Uncertainties in whole-building life cycle assessment: A systematic review

the known-what and known-how questions, this study contributes to the body of knowledge of LCA by providing a compre- hensive and systematic methodology to evaluate the EIs of buildings.


Introduction
Confronted with the pressing challenge on climate change, governments around the globe are prioritising environmental consideration on their agenda. For example, the United Kingdom (UK) became the first major economy to commit to achieving net zero greenhouse gas (GHG) emissions by 2050 [1]. Among the various GHG emitters, the building sector instigates a massive impact on the environment due to its intensive resource depletion and energy consumption [2,3]. However, such a striking phenomenon will not disappear imminently due to the population growth, longer time spent inside buildings (e.g., over 20 h due to COVID-19 restriction rules), and demands for better building services and comfort (e.g., 300,000 new homes per year by the mid-2020s in England) [4]. Therefore, concepts such as green buildings, sustainable buildings and net-zero energy buildings [5], and different types of building rating systems, including Building Research Establishment Environmental Assessment Method (BREEAM), Leadership in Energy and Environmental Design (LEED), and Deutsche Gesellschaft für Nachhaltiges Bauen (DGNB) [6] have been developed and adopted by countries to optimise building design and reduce energy consumption and emissions. To name a few, a net-zero building requires that the energy use of a building equals to its energy generation [7], and the LEED rating system requires a building to earn credits in six categories, covering location and site selection, water and energy efficiency, materials, and resources [8]. Nevertheless, endeavours of this kind only consider one or a few aspects of building performance, failing to capture buildings' full inventory and variations over time. Given that the ultimate goal is to deliver overall sustainable buildings throughout their life cycle [9,10], there is a need to develop a more comprehensive method to evaluate the 'cradle to grave' EIs of a building.
To do so, whole-building life cycle assessment (WBLCA) has pervaded the analysis of the overall building performance [11,12] by monitoring and assessing buildings' life-cycle EIs (e.g., production, construction, operation and maintenance, and decommission phases) [13]. According to Feng et al. [14], WBLCA can avoid passing the environmental load from one life cycle phase to another in the decision making process. However, it should be noted that buildings' lifecycle is relatively long (e.g., 50-70 years), contains complex structures, and necessitates a great number of materials [13]. This may explain the copious LCA studies that have focused on materials. For example, Lan et al. [15] emphasied the integration of system-level management (e.g., forest management) into harnessing the benefits of cross-laminated timber in GHG emission. Hollberg et al. [16] argued that the building information modelling (BIM)-LCA appraoch (using BIM to automatocally take bill of quantities of materials) could be misleading due to the use of placeholder materials. However, a BIM-based life cycle sustainability assessment (covering wider aspects than LCA) helped Patel and Ruparathna [17] confirm geomembrane can be a sustainable material of roads. As an important material in construction, Zhang et al. [18] investigated how LCA should be properly applied to evaluate the application of recycled aggregate concrete. Despite these promising scholarships, their findings have not been widely adopted in the building sector, and more importanly, Nwodo and Anumba [10] contend that the lack of uncertainty analysis strikes as a major challenge in building LCA. Failure to do so, as argued by Igos et al. [19], would decrease the reliability and credibility of LCA results.
Faced with the uncertainties casued by these 'dynamics' and the subsequent inconsistent and perhaps unreliable final WBLCA results [20,21], several uncertainty analyses have been conducted to improve the WBLCA results and facilitate decision making. For example, Robati et al. [22] applied Monte Carlo simulation (MCS) to examine the uncertainty in materials. Harter et al. [23] proposed the variance-based method to understand uncertainties in design parameters at different building development levels. For uncertainty emanated from the LCA method itself, Buyle et al. [24] used consequential LCA to identify the uncertain marginal suppliers, including market boundaries and market volume trends, as compared with the single set of model assumptions in conventional LCA. Nevertheless, these studies have a tendency to: (1) select specific methods (e.g., MCS): or a mixture of them (e.g., MCS and sensitivity analysis) to address specific uncertainties (e.g., materials and parameters) (i.e., they appear in a piecemeal manner); and (2) use uncertainty analysis as a 'procedure' in the paper without providing how it was conducted and associated implications [25,26]. In other words, a thorough investigation of the complete uncertainty sources, solutions and practical guidance is currently not available in the literature. Without such a line of inquiry, the capability to further minimise the uncertainties of WBLCA results is hindered. More importantly, identifying the roots that cause the uncertainties of WBLCA results and illuminating the possible solutions are of the uttmost concern of decision makers to realise sustainable building developments. Therefore, this present study aims to critically review the current status of WBLCA, the uncertainties of WBLCA results, and the latent methods to reduce the uncertainties, as well as propose a conceptual framework to assist LCA practitioners in understanding and curbing the uncertainties of WBLCA. Unlike previous examples, this study provides an aggregated view of the uncertainties of WBLCA, their solutions and a practical pathway. Acknowledging the proliferating signifance of WBLCA in improving building performance, this timely inquiry also paves an avenue for future headway to be made.
The remainder of this paper is structured as follows: Section 2 explains the systematic method followed throughout. Section 3 and Section 4 critically review the state-of-the-art WBLCA and the factors/sources that lead to its uncertainties, respectively. Section 5 details the existing methods to quantify uncertainties of WBLCA. Building on the uncertainties and their solutions, Section 6 proposes a conceptual framework to facilitate LCA practitioners' decision making. This paper finishes by summarising its conclusions and channelling future work.

