Prediction of Surface Temperature and CO 2 Emission using a novel grey system model

The increase in surface temperature and CO 2 emissions are two of the most important issues in climate studies and global warming. The ‘Global Emissions 2021’ report identies the six biggest contributors to CO 2 emissions; China, USA, India, Russia, Japan, and Germany. The current study projects the increase in surface temperature and the CO 2 emissions of these six countries by 2028. The EGM (1,1,α,θ) grey model is an even form of the model with a rst order differential equation, that has one variable and a weightage background value that contains conformable fractional accumulation. The results show that while the CO 2 emissions for Japan, Germany, USA and Russia show a downward projection, they are expected to increase in India and remain nearly constant in China by 2028. The surface temperature has been projected to increase at a signicant rate in all these countries. By comparing with the EGM (1,1) grey model, the results show that the EGM (1,1, α, θ) model performs better in both in-sample and out-of-sample forecasting. The paper also puts forward some policy suggestions to mitigate, manage and reduce increases in surface temperature as well as CO 2 emissions. useful CO 2 emissions next three in policies to minimise CO 2 emissions by reducing unnecessary energy use. The (Lin 2011) used the grey forecasting model to anticipate future CO 2 emissions in Taiwan from 2010 to 2012. Guo et al.( 2011) conrm that the Even form of Grey Forecasting model (EGM) is a non-optimised model in its original form. Its optimisation can be improved using conformable fractional accumulation and weighted background value generation. Self-suciency is an energy resource, an essential indicator of the gap between energy supply and demand. The biofuel self-suciency of these countries is also predicted. The top CO 2 -producing countries are not only major polluters, but many of them are also major oil producers. policymakers.


Introduction
Environment and climatic conditions affect human life; with global warming drawing the attention of scientists and researchers to the rising atmospheric temperature. Global warming negatively impacts human lives in terms of rising sea levels and the increasing number of extreme events (Melillo et al., 2014); while air temperature directly affects the land surface (Tajfar, Bateni, Lakshmi, et al., 2020), (Valipour et al., 2020) (Tajfar, Bateni, Margulis, et al., 2020). Health issues emerge due to variations in temperature (Lan et al., 2010), (Schulte et al., 2016), which also causes ora and fauna loss. An appropriate approach for air temperature prediction may help reduce the consequences of climate change and global warming. It can also play a vital role in framing policy for various business activities and energy-related matters. Nowadays, extreme weather is a common phenomenon that is being more frequently observed. Therefore, it is necessary to understand the changes in the weather condition. Temperature plays an important role in weather forecasting. Temperature prediction ability is useful for various activities performed in the future that determine economic abilities and ecological phenomenon (Sharma et al., 2011), (Sardans et al., 2006). Under climate change, temperature forecasting is an important research area. It is useful in understanding the macroscopic evolutionary processes, and also provides a signi cant reference source for sustainable economic development (H. Wang et al., 2019). Akram & El (2016) show that the LSTM based neural networks perform better in temperature prediction. H. Wang et al. (2019) used VMD-ARIMA model, ARIMA model, and Grey Model (1, 1) and found that VMD-ARIMA provides more accurate forecasts. Kärner (2009) advocate an intensive study for the short-term changes in different climate zones and total solar irradiance at the topmost of the atmosphere and surface air temperature series. Studies have been performed using ARIMA and its similar methods to predict weather conditions. Prybutok Peng et al. (2020) to improve the prediction skills of the 2-m maximum air temperature with lead times of 1-35 days over East Asia. Post-processing approaches may effectively reduce prediction biases and uncertainties in the rst two weeks during the validation phase. Neural networks and NGBoost perform as the best models in more than 90% of the study area (Peng et al., 2020). Cifuentes et al. (2018) describe the development and application of data-intelligent models for air temperature estimation without climate-based inputs, using only geographic factors in a large spatial region in central India. The GRNN model is a quali ed data-intelligent tool for temperature estimation without the need for climate-based inputs. This model can be investigated for its utility in energy management, building and construction, agriculture, heatwave studies, health, and other socio-economic areas, particularly forestry. LSTM and Facebook Prophet have been used to simulate the forecast of ve-year daily air temperatures in Bandung. The results reveal that Prophet outperforms LSTM on maximum air temperature (Toharudin et al., 2021). and metal rms and analyse and measure the change in productivity in these industries. The study contributes to a better understanding of India's mining industry, which is vital to the country's economy (S. Liu et al., 2012). Faghih Mohammadi Jalali & Heidari (2020) used the grey system theory to forecast Bitcoin's price and changes in their research. Lin et al. (2011) indicated that CO 2 emissions would rise over the next three years in Taiwan. It is a useful reference for the Taiwanese government to develop policies to minimise CO 2 emissions by reducing unnecessary energy use. The study (Lin et al., 2011) used the grey forecasting model to anticipate future CO 2 emissions in Taiwan from 2010 to 2012. Guo et al.( 2011) con rm that the Even form of Grey Forecasting model (EGM) is a non-optimised model in its original form. Its optimisation can be improved using conformable fractional accumulation and weighted background value generation. Self-su ciency is an energy resource, an essential indicator of the gap between energy supply and demand. The biofuel selfsu ciency of these countries is also predicted. The top CO 2 -producing countries are not only major polluters, but many of them are also major oil producers.
(X. Wang et al., 2014). Studying and understanding their behaviour is important for general readers, environmentalists, biofuel dealers, and energy policymakers. Furthermore, even though grey forecasting models have been widely used in energy projections (including renewable energy), we are aware of only a few instances where they have been used to anticipate biofuels. The current work is notable in theory and application because it is the rst attempt to estimate Surface temperature change and CO 2 emission using a unique grey forecasting model, EGM (1, 1, α, θ), which generalised the classical model EGM (1,1).

