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Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
1
REGIME TRANSITION THEOREMS ON THE PHOTOCHEMICAL OZONE FORMATION

Akiyoshi Kannari*
Independent researcher, NIES visiting researcher, Tokyo, Japan

Toshimasa Ohara
National Institute for Environmental Study, Tsukuba, Japan


1. INTRODUCTION

Increase of ozone concentrations on the
weekend despite a weekend decrease in the
emissions of ozone precursors is called the “ozone
weekend effect” (OWE). Kannari(2006) found that
the weekend ozone concentrations are
systematically changing between the “weekend
increase” and the “weekend decrease” over the
broad areas in Japan (OWE reversals). By the
analysis using a simple advection-reaction model,
we showed that these systematic changes are
signals of regime changes of ozone formation
(Kannari & Ohara, 2010). Further, we believe that
several important theorems are established
concerning the regime transition of the ozone
formation.

2. OBSERVED OZONE WEEKEND EFFECT
AND ITS REVERSAL

We compared cumulative frequency curves of
the daily maximum ozone concentration (O
3max
)
between weekdays and Sundays at individual
monitoring sites in the broad area in Japan (Fig.
1a). By comparing O
3max
between weekdays and
Sundays at the same percentile rank, we ensured
that we were comparing values under similar
meteorological conditions (figures not shown).
Weekend changes in O
3max
at all 899 monitoring
sites are shown in Fig.1b. The ratio of the
weekend (Sunday) O
3max
to the weekday value
(colored scale) changes remarkably with the
percentile rank; namely, most monitoring sites
show a change from a weekend increase at lower
percentile ranks to a weekend decrease at higher
percentile ranks.
These changes accompany the clear spatial
structure as shown in Fig.2; namely “ozone
weekend increase” at near points from the huge


*Corresponding author: A. Kannari, 2-33-18-401,
Mishuku, Setagayaku, Tokyo, 154-0005, Japan, mail:
kannari.akiyoshi@circus.ocn.ne.jp

Sunday
Weekday
a)
Percentile rank
Daily maximum ozone concentration (ppb)
Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
2
precursor source areas changes to “ozone
weekend decrease” at more remote points
These very clear systematic reversals of OWE
are thought to be correlated with the weekend
changes of precursor’s day time mean
concentrations shown as follows.

[NOx]
weekend
=0.53 [NOx]
weekday ,

R=0.96, N=1,015 sites
[VOC]weekend= 0.78 [VOC]weekday,
R=0.95, N=251 sites
and
[VOC/NOx]
weekend
= 1.44 [VOC/NOx]
weekday

R=0.96, N=242 sites

Because NOx reduction rate is much higher than
that of VOC, weekend VOC/NOx ratio becomes
much higher than on the weekdays.
,
3. MODEL ANALYSIS

3.1 Advection–reaction model

It is well known that as an air mass is
transported, there are two chemical regimes for
ozone formation (Jacob, 1999; Jenkin, 2000).
Though ozone formation in an air mass is
governed by VOC-limited chemistry just after the
air mass leaves an urban source area, during the
air mass's transport to a remote area the regime
ultimately becomes NOx-limited as a result of the
elimination of NOx by the reaction between NO
2

and OH. Moreover, similarity theory predicts that
the regime boundary at a given time depends only
on the ratio of initial VOC and NOx concentrations
(e.g., Sillman, 1999). This Lagrangian basis
regime change can easily be supposed to be
related to the OWE reversals observed on the
Eulerian basis geography. We introduce a simple
model to investigate the mechanism of the OWE
reversals by estimating chemical regime changes
for O
3max
formation in a Eulerian coordinate system.
This advection–reaction model, which
calculates ozone concentrations in air masses
continually arriving at a receptor point from a
steady-state emission source, is based on a
Lagrangian transport model, and for simplicity it
excludes diffusion and deposition. The daily
maximum ozone concentration (O
3max
) is defined
by the maximum value in the time series for each
receptor point (Fig. 3). According to the
Lagrangian model, an air mass originating at the
upwind edge of a source area continues to acquire
precursor gases at a constant rate in the source
area, and reactions occur continuously during its
advection from its start point to the receptor point,
in both urban and rural areas. The normalized
distance (D) from the upwind edge of the source
area is defined as D = X/U, where X is the
distance from the start point and U is wind speed.
The length of the source area is also defined by
Fig. 2 An example of spatial distribution of weekend
ratio of O
3max
(at 90 percentile rank)
Fig. 3 Schematic diagram of time-dependent O
3

