# Assessing the Effects of Time Interpolation of NDVI Composites on Phenology Trend Estimation

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Study Area and Sites

#### 2.2. Data and Pre-Processing

- (1)
- Calculating daily NDVI during 2001–2019

_{NIR}is the mean of 3 × 3 pixels of near-infrared band surface reflectance; and R

_{Red}is the mean of 3 × 3 pixels of red band surface reflectance.

- (2)
- Constructing single-year daily NDVI data

- (3)
- Denoising single-year daily NDVI data

- (4)
- Constructing single-year composite NDVI data

#### 2.3. Methods

#### 2.3.1. Time Interpolation

#### 2.3.2. Phenology Extraction

#### 2.3.3. Phenology Trend Estimation

_{ij}| ≥ 30:

_{ij}is the NDVI data of year i on site j; m is a general mean (usually set to zero for finding a well-defined solution); a

_{i}is the effect of year i (2001–2019); and b

_{j}is the effect of site j (j = 1, …, 120).

#### 2.3.4. Statistical Analysis

## 3. Results

#### 3.1. Comparisons between Trends from Daily NDVI Data and NDVI Composites Based on Different Time Interpolation Methods

#### 3.2. Comparisons between Trends from Daily NDVI Data and NDVI Composites among Different Vegetation Types

#### 3.3. Comparisons between Trends from Daily NDVI Data and NDVI Composites Based on Different Combinations of Time Interpolation Methods and Phenology Extraction Methods

#### 3.4. Comparisons between Trends from the 8-Day and the 16-Day NDVI Composite Data

## 4. Discussion

#### 4.1. Effects of Time Interpolation on Trend Estimation among Different Interpolation Methods

#### 4.2. Effects of Time Interpolation on Trend Estimation among Different Vegetation Types

#### 4.3. Effects of Time Interpolation on Trend Estimation among Different Combinations of Time Interpolation Methods and Phenology Extraction Methods

#### 4.4. Effects of Time Interpolation on Trend Estimation among Data with Different Temporal Resolutions

#### 4.5. Limitations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sites and the distribution of vegetation types. DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively.

**Figure 2.**Typical NDVI curves of four vegetation types in the study area. DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively; data of (

**a**–

**d**) are from Fluxnet sites CA-TP3, CZ-BK1, US-Wkg, and US-IB2, respectively; all curves are denoised by the Savitzky–Golay filtering method.

**Figure 3.**Comparisons between phenology trends from daily NDVI data and NDVI composites based on different time interpolation methods over all sites. (

**a**) SOS trends comparisons, and (

**b**) EOS trends comparisons. Phenology trends of daily NDVI data are unfilled, and phenology trends of NDVI composites are filled in colors; the bottom and top areas of boxes are the 25th and 75th percentiles; the lines through the boxes are the medians; the boxes designate the mean value; the diamonds beyond the ends of the whiskers are outliers; SOS and EOS are the start of growing season and the end of growing season; DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively; PL, AG, PCF, Linear, and Spline are piecewise logistic function fitting, asymmetric Gaussian function fitting, polynomial curve fitting, linear interpolation, and cubic spline interpolation, respectively.

**Figure 4.**Comparisons between phenology trends from daily NDVI data and NDVI composites based on different time interpolation methods among different vegetation types. (

**a**) SOS trends comparisons in DBF, (

**b**) SOS trends comparisons in ENF, (

**c**) SOS trends comparisons in GRA, (

**d**) SOS trends comparisons in OSH, (

**e**) EOS trends comparisons in DBF, (

**f**) EOS trends comparisons in ENF, (

**g**) EOS trends comparisons in GRA, and (

**h**) EOS trends comparisons in OSH. Phenology trends of daily NDVI data are unfilled, and phenology trends of NDVI composites are filled in colors; the bottom and top areas of boxes are the 25th and 75th percentiles; the lines through the boxes are the medians; the boxes designate the mean value; the diamonds beyond the ends of the whiskers are outliers; SOS and EOS are the start of growing season and the end of growing season; DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively; PL, AG, PCF, Linear, and Spline are piecewise logistic function fitting, asymmetric Gaussian function fitting, polynomial curve fitting, linear interpolation, and cubic spline interpolation, respectively; * below the box indicates that there is significant difference (p < 0.05) between the phenology trend of the daily NDVI data and the trend estimated based on this time interpolation method.

**Figure 5.**Comparisons between phenology trends from daily NDVI data and NDVI composites based on combinations of different time interpolation methods and extraction methods. (

**a**) SOS trends comparisons in DBF, (

**b**) SOS trends comparisons in ENF, (

**c**) SOS trends comparisons in GRA, (

**d**) SOS trends comparisons in OSH, (

**e**) EOS trends comparisons in DBF, (

**f**) EOS trends comparisons in ENF, (

**g**) EOS trends comparisons in GRA, and (

**h**) EOS trends comparisons in OSH. SOS and EOS are the start of growing season and the end of growing season; DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively; PL, AG, PCF, Linear, and Spline are piecewise logistic function fitting, asymmetric Gaussian function fitting, polynomial curve fitting, linear interpolation, and cubic spline interpolation, respectively; DT, MRC, and RCC are dynamic threshold, maximum rate of change, and change rate of curvature, respectively; grey boxes indicate that there are no significant differences (p > 0.05) between phenology trends from NDVI composites and daily NDVI data; green boxes indicate there are significant differences (p < 0.05) between phenology trends from NDVI composites and daily NDVI data.

