Life cycle impact assessment (LCIA) methods use unspecified archetypes to model situations of imperfect knowledge. There is an inherent uncertainty in characterisation factors to unspecified archetypes, and this study propos es an estimation of this uncertainty using continuous and discrete probability distributions . The extent of “archetype uncertainty” is analysed for several methods and the impact on LC IA scores is quantified for all activities in the database ecoinvent. Results indicate that this source of uncertainty can be very large, introducing systematic as well as random errors in LC IA scores. Based on this research we recommend to use undefined archetypes only when needed and quantify this source of uncertainty by de fault. The continuous and discrete approaches to model uncertainty give similar results, but the continuous approach is easier to implement. 1. INTRODUCTION Life cycle impact assessment (LCIA) methods model different exposure situations using archetypal scenarios such as emissions to indoor air or air in urban area . The characterisation factors (CF s) can vary widely between different archetypical scenarios of release, given the very different fate and exposure factors. For this reason a rchetype s are an effective way to account for the variability of CF s (Mutel et al. 2018) . For example, the carcinogenic impacts of cadmium emitted to soils can vary three orders of magnitude depending on whether it is emitted to agricultural or industrial soils (Fazio et al. 2018) . Regionalised models would need a very high spatial resolution to capture the differences between e.g. rural and urban settings, therefore archetypes are considered a pragmatic approach to capture CF variability (Bulle et al. 2019) . The archetypical scenarios are sometimes called “context”, dividing them into primary context and secondary c ontext (Edelen et al. 2019) . The primary and secondary context s are commonly referred to as compartment and subcompartment in LCA software. LCA software allows to have “unspecified” archetypes, and the CFs for these cases are sometimes defined by modeller developers other times by those who implement the model, but the reasoning behind the choice is rarely explained and appr oaches diverge . In OpenLCA and Simapro the CF s to unspecified archetypes are used to fill data gaps (Acero et al. 2017; Pré 2019) . Brightway2 uses the implementation of LCIA methods maintained by ecoinvent. The ecoinvent implementation uses different approac hes depending on the method (Bourgault 2019) . For example, f or ILCD method, the CFs for unspecified archetypes are sometimes used as a proxy to fill data gaps, but the documentation does not clarify how val ues for un specified archetypes are chosen when not provided by the method developer (Fazio et al. 2018) . Overall, there is no consensus on how to assign CFs to unspecified archetypes. Even un der the assumption that the chosen CFs for unspecified archetypes are a reasonable approximation , these CFs are inherently uncertain . The uncertainty of associated with the use of unspecified archetypes is to my knowledge not accounted in LCA studies, potentially leading to misleading conclusions . Several studies have analysed the variability of CF s. Bulle et al (2019) compared the variability of CF s between archetypes and regions for the method Impact World +. Impacts per kg of PM2.5 in the urban environment were found to be a factor of 30 higher than in the rural environment, and the archetype was found to be more important than the continent in which the emission took place (Bulle e t al. 2019) . Some studies have included CF uncerta inty in the calculation of LCA scores. Henriksson et al. (2015) included uncertainty on global warming and freshwater ec osystem impacts. Recently, Patouillard et al. (2019) included spatial variability of regionalized CF s in their approach to prioritise regionalization efforts. Their study used the regionalised method impact world + (Bulle et al. 2019) and modelled the spatial variability with a four -parameter beta distrib ution, using proxies of probability for an elementary flow to occur in each region (Patouillard et al. 2019) . However, no stud y seem s to have addressed yet what is the uncertainty of unspe cified subcompartments and how it affects LCA scores. In this study , I propose a generic procedure to define the CF s for undefined archetypal scenarios as a probability distribution . The u ncertainty associated with uncertain archetypes can be considered to be a source of epistemic uncertainty (i.e. uncertainty associated to lack of knowledge). The study could be framed as a study of uncertainty due to archetypical aggregation (UNEP -SETAC 2019) . The procedure is implemented using the open -source LCA framework Brightway 2 (Mutel 2017) . The procedure is app licable to all methods that use archetyp es in their modelling. The modified impact assessment methods are then tested with activities of the LCA database ecoinvent 3.6 (Wernet et al. 2015) to assess the effects on widely used LCA databases . 