# A Machine Learning Approach for Remote Sensing Data Gap-Filling with Open-Source Implementation: An Example Regarding Land Surface Temperature, Surface Albedo and NDVI

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## Abstract

**:**

## 1. Introduction

- Using time series analysis to fill in gaps;
- Using spatial information to fill in gaps;
- Using spatio-temporal analysis.

## 2. Materials and Methods

#### 2.1. Proposed Approach

Algorithm 1: Pseudocode of the algorithm for restoring gaps in time series using iterative approximation by polynomial functions |

Data: array_with_gaps;n = degree of a polynomial function; k = the number of known elements for evaluating the coefficients of the polynomial; Result: array without gapsgaps ← all gap elements in array_with_gaps for gap in gaps doend |

- ${p}_{3}$ from 0.459 to 0.479 $\times {10}^{-6}$ m;
- ${p}_{4}$ from 0.545 to 0.565 $\times {10}^{-6}$ m;
- ${p}_{5}$ from 1.230 to 1.250 $\times {10}^{-6}$ m;
- ${p}_{7}$ from 2.105 to 2.155 $\times {10}^{-6}$ m.

#### 2.2. Experimental Studies

- “Saint Petersburg”: 30–31°E, 58–59°N;
- “Madrid”: 5–4°W, 39–40°N;
- “Vladivostok”: 132–133°E, 44–45°N;

## 3. Results

#### 3.1. Validation of the Algorithm on LST Data

#### 3.2. Validation of the Algorithm on NDVI and Albedo Data

- “Saint Petersburg”: 1 NDVI image and 1 albedo image for 5th of June 2019;
- “Madrid”: 1 NDVI image and 1 albedo image for 3rd of September 2019;
- “Vladivostok”: 1 NDVI image and 1 albedo image for 15th of September 2019.

#### 3.3. Comparison with “CRAN Gapfill” and “Gapfilling Rasters”

#### 3.4. Software Implementation

## 4. Discussion

#### 4.1. Accuracy of Data Recovery

#### 4.2. Applications for Different Remote Sensing Products

#### 4.3. Limitations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LST | Land Surface Temperature |

NDVI | Normalized Difference Vegetation Index |

SLSTR | The Sea and Land Surface Temperature Radiometer |

MODIS | Moderate Resolution Imaging Spectroradiometer |

RMSE | Root Mean Squared Error |

MAE | Mean Absolute Error |

MedAE | Median Absolute Error |

SSGP-toolbox | Simple Spatial Gapfilling Processor toolbox |

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**Figure 1.**Scheme for creating a training sample. To restore the gap in pixel d

_{1}, based on previous images a training sample is generated for the machine learning algorithm. Predictors for the temperature value in the image for 3 September 2019 in pixel d

_{1}are pixels with known values a

_{1}, b

_{1}, c

_{1}.

**Figure 2.**Biomes matrix from Sentinel-3 land surface temperature (LST) scene and temperature distribution in the image by biomes. The image on the left shows a matrix with land types, which was obtained from the archive with additional matrices for LST data (Sentinel-3 SLSTR). The matrix covers an area with a size of 3 degrees latitude per 3 degrees longitude. On the right is a kernel estimation of the density distribution of the LST in different biomes in this matrix.

**Figure 3.**Demonstration of the principle of operation of the local time series approximation algorithm for filling in the gaps. For each gap element, the coefficients of the polynomial function are estimated from the neighborhood of the 5 known values closest to the gap in the time series. The degree of the polynomial is 2.

**Figure 4.**Shaded pixels detection; (

**a**) original cloud configuration, (

**b**) the area selected by the algorithm.

**Figure 5.**Results of applying gapfilling algorithm for Sentinel-3 LST Vladivostok case (Gap size 50%); (

**a**) source matrix, (

**b**) imitation of the gap, (

**c**) output matrix.

**Figure 6.**Vladivostok case. Distribution of temperature in the original image and in the image reconstructed by the model. (

**a**) matrix with gap, (

**b**) reconstructed matrix.

**Figure 7.**Vladivostok case with LST data. Biplots with a comparison of actual and predicted values

**(top row**) and a field of calculated bias (

**bottom row**).

**Figure 8.**Results of model verification on six different-time images of the Sentinel-3 LST product (Saint Petersburg case).

**Figure 9.**The dependence of the mean absolute error (MAE) on the gap size and the amplitude of the temperature in the gap; (

**a**) Saint Petersburg case, (

**b**) Madrid case, (

**c**) Vladivostok case. Indent shows the standard error.

**Figure 10.**Results of model verification on normalized difference vegetation index (NDVI) data for three territories: (

**a**) Saint Petersburg case, (

**b**) Madrid case, (

**c**) Vladivostok case.

**Figure 11.**Comparison of gapfilling algorithms by root mean squared error (RMSE) on LST data for Madrid case.

**Figure 13.**Time complexity for the gap-filling algorithm (the average image size was 8500 pixels and train sample contains 250–350 layers). Indent shows the standard error.

