# Time Series Analysis of MODIS-Derived NDVI for the Hluhluwe-Imfolozi Park, South Africa: Impact of Recent Intense Drought

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}and extends between 28°00′ S and 28°26′ S, and 31°43′ E and 32°09′ E in the northern KwaZulu-Natal, South Africa (Figure 1). The reserve was established in 1895 and is managed by Ezemvelo KwaZulu-Natal Wildlife (EKZN Wildlife). The landscape undulates with an altitude ranging from approximately 50 to 500 m.a.s.l. and comprises a mixture of soil types resulting from topographic and climatic heterogeneity [33]. The terrain of the study area on the right side of Figure 1 was plotted using the Global Multi-resolution Terrain Elevation Data 2010 data set. The version of this data is the Breakline Emphasis, 7.5 arc-s, and is archived as USGS/GMTED2010 in the Google Earth Engine (GEE) JavaScript platform. Land cover classification was also performed in the GEE environment so as to show the types of vegetation cover in the HiP.

#### 2.2. Data

#### 2.3. Multiple-Linear Regression

_{i}is the dependent variable (NDVI in this case), x

_{ip}represents the independent variables (soil temperature, precipitation, Niño3.4, and DMI in this case), β

_{0}is the intercept, and β

_{1}, β

_{2}, … β

_{p}are the coefficients of the x terms. The term ε

_{i}represents the error term, which the model always tries to minimize.

#### 2.4. Mann–Kendall Test

^{2}is given by the following equation:

_{j}is the number of data points in the jth tied group, and p is the number of the tied group in the time series. It is important to mention that the summation operator in the above equation is applied only in the case of tied groups in the time series in order to reduce the influence of individual values in tied groups in the ranked statistics. On the assumption of random and independent time series, the statistic S is approximately normally distributed provided that the following z-transformation equation is used:

#### 2.5. Wavelet Transforms and Wavelet Coherence

_{n}(s)] for a given time series (x

_{n}, n = 1, 2, 3, …, N) with respect to wavelet Ψ

_{0}(η) is defined as:

^{′}is the translated time index, n is the localized time index, and Ψ* is the complex conjugate of the normalized wavelet. δt is the uniform time step (which is months in this case). The wavelet power is calculated from |W

_{n}(n)|

^{2}. In this study, the CWT statistical significance at a 95% confidence level was estimated against a red noise model [55,57]. Using a continuous wavelet transform analysis, it is also possible to quantify the relationship between two independent time series of the same time step δt. In this study, the aim was to quantify the relationship between NDVI averaged for the study area and selected climatic parameters. Following Grinsted et al. [57], for the two time series of X and Y, with different CWT ${W}_{n}^{X}\left(s\right)$ and ${W}_{n}^{Y}\left(s\right)$ values, the cross-wavelet transform ${W}_{n}^{xy}\left(s\right)$ is given by

_{i}, i = 1, 2, 3,…, n) can be defined by the following equation:

_{n}(s)) = S

_{scale}(S

_{time}(W

_{n}(s))). The parameter S

_{time}represents the smoothing in time. For further details about the theory of wavelet analyses, the reader is referred to [55,57,59].

## 3. Results and Discussion

#### 3.1. Correlations Statistics and Mann–Kendall Test

^{−16}and 0.000173, respectively. Both Precipitation and Niño3.4 indicate a statistically insignificant association with the NDVI because of p-values which are far greater than 0.05. A positive significant correlation between NDVI and Soil temperature, NDII, and ET, which is also represented as in Figure 7 and Figure 8, indicates that soil moisture, soil temperature, and evapotranspiration play a significant role in vegetation health in the HiP. The significant but negative correlation between Niño3.4 and NDVI confirms the notion that ENSO variability plays a role in the climatic conditions of southern Africa [35,52].

#### 3.2. Wavelet Analyses

## 4. Conclusions

^{−7}, and 0.27 and 8.4 × 10

^{−4}, respectively. While some studies [17] reported temperature as the main meteorological parameter that influences vegetation, in this study, we conclude that the influence of precipitation on vegetation was more significant. Different areas of the HiP are affected differently by the strong El Niño signal because of the special variation of land cover. The southern part of the HiP was affected the most because it is dominated by savanna. On the other hand, the northern part of the HiP seems to not be affected presumably because land cover in this area is dominated by forests which are composed of trees which are drought resistant. Moreover, terrain appears to have additional influence on the state of vegetation in the reserve. For example, the lower NDVI values corresponded with the 2014–2016 drought period, particularly in the south-western (flat) part of the reserve, whereas the northern parts (hilly) seem to have benefited from orographic precipitation which promoted vegetation growth. Terrain is also assumed to restrict wildlife grazing in hilly parts of the reserve where stable NDVI are noticeable, placing more burden in flat areas that are accessible to most grazers.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**The study area showing the Hluhluwe-iMfolozi Park in the north-eastern part of South Africa.

