# Time Series Analysis of Landsat Data for Investigating the Relationship between Land Surface Temperature and Forest Changes in Paphos Forest, Cyprus

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}including two natural areas and it was selected since it represents an ecosystem of great importance. Additionally, according to a recent survey conducted in Cyprus 38.7% of the participants noticed much to very much and 26.92% moderate degradation on coniferous forest in Cyprus, while 44% believed that conifers are the most affected plant species by climate change [37].

## 3. Materials and Methods

#### 3.1. Data

#### 3.2. Methods

_{t}) where (t) is a set of consecutive time points, as expressed by the equation of the additive decomposition model:

_{t}= T

_{t}+ S

_{t}+ R

_{t}

_{t}) is the data, (T

_{t}) is the trend-cycle component, (S

_{t}) is the seasonal component, and (R

_{t}) is the residual component, all at period (t).

## 4. Results and Discussion

#### 4.1. The Effect of Missing Values in the Satellite Time Series

#### 4.2. Annual Density Plots and First Order Statistics

#### 4.3. Remarks on Time Series Trends

#### 4.3.1. Aerial temperature

#### 4.3.2. LST

#### 4.3.3. NDVI

#### 4.4. LST and NDVI Correlations

#### 4.5. Analysis of the Residuals

#### 4.6. Computational Requirements and Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The study area with: (

**a**) Paphos forest boundaries; (

**b**) Paphos forest in RGB with natural colors from Google Earth imagery; (

**c**) Pinus brutia; (

**d**) Pinus brutia foliage; (

**e**) Quercus alnifolia the main substrate in Pathos forest.

**Figure 3.**Diagrams for the LST 1993–2000 time series: (

**a**) Cook’s distance with MA interpolated values; (

**b**) Cook’s distance with the Kalman filter interpolated values; (

**c**) comparative graph where the blue color are the values after MA and where the red color are those after the Kalman filter interpolation. The points that are shown by arrows are the ones with large influence as it was indicated by the Cook’s distance.

**Figure 5.**Density annual plots for: (

**a**) LST time series 2014–2017; (

**b**) aerial temperature time series 2014–2015; (

**c**) NDVI time series 2014–2017; (

**d**) LST time series 1994–1999, (

**e**) aerial temperature time series 1994–1999, and (

**f**) NDVI time series 1994–1999.

**Figure 6.**Diagrams about the aerial temperature 1992–2016 time series: (

**a**) ergodic mean monthly values; (

**b**) boxplot graph showing the mean (red dot) and median (black dash) values volatility, and (

**c**) the monthly values.

**Figure 7.**The LST trend component after decomposition: (

**a**) Trendline (blue line) for the 1993–2000 time series with equation y = 24.818 − 0.0026929x. The arrows point to the areas of trend breakpoints; (

**b**) Trendline (blue line) for the 2013–2018 time series with equation y = 23.17 + 0.046534x.

**Figure 8.**The BFAST algorithm application for the 1993–2000 time series: (

**a**) decomposition with BFAST, one trend breakpoint showed in the blue circle over the trendline (red line); (

**b**) classical decomposition; (

**c**) trend component (black line) with its trendline (red line) and an arrow showing the break; and (

**d**) the trend component (black line) overlying the trendline from the BFAST algorithm (red line) with the blue circle indicating the break.

**Figure 9.**The trend of the updated time series (black) and the trend of the time series with the influential observations (red).

**Figure 10.**The NDVI trend component after decomposition: (

**a**) The trendline (blue line) for the 1993–2000 time series with equation y = 0.44164 + 0.00026747x; (

**b**) The trendline (blue line) for the 2013–2018 time series with equation y = 0.56516 − 0.00033242x. The arrows point to the areas of interesting trend breakpoints.

**Figure 11.**(

**a**) The trend breakpoint for NDVI 1993–2000 time series is shown in the blue circle over the trendline, (

**b**) decomposition of the NDVI 1993–2000 time series. The blue arrow points to the area of the breakpoint, (

**c**) the NDVI 1993–2000 trend component (black line) overlaid over the trendline that was derived from the BFAST algorithm (red line). The blue circle indicates the break, (

**d**) the two trend breakpoints for the NDVI 2013–2018 time series are shown in blue circles, (

**e**) the decomposition of the NDVI 2013–2018 time series. The blue arrows point to the breakpoints, (

**f**) the NDVI 2013–2018 trend component (red line) overlaid over the trendline that was derived from the BFAST algorithm (black line). The blue circle indicates the breaks.

