Quantifying the Climate Impact of Food Systems: A Time-Series Analysis for Policy and Food Security

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Methods: Using FAO Food Balance Sheets, the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D), and Global Data Lab temperature data from 2010 to 2021, we constructed country- and food-group–level time-series datasets. Analytical methods included time-series visualization, autocorrelation and partial autocorrelation (ACF/PACF) analysis, ARIMA modelling, and time-series regression. Findings: Results demonstrated a significant co-movement between food system–related GHG emissions and global mean temperature, with regression analysis indicating that a 1,000 Mt increase in emissions corresponded to a 0.039°C rise (p < 0.05, R² = 0.37). ARIMA forecasts further suggest a structural upward trend in emissions, increasing by ~975 Mt annually. Interpretation: These findings highlight the causal link between food production–based GHG emissions and climate change, identify climate-sensitive food categories, and provide quantitative evidence to support national dGHG reduction targets and climate-responsive food security policies. Funding: This work was supported by a National Research Foundation of Korea grant funded by the Korean government (No. RS-2024-00340840). Earth and environmental sciences/Climate sciences Earth and environmental sciences/Environmental sciences Earth and environmental sciences/Environmental social sciences Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The world’s food systems lie at the nexus of two defining global challenges: climate change and food security. The United Nations 2030 Agenda for Sustainable Development underscores this interconnection across multiple goals—ending hunger and promoting sustainable agriculture (Goal 2), ensuring healthy lives and well-being (Goal 3), and taking urgent action to combat climate change and its impacts (Goal 13) 1 , 2 . Within this framework, food systems—encompassing all processes from production through processing, distribution, consumption, and disposal—play a dual role: they are both a major driver of greenhouse gas (GHG) emissions and one of the most climate-vulnerable sectors. Food system–related activities account for approximately one-third of total anthropogenic GHG emissions, primarily through agricultural production, land-use change, and energy-intensive processing, packaging, and transportation 1 , 3 . According to the Food and Agriculture Organization (FAO), agrifood systems emitted nearly 18 Gt CO₂-equivalent in 2015, representing about 34% of global emissions 3 . These emissions originate from multiple stages across the “farm-to-fork” continuum, including crop and livestock production, post-harvest processing, transport, packaging, and waste management 1 . As global food demand continues to grow, the contribution of these systems to atmospheric GHG accumulation is projected to intensify unless transformative mitigation measures are implemented. At the same time, climate change increasingly threatens the very foundations of food security. Rising global temperatures and shifting precipitation patterns reduce agricultural productivity, crop yields, and nutritional quality, while greater climate variability destabilizes food availability and ecosystem resilience 1 , 4 . According to the U.S. Environmental Protection Agency (EPA), increasing temperatures are projected to decrease yields of key commodity crops such as maize, rice, and oats 5 . This interplay forms a self-reinforcing feedback loop: food systems contribute to global warming, and global warming, in turn, undermines the stability and sustainability of food systems themselves 1 , 2 . Despite the clear significance of this feedback, empirical analyses of how food system emissions and climate indicators evolve together over time remain limited. Most previous research has relied on static or cross-sectional assessments of carbon footprints associated with specific foods, production processes, or dietary patterns 6 , 7 . While these studies have been instrumental in quantifying the environmental intensity of individual foods, they provide only temporally constrained insights and rarely capture the dynamic, structural evolution of national food system emissions. Consequently, the temporal co-movement between food system GHG emissions and climate variables such as global mean temperature remains poorly understood. Moreover, none of the studies have investigated the autoregressive behavior and temporal persistence of food system emissions, or tested whether these emission trajectories exhibit statistically significant correlations with long-term global temperature trends. This absence of longitudinal evidence limits our understanding of the structural risks posed by sustained food production–related emissions and their cumulative influence on climate change 8 . Bridging this gap is essential to support climate-resilient food system strategies, align national mitigation targets with the Paris Agreement, and provide a scientific foundation for data-driven policymaking under the Sustainable Development Goals (SDGs) 9 . Against this background, the present study conducts a time-series analysis to investigate the relationship between food system GHG emissions and global mean temperature from 2010 to 2021. Drawing on harmonized datasets from the FAO Food Balance Sheets (FBS) 10 , the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D) 11 , and Global Data Lab (GDL) temperature records 12 , the analysis explores the structural association and co-movement between emission trajectories and climate variability. By identifying the autoregressive nature of global food system emissions and their statistically significant influence on temperature rise, this study provides empirical evidence of the climate impact of food production systems and highlights the urgent need for targeted emission-reduction strategies to mitigate long-term climate risks. Materials and Methods Data Sources Food Supply and Production Data This study primarily utilized data from the FAO FBS to quantify food production and supply at the national level. Although multiple international data sources were initially considered, inconsistencies in data collection methods, temporal coverage, and definitional units made direct comparison difficult. Therefore, FAO data were adopted exclusively because of their high reliability, standardized definitions, and long-term temporal consistency, making them suitable for time-series analysis. The FAO FBS provides harmonized statistics on food supply and utilization by commodity and country. For this analysis, data were collected for 175 countries between 2010 and 2021, covering 98 standardized food groups based on the official FAO classification. Greenhouse Gas Emission Factors Food system–related GHG emissions were estimated using the FS-GHGEF-D, developed in 2024 by the corresponding author. This database contains 3,894 food items with system-level emission factors expressed as kg CO₂ eq per ton of product, encompassing all life-cycle stages from production through distribution and waste management. Each FS-GHGEF-D item was reclassified into the FAO’s 98 food groups, and average emission factors were computed for each group. GHG emissions (Mt CO₂ eq) were then calculated by multiplying the emission factor (kg CO₂ eq / ton) by the corresponding national production quantity (ton) for each food group, country, and year. Temperature Data Annual mean temperature data were obtained from the GDL, which provides standardized national-level climate indicators suitable for time-series analysis. While data from the World Meteorological Organization and national meteorological