Methodology
Grey forecasting enables one to extract helpful insights about the future from small data, which can be as small as four and can be used for both short term are two of the four basic models of grey forecasting theory. EGM is suitable for making predictions through non-exponential increasing data sequence, while DGM is suitable for making predictions through a homogenous exponential data sequence (D. Liu, 2017). DGM and EGM can be considered as different forms of the same model (Naiming & Sifeng, 2005). To execute these models, the minimum requirement for data is at least four, as proven from literature. Raw data contains noise, thus considering its direct use in grey forecasting theory, where the sample size is usually small with signi cant noise in raw data, can decrease forecast accuracy, Professor Julong Deng introduced the concept of accumulation of raw data (and inverse accumulation of the simulation of raw data) (Deng, 2004). In both Even and Discrete forms of GM (1,1), the data accumulation is usually done through the "once accumulating generation operator" (1-AGO), which is basically a cumulative sum operator. If the sequence of raw data is where, x (1) Even though 1-AGO is popular for data in grey prediction approaches, its limitations have prevented the application of GM (1,1) series models in various complicated situations, thus prompting scholars to propose alternative operators for data accumulation. One such fruitful attempt was recently made by Ma EGM (1, 1,α, θ) represents the even form of a grey model with a rst-order differential equation containing one variable and weighted background value containing conformable fractional accumulation. Let the sequence of actual data be where, In the classical, even grey model, α = 1, however, in EGM(1,1,α, θ), α, ∈ (0,1).
The Adjacent neighbour average sequence of X ( 1 ) will be , k = 1, 2, . . . . , n (14) There has been a rise in temperature around the world since the 1980s. Developments in Europe, North America, and Asia are particularly notable, where there are sometimes signi cant temperature increases. On the other hand, in the countries of Oceania, the trend has even been declining for several years. Antarctica is not included here due to a lack of consistent data series. However, there too we can clearly observe a stagnation in the temperature increase (with restrictions). The Germanwatch Institute presented the Global Climate Risk Index 2020. Due to the impacts of extreme weather, the places most affected today by climate change are Japan, the Philippines, and Germany (Eckstein, 2019, p. 20).
The balance between entering and exiting energy is an essential factor for the earth's temperature. Natural and human factors can disrupt the earth's energy these together contribute around 63 percent in total CO 2 emissions worldwide (Ortega, 2021), (UCSUSA, 2020). However, surface temperature data for the current study has been collected from FAOSTAT (2021) for the period 2010-20 and CO 2 emission data for the period 2009-2019 from World Data Bank 2021.

Accuracy Measurement Methods
In the literature, various performance measures have been proposed in order to determine the accuracy of the forecasting approaches. In the current study, ve performance measures such as normalized mean absolute percentage error (NMAPE), mean absolute percentage error (MAPE), mean square error (MSE), root mean square error (RMSE), and normalized root mean square error (NRMSE) has been used to measure the accuracy of GM (1,1) and EGM (1,1,α,θ). The following equations show the calculation of the performance measures: The Mean Square Error is Where, A t = Actual values at data time t, and F t =forecast value at data time t Where N denotes the number of samples, is the model forecast value, is the real value, and is the mean value of y i . long-term sustainable development, as shown in Fig. 1 and Table 1. Generally, the trend is increasing; however, this increasing trend is relatively more for surface temperature than CO 2 emission. Germany is projected to produce 8.55 metric ton CO 2 emissions per capita, which will increase surface temperature by 6.07 Celsius by 2028, as shown in table 1. Further, as shown in Fig. 2, positive changes in CO 2 emissions are almost stagnant, while surface temperature is rapidly changing. It is important for German policymakers to decide to maintain the changes in surface temperatures.