2. Materials and methods 2.1. Uncertainty characterization The functions developed for this study take an impact assessment method as an input, and return a version of the method where the elementary flows to uncertain archetypes have their CFs defined as a probability distribution instead of a scalar value . The CF for a given substance and “compartment” and undefined archetype is logically a value within the range of CF s for defined archetypes. This range is used to define the minimum and maximum of the probability distribution. If th e minimum and maximum have a relative difference of less than 0.1 %, we attribute the difference to rounding errors and assume a range of 0 (i.e. no uncertainty). The CF s used in the original implementation of the method is used as an estimator of the mode . The functions allow choosing between the uniform and the triangular probability distribution to model the archetype uncertainty . Using the uniform distribution we take the position that we do not know anything about the CF s of unspecified archetypes apart of their upper and lower bounds. In the implementation of the triangular distribution, the mode is equal to the value of the CF for the unspecified archetype. The triangular modelling gives weight to the choice of the CF for uncertain archetypes given in the original implementation of the impact category . The uniform and triangular distributions are chosen because , in the absence of more information, they are the simplest and introduce fewer assumptions than other distributions , following thus the princip le of insufficient reason . Another option is to describe archetype uncertainty as a discrete (categorical) probability distribution . For example, if a substance has CF for air, in rural and urban archetypes of 1 and 10 respectively , the CF to the uncertain archetype would have possible values of 1 or 10. Different weights could be given to different CF s, depending on the likel ihood of occur rence. Furthermore, CFs from specified archetyp ical scenarios could be uncertain themselves, compounding diffe rent sources of uncertainty such as spatial variability. Discrete probability distributions are not natively supported by Brightway2 but can be handled with the package presamples (Lesage et al. 2018) to modify the matrix of characterisation factors . With th is approach, the CF s of substances to underspecified archetypes are taken from a list of possible values in each iteration. As for the continuous case, The modelling follows the principle of insufficient reason , and assign equal probability to each CF . Wit h more information about the likelihood of occurrence, th is approach can calculate CF s more accurately . 2.2. Assessing the uncertainty of existing impact assessment methods The uncertainty of CF s to unspecified archetypes is analysed for several impact assessme nt methods. The analysis explores how CF s to uncertain archetypes compare to the values of specified archetypes. The analysis is only done for the methods currently maintained by ecoinvent and for which the concept of archetype is relevant. The latter criterion excludes methods where CF s do not change with the archetype (e.g . the current implementation of global warming potentials of greenhouse gases ). For illustrative purposes, the methods ReCiPe 2008 (Goedkoop et al. 2013) , Environmental Footprint 2.0 (Fazio et al. 2018) and ecological scarcity 2013 (Frischknecht and Büsser Knöpfel 2014) are analysed. 2.3. Testing the methods on background LCA databases The methods are tested with activities of ecoinvent 3.6 (consequential) , in an attempt to identify activit ies affected by archetype uncertainty and the extent of these effects . For simplicity, only the impact assessment method Environmental Footprint 2.0 is used, as it is one of the few maintained by ecoinvent and recently updated . The analysis only evaluates uncertainty of the CF s, ignoring uncertainty coming from the inventory (i.e. flows in technology and intervention matri ces). This simplificat ion is done because analysing both sources of uncertainty for all activities of the dat abase would be exces sively computationally demanding from a normal laptop. We use the concept of intensity matrix proposed by (Heijungs and Suh 2002) defined as Λ=𝐵𝐴−1 where A is the technology matrix and B is the intervention matrix , each column of A and B represent an activity in ecoinvent . The intesity matrix is calculated only once while the matrix o f CFs is updated in each iteration. Calculating the inverse of A for databases such as ecoinvent , with more than 15000 activities is computationally demanding , and with this approach , we only do it once. Uncertainty is propagated using the Monte Carlo technique . For a limited number of cases, archetype uncertainty was combined with inventory uncertainty. In each iteration, the technology, intervention, and intensity matrix are calculated, and differences come from the matrix of CFs. This is done to avo id spurious uncertainty due to correlation. 3. RESULTS The results first explore to what extent impact assessment methods are affected by archetype uncertainty, using as example three case studies. The results follow with the impact of archetype uncertainty i n the LCA database ecoinvent. 