# Neural Network Approach to Forecast Hourly Intense Rainfall Using GNSS Precipitable Water Vapor and Meteorological Sensors

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Data Description

#### 2.1. Neural Network Approach

#### 2.2. Study Region

#### 2.3. SEVIRI Data

#### 2.4. GNSS Data Processing

#### 2.5. Data Handling and Integration

## 3. Results and Discussion

#### 3.1. Neural Network Configuration

#### 3.2. Network Sensitivity to Parameters

#### 3.3. Network Sensitivity to Input Variables

#### 3.4. Network Sensitivity to Data Division

#### 3.5. Best Case with Optimized Parameters

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the data used for this work within the Lisbon city area, Portugal, superimposed over a Sentinel-2 true color composition image.

**Figure 2.**Cloud top temperature, pressure and height products representing the region of interest of the spaceborne Spinning Enhanced Visible and Infrared Imager (SEVIRI) images used for this study. The Lisbon area is marked with a red circle and the data corresponds to a heavy rain event that occurred on 26 October 2015 at 01:00 with a precipitation rate of 20 mm/h.

**Figure 3.**Structure of the nonlinear autoregressive exogenous neural network model (NARX) neural network model used in this work, where y(t+1) is the predicted variable, y(t) the input variable, x(t) the exogenous input variables, n the input delays, m the feedback delays, N and M the number of layer’s neurons and w and b the respective weights and biases.

**Figure 4.**Linear fitting between the predicted rain values from the neural network and the observed rain values, in units of mm/h, for the year 2015 (

**a**). The same comparison is illustrated for all values of the year 2015 organized by time (

**b**). Results correspond to the best score for 100 runs with the initial network parameters set in Table 2.

**Figure 5.**Confusion matrix relating the precipitation forecast provided by the neural network output and the observed or measured rainfall input (ground truth), classified after the neural network result using Table 3. Results correspond to the best score for 100 runs with the optimized network parameters (2 neurons, 1 hidden layer, 8 feedback and input delays and Bayesian training), Global Navigation Satellite System (GNSS) precipitable water vapor (PWV) one input variable configuration and test dataset 2015.

Variable Name | Source | Acronym | Units | Function |
---|---|---|---|---|

Hourly precipitation | Meteorological station | Rain | mm/h | Input/Output |

Precipitable water vapor | GNSS station | PWV | mm | Input |

Pressure | Meteorological station | P | hPa | Input |

Temperature | Meteorological station | T | °C | Input |

Relative Humidity | Meteorological station | RH | % | Input |

Cloud Top Temperature | Remote sensing | CTT | K | Input |

Cloud Top Pressure | Remote sensing | CTP | hPa | Input |

Cloud Top Height | Remote sensing | CTH | m | Input |

Variable Name | Values |
---|---|

# Hidden layers | 1 |

# Neurons | 10 |

# Delays | 6 |

Training function | Levenberg-Marquardt |

Data weighting | Random |

Performance evaluation | Mean square error |

Data division | Step 1: (66%/10%/24%)—4 years |

(training/validation/testing) | Step 2: (0%/0%/100%)—1 year |

# Total input variables | 8 |

# Output variables | 1 |

# Number of samples | 41427 |

**Table 3.**Details of the classification of precipitation data and the corresponding number of observations concerning the neural network data division.

Precipitation Class | Rain Classification (mm/h) | Number of Samples (hour) | ||
---|---|---|---|---|

4 Years | 1 Year | Total | ||

No rain | 0 | 31284 | 7527 | 38811 |

Moderated rain | > 0 < 5 | 2184 | 252 | 2436 |

Intense rain | >= 5 | 159 | 22 | 181 |

**Table 4.**Statistical assessment of the neural network experiments, comparing the initial and optimized network parameters. Results correspond to the mean value score for 100 runs. Good classification and false positives are presented in % of intense rain class, and network RMS is in mm/h.

Neural Network with 7 Variables (GNSS+Meteo+Sat.) | Intense Rain Class | Test Dataset | ||
---|---|---|---|---|

Good Classification | False Positives | Net.RMS | Correlation Coefficient | |

10 N, 6 ID 6 FD, Levenberg-Marquardt | 59.1% | 29.6% | 0.467 | 0.824 |

10 N, 8 ID 8 FD, Levenberg-Marquardt | 59.1% | 28.7% | 0.470 | 0.821 |

2 N, 6 ID 6 FD, Levenberg-Marquardt | 59.1% | 26.4% | 0.472 | 0.818 |

10 N, 6 ID 6 FD, Bayesian regularization | 59.1% | 26.0% | 0.489 | 0.803 |

**Table 5.**Statistical assessment of the neural network input experiments with 4 different input configurations, using optimized parameters. Results correspond to the mean value score for 100 runs. Good classification and false positives are presented in % of intense rain class and Network RMS is in mm/h.

Neural Network with 7 Variables (GNSS+Meteo+Satellite) | # var. | Intense Rain Class | Test Dataset | ||
---|---|---|---|---|---|

Good Classification | False Positives | Net.RMS | Correlation Coefficient | ||

GNSS + Meteo. + Satellite (PWV,P,T,RH,CTT,CTP,CTH) | 7 | 59.1% | 26.5% | 0.475 | 0.819 |

GNSS + Meteo. (PWV,P,T,RH) | 4 | 58.9% | 27.1% | 0.471 | 0.821 |

GNSS (PWV) | 1 | 59.3% | 22.6% | 0.471 | 0.817 |

Precipitation (NAR model) | 1 | 58.2% | 22.7% | 0.474 | 0.815 |

**Table 6.**Statistical assessment of the neural network experiment with variations in the data division. Optimized parameters and PWV exogenous input variable configuration is considered. Results correspond to the maximum value score for 100 runs. Good classification and false positives are presented in % of intense rain class, and Network RMS is in mm/h.

Neural Network with 7 Variables (GNSS+Meteo+Satellite) | #Intense Rain | Intense Rain Class | Test Dataset | ||
---|---|---|---|---|---|

Good Classification | False Positives | Net.RMS | Correlation Coefficient | ||

2015 test dataset | 22 | 63.6% | 22.2% | 0.464 | 0.826 |

2011 test dataset | 57 | 63.3% | 35.6% | 0.875 | 0.828 |

2012 test dataset | 32 | 71.9% | 23.3% | 0.589 | 0.875 |

2013 test dataset | 37 | 66.0% | 20.5% | 0.807 | 0.820 |

2014 test dataset | 41 | 64.3% | 30.8% | 0.726 | 0.831 |

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## Share and Cite

**MDPI and ACS Style**

Benevides, P.; Catalao, J.; Nico, G.
Neural Network Approach to Forecast Hourly Intense Rainfall Using GNSS Precipitable Water Vapor and Meteorological Sensors. *Remote Sens.* **2019**, *11*, 966.
https://doi.org/10.3390/rs11080966

**AMA Style**

Benevides P, Catalao J, Nico G.
Neural Network Approach to Forecast Hourly Intense Rainfall Using GNSS Precipitable Water Vapor and Meteorological Sensors. *Remote Sensing*. 2019; 11(8):966.
https://doi.org/10.3390/rs11080966

**Chicago/Turabian Style**

Benevides, Pedro, Joao Catalao, and Giovanni Nico.
2019. "Neural Network Approach to Forecast Hourly Intense Rainfall Using GNSS Precipitable Water Vapor and Meteorological Sensors" *Remote Sensing* 11, no. 8: 966.
https://doi.org/10.3390/rs11080966