concentrations calculated at points A (near the source,
D = 2 h), B (middle range, D = 4 h), and C (remote, D
= 8 h), by assuming a constant emission rate
(beginning at 07:00 LT) and wind speed, with solar
radiation and temperature dependent on the time of
day. Arrows indicate the advection duration of the air
mass bringing O
3max
. The le
n
gth L of the precursor
source was assumed to be 2 h (indicated by the black
parts of the arrows)

Point A
Point B
Point C
O
3
(ppb)
Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
3
the passing duration L (h), assuming a uniform
injection rate q (ppb/h) of precursors, and the
supplied amounts of precursors are their initial
concentrations, expressed as qL (ppb). The most
important parameters in the model are the diurnal
changes in solar radiation and temperature; O
3max

occurs at the time of day when solar radiation and
temperature are highest during the advection (Fig.
4). Reflecting this property, the occurrence time of
O
3max
(T
max
) delays with D by nearly 0.5
Δ
D. VOC
compositions in the Tokyo metropolitan area
estimated from the emission inventory (Kannari et
al., 2007) are used in the CBIV model.

3.2 O
3max
isopleth diagrams

By the many calculations for initial
concentrations of VOC
0
= 10–1000 ppbC and of
NOx
0
= 1–100 ppb, isopleth diagrams of O
3max

were output by the advection–reaction model for D
= 3 and 6 h (Fig. 4a and b respectively). Point A
and B in Fig.4, the typical initial concentrations on
weekday and Sunday, show the reversal of the O
3max
concentrations from B>A (weekend
increase) at D=3h to A>B (weekend decrease) at
D=6h. This suggests that the observed reversals
of OWE occur because of the large change of
initial VOC/NOx on Sunday.
On the diagrams, the line connecting
maximum O
3max
values for each VOC
0
(the “ridge
line”) is defined as the boundary between the
VOC-limited regime (above the line) and the NOx-
limited regime (below the line). This boundary is
approximately linear and is extrapolated to the
origin. Thus, we confirm the similarity of the O
3max

AAAA
BBBB
a. Ozone isopleths for D = 3 h
NOx
0
(ppb)
VOC
0
(ppbC)
A
AA
A
BBBB
b. Ozone isopleths for D = 6 h
NOx
0
(ppb)
VOC
0
(ppbC)
Fig.5 Isopleth diagrams of O
3max
(ppb) for the
normalized distance D = 3 or 6 h under the 95-100
percentile rank meteorology. Points A and B indicate
typical initial concentrations for weekdays and
weekend. (Kannari & Ohara, 2010)
40
50
60
70
80
90
100
0 4 8 12 16 20 24
Humidity %
Solar radiation, MJ/m
2
/h
0
1
2
3
0 4 8 12 16 20 24
Temperature, ℃
15
20
25
30
0 4 8 12 16 20 24
Time of day
Fig.4 Mean meteorological conditions for the 95–
100th (solid lines) and the 75–80th (dashed lines)
percentile rank intervals of O
3max
in the TMA.
Values are for weekdays, but those on Sundays are
similar. Daytime water vapor concentrations
(volume mixing ratios) are nearly constant (2.1% for
the 95–100th, and 1.4% for the 75–80th percentile
rank interval) (kannari & Ohara, 2010).
Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
4
regime boundary, denoted below, which was
similarly established on a Lagrangian basis.
∂[O
3max
]/∂[NOx
0
] ⋚ 0 if [VOC
0
] ⋚ α[NOx
0
] (1)

where α is the regime boundary (a constant
representing the ratio of VOC
0
to NOx
0
on the
boundary)
This theorem has not been approved
mathematically but assured by numerical studies.
The regime boundary (α) moves as the
normalized distance D increases (e.g., from α =
18.8 at D = 3 h to α = 9.7 at D = 6 h; thus, the
boundary line revolves counterclockwise between
the isopleth diagrams) together with increasing O
3max
. Therefore, α is clearly an important
measure of the progress of photochemical
reactions. Decreasing α means that the NOx
0

concentration that causes the highest O
3max
for an
arbitrary VOC
0
increases continuously with D.