**Figure 6.**Comparisons between mean phenology trends from the 8-day and 16-day NDVI composite data among different interpolation methods. (

**a**) SOS trends comparisons in DBF, (

**b**) SOS trends comparisons in ENF, (

**c**) SOS trends comparisons in GRA, (

**d**) SOS trends comparisons in OSH, (

**e**) EOS trends comparisons in DBF, (

**f**) EOS trends comparisons in ENF, (

**g**) EOS trends comparisons in GRA, and (

**h**) EOS trends comparisons in OSH. SOS and EOS are the start of growing season and the end of growing season; DBF, ENF, GRA, and OSH are deciduous broadleaf forest, evergreen needleleaf forest, grassland, and open shrubland, respectively; PL, AG, PCF, Linear, and Spline are piecewise logistic function fitting, asymmetric Gaussian function fitting, polynomial curve fitting, linear interpolation, and cubic spline interpolation, respectively; * below the 16-day NDVI composite data indicates there is significant difference (p < 0.05) between the mean phenology trends from the 8-day and from the 16-day NDVI composite data.

**Figure 7.**Extraction results and trends of the start of growing season (SOS) from the daily and the 8-day NDVI composite data in deciduous broadleaf forest (DBF) and evergreen needleleaf forest (ENF). (

**a**) SOS trends of DBF from 2001 to 2019, (

**b**) SOS trends of DBF in 2004, (

**c**) SOS estimation results of DBF in 2004, (

**d**) SOS trends of ENF from 2001 to 2019, (

**e**) SOS trends of ENF in 2008, and (

**f**) SOS estimation results of ENF in 2008. Piecewise logistic function fitting and linear interpolation are chosen as interpolation method examples; the dynamic threshold 30% is chosen as the extraction method.

**Figure 8.**Extraction results and trends of the end of growing season (EOS) from the daily and 8-day NDVI composite data in deciduous broadleaf forest (DBF) and evergreen needleleaf forest (ENF). (

**a**) EOS trends of DBF from 2001 to 2019, (

**b**) EOS trends of DBF in 2005, (

**c**) EOS estimation results of DBF in 2005, (

**d**) EOS trends of ENF from 2001 to 2019, (

**e**) EOS trends of ENF in 2016, and (

**f**) EOS estimation results of ENF in 2016. Piecewise logistic function fitting and linear interpolation are chosen as interpolation method examples; a dynamic threshold of 30% is chosen as the extraction method.

Method | Equation | Parameter |
---|---|---|

Savitzky-Golay filter | ${Y}_{j}^{*}={\displaystyle \sum}_{i=-m}^{i=m}{C}_{i}{Y}_{j+i}/N$ | Y^{*} is the resultant NDVI value; Y is the original NDVI value; j is the running index of the original ordinate data; m is the half-width of the smoothing window (filter); C_{i} is the coefficient for the ith NDVI value of the filter; N is the amount of convoluting integers; the half-width of the smoothing window is set to 1/4 of the year length (90 days); the smoothing polynomial degree is set to 4 [58]. |

Maximum value composite | ${y}_{new}=MAX\left({y}_{1}+{y}_{2}+\dots +{y}_{n}\right)$ | y_{new} is the resultant NDVI value; y_{n} is the original NDVI value; n is the days for compositing. |

Method | Equation | Parameter |
---|---|---|

Piecewise logistic function fitting (PL) | $y\left(t\right)=\frac{c}{1+{e}^{a+bt}}+d$ | y(t) is the resultant NDVI value at time t; t is the Julian days; a and b are fitting parameters; c is the amplitude of the NDVI curve; d is the minimum NDVI value [71]. |

Asymmetric Gaussian function fitting (AG) | $y\left(t\right)=w\mathrm{NDVI}+\left(m\mathrm{NDVI}-w\mathrm{NDVI}\right)\times g\left(t\right)$$\left(t;{a}_{1},{a}_{2}\cdots {a}_{5}\right)=\{\begin{array}{c}\mathrm{exp}\left[-{\left(\frac{t-{a}_{1}}{{a}_{2}}\right)}^{{a}_{3}}\right],\mathrm{if}t{a}_{1}\\ \mathrm{exp}\left[-{\left(\frac{{a}_{1}-t}{{a}_{4}}\right)}^{{a}_{5}}\right],\mathrm{if}t{a}_{1}\end{array}$ | y(t) is the resultant NDVI value at time t; g(t) is the original NDVI value; wNDVI and mNDVI are the minimum and maximum NDVI value of the fitting part; a_{1} is the position of the maximum or minimum value with respect to time t; a_{2} (a_{4}) and a_{3} (a_{5}) are the width and flatness of the right (left) half of the function [56]. |

