Nature reference: MS2004-04-17839C
Short term variations in the oxidizing power of the atmosphere:
Supplementary Material
Martin R Manning*, David C. Lowe†, Rowena Moss†, Greg Bodeker†, W. Allan†
*
IPCC Working Group I Support Unit, Boulder, Colorado, USA
†
National Institute of Water and Atmospheric Research, Wellington, New Zealand
Supplementary Methods
1. Model details
While the vertical distribution of 14C in the atmosphere is expected to change slightly with
solar activity, model analyses by Jöckel et al1 suggest that this has little effect on near surface
14
CO concentrations so the effect has been ignored.
Monthly average values for the a priori loss rate L0T were calculated as the air-mass
weighted average value of monthly [OH] concentrations from Spivakovsky et al2 times the
pressure dependent rate constant for CO + OH over the latitude range 90S to 40S and from the
surface to 100 mBar. A sinusoid with 12- and 6-monthly components was fitted to these monthly
values and used to interpolate to other times.
The differential equations (1) are integrated using a Runge Kutta procedure starting from
January 1, 1985, with concentrations of zero. Spin-up times are less than two years.
2. Model results
Although our two-box model is only intended for the very specific purpose of diagnosing
temporal changes in 14CO in the region between New Zealand and Antarctica, some comparisons
with more general models of 14CO can be considered. One useful diagnostic in this respect is the
fraction of 14CO occurring in the troposphere that originates in the stratosphere. This stratospheric
1
fraction can be determined by setting tropospheric production to zero and comparing results with
a standard run. Our two-box model gives a seasonal cycle in the stratospheric fraction ranging
from about 12% in May to 17% in December. In addition, there are small interannual variations
in the stratospheric fraction which increases by about 0.5% after several years of high 14C
production, and decreases after a year of low 14C production.
Our stratospheric fractions are lower than those found for two 3-D chemical tracer models
by Jöckel et al3. Based on Figure 2 of that study values of the stratospheric fraction, in the
latitude region considered here, range from 20 to 28% for the TM3 model and from 40 to 50% for
the MATCH model. These two models have seasonal cycles for the stratospheric fraction that are
out of phase with each other and neither agrees with the seasonality of our model.
As noted below, our model results are not particularly sensitive to the phasing of STE and it
seems quite feasible that the seasonal cycle of our stratospheric fraction could be adjusted to
agree with one or other of the above mentioned 3-D models without significantly degrading the
fit to our data. However, the significant difference in the magnitudes of the stratospheric fractions
reported from various studies remains a matter for further consideration. As mentioned in the
main text, we believe that the absence of 14CO anomalies during a period of extraordinary
behaviour in the Antarctic polar vortex4, and the fact that stratosphere – troposphere differences
in 14CO concentrations are expected to be greatest in this region, provide some observational
basis for believing that the stratospheric fraction of 14CO is low.
To investigate the sensitivity of our results to the choice of 14C production function, two
alternative production functions are compared with that used in the main text due to Lowe and
Allan5 and based on Masarik and Beer6. The first alternative, due to Lal7, is derived from neutron
count rate data and the second alternative, due to O’Brien8, is derived by adjusting Lingenfelter’s9
production estimates for variations in solar activity determined from sunspot numbers. Each of
2
the three production functions has been used without adjusting the other a priori parameters and
the corresponding model simulations are shown in Supplementary Figure 1. It can be seen that
CO concentrations determined using Lal’s production function are quite similar to those shown
14
in the main text during the solar maximum in 1990 and 1991 but are significantly too large during
the solar minimum period, 1994 – 1999. O’Brien’s production function on the other hand
produces concentrations that are too large during the solar maximum period and are either
comparable with those shown in the main text or too small during the solar minimum.
While the discrepancies between model and observations for both the Lal and O’Brien
production functions can be compensated to some extent by adjusting the other parameters in our
model, their systematic behaviour means that discrepancies can not be avoided for the entire solar
cycle by scaling OH or STE values up or down. To obtain a fit of the same quality as that
obtained with our standard production function requires adjusting tropospheric OH values from
year to year in a way that is correlated with 14C production. This suggests that the Lowe and
Allan production function is clearly preferred by our model analysis.
