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. The standard formula used to estimate the radiation extinction coefficient, kb (m–1), of solid porous natural fuel beds is examined and tested against laboratory experiments with isotropic beds of pine needles in the range of packing ratio, β, of 0.01–0.02. To measure kb in the tests, a setup using a parallel beam of white light radiation was constructed. The error of the standard formula is observed to be smaller than 10%. Similar tests were performed for a non-isotropic bed of pine needles with β ≈ 0.02, in which the maximum angle of inclination of the needles was limited to 30°, for two directions of incidence of radiation: horizontal and vertical. For each one of these two cases, original estimation formulae for kb are proposed alternative to the standard one. In these cases it is concluded that, while the standard formula may be in error by up to 20%, the new formulae have errors around 5% or smaller.

Purpose The purpose of this paper is to enhance the mathematical and physical understanding of practitioners of uncertainty analysis of life cycle inventory (LCI), on the application of possibility theory. The main questions dealt with are (1) clear definition of the terms-"necessitypossibility," "probability," "belief-plausibility," and of their mutual relationships;(2) what justifies the substitution of classical probability for possibility; (3) mutual comparison of, and transformations in both senses between probability and possibility uncertainty measures; (4) how to construct meaningful input possibility measures from available probabilistic/statistic information; and (5) comparative analysis of the solutions of the problem of data uncertainty propagation in LCI, afforded, respectively, by probabilistic Monte Carlo simulation and possibilistic fuzzy interval arithmetic. Methods The questions above are addressed from the rigorous mathematical formulations of the theories of probability and statistics, of possibility, and of random sets and belief/ plausibility functions, although directed to LCI uncertainty analysis practitioners. On this respect, the paper allows two different levels of reading: a basic level (main text) and a deeper level (Electronic supplementary material). Particular tools used are (a) various transformations between possibility and probability distributions, in both senses, for the continuous case, proposed by Dubois et al. (e.g., Reliable Comp 10:273-297, 2004); (b) Monte Carlo simulation for either independent or dependent input random variables; (c) fuzzy interval arithmetic; and (d) Heijungs and Suh's (2002) matrix formulation of LCI problems.Results and discussion The links among uncertainty measures, uncertain variables, and uncertainty analysis are cleared up. It is recalled how a probability measure can be constructed and attached to an input variable, and its probability distribution and unknown "correct value" be related, in a physically meaningful way. It is justified that, usually, a dual necessity-possibility measure has much less uncertainty information than a comparable probability measure. Although the specialists are not unanimous, it is opined that the theoretical framework developed by Dubois et al. (e.g., Reliable Comp 10:273-297, 2004) is the most convenient one to use in uncertainty analysis, to compare and mutually transform probability and possibility data. This is exemplified in (a) the transformation of the very common triangular possibility and normal standard probability distributions; (b) the general construction of possibility measures from different probability data previously available; and, above all, (c) the comparison of the output information of possibilistic and probabilistic uncertainty analyses of an LCI problem proposed by Tan (Int J Life Cycle Assess 13:585-592, 2008). The general problem of data uncertainty propagation through deterministic models (e.g., of LCI) is tackled with (1) classical probabilistic Monte Carlo simulation (for either inde...

This paper presents an experimental method using computer-based image processing techniques of visual and infrared movies of a propagating fire front, taken from one or more cameras, to supply the time evolutions of the fire front shape and position, flame inclination angle, height, and base width. As secondary outputs, it also provides the fire front rate of spread and a 3D graphical model of the fire front that can be rendered from any virtual view. The method is automatic and non-intrusive, has space–time resolution close to continuum and can be run in real-time or deferred modes. It is demonstrated in simple laboratory experiments in beds of pine needles set upon an inclinable burn table, with point and linear ignitions, but can be extended to open field situations.