# A Deep Learning Multimodal Method for Precipitation Estimation

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## Abstract

**:**

## 1. Introduction

- An extension of our previous work [20] by adding radar data to the list of modalities used by our model.
- An improved spatial resolution, reduced from 3 km down to 2 km.
- A couple of architecture updates allowing for optimization of the computational cost of our model and removal off some artifacts present in its output.
- A method to eliminate the bias between different rain gauge networks.
- A method to correct daily total precipitation accumulation bias.
- A direct comparison of our results, a radar method (the OPERA product) and a gauge-adjusted radar method (the quasi-gauge-adjusted five-minute precipitation rate RADOLAN YW product [27]).

## 2. Methodology

#### 2.1. Data

#### 2.2. Model Architecture

#### 2.3. Training Method

#### 2.4. Bias Reduction between Rain Gauge Networks

#### Bias Correction through the Satellite Modality

## 3. Results

#### 3.1. Evaluation Method

#### 3.2. Ablation Study

#### 3.3. Comparison with OPERA

#### 3.4. Comparison with RADOLAN

#### 3.5. Spatial Variability of the Results

#### 3.6. Visual Evaluation for Instantaneous Precipitation Estimation

#### 3.7. Daily Precipitation Accumulation Estimation Performance

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

General abbreviations | |

LEO | Low Earth Orbit |

GEO | Geostationnary Earth Orbiting |

SEVIRI | Spinning Enhanced Visible and Infrared Imager |

DL | Deep Learning |

CNN | Convolutional Neural Network |

RMIB | Royal Meteorological Institute of Belgium |

KNMI | Koninklijk Nederlands Meteorologisch Instituut |

DWD | Deutscher Wetterdienst |

EUMETNET | the European Meteorological Network |

DL-S | model using the satellite modality as input |

DL-G | model using the rain gauge modality as input |

DL-R | model using the radar modality as input |

DL-SG | model using the satellite and rain gauge modalities as input |

DL-SR | model using the satellite and radar modalities as input |

DL-GR | model using the rain gauge and radar modalities as input |

DL-SGR | model using the satellite, rain gauge and radar modalities as input |

Scores abbreviations | |

POD | Probability Of Detection |

FAR | False Alarm Ratio |

POFD | Probability Of False Detection |

ACC | Accuracy |

CSI | Critical Success Index |

F1 | F1 score |

ME | Mean Error |

MAE | Mean Absolute Error |

RMSE | Root Mean Squared Error |

RV | Reduction of Variance |

PCORR | Pearson Correlation |

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**Figure 1.**Visualization of the three modalities of data source used as input, and also target for the rain gauges (

**a**). The OPERA rain rate composite (

**b**) and the SEVIRI 24-h cloud microphysics RGB (

**c**) images are from 29 September 2019 12:55:00.

**Figure 2.**The architecture of our multiscale convolutional model. Each block defines the type of layer and number of filters.

**Figure 3.**Map of the average ME (

**a**), and the standard deviation of the ME (

**b**), for the estimation of the satellite model trained on the DWD network. The map is interpolated from the ME mean and standard deviation values of every rain gauge used in our study.

**Figure 4.**Map of the average ME for the satellite model trained on the DWD network, using our bias correction method.

**Figure 5.**Map of the average ME, for the model using the three modalities of data (satellite, radar and rain gauges), using our bias correction method.

**Figure 6.**The estimation map made by our model with each different combinations of the three modalities, and the rain rate map of OPERA with a minimum rain rate value thresholding, and the RADOLAN YW product, for 31 May 2016 17:40.

**Figure 7.**The estimation map made by our model with each different combinations of the three modalities, and the rain rate map of OPERA with a minimum rain rate value thresholding, and the RADOLAN YW product, for 27 October 2019 17:25.

**Table 1.**The test ME (in mm/h) for each network of rain gauges for the rain estimates produced by the model when using the three modalities of data (satellite, radar and rain gauges) using the non-null rain rate values. As a reference, the mean rain rate of the test rain gauges for the non-null measurements is 0.988 mm/h.

