1.1 The relationship between normalized difference vegetation index and carbon dioxide

The use of atmospheric carbon dioxide (CO₂) seasonal index measures its sources and sinks with high precision. Understanding the seasonal dynamics of these emissions is necessary to enable an effective global mitigation. However, it is difficult to estimate carbon-driven emissions using only direct measurements, in contrast to regional estimation (^{Le Quere et al., 2009}). ^{Komhyr et al. (1989)} established that CO₂ measurements made at the Mauna Loa Observatory are conducted with great precision. The observatory, which measures the mole fraction of CO₂ using infrared absorption, gives quantitative information about its global trend. ^{Kaufmann et al. (2008)} used autoregression to test their approach and conclude that measurements based on distance are adequate. This information contradicts the results of ^{Le Quere et al. (2009)}, who developed a model that effectively replicated the activity of land-ocean CO₂ sinks and its impact on the increase of CO₂ levels from 2000-2008.

The increase of CO₂ sources has been attributed to fossil fuel, and carbon intensity depends on the regional scale (^{Weber et al., 2008}). The interplay between carbon-driven emissions and the resultant climate change effect is already well-known (^{Plass, 1956}; ^{Kaplan, 1960}; ^{Tans et al., 1989}; ^{Siegenthaler and Sarmiento, 1993}; ^{Houghton and Hackler, 1999}; ^{Seekell, 2016}). An estimation using different model methods has shown that, over the decades, a significant proportion of CO₂ released into the atmosphere has been absorbed by the biosphere and oceans (^{Rayner et al., 1999}; ^{Battle et al., 2000}; ^{Le Quéré et al., 2003}; ^{Manning and Keeling, 2006}). The variability in relative carbon sequestration by the two sinks causes variability in the overall CO₂ atmospheric loading and, by extension, it produces climate variability and change. The idea of using greening in carbon capture and storage aims to limit the corresponding concentrations and stabilize the Earth’s radiative forcing. Prior studies have demonstrated the applications of greening (^{Bartlett et al., 1990}; ^{Hope et al., 1993}; ^{Sharkey, 2006}; ^{Rigby et al., 2008}; ^{Turnbull et al., 2011}; ^{McKain et al., 2012}; ^{Rogers et al., 2017}), therein validating the option as applicable to broader efforts in the mitigation of climate change. Calculating dynamical trends in CO₂, temperature and normalized index across the regions of Africa, Europe and Asia would be a worthwhile, relevant exercise. The results of the dynamical trend will provide a possible mitigation strategy. The idea of using greening to regulate surface CO₂ storage aims to limit the corresponding increasing frequency of heat waves and stabilize the Earth’s radiative forcing. The normalized difference vegetation index (NDVI) uses the quotient of near infrared radiation and visible wavelength radiation. Its usage is in global climate change and environmental issues. NDVI compensates for reflectivity changes at certain frequencies and tracks greening. The degree of greenness ranges from -1 to +1, where the positive value is indicative of greening. Using the seasonal index to validate the relationship between CO₂ and NDVI is not an approach which has been well investigated. There is a robust review of literature from multiple prior analyses, but no one has investigated the interplay between NDVI and CO₂ with latitude, seasons and the solar cycle. This paper discusses the current state of understanding of this interplay and attempts to bridge the knowledge gap between seasonal trends of carbon and their possible mitigation strategy.

