Assessing uncertainty in building material emissions using scenario-aware Monte Carlo simulation

Global greenhouse gas emissions from the built environment remain high, driving innovative approaches to develop and adopt building materials that can mitigate some of those emissions. However, life-cycle assessment (LCA) practices still lack standardized quantitative uncertainty assessment frameworks, which are urgently needed to robustly assess mitigation efforts. Previous works emphasize the importance of accounting for the three types of uncertainties that may exist within any quantitative assessment: parameter, scenario, and model uncertainty. Herein, we develop a quantitative uncertainty assessment framework that distinguishes between different types of uncertainties and suggest how these uncertainties could be handled systematically through a scenario-aware Monte Carlo simulation (MCS). We demonstrate the framework’s decision-informing power through a case study of two multilevel ordinary Portland cement (OPC) manufacturing scenarios. The MCS utilizes a first-principles-based OPC life-cycle inventory, which mitigates some of the model uncertainty that may exist in other empirical-based cement models. Remaining uncertainties are handled by scenario specification or sampling from developed probability distribution functions. We also suggest a standardized method for fitting distributions to parameter data by enumerating through and implementing distributions based on the Kolmogorov–Smirnov test. The level of detail brought by the high-resolution parameter breakdown of the model allows for developing emission distributions for each process of OPC manufacturing. This approach highlights how specific parameters, along with scenario framing, can impact overall OPC emissions. Another key takeaway includes relating the uncertainty of each process to its contributions to total OPC emissions, which can guide LCA modelers in allocating data collection and refinement efforts to processes with the highest contribution to cumulative uncertainty. Ultimately, the aim of this work is to provide a standardized framework that can provide robust estimates of building material emissions and be readily integrated within any uncertainty assessment.


Introduction
The buildings and construction sector accounted for 36% of final energy use and 39% of energy and process-related CO 2 emissions globally in 2018 [1], 11% of which resulted from manufacturing building materials and products such as steel, cement, and glass (i.e., embodied impacts) [2].Building operations worldwide account for 28% of energy-related greenhouse gas (GHG) emissions [3].While optimizing the 'operational' energy use of buildings and associated GHG emissions has been the major focus recently, meeting climate change mitigation needs would need one to go beyond operational energy consumption and related GHG emissions of buildings and address their full life-cycle [3].Building emissions are often complicated by trade-offs along the building life-cycle, especially between the embodied emissions (from building materials production) and operational emissions [4].A quantitative analysis of global resource requirements for future urbanization by the United Nations Environment Programme (UNEP) shows that the world's cities will consume 90 billion tonnes of materials by 2050, up from 40 billion tonnes in 2010 [5].Between 2020 and 2050, it is predicted that about 50% of GHG emissions associated with new buildings will be embodied [6].Increased resource consumption poses a challenge to climate change mitigation, given the high GHG emissions of material production and fossil fuel extraction, processing, and use [7].
Concrete is a primary structural material fundamental to construction projects throughout the world [8].Cement is the hydraulic binder that holds concrete aggregates together, enabling structural performance, and it is the primary driver of GHG emissions from concrete production [9][10][11].Global cement production reached 4.16 billion metric tonnes in 2022 [12].In parallel with its production, 2.6 billion metric tonnes of CO 2 was emitted, accounting for almost 8% of all global CO 2 emissions in 2021 [13].
There are two major sources of direct CO 2 emissions from cement production: calcination of limestone and fuel combustion.In the calcination process, carbonates (mostly limestone, CaCO 3 ) are decomposed into oxides (mostly lime, CaO) and CO 2 .At a higher temperature, calcium silicates are formed, and this higher temperature kilning currently leverages notable fossil fuel resources, such as coal and petroleum coke (petcoke), leading to additional emissions.The resulting product is the main component of cement (i.e., clinker) [14].According to Miller and Myers [15], about 0.513 kg of process-based (calcination) CO 2 is emitted per kg of ordinary Portland cement (OPC) (i.e., excluding CO 2 emissions from other processes such as material extraction and transportation).An earlier study by Marceau et al [16] estimated the calcination emissions to be 0.553 kg CO 2 per kg of cement.The second source of emissions is from fuel combustion as cement production thermodynamically requires 1.67 MJ per kg of cement [15].
Overall, for one kg of United States (US) Portland cement, an average of 0.80 kg CO 2 is released into the atmosphere.Emission factors vary between 0.96 kg CO 2 for wet kilns and 0.78 kg CO 2 per kg of cement for precalciner kilns [9].The globally-averaged emission factor (including both combustion and process-based CO 2 emissions) for cement production in 2022 was estimated to be 0.58 kg CO 2 per kg of cement [12].Variations occur due to the differences in location, technology, production efficiency, mix of energy sources used in electricity generation, the selection of kiln fuels, clinker/cement ratio, as well as the uncertainty in data used for cement life-cycle assessments (LCAs) [14].The presence of uncertainty and variability in cement production processes from raw material extraction to the final production at the gate of the cement plant (cradle-to-gate) is expected and requires further consideration within LCAs.Given the growing impact of embodied GHG, it is important to understand the uncertainty associated with each process in the production of cement and other constituents of concrete.Implementing and understanding mitigation measures for emissions from concrete and other building materials requires a representative characterization of their life-cycle emission profiles, which could be challenging given issues such as data quality and availability, differences in application of LCA framework, and the different models that can be used to characterize the relationships of the product being assessed.The lack of consistent guidelines on how parameter, scenario, and model uncertainty should be handled in assessing emissions compounds this challenge.Given the lack of standardized quantitative uncertainty assessment methods in environmental product declarations (EPDs) and LCA software, the integration of a standardized uncertainty framework would allow for more robust conclusions to be drawn.
In this study, we develop a detailed yet practical method to assess parameter, scenario, and model uncertainty in the life-cycle inventory (LCI) of major building materials.Because OPC is a significant source of global GHG emissions and a well-studied material, we use it as a case study to showcase the sources and effects of data uncertainty as well as the efficacy of the proposed uncertainty framework.We first provide some background regarding the current state of uncertainty assessment of building materials to contextualize the need for a robust quantitative uncertainty method, which leads to the development of a scenario-aware Monte Carlo simulation (MCS).

Background
Assessment of the environmental impacts of building materials using LCAs incorporates different types of uncertainties.Data uncertainty, a function of data quality for the system being modeled, and data variability, an intrinsic characteristic of the supply chains, are inherent to life-cycle environmental impact modeling [17].Uncertainty analysis is an effective method that allows LCA practitioners to evaluate possible variations in LCA results using different parameters, scenarios, and models [18].To quantitatively evaluate variations in building LCA results, it is necessary to acquire a large, accurate material and construction process database to generate input probability distributions for uncertainty models.The treatment of uncertainty for different types of LCA models is further explained in supporting information (SI) (section S.A.) and described illustratively in figure S1.