Methodology
To fulfill the research aim identified above, a systematic literature review was conducted to identify, evaluate and interpret the current status of WBLCA, the uncertainties of WBLCA results, their solutions, and the prospect of a framework in mitigating the uncertainties of WBLCA results. Literature review, as a research methodology, is robust in synthesising research findings and facilitating new knowledge production [27]. On the other hand, an unthorough, unsystematic and selective literature review will result in flaws in the target research [27]. Hence, a step-by-step (i.e., systematic) searching and sifting process similar to Feng et al. [14] was implemented to eschew authors' bias in selection (i.e., thorough and impartial). Fig. 1 outlines the research flow of this study, comprising: (1) database and sequential search; (2) screening and sifting; and (3) evaluation and interpretation.

Database and sequential search
Web of Science (WoS) was selected to conduct the literature search as it is a well-recognized database for academic articles and publications, which allows users to retrieve pertinent research with the function of advanced search [28]. In order to focus on the most valuable studies in the database and minimise authors' bias in selecting publications [27], titles, abstracts and keywords (T/A/K) were manually examined at each sequence. Moreover, four criteria were established and maintained to mitigate subjectivity throughout the screening and sifting process: (1) Year: 2000 to 2020 (both sides inclusive); (2) Type: peer-reviewed journals; (3) Language: English; and (4) Relevance: T/A/K related to search strings. In other words, only journal articles which are from 2000 to 2020, written in English, and focussed on building LCA were initially included. For instance, although Dai et al. [29] proposed a multilevel modelling approach to quantify uncertainties in terms of missing data, and temporal and geographical characteristics in the life cycle inventory (LCI) databases, this article was excluded as it applies to the agriculture sector (i.e., nitrogen fertilizer application for corn production).
The keyword "building LCA" was first used to identify the related literature. Consequently, a total of 5890 results were generated to analyse the status of WBLCA. Then, the keyword "uncertainty" was added to the previous search output, providing 426 results to have an in-depth view of the uncertainty related to building LCA. Furthermore, among the 426 articles, those that not only mention 'uncertainty' but also present a 'solution' were shortlisted (i.e., 43 publications) to examine the existing solutions to WBLCA. This sequential literature identification process provides a staged and comprehensive view of each aspect (Table 1) studied in this research. It also shows the priorities and 'negligences' of existing studies, for example, only 43 out of 426 articles have performed an uncertainty analysis. A similar procedure has been followed in Feng et al. [14] and Muazu et al. [30].

Evaluation and interpretation
Bibliometric analysis and content analysis were applied to evaluate and interpret the selected literature (Table 1) [31,32]. Specifically, VOSViewer was adopted to facilitate the bibliometric analysis to provide a visualised view of the status quo of WBLCA in the existing literature, viz. development trend (i.e., publication yearly distribution), publication sources (i.e., density visualisation), and research hotspots (i.e., keywords occurrence). VOSViewer is a computer program that is capable of creating maps of scientific journals, researchers, keywords, etc. based on co-occurrence, bibliographic coupling or co-citation networks extracted from literature database [33]. Content analysis, on the other hand, was performed to deepen our understanding of the uncertainties associated with the WBLCA and the existing methods proposed to increase the accuracy of WBLCA results. By synthesising the findings from the review, new knowledge on how practitioners can better conduct a full WBLCA, treat WBLCA uncertainties, and make informed building performance decisions were acquired. Among the 5890 papers published, Journal of Cleaner Production and International Journal of Life Cycle Assessment were found two be the top two journals that have the most journal papers published in this topic, which accounted for 26% in total. Energy and Building and Building and Environment are the second top group that contributed a total of 13%. Sustainability, Journal of Industrial Ecology and Renewable & Sustainable Energy Reviews are the third top group that shared 10% of the selected journals. Among the bulky portions of journals that sometimes overwhelm academics and practitioners [34], the resultant publication names can be readily used by them to search and publish studies relating to building LCA. We now commence with the analysis of the status of WBLCA.

