# A Method for Robust Estimation of Vegetation Seasonality from Landsat and Sentinel-2 Time Series Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Description

#### 2.2. Assumptions and Modelling Principles

#### 2.3. Implementation

#### 2.3.1. Model Function and Shape Priors

#### 2.3.2. Base Level

#### 2.3.3. Determining the Shape Prior

#### 2.3.4. Determining a Model Function That Accounts for Intra-Seasonal Variations

#### 2.3.5. Data Storage and Compression

#### 2.3.6. Evaluating the Robustness of the Method

## 3. Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Study area in Central Sweden. The image to the left is a false color composite from Sentinel-2, acquired on 8 July 2016. The white line marks the area of the MODIS data used, and the blue line marks the area of the Sentinel-2 and Landsat data used.

**Figure 2.**Landsat observations for 2006–2014 extracted for a pine forest pixel (60.0863°N, 17.4795°E) denoted as “Clear” or “Other” (i.e., assigned another QA class than clear-sky in the FMASK algorithm). Note the large proportion of non-clear observations and the weak seasonal dynamics for this pixel.

**Figure 3.**Shape prior for time series data from Landsat NDVI 2000–2005. The base level has, after analyzing the histogram for this pixel, been fixed to NDVI = 0.59. As the shape prior does not describe individual years, its main use is for stabilizing the fitting procedure during data-sparse periods.

**Figure 4.**(

**a**) Double logistic fits with free seasonal parameters. Note the unrealistically short second growing season due to lack of clear observations at the end of the season (arrow); (

**b**) fit where the right inflexion point and the parameter determining the fall time are constrained and taken as the corresponding values of the shape prior.

**Figure 5.**Seven regions in which data points must exist, according to Table 2, to allow free parameters to be used. Circles denote levels 0.01, 0.25, 0.75 and 0.99 of the amplitude to the left and right of the center.

**Figure 6.**Examples of time series over deciduous (

**top**), coniferous (

**middle**), and agricultural (

**bottom**) areas from Landsat (

**left**) and S2 (

**right**).

**Figure 7.**Phenology data from Landsat (

**top row**) and Sentinel 2a (

**bottom row**). Left hand images show estimated start of season (unit: day-of-year, DOY), and the center images show zoom-ins over an agricultural area. The right hand top image shows a false color composite (FCC) from Landsat 8 for comparison, and the bottom right image shows pixels where shape prior was used for estimating parameter ${x}_{1}^{i}$, determining the start of season. Coordinates of the study area are shown in Figure 1.

**Figure 8.**Reduced RMSE and bias when estimating start of season (

**left**) and end of season (

**right**) for 2016 from simulated S2 NDVI data by double logistic function fitting without shape prior (SP; blue dots) as compared to fitting with shape prior (red dots). Parameters from simulated S2 data are plotted against reference data of SOS and EOS from daily MODIS NDVI. Equations and statistics of the linear relationships are printed in the graph in blue (no SP) and red (with SP).

No. | Source | Time Period | No. of Scenes/Tiles |
---|---|---|---|

1 | Landsat 5 and 7 | January 2000–December 2014 | 452 |

2 | Landsat 8 (HLS) | March 2013–April 2017 | 352 |

3 | Sentinel-2 | July 2015–July 2017 | 109 |

4 | MODIS MOD09GA 500 m | January 2011–December 2016 | 2190 |

**Table 2.**Parameters in Equations (1) and (2), and the corresponding regions in Figure 5, in which at least one point is required to allow the parameter to vary freely. If no points are found in a region, the corresponding parameter from the shape prior is used.

Parameter | Seasonal Region (Figure 5) |
---|---|

${\mathit{c}}_{\mathit{i}}$ | 4 OR (2 AND 3 AND 5 AND 6) |

${\mathit{x}}_{\mathbf{1}}^{\mathit{i}}$ | 2 OR (1 AND 3) |

${\mathit{x}}_{\mathbf{2}}^{\mathit{i}}$ | 1 AND 3 |

${\mathit{x}}_{\mathbf{3}}^{\mathit{i}}$ | 6 OR (5 AND 7) |

${\mathit{x}}_{\mathbf{4}}^{\mathit{i}}$ | 5 AND 7 |

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**MDPI and ACS Style**

Jönsson, P.; Cai, Z.; Melaas, E.; Friedl, M.A.; Eklundh, L. A Method for Robust Estimation of Vegetation Seasonality from Landsat and Sentinel-2 Time Series Data. *Remote Sens.* **2018**, *10*, 635.
https://doi.org/10.3390/rs10040635

**AMA Style**

Jönsson P, Cai Z, Melaas E, Friedl MA, Eklundh L. A Method for Robust Estimation of Vegetation Seasonality from Landsat and Sentinel-2 Time Series Data. *Remote Sensing*. 2018; 10(4):635.
https://doi.org/10.3390/rs10040635

**Chicago/Turabian Style**

Jönsson, Per, Zhanzhang Cai, Eli Melaas, Mark A. Friedl, and Lars Eklundh. 2018. "A Method for Robust Estimation of Vegetation Seasonality from Landsat and Sentinel-2 Time Series Data" *Remote Sensing* 10, no. 4: 635.
https://doi.org/10.3390/rs10040635