South Africa is, by most measures, the most industrialised economy on the African continent, and its development trajectory after 1994 has been closely tied to the supply of cheap electricity. The country produces roughly nine-tenths of that electricity from coal, and the consequences for atmospheric emissions are well documented: South Africa is the leading CO₂ emitter in Africa and around the thirteenth largest in the world [1][2]. Eskom, the state-owned utility, supplies close to 95% of national demand, and the upstream coal supply chain accounts for an additional, less visible share of the environmental burden [3].

Earlier work has examined the relationship between South Africa’s economic growth and its energy and emissions footprint through several lenses. OECD [4] and Tapio [5] decoupling indices have been used to compare environmental pressure against economic activity; index-decomposition techniques such as the Logarithmic Mean Divisia Index (LMDI) have been applied to identify the relative contribution of activity, intensity and structural effects; and the Kaya identity has helped attribute changes in emissions to population, affluence and energy intensity [5]-[8]. The input-output life-cycle approach has further been used to quantify direct and indirect environmental impacts attributable to each sector [9].

These methods, while productive, share a common limitation: they require relatively complete, low-noise datasets, and most are descriptive rather than predictive. They identify how things have changed, but they say comparatively little about how things might change next, or about how a heterogeneous group of sectors should be ranked when no single damage metric is decisive. Grey-system theory, introduced by Deng [10], was developed for situations in which the available information is partial, the sample size is modest, and the structure of uncertainty is not normal. Two of its tools are well suited to the South African case: Grey Relational Analysis (GRA), which compares observed sequences against an ideal reference to produce a single composite ranking, and the GM (1, 1) Grey Prediction Model, which fits a first-order grey differential equation to a short historical sequence to generate short- and medium-term forecasts.

This paper applies both techniques to data originally compiled by Beidari [3] in his doctoral dissertation at National Cheng Kung University. Two complementary objectives are pursued. First, the twelve sectors identified in the dissertation as having the largest environmental burden are ranked against four IMPACT 2002+ damage categories using GRA. Second, four national macro-energy indicators, GDP, CO₂ emissions, TPES and TFC, are projected to 2030 using GM (1, 1). The overall methodological framework is illustrated in Figure 1. The 2030 horizon is chosen deliberately: it spans the JET-IP coal-closure window (Komati 2022; Hendrina, Grootvlei and Camden 2023 to 2027) and reaches South Africa’s Nationally Determined Contribution mid-point, which lets the grey-system baseline be read directly against the policy targets it might or might not meet. The intention is not to displace the methods already applied to this dataset, but to layer onto them a grey-system perspective that is robust to small samples and that suits the medium-horizon policy work South Africa’s power-sector roadmap requires.

Figure 1. Methodological workflow. National statistics and the sectoral IO-LCA inventory feed two parallel grey-system analyses: a cross-sectional GRA producing a composite ranking of the twelve high-impact sectors, and four univariate GM (1, 1) forecasts to 2030. The two streams converge on a common policy reading.

Grey-system theory occupies a niche between deterministic mathematical modelling and probabilistic statistics. Deng [10][11] proposed it to deal with systems whose information is, in his terminology, partly known and partly unknown, rather than white (fully known) or black (fully unknown). Two operational tools emerged early: the GM (1, 1) model, which uses an accumulated generating operator to convert irregular sequences into smoother ones before fitting a first-order linear differential equation, and Grey Relational Analysis, which measures the geometric similarity of one sequence to another and aggregates that similarity across several criteria. Both tools have since been refined extensively [12].

The grey-forecasting literature in energy and emissions modelling has grown substantially in the past five years. Ding, Xu, Ye, Zhou and Zhang [13] developed a discrete grey prediction model with multivariate structure and applied it to Chinese energy-related CO₂ emissions, reporting accuracy improvements over standard GM (1, 1) on noisier series. Ding and Zhang [14] extended this work with a new-information-based grey model for provincial CO₂ forecasts. On the methodological side, Wei, Xie and Yang [15] clarified the role of the cumulative-sum operator in grey prediction by recasting it as an integral matching problem, which sharpens the interpretation of the development coefficient. Sapnken, Noume and Tamba [16] demonstrated the applicability of grey models to African data by forecasting CO₂ emissions from road fuel combustion in Cameroon, a setting that shares with South Africa the combination of short, partially uncertain time series and a rapidly changing energy structure.