Status of whole-building LCA
Using the function of keywords occurrence VOSViewer, 'LCA' and 'building' were shown to be the most occurred keywords, and "LCA" has different kinds of notation styles. 'Energy', 'embodied energy', 'impact(s)', and 'environmental impact(s)' were the second most occurred keywords. Based on the keywords occurrence density, current studies on building LCAs mainly focused on energy or environmental performance. While the embodied energy/carbon were highlighted as the most occurred keywords, the operational energy/carbon emission haven't been paid enough attention. However, studies show that the operational energy/carbon emission is as important as the embodied energy/carbon emission [35,36]. Furthermore, these two aspects are intertwined and need to be considered together. Table 2 lists the relationships between the operational and embodied carbon emissions compiled by different researchers for different buildings. It shows that a comprehensive analysis of building emissions requires the consideration of embodied emissions in material production stage and the emissions in the operation stage, since the emission percentage from other building life-cycle stages would increase when operational energy consumption reduces. Based on the keyword occurrence density, it is suggested that more studies should be conducted to analyse the operational energy/carbon emissions.
'Design' and 'construction' were the other highlighted keywords in building LCA; however, there are other life cycle stages (e.g., the maintenance and repair stage and disposal stage) that have not been highlighted. However, Bruce-Hyrkäs et al. [48] and Pasanen et al. [49] have shown that the percentage of emissions from maintenance and repair stages increases with a corresponding significant reduction in operational emissions. By only focusing on the design and construction stages, it is unlikely that designers can garner a complete understanding of the building energy/environmental performance. In turn, according to Robati et al. [22] and Chau et al. [50], this creates difficulties for designers to make the best decisions on the overall building environmental performance. Therefore, the next step is to focus on the building over its whole life cycle from the building material manufacturing stage, construction stage, to operation and maintenance stage, and disposal stage. By following the EN15978 standard, WBLCA is a comprehensive method that measures the building performance at all the life cycle stages, which allows the designers to work out the optimal solution to improve building performance [51,52].
'Residential buildings' is another keyword that occurs frrequently in the building LCA keyword search output, which demonstrates a number of research have been conducted on residential buildings. For example, Kylili et al. [51] conducted a WBLCA for a passive   [47] house located in Cyprus to assess the environmental performance. In Norway, Kristjansdottir et al. [53] performed a LCA for eight different single-family houses, and the results illustrated the relationships between the operational and the embodied environmental impacts. Atmaca and Atmaca [54] analysed the life cycle carbon and energy emissions of two residential buildings from the construction phase to the demolition phase. Evangelista [55] presented a "cradle to grave" LCA analysis for four typical Brazilian residential buildings under eight impact categories. However, WBLCA has not been widely used in other building types, such as commercial and industrial buildings. One of the reasons could be the relatively simple structures of residential building, which makes it possible to conduct the comprehensive WBLCA. Therefore, more attention should be paid to apply WBLCA to other building types besides residential buildings. WBLCAs are becoming increasingly popular in building construction-related decision making due to the comprehensive and systematic approach of LCA to environmental evaluation [56,57]. Green building rating systems worldwide also start to assign credits to WBLCA. Table 3 outlines a few popular building rating schemes around the world that adopt WBLCA into the assessment criteria. Most of these rating schemes analyse all the materials that form the building structure and enclosure, and a whole-building life cycle is included from material production, building construction, to building operation and demolition. Since no keywords related to building rating systems were highlighted, future research could focus on analysing the impacts after applying WBLCA into the green building rating systems.
WBLCA is a valuable tool to help the public understand the life cycle impacts of buildings on energy/carbon emissions. It also helps the government to fulfil the legislative requirement and achieve the environmental targets. However, due to the uncertainties related to modelling, material choices, data variability, and source parameters throughout the LCA process, ensuring the reliability of WBCLA results is always a challenge [58,59]. Therefore, it is significant to elucidate all the factors that might create uncertainties on WBLCA results and summarise all the possible methods in the literature that could help reduce the uncertainties of WBLCA.