**Figure 12.**(

**a**) Autocorrelation graph for the LST time series 1993–2000; (

**b**) autocorrelation graph for the NDVI time series 1993–2000; (

**c**) autocorrelation graph for the LST time series 2013–2018; (

**d**) autocorrelation graph for the NDVI time series 2013–2018; (

**e**) lag plots (for lag = 1 until lag = 15) for the LST time series 1993–2000 and (

**f**) lag plots for the NDVI time series 1993–2000.

**Figure 13.**(

**a**) Cross-correlation graph for the LST 1993–2000 and the NDVI 1993–2000; (

**b**) cross-correlation graph for the LST 2013–2018 and the NDVI 2013–2018; (

**c**) a grid of scatterplots of the LST versus the NDVI 1993–2000 time series.

**Figure 14.**Cross-variogram for (

**a**) the LST and the NDVI 1993–2000 time series; (

**b**) the LST and the NDVI 2013–2018 time series.

**Figure 15.**(

**a**) The LST 1993–2000 residuals plot with the mean value (green line) and ergodic mean (red line); (

**b**) autocorrelation plot for the LST 1993–2000 residuals; (

**c**) The NDVI 1993–2000 residuals plot with the mean value (green line) and ergodic mean (red line); (

**d**) autocorrelation plot for the NDVI 1993–2000 residuals; (

**e**) LST 2013–2018 residuals plot with the mean value (green line) and ergodic mean (red line); (

**f**) autocorrelation plot for the LST 2013–2018 residuals; (

**g**) The NDVI 2013–2018 residuals plot with the mean value (green line) and ergodic mean (red line); (

**h**) autocorrelation plot for the NDVI 2013–2018 residuals.

**Figure 16.**The time series for: (

**a**) LST 1993–2000; (

**b**) NDVI 1993–2000; (

**c**) LST 2013–2018; (

**d**) NDVI 2013–2018. For each time series plots include: (

**1**) a residuals vs. fitted plot; (

**2**) a normal Q-Q plot; (

**3**) a scale-location plot, and (

**4**) a residuals vs. leverage plot.

**Figure 17.**Cross-correlation coefficients plots between the LST and the NDVI residuals per month: (

**a**) in the 1994–1999 time series; (

**b**) in the 2014–2017 time series. Seasonal plots: (

**c**) for the LST 1994–1999; (

**d**) for the NDVI 1994–1999; (

**e**) for the LST 2014–2017; and (

**f**) for the NDVI 2014–2017. In (

**c**–

**f**) diagrams, there is a black dashed line indicating the month of April, which showed a peculiar behavior in the correlation. In these diagrams, the numbers 1,2,3,4,5,6 indicate the years 1994, 1995, 1996, 1997, 1998, 1999, for the 1994–1999 time series and the years 2014, 2015, 2016, 2017, for the 2014–2017 time series.

Time Series | Min. | 1st Quantile | Median | Mean | 3rd Quantile | Max. | Stdev |
---|---|---|---|---|---|---|---|

LST 1993–2000 | 8.40 | 18.38 | 25.50 | 24.89 | 32.25 | 36.80 | 7.722 |

NDVI 1993–2000 | 0.34 | 0.41 | 0.45 | 0.45 | 0.49 | 0.55 | 0.049 |

aerial 1993–2000 | 5.70 | 10.57 | 18.20 | 18.44 | 25.50 | 31.70 | 7.755 |

LST 2013–2018 | 9.50 | 17.32 | 25.85 | 25.01 | 32.73 | 38.60 | 8.892 |

NDVI 2013–2018 | 0.47 | 0.52 | 0.56 | 0.56 | 0.59 | 0.63 | 0.044 |

aerial 2013–2016 | 7.30 | 13.10 | 19.05 | 19.00 | 24.43 | 30.10 | 7.108 |

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**MDPI and ACS Style**

Andronis, V.; Karathanassi, V.; Tsalapati, V.; Kolokoussis, P.; Miltiadou, M.; Danezis, C.
Time Series Analysis of Landsat Data for Investigating the Relationship between Land Surface Temperature and Forest Changes in Paphos Forest, Cyprus. *Remote Sens.* **2022**, *14*, 1010.
https://doi.org/10.3390/rs14041010

**AMA Style**

Andronis V, Karathanassi V, Tsalapati V, Kolokoussis P, Miltiadou M, Danezis C.
Time Series Analysis of Landsat Data for Investigating the Relationship between Land Surface Temperature and Forest Changes in Paphos Forest, Cyprus. *Remote Sensing*. 2022; 14(4):1010.
https://doi.org/10.3390/rs14041010

**Chicago/Turabian Style**

Andronis, Vassilis, Vassilia Karathanassi, Victoria Tsalapati, Polychronis Kolokoussis, Milto Miltiadou, and Chistos Danezis.
2022. "Time Series Analysis of Landsat Data for Investigating the Relationship between Land Surface Temperature and Forest Changes in Paphos Forest, Cyprus" *Remote Sensing* 14, no. 4: 1010.
https://doi.org/10.3390/rs14041010