3.3 Transition of the regime

As stated above, transition of the chemical
regime boundary α of O
3max
with downwind
distance D(h) from the urban source area can be
estimated by using the advection-reaction model.
Examples of the α−D diagram are shown in Fig.6.
Transition of the regime depends mainly on the
three parameters listed below.
a. Cumulative solar radiation: O
3max
at more
remote points reflects larger cumulative solar
radiation during the transport process; then
has lower α value than at points closer to the
source (variation along each line in Fig. 6).
b. Intensity of solar radiation: More intense solar
radiation accelerates photochemical reactions,
thus causing α to decrease more rapidly (the
variation among the meteorological conditions
shown in Fig. 6).
c. VOC reactivity: We discuss the effect of VOC
reactivity only briefly. The red line in Fig. 6
shows the simulated change in α when the
isoprene (ISOP; most reactive in CBIV
species) percentage in the emitted precursors
is doubled, using the 95–100th percentile rank
meteorology. This result shows that when the
VOC composition has higher reactivity, α
decreases more rapidly.
Occurrence time of O
3max
(T
max
, LT) correlates
to the advection time D. Especially on the regime
boundary, it corresponds to the specific D.
Therefore, α−T
max
diagrams can be estimated
similarly as shown in Fig. 7.
α−D diagrams provide useful information, e. g.
an urban plume with initial VOC/NOx~10 reaches
the NOx-limited regime remoter than D~6 hours,
but that with VOC
0
/NOx
0
~7 cannot reach the NOx-
limited regime in a single day, even under the
most photochemically preferable meteorological
condition.

Fig. 6 Transition of regime boundary α (VOC
0
/NOx
0
)
with normalized distance D (hours) under the
meteorological conditions of various ozone
percentile intervals (black lines). The red line shows
the boundary for ISOP = 5.24% of VOCs (instead of
2.62%), under 95–100th percentile rank conditions.
5
10
15
20
2 3 4 5 6 7 8 9 10
D (hours)
65
-
70
%
75
-
80
%
85
-
90
%
95
-
100
%
VOC-limited
NOx-limited
α
(VOC
0
/NOx
0
)
ISOP X 2
5
10
15
20
13 14 15 16 17
Tmax (LT)
α
(VOC
0
/NOx
0
)
65
-
70
%
75
-
80
%
85
-
90
%
95
-
100
%
VOC-limited
NOx-limited
95-100% (ISOP x 2)
Fig. 7 Relationship between O
3max
occurrence time
(T
max
) and regime boundary α.
Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
5
3.4 Observed regime boundary

Regime boundary can be estimated from the
observed reversals of OWE. Figure 2 is an
example of the reversals, and the regime
boundary line (reversal line) is indicated in Fig.8a.
Observed T
max
is spatially distributed, delaying by
distance from the coastal source areas.
Relationship between O
3max
weekend ratio and
T
max
is shown in Fig. 8b, indicating that the T
max
on
the regime boundary is around 14:40 LT.
Boundary α corresponding it can be estimated
from the weighted mean observed morning
VOC/NOx concentration ratio at the source areas
on weekdays and weekends. Examples of the
comparison between the observed α–T
max
and the
simulated α–T
max
are plotted in Fig. 9. Because
solar radiation and emitted VOC composition is
different between Tokyo and Osaka, observed
regime boundary in Osaka is lower (more reactive)
than in Tokyo. This feature is roughly reproduced
by the model calculation.

