All the data I have analyzed are evidence that reported monthly averages are measurements of a global distribution of background levels of CO2. Event flask measurements that were exceptionally high (that could be from local anthropogenic sources) have been flagged and were not included in monthly averages. The result is a consistent global uniformity with no significant variation with longitude and a latitude dependent seasonal variation.
The Scripps data set from sites that were selected to represent background, http://scrippsco2.ucsd.edu/data/atmospheric_co2.html, has the longest time coverage for both CO2 and 13CO2 index. The tenth column, in their tables of data, factors out seasonal variations and fills in missing values with model fit values. The seasonal variations are caused by natural processes so any anthropogenic contribution will be contained in the column 10 data. I have compiled data sets of 13CO2 and CO2 for all but the Baja site. That site covers a short time span and the recorded values are higher than for the other sites. It is likely not representative of background.
Year to year increasingly negative 13CO2 index values indicate that the atmosphere is accumulating the lighter CO2 faster than it does the heavier. Since the lighter is more from organic origin and the heavier more from inorganic, it has been assumed that the consistently increasing burning of fossil fuel has caused the difference. This assumption does not consider long-term changes in natural source and sink rates. The long-term proxied data for atmospheric CO2 concentrations indicate that these natural changes are significant and should be considered in any mass balance type of calculation.
The C 13/12 ratio is calculated as:
Delta C13= ((C13/C sample)/(C13/C PDB)-1)*1000.
If we assume that all the CO2 from organic origin can be represented by an average Delta C13 value of -27.3 and that from inorganic origin has a value represented by the PDB standard, we can partition the two sources by dividing the index by -27.3. Actually, both fractions have ranges of values and there are inorganic fractionation processes that can produce values within the organic range. We can divide the calculated Delta C13 by -27.3 to get an estimate of the organic source fraction. This simple conversion of the Delta C13 index to an organic fraction has no effect on the accuracy of values and reverses the sign so that the accumulation is shown as positive. The index values were multiplied by -100/27.3 to express the organic fraction as a percentage of the total. The results are shown in the following plot.
The consistent rise in the percentage may be attributable to increasing burning of fossil fuels. The variation with latitude is likely caused by a long-term natural fractionation process. With this in mind, I regressed the combined data on global CO2 emissions and a cosine function of latitude. The form of the function is cos(lat/a+b) where north latitude is positive and south latitude is negative. The coefficients a and b were determined by trial and error to maximize R^2 in the regression.
The emissions were converted to global ppm/year of CO2 and a curve fitting regression technique used to produce an emissions time function. This function is needed to produce monthly data for regression with monthly concentrations of CO2. The resulting function is linear with four additional cosine function perturbations that are statistically significant. The linear portion is
The cosine functions have the form :
c*cos(t/b+a) where t=2*PI*year.
The resulting coefficients that give an R^2 of 0.998 are:
The mean residence time of CO2 in the atmosphere as a gas is likely a matter of days, however the mean residence time in the environment can be years as CO2 cycles between the atmosphere and the surface (water, land, and biosphere). This residence time can be estimated by adjusting the emissions time scale to maximize R^2 in a regression (match up perturbations). The best fit regression of atmospheric CO2 on the latitude function and anthropogenic emissions is found at a mean environmental residence time of 9.8 years. That is like saying that emissions this year will show up as an atmospheric increase in around 9.8 years. The coefficients for the best fit are given in the following table.
With the emissions coefficient we can calculate the percentage of anthropogenic CO2 in the atmosphere as a function of time. The results are shown in the following plot.
Most of the CO2 in the atmosphere is from natural sources. We can determine how these natural processes change with time by subtracting the anthropogenic portion from the total measured atmospheric CO2. A statistical curve fit of this natural fraction gives the following results.
Subtracting the regression fit values from the total values for CO2 we can back check for the anthropogenic contribution and determine changes with time. Regressing on emission rates and adjusting the time scale to maximize R^2 gives the following best fit.
The following plot shows the goodness of fit when a mean environmental residence time is considered as a factor (matching up the perturbations).It should be noted that the best fits for both the 13C and the total CO2 data give the same lead time.
I have used these statistical models to project expected global background atmospheric CO2 concentrations out to 2050. The following plot is for Mauna Loa. Included is a “what if” plot of an annual 4% global reduction in emissions starting in 2012.
Now we need an economist to do a cost/benefit analysis on these projections.