Uncertainty analysis in LCAs of building and construction materials-literature review
Our analysis begins by examining the state-of-the-art uncertainty assessment in LCA of building materials.Examination of peer-reviewed articles included reviewing uncertainty analysis conducted as part of building materials and building system LCAs both nationally and globally.The literature informed the development of our uncertainty assessment model.We assess the embodied GHG (in terms of CO 2 e) emissions of OPC in this paper, but the model could theoretically be applied to any building material or environmental impact.

Sources of uncertainties in building material LCAs
Embodied GHG emissions are attributed to the materials and energy required to construct and maintain the buildings, and they result primarily from the burning of fossil fuels (e.g., electricity generation, transportation, and on-site energy use) and chemical reactions (e.g., CO 2 emissions during the calcination of limestone to produce cement) [19].Embodied GHG emissions in building materials also include carbon uptake (e.g., plant photosynthesis in biogenic materials and cementitious carbonation in mineral-based materials during the use phase of the material) [20].Studies such as Andersen et al investigated how biogenic carbon accounting in LCA can affect the total embodied GHG emissions of a building.By looking into the different approaches to include biogenic carbon, authors found that methodological uncertainties in dynamic LCAs affect the embodied emissions to a great degree [21].Due to the higher contribution of materials production to GHG emissions over the life-cycle of buildings, many building LCAs focus on the uncertainties associated with embodied impacts [22][23][24][25][26][27][28][29][30][31].These studies considered database choices, LCI, replacement scenarios, methodological choices such as system boundary definitions, and service life as major sources of building LCA uncertainties [24,25,31,32].
In addition to building LCAs, several LCAs (including those of pavements and automobiles) have addressed major uncertainty sources such as material quantities, embodied impact (in terms of carbon and energy intensity) coefficients, material waste rates, material densities, process-specific variations, temporal and spatial variations, thermal properties, and system boundaries [31,[33][34][35][36][37][38][39][40].In general, these studies indicate that despite the higher contribution of the material production to the total embodied impacts of buildings, uncertainties in material LCAs are lower compared to other life-cycle stages as a result of the availability of materials LCA data [22].
In the context of transportation, assumptions about the sources of materials or components as well as transportation modes when such data are lacking may lead to larger uncertainties in this stage of building and construction LCAs [30].The overall accuracy of the environmental impact of the transportation phase is contingent on the quality of the input data, which may be difficult to improve due to massive amounts of components and materials used in each building.Of the literature reviewed, the transportation modes and distances, as well as types of vehicles used for transport were mostly unspecified in any of the available primary data sources, including commonly used EPDs [41].Two concrete material LCAs [38,42] and two pavement LCAs [33,36] have included transportation-related uncertainties and variabilities associated with distance and mode of transportation used in delivering concrete and pavement constituents, respectively.In addition to the transportation-related uncertainty, service life of the building, future replacement scenarios over the life of a building and end-of-life (EOL) scenarios have considerably higher levels of uncertainties as data quality issues are paired with factors such as projections of future behavior and resource availability, which are themselves inherently uncertain.

Uncertainty analysis methods in building material LCAs
Through literature analysis, we have identified six possible methods to analyze uncertainty and variability: MCS, sensitivity analysis, pedigree matrix and data quality indicators (DQIs), fuzzy related method, analysis of variance, and variants thereof (e.g., MCS mixed with pedigree matrix) have been previously utilized.