Hybrid grey-machine-learning approaches have also emerged as a productive line of work. Saxena, Zeineldin and Mohamed [17] coupled a polynomial-kernel grey model with an augmented crow-search optimiser to forecast energy consumption, electricity generation and CO₂ emissions jointly, reporting accuracy gains over standalone GM (1, 1) on small samples. These hybrids do not invalidate the simpler grey approach used here; they extend it for cases where additional explanatory series are available and where the added model complexity is justified by the data.

The South African literature on coal-transition modelling has expanded markedly since 2020 around the country’s Just Energy Transition Investment Plan (JET-IP). Xaba [18] evaluated the implementation of the JET in coal-producing regions and documented the planned decommissioning sequence (Komati shut down in 2022; Hendrina, Grootvlei and Camden scheduled between 2023 and 2027). The South African quantitative literature, however, remains dominated by decoupling, decomposition and input-output analyses [7][8][19]. The present paper does not propose a new method; it brings established grey-system tools to bear on a dataset on which they have not, to the author’s knowledge, been jointly used, and reads the resulting forecasts against the structural break that the JET-IP is meant to introduce.

The two stages of the analysis address different questions but converge on a common message. The GRA stage tells us, with relatively little ambiguity, that South Africa’s integrated environmental footprint is overwhelmingly produced by two sectors. The GM (1, 1) stage tells us that, on present trends, the absolute level of pressure those sectors generate is likely to keep rising for at least another decade. Both findings echo, in compressed form, the conclusions of Beidari’s dissertation, where the input-output life-cycle analysis identified electricity and coal mining as the principal contributors and the LMDI decomposition attributed most of the upward push to the economic-activity term.

Three caveats are worth noting. First, the GM (1, 1) model assumes that the underlying trajectory is smooth in the cumulative sense. Structural breaks, such as a rapid build-out of renewables, an unanticipated decline in coal generation, or a sustained slowdown in GDP growth, will be absorbed only sluggishly by the model. The 2030 horizon adopted here in fact straddles the JET-IP coal-closure window (Komati 2022; Hendrina, Grootvlei and Camden 2023 to 2027) and the REIPPPP renewable build-out, neither of which the GM (1, 1) baseline sees. The medium-term forecast of CO₂ emissions should therefore be read as a counterfactual baseline of ‘no major structural change’, not as a prediction of what will actually happen; the literature on JET-IP implementation [18] makes plain that a structural break is in fact under way. The gap between the grey-system baseline and realised emissions over 2023 to 2030 will be informative about the pace of that transition. Second, the GRA results are sensitive to the choice of damage categories. IMPACT 2002+ aggregates a large number of impact midpoints into the four damage endpoints used here; an analysis based on midpoints (for example particulate matter or stratospheric ozone) would produce slightly different rankings, although the dominance of Electricity and Coal mining would survive. Third, the analysis stops at 2012 because that is where the dissertation’s sectoral inventory ends. An updated dataset incorporating Eskom’s post-2015 emissions and the early effects of the REIPPPP would be a natural extension and would let the GM (1, 1) forecast be refitted on a longer base period that spans the structural break.

Even so, a few policy implications are reasonably clear. For the electricity sector, the priority is the same one argued in successive Integrated Resource Plans: substitute non-coal capacity for retiring coal plants, and where coal is retained, push the fleet toward higher-efficiency, supercritical or ultra-supercritical units with retrofit emission controls. For the coal-mining sector, whose resource burden is, on the IO-LCA, almost as large as Electricity’s climate burden, the natural lever is the demand side: anything that reduces coal-fired generation also reduces upstream mining throughput, and the two sectors should be treated jointly in mitigation accounting. On the macro side, the GM (1, 1) baseline trajectory of TPES (224 Mtoe by 2030) and CO₂ (657 Mt by 2030) sits clearly above what would be needed to land inside South Africa’s NDC peak-plateau-decline band of 398-614 Mt CO₂-eq on a coal-dominated mix. Closing that gap requires the planned coal-fired closures to remove at least 43 Mt of annual CO₂ by 2030 relative to the GM (1, 1) trajectory; on the IRP 2019 retirement schedule (Komati 2022; Hendrina, Grootvlei and Camden 2023 to 2027; Arnot 2029; Kriel 2029) that is plausible, but only if delays to coal-plant decommissioning of the kind documented in 2023 to 2024 do not recur. Where they do, the JET-IP target will require either a faster fuel switch than presently scheduled or an explicit demand-management lever such as carbon pricing.