**Figure 2.**The standardized monthly Niño3.4 (

**a**) and dipole mode index (DMI) (

**b**) time series for the period from 1980 to 2017.

**Figure 3.**The spatiotemporal variability of normalized difference vegetation index (NDVI) at the Hluhluwe-iMfolozi Park for the period from 2002 to 2017. The scale represents the range of NDVI values from 0 to 1.

**Figure 4.**(

**a**) The deseasonalized monthly mean NDVI time series for HiP. The continuous red line indicates the trend estimate and the dashed red lines show the 95% confidence interval for the trend based on resampling methods. (

**b**,

**c**) show the histogram and yearly mean time series, respectively.

**Figure 5.**The monthly mean time series values of (

**a**) NDVI, (

**b**) Enhanced Vegetation Index (EVI), (

**c**) Burned Area (BAI), and Modern Retrospective Analysis for the Research Application (MERRA-2) model soil temperature (

**d**) and precipitation (

**e**), Global Land Data Assimilation System (GILDAS) evapotranspiration (

**f**) and Normalized Difference Infrared Index (NDII) (

**g**). The dotted lines represent the 12-month smooth trends.

**Figure 6.**The (

**a**,

**b**) NDVI, (

**c**,

**d**) EVI and (

**e**,

**f**) BAI (blue dashed line) 12-month smooth trends versus Niño3.4 (left panels) and DMI (right panels) for the period from 2002 to 2017 for the HiP.

**Figure 7.**The heat map of Pearson correlation coefficients for NDVI, NDII, precipitation (Prec), soil temperature (Soil.Temo), ET, BAI, Niño3.4, and DMI.

**Figure 8.**The inter-annual variability of linear correlations between NDVI and BAI, Soil Temp, Prec, Niño3.4, DMI, ET, and NDII for the period 2002 to 2017.

**Figure 9.**(

**a**) The inter-annual variation of Mann–Kendall z-scores (α = 0.05, Z1 = –1.96, Z2 = 1.96) for the HiP from 2002 to 2017. (

**b**) Sequential statistics values of progressive (Prog) $u\left(t\right)$ (solid red line) and retrograde ${u}^{\prime}\left(t\right)$ (black solid line) obtained by Sequential Mann-Kendall (SQ-MK) test for HiP monthly mean NDVI data for the period from 2002 to 2017.

**Figure 10.**The normalized wavelet power spectra of monthly mean (

**a**) NDVI, (

**b**) precipitation, (

**c**) Soil temperature, (

**d**) DMI, (

**e**) Niño3, (

**f**) NDII, and (

**g**) ET, plotted for the period from 2002 to 2017. The black lines which encircle the yellowish colors indicate the areas of significance at the 95% confidence level using the red noise model.

**Figure 11.**The squared cross-wavelet power spectra for NDVI–Niño3.4, NDVI–DMI, NDVI-precipitation, NDVI–soil temperature, NDVI–NDII, and NDVI–ET. The continuous black lines demarcate the areas of significance at the 95% confidence level using the red noise model. The arrows are vectors indicating the phase difference between the cross-wavelet parameters (see the legend in the bottom left corner).

**Table 1.**The output of the Multiple Linear Regression (MLR) model in which Normalized Difference Vegetation Index (NDVI) is a dependent variable and soil temperature, precipitation (Soil Temp), Niño3.4, Normalized Difference Infrared Index (NDII), Dipole Model Index (DMI), and Evapotranspiration (ET) are independent variables.

Variable | Estimate | Std. Error | t-Value | p-Value | Sig |
---|---|---|---|---|---|

Soil. Temp | −1.23 × 10^{−02} | 3.39 × 10^{−03} | −3.615 | 0.000386 | *** |

Prec | 7.35 × 10^{−05} | 1.72 × 10^{−04} | 0.427 | 0.669736 | |

Niño3.4 | −6.44 × 10^{−03} | 7.62 × 10^{−03} | −0.845 | 0.399427 | |

NDII | 1.46 × 10^{+00} | 7.60 × 10^{−02} | 19.214 | <2.00 × 10^{−16} | *** |

ET | 4.03 × 10^{+03} | 1.05 × 10^{+03} | 3.833 | 0.000173 | *** |

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**MDPI and ACS Style**

Mbatha, N.; Xulu, S.
Time Series Analysis of MODIS-Derived NDVI for the Hluhluwe-Imfolozi Park, South Africa: Impact of Recent Intense Drought. *Climate* **2018**, *6*, 95.
https://doi.org/10.3390/cli6040095

**AMA Style**

Mbatha N, Xulu S.
Time Series Analysis of MODIS-Derived NDVI for the Hluhluwe-Imfolozi Park, South Africa: Impact of Recent Intense Drought. *Climate*. 2018; 6(4):95.
https://doi.org/10.3390/cli6040095

**Chicago/Turabian Style**

Mbatha, Nkanyiso, and Sifiso Xulu.
2018. "Time Series Analysis of MODIS-Derived NDVI for the Hluhluwe-Imfolozi Park, South Africa: Impact of Recent Intense Drought" *Climate* 6, no. 4: 95.
https://doi.org/10.3390/cli6040095