Monte Carlo simulation (MCS)
Notably, MCS, which has had the most frequent and widespread applications in LCAs, is used to assess the propagation of the uncertainty of unit process data.To run MCS, the specification of a distribution describing the potential range and likelihood of every stochastic parameter value is required [23].
Some LCA software platforms, such as OneClick LCA [43], Open LCA [44], and SimaPro [45] offer the ability to calculate uncertainty using some form of MCS.The ecoinvent LCA database [46] also includes quantitative uncertainty values for parameters in many of its processes.
In our database of studies investigated, 19 (out of 38) building and material LCA studies assessed uncertainty with MCS [22-24, 26, 27, 31, 33-36, 38-40, 47-52].MCS has been applied to different building types (high-and mid-rise residential, office buildings), various building materials (bio-based materials, composite materials reinforced with natural fiber, concrete mixtures, insulation materials, cement plaster, brick, painting, etc) and components/elements (structural and non-structural) in different geographical locations.These studies have addressed uncertainties associated with service life, LCI, material properties, process-specific variations, temporal and spatial variations, thermal properties, and system boundaries, among others.
Out of 19 LCAs with MCS applications, seven of the studies particularly focused on uncertainties associated with various building materials, including concrete.For example, Li et al [50] adopted a probabilistic LCA approach to estimate the carbon emission intensity of magnesium phosphate cementitious (MPC) materials.Utilizing MCS, the authors generated multiple simulated carbon emission intensities for MPC materials.Subsequently, these simulated values were contrasted with the carbon emission intensity of OPC, as already established in existing research.Morales et al [24] evaluated the influence of uncertainties associated with service life and LCI of four building elements, namely external cement plaster, external clay brick wall, external painting, and internal painting.The inventory data quality was assessed through MCS using the Pedigree matrix.Miller [38] performed statistical analysis of GHG emissions and air pollutants from concrete production in California incorporating sources of variability and uncertainty through MCS as well as used MCS to inform the likelihood of mitigating emissions from decarbonization efforts.AzariJafari et al [52] developed a MCS tool with the purpose of robust comparisons of concrete EPDs.They applied the tool to compare the global warming potential (GWP) of 219 concrete mix designs with three different levels of compressive strength against those of US industry average.The authors showed that the major source of variation in the stand-alone LCA results originated from the methodological choice of database selection with Portland cement inventory data.However, the impact of methodological choices on the variance of the comparative results was trivial and the variability of Portland cement content dominated the variance.Moreover, the slag, a type of supplementary cementitious material (SCM), data quality and variability played a major role in the variance of the comparative results.DeRousseau et al [42] analyzed the variability in embodied carbon of concrete mixtures in the US by attributing probability distributions to each life-cycle impact using a variety of LCI data sources.Results, on a per mass basis, showed that cement and superplasticizer as raw materials had the highest values of embodied carbon; however, on a per volume of concrete basis, cement contributed the vast majority of impacts to estimates of the embodied carbon of concrete.Su et al [35] systematically considered parameter uncertainty and variability related to the properties (density, thermal conductivity, embodied energy, etc) of eight major building insulation materials in China.Miller et al [39] calculated the service-life (in-use degradation) of natural fiber-reinforced (wood-polymer) composites using a stochastic moisture-induced deterioration (also MCS) model paired with an LCA model developed for these composites.
Five pavement LCA studies applied MCS for the quantification of uncertainties [33,36,40,47,49].Bressi et al [47] assessed the environmental performance of sixteen cement treated base pavement mixtures, with and without recycled asphalt pavement (RAP), with different cement percentages, different production methods, and different recycling procedures.The authors estimated and introduced data uncertainty into the LCA calculation procedure using the MCS approach.Cao et al [33] performed MCS on four major uncertainty categories related to asphalt pavements-material energy consumption, equipment energy consumption, mixing temperature reduction, and material transportation distance-in China and Hong Kong.Yu et al [49] analyzed different asphalt pavement maintenance projects to estimate energy consumption and CO 2 emissions from various recycling strategies.They considered two uncertainty categories (data quality uncertainty and model parameter uncertainty) and introduced an environmental burden comparison parameter for testing the statistical significance of the results of different solutions.AzariJafari et al [40] conducted MCS and applied it to a comparative LCA of asphalt and concrete pavements in Quebec, Canada.The uncertainty of the results was first estimated by DQI embedded in the ecoinvent database.The variability in materials, construction methods, and repair stages of the pavement life-cycle were calculated by assigning continuous uniform probability distributions to each variable.Ultimately, the probability of methodological choices was modeled using uniform distributions and assigning a portion of the area of the distribution to each scenario.Vidal et al [36] performed MCSs to estimate the variability of the environmental impacts (using ReCiPe method incorporated within the SimaPro software application) of three types of asphalt pavements, which included hot mix asphalt, warm mix asphalt pavements, and asphalt mixes with various contents of RAP manufactured in Spain.
The remaining eight studies applied uncertainty analysis in the context of whole building LCAs [22,23,26,27,31,48,51,53]. Loli et al [53] estimated and compared uncertainty in embodied GHG emissions of building elements (e.g., superstructure, floor structure, outer walls, inner walls, etc) and materials of a laboratory building in Norway using two approaches: in the first approach, most data were obtained from EPDs, while the second approach only used generic data from the ecoinvent database.MCS was used to investigate selected building elements' contribution to the variability in the GWP results both in the generic mode (MCS function implemented in SimaPro-ecoinvent database) and the EPD-based tool.Robati and Oldfield [27] and Robati et al [26] used uncertainty analysis to determine and compare the range of embodied carbon from for mixed use and office buildings in Australia using a MCS method.Ansah et al [22] analyzed parameter uncertainties by performing different sets of MCSs for different life-cycle stages and scenario analyses for a housing block in Hong Kong.Morales et al [23] analyzed the influence of the uncertainties of service life models using statistical analysis of MCS results for fifteen different building elements considering eleven different maintenance, repair, and replacement models from seven countries.Zhang et al [31] analyzed the life-cycle GHG emissions from a high-rise residential building located in Harbin, China using both deterministic and stochastic (MCS) approaches for parameter uncertainty.Chhabra et al [48] considered environmental impacts due to seismic hazard-related repair actions in California.The authors performed MCS in the form of a probability distribution of GWP conditioned on a target design life of a building for the entire building system and individual components.Pomponi et al [51] also used Monte Carlo algorithms based on building embodied energy data from EU manufacturers as inputs for the stochastic modeling of uncertainty.

Sensitivity analysis
While there are methods (e.g., MCS) aiming to understand the uncertainty of an LCA, sensitivity analysis is commonly applied to understand which parameters are the most impactful [54].The scenario-based approach is considered to be complementary to uncertainty analysis (sometimes even treated as the same) and a combination of them facilitates better decision-making [55].In the selected studies, the most prevalent practice is a mixture of sensitivity analysis and MCS to target uncertainties in parameters related to design features and background LCI data [56], foreground and background LCI data and transport (e.g., distance and types of vehicles) [57], and EOL management strategies [22].
Recently, Hossain et al [58] conducted a sensitivity analysis on variable input parameters (e.g., transport distance of concrete constituents to the concrete plant) and allocation rule (for industrial SCMs such as GGBS, pulverized fly ash, limestone) in Hong Kong.AzariJafari et al [52] captured the simultaneous effect of different sources of uncertainty and variability in the comparative analysis of concrete mixtures but also incorporated the interdependencies of different scenarios and sample values in their MCS.For the value parameters, related to the allocation choice of slag and fly ash as well as database selection between ecoinvent v.3.4 and GaBi v.9.2, the possible scenarios were considered as discrete choices in the AzariJafari et al study.Miller [38] applied sensitivity analysis on the influence of changing cementitious content and three procedural changes (as mitigations).Impacts of fuel changes, grid changes, and carbon capture are examined relative to the baseline concrete mixture.Su et al [35] used sensitivity analysis to compare the environmental impacts associated with insulation materials.Seto et al [59] addressed the uncertainty due to choices, investigating the effect of allocation approaches of fly ash production on the LCA results of concrete by four allocation scenarios: no allocation, mass allocation, economic allocation and disposal avoidance.Cellura et al [60] performed sensitivity analysis on secondary data, Environmental Impact Assessment methods, and characterization factors for GWP calculations of roof tiles manufactured in Italy.

Pedigree matrix and DQI
Apart from standard qualitative discussions of uncertainty in building material LCA literature, studies have applied hybrid methods including the pedigree matrix, MCS and sensitivity analysis to estimate uncertainty [18,22,23,25,31,38,61].Several pavement LCA studies have covered uncertainty due to data quality using the pedigree matrix in different versions of the ecoinvent database [36,40,47].Other studies such as Blengini and Di Carlo [62] evaluated the LCA impact of a building through DQIs.
In summary, the the literature review encompassed 38 building and material (out of 132) LCA articles that focus on uncertainty.Of these 38 studies, only a few considered uncertainty and data variability at the material composition (such as major minerals in OPC), production technology, and process (raw material extraction, grinding, pyroprocessing, milling, etc) levels.The Excel file found in the Supplementary Information (SI) provides the list and details of 132 studies.With regards to cement-related uncertainty applications, Li et al [50], Miller [38], AzariJafari et al [52], and DeRousseau et al [42] studies are the four known studies that address uncertainty and data variability in LCAs of cement and concrete mixes.

