Francis Massen francis.massen@education.lu http://meteo.lcd.lu
Authors:
Francis Massen, Ernst Beck, Hans Jelbring, Antoine Kies
History: version 1.0: original version 23Mar07 version 1.1: changed title added decadal dependancy to calculations page 5, corrected error in latitude difference between Orleans and Mauno Loa (should be 28) added table for clearness (p.6) added remark on possible decadal oscillation in time dependancy (p.5) corrected references (still uncomplete) added a conclusion added legends to figures do be done: add explanation on Massen et al CO2/windspeed method? use more data to compute CO2 gradient? version 1.2.: 24 Mars07: added 3D plot
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Using the time dependant CO2 variation with latitude page 1

Abstract:
A short investigation on the dependance of winter and summer CO2 mixing ratios with latitude shows that CO2 increases linearly with latitude, from South-Pole to
North-Pole. The slope of this linear function increases with time. A corrective formula is proposed, and used to validate historical CO2 measurements.
1. The source of the CO2 data.
All data in this study come from the NOAA Globalview ftp site at ftp://ftp.cmdl.noaa.gov/ccg/co2/GLOBALVIEW/gv/ [1]
The data files hold 4 columns like:
Creation Date: Thu Aug 31 09:28:42 2006
# of rows after column header: 1297
UTC S(t) REF(t) diff
1979.000000 335.4340 336.7548 -1.3208
1979.020833 335.7970 337.1502 -1.3532
The CO2 mixing ratio is the sum of REF(t) + diff.
2. Stations and time-span used
10 stations from South-Pole to Spitzbergen are used in this study, having the following latitudes:
Station
South Pole
NOAA code spo_01D0
Mawson Station maa_02D0
Barring Head, NZ bhd_15C0
Amsterdam Island ams_11C0
Samoa Island smo_04D0
Mauna Loa mlo_01D0
Latitude
-90
-68
-41
-37
-14
20
La Jolla Pier
Gozo (Malta)
Orleans (F)
Barrow Station ljo_04D0 goz_01D0 orl005_11D2 brw_01D0
33
36
48
71
Spitzbergen zep_01D0 79
The data used are from 1985, 1990, 1995, 2000 and 2005; winter data correspond to yyyy.0000 , summer to yyyy.5000 UTC.
Table 1 gives the measurements used, yyyyW denotes winter and yyyyS summer.
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Using the time dependant CO2 variation with latitude page 2

table 1: data used fig 0 shows the data in a 3D-plot: fig.0
3. Variation with latitude
The plot of CO2 versus latitude gives the following results for both seasons:
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Using the time dependant CO2 variation with latitude page 3

fig.1. Variation in CO2 mixing ratios with latitude, first month of the year (i.e. NH winter), computed from 11 stations. fig.2. Variation in CO2 mixing ratios with latitude, first month of the year (i.e. NH winter), computed from 11 stations.
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Using the time dependant CO2 variation with latitude page 4

The conclusions to draw are obvious from inspection:
1. the gradient increases more or less linearly with latitude
2. the winter gradient is 4 to 5 times higher than the summer gradient
3. the relative variability from year to year is lower in winter (maximum factor 1.25) than in summer (maximum factor 5.54)
The mean winter gradient is 0.05824
+/- 0.00585, the mean summer gradient 0.01384
+/- 0.00693 (about 1/4th of the winter gradient)
An example: if the January CO2 concentration at the South-Pole is 370ppm, one should expect 370 + 0.05824*(90+48) = 370 + 8 = 378 ppm for Orleans; at mid-year the difference would be +1.9 ppm.
Over the whole year an average gradient of 0.03604
could be used as a first approximation.
4. Latitudinal gradient variation with time.
Plotting the different gradients versus a decadal time increment (taking year1985 as 0) shows a linear increase with time (with a possible superposed decadal oscillation):
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Using the time dependant CO2 variation with latitude page 5

