With the Ecosystem Service (ES) concept's popularisation, the need for robust and practical methodologies for ES assessments has increased. The ES matrix approach, linking ecosystem types or other geospatial units with ES in easy-to-apply lookup tables, was first developed ten years ago and, since then, has been broadly used. Whereas detailed methodological guidelines can be found in literature, the ES matrix approach seems to be often used in a quick (and maybe even "quick and dirty”) way. Based on a reviewa of scientific publications, in which the ES matrix approach was used, we present the diversity of application contexts, highlight trends of uses and propose future recommendations for improved applications of the ES matrix. A total of 109 studies applying the ES matrix approach and one methodological study without concrete applications were considered for the review. Amongst the main patterns observed, the ES matrix approach allows the assessment of a higher number of ES than other ES assessment methods. ES can be jointly assessed with indicators for ecosystem condition and biodiversity in the ES matrix. Although the ES matrix allows us consider many data sources to achieve the assessment scores for the individual ES, in the reviewed studies, these were mainly used together with expert-based scoring (73%) and/or ES scores that were based on an already-published ES matrix or deduced by information found in related scientific publications (51%). We must acknowledge that 27% of the studies did not clearly explain their methodology. This points out a lack of method elucidation on how the data had been used and where the scores came from. Although some studies addressed the need to consider variabilities and uncertainties in ES assessments, only a minority of studies (15%) did so. Our review shows that, in 29% of the studies, an already-existing matrix was used as an initial matrix for the assessment (mainly the same matrix from one of the Burkhard et al. papers). In 16% of the reviewed studies, no other data were used for the matrix scores or no adaptation of the existing matrix used was made. However, the actual idea of the ES scores, included in the Burkhard et al.'s matrices published 10 years ago, was to provide some examples and give inspiration for one's own studies. Therefore, we recommend to use only scores assessed for a specific study or, if one wishes to use pre-existing scores from another study, to revise them in depth, taking into account the local context of the new assessment. We also recommend to systematically report and consider variabilities and uncertainties in each ES assessment. We emphasise the need for all scientific studies to describe clearly and extensively the whole methodology used to score or evaluate ES in order to be able to rate the quality of the scores obtained. In conclusion, the application of the ES matrix has to become more transparent and integrate more variability analyses. The increasing number of studies that use the ES matrix approach confirms its success, appropriability, flexibility and utility for decision-making, as well as its ability to increase awareness of ES.

Matrices or look-up tables are increasingly popular flexible tools for ecosystem services mapping and assessment. The matrix approach links ecosystem types or land cover types to ecosystem services by providing a score for ecosystem service (ES) capacity, supply, use, demand or other concepts. Using expert elicitation enables quick and integrative ES scoring that can meet general demand for validated ES mapping and assessment at different scales. Nevertheless, guidance is needed on how to collect and integrate expert knowledge to address some of the biases and limits of the expert elicitation method. This paper aims to propose a set of guidelines to produce ES matrices based on expert knowledge. It builds on existing literature and experience acquired through the production of several ES matrices in several ES assessments carried out in France. We propose a 7-steps methodology for the expert-based matrix approach that aims to promote cogency in the method and coherency in the matrices produced. The aim here is to use collective knowledge to produce semi-quantitative estimates of ES quantities and not to analyse individual or societal preferences or importance of ES. The definition of the objectives and the preparation phase is particularly important in order to define the components of capacity to demand ES chain to be addressed. The objectives and the ES components addressed will influence the composition of the expert panel. We recommend an individual filling of an empty matrix in order to strengthen the statistical analysis of the scores' variability and the analysis of congruency between experts. Expert scoring should follow a process of discussion, information-sharing and collective appropriation of a list of ecosystem types and ES to be assessed. We suggest that the ES matrix should not only focus on ES central scores but also address the variabilities and uncertainties as part of the ES assessment. The analysis of these sources of variability allows the documentation of variations in the ES quantity but also an exploration into the lack of consensus or knowledge gaps that needs to be addressed.