Bayesian Spatio-temporal Analysis of Greenhouse Gas Emissions in Africa

Global warming is a driver of climate change and is attributed to the increasing concentration of greenhouse gases in the atmosphere due to human activities. Although Africa contributes the least to global greenhouse gas emissions, its emissions are still on the increase. This study analyzes the spatial eﬀect, temporal eﬀect, and the interaction of these eﬀects on these emissions in Africa. A 27-year greenhouse gas emissions data of some selected African countries was studied using Bayesian spatiotemporal analysis within a Bayesian framework. Inference was based on integrated nested Laplace approximation implemented using the R-INLA package in R. Various subsets of spatio-temporal models were ﬁtted, including those that accounted for boundary shared among countries. Results show that models with the spatio-temporal interaction eﬀect outperform models that did not take this eﬀect into account, conﬁrming ﬁndings from existing literature. Findings from this study also revealed that the boundary shared among countries impacts greenhouse gas emissions. Countries that are less likely to have high greenhouse gas emissions but shared boundaries with those likely to have high estimates eventually had a high estimate of emissions over a long period. Controlling and reducing greenhouse gas emissions in Africa should be a collective eﬀort, particularly among countries sharing boundaries.


Introduction
Stabilizing the global average temperature is the beauty of greenhouse gases (GHGs) presence in the atmosphere. However, this is changing into being ugly over the years because of their alarming increasing concentration in the atmosphere. Many researchers have traced this increase to the anthropogenic emissions of these GHGs (Stott et al., 2000;Leila, 2013;Stocker, 2013;Niang et al., 2015). Edenhofer et al. (2014) reported an increase of 81% in anthropogenic emissions of GHGs since 1970. Over the years, global warming attributed to the anthropogenic emission of greenhouse gases has been of topmost concern. By 2100, the Intergovernmental Panel on Climate Change (IPCC) predicts 1.8 • -3.9 • C increase in average global temperature (IPCC, 2007c). Global warming contributes significantly to climate change that has negative consequences such as extremely high temperature, drought, heatwaves, melting of ice, rise in sea level, flooding, and much more (Koneswaran and Nierenberg, 2008;Leila, 2013).
Africa as a continent has been at the receiving end of the negative impacts of global warming the most (Bewket, 2012;IPCC, 2014). Warmer temperatures and reduced rainfall in Tanzania caused about 49% loss of ice in Mt. Kilimanjaro between 1976 and2002, resulting in the drying up of most rivers around it (Ngaira, 2007). Without curbing the increase in the emission of GHGs, prediction reveals that there will be no ice in Mt. Kilimanjaro, the highest mountain in Africa, in 2033. These may, in turn, affect the revenue of Tanzania as the mountain, which is a source of tourist attraction, serves as a means of revenue generation for the country (Vastag, 2009). Darghouth and Bouattour (2008) reported that Tunisia is most likely to experience a decrease in annual precipitation by 2030 and attain an increase of 2.1 • C in its mean temperature by 2050. Consequently, the risk of water scarcity will be high. And, in turn, harm the inhabitants of the country.
Between 2000 and 2016, there was a significant decrease in the yield of crops in West Africa as a result of the negative impacts of GHGs emissions on crop production (Osabohien et al., 2019). According to the IPCC, Africa's agriculture sector is threatened, especially in West Africa. The threat is due to the reduced output of crop yield and production linked to much increase in the number of hot days Africa will experience. These signal that there will be reduced precipitation, and its prolongation will lead to drought. However, the high tendency to reduce crop yield will not leave a good imprint as the demand for food will surpass the food supply by numerous amounts. This paints a picture of food scarcity that may likely explode into famine if not handled carefully. By 2080, as a result of climate change, over 100 million people will be prone to hunger, with 80% coming from Africa (Carter, 2007).