Sources of uncertainties on WBLCA results
The uncertainties of WBLCA results are mainly because of the complication of LCA development processes and the complexity of building structures [60,61]. For example, due to the data availability in LCA, the system boundary might not be complete which leads to uncertainty in results. Citherlet and Defaux [62] conducted a WBLCA for three home designs in Switzerland. However, the system boundary of this study was not complete and additional material losses were considered in the LCA. Due to the variety of LCA methods and databases, the LCA results could also be significantly different with uncertainties. One study indicates that the embodied CO 2 e results could be over 50% different between Ecoinvent database and ICE database for different building designs [63].
On the other hand, the variances in building materials and cut-off rules could lead to LCA result uncertainty, and the reference service life of the building could also result in a variation of WBLCA results. For example, studies have indicated that the annual energy demand could decrease approximately 14% when the building service life changes from 50 years to 75 years [43,64]. Silvestre et al. [65] further argue that the prediction of construction materials' service life is subjected to methodological uncertainty (i.e., the deterministic approach and the stochastic approach) that can impact LCA decisions at the design stage. Moreover, Su et al. [66] reveal that the parameter identification of building insulation materials, and in particular, physical parameters (e.g., thermal conductivity) of glass wool are a significant source of the uncertainty of its life cycle energy consumption.
Furthermore, the variances on construction practices and design parameter selection could also lead to LCA results uncertainties. For example, Hong et al. [71] stated that the inherent uncertainty during building construction phase could result in a coefficient of variation of 18% in uncertainty analysis. The major uncertainty sources during building construction, such as transport measurement method and geographic representativeness, were identified in this study. Escamilla and Habert [68] also indicated that the use of proper construction practices could build high technical performance building with low LCA impacts using geographic information system (GIS). In terms of design, Vuarnoz et al. [69] stated that the adoption of reality-based input parameters at the building design stage, such as occupancy rate, appliance usage, and energy conversation factor, would substantially impact LCA results. Therefore, the selection of construction practice and design parameters are also sources of uncertainties on WBLCA results.
Huijbregts [70] listed the types of uncertainty that are related to LCA development phases, which could be at the goal and scope definition phase, inventory analysis phase, as well as life cycle impact assessment phase including life cycle inventory analysis (LCIA) method and database (choice of impact categories, classification, characterisation and weighting methods). The source of uncertainty could be parameter uncertainty, model uncertainty, and uncertainty due to choices [59,70]. Elsewhere in the existing literature, Hong et al. [71] summarised those uncertain sources could result from data availability and quality [72], technical performance, emission factors and the functional unit [73] and cut-off, aggregation, temporal and geographic considerations [74]. To encapsulate the sources, Huijbregts et al. and Lloyd and Ries concluded that they can be categorised as parameter uncertainty, scenario uncertainty, and model uncertainty [75,76]. Favi et al. [95] further cited Der Kiureghian and Ditlevsen [77] and classified them into epistemic uncertainty, which can be mitigated by collecting more data and/or optimising models, and uncertainty in aleatory, which exists in the natural randomness in a process and thus is unavoidable. Here, Table 4 identifies the most notable factors from the 426 papers that create uncertainties on WBLCA results, namely system boundary (including service life), different building components/elements, LCI, databases and methods used. In addition, Table 4 summarises the most relevant WBLCA development details to facilitate a better understanding of the uncertain sources of WBLCA results. The results show that the current WBLCA development methods are inconsistent in different LCA phases, and the WBLCA results are presented with uncertainties, which point out the necessity of proposing solutions to address them.

Solutions to reduce the uncertainties
Through the literature review, it is revealed that while most of the studies (i.e., 426 publications) acknowledge the existence of uncertainties of WBLCA results, less than 1/4 of them (i.e., 43 publications) attempt to resolve the problem. This finding concurs with Blengini and Carlo [89] and Rodrigues et al. [90] arguing that existing LCA approaches generally do not address uncertainty. During the third round of literature retrieval, a total of eight potential solutions, namely, MCS, sensitivity analysis, pedigree matrix and data quality indicators (DQI), fuzzy related method, Taylor series expansion and analysis of variance (ANOVA), decision support diagram, structured under-specification, and variants thereof (e.g., MCS mixed with pedigree matrix) have been identified. Notably, MCS is the most popular method (25 times) adopted to understand the uncertainties of WBLCA results, followed by sensitivity analysis (19 times), pedigree matrix and DQI (12 times), and fuzzy methods (three times). Those mentioned only one time are categorised as 'other miscellaneous methods' hereinafter. The total number of times appeared is over 43 as some studies deployed more than one solution in a single study.

Monte Carlo simulation
Compared with a single value assigned to each parameter (i.e., deterministic approach) [76], MCS is a tool through which uncertainty can be quantified (i.e., probability distribution of output parameters) by using random values of input parameters [22,91]. Within the identified WBLCA studies, it has been applied to different parts (e.g., brick/fired-clay walls, insulation, flooring, etc.), phases (i.e., different system boundaries) and types (e.g., commercial and residential, traditional and contemporary) of buildings in different regions (e.g., Canada, Australia, Belgium) to address the result uncertainty caused by a variety of factors (e.g., materials, data, and model parameters). For example, MCS is employed by Rodrigues et al. [90] and Rezaei et al. [92] to compensate information shortage on materials at the early design stage of residential buildings in the South European Climate and Canada, respectively. In this sense, designers can become aware of the EIs of their design and select materials that are environmental-friendly. Using MCS, Burek and Nutter [93] analysed the LCIA uncertainties of Walmart's distribution centres and confirmed electricity generation to be the biggest source of uncertainty. However, they consider only the uncertainties resulted from LCI input data while overlook the characterisation factors. The LCI data uncertainty was also examined by Hasik et al. [91] via MCS in three types of water systems of buildings and they attributed the uncertainties to a low number or large variability of samples and spatial and temporal scales. In addition, this uncertainty relates to how data are distributed (i.e., normally and uniformly). However, Pomponi et al. [94] argued that this relevance disappears in the MCS result after 104 random samplings from within the data variation range. There are other uncertain sources, such as material composition, transportation, energy usage, and service life prediction methods of materials that have been measured by MCS [65,95]. For instance, Robati et al. [22] predicted the EIs of each of 19 building materials for a 50-year building lifespan by considering uncertain variables such as materials' lifetime, CO 2e and transport distance.