Scenario-aware MCS development and contributions
While the aforementioned qualitative and quantitative methods have inherent benefits rendering them useful uncertainty assessments in LCAs, MCS is a practical yet robust method that can be used to assess all the different types of uncertainties under a singular framework.The MCS model developed in this work is built on top of a first-principles cement model detailed extensively in Kane et al [63].The base cement model yields deterministic results for CO 2 e emissions that are only valid for a certain set of assumptions and conditions, even under a framework built around first principles.The goal of developing and incorporating uncertainty assessment methods into these modeling frameworks is to provide a robust estimate of the possible CO 2 e emissions of building materials that accounts for the uncertainty and variability in modeling parameters and methods.This signals the need for a stochastic approach, which can be handled using a scenario-aware MCS.
The background and literature review section provides an extensive summary of the current state of MCS uses in LCA studies to handle uncertainty.The MCS methods developed here leverage the strengths of the MCS methods used in past works while also providing methodological contributions that build a more comprehensive MCS model to be applied to building materials.
The first of these contributions lies within the modeling resolution, where we show how a detailed breakdown of the process flows of these materials allows for a more comprehensive look at the uncertainty that exists within each life-cycle phase of building materials.Such a resolution allows one to address the uncertainty of each parameter within the process flow, while also highlighting where first principles come into play in removing some modeling uncertainties.
An important issue to address within MCS methods used in LCA is distinguishing between scenario uncertainty and parameter uncertainty [37,64,65].Parameter uncertainty emerges from data quality and availability, while scenario uncertainty emerges from (1) the choices available to an individual decision-maker in framing the LCA and (2) the distinctive states a product can exist within that cannot be simultaneously present.Not distinguishing between scenario uncertainty and parameter uncertainty in the MCS can yield distribution ranges that are relatively large given that it groups together a wide range of possible scenarios for a process or product.Doing so also loses information regarding the decisions that can be made about a process or product and the several states it can exist within.Thus, the second major feature of the MCS framework developed in this research is allowing it to be scenario-aware such that distinctive scenarios are not exclusively evaluated in a probabilistic fashion that can add ambiguity to the final distribution results [37].Past works have focused on differentiating between parameter uncertainty, scenario uncertainty, as well as model uncertainty (i.e., uncertainty in the mathematical relationships of the parameters in the model) [66,67], how these differences can be accounted for within an uncertainty model such as MCS [37,40,64,65,[68][69][70], and how to derive conclusions from the quantified uncertainties [71,72].Parameter uncertainty is typically dealt with by assuming an appropriate probability distribution function (PDF) for each parameter and then randomly sampling values within the MCS [37,64,65,68,71,73].Different approaches are used for handling scenario and model uncertainty.Some argue against the probabilistic handling of these types of uncertainties due to the inability of meaningfully representing them through probability distributions.Their influence on the final results is also masked and lost through these types of representations [37,66].However, there are still some studies such as Huijbregts et al [64] and de Koning et al [65] that have used weighted probability functions to represent non-parameter types of uncertainties.Studies such as van Zelm and Huijbregts [68] and Mattila et al [73] propagate through scenario and modeling alternatives using discrete choice methods or specifying a set of scenarios to represent the different possible outcomes and their impacts.Studies such as Gregory et al [71] handle scenario analysis using a combined approach where they conduct an analysis using discrete scenarios as well as a probabilistic scenario analysis of key parameters to understand the implications of changing scenario assumptions.In most cases, specifying representative scenarios can be difficult especially if the scenario space is large and adds computational difficulty on obtaining a representative sample.Furthermore, formulating scenario and modeling uncertainty probabilistically can help represent extreme cases of a specific alternative and allow for a sensitivity analysis on the influence of those factors on the results.Therefore, it is not uncommon for studies to define uniform distributions for these types of uncertainties such that different scenario and modeling alternatives can be systematically sampled with equal likelihood to understand their varying impacts while also avoiding the issue of specifying the likelihoods for these scenarios [37,40].Conclusions drawn from these studies point out how scenario and modeling uncertainty in certain cases can be more influential in dictating the relative impacts of a process or product more so than parameter uncertainty.For scenario uncertainty, we use a combined approach of defining uniform distributions for some uncertain aspects as well as specifying discrete scenarios for certain alternative options.We assume that the first-principles nature of the underlying cement model removes most aspects of the model uncertainty.
The third contribution is developing a systematic way in which parameters are fitted with distributions depending on the amount of available data points, an aspect that was lacking in previous LCA-based MCS applications [37,38].
The final contribution involves relating the uncertainty associated within each process of the cement model to its expected emissions contributions.This will inform future cement models and EPD developers how to allocate data collection efforts in a more effective manner, where they can focus uncertainty mitigation on high-emission contributing phases that are attributed with higher uncertainty.
Our framework for developing and running a scenario-aware MCS for building materials requires the following steps: 1. Developing a parameter breakdown of each process of the life-cycle of the material and characterizing the uncertainty and/or variability in each parameter.2. Collecting data for modeling parameters.3. Specifying a set of possible scenarios for material emissions based on the different available scenario-framing options.4. Developing PDFs for parameters through a standardized distribution fitting methodology.5. Running the scenario-aware MCS. 6. Interpreting MCS emission distribution results.
The Methods section describes each of the steps in more detail.