In addition to these effects, GHG emissions harm the health and well-being of humans. According to World Health Organization, extreme heat causes asthma, respiratory and cardiovascular diseases to increase. Respiratory disease, in particular, increases among children during heatwave (Xu et al., 2012). Activities such as the burning of fossil fuels, coal, natural gas, and oil contribute to GHGs emissions (Bruckner et al., 2014), and emissions related to fossil fuels is accountable for about 65% of excess mortality rate attributable to air pollution (Lelieveld et al., 2019). In Africa, increasing carbon emissions has been found to have a significant effect on child mortality (Shobande, 2020).
Many studies report that Africa contributes the least to the world's total GHGs emission (Bewket, 2012;IPCC, 2014;Adzawla et al., 2019). However, there has been a continuous increase in the anthropogenic emission of GHGs in Africa. In East Africa, the total GHGs emission increased by 42% between 1990 and 2011. Also, West Africa recorded a 17% increase in GHGs emissions between 1990 and 2014, with Nigeria contributing about 46% of these emissions (USAID, 2011(USAID, , 2019. By 2050, the projection of GHG emissions in sub-Sahara Africa will increase by as much as 50% (Leimbach et al., 2018), and double-fold increase in Africa as a whole (van der Zwaan et al., 2018). The IPCC state that "Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic (produced by humans) greenhouse gas emissions". According to the United Nations Framework Convention on Climate Change (UNFCCC), the main GHGs are carbon dioxide (CO 2 ), methane (CH 4 ), nitrous oxide (N 2 O) and fluorinated gases (per-fluorocarbons (PFCs), hydro-fluorocarbons (HFCs), and sulphur hexafluoride (SF 6 )).
Several studies have looked into the analysis of GHG emissions in Africa. Energy consumption based on fossil fuel, agriculture production, and other determinants contribute to CO 2 emissions in North Africa and some selected countries in East and South Africa (Siti, 2014;Umar et al., 2021). In addition, Olubusoye and Musa (2020) in their study showed that an increase in economic growth as well induces more of CO 2 emissions in most African countries. Using the Kaya identity, Ayompe et al. (2020) studied energy-related CO 2 emissions data of 27 African countries from 1990-2017. Results reveal an increasing trend in the emissions of CO 2 over the study period, with Mozambique as the highest emitter. The short and long-run impact of economic growth and energy consumption on GHG emissions was examined by Yusuf et al. (2020). CO 2 , CH 4 , and N 2 O emissions from six oil-producing African countries were used as a case study. Findings from this study showed evidence of a positive impact of economic growth on CO 2 , CH 4 emissions in the long run, and on CH 4 emissions in the short run. On the other hand, the energy consumption had an insignificant impact on CO 2 , CH 4 , and N 2 O emissions in both the short and long run.
The effect of GHG emissions on health outcomes in Africa is studied as well. Using Nigeria as a case study, Matthew et al. (2018), and Nkalu and Edeme (2019) adopted different methodology, and both results showed that an increase in The mentioned studies and most literature have looked into the analysis of CO 2 emissions of some selected African countries in the light of its source of emission and their various impacts. However, few studies have focused on other anthropogenic GHG emissions. These are methane (CH 4 ), nitrous oxide (N 2 O), and fluorinated gases. Although CO 2 emissions constitute most of anthropogenic GHGs emission and are the most likely cause of global warming (Chen et al., 2018), CH 4 has 28-36 global warming potential (GWP) times that of CO 2 , N 2 O has a GWP 265-298 times that of CO 2 , and fluorinated gases have over thousand or ten of thousands GWP (EPA, 2021). To this effect, our study focuses on these aforementioned GHG emissions with CO 2 emissions inclusive.
