Abstract
A numerical stochastic model is developed for the upcrossing rate across a specified threshold concentration. The model assumes that the concentration time series at a given spatial point within a dispersing plume can be approximated as a first-order Markovian process designed to be consistent with a given time-invariant concentration probability density function (pdf). The model requires only the specification of a concentration pdf with a given mean and variance and a concentration fluctuation integral time scale. Predicted upcrossing rates are compared with atmospheric plume concentration data obtained from a point source near the ground. For this data set, a log-normal pdf is found to give better estimates of the threshold crossing rate than a gamma pdf.
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Du, S., Wilson, D.J. & Yee, E. A Stochastic Time Series Model for Threshold Crossing Statistics of Concentration Fluctuations in non-Intermittent Plumes. Boundary-Layer Meteorology 92, 229–241 (1999). https://doi.org/10.1023/A:1002022610496
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DOI: https://doi.org/10.1023/A:1002022610496