Calculation of wildfire Plume Rise
Bo
Yan
School of Earth and Atmospheric Sciences
Georgia Institute of Technology
Outline






Introduction
Fundament of principles
Calculation of plume rise of wild fire
Calculation of wildfire plume rise
Case study
Conclusions
Introduction of plume rise
Plume rise - the height to which a
plume emitted from an elevated
source will rise.
Importance: to the estimation of ambient
pollutant concentration, impact on the
local and distant environment.
Affected by: the initial sources conditions
(exit velocity and temperature difference
between the plume and the air), the
stable class and stratification of the
atmosphere, and the wind field.
General calculation of plume rise
Basic formulas of plume rise
h 
Ex b
u
a
General calculation of plume rise (con’t)
Calculation of fire-plume rise
Features of wild land fire plume

-
can not be treated in the same sense as those stack
-
point sources, but usually be considered as an area
source.
with a low initial momentum, the wildfire plume rise is
dominated by the buoyancy.
continue near-surface release.
-
Calculation of fire-plume rise
Basic equation
  3r0 x
h   
  4 2 F 2 K 3

2
  r0
  

 



3
1
3

  r0



Δh : the plume rise of fire plume, m
x: the downward distance,
r0: fire radius, m
U
K: the velocity ratio, ( w 0 )
U 10-m wind speed, m/s
β : the entrainment coefficient (β=0.6)
F : the Froude number,
1
 w2   2
F   0 a 
 2g 
w0 : the initial vertical velocity, m/s
ρ a: ambient density, kg/m3
Δρ: the initial density difference between ambient
air and the fire plume. (ρa-ρp)
w0 
8.8 10 6 Qh TP
g TP  Ta rP
2
TP, Ta : temperature of plume and ambient
respectively, K
rP: the radius of fire, m
Qh: the heat release rate, J/s
Different cases of calculation of
fire-plume rise

Stable conditions
Plume rise is limited by thermal stratification
 r0U 2
h f  2.1 2 2 3
N F K
Δhf is the final rise, m
N is the Brunt Vasaila frequency




1
3
1
 g   2
N 

  z 
Different cases of calculation of
fire-plume rise (con’t)

Neutral conditions
Ambient turbulence limits the final plume rise by
breaking up the plume
 r0U 2
h f  0.76 2 2 3
u F K
 *
u*: friction velocity, m/s




(Briggs, 1984)
Different cases of calculation of
fire-plume rise (con’t)

Unstable conditions
Plume rise is also limited by turbulence

2
 r0U z i
h f  4.5
2
 4w* F 2 K 3

2
3





3
5
(Briggs, 1989; Weil, 1988)
1
zi : inversion height, m
 g ' ' 3
w  zi 
w*: the convection velocity scale, m/s w*  


 v



Case study

CAMx (comprehensive air quality model with
extensions)
Meteorological data:
Wind speed,
Ambient temperature
Mixing height
Surface heat flux
+
Plume characteristics:
Temperature of release
Radius of wild fire
Heat release
Exit vertical velocity
Calculation of plume rise
Case study (con’t)
Fireplume calculations
Aug 30, Fire ID 1033 , 1000 acres
1600
plume rise (m.)
1400
11
1200
10
1000
9
800
8
600
7
6
400
5
4
200
3
0
0
2
4
6
8
10
12
time
14
16
18
20
22
18
20
22
Fireplume calculations
Sep 1, Fire ID 1094 , 800 acres
1600
plume rise (m.)
1400
11
1200
1000
800
600
6
400
5
4
200
3
2
0
0
2
4
6
8
10
12
time
14
16
Case study (con’t)
The calculation value shows that trend of plume rise with low height at
night time and peak during the late afternoon
Conclusions



Basic concept about plume rise was introduced;
General calculation of plume rise was described;
Wildfire plume rise calculation was specifically
discussed; Based on three conditions,
calculations were modified
The basic theory of the plume rise model (CAMx)
is limited to assumptions of uniform wind field
and constant stability in the atmospheric layers.
References

Uarporn Nopmongcol. Plume rise model for Forest Fire Using
ArcGIS Modeling Tool.
www.utexas.edu/gis/gishydro03/classroom/trmproj

Brown, et al. Fireplume model for plume dispersion from fires:
Application to uranium hexafluoride cylinder fires
www.osti.gov/dublincore/gpo/servlets/purl/510554-2x6vjV

Seinfeld J.H. Atmospheric chemistry and physics: from air
pollution to climate change. 1997