Long-term goals of achieving net-zero emission by 2050 around the world require urgent action and nationally determined contributions (UNCC, 2021). As a response, Africa is pursuing policies that will aid in minimizing its GHGs emissions as these GHGs have a long-life span of over thousands of years in the atmosphere (IPCC, 2014;EPA, 2021). However, a limitation of the efforts to mitigate GHG emissions in developing economies is the commitment of financial and technological resources (Adzawla et al., 2019). In addition, the world's top ten poorest countries in 2020 are from Africa (Luca Ventura, 2020). Therefore, the effectiveness of policies will require understanding how these GHG emissions evolve across space and time simultaneously and the impact of the interaction of space and time on these emissions in Africa to maximize these minimal resources. To this end, this study considers spatio-temporal models fitted within the Bayesian framework to the total GHG emissions from major sectors in Africa over 27 years. Inference was based on integrated nested Laplace approximation (INLA) implemented through the R-INLA package in R.
Bayesian spatio-temporal models have proved helpful in understanding space-time dynamics of different outcomes, including infectious disease modelling (Wang et al., 2008;Raghavan et al., 2016), criminal studies (Law et al., 2014), and breastfeeding initiation and duration Gayawan and Adjei (2020). In particular, Hundera et al. (2020) studied the dynamics of land-use and land-cover, and its implication to GHGs in Adama District, Ethiopia, by adopting spatio-temporal analysis. The findings of our study will hopefully provide helpful information that will serve as guides to policymakers in curbing the continuous increase of these emissions in Africa.

Data
The data used for the study were obtained from the World Resource Institute (WRI), https://www. wri.org, responsible for the collection and keeping of climatic data. The yearly data were on the total GHGs emissions in Africa from 1990-2016, a period of 27 years. Due to the strict requirements of the spatio-temporal method adopted, an entity in the spatial component must share boundaries with one or more entities. The data on African countries sharing boundaries with at least one African country was extracted. A total of 44 countries that met the requirement were considered for this study. The total GHG emissions included in the study are CO 2 , CH 4 , N 2 O, and fluorinated gases. These GHGs excluding CO 2 are reported in their Million metric tons of CO 2 equivalent (M tCO 2 e) and summed up with CO 2 emissions to make the total GHG emissions for each country. These emissions are a combination of emissions from five sectors: agriculture, energy, industrial, land-use, and waste. The countries represent the spatial component, while the years serve as the temporal component for the analysis. Fig. 1 presents a ratio map of Africa, showing the countries included in the study.

Statistical analysis Bayesian spatio-temporal modelling
Bayesian spatio-temporal models takes into account the spatial effect, temporal effect, and the interaction between these two effects. Let Y be the vector of natural logarithm transform of GHG emissions where y ij represents the natural logarithm transform of GHG emissions at location i for i = 1, 2, 3, . . . , 44 and time j for j = 1, 2, 3, . . . , 27. y ij is assumed to be normally distributed with mean µ and variance σ 2 and is denoted as The mean µ ij of the normal distribution can be linked to the spatial and temporal effects through a linear predictor specified as: where b 0 is the intercept, u i and s i are the forms of spatial effect, φ j and γ j are the forms of temporal effects, and δ ij is the spatio-temporal interaction effect.
Various models based on the subset of the full model were explored. The purpose was to determine what could be gained or lost by fitting models without spatio-temporal interactions. The complete models are described: The first four models do not account for spatio-temporal interaction (δ ij ) while the last four models account for this. Model 1 considers the structured spatial effect (s i ) and the unstructured temporal effect (φ j ). The unstructured spatial effect (u i ) and the structured temporal effects(γ j ) are considered in Model 2. Model 3 accounts for the structured spatial and structured temporal effects. Models 1 and 2 are nested in Model 4. Unstructured spatial, unstructured temporal effects and the interaction between both effects are considered in Model 5. Models 1 and 4, with the inclusion of their interaction effects, make Model 6 and 7, respectively. Model 3 with an added interaction effect makes Model 8.
Model comparison and selection was made using the Deviance Information Criterion (DIC), defined as DIC = pD +D, where pD is the effective number of parameters, andD is the mean deviance. The model that has the smallest DIC value is selected as the model that fits the data best.

