Probabilistic approach of water residence time and connectivity using Markov Chains with application to tidal embayments

Markov Chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g. depletion index, carrying capacity assessment. Markov Chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.

Modeling the Arctic Freshwater System and its integration in the global system: Lessons learned and future challenges

Numerous components of the Arctic freshwater system (atmosphere, ocean, cryosphere, terrestrial hydrology) have experienced large changes over the past few decades, and these changes are projected to amplify further in the future. Observations are particularly sparse, both in time and space, in the Polar Regions. Hence, modeling systems have been widely used and are a powerful tool to gain understanding on the functioning of the Arctic freshwater system and its integration within the global Earth system and climate. Here, we present a review of modeling studies addressing some aspect of the Arctic freshwater system. Through illustrative examples, we point out the value of using a hierarchy of models with increasing complexity and component interactions, in order to dismantle the important processes at play for the variability and changes of the different components of the Arctic freshwater system and the interplay between them. We discuss past and projected changes for the Arctic freshwater system and explore the sources of uncertainty associated with these model results. We further elaborate on some missing processes that should be included in future generations of Earth system models and highlight the importance of better quantification and understanding of natural variability, amongst other factors, for improved predictions of Arctic freshwater system change.