3.5 Long term changes of regime
boundary

By the economic development and various
emission control strategy, VOC and NOx
concentrations had been largely changing since
1970s.On the other hand, meteorological condition,
solar radiation and temperature, had been
changing also in the same period.
Historical changes of α–T
max
relationship are
estimated from the observed OWE reversals in the
b)
WER(O
3max
weekend ratio)
OWE reversal line
a)
Fig.8 a) Spatial distribution of O
3max
occurrence time
(T
max
) in the 95-100
th
percentile rank interval in the
Tokyo metropolitan area. b) Regression between T
max
and O
3max
weekend ratio and the estimated
T
max
on the regime boundary. Colors of the dots
distinguish the districts and is not connected to the
colors of the
panel a.


5
10
15
20
13 14 15 16 17
α
T
max
(LT)
Osaka
Tokyo
Fig. 9 Comparison between observed α–T
max
and
simulated α–T
max
in Tokyo and Osaka under the 95-
100
th
percentile rank interval met. condition.
Meteorological Observatory data were used instead
of Fig. 4.
Presented at “Air Quality Modeling in Asia 2011” Conference, Seoul, Korea, January 24-25, 2011
6
95-100
th
percentile rank interval of O
3max
in the
Tokyo Metropolitan Area (Fig. 10). Because we do
not have historical data of emitted VOC
composition, long term changes of α–T
max

diagram only depending on the change of
meteorological condition were calculated and
attached in Fig. 10.
By the change of meteorological condition,
simulated regime boundary has been lowering
(becoming more reactive) during 1981~2004.
Observed regime boundary also has been
lowering, moreover the changes seem to be larger
than that by the simulations (became more
reactive than expected). This suggests that there
are some changes in VOC reactivity, VOC
compositions, in this period.

4. SUMMARY

Theoretical relationship between the distance
from sources and O
3max
(daily maximum ozone
concentration) formation regime are suggested by
a simple advection-reaction model. Fundamental
theorems, similarity of regime boundary and its
dependence to solar radiation and VOC reactivity,
are represented on the α−D and α–T
max
diagrams.
Observed regime boundary, estimated by the
reversals of OWE, supports the theoretical
implication.
We think that the theorems are useful as
fundamental nature of ozone chemistry for users
of modern complex 3D chemical-transport models
to interpret and understand their model results.

References
Jacob, D. J., 1999: Introduction to atmospheric
chemistry, Princeton University Press
Jenkin, M. E. and K. C. Clemitshaw, 2000: Ozone
and other secondary photochemical pollutants:
chemical processes governing their formation in
the planetary boundary layer, Atm. Env. 34,
2499-2527.
Kannari, A.,2006: An analysis of weekend effects
on photochemical oxidant concentrations in the
Kanto and Kansai regions, J. Jpn. Soc. Atmos.
Environ. 41(4), 209-233 (In Japanese with
English abstract)
Kannari A., Y. Tonooka, T. Baba and K. Murano,
2007: Development of multiple-species 1 km x 1
km resolution hourly basis emissions inventory
for Japan, Atm. Env., 41, 3428-3439.
Kannari, A., T. Ohara,2010: Theoretical implication
of reversals of the ozone weekend effect
systematically observed in Japan, Atmos. Chem.
Phys., 10, 6765–6776
Sillman, S., He, D., M. Pippin, P. Daum, L.
Kleinman, J. H. Lee and J. Weinstein-Lloyd,
1998: Model correlations for ozone, reactive
nitrogen and peroxides for Nashville in
comparison with measurements: implications for
VOC-NOx sensitivity. J. Geophys. Res. 103,
22629-22644.
8
10
12
14
14.00 14.50 15.00 15.50
α
Tmax (LT)
1981~1986
1987~1992
1993~1998
1999~2004
Fig. 10 Long term changes of observed α−Tmax in the
Tokyo metropolitan area, and simulated α−T
max

curves based on the historical met. condition in the
O3max 95-100
th
percentile rank interval days and
based on the VOC compositions in 2000. Tokyo
Meteorological Observatory data were used in the
calculation.