Prior specification
A Bayesian approach was adopted for inference, which requires prior specifications for all model parameters. A normal prior is assigned to the unstructured spatial and temporal components that assume no dependency among the spatial units and time points. They are modeled as independent and identically distributed (iid) with the unstructured spatial effect u i given as u i ∼ N (0, σ 2 u ), and the unstructured temporal effect φ j given as φ j ∼ N (0, σ 2 φ ). The spatially structured effects are assigned a conditional autoregressive (CAR) prior distribution that accounts for the boundary shared among countries (i.e. neighbours) and is given as where s j are neighbors of s i , σ 2 is the variance, and N (i) is the number of the neighbors of i.
A second-order random walk is assigned as a prior to the structured temporal effect to account for the temporal autocorrelation and is given as where y t is the observation at current time t, y t−1 , y t−2 are observations at previous time, and σ 2 is the variance.
The Bayesian computation was done using the Integrated Nested Laplace Approximation (INLA) Blangiardo and Cameletti (2015) to obtain posterior estimates of the model parameters.  Table 1 shows the model diagnostic statistics for the seven models fitted to the dataset. Models 2-4 without spatio-temporal interactions have similar DIC values and outperform Model 1 that considers the unstructured temporal effect and structured spatial effect. This implies that the model performs better when the temporal effect is structured or a combination of both structured and unstructured than when only the unstructured temporal effect is accounted for. Models 5-8, on the other hand, reveals the importance of capturing the spatio-temporal interactions within spatio-temporal models as they all outperform Models 1-4 except for Model 6. Results presented in Fig. 3 and Fig. 4 are based on Model 7 with the least DIC value. The intercept of Model 7 has an estimated mean of 3.6392 with a 95% credible interval (CI) of [3.6225, 3.6558]. This implies that the average total GHGs emission from the 44 African countries is estimated to be 38.0614 M tCO 2 e and is statistically significant since its 95% CI does not include zero.       1993, 1996, 2002, 2007, and 2008 respectively. The countries maintained this category until 2016, except for Sudan that fell out of the category between 2013 to 2015 and later bounced back in 2016. Countries with the least estimates of GHGs emissions in Africa over the study period are Mauritania, Gabon, Equatorial Guinea, Rwanda, Eritrea, Guinea-Bissau, Sierra-Leone, Burundi, and Djibouti. Interestingly, there was a drastic reduction in GHGs emissions from Kenya between the years 2000-2006, but there has been an increase afterward. Generally, the total GHGs emissions in Africa are increasing steadily within each country, with more countries having a high tendency to join the train of top emitters over time.

Discussions and conclusion
The increased emission of greenhouse gases has been a major concern across the globe. The importance of studying the behavior of GHGs emissions cannot be overlooked because they contribute to global warming and global warming, contributing to climate change. This study analyzed the patterns in the emissions of GHGs employing Bayesian spatio-temporal approach that considered space and time effects and the interaction between these two entities.
Different forms of spatial and temporal effects were considered in the spatio-temporal models developed in the study. Interestingly, models that accounted for the spatio-temporal interactions outperformed the models that did not account for these interactions. These interactions often provide useful and helpful information in situations where temporal trends vary spatially, and the omission of these interactions in spatio-temporal models may lead to loss of such useful information (Anderson and Ryan, 2017). Some study results on spatio-temporal modelling as well have shown that models with spatio-temporal interaction terms performed better than simpler models (Wang et al., 2008;Law et al., 2014). Our study findings reveal that the model that accounts for the structured spatial effect, structured temporal effect, and the interaction between these two effects best fit the dataset. This implies that spatial correlation and temporal correlation exist in GHG emissions from Africa across the 27 years. This may be a result of the long lifespan of these GHGs in the atmosphere. According to IPCC, the life-span of CO 2 in the atmosphere is between 5 to 200 years while the life-span of CH 4 , N 2 O, SF 6 , PFCs, and HFCs in the atmosphere are 12, 114, 3200, 50000, and 270 years, respectively.
