Utilizing state estimation to determine the source location for a contaminant Andrew J. Annunzio a, b, c, * , George S. Young a , Sue Ellen Haupt a, b, c a Meteorology Department, 503 Walker Building, The Pennsylvania State University, University Park, PA 16802, USA b Applied Research Laboratory, The Pennsylvania State University, P.O. Box 30, State College, PA 16804, USA c Research Applications Laboratory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA article info Article history: Received 27 April 2010 Received in revised form 27 April 2011 Accepted 28 April 2011 Keywords: Source term estimation Atmospheric transport and dispersion FUSION field trial 2007 Contaminant spread State estimation abstract In the event of an atmospheric contaminant release, it is crucial to ascertain the source information for the contaminant, both for mitigation purposes and to predict subsequent transport and dispersion. Here, obtaining part of this information, namely the contaminant source location, is accomplished by adopting a state estimation approach for instantaneous and continuous contaminant releases. The relevant state components that we exploit here are the contaminant cloud’s axis and spread. For an instantaneous release, we can adopt a Lagrangian approach to obtain the source location by extrapolating state observations back to the initial state. In contrast, the formulation for a continuous release cannot adopt this strictly Lagrangian approach because a steady flow of contaminants implies that the contaminant cloud is statistically stationary with respect to the sensor grid. Therefore, the concentration data are averaged in time and a hybrid Lagrangian/Eulerian framework is used to determine the average state. It is shown that with these frameworks it is possible to ascertain the contaminant source location for both dense and sparse sensor grids. An advantage of these algorithms is that no meteorological input is required. The algorithms in the form presented here, are relevant for short-range transport and dispersion. However, the source term estimation method presented here can be extended to longer- range applications by relaxing assumptions on the contaminant atmospheric transport and dispersion. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Determining the source information for an accidental or inten- tional contaminant release is an important issue in homeland and defense security. This information is needed to mitigate the source and to accurately predict subsequent atmospheric transport and dispersion (AT&D) for warning purposes and to diminish the contaminant threat. Both Eulerian and Lagrangian approaches can be utilized to determine the source information for a contaminant (e.g., Pudykiewicz, 1998; Stohl, 1996). A source term estimation method is Eulerian if determining the source information is dependent on computing a prediction of the entire concentration field. Most Eulerian (i.e., field) methods minimize the difference between concentration observations and concentration predictions to obtain the source information. Alternately, one can adopt a Lagrangian or entity approach, where an entity is a discrete, identifiable object (e.g., a particle or puff), and utilize state esti- mation to determine the contaminant source information. These Lagrangian source term estimation algorithms generally do not attempt to predict the concentration field, but instead propagate backwards the state of one or more entities that describe the contaminant field. For example, in traditional Lagrangian back- tracking, the entities are fluid parcels, and these fluid parcels are tracked backwards in time to their initial location (i.e., the contaminant source) (Stohl, 1996). This approach can successfully handle meandering or evolving flows if adequate meteorological data are available. In contrast, at shorter ranges where the flow can be assumed steady over the advective time scale and representative meteorological data are not available, an alternative approach is needed. In these situations the Lagrangian/entity framework can be implemented by approximating the concentration field by a superposition of contaminant entities that are of larger scale than a fluid parcel (e.g., puff or plumes), and determining the state of each entity. The latter approach is analogous to finding the relevant distribution moments of each entity. The state of each entity is then propagated backwards until its spread (i.e., 2nd moment) matches that of the source, a process that we will define as Lagrangian entity backtracking. This is the method explored herein. It is worth noting that either Lagrangian approach may be implemented with * Corresponding author. Research Applications Laboratory, The National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA. Tel.: þ1-303- 497-8492; fax: þ1-303-497-8386. E-mail addresses: aja199@psu.edu (A.J. Annunzio), young@meteo.psu.edu (G.S. Young), seh19@psu.edu (S.E. Haupt). Contents lists available at ScienceDirect Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv 1352-2310/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2011.04.080 Atmospheric Environment 46 (2012) 580e589