Threshold based footprints (for water)

Thresholds are an emergent property of complex systems and Coupled Natural Human Systems (CNH) because they indicate "tipping points" where a complicated array of social, environmental, and/or economic processes combine to substantially change a system's state. Because of the elegance of the concept, thresholds have emerged as one of the primary tools by which socio-political systems simplify, define, and especially regulate complex environmental impacts and resource scarcity considerations. This paper derives a general framework for the use of thresholds to calculate scarcity footprints, and presents a volumetric Threshold-basedWater Footprint (TWF), comparing it with the BlueWater Footprint (BWF) and the Relevant for Environmental Deficiency (RED) midpoint impact indicator. Specific findings include (a) one requires all users' BWF to calculate an individual user's TWF, whereas one can calculate an individual user's BWF without other users' data; (b) local maxima appear in the Free from Environmental Deficiency (FED) efficiency of the RED metric due to its nonlinear form; and (c) it is possible to estimate the "effective" threshold that is approximately implied by the RED water use impact metric.