RMIB | SPW | VMM | KNMI (Land) | KNMI (Sea) | DWD | |
---|---|---|---|---|---|---|

ME mean | −0.191 | −0.442 | −0.154 | 0.177 | 0.203 | −0.074 |

**Table 2.**The test ME (in mm/h) for each network of rain gauges for the rain estimates produced by the model when using only the satellite modality and trained only on the DWD network of rain gauges.

RMIB | SPW | VMM | KNMI (Land) | KNMI (Sea) | DWD | |
---|---|---|---|---|---|---|

ME mean | −0.330 | −0.581 | −0.121 | 0.307 | 0.378 | −0.089 |

**Table 3.**The values of the rain gauge measurements rescaling factors ${\alpha}_{n}$ for each network.

RMIB | SPW | VMM | KNMI (Land) | KNMI (Sea) | DWD | |
---|---|---|---|---|---|---|

$\alpha $ | 0.809 | 0.641 | 0.861 | 1.372 | 1.819 | 0.941 |

**Table 4.**The test ME (in mm/h) of each network of rain gauges, for the model using the three modalities of data (satellite, radar and rain gauges), using our bias correction method.

RMIB | SPW | VMM | KNMI (Land) | KNMI (Sea) | DWD | |
---|---|---|---|---|---|---|

ME mean | −0.154 | −0.069 | −0.001 | 0.218 | 0.077 | −0.017 |

**Table 5.**The classification scores equation, value range and optimum value. The F1 score is calculated from the precision P and the recall R.

Equation | Range | Optimum | |
---|---|---|---|

POD | $\frac{tp}{tp+fn}$ | [0, 1] | 1 |

FAR | $\frac{fp}{fp+tp}$ | [0, 1] | 0 |

POFD | $\frac{fp}{fp+tn}$ | [0, 1] | 0 |

ACC | $\frac{tp+tn}{tp+fp+tn+fn}$ | [0, 1] | 1 |

CSI | $\frac{tp}{tp+fp+fn}$ | [0, 1] | 1 |

F1 | $2\xb7\frac{P\xb7R}{P+R}$ with $P=\frac{tp}{tp+tn}$, $R=\frac{tp}{tp+fn}$ | [0, 1] | 1 |

**Table 6.**Contingency table between the observations and the estimations, recording the number of true negatives $tn$, the number of false negatives $fn$, the number of false positives $fp$ and the number of true positives $tp$.

Observations | |||
---|---|---|---|

r = 0 | r > 0 | ||

Estimations | r = 0 | $tn$ | $fn$ |

r > 0 | $fp$ | $tp$ |

**Table 7.**The regression scores equation, value range and optimum value. ${y}_{i}$ is an observation and ${\widehat{y}}_{i}$ is its estimation.

Equation | Range | Optimum | |
---|---|---|---|

ME | $\frac{1}{N}{\sum}_{i=1}^{N}({\widehat{y}}_{i}-{y}_{i})$ | [$-\infty ,\infty $] | 0 |

MAE | $\frac{1}{N}{\sum}_{i=1}^{N}|{\widehat{y}}_{i}-{y}_{i}|$ | [$0,\infty $] | 0 |

RMSE | $\frac{1}{N}{\sum}_{i=1}^{N}\sqrt{{({\widehat{y}}_{i}-{y}_{i})}^{2}}$ | [$0,\infty $] | 0 |

RV | $1-\frac{\frac{1}{N}{\sum}_{i=1}^{N}{({\widehat{y}}_{i}-{y}_{i})}^{2}}{{s}_{y}^{2}}$ with ${s}_{y}^{2}=\frac{1}{N}{\sum}_{i=1}^{N}{({y}_{i}-\overline{y})}^{2}$ | [$-\infty $, 1] | 1 |

PCORR | $\frac{\frac{1}{N}{\sum}_{i=1}^{N}({\widehat{y}}_{i}-\overline{\widehat{y}})({y}_{i}-\overline{y})}{{s}_{\widehat{y}}\xb7{s}_{y}}$ | [−1, 1] | 1 |