Developing a parameter breakdown of each process of the life cycle of the material and characterizing the uncertainty and/or variability in each parameter
To determine the OPC LCI, a first-principles-based model was adopted from Kane et al [63].The model encompasses four stages for OPC manufacturing, including mining and quarrying, pre-pyroprocessing milling and grinding, pyroprocessing, and finish grinding.Apart from facility overhead, the model also accounts for the transportation of the minerals to the cement kiln as well as the final transportation to the concrete plant.Emission sources within these stages are further drawn out such that MCS emission distributions for nine different sources are generated.These include: (1) mineral extraction, (2) pre-milling, (3) pyroprocessing (required energy-related emissions), ( 4) pyroprocessing (inefficiencies-related emissions), ( 5) pyroprocessing (required energy-related chemical emissions), ( 6) pyroprocessing (inefficiencies-related chemical emissions), (7) post-milling, (8) overhead, and (9) transportation emissions.
The first step in developing the MCS is outlining a detailed parameter breakdown of each of the aforementioned emission sources.This breakdown allows for a better accounting of the interactions that exist between the different parameters within the OPC model as well as being able to determine if each subprocess/parameter carries any parameter uncertainty (herein referred to as uncertainty), scenario uncertainty (herein referred to as variability), or falls under first principles.
A detailed breakdown of the sub-processes and parameters also facilitates the development of emission distributions for each of those life-cycle phases/processes.An example of such a breakdown is shown in figure 1, which displays the parameter breakdown related to the mineral extraction process of OPC minerals.Figure 1 shows that quantifying mineral extraction emissions can be broken down into three main dependencies, which include raw material extraction, mining losses, and fuel and electricity emission factors.Each one of those main dependencies is then further broken down into its most fundamental parameters, which are then designated as having either uncertainty, variability, or is a first-principles parameter.The general adopted approach follows developing PDFs for parameters with uncertainty from literature-collected data, which are then sampled from during the MCS process.Parameters with variability are assumed to fall under scenario uncertainty and are handled through scenario analysis if those scenarios can be realized.Otherwise, they will be fitted with a uniform distribution and sampled through the MCS.To reduce modeling complexity, all parameters with variability will be fitted with uniform distributions, except the ones which are specifically mentioned in the subsequent scenario development subsection.
In terms of the finer level parameters, figure 1 shows that raw material extraction is dictated by the final mineral composition of the OPC product, which we use to determine the mining inventory energy demand and the stoichiometric reactions taking place between the minerals in the cement kiln.Large variability exists within the mineral composition of different OPC products, meaning that the mineral composition must be specified prior to running the model, or different combinations of mineral compositions can be sampled through the MCS with equal likelihood.The mineral composition of the OPC is input into the stoichiometric reaction's component of the model, however, no uncertainty or variability exists within the products of those reactions given that they are governed by first principles.The proportion of mineral losses occurring within the OPC supply chain is uncertain.Thus, a PDF for the potential losses must be established and sampled through the MCS.Similarly, energy input requirements for mineral extraction and fuel carbon intensities are uncertain and must be sampled.Electricity emission factors are spatially variable depending on the electricity mix of where and when the process takes place, and it is a component that can be fixed and specified prior to running the MCS.The parameter breakdown and data requirements for all remaining cement life-cycle phases can be found in the SI.

Collecting data for modeling parameters
Once a detailed breakdown of each life-cycle phase is determined, data collection for the parameters is carried out.Different mineral-related and energy-related data are retrieved from the literature.The data are used to either develop PDFs for parameters with uncertainty or parameters with variability, or to develop the scenarios outlined in the upcoming subsections.Details regarding the collected data and data sources used can be found in the SI section S.B.2.

Scenario development using variable parameters
A major component of the MCS model is distinguishing between scenario uncertainty (defined here as variability) and parameter uncertainty.As mentioned, scenario uncertainty is handled by either specifying and fixing parameters defining that scenario or developing uniform distributions of those parameters and sampling them with equal probability.A set of multilevel scenarios have been developed to demonstrate the capabilities of the scenario-aware MCS and are show in figure 2. The first level is used to assess how MCS emission distributions differ when there is variability with the cement material composition, given that a major source of variability perpetuated throughout the model is related to the cement material composition.To demonstrate how varying the cement composition affects total cement-and subsequent-stage-related emissions, two different analyses are carried out: a variable cement clinker material composition and a fixed cement clinker material composition.The variable composition scenario samples in different cement clinker material compositions from a possible set of compositions for each MCS realization (the minimum and maximum cement clinker material compositions are shown in figures S13 and S14 in the SI), while the second scenario assumes the fixed composition assumed in the baseline cement model (alite: 63%; belite: 15%; tricalcium aluminate: 8%; tetracalcium alumino ferrite: 9%; gypsum: 5%).Distinguishing between fixed and variable compositions within these scenarios also helps demonstrate how uncertainty and variability can still manifest within a modeling framework that assumes first principles since the clinker material composition is the major factor influencing material first-principles formation reactions in the case of cement.
The second level of scenarios handle variability with parameter specification as opposed to sampling from uniform distributions.This level of scenarios assesses how regional differences in electricity mixes, cement kiln fuel mixes, and transportation modes utilized (as well as the associated transportation distances) can affect the overall MCS emission distributions.To demonstrate this, two energy and transportation (ET) scenarios are assumed.ET Scenario 1 develops emission factors based on PG&E's (Northern California's electric utility's) electricity mix [74] and the current California-averaged cement kiln fuel mix [75].ET Scenario 2 develops emission factors based on DTE Energy's (Detroit's electric utility's) electricity mix [76] and the current US-averaged cement kiln fuel mix [77], which is more carbon intensive on both accounts.In terms of transportation, ET Scenario 1 assumes all transportation is carried out using freight trucks, while ET Scenario 2 assumes most transportation is carried out through rail.Transportation distances for mineral and cement transport are often unknown.Thus, a uniform distribution of assumed distances for both modes were generated and were sampled through the MCS.Transportation distances for truck and rail transport of raw materials and cement were obtained from a number of different sources [16,38,78,79].Truck transport distances of raw materials varied between 1 and 25 km, except for gypsum, which varied between 150 and 400 km.Final truck transport of cement varied between 60 and 670 km.Rail transport distances were higher, varying between 100 and 660 km for raw materials and 150 and 550 km for cement.While the scenarios developed here are not exhaustive of all possible scenario uncertainty possibilities, they offer a reasonable demonstration of how different ways of handling scenario uncertainty can affect the emission profiles of building materials.

Developing PDFs for parameters through distribution fitting
The next step of the MCS process handles parameter uncertainty.The outcome of this step is fitting PDFs to the different parameters using data collected from the literature.This section outlines a systematic way in which an appropriate probability distribution can be selected for each parameter.Two approaches are adopted for distribution fitting.The first approach involves adopting distributions from the literature when available and applicable to the parameters.The second approach involves fitting collected parameter data with an appropriate PDF when a distribution from the literature is unavailable.When only one data point is available for a parameter, the parameter value is assumed to be deterministic and that data point is used for all MCS realizations.For parameters with two and three available data points, we follow Miller [38] which suggests using a uniform and triangular distribution, respectively.For the uniform distribution, it is assumed that the two available data points represent the lower and upper bound of possible parameter values.
When four or more data points are available, a more methodical approach is used to fit the parameters with the appropriate distribution.First, a set of applicable distributions (shown in table S4 the SI) that may be suitable for fitting the underlying OPC parameter data are collected.Next, each distribution is fitted to the parameter data points using maximum likelihood estimation (MLE) through Python's SciPy Package [80].MLE is chosen due to its many desirable properties, including its better performance when only a small number of data samples are available, which is the case in this study and other LCA applications [81].Once all distributions are fitted, the most appropriate distribution is selected using the Kolmogorov-Smirnov test (KS test) [82].The KS test compares the empirical data-based distribution function to the cumulative distribution function of the fitted distribution, which yields a KS statistic measuring the maximum difference between the empirical and cumulative distribution functions.The distributions yielding the smallest KS statistics would be considered best fits of the data.Further inspection of the distributions (e.g., using Q-Q plots) is carried out to ensure that the chosen distribution is physically representative and an appropriate fit of the underlying data.The significance of the KS statistic for each distribution is also assessed and verified to fall below KS test critical values at a significance level: α = 0.05.This provides confidence in the goodness-of-ft assessment and ensures that the KS statistic is not only a low value (i.e., indicating a good fit) but is also statistically significant [83].Once all the scenarios and parameter distributions are set up, the MCS can finally be run by sampling parameter values from PDF distributions for each MCS realization.A more detailed breakdown of the data, PDF distributions used in the MCS, the KS statistics and their associated KS test critical values can be found in the supplementary MCS Data Excel File.

