## 2 Materials and Methods
### Spatial Multicriteria Model Development to Support Biogas Facilities Location  
Multicriteria and multiobjective evaluation allows unit location and resource allocation spatial assessment processes by structuring decision problems. Different location studies of bioenergy production facilities use spatial multicriteria decision methodologies [22; 24; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60], with emphasis on fuzzy spatially explicit multicriteria decision systems using AHP [61; 62; 63], followed by multiobjective analysis [23] and associated resource allocation [24; 41; 64; 65]. Criteria spatial modelling and its analytical hierarchical process aims to find suitable locations. A multiobjective analysis ensures comparison between candidate location criteria and models, as well as alternative locations. These models and methods help decision makers to categorize decision problems logically by considering the land use options, legal framework, and stakeholders' perspectives and complementary/conflicting preferences [35]. The evaluation process requires criteria weighting, reasonability, gradual detail and multidisciplinary in environmental technology themes, spatial science and economy. The developed spatial model integrates operations of distance analysis, overlap, interpolation, reclassification, 3D surface analysis and network analysis, and technical and political options regarding the following aspects: (i) social aspects (service level, acceptance, social innovation; (ii) economic dimensions (related to investment, maintenance and operation costs) [66]; (iii) and environmental conditions (environmental impact and management towards environmental protection) (Table 1). Each criterion and dataset is standardized in spatial reference systems (ETRS89 TM06), and final thematic criteria values were reclassified into categorical scales (0 for exclusion, and a scale from 1, low value, to 5, optimal value) (Table 1). \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
These criteria include: (i) critical aspects of natural suitability, distance and accessibility; (ii) social conditions associated with collective acceptance and potential economic and environmental viability; (iii) risk reduction objectives, by imposing distances to water-courses, coastlines, and ecologically and agriculturally sensitive areas considering geological risks; and (iv) other aspects relevant to the economy, such as distance to the electrical grid, roads and land surface analysis (Table 1). The collection, management and analysis of spatial data, which inform each criterion, involved metadata production (ISO19115 and 19139 profiles), data modelling (INSPIRE spatial data specification), spatial analysis and database quality assessment (ISO19157 and ISO19158) [25]. Criteria reclassification and standardization precede the weighted overlay (AHP) product to establish reclassification criteria of continuous values of the suitability map regarding finding/assigning adequate locations for biogas facilities. The AHP approach is a flexible decision-making tool for determining the relative importance, preference or likelihood of occurrences considered by users (decision makers, researchers, entrepreneurs and population) by comparing criteria pairs [67]. Peer comparison helps decision makers to evaluate the contribution of each criterion or factor to the objective, in an independent and simple way. In this study, the AHP allowed the ranking and weighting of the relative importance of the different factors/criteria in the final results [22]. Final values were obtained based on the 9-point classification system described by [67], with consistency coefficients (CC) with values below 0.10 being accepted.