DL-S | DL-G | DL-R | DL-SG | DL-SR | DL-GR | DL-SGR | |
---|---|---|---|---|---|---|---|

POD | 0.578 | 0.674 | 0.700 | 0.693 | 0.724 | 0.776 | 0.788 |

FAR | 0.532 | 0.244 | 0.286 | 0.233 | 0.287 | 0.235 | 0.243 |

POFD | 0.058 | 0.019 | 0.025 | 0.018 | 0.025 | 0.021 | 0.022 |

ACC | 0.914 | 0.957 | 0.954 | 0.959 | 0.956 | 0.964 | 0.964 |

CSI | 0.347 | 0.554 | 0.541 | 0.572 | 0.559 | 0.627 | 0.629 |

F1 | 0.513 | 0.711 | 0.701 | 0.726 | 0.716 | 0.769 | 0.771 |

**Table 9.**Regression scores averaged on the automatic test stations. The ME, the MAE and the RMSE are expressed in mm/h.

DL-S | DL-G | DL-R | DL-SG | DL-SR | DL-GR | DL-SGR | |
---|---|---|---|---|---|---|---|

ME | −0.170 | −0.095 | 0.109 | −0.065 | 0.059 | 0.034 | −0.082 |

MAE | 0.776 | 0.659 | 0.688 | 0.653 | 0.663 | 0.590 | 0.557 |

RMSE | 1.846 | 1.759 | 1.611 | 1.704 | 1.589 | 1.516 | 1.488 |

RV | 0.141 | 0.244 | 0.340 | 0.271 | 0.359 | 0.418 | 0.445 |

PCORR | 0.433 | 0.504 | 0.637 | 0.554 | 0.634 | 0.683 | 0.688 |

OPERA | DL-R | DL-SGR | |
---|---|---|---|

POD | 0.604 | 0.700 | 0.788 |

FAR | 0.407 | 0.286 | 0.243 |

POFD | 0.037 | 0.025 | 0.022 |

ACC | 0.934 | 0.954 | 0.964 |

CSI | 0.422 | 0.541 | 0.629 |

F1 | 0.590 | 0.701 | 0.771 |

**Table 11.**Regression scores comparison between OPERA and our DL-R and DL-SGR models. The ME, the MAE and the RMSE are expressed in mm/h.

OPERA | DL-R | DL-SGR | |
---|---|---|---|

ME | −0.428 | 0.109 | −0.082 |

MAE | 0.721 | 0.688 | 0.557 |

RMSE | 1.872 | 1.611 | 1.488 |

RV | 0.055 | 0.340 | 0.445 |

PCORR | 0.505 | 0.637 | 0.688 |

**Table 12.**Classification scores comparison between RADOLAN YW and our DL-SGR model on the automatic test stations from the DWD network.

DL-SGR | RADOLAN YW | |
---|---|---|

POD | 0.905 | 0.545 |

FAR | 0.109 | 0.319 |

POFD | 0.011 | 0.022 |

ACC | 0.983 | 0.942 |

CSI | 0.818 | 0.432 |

F1 | 0.897 | 0.598 |

**Table 13.**Regression scores comparison between RADOLAN YW and our DL-SGR model on the automatic test stations from the DWD network. The ME, the MAE and the RMSE are expressed in mm/h.

DL-SGR | RADOLAN YW | |
---|---|---|

ME | 0.140 | −0.207 |

MAE | 0.395 | 0.722 |

RMSE | 1.140 | 1.788 |

RV | 0.639 | 0.012 |

PCORR | 0.885 | 0.566 |

**Table 14.**RMSE statistics (the standard deviation, the mean and the standard deviation normalized by the mean) across all test stations.

DL-S | DL-G | DL-R | DL-SG | DL-SR | DL-GR | DL-SGR | |
---|---|---|---|---|---|---|---|

std | 0.104 | 0.110 | 0.093 | 0.103 | 0.089 | 0.088 | 0.084 |

mean | 0.834 | 0.679 | 0.715 | 0.679 | 0.684 | 0.604 | 0.576 |

std/mean | 0.125 | 0.162 | 0.130 | 0.152 | 0.130 | 0.145 | 0.146 |

**Table 15.**Classification and regression scores comparison between the different networks of rain gauges for the DL-S model. The ME, the MAE and the RMSE are expressed in mm/h.