stations were initially reviewed, these sources exhibited irregular reporting intervals, inconsistent units, and missing annual means. The GDL dataset was therefore selected for its continuity, accessibility, and harmonized country-year structure. For countries included in the FAO dataset but not present in the GDL records, annual mean temperatures were estimated using a distance-weighted interpolation model combined with latitude and elevation–based regression correction to ensure spatial coherence and minimize data gaps 13 , 14 . Data Processing and Integration All datasets were standardized and merged into a long-format time-series structure at the country–year–food group level. FAO production quantities and FS-GHGEF-D emission factors were linked to compute country-level food system GHG emissions. Temperature data were aligned by year to ensure consistency across datasets. All variables were expressed in metric units—GHG emissions in million tons of CO₂ eq (Mt CO₂ eq) and temperature in degrees Celsius (°C). Statistical Analysis All statistical analyses were conducted using R software (version 4.3.2; R Foundation for Statistical Computing, Vienna, Austria). Data preprocessing, visualization, and model fitting were performed using the tidyverse, forecast, and ggplot2 packages. Analytical procedures were designed to examine the temporal dynamics and interdependence between food system GHG emissions and global mean temperature over the period 2010–2021. Annual global totals of food system GHG emissions were calculated by aggregating country-level estimates, while global mean temperature was computed as the population-weighted average of national mean temperatures for each corresponding year 15 . Both indicators were plotted on a dual-axis time-series graph—emissions on the left axis (Mt CO₂ eq) and temperature on the right axis (°C)—to visually assess long-term trends and the degree of temporal co-movement between the two variables. The temporal structure of global food-system GHG emissions was analyzed using time-series statistical methods. The internal dependency and autocorrelation patterns of the emission series were examined through the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify autoregressive behavior and non-stationarity 16 . Based on these diagnostics, an autoregressive integrated moving average (ARIMA) model was specified and fitted to the differenced annual data 17 . A series of candidate ARIMA models was tested, and model selection followed the minimum Akaike Information Criterion (AIC) 18 . Because the dataset consisted of annual observations without seasonal variation, Seasonal ARIMA (SARIMA) models were excluded 18 . Model adequacy was assessed using standard fit metrics, including Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE), alongside residual autocorrelation checks 19 . Subsequently, a linear time-series regression model was applied to estimate the statistical association between annual food-system GHG emissions and global mean temperature 20 . In this regression, temperature (°C) was treated as the dependent variable, and total annual emissions (Mt CO₂-eq) as the independent variable. Results Trends in Global Food System GHG Emissions and Temperature Between 2010 and 2021, global GHG emissions from food production systems showed a consistent upward trajectory (Fig. 1 ). Annual emissions increased from approximately 13.7 Gt CO₂ eq in 2010 to over 17.9 Gt CO₂ eq in 2021, with an average annual growth rate of 2.8%. During the same period, the global mean surface temperature increased from 14.6°C to 15.0°C, corresponding to a rise of 0.4°C. Dual-axis time-series visualization showed that GHG emissions (left y-axis, Mt CO₂ eq) and global mean temperature (right y-axis, °C) exhibited parallel upward movements throughout the observation period. Autocorrelation Structure of Emissions ACF and PACF analyses indicated significant short-term persistence in food system GHG emissions (Fig. 2 ). Positive autocorrelation was observed at lags 1 to 3, while coefficients gradually decreased after lag 4. The PACF plot showed a sharp decline after the first lag, supporting the inclusion of an autoregressive component in the model. These findings confirmed that the series was non-stationary, and first differencing was required before model fitting. ARIMA Model Performance and Forecasting After differencing the non-stationary series, several ARIMA models were tested. The ARIMA(1, 1, 0) with drift model achieved the lowest AIC (AIC = 205.22) (Table 1 ). Model residuals showed no significant autocorrelation. Table 1 Summary of ARIMA(1,1,0) Model Results Item Value Model type ARIMA(1,1,0) with drift AR(1) coefficient – 0.8482 Drift + 975.20 Mt per year AIC 205.22 MAPE 4.83% RMSE 1,872.89 Mt Model fit statistics indicated satisfactory performance, with MAPE = 4.83% and RMSE = 1,872.89 Mt CO₂ eq. The drift term (+ 975.2 Mt per year) represented a steady annual increase in emissions. Forecasts based on the selected model indicated continued growth, with total global food system emissions projected to reach approximately 19.8 Gt CO₂ eq by 2025 under current trajectories (Fig. 3 ). Relationship Between GHG Emissions and Global Temperature A linear time-series regression was conducted to examine the statistical association between annual food system GHG emissions and global mean temperature (Table 2 ). The regression coefficient was β = 3.87 × 10⁻⁵ (p = 0.0357, R² = 0.3704). Table 2 Summary of Regression Analysis Between GHG Emissions and Temperature Item Value Regression coefficient (slope) + 3.865 × 10⁻⁵ ( ≈ + 0.000039) p-value 0.0357 R² 0.3704 (Explained variance: 37%) This indicates that an increase of 1,000 Mt CO₂ eq in global food system emissions corresponded to an estimated 0.039°C rise in global mean temperature during the study period (Fig. 4 ). Model assumptions were confirmed through residual diagnostics and autocorrelation checks. Discussion Across 175 countries (2010–2021), global food-system GHG emissions increased steadily and exhibited short-lag persistence consistent with an autoregressive process. Visual inspection revealed co-movement between emissions and global mean temperature, which was corroborated by a statistically significant linear association (β = 3.87 × 10⁻⁵; p = 0.0357; R² = 0.3704). The preferred ARIMA(1,1,0) model with drift captured the emissions trajectory with acceptable forecast error, and the positive drift (+ 975 Mt CO₂-eq yr⁻¹) indicates a structural upward trend over the study window. These results directly address the study’s objective to quantify temporal structure in food-system emissions and its statistical linkage to temperature, building on and extending a literature that has largely emphasized static footprints of foods and diets rather than longitudinal dynamics 3 , 7 . The choice of a non-seasonal ARIMA(1,1,0) with drift model was both methodologically and scientifically appropriate for analyzing annual global food-system GHG emission data. Given that the data are annual, seasonal components are neither observable nor theoretically expected at a 12-month resolution; therefore, excluding SARIMA avoids over-parameterization and enhances interpretability 15 . The ACF and PACF structures—showing short-lag positive autocorrelation and a PACF cut-off at lag 1—are consistent with an AR(1) term on the differenced series, supporting the selection of an ARIMA(1,1,0) specification. This conforms to the Box–Jenkins framework, in which differencing addresses non-stationarity and an AR(1) term captures short-run persistence 21 . Model diagnostics confirmed adequacy and robustness: the chosen model minimized the Akaike Information Criterion (AIC), achieved low forecast errors (MAPE = 