Some of the most relevant problems today both in Science and practical problems involves Coupled Socio-ecological Systems, which are some of the best examples of Complex Systems. In this work we discuss groundwater-management as an example of these Coupled Socio-ecological System, also known as Coupled Human and Natural Systems. We argue that it is possible and even necessary to construct a contextual statistical theory of groundwater management. Contextuality implies some very different statistical features as entanglement and complementarity. We discuss some (...) interpretation about statistical entanglement and statistical complementarity in terms of groundwater flow theory and extraction equation. To this end, we propose a non-Kolmogorobian approach following the Växjö school of thought. One of the most straightforward conclusions is that in this way, a statistical-contextual treatment of groundwater management may not only give place to new flow equations, but it could have a profound impact in resource management. Then the new basic unity of analysis should be the indivisible pair. We should not talk any more about aquifer dynamics or resource management plans by themselves. Physical and social systems are coupled in a statistical-contextual fundamental way, and a socio-hydrogeological theory should be developed. (shrink)