Atmospheric Chemistry and Physics Discussions
www.atmos-chem-phys-discuss.net
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2005
10.5194/acpd-5-12957-2005
http://www.atmos-chem-phys-discuss.net/5/12957/2005/
http://www.atmos-chem-phys-discuss.net/5/12957/2005/acpd-5-12957-2005.html
http://www.atmos-chem-phys-discuss.net/5/12957/2005/acpd-5-12957-2005.pdf
12957
12983
2005-12-19
A scaling analysis of ozone photochemistry: I Model development
B. Ainslie
bainslie@eos.ubc.ca
D. G. Steyn
Atmospheric Science Programme, The University of British Columbia, Vancouver, Canada
A scaling analysis has been used to capture the integrated behaviour of
several photochemical mechanisms for a wide
range of precursor concentrations and a variety of environmental
conditions. The Buckingham Pi method of dimensional analysis was used
to express the relevant variables in terms of dimensionless groups.
These grouping show maximum ozone,
initial NO<sub>x</sub> and initial VOC concentrations are made non-dimensional
by the average NO<sub>2</sub> photolysis rate (<i>j<sub>av</sub></i>) and the rate
constant for the NO-O<sub>3</sub> titration reaction (<i>k</i><sub>NO</sub>);
temperature by the NO-O<sub>3</sub> activation energy (<i>E</i><sub>NO</sub>)
and Boltzmann constant (<i>k</i>) and total irradiation time by the cumulative
<i>j<sub>av</sub></i>Δ<i>t</i> photolysis rate (π<sub>3</sub>). The analysis shows
dimensionless maximum ozone concentration can be described by a
product of powers of dimensionless initial NO<sub>x</sub> concentration,
dimensionless temperature, and a similarity curve
directly dependent on the ratio of initial VOC to NO<sub>x</sub> concentration
and implicitly dependent on the cumulative NO<sub>2</sub> photolysis
rate. When Weibull transformed, the similarity relationship shows a scaling
break with dimensionless model output clustering onto two straight
line segments, parameterized using four variables: two describing the
slopes of the line segments and two giving the location of their
intersection. A fifth parameter is used to normalize
the model output. The scaling analysis, similarity curve and
parameterization appear to be independent of the details of the
chemical mechanism, hold for a variety of VOC species and mixtures and
a wide range of temperatures and actinic fluxes.