PNNL-13501 - Pacific Northwest National Laboratory

Wind Direction (°)
450 90
360
270
180
90
0
0
3
6
9
12
15
18
21
0
3
6
9
12
15
18
21
0
3
6
9
12
15
18
21
Local Time
Direction
Velocity
Figure 1. Measured activities of 212 Pb and 214 Pb versus
transport time from the Pacific Coast
averaged every hour over the five METAR (National
Weather Service) stations. The bracketed areas show the
times samples were collected.
The winds during the collection period were blowing at
an average angle of 330 degrees. At this angle, air
coming into Portland was from the Pacific and traversed
approximately 60 miles of land before entering the city.
A transit time was calculated on a simple 1-hour average.
For example, if the air speed was 5 knots over the first
hour and 10 knots over the second hour, then the transit
time for the first 15 nautical miles was 2 hours. Using
this method, the time required to transit 60 nautical miles
was calculated for each sample.
Figure 2 plots the measured 212 Pb and 214 Pb activities for
each sample versus transit time for the associated air mass
from the ocean to the sampling site. This plot shows the
measured 212 Pb activity was independent of transit time
(6 to 16 hours). The units in this figure are counts/m 3 , not
Bq/m 3 . This correction will be made once detector
efficiencies have been more rigorously calculated.
Pb-214 (counts/cubic meter)
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
Pb-214, June 17
Pb-214, June 16
Pb-214, June 18
Pb-212, June 17
Pb-212, June 16
Pb-212, June 18
0
0
5 7 9 11 13 15 17
Transport Time (hr)
274 FY 2000 Laboratory Directed Research and Development Annual Report
20
18
16
14
12
10
8
6
4
2
0
0.0045
0.0035
0.0025
0.0015
0.0005
Figure 2. Average surface wind direction and velocity data
0.004
0.003
0.002
0.001
Wind Velocity (knots)
Pb-212 (counts/cubic meter)
The measured 214 Pb activity shows an initial decrease
followed by a steep rise. For comparison, a simple onedimensional
model was developed for both the 212 Pb and
214 Pb systems. Figure 3 plots the theoretical activity of
214 Pb as a function of several different land-based 222 Rn
fluxes versus transit time. The 214 Pb model assumes that
initially the 214 Pb is in equilibrium with the 222 Rn parent,
therefore [ 214 Pb]/[ 222 Rn]o=1. The model ignores the 218 Po
intermediate due to its short half-life of 3 minutes. The
following equation was used to calculate the theoretical
activity of 214 Pb based on these assumptions
⎧
⎛ − λ − ⎞⎫
⎡ ⎤ ⎡ ⎤ − ⎪ ⎡ ⎤ ⎜ 2t
λ
− 1t
214
⎟⎪
=
214 λ2t
+
222 e e
Pb Pb e ⎨λ
⎜
⎟⎬
+
⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦
1 Rn
λ
⎢⎣ ⎥⎦
⎪
⎜ −
1
0
0 λ ⎟⎪
⎩
⎝
1 λ2
⎠⎭
⎡ 222
Rn
⎤
⎢⎣ ⎥⎦
⎧
flux ⎪ 1
⎨
⎡ 222
Rn
⎤ ⎪
⎢⎣ ⎥⎦ ⎩
0
( λ − λ )
− λ − ⎫
+ 1t
λ
− 2t
2 λ2e
λ1e
⎪
λ1λ2
⎬
( λ1
− λ2
) ⎪
⎭
where t= transit time
λ1=decay constant for 222 Rn
λ2=decay constant for 214 Pb
A
10000
1000
100
10
1
0.1
0.01
0.001
0
0.0001
0.0004
0.0016
0.0064
0.0256
0.102
0.410
1.64
6.55
26.2
F lux [R n-222]/[R n-222]o
0.01 0.1 1 10 100 1000 10000
Transport Time (hr)
Figure 3. Theoretical concentration of 214 Pb versus
transport time over land with several fixed 222 Rn source
terms
similar model was developed for 212 Pb. The 212 Pb model
assumes a final 212 Pb activity of 1 Bq/m 3 and ignores the
216 Po intermediate due to its short half-life of 0.15
seconds. Figure 4 plots the modeled 212 Pb activity as a
function of several different geological flux rates over
time.
From Figure 3, one sees that the model predicts the initial
decrease observed in the measured 214 Pb activity. Based
on the general shapes of the curves and the counting error
associated with the 214 Pb measurement, this model is most
sensitive for predictions between approximately 1 to
20 hours of transport time. The 222 Rn flux over the land