Variable cement clinker composition greenhouse gas emissions results
When all MCS realizations (100 000 iterations) are obtained for each phase of the cement manufacturing process, they are used to generate emissions distributions in units of kgCO 2 e/kg of cement.Figure 3 shows the total emission distributions as well as the distributions of each of the cement manufacturing processes for both ET scenarios.The results in figure 3 are only shown for the variable composition case.The processes whose emissions depend mostly on the carbon intensity of the electricity mix include pre-milling (ET 1 [median]: 0.0097 kgCO 2 e/kg; ET 2: 0.074 kgCO 2 e/kg), post-milling (ET 1: 0.0034 kgCO 2 e/kg; ET 2: 0.026 kgCO 2 e/kg), and facility overhead (ET 1: 0.0020 kgCO 2 e/kg; ET 2: 0.015 kgCO 2 e/kg).These processes show the largest emission differences between both energy mixes due to the lower carbon intensity of the PG&E electricity mix relative to the DTE mix (7.5× higher).Similarly, there is a considerable difference in the emissions distributions between the two transportation scenarios (ET 1: 0.014 kgCO 2 e/kg; ET 2: 0.030 kgCO 2 e/kg).Despite the rail emission factor being lower than that of freight truck transportation (∼80% lower), rail travel distances are typically higher to transport minerals (up to 25×) and cement (up to 10× in some cases) [16,78,79], leading to higher emissions.If travel distances were assumed to be the same for both scenarios, then truck transportation would lead to higher emissions.The mineral extraction process (ET 1: 0.056 kgCO 2 e/kg; ET 2: 0.068 kgCO 2 e/kg) shows a smaller difference in emission distributions due to being dependent on both the electricity mixes but also other fuel emissions, which are dictated by the mineral composition sampled and are similar for both ET scenarios.
A smaller difference in emissions is found for processes that only rely on the cement kiln fuel proportions of both scenarios.These include the pyroprocessing energy-based emissions (ET 1 and ET 2: ∼0.18 kgCO 2 e/kg) pyroprocessing energy-based inefficiency emissions (ET 1 and ET 2: ∼0.20 kgCO 2 e/kg).As expected, no discernable difference is found between the pyroprocessing chemical-based emissions (ET 1 and ET2: 0.52 kgCO 2 e/kg) and pyroprocessing chemical-based inefficiency emissions (ET 1 and ET2: 0.060 kgCO 2 e/kg) for both scenarios.MCS emission realizations can also be combined to generate total emission distributions for all cement manufacturing processes, which is shown in figure 3. Relative differences between both energy mix scenarios for all processes are shown in table S7.The difference in emissions distributions shows the benefits of a scenario-aware MCS, where tighter distributions are achieved as opposed to a single distribution with a wider range.It also shows that discernable shifts in distributions can occur due to differences in scenario assumptions, which may have been lost had scenario uncertainty been handled in a similar manner to parameter uncertainty.Tables S5 and S6 show distribution percentiles for each phase of ET scenarios as well as the baseline cement model results.

Cement process emissions contribution and associated uncertainty
Figure 4 shows the potential emission contribution distributions of each of the cement manufacturing processes.Figure 4 also displays the coefficient of variation (COV) of the emission distribution of each of those processes.This helps relate the uncertainty of each process to its emission contributions, such that cement LCA modelers can allocate data collection efforts more effectively and can focus uncertainty mitigation on emission-intensive processes with the highest contribution to cumulative uncertainty.Pyroprocessing is responsible for the majority of the emission contributions, with the pyroprocessing chemical emissions' median contribution leading to 49% of all emissions in ET Scenario 1.These contributions drop to about 44% in ET Scenario 2 due to the higher carbon intensity electricity mix, which increases the emissions contributions of processes that rely on electricity.The energy-related and inefficiency-related emissions from pyroprocessing in ET Scenario 1 have median contribution of 17% and 19%, respectively, which drop to 15% and 17% in ET Scenario 2. The chemical-emission inefficiencies have a potential maximum contribution that can reach up to 30% for extremely inefficient processes, but the median contributions are approximately 5% in both scenarios.
The differences in emission contributions between both ET Scenarios mainly manifest in the non-pyroprocessing processes.The remaining processes have median contributions that range from <1% to 10% for ET Scenario 1 but are slightly higher in ET Scenario 2. The lowest contributing process in both scenarios is facility overhead, which has a median contribution of 0.18% and 1.2% in ET Scenario 1 and ET Scenario 2, respectively.For ET Scenario 1, post-milling and pre-milling have the next highest emission contributions ranging between 0.31% and 0.91%.However, these contributions are higher in ET Scenario 2 (2.1%-6.1%).The higher transportation emissions in ET Scenario 2 also cause the median emission contributions to double relative to ET Scenario 1 (from 1.3% to 2.6%).Mineral extraction emission contributions remain constant at around 4% in both scenarios.
COV is used as a measure of the spread of the emission distributions of each process and can be used as a proxy for uncertainty.The pyroprocessing chemical emissions process has the lowest COV values (∼1.5% in both scenarios).The pyroprocessing energy-related emissions have low COV values in both scenarios (∼8%).This indicates that the main emission contributors have the lowest associated uncertainty.The potential inefficiencies in the pyroprocessing process (especially the chemical emissions) have relatively high COV (25%-62%) values and moderately high emission contributions, meaning that they are an important emission source to focus uncertainty mitigation on.Similarly, the mineral extraction process has a high COV value (35%-46%) and can potentially have high emission contributions, meaning that it is a significant process to consider in the modeling process.For ET Scenario 1, the post-milling and pre-milling processes are associated with relatively high uncertainty, (38%-50%), but have relatively low emission contributions in this case.Their importance for uncertainty mitigation becomes higher in ET Scenario 2, where their emission contributions are relatively higher.The remaining processes (overhead and transportation) have relatively low COV values (18%-20%) in addition to having low emission contributions compared to the other processes.