Results And Discussion
Although an economic shutdown, renewable energy use has led to reduced CO 2 emissions in four decades in India for some time (IEA,2020). But a study conducted by Koshy (2021) said that India's CO 2 emission rose faster than that the world average. In the current study, India is expected to produce CO 2 emissions of 2.95 metric tones per capita and 3.58 Celsius increase in surface temperature. As Fig. 3 shows, there is a large uctuation in the actual value of India's surface temperature, which explains a relatively larger error in the prediction. CO 2 emission per capita in metric tones in Japan is projected to be 8.90, followed by 10.77 in Russia and 13.48 in USA by 2028. They are top in per capita CO 2 emission worldwide, as shown in table 2-3. There is an urgent requirement to take immediate actions to manage climate change and mitigate greenhouse gases (GHGs).
To accomplish the target of carbon neutrality, a downward modi cation of economic growth is essential, which will help the country decrease pollution emissions. Japan is trying to use innovative ideas to reduce CO 2 (Yang et al., 2021) suggested that in the long-run output, renewable energies, green growth, and globalisation are signi cant factors in affecting CO2 emission in the USA. Beijing has taken the initiative to control the growth of private vehicles to reduce CO2 emissions (Li & Jones, 2015). As shown in Fig. 4-6 (right-Fig.), the trend of CO2 emission in Japan, Russia, and the USA is moving in a downwards direction and is expected to decrease in  there is a need to take su cient initiative to reduce CO 2 emissions (Safonov et al., 2020). Generally, the trend is increasing for Surface temperature in Japan, Russia, and the USA. However, the trend is relatively less predictable compared to CO 2 emission in these countries, which will yield a larger error in the forecasting process of surface temperatures. The accuracy level of the grey system theory models: GM (1, 1) and EGM (1, 1, α, θ) has been showsn in Table 4 & 5.  (Sardans et al., 2006). This study also nds that the EGM (1,1,α,θ) grey model performs better than the EGM (1,1) grey model in terms of both in-sample and out of sample testing.
The current work is limited to the top six countries in terms of GHG emissions as per the Germanwatch Institute's Global Climate Risk Index 2020. Further studies including the impact of lockdowns on CO 2 emissions, along with predicting the general trend of all the other major GHG emissions. The study can also be extended in scope to include other countries of the world, especially predications for the major developing countries of the world and oil-exporting countries.

Policy Suggestions
The results of the current study point to an important trend in surface temperature changes, which is a major issue at the gobal as well as national levels. The increase of surface temperature is an increasingly concerning issue that affects a range of factors that concern human life as well as ora and fauna. These, therefore, in conjunction with GHG and particularly CO 2 emissions, need to be addressed by governments and other stakeholders. The following suggestions are hereby forwarded. First, with reference to GHG and CO 2 emissions, the governments must put into place strategic and comprehensive plans that ensure lower emissions without compromising on the quality of economic growth and human development. Such strategies are already in force in Japan, particularly in the iron and steel industry. More countries should adopt such measures and innovate keeping in mind their local constraints and the larger public interest. Second, to reduce GHG and CO 2 emissions, the governments should take into consideration the risk-reward tradeoff for all the major stakeholders. The adoption of strategies that are based on an active participation of stakeholders will ensure maximum participation and minimum need for control and intervention. Third, to reduce the overall emissions, governments can adopt strategies that are based on the relative contribution of speci c sectors. Such an approach will give maximum results with the acknowledgement of target areas and help in devising detailed, innovative and focused solutions.
Fourth, with respect to the rising surface temperatures for nearly all the six countries under study, an attempt must be made to bring down surface temperature, and avoid promotion of industries and sectors that contribute highly to GHG emissions. An important consideration along with reducing GHG emissions, is the increase of forest area and green cover. Finally, to mitigate rising surface temperatures, the governments should foucs on switching to renewable energy and low-emission energy sources and roll out such policies in a phased manner. The adoption of a series of detailed and short and medium term phased plans are more effective than broad and vague long term goals.