Sensitivity analysis
While there are solutions (e.g., MCS) aiming to understand the uncertainty of the LCA result, sensitivity analysis is commonly used to understand what parameters impact the result most [94]. Notably, a comprehensive list of the uncertainty types and their classification within the selected studies is presented in Section 4. This scenario-based approach is considered to be complementary to uncertainty analysis (sometimes even treated as the same, e.g., Walker et al. [96]) and a combination of them facilitates better decision-making (Roder et al., [97]). In the selected studies, we identify the most prevalent practice is a mixture of sensitivity analysis and MCS to target uncertainties in design features and background LCI data (Eckelman et al., [98]), foreground and background LCI data and transport (distance and types of vehicles) (Cuenca-Moyano et al., [99]), materials (Favi et al., [100]), commodity prices (Teh et al., [101]), key performance indicators (Walker et al., [96]), etc. An example is Ross and Cheah [102] adopted MCS to study LCA uncertainty of buildings' air conditioning systems resulted from different user behaviours and a subsequent sensitivity analysis identified system cooling and unoccupied room to be the highest influential factors. Similarly, maintenance frequency (frequent or periodic) and types (vacuum, sweep, or mop) can contribute to different LCA results of different floors. However, the sensitivity analysis in Minne and Crittenden [103] confirmed vacuuming's significant role in EIs. Aktas and Bilec [104] addressed the different lifetime of residential buildings in affecting their interior renovation energy consumption using MCS. Compared with the lifetime of carpet, ceramic, paint and Vinyl, residential building lifetime was found to be most significant using a sensitivity analysis. Different from the 'normal' procedure, Benetto et al. [105] firstly conducted a sensitivity analysis and then an uncertainty analysis through MCS. However, they only considered limited parameters in the sensitivity analysis and overlooked the uncertainties resulted from data recordings and data collection, which in turn jeopardise the accuracy of the final result. By contrast, the normal procedure followed in Su et al. [66] was able to examine all uncertain sources in the MCS and uncovered that physical parameters (i.e., conductivity and density) affect the LCA of building insulation materials most (i.e., 47% and 66.9%). Nevertheless, the use of hypothesis or empirical information in MCS can lead to this big uncertainty of physical parameters. In addition, Teh et al. [101] stated that the economy-wide system boundary embedded with the methodology resulted in higher GHG emissions. Obviously, these point out the importance of selecting appropriate uncertainty analysis methods per se and the awareness of their inherent uncertainty.
Sometimes (e.g., Cellura et al. [106], Walker et al. [96]), it is noted that sensitivity analysis is treated as the same as uncertainty analysis. This way, they tend to identify several variables that may be of high impact on the result and calculate their 'uncertainties' under a certain range (e.g., ±10%) or different scenarios (e.g., different impact assessment methods). For example, Cellura et al. [106] constructed different scenarios to study the uncertainties arisen from the secondary input data (i.e., transportation, electricity, and baking step) and methods (i.e., CML 2 baseline 2000, Ecoindicator 95, EDIP/UMIP 97, IPCC 2007 and Impact 2002+) for roof tiles. However, problems can include: (1) it is not clear how these critical variables are identified; and (2) result shows the variables may not be critical, impeding a better understanding of the uncertainty. A case is, in Lu et al.'s study [107], three variables (change between −10% and +10) were presumably selected to check their uncertainties, and emissions from transportation processes was tested to be insensitive. In comparison, a hotspot analysis was undertaken by Wang et al. [108] to search the significant variables (i.e., transportation) and then calculated its variability. Therefore, it signifies not only the awareness of variances between uncertainty methods as mentioned above but also the careful selection of a single method with different types. As stated in Pannier et al. [109], different types of sensitivity analysis, such as screening and global ones, can present different relative influences of uncertain factors.

Pedigree matrix and data quality indicators
Pedigree matrix is introduced to ensure the reliability and applicability of LCA results by managing data quality. It encompasses five indicators, such as reliability, completeness, temporal correlation, geographical correlation, and further technological correlation, which have a score of 1-5, to adapt the actual data to a specific data quality goal [72]. In the target literature, we have witnessed the synergies of pedigree matrix, MCS and sensitivity analysis to estimate uncertainty and almost a half of them in CO 2 emission and embodied energy. Zhang et al. [110] used DQI and MCS to cope with parameter uncertainty followed by a scenario analysis to treat scenario uncertainty (e.g., different system boundaries and energy efficiency) and model uncertainty (e.g., different transformational relationships and distribution selection) for building life cycle carbon emission. The identical approach was applied in Zhang et al. [110] but for carbon emission during building construction. Similarly, the GHG emission during the construction was computed in Hong et al. [71] by combining MCS and DQI to ascertain input data that were deemed highly uncertain. The addition of MCS to DQI can mitigate the subjective evaluation and lower the calculation cost. However, compared with statistical methods, the result is not accurate. Therefore, a hybrid MCS-DQI-statistical method was proposed by Wang and Shen [111] for whole building embodied energy analysis and more accurate result and cheaper cost were observed than pure DQI and statistical methods, respectively. Moreover, recognising DQIs do not always contribute equally, a weighting mechanism is considered in the sole use of the pedigree matrix. For example, the analytical hierarchy process was employed by Wang et al. [112] to determine the weighting of each DQI and estimate better probabilistic values of embodied energy intensity for concrete, steel and glass. Similarly, Taborianski and Prado [113] and Henriksson et al. [114] considered the weighting level of each life cycle stage and data's central value when multiple reported values are available, respectively.
In addition to the MCS and DQI to address absolute accuracy of the final LCA result, it is common to compare the uncertainty between scenarios, such as different earth-retaining walls [115], fired-clay bricks produced by different manufacturers [116], contemporary and traditional housing [117] and country-wide clay hollow brick walls [58]. According to Piroozfar et al. [117], the pedigree matrix showed that uncertainty for traditional houses is higher than contemporary houses, but the LCA results stimulated by MCS presented better EIs in the traditional houses. On the one hand, it challenges the environmental-friendly materials (e.g., limestone and lime mortar) as touted in the contemporary houses. On the other hand, it reinforces the importance of recording real data relating to building materials and methods that would otherwise generate uncertainties. This meaningful comparison perhaps corroborates Blengini and Carlo's [89] statement on the relatively more accurate comparative LCAs due to a higher correlation within scenarios' uncertainty.