Effects of varying cement clinker composition on cement greenhouse gas emissions
Figures 5(a) and (b) show the MCS total and pyroprocessing chemical emission distributions of the varied and fixed cement clinker composition mixes, respectively.Results are shown for ET Scenario 1.The main parameters that lead to differences in the emission distributions from first-principles modeling are due to the material composition of the manufactured cement.Varied emissions distribution from first-principles modeling manifests mostly within the pyroprocessing (required energy-related chemical emissions) process, which is shown in figure 5(b), whereas all other processes under a fixed composition scenario show smaller differences in distributions to the varied composition case.The main effects of assuming a fixed composition (i.e., knowing the composition of the final cement mixture prior to modeling emissions) would lead to a deterministic chemical emissions value, whereas varying the composition would lead to varying emissions predicted from first-principles modeling.All other phases of the cement manufacturing process are not solely dependent on, and some are even independent of, material composition, meaning that a large spread in the predicted emissions due to uncertainty is still expected.This can be seen in figure 5(a), where the difference in the COV values of the fixed and varied composition total emission distributions is only reduced by 3%.However, the results also show that the pyroprocessing chemical emissions COV is the smallest among all the phases (∼1.5%), meaning that first principles can predict pyroprocessing chemical emissions (the highest emissions contributor) relatively well even if there is some uncertainty in the cement material composition.

Summary of study motivation
The impacts of emissions associated with the built environment remain high and will continue to grow as a global issue.Implementing mitigation measures towards building material emissions requires obtaining a representative characterization of their life-cycle emission profiles, which could be challenging given issues such as data quality and availability, the various ways one can frame the LCA, and the different models that can be used to characterize the relationships of the product being assessed.The lack of consistent guidelines on how parameter, scenario, and model uncertainty should be handled in assessing emissions compounds this challenge, especially for ubiquitous products such as building materials.In this work, we provide a framework for how uncertainty analysis could be handled systematically for building materials, and apply this framework to OPC as a case study.We leverage insights from past works to develop guidelines on how parameter, scenario, and model uncertainty should be handled.For that, we develop a scenario-aware MCS that sits on top of a first-principles-based OPC emissions model.We assume that the major uncertainty of the modeling approach is mitigated given that its mathematical relationships are guided by first principles.Parameter uncertainty is handled by developing PDFs from literature data and sampling values for those parameters for each iteration of the MCS.Scenario uncertainty (defined as variability) was handled in two ways.The parameters that shape a scenario were either specified or sampled with equal likelihood for each iteration from a uniform distribution, which was the case for the mineral composition of the cement mixture.
When using this framework, deciding when to specify a scenario or to generate a uniform distribution to characterize it depends on the available information and how an LCA practitioner chooses to frame the study.For example, the cement kiln fuel and electricity mix used within the manufacturing process is often known, so those are scenario parameters that can often be specified, as was done in this study.Ideally, all scenario-related parameters would be specified; however, certain aspects such as the mineral composition of the cement product is not always known or discernable, which would require it to be sampled.In some cases, both approaches could be used to characterize a scenario to limit uncertainty and ambiguity surrounding the scenario when possible.This was demonstrated in the case of the transportation modeling, where the modes were specified but the transportation distances were sampled from a uniform distribution of minimum and maximum travel distances assumed for those modes.As with past studies, we emphasize accounting for and distinguishing between these different types of uncertainties because their relative importance to the overall uncertainty analysis is not discernable until the actual analysis is carried through.Neglecting one or more of these uncertainties could severely impact the conclusions drawn from the study [37,40,64,65,[68][69][70].

Development of scenario-aware MCS and associated challenges
We show that the first step for conducting a scenario-aware MCS is developing a detailed account of each process in the manufacturing of the material.This detailed account allows for a better understanding of the interactions that exist between the parameters that make up the process as well as facilitating the characterization of the type of uncertainty associated with the parameter.The process breakdown also facilitates the following steps which involve data collection for forming PDFs and scenario development.However, certain challenges remain with implementing this framework.For one, data collection can be a time-consuming process and some materials could be data-poor, making data collection for certain parameters difficult.Furthermore, for data-rich materials like cement, developing representative PDFs is feasible given the widespread documentation of cement manufacturing and its associated data.However, how representative the PDFs are of the actual parameters largely depends on the quality of the data collected.Having more data points might yield better-characterizing distributions, but the utility of the PDFs developed is only as valuable as the underlying data.Another challenge within the MCS space is developing a systematic method for distribution fitting parameters.As mentioned, previous studies simply assume a distribution based on the number of data points collected.We follow this approach when two or three data points are available (we assume uniform and triangular distributions, respectively), but we choose distributions based on the KS test when four or more data points are available.While this approach worked for the majority of the parameters, there were a few instances in which the distribution that yielded the lowest KS test statistic did not always generate appropriate sampled values (e.g., it would lead to negative values for some parameters or infeasibly large values in other instances).Thus, a different distribution with a low KS test statistic that is physically representative of the underlying data was assumed in those cases, which shows that further inspection of the chosen distribution (e.g., through a Q-Q plot) is necessary.If this approach were to be automated and implemented in an LCA software or any other general framework, it should be noted that further refinement of this approach, an inspection of the chosen distributions, may be required to ensure the suitability of the assumed distributions.Furthermore, while specifying scenario parameters removes some ambiguity from the overall uncertainty results, poor framing of the process and scenario could lead to incorrect conclusions to be drawn from the study.Similarly, while we assume that most model uncertainty is mitigated given the use of a first-principles OPC LCI, other sources of model uncertainty (e.g., those related to model scope and included processes) may still be present.