3
BHD
SCT
Lal
OBrien
Standard
20
14
-3
CO molec cm STP
25
15
10
5
1990
1995
2000
Year
Supplementary Figure 1. A priori model results for three different 14C production terms for
the period 1989 – 2003. Production functions are: Lowe and Allan5 (Standard), Lal 7, and
O’Brien8 and the corresponding results are shown as smooth curves. Concentration data from
Baring Head and Scott Base are shown as blue and red circles respectively.
3. Statistical procedures
To test non-randomness in the residuals shown in Figure 1 we use a non-parametric test
counting the number of sign changes in the sequence of residuals10. This count is much smaller
than expected for random data (P < 0.001) indicating a high degree of temporal coherence.
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4. Model optimisation
Bayesian parameter constraints are imposed using a priori uncertainties assigned as
described below to the scaling and time shift parameters defined in equations (2) of the main text.
Spivakovsky et al2 cite a relative uncertainty of 15% in their OH estimates used to
calculate L0T thus we assign a relative uncertainty of 15% to both l0 and l1. Similarly the original
estimates5,6 of 14C production underlying PA0 were assigned relative uncertainties of 10%.
However, as there is also uncertainty in the partitioning of production between the stratosphere
and troposphere we use a relative a priori uncertainty of 20% in p1. A priori uncertainties in the
scale and shift parameters for STE and the ratio of stratospheric to tropospheric loss rates are set
to 20%, and uncertainties in the two time lag parameters are set at 2 weeks.
A total of 459 data points from the two sites are used to fit model parameters defined in (2)
(with the exception of p0 = 1), giving 451 degrees of freedom. Recognising that the data have
some outliers and anomalous periods, we make the optimisation step robust to these by
automatically excluding the largest 10% of error weighted data residuals from the sum of squares
that is minimised.
Estimation of a posteriori parameter uncertainties in Bayesian constrained non-linear least
squares problems can be done in several ways. Here we have used the inverse of the Hessian of
second derivatives of the sum of squares function at its minimum as a parameter variancecovariance matrix, effectively linearising the problem11. The advantage of parameter uncertainties
calculated in this way is that they include the effect of correlations with other parameters.
However, it should be noted that this method does not capture asymmetry in a posteriori
probability density functions (pdfs) caused by non-linearities in the model.
5
Best fit parameter values, corresponding uncertainty estimates, and parameter correlation
coefficients are given in Table 1. It can be seen that a posteriori uncertainties are reduced by a
factor of about 20 to 30 relative to a priori uncertainties for most parameters with the two
exceptions of X1 and wX, indicating that our data impose strong constraints on the corresponding
model terms. In particular, in the context of our simplified model, the average 14CO tropospheric
loss rate, relative to the assumed average production rate, and the amplitudes of the seasonal
cycle in OH, and of the solar cycle in 14C production, are constrained to within about 1% of their
best fit values.
Supplementary Table 1. A priori and fitted parameters and their uncertainties
including correlation coefficients. The uncertainty reduction is the ratio of a priori to
a posteriori uncertainties.
Parameter
A priori
value
A posteriori
value
Correlation coefficients (%)
Uncertainty
reduction
l0
l1
wL
x0
x1
wX
p1
f
-
66.0
-21.5
48.1
-30.7
-22.0
-39.7
-76.3
l0
1 ± 0.15
0.9848 ± 0.0052
29.1
l1
1 ± 0.15
0.9333 ± 0.0068
22.0
66.0
-
-23.5
9.2
-27.9
-28.0
-35.4
-53.3
0 ± 0.0385 -0.0416 ± 0.0013
30.4
-21.5
-23.5
-
-23.3
-5.5
-5.6
-6.4
3.1
x0
1 ± 0.2
1.0531 ± 0.0087
23.0
48.1
9.2
-23.3
-
-29.7
-26.1
-31.0
-42.2
x1
1 ± 0.2
1.0237 ± 0.0610
3.3
-30.7
-27.9
-5.5
-29.7
-
-10.6
-4.2
8.9
wL /yr
0 ± 0.0385 0.0004 ± 0.0116
3.3
-22.0
-28.0
-5.6
-26.1
-10.6
-
-6.6
3.9
p1
1 ± 0.2
1.1271 ± 0.0081
24.8
-39.7
-35.4
-6.4
-31.0
-4.2
-6.6
-
15.6
f
1 ± 0.2
1.0499 ± 0.0114
17.6
-76.3
-53.3
3.1
-42.2
8.9
3.9
15.6
-
wX /yr
6
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14
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