In hydrogeological applications, connectivity is generally related to the existence of paths enabling preferential (fast) flow and transport from one location to another (e.g. Renard and Allard, 2013). In spite of the apparent simplicity of this concept, connectivity is not yet widely used in practical applications, possibly owning to the difficulties to incorporate connectivity within groundwater flow and transport models.

The goal of the course is to provide an overview of the different theories existing to define connectivity and to suggest potential approaches to adopt this concept in practical hydrogeological applications, particularly those based on numerical flow and transport models. The course offers an overview of recent development in the fields from laboratory and field experiments, as well as from stochastic modeling analyses.

This short course is based on two main parts.
• The first part of the course provides a quick summary of key theoretical aspects on connectivity based on recent literature, with emphasis on the different metrics and indicators developed in the last decade to quantify connectivity (e.g. Fogg, 1986; Knudby and Carrera, 2005, 2006; Renard and Allard, 2013; Western et al., 1998). Examples on the use of these metrics for the assessment of the impact of connectivity on flow and transport in heterogeneous media are shown based on the results from laboratory experiments (e.g. Fernàndez-Garcia et al., 2002; Molinari et al., 2015; Pedretti et al., 2016) and field-scale experiments (e.g. Bianchi et al., 2011)
• The second part of the course focuses on the use and implementation of connectivity in groundwater models. First, connectivity metrics from numerical simulations under uniform and radial flow (e.g. Pedretti et al., 2013; Willmann et al., 2008) are explained. Then, methods to embed connectivity using upscaling procedures (e.g. Tyukhova and Willmann, 2016), conditional mapping of stochastic simulations (e.g. Fernàndez-Garcia et al., 2010) and transition probability based Markov chain models (e.g. Bianchi and Pedretti, under review) are discussed.

We welcome any person interested in learning more about connectivity in hydrogeological applications. The course is open to any scientist with background in fluid dynamics of porous and fractured media, hydrogeologists or practitioners in the field of groundwater applications, including modelers and experts in laboratory and field applications.

The course is developed over two time blocks (TBs), each of 1.30h (between 15.30-17:00).
• The first time block is focused on the introduction of connectivity as a theoretical concept and on the results from laboratory and field experiments.
• The second time block focused on numerical models, with key results from recent analyses and illustration of methods to implement connectivity in groundwater flow and transport models.