Planned Burn-Piedmont. A local operational numerical meteorological model for tracking smoke on the ground at night: model development and sensitivity tests
Gary L. AchtemeierUSDA Forest Service, Southern Research Station, Forest Sciences Laboratory, Athens, GA 30602, USA. Telephone: +1 706 559 4239; fax: +1 706 559 4317; email: gachtemeier@fs.fed.us
International Journal of Wildland Fire 14(1) 85-98 https://doi.org/10.1071/WF04041
Submitted: 24 August 2004 Accepted: 21 December 2004 Published: 7 March 2005
Abstract
Smoke from both prescribed fires and wildfires can, under certain meteorological conditions, become entrapped within shallow layers of air near the ground at night and get carried to unexpected destinations as a combination of weather systems push air through interlocking ridge–valley terrain typical of the Piedmont of the Southern United States. Entrapped smoke confined within valleys is often slow to disperse. When moist conditions are present, hygroscopic particles within smoke may initiate or augment fog formation. With or without fog, smoke transported across roadways can create visibility hazards. Planned Burn (PB)-Piedmont is a fine scale, time-dependent, smoke tracking model designed to run on a PC computer as an easy-to-use aid for land managers. PB-Piedmont gives high-resolution in space and time predictions of smoke movement within shallow layers at the ground over terrain typical of that of the Piedmont. PB-Piedmont applies only for weather conditions when smoke entrapment is most likely to occur––at night during clear skies and light winds. This paper presents the model description and gives examples of model performance in comparison with observations of entrapped smoke collected during two nights of a field project. The results show that PB-Piedmont is capable of describing the movement of whole smoke plumes within the constraints for which the model was designed.
Additional keywords: drainage winds; nocturnal smoke; smoke entrapment; visibility.
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where D0(a,k) is a response function. Barnes (1964) showed that
if the original data field is described by the function
where
and λ refers to wavelength. The optimal response for the 2-pass successive corrections Gaussian objective analysis is
(Achtemeier 1987). To create the A-Function, add a constant to the original function so that
Then, using equation (A1), perform two separate single-pass interpolations with different k to yield two new functions:
The A-Function is defined as the ratio of the square of G2 to G1 and subtracting the constant:
The response equation for the A-Function is
where the response function for C0 = 1. Expanding equation (A9) yields
The response equation for the A-Function is a complex summation of products of functions with response functions. In addition, the presence of the second term in the denominator of equation (A10) acts to increase (decrease) the estimate for R depending on whether the sign of the term is negative (positive). This problem can be solved and equation (A10) simplified by choosing for C0 a value that is much greater than the amplitude of f(x, y). Thus terms not multiplied by C0 can be neglected in equation (A10). Furthermore, from equation (A7) and the definition in equation (A3), let k1 = 2k2. Then
which is equivalent to equation (A5). Thus the A-Function has the same response as the optimal 2-pass Gaussian method but without the additional interpolation.