Fuzzy-related methods
Fuzzy-related methods (e.g., fuzzy rough sets, fuzzy variables, fuzzy logic approach and intuitionistic fuzzy sets) have been performed to counter the uncertainties in variables/parameters and input data of LCA. For example, Li et al. [118] applied fuzzy rough sets to study the LCA uncertainty of a distributed renewable energy system derived from its power plant capacity, annual operation hours, and upstream Technosphere performance. Due to the different results from a sensitivity analysis, they believed that fuzzy rough sets are a new way of addressing uncertainties. However, how the different results impact decision-making should have been made clear. In the wind energy sector, intuitionistic fuzzy sets have been adopted by Gumus et al. [119] to examine uncertainties in indicators and lifecycle span of energy planning alternatives. In essence, a survey conducted by Lloyd and Ries [76] indicated that fuzzy data sets are ranked as the third most commonly used uncertainty method in addition to stochastic modelling (e.g., MCS) and scenarios. However, this does not appear to hold in the context of WBLCA in this research because there were only two articles that were qualified for review. Nevertheless, their applications in other areas shed light on how the fuzzy concept can potentially be mobilised in WBLCA.
Using linguistic rules, fuzzy set theory assumes the elements of a set following a membership function with the value ranging from 0 to 1 rather than binary terms [120]. This can solve the problem where an arbitrary number is assigned to a variable or where precise values are not available in WBLCA. As such, Ardente et al. [121] proposed a software based on fuzzy logic to define uncertain data on their age, underlying technology, statistical and geographic representativeness. In the case of plaster materials, it allowed WBLCA practitioners to view the whole calculation process and describe the sensitivities of each solution. More recently, Kaziolas et al. [122] chose two most uncertain variables, namely the end transport and recycling rate as fuzzy variables to calculate the EIs of a timber residential building and a steel building, respectively. A common feature of these two studies is that the fuzzy application to WBLCA requires expert knowledge and judgement, indicating the importance of experienced experts.

Other methods
Through the literature review, a variety of 'non-mainstream' methods have been identified, which however, have provided a new stream of solutions to tackle uncertainties of LCA. For example, Hoxha et al. [123] adapted the Taylor series expansion and ANOVA to depict uncertainties (represented by mean value and the variance) in impact coefficient, density, mass and service life of building materials (see Hoxha et al. [124] p. 56 and Scherre [125], p. 534 for equations of the two methods). One benefit of this mixed method lies in that the Taylor series method can only calculate the mean value and the variance of continuous variables while ANOVA complements this by serving the discrete variables (e.g., the number of uses of material). Targeting at the specific spatial dimension to reduce geographic uncertainty at every LCA stage, Patouillard et al. [126] developed an iterative decision-support diagram to guide the inventory regionalisation and inventory spatialisation process by considering existing approaches (e.g., GIS) in the literature. While this provides a portable tool for practitioners to minimise spatial uncertainty without having to develop new instruments, it is suggested that uncertainty contribution analysis (i.e., determine if the uncertainty comes from inventory data or spatial variability of characterisation factors) should be developed in the long-term. Standing at the early design stage when detailed information on the system under investigation is unavailable, Tecchio et al. [127] proposed the structured under-specification where a hierarchical data structure is established to classify building materials and assemblies with different levels of specificity. Harter et al. [23], on the other hand, shifted the specificity to different building development levels and used the variance-based method to quantity uncertain design parameters, such as geometry, technology, operational design and system efficiency. Primarily, they focused on decomposing the model output variance and calculating the first-order effect and total effect to indicate the importance and effects of a parameter on uncertainty. In this sense, it can be regarded as a form of sensitivity analysis.
There are some other advanced uncertainty calculation methods that can be considered in WBLCA. A germane example is the Polynomial Chaos (PC) expansion where Sepahvand et al. [128] demonstrated the use of orthogonal polynomials as the expansion base in various random variables to compute the parameter uncertainty. Compared with the sampling method (e.g., MCS), PC expansion represents the uncertain quantities as an expansion in a non-sampling and surrogate way, and proves to be more accurate and time efficient. In fact, it has been pioneered by Galimshina et al. [129] to understand the uncertainty value in LCA and life cycle cost of residential building renovation in Switzerland. In addition, Latin hypercube sampling and quasi-MCS, which employ the stratified sampling approach (i.e., the input parameters are more uniformly distributed) and quasi-random numbers, respectively, have been identified by Groen et al. [130] to be more accurate in calculating the sample mean than MCS in LCA. Bayesian approach is another parameter uncertainty quantification method applied in Liang et al. [131]. It features a posterior probability distribution of the parameter by combining prior information (i.e., existing knowledge) and the likelihood information (i.e., the proximity of simulated and observed data). While these methods may not be readily available in WBLCA, it explicitly implicates that WBLCA researchers and practitioners need to learn from other areas and adapt the methods to their own needs.

