0.12% | 0.13% |

5 days | 0.13% | 0.27% | 0.23% | 0.30% | 0.24% | 0.34% |

10 days | 0.24% | 0.22% | 0.46% | 0.58% | 0.54% | 0.44% |

20 days | 0.42% | 0.94% | 0.47% | 0.68% | 0.47% | 0.38% |

30 days | 0.60% | 0.43% | 0.76% | 0.88% | 0.53% | 0.46% |

45 days | 0.90% | 0.91% | 0.59% | 0.84% | 0.85% | 0.78% |

60 days | 1.20% | 0.75% | 1.09% | 0.90% | 0.85% | 0.91% |

120 days | 2.09% | 2.19% | 1.50% | 1.24% | 1.55% | 1.40% |

**Table 6.**Benchmark performance comparison of algorithms; figures indicate difference of MAPE values compared with Naïve Method.

Algorithm/Prediction Period | ANN | LSTM | GRU | Stacked LSTM | Bidirectional LSTM |
---|---|---|---|---|---|

1 day | −0.06 | −0.14 | −0.34 | −0.09 | −0.10 |

5 days | −0.14 | −0.10 | −0.17 | −0.11 | −0.21 |

10 days | 0.02 | −0.22 | −0.34 | −0.30 | −0.20 |

20 days | −0.52 | −0.05 | −0.26 | −0.05 | 0.04 |

30 days | 0.17 | −0.16 | −0.28 | 0.07 | 0.14 |

45 days | −0.01 | 0.31 | 0.06 | 0.05 | 0.12 |

60 days | 0.45 | 0.11 | 0.30 | 0.35 | 0.29 |

120 days | −0.10 | 0.59 | 0.85 | 0.54 | 0.69 |

**Table 7.**Forecast difference results of Naïve Method, ANN, and RNN algorithms based on Diebold–Mariano (DM) test for increasing day intervals from day 1 to day 120 (p-value ≤ 0.05 indicates the significance of the DM test results, Green boxes indicate significantly different prediction results with distinct tones, red boxes indicate insignificant results).

Day-1 | Day-5 | Day-10 | Day-20 | Day-30 | Day-45 | Day-60 | Day-120 | |
---|---|---|---|---|---|---|---|---|

Naïve Method-ANN | 0.578 | 0.094 | 0.984 | 0.055 | 0.055 | 0.815 | 0 | 0.222 |

Naïve Method-LSTM | 0.122 | 0.31 | 0.007 | 0.612 | 0.009 | 0.014 | 0.003 | 0 |

Naïve Method-GRU | 0.005 | 0.031 | 0 | 0 | 0 | 0.006 | 0.012 | 0 |

Naïve Method-Stacked LSTM | 0.485 | 0.181 | 0 | 0.506 | 0.009 | 0.253 | 0.009 | 0 |

Naïve Method-Bidirectional LSTM | 0.261 | 0.007 | 0.011 | 0.686 | 0.161 | 0.923 | 0.187 | 0 |

ANN-LSTM | 0.264 | 0.474 | 0.008 | 0 | 0 | 0.025 | 0 | 0 |

ANN-GRU | 0.011 | 0.581 | 0 | 0 | 0 | 0.443 | 0.046 | 0 |

ANN-Stacked LSTM | 0.878 | 0.71 | 0 | 0.072 | 0.072 | 0.169 | 0.058 | 0 |

ANN-Bidirectional LSTM | 0.523 | 0.233 | 0.012 | 0.593 | 0.593 | 0.741 | 0.002 | 0 |

LSTM-GRU | 0.099 | 0.21 | 0.032 | 0 | 0.004 | 0.003 | 0 | 0.015 |

LSTM-Stacked LSTM | 0.326 | 0.728 | 0.244 | 0.874 | 0.006 | 0 | 0 | 0.995 |

LSTM-Bidirectional LSTM | 0.608 | 0.062 | 0.878 | 0.364 | 0 | 0.011 | 0.017 | 0.752 |

GRU-Stacked LSTM | 0.014 | 0.358 | 0.319 | 0.001 | 0 | 0.541 | 0.917 | 0.014 |

GRU-Bidirectional LSTM | 0.037 | 0.516 | 0.022 | 0 | 0 | 0.662 | 0.229 | 0.033 |

Stacked LSTM-Bidirectional LSTM | 0.623 | 0.122 | 0.188 | 0.287 | 0.202 | 0.295 | 0.192 | 0.747 |

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**MDPI and ACS Style**

Ozdemir, S.; Ozkan Yildirim, S.
Prediction of Water Level in Lakes by RNN-Based Deep Learning Algorithms to Preserve Sustainability in Changing Climate and Relationship to Microcystin. *Sustainability* **2023**, *15*, 16008.
https://doi.org/10.3390/su152216008

**AMA Style**

Ozdemir S, Ozkan Yildirim S.
Prediction of Water Level in Lakes by RNN-Based Deep Learning Algorithms to Preserve Sustainability in Changing Climate and Relationship to Microcystin. *Sustainability*. 2023; 15(22):16008.
https://doi.org/10.3390/su152216008

**Chicago/Turabian Style**

Ozdemir, Serkan, and Sevgi Ozkan Yildirim.
2023. "Prediction of Water Level in Lakes by RNN-Based Deep Learning Algorithms to Preserve Sustainability in Changing Climate and Relationship to Microcystin" *Sustainability* 15, no. 22: 16008.
https://doi.org/10.3390/su152216008