4.83%, RMSE = 1,872 Mt CO₂-eq), and exhibited white-noise residuals with no remaining autocorrelation, satisfying standard criteria for time-series model validation 22 . The drift term (+ 975 Mt yr⁻¹) represents a persistent upward trajectory in global agrifood emissions, reflecting structural inertia rather than short-term variability. Comparable applications of ARIMA frameworks to national CO₂ and temperature series further validate this model’s suitability for aggregated environmental data. Overall, the ARIMA(1,1,0) with drift provides a parsimonious yet rigorous representation of long-term persistence and stochastic dynamics in food-system GHG emissions—capturing both the autoregressive behavior and deterministic upward trend characteristic of global production and supply-chain activities. The observation of a positive drift term in the ARIMA(1,1,0) model (+ 975 Mt CO₂-eq per year) reflects more than a short-term fluctuation: it captures a persistent mean increase in global production-based food-system emissions. This methodological choice is scientifically justified because structural features of the food system—such as capital investment in production and processing, logistics networks, packaging infrastructure, and food-waste streams—adjust only gradually over time. Empirical inventories indicate that food systems account for roughly one-third of anthropogenic GHG emissions; FAO data, for instance, estimated ~ 18 Gt CO₂-eq in 2015 (~ 34% of global total) 3 . Moreover, recent analysis shows that emissions from pre- and post-production stages (manufacturing, packaging, transport, retail, waste) have doubled in many regions and now exceed those from the farm gate alone 23 . This growing dominance of supply-chain emissions provides a mechanistic rationale for the observed autoregressive persistence: as processing, transport, and waste systems evolve slowly, each year’s emissions become the baseline for the next. In other words, the drift captures structural increase (deterministic trend) while the AR(1) term captures inertia (stochastic persistence). The model thus aligns with known system behaviour: as food systems industrialize, grow, and globalize, incremental gains alone are unlikely to reverse emission trajectories without systemic transformation. Reviews of food-supply-chain impacts (e.g., OECD 2022) reinforce that environmental burdens accrue not only at farm level but primarily in logistics, processing, and waste phases—exactly the sectors contributing to the drift 24 . From the perspective of climate mitigation, the drift underscores that food-system emissions are not simply seasonal or cyclical but reflect compounded growth 24 . Accordingly, models of food-system emissions should capture both long-run trends and short-term persistence; the ARIMA(1,1,0) with drift accomplishes this by combining differencing, autoregression, and deterministic growth. It is methodologically sound and conceptually coherent in the context of global food systems. Future research could explore whether the drift magnitude differs by food-group, region or supply-chain segment, thereby informing targeted mitigation policy. Linking annual temperature to annual food-system emissions provides a broad, first-order assessment of their relationship. Although this approach is associative rather than causal, the observed positive slope is scientifically consistent with fundamental climate dynamics: cumulative greenhouse gases—particularly CO₂, CH₄, and N₂O—enhance radiative forcing, trapping infrared radiation and raising global mean surface temperature 25 . The magnitude and direction of the association are plausible given that food systems contribute roughly one-third of anthropogenic GHGs 3 , with emissions rising steadily from both agricultural and pre-/post-production stages 23 . The regression relationship thus provides empirical coherence between environmental physics and socio-industrial trends: as food production expands, CO₂ from energy use, CH₄ from livestock and rice cultivation, and N₂O from fertilizers together amplify warming 1 . Though the model is ecological and not mechanistic, the consistent statistical association aligns with physical causation already established by radiative forcing theory. It captures how long-lived atmospheric GHGs accumulate year-to-year, integrating the systemic inertia of global food systems into the broader climate trajectory. High-impact syntheses quantify the environmental intensity of foods and producers and position food systems as a major mitigation arena 7 , but most evidence is static or cross-sectional. Our study contributes the missing temporal dimension at global scale, illuminating persistence and co-movement with temperature over time 7 , 26 . The upward pressure from non-farm segments documented in FAO/EDGAR-FOOD updates aligns with the positive drift we observe 3 , reinforcing that the detected signal reflects systemic behavior rather than a modeling artifact 27 . The SDG and planetary-health discourse emphasizes the interdependence of food security and climate stabilization. By quantifying temporal structure and linkage to temperature, our results provide empirical scaffolding for integrating explicit food-system targets within national mitigation plans and monitoring frameworks 4 . Crippa et al. (EDGAR-FOOD) report that agriculture and land-use/land-use change dominate food-system emissions, with substantial contributions from retail, transport, consumption, fuel production, waste, and packaging—sectors that evolve slowly, supporting the persistence we observe. FAO’s agrifood accounts similarly position food systems near one-third of global GHGs 3 . Micro-level studies link foods and diets to environmental burdens and health outcomes (e.g., Poore & Nemecek’s producer heterogeneity; Clark et al.’s health-environment trade-offs; recent product-level environmental scores), collectively underscoring that mitigation potential exists but is uneven across categories. Our macro time-series complements these studies by showing that, in aggregate, the global food system exhibits inertia that requires structural policy interventions 7 , 28 . Recent reviews on decarbonizing agriculture highlight methane/nitrous-oxide abatement, fertilizer management, and energy shifts in processing/logistics as high-leverage options—consistent with the sectors contributing to persistence in system emissions 29 . The measured drift suggests that efficiency-only approaches are unlikely to bend the curve rapidly. Production-side priorities include CH₄/N₂O mitigation (enteric fermentation, manure, rice), fertilizer optimization and nitrification inhibitors, low-carbon process heat/electricity in processing, and loss/waste reduction along supply chains. These align with the documented distribution of emissions across the “farm-to-fork” continuum. Incorporating explicit food-system modules into NDCs and national MRV systems would enable tracking of “desired GHG reduction (dGHG)” trajectories by food group and process stage 3 . This study offers several methodological and conceptual strengths. First, its scope and harmonization enhance external validity: it encompasses 175 countries over a 12-year period (2010–2021), using harmonized FAO food-supply and production statistics combined with a systematic item-to-group mapping of emission factors from the FS-GHGEF-D database. This large and consistent dataset provides a rare global longitudinal view of food-system GHG dynamics. Second, the temporal focus represents a key innovation. By separately modeling emissions dynamics through an ARIMA framework and assessing their relationship with temperature via regression analysis, the study distinguishes between internal persistence and