A conceptual framework
The WBLCA community is in urgent need of a clear understanding of uncertainties associated with WBLCA to underpin decisions for sustainable development [110,122]. However, despite the sporadic efforts as we have uncovered, a comprehensive taxonomy of WBLCA uncertain sources and corresponding solutions are far from being at the fingertips. Having in place a typology of uncertainties and promising solutions, therefore, is important as this proposed pathway (Fig. 3): (1) configures life-cycle stages and function units to achieve a true WBLCA; (2) considers an exhaustive list of uncertainties and categorises them based on different LCA stages; and (3) provides pinpoint solutions to treat each uncertainty. To better employ the framework, the practitioners first need to decide on whether a true WBLCA or a 'fitness for purpose' LCA (e.g., not all life-cycle stages and function units are assessed) is needed. With the determined goal in mind, they then need to understand the life-cycle stages, function unit and their corresponding uncertainty taxonomy and solutions as depicted in Fig. 3. For example, if the 'fitness for purpose' scenario selects the 'production to demolition' stage for external walls, Fig. 3 then makes it clear to the practitioners that there will be five categories of uncertainties along the assessment process that should be noticed, and provides corresponding solutions to measure them.
Current research tends to frame WBLCA into different stages, such as the construction stage [71] and the replacement stage [58], and specific parts and materials, such as walls [115], floors [108] and concrete and cement [101], rendering a somewhat 'quasi-WBLCA'. While it is difficult to obtain a complete LCI and best-guess values have to be used, it is possible to create a 'true' WBLCA by integrating life-cycle stages and function units. For example, Hoxha et al. [123] calculated the EIs of a building by calculating the cumulative sum of materials' (or components') EI and energy's EI. Put simply, the WBLCA should perhaps consider every material and component and their associated impact over the life cycle. In a 'fitness for purpose' scenario, where true WBLCA is costly and time-consuming, the framework can be adapted to target components (e.g., materials and embodied energy) that may be of high impact. However, these components should be determined scientifically (e.g., a contribution analysis) as subjective choices can be counterintuitive [117]. To realise the true WBLCA or 'fitness-for-purpose', we underlie a feeding mechanism where information can flow and be recorded throughout the assessment of the present project and lessons can be transposed to future projects. Another element relies on the understanding of the uncertainties as part of the WBLAC process.
There are studies that have outlined the sources of uncertainties [71,76]. However, a degree of ambiguity resides with the taxonomy of uncertainties and the correlation between each uncertainty and each solution. Building on the LCA stages and the factors we identified from the review, the goal and scope definition stage can contain such uncertainties as system boundary and function unit, and the inventory analysis stage can include parameter uncertainty. For the impact assessment stage, database and the LCIA methods are the main uncertain sources while human related factors (e.g., knowledge and experience) are evident at the interpretation stage. This classification allows LCA practitioners to be aware of the uncertainties and conveniently locate them throughout the assessment. More importantly, our framework suggests that the inventory stage and assessment stage are more uncertain than other stages with parameter uncertainty and database uncertainty being the prominent factors. To solve them, MCS, sensitivity analysis, DQIs and fuzzy related methods can be useful, and MCS and sensitivity analysis are able to address a broader range of uncertainties. However, we argue these different solutions themselves can embed uncertainties (i.e., uncertainty methods). Similarly, Cellura et al. [106] contend that the EIs are different using different LCIA methodologies. This, again points out the importance of: (1) LCA practitioners' capability to select an appropriate LCIA method and uncertainty quantification method to minimise uncertainties; (2) using a mixture of uncertainty methods and developing new and effective tools; and (3) an accurate way of recording data in industry and academia as they are often the data source or benchmark of the LCA ('three principles'). Hoxha et al. [123] and Feng et al. [14] have reported that environmental product declarations (EPD) is a good example of reliable material information as EPD records data directly from manufacturers and companies, and is developed strictly following ISO 21931 and EN 15643 at the building level. Equally, this conceptual framework demonstrates a pathway for a suitable uncertainty method to be chosen and new ones to be developed for LCA practitioners.
Nevertheless, we are cognisant of the harsh reality that sometimes research findings are not applied to practice and vice versa [132]. In our case, the solutions identified in Section 5 may not be easily implemented by 'new' researchers and practitioners in the LCA field. This could be because some studies (e.g., Morales et al. [58], Teh et al. [101], Su et al., [66]) only mentioned, for example, that MCS is employed to quantify uncertainties without detailing the procedure. To facilitate the convergence of knowledge (i.e., understanding WBLCA uncertainties) between two communities, we summarised in Table 5 some promising tools emerged from the review process to bridge this gap. Taking the SimaPro software as an example, Silvestre et al. [65] elaborate five steps (see Heijungs et al. [133]) to be taken when using MCS to incorporate the parameter uncertainty. With these tools, the problem becomes 'how to use them and how to interpret the results after clicking buttons'.
It has been noted by Blengini and Carlo [89] that existing tools have their respective characteristics that may (dis)encourage LCA researchers and practitioners from adopting them. For instance, generic tools (e.g., SimaPro) are considered to be flexible by modelling different kinds of systems and having access to powerful databases. They, however, may not be attractive to users who prefer less complex analysis and friendly operation interface as in some building-specific tools (e.g., ATHENA system). Similarly, Meex et al. [137] suggest that current LCA-based EI assessment tools have complex methodologies and cannot be easily adapted, which hamper their adoption in the early design stage by architects. Therefore, it is important for researchers and practitioners to learn and grasp skills (e. g., software operation) to undertake WBLCA. Alternatively, we concur with Güereca et al. [138] that proper guidance and training should be provided to ensure the quality of LCA. Akin to the feeding mechanism in Fig. 3, the payoff for such investment will not be  [127] Note: Different from the uncertainty tools in Table 5, Al-Ghamdi and Bilec [56] provided a comparative review of existing WBLCA tools. Notably, some WBLCA tools (e. g., SimaPro and OpenLCA) are embbed with a function to perform an uncertainty analysis. A more recent review of the tools for visualising LCA results can be found in Hollberg et al. [136].
one-off as the knowledge can be passed down internally. Another benefit is that the increasing proficiency of LCA practitioners can counter the uncertainty caused by the users themselves as stated in Henriksson et al. [114]. In tandem, we need to reiterate that the solutions and relevant tools exist to help understand and reduce WBLCA uncertainties so that cautious decisions can be made. It would not be ideal to completely rely on the tools to extirpate the uncertainties as some of them cannot be reduced due to the natural randomness (see, Favi et al. [95]). In addition, the tools may embed shortcomings as Burek and Nutter [87] state that SimaPro 8.4 software cannot quantify the uncertainty of characterisation factors. This reinforces the awareness of the 'three principles' as we proposed above. What is more, the review results can shed light on further collaboration between policy-makers, researchers and practitioners about making sense of WBLCA uncertainties by demonstrating their sources, solutions, tools and pathways.