fig.3.Decadal time dependancy of the latitudinal gradient
The winter gradient increases by 0.055 per decade, the summer by 0.0121, about 4 times less .
Latitudinal and time dependencies can be summarized by the following relationship
CO2(t,L), with t being the time in decades from 1985 on, and L the latitude:
Season Latitude and time correction
Example: 2005 Orleans versus South Pole
Winter (0.055 + 0.0032*t)*L + 8.5
Summer (0.012 + 0.0018*t)*L + 2.2 avg_year (0.034 + 0.0025*t)*L + 5.4
Measured CO2 difference
9.4
-3.9
2.8
The difference between the gradient computed using the formula and the real measured data is not negligeable, especially in summer. Nevertheless, the formula can help to make a raw check for instance on the validity of historic data, as will be shown in the next paragraph .
5. Applying the correction to a historical data series
As an example, we will use the measurements done by Steinhauser in Wien during the
8 months Mai-August 1957 and Nov-Feb 1957/58 [2] . This is one of the few well documented chemical measurement series overlapping with the first NDIR measurements by Keeling. From the digitized Steinhauser plots of CO2 versus wind
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Using the time dependant CO2 variation with latitude page 6

speed one gets a mean rounded value of 327 ppm, the asymptotic CO2-windspeed rule explained in [4] suggests a baseline of 324ppm.
To compare with the first Keeling measurements, we will use the results from fig.5.
Keeling made early measurements at Mauna Loa, lat. 20°, in 1958; the yearly mean is about 313 ppm.. The latitude of Wien is the same as Orleans (48°); applying the gradient to the Keeling data gives the following results
Keeling
Mauna
Steinhauser, Wien,
1957-1958, chemical
Latitude/time gradient to add to
1958 Wien data
Difference between
Loa,
1958
Average over
Base-level from
NDIR 8 months windspeed
313 ppm 327 ppm 324 ppm
Keeling data
0.034+
0.0025*(-2.7)*28
= 0.76 ~1 ppm according to
Mauna Loa
314 ppm
Steinhauser and adjusted
NDIR
13 ppm
10 ppm
If we use the winter ice floe data (assuming a latitude of -70° which gives a difference of 118° with Wien) and the Steinhauser Nov57-Feb58 series, the results are:
Keeling, ice floe
Feb.,
1958
NDIR
Steinhauser, Wien,
1957-1958, chemical
Average over
4 winter
Base-level from windspeed[ months
316 ppm 336 ppm 329 ppm
Latitude/time gradient to add to
Keeling data
1958 Wien data according to ice floe
Difference between
Steinhauser and adjusted
NDIR
0.055+
0.0032*(-
2.7)*118
= 5.5 ~6 ppm
322 ppm 14 ppm
7 ppm
6. Conclusion
Two conclusions can be made from this comparison:
1. To evaluate historic chemical measurements, the base-level computed using the asymptotic windspeed adjustement [4] and applying a latitude/time gradient reduces the difference between the NDIR and the original chemical measurements.
2. The rather small difference of ~7 -10 ppm found in this study shows that at least some of the historical chemical CO2 measurements can be considered as valid, and could be used to complement (or correct) the traditional ice core data which are exclusively used today to represent the CO2 mixing ratios preceeding the NDIR measurements. ( [5] ).
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Using the time dependant CO2 variation with latitude page 7

fig.4. Base-level CO2 computed from a (CO2, wind speed) scatter plot [4] fig.5 The early Keeling curve (from Scripps Institution of Oceanography)
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2.
References:
1. GLOBALVIEW-CO2: Cooperative Atmospheric Data Integration
Project - Carbon Dioxide. CD-ROM, NOAA/CMDL, Boulder, Colorado.
[Also available on Internet via anonymous FTP to ftp.cmdl.noaa.gov,
Path: ccg/co2/GLOBALVIEW], 2006.
Steinhauser F., Der Kohlendioxyd-Gehalt der Luft. DK 551.510.41
3. The early Keeling Curve. http://scrippsco2.ucsd.edu/program_history/early_keeling_curve_2.html
4. Massen F. et al: Seasonal and Diurnal CO2 Patterns at Diekirch, LU. http://meteo.lcd.lu/papers/co2_patterns/co2_patterns.html
5. Beck E., 180 Years of Atmospheric CO2 Gas Analysis by Chemical Methods.
ENERGY & ENVIRONMENT; VOLUME 18 No. 2 2007
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