Is our urban water system still sustainable? A simple statistical test with complexity science insight

Sustainable development is being reconsidered as a process with unknown endpoint. Outputs of sustainable urban water systems defined as 'policies, projects, laws, technologies, and consumption and reuse amounts associated with urban water sustainability goals' are therefore being viewed as inadequate monitoring instruments. I propose a new methodology for sustainability monitoring whereby normality of a system is diagnosed through normality of its supporting inputs in lieu of normality of its complex outputs. Supporting inputs are 'intents and behaviors that support system goals'. Supporting inputs follow a principle of self-organization to remain in the norm and behavior zone commonly associated with system goals. This implies that normality of supporting inputs can be inferred from their longitudinally normal or Gaussian distribution that can be explored by significance tests; in particular, the Shapiro-Wilk test which is most powerful for n < 50. We identify fourteen supporting inputs of sustainable urban water systems - such as internet searches, community campaigns, staff training, agent-principal reporting and legislation propositions about water sustainability - and define quantitative indicators for them. The Shapiro-Wilk test and Kolmogorov-Smirnov test (K-S) of these indicators and a subsequent Boxplot outlying examination of non-normal indicators are undertaken in Yazd - a desert city in central Iran with a historic record in water conservation - in the light of its complex wastewater speculation. Qualitative examination of non-normal supporting inputs confirms the ability of our statistical methodology to detect problems in the system.