inter-variable association, thereby avoiding the conflation of correlation and serial dependence often found in static footprint analyses. Third, the model transparency strengthens reproducibility: model selection relied on the AIC, while performance was evaluated using standard error metrics (MAPE, RMSE) and residual autocorrelation diagnostics, consistent with established time-series modeling practices in environmental and climate research. Nonetheless, several limitations should be acknowledged. First, causality cannot be inferred because the temperature regression is bivariate and does not partition contributions from other emission sectors or exogenous forcings. Second, the use of global aggregation may obscure heterogeneity in emission drivers and elasticities across regions and food categories. Third, measurement uncertainty arises from the averaging of emission factors within 98 FAO food groups and from differences in system boundaries—such as whether land-use change and upstream inputs are included. Fourth, the accounting perspective is production-based; thus, it does not reflect emissions embodied in international trade or consumption-based patterns. Finally, the temporal span of 2010–2021 may omit longer-term structural shifts or policy shocks, and the use of annual data precludes analysis of seasonal variability. To enhance robustness and extend this line of inquiry, several future research directions are proposed. First, greater econometric depth could be achieved through unit-root and cointegration testing (ADF, KPSS; Engle–Granger or Johansen), heteroskedasticity- and autocorrelation-consistent (HAC) inference, structural break detection (Bai–Perron), and alternative dynamic specifications such as ARDL, distributed-lag, or structural time-series models. Second, panel time-series modeling at the country level (e.g., panel ARDL or dynamic common correlated effects) would allow estimation of heterogeneous elasticities linked to structural features such as livestock intensity, rice cultivation, fertilizer use, and energy mix. Third, process-level and food-group decomposition could attribute temporal changes to farm-gate versus post-production stages and to specific food groups, guiding prioritization of “desired GHG reduction” (dGHG) pathways. Finally, future work should pursue integration with diet and health models, coupling production-side emission dynamics with consumption patterns and health outcomes to align food-system mitigation with planetary-health and sustainability objectives 4 , 26 . Declarations Conflicts of interest The authors have no conflicts of interest to declare. Funding This work was supported by the National Research Foundation of Korea grant funded by the Korea government (No. RS-2024-00340840). Funding: This work was supported by a National Research Foundation of Korea grant funded by the Korean government (No. RS-2024-00340840). Author Contribution Jee Yeon Hong : Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Software; Resources; Validation; Visualization; Project administration; Supervision; Writing – original draft; Writing – review & editing Data Availability All data used in this study are publicly available from established open-access sources.Food production and supply data were obtained from the FAO Food Balance Sheets (FBS).Food system greenhouse gas emission factors were sourced from the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D) developed by the authors and available upon reasonable request.Global mean temperature data were accessed from the Global Data Lab climate dataset.The processed time-series datasets and analysis scripts generated during this study are available from the corresponding author on reasonable request. References IPCC. 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Environmental impacts along food supply chains: Methods, findings, and evidence gaps. Paris: OECD Publishing, 2022. Etminan M, Myhre G, Highwood EJ, Shine KP. Radiative forcing of carbon dioxide, methane, and nitrous oxide: a significant revision of the methane radiative forcing. Geophysical Research Letters 2016; 43(24): 12614–23. Clark MA, Springmann M, Hill J, Tilman D. Multiple health and environmental impacts of foods. Proc Natl Acad Sci U S A 2019; 116(46): 23357–62. FAO. Greenhouse gas emissions from agrifood systems: Global, regional and country trends, 2000–2020 (FAOSTAT Analytical Brief No. 50). Rome: FAO, 2023. Clark M, Springmann M, Rayner M, et al. Estimating the environmental impacts of 57,000 food products. Proc Natl Acad Sci U S A 2022; 119(33): e2120584119. Kazimierczuk K, Barrows SE, Olarte MV, Qafoku NP. Decarbonization of Agriculture: The Greenhouse Gas Impacts and Economics of Existing and Emerging Climate-Smart Practices. ACS Eng Au 2023; 3(6): 426–42. 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The United Nations 2030 Agenda for Sustainable Development underscores this interconnection across multiple goals\u0026mdash;ending hunger and promoting sustainable agriculture (Goal 2), ensuring healthy lives and well-being (Goal 3), and taking urgent action to combat climate change and its impacts (Goal 13) \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Within this framework, food systems\u0026mdash;encompassing all processes from production through processing, distribution, consumption, and disposal\u0026mdash;play a dual role: they are both a major driver of greenhouse gas (GHG) emissions and one of the most climate-vulnerable sectors.\u003c/p\u003e \u003cp\u003eFood system\u0026ndash;related activities account for approximately one-third of total anthropogenic GHG emissions, primarily through agricultural production, land-use change, and energy-intensive processing, packaging, and transportation \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. According to the Food and Agriculture Organization (FAO), agrifood systems emitted nearly 18 Gt CO₂-equivalent in 2015, representing about 34% of global emissions \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. These emissions originate from multiple stages across the \u0026ldquo;farm-to-fork\u0026rdquo; continuum, including crop and livestock production, post-harvest processing, transport, packaging, and waste management \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. As global food demand continues to grow, the contribution of these systems to atmospheric GHG accumulation is projected to intensify unless transformative mitigation measures are implemented.\u003c/p\u003e \u003cp\u003eAt the same time, climate change increasingly threatens the very foundations of food security. Rising global temperatures and shifting precipitation patterns reduce agricultural productivity, crop yields, and nutritional quality, while greater climate variability destabilizes food availability and ecosystem resilience \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. According to the U.S. Environmental Protection Agency (EPA), increasing temperatures are projected to decrease yields of key commodity crops such as maize, rice, and oats \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. This interplay forms a self-reinforcing feedback loop: food systems contribute to global warming, and global warming, in turn, undermines the stability and sustainability of food systems themselves \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDespite the clear significance of this feedback, empirical analyses of how food system emissions and climate indicators evolve together over time remain limited. Most previous research has relied on static or cross-sectional assessments of carbon footprints associated with specific foods, production processes, or dietary patterns \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. While these studies have been instrumental in quantifying the environmental intensity of individual foods, they provide only temporally constrained insights and rarely capture the dynamic, structural evolution of national food system emissions. Consequently, the temporal co-movement between food system GHG emissions and climate variables such as global mean temperature remains poorly understood.