# Prediction of Flow Based on a CNN-LSTM Combined Deep Learning Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Acquisition

#### 2.2. Convolutional Neural Network (CNN)

#### 2.3. Long Short-Term Memory (LSTM)

#### 2.4. River Flow Simulation

#### 2.5. Performance Evaluation

## 3. Results

#### 3.1. Flow Time Series

^{3}/s and 2870 m

^{3}/s, respectively. After that, the flows through Schoena and Torgau in January 2011 reached 2040 m

^{3}/s and 2260 m

^{3}/s, respectively. In addition, the maximum recorded flows at Schoena and Torgau in June 2013 reached 3710 m

^{3}/s and 4040 m

^{3}/s, respectively, as the largest flows recorded in recent years. According to research based on statistical data from 1951 to 2006 [59], the high-water recurrence periods in 2006, 2011, and 2013 were ~25, ~8, and ~200 years, respectively. Similarly, the Elbe River experienced two periods of low flows in 2015 and 2018. In July, August, and September 2015, Schoena and Torgau recorded minimum flows of 75.8 m

^{3}/s and 89 m

^{3}/s, respectively. Moreover, in August and September 2018, Schoena and Torgau recorded minimum water flows of 70.6 m

^{3}/s and 90.1 m

^{3}/s, respectively.

#### 3.2. Input Selection

^{3}/s. Therefore, the following training situation was divided into high-water period prediction and low-water prediction based on the flow of Schoena (209 m

^{3}/s).

#### 3.3. Flow Simulation

^{2}of the whole testing phase (K6) to 0.79. While k2 attained an R

^{2}of 0.56, the other phases attained an R

^{2 }of more than 0.95.

## 4. Discussion

^{3}/s. However, three of them (including two maximum cases) were included in the k2 validation set. Therefore, the training data of k2 were not assigned to most of the extreme values, resulting in poor learning during the training process and a lack of training for high-water value output. In summary, a lack of full scope coverage in the training data could result in low prediction values for some high-water periods during the validation phase, leading to poor prediction results. Therefore, the CNN-LSTM model is particularly important for the selection of input data scope coverage.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area and precipitation radar map. (

**A**) The Elbe River flows into Sachsen, Germany, from Schoena, and flows out of Sachsen from Torgau. (

**B**) An example of the precipitation radar map in this study.

**Figure 2.**The Pearson correlation between downstream (Torgau) flow data and one-day or two-days-ahead upstream (Schoena) flow data.

**Figure 3.**Comparison of the predicted values and the measured values in the high-water period.

**a**(

**1**),

**b**(

**1**),

**c**(

**1**),

**d**(

**1**) and

**e**(

**1**) are the predicted and measured values for k1 to k5 folds, respectively, and

**f(1**

**)**is the predicted and measured values for all validation sets.

**a**(

**2**),

**b**(

**2**),

**c**(

**2**),

**d**(

**2**) and

**e**(

**2**) are the scatter plots of the predicted and measured values for k1 to k5 folds, respectively, and

**f**(

**2**) is the scatter plot for all validation sets from k1 to k5.

**Figure 4.**Comparison of the predicted values and the measured values in the low-water period.

**a**(

**1**),

**b**(

**1**),

**c**(

**1**),

**d**(

**1**) and

**e**(

**1**) are the predicted and measured values for k1 to k5 folds, respectively, and

**f(1**

**)**is the predicted and measured values for all validation sets.

**a**(

**2**),

**b**(

**2**),

**c**(

**2**),

**d**(

**2**) and

**e**(

**2**) are the scatter plots of the predicted and measured values for k1 to k5 folds, respectively, and

**f**(

**2**) is the scatter plot for all validation sets from k1 to k5.

R^{2} | NSE | KGE | r | $\mathit{\alpha}$ | $\mathit{\beta}$ | |
---|---|---|---|---|---|---|

k1 | 0.96 | 0.96 | 0.87 | 0.99 | 0.87 | 1.01 |

k2 | 0.46 | 0.46 | 0.47 | 0.75 | 0.58 | 0.80 |

k3 | 0.92 | 0.92 | 0.92 | 0.97 | 0.95 | 1.05 |

k4 | 0.97 | 0.97 | 0.92 | 0.99 | 0.96 | 1.06 |

k5 | 0.90 | 0.90 | 0.75 | 0.97 | 0.76 | 1.05 |

k6 | 0.78 | 0.78 | 0.75 | 0.89 | 0.78 | 0.98 |

R^{2} | NSE | KGE | r | $\mathit{\alpha}$ | $\mathit{\beta}$ | |
---|---|---|---|---|---|---|

k1 | 0.63 | 0.63 | 0.82 | 0.82 | 1.03 | 1.00 |

k2 | 0.76 | 0.76 | 0.86 | 0.89 | 0.93 | 1.02 |

k3 | 0.86 | 0.86 | 0.93 | 0.95 | 0.96 | 0.98 |

k4 | 0.81 | 0.81 | 0.73 | 0.92 | 0.74 | 0.99 |

k5 | 0.82 | 0.82 | 0.68 | 0.95 | 0.69 | 0.97 |

k6 | 0.81 | 0.81 | 0.76 | 0.91 | 0.77 | 0.99 |

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Li, P.; Zhang, J.; Krebs, P.
Prediction of Flow Based on a CNN-LSTM Combined Deep Learning Approach. *Water* **2022**, *14*, 993.
https://doi.org/10.3390/w14060993

**AMA Style**

Li P, Zhang J, Krebs P.
Prediction of Flow Based on a CNN-LSTM Combined Deep Learning Approach. *Water*. 2022; 14(6):993.
https://doi.org/10.3390/w14060993

**Chicago/Turabian Style**

Li, Peifeng, Jin Zhang, and Peter Krebs.
2022. "Prediction of Flow Based on a CNN-LSTM Combined Deep Learning Approach" *Water* 14, no. 6: 993.
https://doi.org/10.3390/w14060993