3.1. Characterization factors of undefined archetypes Fig.1 illustrates the normalised CF s of flows to unspecified archetypes relative to the range of values of the same substance and compartment to specified archetypes . The normalization bounds the CF s in the interval [0,1], being 1 the maximum observed CF for the defined archetypes and 0 the minimum. The value in the label is the maximum range observed for that impact category normalised by the median CF in that impact category . The larger the range the more important is the definition of subcompartment. The highest inter -subcompartment CF variability” for ReCiPe 2008 is found for human toxicity, where the difference between minimum and maximum can be up to eight orders of magnitude higher than the median CF, illustrating the relevance of a well -defined subcompartment. Overall, it seems toxicity impact categories are the most sensible to archetypes. In some impact categories, flows to unspecifie d subcompartments have a CF equal to the maximum or the minimum of CF s of the same substance and compartment, but in other cases is an intermediate value. Given the diversity of assumptions , it is only possible to say w hether under specifi cation of archetyp es results in an overestimate or underestimate impacts for certain impact categories . For example, CFs of uncertain archetypes for the impact category respiratory inorganics in Environmental Footprint 2.0 is equal to the maximum of the observed range of va lues ( Fig.1). Therefore, for this category using unspecified archetypes should overestimate impacts. It is also apparent that methods do not use a coherent approach to quantify the CF of undefined archetypes for all their impact categories . Fig.1 only shows impact categories with uncertainty associated to archetypes, the rest of categories do not have any archetype uncertainty. Furthermore, i t was also found that the list of possible elementary flows and emissions scenario is sligtly inconsisent 1. 1 There seems to be an incomplete definition of unspecified archetypes in the list of possible triples (elementary flow, compartment, subcompartment) in Brigh tway2 (which derives this list from ecoinvent). Many pairs “elementary flow – compartment” do not h ave an “undefined archetype” case. In most of the cases where the unspecified case is not defined, these pairs only have one subcompartment defined, which stands to reason. However, in some cases, several archetypical emission scenario exist, without an “underspecified” archetypical option. Fig. 1 Normalized CF of elementary flows to unspecified archetypes, for impact categories with archetype uncertainty. Each point in the figure represents a CF. The maximum observed range is added in parenthesis. 3.2. Effects of archetype uncertainty on LCIA scores This section assesses the effects of introducing uncertainty from underspecified archetypes in the LCA scores of activities in the database ecoinvent . The mean absolute percentage deviation (MAP D) is used as a metric to compare the effects across all activities in the database . To compare different approaches , the case with no uncertainty is used as a reference score (S ref) while the cases with uncertainty are considered as alternative scores (S alt). The MAPD in this context should not be interpreted as a measure of error (it is unclear which approach provides scores closer to the true value ) but as a measure of deviation from the reference case. 1 𝑛∑|𝑆𝑟𝑒𝑓−𝑆𝑎𝑙𝑡 𝑆𝑟𝑒𝑓| Archetype uncertainty can increase the overall uncertainty of LCA scores without introducing systematic errors but introducing random errors instead . An increase in unce rtainty would make scores less discernib le. In other words, it would be more difficult to ascertain if two comparable products have “significantly” different scores. The “random errors” introduced by archetype uncertainty are assessed using the normalised standard deviation, also known as coefficient of variation , using the absolute value of the mean as normalising factor . 3.2.1. systematic and random errors The sensitivity of ecoinvent to archetype uncertainty are represented in Fig . 2 and 3. Fig 2 displays the M APD with a cut -off of 0.1% (i.e. deviations below 0.1% are not displayed) . Results are skewed, t he MAPD is below 1% for around 64% of the activities and scores, while for 0.5% of activities deviations are higher than 100%. Higher systematic errors are consistently observed for the category of respiratory effects, inorganics . The categories of ionising radiation , freshwater and terrestrial acidification and terrestrial eutrophication do not have significant uncertainty and are not displayed. The MAPD is lower when the archetype uncertainty is assumed to follow a triangular distribution. This is an expected result as MAPD measures differences with the reference case, and the reference case sets the mode of the triangular distribution. Fig. 2: Systematic errors due to archetype uncertainty: mean absolute percentage deviation for all the activities in Ecoinvent 3.6 consequential. MAPDs are ordered by the “uniform” case. Each element in the x axis represents an activity in the database. The coeff icient of variation is presented in Fig. 3 for the cases of uniform , triangular and discrete distribution. Fig. 3 has a cut -off of 0.1%, meaning that coefficients of variation below that value are considered not relevant and not displayed. Respiratory inor ganics has the most consistent random errors (i.e. highest median coefficient of variation), followed by non- carcinogenic effects . The coefficient of variation is low for m ost of the activities but high for some . The coefficient of variation is always lowe r if we assume uncertainty follows a triangular distribution . This is also expected because for distributions with the same range, standard deviations of uniform distributions are always higher than for triangular distributions. Fig.3 Uncertainty introd uced by unspecified archetypes on LCA scores measured as relative standard deviation for Ecoinvent 3.6 consequential. The scores are ordered by the uniform case. An exploratory analysis indicates that some regions have higher archetype uncertainty than others. The UN-Oceania region has the highest followed by Indian regions (see supplementary information for