# Deep Learning-Based Univariate Prediction of Daily Rainfall: Application to a Flood-Prone, Data-Deficient Country

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## Abstract

**:**

## 1. Introduction

## 2. Discrete Wavelet Transform

## 3. Long Short-Term Memory Network

_{t}), which allows the network to either keep or forget the memory in transit. Next is the new memory control, which allows new memories to pass through and later on merge with the memories that passed through the forget control. The merging of these memories will happen with the help of the merged control. On the other hand, a set of new memories is being processed by another neural network. Eventually, these new memories will join the first two memories through the merged control. The last control is the output control, which checks how much memory should be produced as an output to the next LSTM unit (Figure 2).

_{t}is the input. Rectified linear activation function (ReLU), σ, which allows the LSTM network to approximate not just a linear function (if it exists), but also accounts for the nonlinearity of the time series, is represented by the formula:

## 4. Model Performance Indicators

_{KGE}(see Equation (22)), of the simulated and observed variables together with the two aforementioned biases, were the input values in the KGE, as shown in Equation (23):

## 5. Study Area

Subcatchment Name | Station Number | From | To |
---|---|---|---|

S-7 (Oras) | 1155 | 6 November 2013 | 22 December 2018 |

S-8 (Dolores) | 1767 | 22 March 2016 | 31 December 2018 |

S-9 (Can-avid) | 93 | 2 January 2013 | 31 December 2018 |

S-10 (Catubig) | 547 | 9 July 2013 | 2 May 2018 |

## 6. Data Collection and Characteristics

## 7. Overview of the Process

## 8. Noise Analysis Using DWT and LSTM

## 9. Rainfall Noise Modeling Using LSTM

## 10. Discussion

## 11. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**LSTM Diagram [4].

Authors | Subject Area | Technique | Variable | Performance Indicator Used |
---|---|---|---|---|

[18] | Global | ANN | Mean rainfall | Relative percentage error |

[19] | Global | ANN | Rainfall | MSE |

[20] | Global | Regression | Rainfall, humidity, wind direction, minmax temp | MSE |

[21] | Local | ARIMA, ARNN | Rainfall | IA |

[22] | Local | Decision Tree, K-mean, Regression tree | Temperature, pressure, wind speed, rainfall | MSE |

[23] | Local | DWT, ANN | Rainfall | RMSE, R, COE |

[24] | Local | Clustering, Bayesian regularization | Relative humidity, pressure, temperature, precipitable water, wind speed | Accuracy, precision, recall |

[25] | Local | Bayesian | Temperature, station level pressure, mean sea level pressure, relative humidity, vapour pressure, wind speed, rainfall | Accuracy |

[26] | Local | SLIQ decision tree | Humidity, pressure, temperature, wind speed, dew point | Accuracy |

[27] | Global | Regression | Rainfall | RMSE |

[28] | Local | Regression tree algorithm, naive Bayes approach, k-nearest neighbour, 5-10-1 pattern recognition neural network | Mean temperature, dew point temperature, humidity, pressure of sea and wind speed | MSE |

[29] | Local | Neural network, support vector machine | Rainfall | NSE, std. deviation ratio, CC, IA, RMSE |

[30] | Local | SARIMA, FFNN, Bayesian, time-warping | Rainfall | Similarity, NMAE, RMSE |

[31] | Local | SD, ANN, DWT | Rainfall | R, RMSE, MAE |

[32] | Local | Decision tree, random forest, SVM, DNN, linear regression, PCA | Heavy rain damage, rainfall | RMSE, MAPE, CC |

[33] | Local | ARIMA, DWT, LSTM | Rainfall | RMSE, MAE, R-squared |

[34] | Local | CNN, LSTM, DWT, DCCNN | Rainfall | RMSE, MAE, NSE |

[35] | Local | HK-SARIMA, NSTF, YJNSTF, naive | Rainfall | RMSE, MAE, NSE |

S-7 | S-8 | S-9 | S-10 | |
---|---|---|---|---|

count | 1873 | 1015 | 2190 | 1759 |

mean | 0.37 | 3.18 | 1.44 | 0.58 |

std | 0.75 | 8.84 | 5.18 | 1.01 |

min | 0.00 | 0.00 | 0.00 | 0.00 |

25% | 0.00 | 0.00 | 0.00 | 0.00 |

50% | 0.20 | 0.00 | 0.20 | 0.20 |

75% | 0.55 | 1.00 | 0.95 | 0.80 |

max | 22.40 | 91.00 | 71.50 | 14.00 |

Subcatchment | RMSE | CC | NSE | KGE | IA | LMI | MAPE | PBIAS | RSR |
---|---|---|---|---|---|---|---|---|---|

S-7 | 0.20 | 0.96 | 0.93 | 0.92 | 0.98 | 0.92 | 0.00 | −0.88 | 0.01 |

S-8 | 2.70 | 0.94 | 0.91 | 0.82 | 0.97 | 0.82 | 0.01 | 10.84 | 0.01 |

S-9 | 1.28 | 0.98 | 0.94 | 0.87 | 0.98 | 0.87 | 0.00 | 0.22 | 0.01 |

S-10 | 0.33 | 0.95 | 0.89 | 0.84 | 0.97 | 0.89 | 0.00 | −1.67 | 0.01 |

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**MDPI and ACS Style**

Necesito, I.V.; Kim, D.; Bae, Y.H.; Kim, K.; Kim, S.; Kim, H.S. Deep Learning-Based Univariate Prediction of Daily Rainfall: Application to a Flood-Prone, Data-Deficient Country. *Atmosphere* **2023**, *14*, 632.
https://doi.org/10.3390/atmos14040632

**AMA Style**

Necesito IV, Kim D, Bae YH, Kim K, Kim S, Kim HS. Deep Learning-Based Univariate Prediction of Daily Rainfall: Application to a Flood-Prone, Data-Deficient Country. *Atmosphere*. 2023; 14(4):632.
https://doi.org/10.3390/atmos14040632

**Chicago/Turabian Style**

Necesito, Imee V., Donghyun Kim, Young Hye Bae, Kyunghun Kim, Soojun Kim, and Hung Soo Kim. 2023. "Deep Learning-Based Univariate Prediction of Daily Rainfall: Application to a Flood-Prone, Data-Deficient Country" *Atmosphere* 14, no. 4: 632.
https://doi.org/10.3390/atmos14040632