^{Dagg and Lafleur (2014)} estimated the NDVI and CO₂ relationship over tundra vegetation regions. Their study used a portable chamber to measure CO₂ fluxes and a handheld infrared camera for the estimation of NDVI and CO₂ variations and their contribution to the understanding of landscape characteristics. They found a positive correlation of CO₂ exchange over NDVI, and concluded that NDVI is a good predictor of CO₂ exchange. In an attempt to estimate global CO₂ concentration using MODIS, ^{Guo et al. (2012)} used a model to investigate the carbon cycle between biosphere and atmosphere combined with an observation from eddy covariance. Although the study covered a short period (2009-2011), it aimed to map monthly CO₂ concentrations over Africa, Eurasia, and North and South America using vegetation cover. The results indicate that seasonal trends of CO₂ have local variations and their maxima and minima occur during summer and winter, respectively, over Eurasia, while the fluctuations over Africa were quite small. The study, which also features other parameters, found that land surface temperature has a better potential for validating CO₂ concentration trends. ^{La-Puma et al. (2007)} found a good relationship between NDVI and CO₂ during the summer, when biomass reaches its peak. Their results suggest that NDVI should not be included in model calibration over CO₂ fluxes. These results conflict with ^{Cihlar et al. (1992)}, who measured NDVI and CO₂ interactions from an aircraft over agricultural lands in Kansas, finding that their relationship was linearly correlated over a single day, but nonlinearly over a longer period. ^{Stow et al. (1998)} found similar results and suggested that NDVI is a good parameter to predict variations in CO₂. The same results were corroborated in other studies (^{McMichael, 1999}; ^{Markon and Peterson, 2002}; ^{Boelman et al., 2003}). However, some authors (^{Huete et al., 2002}; ^{Xiao et al., 2004}) gave more credit to an enhanced vegetation index (EVI). ^{Lim et al. (2004)} suggested that NVDI and CO₂ data correlation should not be done directly, for it does not give a better result. Their results show that CO₂ and NDVI have a strong seasonal covariance.

3.1 Africa

Validations of the NDVI and CO₂ relationship in different seasons over Africa are presented. Figure 2a shows a CO₂ peak during winter, indicating high carbon concentrations; conversely, the incident photosynthetic uptake as the result of carbon storage via greening leads to a decline. Figure 2b, c shows the mass uptake of CO₂ during the summer, which does not compensate the emission increase of this compound, leading as a result to a net accumulation of carbon. The inverse correlation of CO₂ with NDVI indicates that this a good mitigation strategy to limit the concentration of carbon. ^{Curtis and Wang (1998)} obtained similar results and suggested an appropriate mitigation of CO₂. In our results, NDVI and CO₂ are positively correlated during the ascending solar activity cycle (Table II), indicating that NDVI records moderate values towards low emission of carbon. The growth in carbon concentration implies larger anthropogenic emission activities in Nigeria, corresponding to low greening. The results of this study also fill the knowledge gap discussed in ^{Le Quere et al. (2009)} regarding a year to year anthropogenic-driven CO₂ emission rate. There is a substantial degree of variation in the degree of CO₂ effect on temperature; however, the photosynthetic capacity during the growing season closely tracked the pace of warming and the temperature record shows convincingly that Africa has experienced the largest warming rate. Towards the intermediate solar activity, Figure 3a, b shows a decreasing trend of NDVI and an increase of CO₂ during summer. This is an indicator of weak radiant energy, as displayed in Table II, which indicates a negative weak correlation of NDVI with CO₂ and a strong correlation of CO₂ as function of NDVI. However, towards the vernal and autumnal equinoxes, CO₂ decreases with maximum NDVI at the corresponding months, manifesting a positive correlation. A similar result is seen in ^{Barchivich et al. (2013)}, and it could therefore be concluded that anthropogenic carbon emission is seasonally dependent. In the descending solar activity cycle as seen in Table II and Figure 4a, b, CO₂ reaches peaks during winter and summer, corresponding to a declining trend of NDVI at particular seasons. In Figure 5a, Mauritania displays a moderate CO₂ concentration trend, while NDVI peaks during the vernal and autumnal seasons, indicating a reduced value of CO₂ as seen in Figure 5a, b. However, in Figure 6a, b, the CO₂ concentration reaches its maximum during the winter and summer, as seen during the intermediate solar activity year. Figure 7a, b shows similar results to Figure 5a, b, but varies in regard to the carbon storage rate. This shows that NDVI and CO₂ variations strongly depend on seasonality.

