# Estimating Spatial and Temporal Trends in Environmental Indices Based on Satellite Data: A Two-Step Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Description

#### 2.1. Case Study

#### 2.2. Fractional Cover Data

#### 2.3. Data Pre-Processing

#### 2.4. Data Exploration

## 3. Methods

#### 3.1. Linear Model

#### 3.1.1. Extraction of Slope Coefficients

#### 3.2. Boosted Regression Tree

#### Hyperparameter Tuning and Goodness of Fit Evaluation

## 4. Results

#### 4.1. BRT Predictions

#### 4.1.1. Overall Results of the Entire Data Set

#### 4.1.2. Decadal Analyses

#### 4.1.3. Segmented Areas

#### 4.2. Relative Influence

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Fractional Cover (FCover) data are overlaid with an evenly spaced grid where each grid cell contains 100 × 100 pixels and covers an area of 3000 × 3000 m. Each of the total 5530 grid cells will be used to delineate the slope coefficients showing green vegetation trend on unique locations of the spatial grid. The FCover scene shows the relationship of the three ground cover classes of green vegetation (green), non-photosynthetic vegetation (blue) and bare soil (red) referenced on the Worldwide Reference System-2 [12].

**Figure 2.**Development of green vegetation fractions and their trends over time shown as boxplots in Figure 2a or as the three most distinctive trends in Figure 2b. (

**a**) boxplots showing a strong variation of green vegetation for each year over the 30 year timeframe, 1987–2016. For consistency over time, and because the FCover in the study area is dominated by wet and dry seasons, only December scenes have been used for this case study; (

**b**) trend of green vegetation in a 30 years time frame overlaid with a blue linear regression line showing the direction of trends. (top) most neutral, (middle) maximum positive slope and (bottom) minimum negative slope. Only sites with at least 15 observations over the time period were considered for this plot.

**Figure 3.**Two-step modelling approach to predict extracted slope coefficients (as spatial trends) using a BRT model.

**Figure 6.**Combination of two algorithms, namely Boosting and linear regression tree within a BRT. (

**a**) Regression Trees: hierarchical regression and the binary splitting process showing observations in the nodes, predicted values in the terminal nodes and splitting criteria along the tree branches [12]; (

**b**) boosting: BRT as an ensemble approach combines several binary splits to create complex prediction rules that offer more flexibility in dividing the feature space than a single regression tree. Boosting additively fits binary trees and gradually prioritise poorly modelled data to produce a set of binary splits that maximally reduce the BRT loss function, adapted from [12,28].

**Figure 7.**Data set showing 30 years in (

**a**) marginal effects; (

**b**) histogram of observed values and (

**c**) of predicted values. (

**a**) the BRT performance on predicting the slope coefficients strongly relate with the observed values; (

**b**) histogram showing distribution of observed values; and (

**c**) histogram showing distribution of predicted values.

**Figure 8.**Plots of the decades showing (

**a**) marginal effects; (

**b**) histogram of observed values and (

**c**) of predicted values. The top panel shows the decade starting at 1987, the middle panel starting at 1997, and the last panel starts with 2007.

**Figure 9.**Partial dependency plots (PDP) of all eight scenarios in the order from top to bottom. All 30 years, first 10 years, middle 10 years, last 10 years, segment 1 (

**upper left**), segment 2 (

**upper right**), segment 3 (

**lower left**), and segment 4 (

**lower right**). On the left, there is the PDP of the latitude (North–South gradient) and the right shows the longitude (East–West gradient).

**Table 1.**Descriptive statistics of the green vegetation fractions for the whole data set covering 30 years.

Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. |
---|---|---|---|---|---|

0.00 | 11.64 | 17.03 | 18.37 | 23.16 | 73.92 |

**Table 2.**Six categories of slope coefficients with corresponding numbers of observations in the data set, and their overall representation/contribution as percentages in the case study.

Slope Coefficient Categories | Observations | Percentages % |
---|---|---|

slope coefficient > 1 | 14 | 0.02% |

slope coefficient >= 0.5 and slope coefficient < 1 | 5088 | 5.44% |

slope coefficient >= 0 and slope coefficient < 0.5 | 79032 | 84.48% |

slope coefficient >= −0.5 and slope coefficient < 0 | 9364 | 10.01% |

slope coefficient >= −0.5 and slope coefficient < −1 | 30 | 0.03% |

slope coefficient < −1 | 19 | 0.02% |

**Table 3.**Root Mean Square Error (RMSE) on the test data using all 30 years, first 10 years, middle 10 years and last 10 years and in four segmented areas comprising a 30-year time frame.

Scenario | RMSE |
---|---|

All 30 years | 0.1150 |

First 10 years | 0.1112 |

Middle 10 years | 0.1214 |

Last 10 years | 0.1063 |

Four segments | |

1—Upper left | 0.1076% |

2—Upper right | 0.0915% |

3—Lower left | 0.1112% |

4—Lower right | 0.1265% |

**Table 4.**Relative influence of the longitude in explaining the response using all 30 years, first 10 years, middle 10 years, last 10 years, and in all four segments of the FCover scene.

Scenario | North–South Gradient |
---|---|

All 30 years | 56.77% |

First 10 years | 57.04% |

Middle 10 years | 55.68% |

Last 10 years | 57.67% |

Four segments | |

1—Upper left | 34.63% |

2—Upper right | 47.71% |

3—Lower left | 40.79% |

4—Lower right | 43.24% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Colin, B.; Mengersen, K.
Estimating Spatial and Temporal Trends in Environmental Indices Based on Satellite Data: A Two-Step Approach. *Sensors* **2019**, *19*, 361.
https://doi.org/10.3390/s19020361

**AMA Style**

Colin B, Mengersen K.
Estimating Spatial and Temporal Trends in Environmental Indices Based on Satellite Data: A Two-Step Approach. *Sensors*. 2019; 19(2):361.
https://doi.org/10.3390/s19020361

**Chicago/Turabian Style**

Colin, Brigitte, and Kerrie Mengersen.
2019. "Estimating Spatial and Temporal Trends in Environmental Indices Based on Satellite Data: A Two-Step Approach" *Sensors* 19, no. 2: 361.
https://doi.org/10.3390/s19020361