A Poisson Random Field Framework Bridges Micro- To Macroscopic Scales In Microbial Transport

Abstract:

Understanding microbial fate and transport in surface water and making accurate predictions is a formidable task. Evidence from experimental and observational studies unequivocally points to temporal and spatial variability in microbial distributions with significant correlation structure; and to the critical role of processes at the microscopic level.

The temporal and spatial variability in microbial distributions arises from inherently random environmental factors and processes. Many cannot be described accurately using deterministic methods, necessitating a stochastic approach to microbial modeling. At the same time, microbial tracking studies identified significant spatial and temporal correlations in microbial distributions in streams, and highlighted the necessity of including microbial interactions with sediments, settling and re-suspension in models of microbial transport. Such understanding must be gained from microscopic, particle-scale research, because microdynamic interactions ultimately give rise to phenomena on higher scales. The challenge then is to be able to describe microbial behavior in probabilistic terms to take care of random drivers, while incorporating processes on microscopic scale and bridging the gap to macroscopic entities like concentrations that are used in watershed management.

We have derived a stochastic modeling paradigm that bridges microscopic processes to macroscopic manifestation of microbial behavior in time and space, where the Markov behavior of individual microbes collectively translates into a non-homogeneous Poisson random field that describes microbial population dynamics. The Poisson framework is applied to a mixed-use watershed and implemented within ArcGIS, which makes a wealth of geographic, topologic, soil and other information, as well as data from national and regional datasets, instantly available. Probabilities of exceeding microbial safety thresholds are then obtained at any point in time and space in the watershed.