Territory | Sentinel-3 LST | MOD11A1 | MOD11_L2 | ||||||
---|---|---|---|---|---|---|---|---|---|

MAE | RMSE | MedAE | MAE | RMSE | MedAE | MAE | RMSE | MedAE | |

Saint Petersburg | 11% | 16% | 8% | 4% | 5% | 3% | 6% | 9% | 5% |

Madrid | 8% | 10% | 7% | 5% | 6% | 4% | 6% | 8% | 5% |

Vladivostok | 5% | 7% | 4% | 5% | 7% | 4% | 8% | 11% | 6% |

**Table 2.**Accuracy metrics for NDVI and albedo data. Column “Amplitude” NDVI or albedo amplitude in the gap, which can be calculated as “max value in the gap–min value in the gap”.

Case (NDVI) | Gap Area, % | MAE | RMSE | MedAE | Amplitude |
---|---|---|---|---|---|

Saint Petersburg | 52 | 0.053 | 0.085 | 0.030 | 1.212 |

Madrid | 50 | 0.028 | 0.053 | 0.016 | 1.128 |

Vladivostok | 50 | 0.037 | 0.059 | 0.025 | 1.491 |

Case (Albedo) | Gap Area, % | MAE | RMSE | MedAE | Amplitude |

Saint Petersburg | 52 | 0.018 | 0.032 | 0.011 | 0.328 |

Madrid | 50 | 0.013 | 0.025 | 0.009 | 0.536 |

Vladivostok | 50 | 0.011 | 0.017 | 0.007 | 0.228 |

Algorithm | Gap Size (Saint Petersburg Case) | ||||||||
---|---|---|---|---|---|---|---|---|---|

4% | 6% | 15% | 28% | 40% | 52% | 70% | 96% | Mean | |

SSGP-toolbox | 0.42 | 0.42 | 0.35 | 0.39 | 0.43 | 0.48 | 0.47 | 0.87 | 0.48 |

CRAN gapfill | 0.8 | 1.28 | 0.94 | 0.99 | 1.31 | 0.98 | 1.08 | 1.07 | 1.06 |

gapfilling rasters | 0.61 | 0.73 | 0.96 | 0.88 | 0.86 | 0.54 | 0.82 | 0.80 | 0.78 |

Nearest neighbour interpolation | 0.59 | 0.68 | 0.55 | 1.10 | 1.12 | 1.02 | 1.00 | 1.22 | 0.91 |

Algorithm | Gap Size (Madrid Case) | ||||||||

5% | 8% | 17% | 29% | 39% | 50% | 78% | 94% | Mean | |

SSGP-toolbox | 0.53 | 0.89 | 0.76 | 0.79 | 0.69 | 0.84 | 1.04 | 0.97 | 0.81 |

CRAN gapfill | 1.03 | 1.19 | 1.39 | 1.17 | 1.11 | 1.19 | 1.32 | 1.42 | 1.23 |

gapfilling rasters | 1.37 | 1.70 | 1.56 | 1.57 | 1.76 | 2.15 | 2.66 | 2.94 | 1.96 |

Nearest neighbour interpolation | 1.26 | 1.74 | 1.41 | 1.91 | 1.75 | 2.20 | 2.90 | 2.77 | 1.99 |

Algorithm | Gap Size (Vladivostok Case) | ||||||||

5% | 10% | 15% | 28% | 44% | 50% | 74% | 93% | Mean | |

SSGP-toolbox | 0.30 | 0.31 | 0.36 | 0.32 | 0.47 | 0.36 | 0.50 | 0.68 | 0.41 |

CRAN gapfill | 0.47 | 0.36 | 0.58 | 0.43 | 0.59 | 0.55 | 0.84 | 0.73 | 0.57 |

gapfilling rasters | 0.67 | 0.63 | 0.66 | 0.72 | 0.77 | 0.81 | 0.85 | 1.24 | 0.79 |

Nearest neighbour interpolation | 0.40 | 0.43 | 0.44 | 0.47 | 0.53 | 0.56 | 0.90 | 1.01 | 0.59 |

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## Share and Cite

**MDPI and ACS Style**

Sarafanov, M.; Kazakov, E.; Nikitin, N.O.; Kalyuzhnaya, A.V. A Machine Learning Approach for Remote Sensing Data Gap-Filling with Open-Source Implementation: An Example Regarding Land Surface Temperature, Surface Albedo and NDVI. *Remote Sens.* **2020**, *12*, 3865.
https://doi.org/10.3390/rs12233865

**AMA Style**

Sarafanov M, Kazakov E, Nikitin NO, Kalyuzhnaya AV. A Machine Learning Approach for Remote Sensing Data Gap-Filling with Open-Source Implementation: An Example Regarding Land Surface Temperature, Surface Albedo and NDVI. *Remote Sensing*. 2020; 12(23):3865.
https://doi.org/10.3390/rs12233865

**Chicago/Turabian Style**

Sarafanov, Mikhail, Eduard Kazakov, Nikolay O. Nikitin, and Anna V. Kalyuzhnaya. 2020. "A Machine Learning Approach for Remote Sensing Data Gap-Filling with Open-Source Implementation: An Example Regarding Land Surface Temperature, Surface Albedo and NDVI" *Remote Sensing* 12, no. 23: 3865.
https://doi.org/10.3390/rs12233865