Testing water pollution in a two layer aquifer

Water bodies around urban areas may be polluted with chemical elements from urban or industrial activities. We study the case of underground water pollution. This is a serious problem, since underground water is high qualified drinkable water in a world where this natural resource is increasingly reduced. This study is focused on a two-layer aquifer. If the superficial layer is contaminated, the deeper layer could be spoiled as well. This contribution checks the equality of the mean or centered composition of the two layers, with the aim of inferring their possible hydraulic conectivity. The data to be examined are different hydro-chemical components of water, such as nitrates and nitrites (related to nitrate/nitrite poisoning of animal stock), tensoactives (toxic to the ecosystem) or potassium (it promotes eutrophization of the water), represented in mg/l. As the data are compositional, we can group the pertinent elements and compare them applying ilr transformation. The ilr transformation is used for simplicity when comparing compositional vectors. MANOVA (Multivariate Analysis of Variance) is applied on the transformed data from the two layers. This provides a hypothesis test to discern whether the two aquifer layers can be considered a homogeneous continuum or, on the contrary, they should be considered as isolated layers. An illustrative example is presented. Used data sets, being synthetic, are inspired by a real case. These analyses suggest that the two aquifers are connected.