*3.2. Wavelet Analyses*

In order to analyze the localized variation of the spectral power within the time series, wavelet analyses, the most common tool for this purpose, was conducted. As mentioned earlier, the wavelet method assists by decomposing a time series into a time–frequency space, which makes it possible to determine the dominant modes of variability and how they vary in time. Figure 10 shows the normalized wavelet power spectra for the monthly mean NDVI, precipitation, soil temperature, DMI, Niño.3.4 NDII, and ET data. The results of the EVI wavelet analyses are not shown here because this time series is identical to that of the NDVI. In Figure 10, the blue color indicates low wavelet power, and the yellow color represents areas of high wavelet power. The horizontal axis is the time scale (in years) and the vertical axis is the period (in months). The thick black line represents the 95% confidence level. The areas of the wavelet power that are considered are those which are within the cone-of-influence (indicated by the solid "u" shaped line). The con-of-influence indicates areas where edge effects occur in the coherence data [55,57].

The NDVI of the HiP seems to follow the distinctive pattern of the seasonality of precipitation in the north-eastern part of South Africa. The region experiences rainfall during the summer period (December–February) and dry winter period (June–August). This is confirmed by a statistically significant peak observed at around the 12-month cycle (see Figure 10a), which seems to correspond with that of precipitation (Figure 10b). The wavelet power spectra of soil temperature (Figure 10c), NDII (Figure 10f) and ET (Figure 10g) also indicate a strong peak at around the 12-month cycle. This is plausible because wet seasons (summer in this case) lead to increased soil moisture and also create conditions of low evapotranspiration and thus accelerate the greening process in the HiP. It should also be noted that the NDVI wavelet power spectra have significant peaks showing the presence of the semi-annual oscillation (6 months), which is observed during the distinctive period from 2006–2007 to 2011–2012. The semi-annual oscillation observed during the 2006–2007 period is also apparent in the NDII wavelet power spectra. The results of the NDVI wavelet spectral presented here are remarkably similar to the findings of Azzali and Menenti [12], who used a Fourier transform-based technique

and reported a substantial seasonal change in NDVI for southern Africa. The significant power of a period of 3–4 months that is observed during the distinctive period 2012–2013 and 2015–2016 in the precipitation power spectra is perhaps related to cyclone Irina in early 2012 and the most recent intense drought of 2014–2016. The wavelet power spectra of the DMI indicate a significant power peak of distinctive periods in the 3–20 months band primarily during the period between 2008 and 2013. On the other hand, the Niño3.4 power spectra exhibit significant power peaks in the 8–32 months band throughout the study period. It should be noted, however, that this frequency of occurrence of peaks observed in the Niño3.4 wavelet spectra is similar to that reported in the studies of Torrance and Compo [55] and also of Jevrejeva et al. [56], who used a much longer time series of the ENSO signal.

**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.

The wavelet coherence between NDVI–Niño3.4, NDVI–DMI, NDVI–precipitation, NDVI–soil temperature, NDVI–NDII, and NDVI–ET was investigated to determine whether NDVI significant wavelet spectra peaks observed at a given time correspond with those observed by the other parameters. Furthermore, the phase relationship between NDVI and the other parameters was calculated and superimposed graphically in Figure 11. The phase relationship is represented by arrows, where two cross-wavelet parameters are in phase if the arrows point to the right, anti-phase if the arrows point to the left, and NDVI leading or lagging if the arrows point upwards or downwards, respectively. The vectors were only plotted for areas where the squared coherence is greater or equal to 0.5. More details about these calculations can be found in References [56,57] and later by studies by Schulte et al. [59].

**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).

The local wavelet coherence spectra together with their distinctive cross-spectra phase for NDVI–Niño3.4, NDVI–DMI, NDVI-precipitation, NDVI–soil temperature, NDVI–NDII, and NDVI–ET are shown in Figure 11. In general, all the wavelet coherence spectra indicate that Niño3.4, DMI, precipitation, soil temperature, NDII, and ET do have some degree of coherence with the HiP NDVI in a variety of both periods and timescales. However, it should be mentioned that because statistically, the significant correlation between any two variables being investigated could occur by chance, a significant commonality in a wavelet coherence spectra analysis does not necessarily imply interconnection. Moreover, there is a possibility of smaller areas of wavelet coherence occurring by chance, which would not indicate interconnection, whereas larger areas of significance are improbable due to chance. For this reason, further investigation is required in regard to a possible teleconnection between any two-time series.

A study by Torrance and Compo [55] investigated the periodicities present in a much longer time series (1871–1996) of Niño3.4 using Morlet wavelets and reported the domination of periods greater than 12 months, with some episodes of shorter periods also present in their spectra. In this study, the wavelet coherence between NDVI and Niño3.4 indicates smaller or no areas of high power significance, which is understandable because the 16-year monthly mean NDVI time series is dominated by periodicities of less than 16 months (Figure 10a) whereas the Niño3.4 wavelet spectra are dominated by periodicities greater than 12 months. Remarkably, there is a significant power at a period band of 22–27 months from 2014 to 2017 with cross-spectra phase pointing at the leading position for Niño3.4, which indicates that the recent strong El Niño event may have started first before the response of NDVI months after the El Niño.

The wavelet coherence between NDVI and DMI is observed to delineate some areas that have high significant power at periods of 2–16 months. It is also important to mention that there are significant peaks which are within the cone of influence at the period band 32–48 months during 2005–2007 and 2013–2014, respectively. The cross-wavelet phase during the years 2013–2014 indicates that the DMI was leading the NDVI. This significant peak seems to be similar to that observed in the Niño3.4–NDVI wavelet coherence spectra, which indicates that it is possible that the DMI and Niño3.4 time series were in phase during this period. If so, their joint effect could have maximized the browning observed during 2014–2016. The wavelet coherence between NDVI and precipitation, soil temperature, and ET indicates high significant power during most parts of the study record. In general, these spectra vectors are observed to have an in-phase relationship especially during the period band 8–18 months. This pattern is also observed in the distinctive periods which are less than 8 months especially for the period band 2006–2013. The NDVI and soil temperature wavelet coherence spectra delineate distinctive high power significance with an anti-phase relationship in a 2–8 months band during 2006–2014. Apart from the two distinctive period bands of 2004–2006 and 2015–2017 of high significant power during which the NDVI time series led the temperature time series during the period band 9–14 months, the annual cycle is dominated by the in-phase relationship. Both these scenarios indicate the possible teleconnection between the two time series. The dominant in-phase relationship in the NDVI–precipitation, NDVI–soil temperature, and NDVI–ET suggests that these parameters are positively correlated to the NDVI. This also indicates that the NDVI of the HiP follows the seasonal cycle of precipitation and temperature that is experienced in this region of southern Africa. As expected, the NDVI–NDII coherence spectra indicate a significant coherence at periods greater than 3 months, with a dominant in-phase relationship which indicates a strong correlation between NDVI and NDII. This is in agreement with the Pearson correlation coefficient results presented in Figures 7 and 8.

Overall, factors such as DMI, Niño3.4, precipitation, soil temperature, NDII, and ET are shown to influence NDVI at different distinctive periods and timescales. During the La Niña years, the relationship between NDVI and precipitation and temperature seemed to not indicate any alarming patterns. However, during strong El Niño years (especially broad and strong El Niño years such as the 2014–2016), intense droughts occur. This condition is associated with less humidity and cloud cover, which allows for more solar radiation reaching the ground and accelerated evapotranspiration, which impedes photosynthetic activity.