KNMI (Sea) | KNMI (Land) | RMIB | SPW | VMM | DWD | |
---|---|---|---|---|---|---|

POD | 0.575 | 0.549 | 0.501 | 0.515 | 0.495 | 0.597 |

FAR | 0.454 | 0.423 | 0.520 | 0.620 | 0.527 | 0.526 |

POFD | 0.077 | 0.055 | 0.056 | 0.053 | 0.043 | 0.057 |

ACC | 0.872 | 0.898 | 0.904 | 0.922 | 0.925 | 0.917 |

CSI | 0.387 | 0.389 | 0.324 | 0.280 | 0.315 | 0.359 |

F1 | 0.557 | 0.560 | 0.489 | 0.436 | 0.478 | 0.526 |

ME | −0.337 | −0.062 | −0.309 | −0.205 | −0.149 | −0.198 |

MAE | 1.173 | 0.844 | 0.705 | 0.715 | 0.829 | 0.774 |

RMSE | 3.639 | 1.705 | 2.127 | 1.713 | 1.852 | 1.859 |

RV | 0.111 | 0.189 | 0.200 | −0.021 | 0.200 | 0.136 |

PCORR | 0.352 | 0.454 | 0.478 | 0.375 | 0.479 | 0.438 |

**Table 16.**Performance results for the daily precipitation accumulation estimation, measured on the climatological rain gauges measurements at the test dates. The ME, the MAE and the RMSE are expressed in mm.

OPERA | DL-S | DL-G | DL-R | DL-SG | DL-SR | DL-GR | DL-SGR | |
---|---|---|---|---|---|---|---|---|

ME | −0.614 | −0.111 | −0.589 | −0.411 | −0.519 | −0.182 | −0.452 | −0.536 |

MAE | 1.351 | 1.314 | 0.905 | 0.984 | 0.868 | 0.915 | 0.817 | 0.829 |

RMSE | 2.893 | 2.720 | 2.292 | 2.232 | 2.041 | 2.067 | 1.910 | 1.944 |

RV | 0.386 | 0.488 | 0.450 | 0.665 | 0.710 | 0.708 | 0.747 | 0.739 |

PCORR | 0.743 | 0.735 | 0.868 | 0.840 | 0.878 | 0.856 | 0.899 | 0.901 |

**Table 17.**Performance results for the daily precipitation accumulation estimation with bias correction, measured on the climatological rain gauges measurements at the test dates. The ME, the MAE and the RMSE are expressed in mm.

OPERA | DL-S | DL-G | DL-R | DL-SG | DL-SR | DL-GR | DL-SGR | |
---|---|---|---|---|---|---|---|---|

ME | −0.012 | −0.104 | −0.044 | −0.154 | −0.031 | −0.139 | −0.066 | −0.067 |

MAE | 1.376 | 1.316 | 0.893 | 0.996 | 0.857 | 0.918 | 0.789 | 0.788 |

RMSE | 2.872 | 2.723 | 2.270 | 2.211 | 2.045 | 2.066 | 1.830 | 1.826 |

RV | 0.287 | 0.487 | 0.251 | 0.667 | 0.699 | 0.707 | 0.757 | 0.762 |

PCORR | 0.743 | 0.735 | 0.868 | 0.840 | 0.878 | 0.856 | 0.899 | 0.901 |

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## Share and Cite

**MDPI and ACS Style**

Moraux, A.; Dewitte, S.; Cornelis, B.; Munteanu, A.
A Deep Learning Multimodal Method for Precipitation Estimation. *Remote Sens.* **2021**, *13*, 3278.
https://doi.org/10.3390/rs13163278

**AMA Style**

Moraux A, Dewitte S, Cornelis B, Munteanu A.
A Deep Learning Multimodal Method for Precipitation Estimation. *Remote Sensing*. 2021; 13(16):3278.
https://doi.org/10.3390/rs13163278

**Chicago/Turabian Style**

Moraux, Arthur, Steven Dewitte, Bruno Cornelis, and Adrian Munteanu.
2021. "A Deep Learning Multimodal Method for Precipitation Estimation" *Remote Sensing* 13, no. 16: 3278.
https://doi.org/10.3390/rs13163278