Mapping the environment.

Maps are our most common graphic representation and approximation of reality. They are fundamental for an integrated and deep understanding of the world that surround us. However the mapping of environmental variables is affected by spatial uncertainty; from this perspective maps of environmental variables can be considered an approximate representation of reality. Overall, maps have the power to show our place and perception of the world (Pickering, 2014). Maps can be used as political and military instruments of power. They can promote social change because they have important impacts on people's imagination and perception of mapped topics. Maps have been used for centuries for political andmilitary purposes, such as planning and executing wars, claiming territories, the creation of nations, collecting taxes and identification of natural resources (Krupar, 2015), and even as propaganda (Harley, 1988). They have been useful to spatially display criminal activity (Spicer et al., 2016), human health issues (Hay et al., 2013; Keddem et al., 2015; Simarro et al., 2012), plant diseases (Bouwmeester et al., 2016), social activities (Tsou et al., 2013), elections forecast and results (Ondrejka, 2016; Pavia et al., 2008) and other social, environmental and economic phenomenon, such as archaeological sites (Wagner et al., 2013), population density (Gomes, 2017) and dynamics (Deville et al., 2014), social values and perceptions (Tyrvainen et al., 2007), population vulnerability (Frigerio and De Amicis, 2016), inequality (Salesses et al., 2013), food and nutrition security (Aliaga and Chaves-dos-Santos, 2014),well-being (Tian et al., 2015) education and poverty (Segun et al., 2012; RafeeMajid et al., 2017), land use intensity (Kuemmerle et al., 2013), land abandonment (Alcantara et al., 2012) and economic growth (Lenzen et al., 2012). Basically, all phenomenon that have a spatial dimension can be mapped and modelled. Objective mapping refers to final map(s) (in space and/or in time, 2D, 3D or 4D) that quantitatively represent, according to a digital representation, a spatio-temporal attribute (SA) related to environmental properties or processes being analysed as realistically and accurately as possible at the scale being utilized. The mapping of the SA of interest (SAI) should also take into consideration the spatial uncertainty that is inherent to the mapping process. From this perspective, in many circumstances, it is satisfactory to produce an exhaustive map of the SAI in an optimal sense: a kind of average scenario of the spatial distribution of the SAI among the possible equiprobable scenarios, with an attached measure of local uncertainty (Journel, 1989; Goovaerts, 1997). However, for some specific tasks, common for example in groundwatermodelling (e.g., Koltermann and Gorelick, 1996; Eaton, 2006; Deutsch, 2002), there is the need to produce a consistent number of equiprobable