Grey-system analysis is a natural complement to the methods already deployed for the South African electricity sector. It does not require large samples, it is comparatively transparent in its algebra, and it produces both rankings (via GRA) and forecasts (via GM (1, 1)) from the same data. Applied here, it supports what input-output, decomposition and decoupling analyses have separately suggested: two sectors dominate South Africa’s environmental footprint, and the country’s aggregate energy and emissions trajectory is on a slowly rising path that needs an explicit structural intervention to bend. The GRA composite grade reduces the ranking question to a single number per sector, useful for policy communication, while the GM (1, 1) forecasts to 2030 provide a small-sample-friendly reference trajectory against which alternative scenarios can be compared. The GM (1, 1) trajectories should therefore be read primarily as counterfactual baseline pathways against which the effectiveness of South Africa’s ongoing energy transition can be evaluated.

The headline number is uncomfortable: on the GM (1, 1) baseline, South Africa’s 2030 CO₂ emissions reach about 657 Mt, which exceeds the upper bound of its NDC peak-plateau-decline band by roughly 7%. As noted in Section 4.2, this headline comparison carries a unit and boundary caveat, since the forecast captures energy-related CO₂ while the NDC band is economy-wide CO₂-equivalent; the qualitative conclusion that the baseline path overshoots the pledged trajectory is nonetheless robust. The JET-IP coal-closure schedule must therefore not merely happen but happen on time.

Three extensions suggest themselves. The Verhulst variant of GM, suitable for series approaching a saturation level, could be tested on TFC; a rolling GM (1, 1) estimated on the most recent four to six observations could supply a near-term forecast that responds more quickly to structural breaks; and a GRA with criterion weights elicited from South African energy-policy stakeholders would give a richer view than the policy-oriented weighting used here. Hybrid grey-machine-learning variants of the kind explored by Saxena, Zeineldin and Mohamed [17] offer a further line of extension when additional explanatory series become available. Each of these would build on, rather than displace, the framework presented in this paper.

The authors gratefully acknowledge the valuable comments and suggestions received during the preparation of this manuscript, which improved its quality and clarity.

Table A1 reports the annual GDP, CO₂ emissions, total primary energy supply (TPES) and total final consumption (TFC) series used to estimate the GM (1, 1) models. The data are reproduced directly from Beidari (2017), who compiled the series from International Energy Agency (IEA), World Bank and BP Statistical Review sources. The inclusion of the complete dataset allows full replication of the GM (1, 1) estimation procedure and addresses the reproducibility requirement of the present study.

Table A1.Annual GDP, CO₂ emissions, TPES and TFC for South Africa, 1990 to 2012.

Source: Beidari, M. (2017) Integrated Study of Energy Consumption, CO₂Emissions and Input-Output Life Cycle Assessment for the Electricity Sector in South Africa. Doctoral Dissertation, National Cheng Kung University, Tainan [3].

Table B1.Raw IMPACT 2002+ endpoint damage values for the twelve highest-impact sectors in South Africa’s electricity supply chain (2012).

Source: Beidari, M. (2017). Integrated Study of Energy Consumption, CO₂ Emissions and Input-Output Life Cycle Assessment for the Electricity Sector in South Africa. Doctoral Dissertation, National Cheng Kung University, Chapter 6, Table 6-3.

These endpoint damage values were generated using the IMPACT 2002+ life-cycle impact assessment methodology and constitute the raw environmental damage data from which the normalized values used in the Grey Relational Analysis were derived. The normalized scores employed in the GRA calculations are reported in Table 2 of the main text.