Fig. 2 Seasonal trend of the CO₂ and NDVI relationship with temperature over Nigeria during the ascending solar activity cycle. 

Fig. 3 Seasonal trend of the CO₂ and NDVI relationship with temperature over Nigeria, during the intermediate solar activity cycle. 

Fig. 4 Seasonal trend of the CO₂ and NDVI relationship with temperature over Nigeria during the weak solar activity cycle. 

Fig. 5 Seasonal trend the CO₂ and NDVI relationship with temperature over Mauritania during the ascending solar activity cycle. 

Fig. 6 Seasonal trend of the CO₂ and NDVI relationship with temperature over Mauritania during the intermediate solar activity cycle. 

Fig. 7 Seasonal trend of the CO₂ and NDVI relationship with temperature over Mauritania during the weak solar activity cycle. 

Seasonal signatures in the atmospheric concentration of CO₂ reflect the changing balance of photosynthetic rate; however, biomass burning accounts for the annual cycle of CO₂ increase. This result agrees with those of ^{Markon and Peterson (2002)}. The CO₂ and NDVI relationship rate indicates an inverse correlation (Table II). This indicates that the CO₂ concentration rate is a landscape dynamic scale and depends on the seasons, which is shown in Figures 6a, b, 7a, b, 8a, b, 9a, b and 10a, b. The seasonal responses of NDVI depend on the atmospheric conditions, as depicted in Figures 11a, 12 and 13b. In Figure 11a, Sudan shows low concentrations of CO₂ due to a high vegetation index during the ascending solar activity cycle, as depicted in Figure 11b, but also shows a reciprocal relation in Figure 13a, b.

Fig. 8 Seasonal trend of the CO₂ and NDVI relationship with temperature over Congo during the ascending solar activity cycle. 

Fig. 9 Seasonal trend of the CO₂ and NDVI relationship with temperature over Congo during the intermediate solar activity cycle. 

Fig. 10 Seasonal trend of the CO₂ and NDVI relationship with temperature over Congo during the weak solar activity cycle. 

Fig. 11 Seasonal trend of the CO₂ and NDVI relationship with temperature over Sudan during the ascending solar activity cycle. 

Fig. 12 Seasonal trend of the CO₂ and NDVI relationship with temperature over Sudan during the intermediate solar activity cycle. 

Fig. 13 Seasonal trend of the CO₂ and NDVI relationship with temperature over Sudan during the weak solar activity cycle. 

3.2 Europe

The increasing or decreasing trend of CO₂ is the major determinant of climate change. However, to validate this relationship, Figure 14a, b indicates a moderate CO₂ concentration. This clearly shows that during the ascending solar activity cycle, the emission-driven CO₂ was regulated. A similar result is depicted in Figure 15a, b, which shows carbon capture during both winter and summer. In Figure 16a there is a CO₂ peak and a drastic increase in the vegetation index. Table II displays a positive weak correlation between NDVI and CO₂. The decline in CO₂ resulting from NDVI increases is shown in Figures 16a, 17a, 18a to 19a. In Figures 20, 21 and 22a, during the ascending, intermediate and weak solar activity, Turkey experiences maximum emissions of CO₂ during winter and summer, which results from heating of the region, as confirmed in Figure 20b. This leads to the conclusion that high concentrations of CO₂ caused the region’s heat wave, thereby resulting in climate change. NDVI and CO₂ interactions are regional, and the range of change in climate also differs. This result is well supported by ^{La-Puma et al. (2007)}. In Table III, NDVI and CO₂ show a weak correlation towards the first and second years, but the moderate correlation in Turkey over the period confirms a high emission rate. In Figures 23a, 24 and 25b there is a moderate CO₂ trend due to high concentrations of NDVI.

Fig. 14 Seasonal trend of the CO₂ and NDVI relationship with temperature over France during the ascending solar activity cycle. 

Fig. 15 Seasonal trend of the CO₂ and NDVI relationship with temperature over France during the intermediate solar activity cycle. 