Conclusions
WBLCA results can be unreliable, and further undermine decisions made for sustainable building development due to the fragmented nature of the construction sector and the complexity of LCA. To address the paucity of research that investigates the comprehensive uncertain sources of WBLCA and their corresponding solutions, this study conducted a systematic review of WBLCA, its uncertainties and solutions and proposed a conceptual framework that depicts their typology for LCA practitioners. Our review on the status quo of WBLCA supports this research by suggesting that WBLCA is experiencing a bottleneck period due to the variety of LCA methods and the complexity of building structures, and thus more studies are needed to better understand its results. This study also indicates that while the importance of uncertainty is recognized, research does not follow the need for addressing or mitigating the uncertainty of WBLCA results.
Among the selected publications, we have identified that life-cycle stages, function unit, system boundary, input parameters, characterisation factors, databases, LCIA methods, practitioners' knowledge and experience, human activities and uncertainty methods can all be sources of the WBLCA uncertainties. Accordingly, there are a total of eight solutions and variants thereof that have been proposed with MCS and sensitivity analysis being the most common. Unlike previous examples, details on how they were employed to estimate uncertainties were analysed. Aiming to facilitate a true WBLCA and establish the correlation between uncertainties and their solutions, a conceptual framework juxtaposed with a feeding mechanism was developed. Its novel way of classifying a comprehensive list of uncertainties and solutions based on LCA stages allows LCA practitioners to be aware of the uncertainties, and conveniently locate and appraise them throughout the WBLCA. Therefore, by answering the known-what (i.e., status quo of WBLCA and the uncertain factors) and known-how (i.e., uncertainty methods and tools) questions, this paper sheds light on the WBLCA literature, and in particular, provides a practical pathway for WBLCA practitioners to conduct uncertainty analysis.
There are limitations of this research, which could form the basis for future work. First, if a WBLCA is costly and time-consuming, a robust method should be developed to help select the components that may have high EIs rather than the arbitrary judgement. Second, a case study can be conducted to demonstrate the application of the solutions identified in Section 5 (especially for the ones that have not been widely implemented in WBLCA), which adheres to the idea that guidance and trainings are important to demystify the 'black box'. Finally, the framework calls for an empirical comparison of the uncertainty methods per se and the development of new effective methods to evade the uncertainty resulted from the methods (i.e., solutions).