# Improving the Quality of Satellite Imagery Based on Ground-Truth Data from Rain Gauge Stations

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## Abstract

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## 1. Introduction

## 2. Data

## 3. Methods

#### 3.1. The Thin-Plate Spline Model with Covariates

#### 3.2. The State-Space Model with Covariates

**G**. The initial state vector ${\mathbf{v}}_{0}$ is assumed to be normally distributed with mean ${\mathbf{\mu}}_{0}$ and covariance ${\mathbf{\Sigma}}_{0}$.

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

EM | Expectation-maximization |

${H}_{mean}$ | Mean humidity |

LST | Land surface temperature |

MVC | Maximum value compositing |

NDVI | Normalized difference vegetation index |

${T}_{max}$ | Maximum mean temperature |

Tps | Thin-plate splines |

TpsWc | Thin-plate splines with covariates |

TpsWoc | Thin-plate splines without covariates |

SSMWc | State-space model |

SSMWc | State-space model with covariates |

SSMWoc | State-space model without covariates |

UTM | Universal Transverse Mercator |

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**Figure 1.**Flowchart of the process for evaluating the performance of the smoothing methods: state-space model with covariates (SSMWc), Tps with covariates (TpsWc), state-space model without covariates (SSMWoc) and Tps without covariates (TpsWoc).

**Figure 2.**Map of Navarre region, located in the north of Spain and with a common border to the south of France. Black dots correspond to the rain gauge stations used in this study.

**Figure 3.**From the top to bottom, boxplots of day LST (in Celsius), night LST (in Celsius), ${T}_{max}$ (in Celsius) and ${H}_{mean}$ (in percentages) for the 46 time periods of 2011.

**Figure 5.**Images of Navarre for the third week of February 2014. At the top, day LST and ${T}_{max}$ images (in Celsius) are presented, and at the bottom, night LST (in Celsius) and ${H}_{mean}$ (in percentages) are shown. These images show similar patterns. Black dots represent rain gauge stations.

**Figure 6.**On the left is the altitude map, and on the right is the NDVI image of Navarre on the second fortnight of February 2014. Both figures show similar patterns because they are highly correlated.

**Figure 7.**Root mean square prediction error versus outlier outbreak percentage obtained for day (on the top) and night (at the bottom). Land surface temperature (LST) by climatological seasons with the four models: space-state model (SSM) with and without covariates (SSWc in red and SSMWoc in green) and Tps with and without covariates (TpsWc in blue and TpsWoc in purple).

**Figure 8.**Root mean square error versus outlier outbreak percentage obtained for the normalized difference vegetation index (NDVI) by climatological season.

**Figure 9.**LST Navarra image in the fourth week of November 2011. In the upper row and from left to right, the 5% distorted image, the thin-plate spline (TpsWc) and the state-space (SSMWc) smoothed images with covariates. In the lower row and from left to right, the 20% distorted image and their respective TpsWc and SSMWc smoothed images with covariates.

**Figure 10.**At the top, boxplots of the 15% distorted images of day LST in the 46 time periods of 2011 are shown, and the bottom presents the boxplots of the smoothed day LST images by TpsWc in the same time periods.

**Table 1.**Reduction percentage of the RMSE in SSM and Tps smoothing procedures with and without covariates for day LST, night LST and NDVI for different sizes of outlier outbreaks.

SSM | Tps | ||||||
---|---|---|---|---|---|---|---|

Outlier | RMSE | RMSE | |||||

Derived Variable | Out. % | Without Covariates | With Covariates | Reduction % | Without Covariates | With Covariates | Reduction % |

Day | 5 | 1.80 | 1.63 | 10.19 | 0.54 | 0.51 | 7.75 |

LST | 10 | 2.33 | 2.20 | 6.21 | 0.76 | 0.68 | 12.09 |

15 | 2.86 | 2.74 | 4.47 | 1.00 | 0.89 | 12.56 | |

20 | 3.54 | 3.44 | 2.89 | 1.37 | 1.21 | 13.31 | |

Night | 5 | 1.34 | 1.29 | 3.90 | 0.41 | 0.37 | 11.89 |

LST | 10 | 1.91 | 1.85 | 2.83 | 0.57 | 0.48 | 19.70 |

15 | 2.52 | 2.47 | 1.73 | 0.78 | 0.65 | 19.94 | |

20 | 3.12 | 3.08 | 1.28 | 1.13 | 0.94 | 20.36 | |

NDVI | 5 | 0.11 | 0.09 | 19.59 | 0.04 | 0.04 | 1.68 |

10 | 0.11 | 0.10 | 15.11 | 0.05 | 0.05 | 1.61 | |

15 | 0.12 | 0.11 | 12.43 | 0.05 | 0.05 | 1.31 | |

20 | 0.12 | 0.11 | 10.08 | 0.05 | 0.05 | 1.56 |

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**MDPI and ACS Style**

Militino, A.F.; Ugarte, M.D.; Pérez-Goya, U.
Improving the Quality of Satellite Imagery Based on Ground-Truth Data from Rain Gauge Stations. *Remote Sens.* **2018**, *10*, 398.
https://doi.org/10.3390/rs10030398

**AMA Style**

Militino AF, Ugarte MD, Pérez-Goya U.
Improving the Quality of Satellite Imagery Based on Ground-Truth Data from Rain Gauge Stations. *Remote Sensing*. 2018; 10(3):398.
https://doi.org/10.3390/rs10030398

**Chicago/Turabian Style**

Militino, Ana F., M. Dolores Ugarte, and Unai Pérez-Goya.
2018. "Improving the Quality of Satellite Imagery Based on Ground-Truth Data from Rain Gauge Stations" *Remote Sensing* 10, no. 3: 398.
https://doi.org/10.3390/rs10030398