\u003c/p\u003e \u003cp\u003eMoreover, none of the studies have investigated the autoregressive behavior and temporal persistence of food system emissions, or tested whether these emission trajectories exhibit statistically significant correlations with long-term global temperature trends. This absence of longitudinal evidence limits our understanding of the structural risks posed by sustained food production\u0026ndash;related emissions and their cumulative influence on climate change \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Bridging this gap is essential to support climate-resilient food system strategies, align national mitigation targets with the Paris Agreement, and provide a scientific foundation for data-driven policymaking under the Sustainable Development Goals (SDGs) \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAgainst this background, the present study conducts a time-series analysis to investigate the relationship between food system GHG emissions and global mean temperature from 2010 to 2021. Drawing on harmonized datasets from the FAO Food Balance Sheets (FBS) \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D) \u003csup\u003e11\u003c/sup\u003e, and Global Data Lab (GDL) temperature records \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, the analysis explores the structural association and co-movement between emission trajectories and climate variability. By identifying the autoregressive nature of global food system emissions and their statistically significant influence on temperature rise, this study provides empirical evidence of the climate impact of food production systems and highlights the urgent need for targeted emission-reduction strategies to mitigate long-term climate risks.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eData Sources\u003c/h2\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003eFood Supply and Production Data\u003c/h2\u003e \u003cp\u003eThis study primarily utilized data from the FAO FBS to quantify food production and supply at the national level. Although multiple international data sources were initially considered, inconsistencies in data collection methods, temporal coverage, and definitional units made direct comparison difficult. Therefore, FAO data were adopted exclusively because of their high reliability, standardized definitions, and long-term temporal consistency, making them suitable for time-series analysis.\u003c/p\u003e \u003cp\u003eThe FAO FBS provides harmonized statistics on food supply and utilization by commodity and country. For this analysis, data were collected for 175 countries between 2010 and 2021, covering 98 standardized food groups based on the official FAO classification.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e\n\u003ch3\u003eGreenhouse Gas Emission Factors\u003c/h3\u003e\n\u003cp\u003eFood system\u0026ndash;related GHG emissions were estimated using the FS-GHGEF-D, developed in 2024 by the corresponding author. This database contains 3,894 food items with system-level emission factors expressed as kg CO₂ eq per ton of product, encompassing all life-cycle stages from production through distribution and waste management. Each FS-GHGEF-D item was reclassified into the FAO\u0026rsquo;s 98 food groups, and average emission factors were computed for each group. GHG emissions (Mt CO₂ eq) were then calculated by multiplying the emission factor (kg CO₂ eq / ton) by the corresponding national production quantity (ton) for each food group, country, and year.\u003c/p\u003e\n\u003ch3\u003eTemperature Data\u003c/h3\u003e\n\u003cp\u003eAnnual mean temperature data were obtained from the GDL, which provides standardized national-level climate indicators suitable for time-series analysis. While data from the World Meteorological Organization and national meteorological stations were initially reviewed, these sources exhibited irregular reporting intervals, inconsistent units, and missing annual means. The GDL dataset was therefore selected for its continuity, accessibility, and harmonized country-year structure.\u003c/p\u003e \u003cp\u003eFor countries included in the FAO dataset but not present in the GDL records, annual mean temperatures were estimated using a distance-weighted interpolation model combined with latitude and elevation\u0026ndash;based regression correction to ensure spatial coherence and minimize data gaps \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003ch3\u003eData Processing and Integration\u003c/h3\u003e\n\u003cp\u003eAll datasets were standardized and merged into a long-format time-series structure at the country\u0026ndash;year\u0026ndash;food group level. FAO production quantities and FS-GHGEF-D emission factors were linked to compute country-level food system GHG emissions. Temperature data were aligned by year to ensure consistency across datasets. All variables were expressed in metric units\u0026mdash;GHG emissions in million tons of CO₂ eq (Mt CO₂ eq) and temperature in degrees Celsius (\u0026deg;C).\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eAll statistical analyses were conducted using R software (version 4.3.2; R Foundation for Statistical Computing, Vienna, Austria). Data preprocessing, visualization, and model fitting were performed using the tidyverse, forecast, and ggplot2 packages. Analytical procedures were designed to examine the temporal dynamics and interdependence between food system GHG emissions and global mean temperature over the period 2010\u0026ndash;2021.\u003c/p\u003e \u003cp\u003eAnnual global totals of food system GHG emissions were calculated by aggregating country-level estimates, while global mean temperature was computed as the population-weighted average of national mean temperatures for each corresponding year \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Both indicators were plotted on a dual-axis time-series graph\u0026mdash;emissions on the left axis (Mt CO₂ eq) and temperature on the right axis (\u0026deg;C)\u0026mdash;to visually assess long-term trends and the degree of temporal co-movement between the two variables.\u003c/p\u003e \u003cp\u003eThe temporal structure of global food-system GHG emissions was analyzed using time-series statistical methods. The internal dependency and autocorrelation patterns of the emission series were examined through the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify autoregressive behavior and non-stationarity \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Based on these diagnostics, an autoregressive integrated moving average (ARIMA) model was specified and fitted to the differenced annual data \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eA series of candidate ARIMA models was tested, and model selection followed the minimum Akaike Information Criterion (AIC) \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Because the dataset consisted of annual observations without seasonal variation, Seasonal ARIMA (SARIMA) models were excluded \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Model adequacy was assessed using standard fit metrics, including Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE), alongside residual autocorrelation checks \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eSubsequently, a linear time-series regression model was applied to estimate the statistical association between annual food-system GHG emissions and global mean temperature \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. In this regression, temperature (\u0026deg;C) was treated as the dependent variable, and total annual emissions (Mt CO₂-eq) as the independent variable.