details) . As for MAPD, it is difficult to explain why some categories or regions have larger uncertainty than others. The uncertainty depends on how u ncertain CF s in a given impact category are , and how often inventories use underspeci fied archetypes . The latter depends on editorial guidelines and how much it is known about the scenario under which these emissions occur. For the cases with highest archetype uncertainty a Monte Carlo simulation was done , compounding CF uncertainty with inventory uncertainty . The addition of CF uncertainty increases the MAPD with respect to the deterministic calculation, and it the tested ca ses the MAPD increased up to 43 % (see supplementary information for details). We note that cases with the highest archetype uncertainty do not necessarily mean cases where archetype uncertainty is more relevant than inventory uncertainty. 3.2.2. Effects of dist ribution choice It can be observed that the continuous modelling of uncertainty and the discrete approach render similar results. As previously stated, the uniform distribution assumption deviates more from the reference case than the triangular but no cle ar pattern is observed for the discrete case. The discrete case is as expected “less smooth” . Overall, the three approaches are broadly comparable , at least under a scenario where no additional information is available. 4. DISCUSSION Unspecified archetypes ar e powerful mental construct when the modeller is aware of its implications but have potentially disruptive side -effects. Thus, it would be better if studies systematically account for this uncertainty . This study proposes an implementation in the o pen- source LCA software Brightway2 (Mutel 2017) . The implementation is licensed with a permissive license and can be reused and improved by the research community. Although the consideration of uncertainty in CFs is uncommon, software providers should consider uncertainty in CFs. With regards to the modelling choice between continuous, uni form , and triangular distributions, the discrete case introduces fewer assumptions than the continuous approaches , since the continuous cases model CFs that were not part of the reported values. However, all the CFs used have an uncertainty that is rarely reported (UNEP -SETAC 2019) ; therefore, in our opinion , it is not unreasonable to model CFs as a continuous probability distribution. Moreover, t he three approaches are in re latively close agreement, and the continuous cases can be used as a n approximation. On the one hand, the continuous cases have the advantage of being easier to handle, as they do not require the additional package presamples and the time to learn how to us e it. On the other hand, the use of presamples allows to model scenarios with a better characterisation of uncertainty. If CF s are uncertain, this uncertainty can be easily compounded with archetype uncertainty . If there is information of the likelihood of one archetypical scenario being more probable than other (e.g. emissions from industries being outside urban areas) th ese likelihoods can be incorporated as weighting factors when the samples are calculated. On the inventory side, m odellers and database d evelopers should specify the archetype scenario when known and leave the “unspecified” option as a default in the absence of better information. A more thorough specification of archetypes would avoid the introduction of systematic errors and unnecessary u ncertainty. In many cases th e specification of archetypes is straight -forward. For instance, most of the field emissions of agriculture are likely to occur outside urban environments . Therefore, archetypes scenarios can be better specified without much eff ort. If the CFs to underspecified archetypes is calculated in a reaso ned way (e.g. as a weighted average of the most likely scenario) it would make more sense to capture this information using the triangular distribution instead of the uniform. With regard s to method implementation, the assumptions around the characterisation of underspecified archetypes need to be better documented and reasoned. This study shows how these assumptions can have a large impact on LCA results, and that current implementations seem to be inconsistent and seldom documented. A commonly agreed inventory and LCIA implementation that all LCA software solutions can use is long overdue, and would help to have a more consistent set of assumptions. In the three modelled approaches, measures of central tendency can be very different for the case where uncertainty is not considered (i.e. the mean or median score of the Monte Carlo simulation being very different to the deterministic score) . This is not only true for archetype uncertainty, but for uncertainty estimates in general. Since the measures of central tendency incorporate more information than the deterministic case, it would make sense to consi der these as a more accurate estimation of the true value of LCA scores, instead of the score that ignores all the uncertainty information. Further work could systematically compare the CF uncertainty with the uncertainty coming from the inventory . This wo rk only does it for a few cases. Fast methods to identify to identify the main sources of uncertainty in an LCA calculation would also be helpful. As current techniques, are very computationally demanding (Patouillard et al. 2019) . ACKNOWLEDGEMENTS The author thanks Pascal Lesage for his help with the presamples package. FUNDING INFORMATION This work was done without external funding.