Fig. 16 Seasonal trend of the CO₂ and NDVI relationship with temperature over France during the weak solar activity cycle. 

Fig. 17 Seasonal trend of the CO₂ and NDVI relationship with temperature over Finland during the ascending solar activity cycle. 

Fig. 18 Seasonal trend of the CO₂ and NDVI relationship with temperature over Finland during the intermediate solar activity cycle. 

Fig. 19 Seasonal trend of the CO₂ and NDVI relationship with temperature over Finland during the weak solar activity cycle. 

Fig. 20 Seasonal trend of the CO₂ and NDVI relationship with temperature over Turkey during the ascending solar activity cycle. 

Fig. 21 Seasonal trend of the CO₂ and NDVI relationship with temperature over Turkey during the intermediate solar activity cycle. 

Fig. 22 Seasonal trend of the CO₂ and NDVI relationship with temperature over Turkey during the weak solar activity cycle. 

Fig. 23 Seasonal trend of the CO₂ and NDVI relationship with temperatur over Ukraine during the ascending solar activity cycle. 

Fig. 24 Seasonal trend of the CO₂ and NDVI relationship with temperature over Ukraine during the intermediate solar activity cycle. 

Fig. 25 Seasonal trend of the CO₂ and NDVI relationship with temperature over Ukraine during the weak solar activity cycle. 

3.3 Asia

TableIV shows a negative, weak correlation between NDVI and CO₂ over China and Mongolia during the intermediate and weak solar activity years. This result is in agreement with ^{Le Quere et al. (2009)}, as shown in Figure 27a, b, which suggests that over 30% of the CO₂ concentrations in China are generated by industrial activities. However, it can be seen that the northern hemisphere is not sensitive to the dynamics of CO₂ variation. Therefore, surface-based observation is recommended in this region. Additionally, the results of ^{Murayama et al. (2004)} confirm that direct measurement in the northern hemispheric zone is valuable. The results of this study contribute to this knowledge gap. Figures 28, 29, 30, 31, 32, 33, 34 and 35 show a moderate trend of CO₂ as a result of an increase in NDVI during winter and autumn. Towards the intermediate solar activity year over India and Afghanistan (Figs. 33, 34, 35, 36 and 37) and the weak solar activity year over this last country, there is a seasonal trend of CO₂ increase indicating high atmospheric accumulation leading to climate variability.

Fig. 26 Seasonal trend of the CO₂ and NDVI relationship with temperature over China during the ascending solar activity cycle. 

Fig. 27 Seasonal trend of the CO₂ and NDVI relationship with temperature over China during the intermediate solar activity cycle. 

Fig. 28 Seasonal trend of the CO₂ and NDVI relationship with temperature over China during the weak solar activity cycle. 

Fig. 29 Seasonal trend of the CO₂ and NDVI relationship with temperature over Mongolia during the ascending solar activity cycle. 

Fig. 30 Seasonal trend of the CO₂ and NDVI relationship with temperature over Mongolia during the intermediate solar activity cycle. 

Fig. 31 Seasonal trend of the CO₂ and NDVI relationship with temperature over Mongolia during the weak solar activity cycle. 

Fig. 32 Seasonal trend of the CO₂ and NDVI relationship with temperature over India during the ascending solar activity cycle. 

Fig. 33 Seasonal trend of he CO₂ and NDVI relationship with temperature over India during the intermediate solar activity cycle. 

Fig. 34 Seasonal trend of the CO₂ and NDVI relationship with temperature over India during the weak solar activity cycle. 

Fig. 35 Seasonal trend of the CO₂ and NDVI relationship with temperature over Afghanistan during the ascending solar activity cycle. 

Fig. 36 Seasonal trend of the CO₂ and NDVI relationship with temperature over Afghanistan during the intermediate solar activity cycle. 

Fig. 37 Seasonal trend of the CO₂ and NDVI relationship with temperature over Afghanistan during the weak solar activity cycle.