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eTrends in Global Food System GHG Emissions and Temperature\u003c/h2\u003e \u003cp\u003eBetween 2010 and 2021, global GHG emissions from food production systems showed a consistent upward trajectory (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Annual emissions increased from approximately 13.7 Gt CO₂ eq in 2010 to over 17.9 Gt CO₂ eq in 2021, with an average annual growth rate of 2.8%. During the same period, the global mean surface temperature increased from 14.6\u0026deg;C to 15.0\u0026deg;C, corresponding to a rise of 0.4\u0026deg;C.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDual-axis time-series visualization showed that GHG emissions (left y-axis, Mt CO₂ eq) and global mean temperature (right y-axis, \u0026deg;C) exhibited parallel upward movements throughout the observation period.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eAutocorrelation Structure of Emissions\u003c/h2\u003e \u003cp\u003eACF and PACF analyses indicated significant short-term persistence in food system GHG emissions (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Positive autocorrelation was observed at lags 1 to 3, while coefficients gradually decreased after lag 4. The PACF plot showed a sharp decline after the first lag, supporting the inclusion of an autoregressive component in the model. These findings confirmed that the series was non-stationary, and first differencing was required before model fitting.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eARIMA Model Performance and Forecasting\u003c/h2\u003e \u003cp\u003eAfter differencing the non-stationary series, several ARIMA models were tested. The ARIMA(1, 1, 0) with drift model achieved the lowest AIC (AIC\u0026thinsp;=\u0026thinsp;205.22) (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Model residuals showed no significant autocorrelation.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of ARIMA(1,1,0) Model Results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eARIMA(1,1,0) with drift\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAR(1) coefficient\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash; 0.8482\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDrift\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;975.20 Mt per year\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e205.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.83%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1,872.89 Mt\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eModel fit statistics indicated satisfactory performance, with MAPE\u0026thinsp;=\u0026thinsp;4.83% and RMSE\u0026thinsp;=\u0026thinsp;1,872.89 Mt CO₂ eq.\u0026nbsp;The drift term (+\u0026thinsp;975.2 Mt per year) represented a steady annual increase in emissions.\u003c/p\u003e \u003cp\u003eForecasts based on the selected model indicated continued growth, with total global food system emissions projected to reach approximately 19.8 Gt CO₂ eq by 2025 under current trajectories (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eRelationship Between GHG Emissions and Global Temperature\u003c/h2\u003e \u003cp\u003eA linear time-series regression was conducted to examine the statistical association between annual food system GHG emissions and global mean temperature (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The regression coefficient was β\u0026thinsp;=\u0026thinsp;3.87 \u0026times; 10⁻⁵ (p\u0026thinsp;=\u0026thinsp;0.0357, R\u0026sup2; = 0.3704).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of Regression Analysis Between GHG Emissions and Temperature\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRegression coefficient (slope)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;3.865 \u0026times; 10⁻⁵ (\u0026thinsp;\u0026asymp;\u0026thinsp;+\u0026thinsp;0.000039)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0357\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3704 (Explained variance: 37%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis indicates that an increase of 1,000 Mt CO₂ eq in global food system emissions corresponded to an estimated 0.039\u0026deg;C rise in global mean temperature during the study period (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Model assumptions were confirmed through residual diagnostics and autocorrelation checks.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eAcross 175 countries (2010\u0026ndash;2021), global food-system GHG emissions increased steadily and exhibited short-lag persistence consistent with an autoregressive process. Visual inspection revealed co-movement between emissions and global mean temperature, which was corroborated by a statistically significant linear association (β\u0026thinsp;=\u0026thinsp;3.87 \u0026times; 10⁻⁵; p\u0026thinsp;=\u0026thinsp;0.0357; R\u0026sup2; = 0.3704). The preferred ARIMA(1,1,0) model with drift captured the emissions trajectory with acceptable forecast error, and the positive drift (+\u0026thinsp;975 Mt CO₂-eq yr⁻\u0026sup1;) indicates a structural upward trend over the study window. These results directly address the study\u0026rsquo;s objective to quantify temporal structure in food-system emissions and its statistical linkage to temperature, building on and extending a literature that has largely emphasized static footprints of foods and diets rather than longitudinal dynamics \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe choice of a non-seasonal ARIMA(1,1,0) with drift model was both methodologically and scientifically appropriate for analyzing annual global food-system GHG emission data. Given that the data are annual, seasonal components are neither observable nor theoretically expected at a 12-month resolution; therefore, excluding SARIMA avoids over-parameterization and enhances interpretability \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. The ACF and PACF structures\u0026mdash;showing short-lag positive autocorrelation and a PACF cut-off at lag 1\u0026mdash;are consistent with an AR(1) term on the differenced series, supporting the selection of an ARIMA(1,1,0) specification. This conforms to the Box\u0026ndash;Jenkins framework, in which differencing addresses non-stationarity and an AR(1) term captures short-run persistence \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Model diagnostics confirmed adequacy and robustness: the chosen model minimized the Akaike Information Criterion (AIC), achieved low forecast errors (MAPE\u0026thinsp;=\u0026thinsp;4.83%, RMSE\u0026thinsp;=\u0026thinsp;1,872 Mt CO₂-eq), and exhibited white-noise residuals with no remaining autocorrelation, satisfying standard criteria for time-series model validation \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe drift term (+\u0026thinsp;975 Mt yr⁻\u0026sup1;) represents a persistent upward trajectory in global agrifood emissions, reflecting structural inertia rather than short-term variability. Comparable applications of ARIMA frameworks to national CO₂ and temperature series further validate this model\u0026rsquo;s suitability for aggregated environmental data. Overall, the ARIMA(1,1,0) with drift provides a parsimonious yet rigorous representation of long-term persistence and stochastic dynamics in food-system GHG emissions\u0026mdash;capturing both the autoregressive behavior and deterministic upward trend characteristic of global production and supply-chain activities.