Spatio-temporal plots were obtained due to the structured spatial effect, structured temporal effect, and spatio-temporal interaction effects considered in the model. The structured effects in the model accounted for the boundaries shared among countries. The plots revealed the impact of the boundary shared among countries on the evolution of GHGs emissions over a long period compared to a short period. Countries that are likely to have high estimates of GHG emissions throughout the study period affect the emissions of some of their neighbouring countries, particularly those that are likely to have lower estimates of GHG emissions. Some of these neighbouring countries later experienced an increase in their emissions, with some eventually having high estimates over a long period. For instance, Algeria, Egypt, and Nigeria maintained high estimates of GHG emissions over the study period. An increase in the emissions of some of their neighbouring countries such as Mali, Morocco, Niger, and Tunisia for Algeria, Cameroun, Chad, and Niger for Nigeria, and Sudan for Egypt became evident over the period. Countries that shared boundaries with these neighbouring countries also experienced an increase in their emissions after some while. For instance, an increase in emission was evident in Ethiopia and Burkina Faso, with both countries sharing boundaries with Sudan and Mali. From these findings, a collective effort among African countries is vital in reducing GHG emissions and achieving net-zero emissions, particularly among countries that share a boundary.
Furthermore, countries such as Angola, Cameroun, Democratic Republic of Congo, Nigeria, South-Africa, Tanzania, and Zambia with high estimates of GHG emission in 1990 maintained this category all through the study period. These may indicate that policies and strategies laid down in these countries to reduce and mitigate GHG emissions may not be effective enough. Therefore, these countries may need to have a re-look at the policies and probably restrategize. The majority of the GHG emissions in Zambia are traced to be from the land-use change and forestry sector, with the country being listed among those with the highest deforestation rate coupled with a projected increase in this rate (USAID, 2011). South Africa is the highest emitter of GHGs in Africa, with most of the emissions of South Africa and Angola emanating from the energy sector (USAID, 2019). Nigeria, on the other hand, is ranked the second-highest emitter of GHG after South Africa with a higher percentage of the GHG emissions of Nigeria, DRC, Tanzania, and Cameroun traced to land-use change and forestry sector(USAID, 2019). The evolution of the GHG emissions across space and time as revealed in the findings indicates that more African countries have high estimates of GHG emissions over time, with the hot-spot countries being Nigeria, DRC, Angola, Zambia, Tanzania, South Africa, Egypt, Ethiopia, Cameroun, Sudan, and Algeria. Though Africa contributes the least to global emissions, our findings show that these emissions in Africa are rapidly increasing, with more countries likely to have high GHG emissions. Individual countries in Africa have laid out plans of mitigating and reducing GHG emissions in their respective countries. For instance, South Africa, the top 20 global emitter and top Africa emitter has launched a mitigating measure called South Africa's Low Emission Development Strategy (SA-LEDS) with a focus on the sectors contributing to the emissions (Katie Capp, 2019).
In conclusion, given that reduction in GHGs emissions is vital for tackling global warming and climate change, the findings from this study can provide insight and helpful information for policymakers in mitigating and controlling GHG emissions in African countries. The spatio-temporal map has identified the impact of boundaries shared among countries on the amount of GHGs emitted over the years. Therefore, the collective efforts from countries in controlling the increase of GHG emissions in Africa will be more effective. Also, the countries that are likely to emit high GHGs are revealed in the spatio-temporal map. These countries can perhaps adopt strategies employed by countries with a low likelihood of high GHG emissions throughout the study period. Since the GHG emissions used for this study are an aggregate from the main sectors in African countries, further work can be done. For instance, a Bayesian spatio-temporal analysis of these emissions can be conducted on individual sectors such as agriculture, waste, land-use change and forestry, energy, and industry. This can help identify the various sectors that are likely to contribute most to these emissions from each African country. In addition, factors such as population size and gross domestic product can be included as covariates in the spatio-temporal models thus, providing additional explanations for the model's result.