Summary of gained insights and model applications
Despite the challenges of this approach, its implementation provides several insights regarding uncertainty in cement GHG emissions.Whereas conventional studies typically only provide the final combined total emissions distribution of a process or product, we were able to determine emission distributions for each of the processes related to cement manufacturing given the detailed parameter breakdowns developed for each of those processes.This allows one to determine how scenario framing and different parameters affect individual process emissions.Apart from the differences in total emission distributions between both scenarios, figure 3 shows how the energy mixes and transportation assumptions affect the process-specific emission distributions differently.Processes such as pre-milling, post-milling, overhead, transportation, and, to a lesser degree, mineral extraction show an evident distinction in the emission distributions, whereas pyroprocessing is mostly independent of the developed scenarios.This is also due to the similarities between the two kiln fuel mixes, which leads to the pyroprocessing energy-related emissions to be quite comparable.The process-specific distributions also allow one to identify conditions that lead to the trends observed in the emissions distributions.For the case of a conventional and widely-used material like cement, the conditions and processes that drive higher emissions are rather obvious.Inefficient processes fueled by carbon-intensive energy sources drive higher emissions; however, for unconventional and not widely studied materials, the processes and conditions may not be entirely evident if such a detailed framework is not implemented.The median total emissions from cement manufacturing are found to be 1.06 and 1.20 kgCO 2 e/kg for ET Scenario 1 and ET Scenario 2, respectively.Nationally averaged US cradle-to-gate cement emissions vary between 0.93 and 1.04 kgCO 2 e/kg [9], which are slightly lower than the results of this study.These values are based on a certain set of assumptions (e.g., using average US electricity mix) that may diverge from the assumptions of included within our two scenarios.To better understand the reasons behind these differences, it should be noted that our run of the base cement model used to develop the MCS model [63] yields a total emissions value of 0.987 kgCO 2 e/kg, which falls within the average expected range.Upon comparing the median emissions of the different modeled processes to the base cement model (tables S5 and S6), pyroprocessing (inefficiency) (0.177 [base] vs 0.204 [MCS median] kgCO 2 e/kg) and pyroprocessing chemical emissions (inefficiency) (0.0370 [base] vs 0.0600 [MCS median] kgCO 2 e/kg) are the two processes that show the most divergence in median emissions from the base cement model emissions.Due to the lack of pyroprocessing inefficiency data, generated inefficiency distribution peaks were centered around the inefficiency values assumed in the base cement model.This assumption yielded inefficiency distributions whose peaks lie around the base cement value emissions (pyroprocessing (inefficiency): 0.177 [base] vs 0.195 [MCS peak density]; pyroprocessing chemical emissions (inefficiency): 0.0370 [base] vs 0.0425 [MCS peak density] kgCO 2 e/kg).However, the MCS also accounted for scenarios where processes inefficiencies may be much higher, which increased the median emissions.Furthermore, the mineral extraction process shows higher emissions than the base cement model (0.0145 [base] vs ∼0.056/0.068kgCO 2 e/kg) due to the two scenarios sampling different mineral compositions, which in some cases may be more energy intensive and lead to higher emissions.As mentioned, ET Scenario 2's total emissions are relatively higher than ET Scenario 1's (which is closer to the average range) due to the higher carbon intensity of the electricity mix and cement kiln.
The framework reveals which processes have the highest impacts on the total emissions distribution and thus can inform which process uncertainties to mitigate.Figure 4 shows the relationship between the emission contribution distribution of each process and its COV, which is used as a proxy for its relative uncertainty.In most cement LCAs, there is large uncertainty regarding the emissions from facility-related energy use and transportation [41]; however, the emission contributions and the COV for these processes were shown to be relatively low under both scenarios.Other processes such as pre-milling had moderate COV values, but the importance of their emission contributions varied based on the scenario analyzed.This shows that assumptions made in a base case scenario may mislead one into thinking that the emissions contributions of a process may be low and may even lead one to exclude it from the modeling scope.However, its actual contribution may be underestimated under differing scenarios and conditions.Processes with high uncertainty and emission contributions include the pyroprocessing chemical inefficiency emissions, suggesting that mitigating the uncertainty surrounding this process can aid in developing a better characterization of the emission profile of cement.Finally, the mineral composition of the cement product, which is typically an unspecified parameter, creates a small variation in the total emissions distribution.Thus, a representative distribution can be attained even if the mineral composition is unknown when using a first-principles approach for modeling cement emissions.
The uses of this type of framework are extensive.While some LCA software include some uncertainty assessment capabilities, there is a lack of standardized stochastic uncertainty assessment methods across LCA software and EPD reports.Currently, LCA software either include qualitative uncertainty assessment methods or quantitative methods that lack the level of detail needed to provide accurate emission profiles [43][44][45][46].Furthermore, most EPDs do not capture any uncertainty within their reports [84].Thus, the integration of a standardized scenario-aware MCS framework would provide more insightful results and allow for more robust conclusions to be drawn.The MCS could also be adapted to include a multitude of impact criteria ranging from energy use to human exposure impacts [85,86].It can even be extended to provide confidence intervals for the carbon storage potential of different sequestering materials such as concrete and biomass-based materials, especially given their large potential for mitigating the carbon impacts of the built environment [20,87].The use of a quantitative uncertainty framework that integrates scenario analysis such as this becomes especially significant when comparing and choosing between alternatives, as this study reaffirms that deterministic analyses are insufficient for drawing robust conclusions [37,64,65,68,71,73,88].

Figure 1 .
Figure 1.Parameter breakdown diagram of the mineral extraction phase of cement modeling.Each parameter is designated as having uncertainty, variability, or falling under first principles, and how each of those designations are handled.Parameter breakdowns of all other processes can be found in the SI.

Figure 2 .
Figure 2. Scenarios developed for OPC MCS modeling.The upper-level scenario differentiates between fixed and variable material composition for cement.The lower-level scenario differentiated between possible energy mixes and transportation modes that can be used in cement manufacturing.The individual energy-transportation scenarios (ET Scenario 1 and ET Scenario 2) on both branches are identical, where each set of scenarios are run under variable and fixed cement clinker composition scenarios.

Figure 3 .
Figure 3. Scenario-aware MCS emission distributions for each phase of the cement manufacturing process.Distributions are shown for the varied cement material composition scenarios and both energy-transportation (ET) scenarios.

Figure 4 .
Figure 4. Emission contribution distributions of each phase of cement manufacturing along with the coefficient of variation of the emission distribution of each of those processes for (a) energy-transportation (ET) Scenario 1 and (b) ET Scenario 2. Distributions are rank-ordered from lowest (top) to highest (bottom) median emission contributions.Black bars within each violin plot show the interquartile range (i.e., range of values falling between the 25th and 75th percentiles) and the white circles represent the median value.(OH: overhead; Tran: transportation; ME: mineral extraction; PostM: post-milling; PreM: pre-milling; mineral extraction; PChI: pyroprocessing chemical inefficiency emissions; PR: pyroprocessing required energy emissions; PI: pyroprocessing required energy inefficiency emissions; PChR: pyroprocessing chemical emissions).

Figure 5 .
Figure 5. (a) MCS total emission distributions of the varied and fixed cement clinker material composition mixes for energy-transportation (ET) Scenario 1.(b) Pyroprocessing chemical emissions distributions of the varied and fixed cement clinker material composition mixes.Given that the fixed cement clinker material composition scenario only represents the base cement clinker compositions, it yields a deterministic emissions value for the pyroprocessing chemical emissions represented by the vertical magenta line (0.517 kgCO2e/kg cement).