\u003c/p\u003e \u003cp\u003eThe observation of a positive drift term in the ARIMA(1,1,0) model (+\u0026thinsp;975 Mt CO₂-eq per year) reflects more than a short-term fluctuation: it captures a persistent mean increase in global production-based food-system emissions. This methodological choice is scientifically justified because structural features of the food system\u0026mdash;such as capital investment in production and processing, logistics networks, packaging infrastructure, and food-waste streams\u0026mdash;adjust only gradually over time. Empirical inventories indicate that food systems account for roughly one-third of anthropogenic GHG emissions; FAO data, for instance, estimated\u0026thinsp;~\u0026thinsp;18 Gt CO₂-eq in 2015 (~\u0026thinsp;34% of global total) \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Moreover, recent analysis shows that emissions from pre- and post-production stages (manufacturing, packaging, transport, retail, waste) have doubled in many regions and now exceed those from the farm gate alone \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. This growing dominance of supply-chain emissions provides a mechanistic rationale for the observed autoregressive persistence: as processing, transport, and waste systems evolve slowly, each year\u0026rsquo;s emissions become the baseline for the next. In other words, the drift captures structural increase (deterministic trend) while the AR(1) term captures inertia (stochastic persistence). The model thus aligns with known system behaviour: as food systems industrialize, grow, and globalize, incremental gains alone are unlikely to reverse emission trajectories without systemic transformation. Reviews of food-supply-chain impacts (e.g., OECD 2022) reinforce that environmental burdens accrue not only at farm level but primarily in logistics, processing, and waste phases\u0026mdash;exactly the sectors contributing to the drift \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFrom the perspective of climate mitigation, the drift underscores that food-system emissions are not simply seasonal or cyclical but reflect compounded growth \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Accordingly, models of food-system emissions should capture both long-run trends and short-term persistence; the ARIMA(1,1,0) with drift accomplishes this by combining differencing, autoregression, and deterministic growth. It is methodologically sound and conceptually coherent in the context of global food systems. Future research could explore whether the drift magnitude differs by food-group, region or supply-chain segment, thereby informing targeted mitigation policy.\u003c/p\u003e \u003cp\u003eLinking annual temperature to annual food-system emissions provides a broad, first-order assessment of their relationship. Although this approach is associative rather than causal, the observed positive slope is scientifically consistent with fundamental climate dynamics: cumulative greenhouse gases\u0026mdash;particularly CO₂, CH₄, and N₂O\u0026mdash;enhance radiative forcing, trapping infrared radiation and raising global mean surface temperature \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. The magnitude and direction of the association are plausible given that food systems contribute roughly one-third of anthropogenic GHGs \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, with emissions rising steadily from both agricultural and pre-/post-production stages \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. The regression relationship thus provides empirical coherence between environmental physics and socio-industrial trends: as food production expands, CO₂ from energy use, CH₄ from livestock and rice cultivation, and N₂O from fertilizers together amplify warming \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Though the model is ecological and not mechanistic, the consistent statistical association aligns with physical causation already established by radiative forcing theory. It captures how long-lived atmospheric GHGs accumulate year-to-year, integrating the systemic inertia of global food systems into the broader climate trajectory.\u003c/p\u003e \u003cp\u003eHigh-impact syntheses quantify the environmental intensity of foods and producers and position food systems as a major mitigation arena \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, but most evidence is static or cross-sectional. Our study contributes the missing temporal dimension at global scale, illuminating persistence and co-movement with temperature over time \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. The upward pressure from non-farm segments documented in FAO/EDGAR-FOOD updates aligns with the positive drift we observe \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, reinforcing that the detected signal reflects systemic behavior rather than a modeling artifact \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. The SDG and planetary-health discourse emphasizes the interdependence of food security and climate stabilization. By quantifying temporal structure and linkage to temperature, our results provide empirical scaffolding for integrating explicit food-system targets within national mitigation plans and monitoring frameworks \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eCrippa et al. (EDGAR-FOOD) report that agriculture and land-use/land-use change dominate food-system emissions, with substantial contributions from retail, transport, consumption, fuel production, waste, and packaging\u0026mdash;sectors that evolve slowly, supporting the persistence we observe. FAO\u0026rsquo;s agrifood accounts similarly position food systems near one-third of global GHGs \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Micro-level studies link foods and diets to environmental burdens and health outcomes (e.g., Poore \u0026amp; Nemecek\u0026rsquo;s producer heterogeneity; Clark et al.\u0026rsquo;s health-environment trade-offs; recent product-level environmental scores), collectively underscoring that mitigation potential exists but is uneven across categories. Our macro time-series complements these studies by showing that, in aggregate, the global food system exhibits inertia that requires structural policy interventions \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Recent reviews on decarbonizing agriculture highlight methane/nitrous-oxide abatement, fertilizer management, and energy shifts in processing/logistics as high-leverage options\u0026mdash;consistent with the sectors contributing to persistence in system emissions \u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe measured drift suggests that efficiency-only approaches are unlikely to bend the curve rapidly. Production-side priorities include CH₄/N₂O mitigation (enteric fermentation, manure, rice), fertilizer optimization and nitrification inhibitors, low-carbon process heat/electricity in processing, and loss/waste reduction along supply chains. These align with the documented distribution of emissions across the \u0026ldquo;farm-to-fork\u0026rdquo; continuum. Incorporating explicit food-system modules into NDCs and national MRV systems would enable tracking of \u0026ldquo;desired GHG reduction (dGHG)\u0026rdquo; trajectories by food group and process stage \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThis study offers several methodological and conceptual strengths. First, its scope and harmonization enhance external validity: it encompasses 175 countries over a 12-year period (2010\u0026ndash;2021), using harmonized FAO food-supply and production statistics combined with a systematic item-to-group mapping of emission factors from the FS-GHGEF-D database. This large and consistent dataset provides a rare global longitudinal view of food-system GHG dynamics. Second, the temporal focus represents a key innovation. By separately modeling emissions dynamics through an ARIMA framework and assessing their relationship with temperature via regression analysis, the study distinguishes between internal persistence and inter-variable association, thereby avoiding the conflation of correlation and serial dependence often found in static footprint analyses. Third, the model transparency strengthens reproducibility: model selection relied on the AIC, while performance was evaluated using standard error metrics (MAPE, RMSE) and residual autocorrelation diagnostics, consistent with established time-series modeling practices in environmental and climate research.