## 1st International Congress on Environmental Modelling and Software - Lugano, Switzerland - June 2002

#### Paper/Poster/Presentation Title

An Approximation Algorithm for the Updating of Non-Gaussian Dynamic Processes

#### Keywords

puff model, bayesian networks, dynamic generalized linear models

#### Start Date

1-7-2002 12:00 AM

#### Abstract

In the environmental issue of forecasting the geographical spread of the release of toxic gases in the event of a chemical or a nuclear accident, puffs of contaminated masses (uncertain quantities) emitted from a source, dispersed by a wind field and fragment into other puffs over time. The number of the fragmented puffs grows enormously. The problem here is to produce realistic estimates of contamination concentration in space and time. The atmospheric dispersion follows the Markovian property, that is the distribution of future puff fragments will depend only on the joint distribution of puffs currently existing. In such complex highdimensional environments, that change dynamically, the vector of puff masses existing on or before time T can be set as a states vector ΘT = (Θ1, . . . ΘT ). These states can be represented on an undirected acyclic graph whose cliques, that are formed by joining nodes with their neighbors if these neighbors have an edge pointing to them, contain components of ΘT . If we assume that the observations are Gaussian, then well established fast data propagation algorithms for Bayesian networks can be used. In this paper I suggest an approximation methodology to accommodate non-Gaussian distributions using a slight generalization of the class of dynamic generalized linear models. The algorithm is very fast and updating is achieved in a closed form.

An Approximation Algorithm for the Updating of Non-Gaussian Dynamic Processes

In the environmental issue of forecasting the geographical spread of the release of toxic gases in the event of a chemical or a nuclear accident, puffs of contaminated masses (uncertain quantities) emitted from a source, dispersed by a wind field and fragment into other puffs over time. The number of the fragmented puffs grows enormously. The problem here is to produce realistic estimates of contamination concentration in space and time. The atmospheric dispersion follows the Markovian property, that is the distribution of future puff fragments will depend only on the joint distribution of puffs currently existing. In such complex highdimensional environments, that change dynamically, the vector of puff masses existing on or before time T can be set as a states vector ΘT = (Θ1, . . . ΘT ). These states can be represented on an undirected acyclic graph whose cliques, that are formed by joining nodes with their neighbors if these neighbors have an edge pointing to them, contain components of ΘT . If we assume that the observations are Gaussian, then well established fast data propagation algorithms for Bayesian networks can be used. In this paper I suggest an approximation methodology to accommodate non-Gaussian distributions using a slight generalization of the class of dynamic generalized linear models. The algorithm is very fast and updating is achieved in a closed form.