Polynomial curve fitting (PCF) | $\begin{array}{c}y\left(t\right)={\alpha}_{0}+{\alpha}_{1}\times {t}^{1}+{\alpha}_{2}\times {t}^{2}+{\alpha}_{3}\times {t}^{3}+\cdots \\ +{\alpha}_{n}\times {t}^{n}\end{array}$ | y(t) is the resultant NDVI value at time t; t is the Julian days; α_{0}-α_{n} are fitting parameters; n is the degree of smoothing polynomial; the smoothing polynomial degree is set to 6 [50]. |

Linear interpolation (Linear) | $y\left(t\right)=\frac{t-{t}_{1}}{{t}_{0}-{t}_{1}}{y}_{0}+\frac{t-{t}_{0}}{{t}_{1}-{t}_{0}}{y}_{1}$ | y(t) is the resultant NDVI value at time t; t_{0} and t_{1} are the nearest day of year (DOY) of the missing value; y_{0} and y_{1} are the nearest NDVI of the missing value; t is the DOY of the interpolating point between t_{0} and t_{1}. |

Cubic spline interpolation (Spline) | ${y}_{i}\left(t\right)={a}_{i}+{b}_{i}\left(t-{t}_{i}\right)+{c}_{i}{\left(t-{t}_{i}\right)}^{2}+{d}_{i}{\left(t-{t}_{i}\right)}^{3}$ | y_{i}(t) is the resultant NDVI value at time t in the ith period; t is the interpolating point between t_{i} and t_{i+1}; a-d are function parameters decided by the DOY and NDVI matrix calculation results in the ith period and the (I + 1) th period. |

Method | Equation | Parameter |
---|---|---|

Dynamic threshold (DT) | $thd=\frac{\mathrm{NDVI}\left(t\right)-{\mathrm{NDVI}}_{min}}{{\mathrm{NDVI}}_{max}-{\mathrm{NDVI}}_{min}}$ | NDVI(t) is the original NDVI value at time t; NDVI_{max} is the maximum value of the entire curve; NDVI_{min} is the minimum value of the left/right curve (divided by the maximum NDVI); thd is the output ratio, ranging from 0–1 [56]. |

Maximum rate of change (MRC) | ${\mathrm{NDVI}}_{ratio}\left(t\right)=\frac{\mathrm{NDVI}\left(t+1\right)-\mathrm{NDVI}\left(t\right)}{\mathrm{NDVI}\left(t\right)}$ | NDVI(t) is the original NDVI value at time t; NDVI (t+1) is the original NDVI value at time t+1; NDVI_{ratio}(t) is the NDVI ratio at time t [50]. |

Change rate of curvature (RCC) | $\mathrm{NDVI}\left(t\right)=\frac{y{\left(t\right)}^{\u2033}}{{\left(1+y{\left(t\right)}^{\prime}{}^{2}\right)}^{3/2}}$ | NDVI(t) is the rate of change of curve at time t; y(t)′ and y(t)″ are the first and the second derivative of curve at time t [71]. |

Number | Temporal Resolution | Time Interpolation Methods | Phenology Extraction Methods |
---|---|---|---|

(1) | 1 d vs. 8 d, 1 d vs. 16 d | PL, AG, PCF, Linear, Spline | Mean of DT, MRC, and RCC |

(2) | 1 d vs. 8 d, 1 d vs. 16 d | PL, AG, PCF, Linear, Spline | DT, MRC, RCC |

(3) | 8 d vs. 16 d | PL, AG, PCF, Linear, Spline | Mean of DT, MRC, and RCC |

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## Share and Cite

**MDPI and ACS Style**

Li, X.; Zhu, W.; Xie, Z.; Zhan, P.; Huang, X.; Sun, L.; Duan, Z.
Assessing the Effects of Time Interpolation of NDVI Composites on Phenology Trend Estimation. *Remote Sens.* **2021**, *13*, 5018.
https://doi.org/10.3390/rs13245018

**AMA Style**

Li X, Zhu W, Xie Z, Zhan P, Huang X, Sun L, Duan Z.
Assessing the Effects of Time Interpolation of NDVI Composites on Phenology Trend Estimation. *Remote Sensing*. 2021; 13(24):5018.
https://doi.org/10.3390/rs13245018

**Chicago/Turabian Style**

Li, Xueying, Wenquan Zhu, Zhiying Xie, Pei Zhan, Xin Huang, Lixin Sun, and Zheng Duan.
2021. "Assessing the Effects of Time Interpolation of NDVI Composites on Phenology Trend Estimation" *Remote Sensing* 13, no. 24: 5018.
https://doi.org/10.3390/rs13245018