\u003c/p\u003e \u003cp\u003eNonetheless, several limitations should be acknowledged. First, causality cannot be inferred because the temperature regression is bivariate and does not partition contributions from other emission sectors or exogenous forcings. Second, the use of global aggregation may obscure heterogeneity in emission drivers and elasticities across regions and food categories. Third, measurement uncertainty arises from the averaging of emission factors within 98 FAO food groups and from differences in system boundaries\u0026mdash;such as whether land-use change and upstream inputs are included. Fourth, the accounting perspective is production-based; thus, it does not reflect emissions embodied in international trade or consumption-based patterns. Finally, the temporal span of 2010\u0026ndash;2021 may omit longer-term structural shifts or policy shocks, and the use of annual data precludes analysis of seasonal variability.\u003c/p\u003e \u003cp\u003eTo enhance robustness and extend this line of inquiry, several future research directions are proposed. First, greater econometric depth could be achieved through unit-root and cointegration testing (ADF, KPSS; Engle\u0026ndash;Granger or Johansen), heteroskedasticity- and autocorrelation-consistent (HAC) inference, structural break detection (Bai\u0026ndash;Perron), and alternative dynamic specifications such as ARDL, distributed-lag, or structural time-series models. Second, panel time-series modeling at the country level (e.g., panel ARDL or dynamic common correlated effects) would allow estimation of heterogeneous elasticities linked to structural features such as livestock intensity, rice cultivation, fertilizer use, and energy mix. Third, process-level and food-group decomposition could attribute temporal changes to farm-gate versus post-production stages and to specific food groups, guiding prioritization of \u0026ldquo;desired GHG reduction\u0026rdquo; (dGHG) pathways. Finally, future work should pursue integration with diet and health models, coupling production-side emission dynamics with consumption patterns and health outcomes to align food-system mitigation with planetary-health and sustainability objectives \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThe authors have no conflicts of interest to declare.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by the National Research Foundation of Korea grant funded by the Korea government (No. RS-2024-00340840).\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThis work was supported by a National Research Foundation of Korea grant funded by the Korean government (No. RS-2024-00340840).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJee Yeon Hong : Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Software; Resources; Validation; Visualization; Project administration; Supervision; Writing \u0026ndash; original draft; Writing \u0026ndash; review \u0026amp; editing\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data used in this study are publicly available from established open-access sources.Food production and supply data were obtained from the FAO Food Balance Sheets (FBS).Food system greenhouse gas emission factors were sourced from the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D) developed by the authors and available upon reasonable request.Global mean temperature data were accessed from the Global Data Lab climate dataset.The processed time-series datasets and analysis scripts generated during this study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eIPCC. 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Rome: FAO, 2023.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eClark M, Springmann M, Rayner M, et al. Estimating the environmental impacts of 57,000 food products. \u003cem\u003eProc Natl Acad Sci U S A\u003c/em\u003e 2022; 119(33): e2120584119.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKazimierczuk K, Barrows SE, Olarte MV, Qafoku NP. Decarbonization of Agriculture: The Greenhouse Gas Impacts and Economics of Existing and Emerging Climate-Smart Practices. \u003cem\u003eACS Eng Au\u003c/em\u003e 2023; 3(6): 426\u0026ndash;42.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8321666/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8321666/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground:\u003c/strong\u003e This study aims to examine the temporal relationship between greenhouse gas (GHG) emissions from national food systems and changes in annual mean temperature.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods:\u003c/strong\u003e Using FAO Food Balance Sheets, the Food System Greenhouse Gas Emission Factor Database (FS-GHGEF-D), and Global Data Lab temperature data from 2010 to 2021, we constructed country- and food-group–level time-series datasets. Analytical methods included time-series visualization, autocorrelation and partial autocorrelation (ACF/PACF) analysis, ARIMA modelling, and time-series regression.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFindings:\u003c/strong\u003e Results demonstrated a significant co-movement between food system–related GHG emissions and global mean temperature, with regression analysis indicating that a 1,000 Mt increase in emissions corresponded to a 0.039°C rise (p \u0026lt; 0.05, R² = 0.37). ARIMA forecasts further suggest a structural upward trend in emissions, increasing by ~975 Mt annually.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInterpretation:\u003c/strong\u003e These findings highlight the causal link between food production–based GHG emissions and climate change, identify climate-sensitive food categories, and provide quantitative evidence to support national dGHG reduction targets and climate-responsive food security policies.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding: \u003c/strong\u003eThis work was supported by a National Research Foundation of Korea grant funded by the Korean government (No. RS-2024-00340840).\u003c/p\u003e","manuscriptTitle":"Quantifying the Climate Impact of Food Systems: A Time-Series Analysis for Policy and Food Security","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-15 08:19:36","doi":"10.21203/rs.3.rs-8321666/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3c4cb65a-d6ad-46b0-891d-e76218e9dc22","owner":[],"postedDate":"December 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59451098,"name":"Earth and environmental sciences/Climate sciences"},{"id":59451099,"name":"Earth and environmental sciences/Environmental sciences"},{"id":59451100,"name":"Earth and environmental sciences/Environmental social sciences"}],"tags":[],"updatedAt":"2025-12-15T08:19:36+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-15 08:19:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8321666","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8321666","identity":"rs-8321666","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}