Measured atmospheric CO2 data is probably our most accurate indicator of climate change, but not a significant cause(or forcing factor). Scripps and NOAA operate several monitoring sites in the Arctic. All these sites north of 60 degrees measure CO2 values that differ from each other by less than an average of one ppm. This observation is consistent with a downward vertical flow of air from the upper atmosphere to the surface of ice and cold water. A perpetual inversion exists where the air temperature above the surface is always warmer than the ice or water surface.

Ice does not absorb CO2 but cold Arctic water with periodic phytoplankton blooms is a very strong sink. CO2 that reaches the ice surface must flow to open water before it is absorbed. The flow rate is controlling the rate of absorption, not Henry’s law of thermodynamics.Thus, the resulting high CO2 values in the winter when most of the Arctic is covered with ice and low values in summer when most of the ice is melted.

The following plot not only shows long term increase and shape of the annual cycle, but also, how well four sets of flask data agree.

Figure 1. Arctic monthly average CO2 concentrations from 1982 to 2015 showing an 8 ppm annual variation with a 75 ppm increase over the 33 year time period.

Mass spectrometer measurements were made on the flask samples taken at these same sites and the monthly average 13C indexes calculated. These results are averaged and presented in Figure 2.

Figure 2. Monthly average 13C index in Arctic.

The shape of the annual cycles of the 13C index appears as a mirror image of the shape of the annual cycles of CO2 concentrations because they are mathmatically related. Both values are fractions. Concentration is the volumetric fraction of CO2 in the atmosphere while the 13C index is a relative fraction of that concentration that has been slightly depleted of 13C by the process of kinetic fractionation. The relationship between the two is:

Equation 1.

I*avgI13C= 13C*CO2concentration

where I is the concentration of the fractionated fraction and avgI13C is the average 13C index for I.

Since 13C is the average of the total concentration which includes I with the non-fractionated fraction (which has an index close to the standard of zero) the two sides of the equation are equal. At any one point in time the fraction of the concentration that has been fractionated is equal to 13C/avgI13C. Both I and avgI13C are changing with time so an interaction with time should be included when statistically relating 13C with total concentration of CO2.

The regression equation is:

Equation 2.

a*[Y-Yavg)*13C]+b*13C +c= CO2

where Y is the time and Yavg is the average time for the total period with common 13C index and CO2 concentration data. The resulting regression constants are a, b, and c.

There are 33 years of common data from April 1982 to March 2015.

The results of the regression are shown in Table 1.

Table 1. The regression results are the constant c which represents the average non-fractionated CO2 concentration for the average time of 1998.75, b is the average fractionated 13C index at the average time, a is the rate of change of that index over the 33 year period.

The fraction of the Arctic Ocean that is covered with sea ice at any one point in time has been measured and reported as concentration. Figure 3. is a plot of data produced at knmi Climate Explorer.

Figure 3. Climate Explorer ice concentration time plot for the Arctic Ocean north of 70N.

This fraction changes most annually and the magnitude of that cycle changes from year to year. These rates are shown in Figure 4.

Figure 4. The running two-month rate of change is calculated as 6*(fraction at month i – fraction at month i-2)

The ppm data shown in figure 1 was converted to kg/m^2 at one atmosphere by multiplying by 0.0158. The running two-month rate of change in these data are shown in figure 5.

Figure 5. The running two-month rate of change is calculated as 6*(fraction at month i – fraction at month i-2)

The results of regressing CO2 concentration change rate on the sea ice change rate and an interaction of that rate with time is given in Table 2.

Figure 6. shows how well the regression model fits the data and is strong evidence that the sea ice is controlling sink rate.Figure 6. Agreement between observed and regression model CO2 rate changes.

These values represent the difference in the rate of input at the top of the atmosphere and the sink rate at the surface. When the value is positive, the input is greater than the output, When it is negative, the output at the surface is greater than the input at the top of the atmosphere. When the value is 0, input and output rates are equal. Since the Arctic ocean water is always a sink and is never completely covered, we need to estimate the input and output fluxes when they are equal.

The maximum positive values occur in October while the greatest negative values occur in July. The values closest to 0 occur in April. An estimate of the actual downward flux in April is one-half the difference in the value in October and the value in July. The average estimate calculated on the 45 years of data shown in Figure 1. is 0.956 kg/m^2/year with a standard deviation 0.097 kg/m^2/ye

We can factor out the effect of the annual change in sink rate by calculating a running twelve months difference. These results represent the variation in the input at the top of the atmosphere. Adding 0.956 kg/m^2/year gives us an estimate of the input flux as a function of time. Figure 7. shows the results of these calculations.

Figure 7. Input flux of CO2 at the top of the atmosphere in the Arctic.

Reported anthropogenic emissions of CO2 were converted to kg/m2/year by dividing by the area of the earth. This necessarily makes the extreme assumption that these emissions are rapidly pumped into the top of the atmosphere where it is rapidly uniformly distributed over the globe. For statistical evaluation, the reported annual data was interpolated monthly. Figure 8. is a plot of the results .

Figure 8. Global anthropogenic CO2 emission rates.

Plotting the two sets of data together in Figure 9. graphically illustrates how unlikely that anthropogenic emissions of CO2 contribute significantly to global emissions. Not only is the average Arctic CO2 flux 27.3 times greater than the average anthropogenic emission rate, but the variability of the former is 6.8 times greater than the latter. Any possible contribution of anthropogenics is lost in the variability of natural emissions.

Figure 9. Comparing anthropogenic emissions of CO2 with top-of-the-atmosphere CO2 fluxes in the Arctic.

Equation 1. data can be similarly analyzed to determine the possible contribution of anthropogenics to the kinetically fractionated fraction. The results from analyzing running two-month differences indicates that -28.33 should be added to the running twelve-month differences. These results are shown in Figure 10.Figure 10. Flux value for fractionated fraction for c13 in the Arctic.

Similar values can be calculated for anthropogenic emissions by multiplying emission rates from gases, liquids, and solids by there respective C13 indexes and summing the products. The C13 index values for gases, liquid, and solids are assumed to be -60, -30, and -25 respectively. The index value for cement is assumed to be zero and is not included in these calculations. The results are shown in Figure 11.Figure 11. Estimated maximum C13 flux values of anthropogenic emissions in the Arctic.

Plotting the data in Figures 10 and 11 together in Figure 12 illustrates how unlikely that anthropogenic emissions of CO2 are contributing measurably to changes in atmospheric C13 index values. Those changes are more likely due to natural kinetic fractionation processesFigure 12. Comparing estimated total to anthropogenic flux values fo C13 index in the Arctic.

The average value for total is 17.4 times the value for anthropogenics and the standard deviation is 1.5 times greater. Any measurable variability in the atmospheric index due to anthropogenic emissions is lost in the natural variability.

The two strong peeks at 1988 1nd 1998 in both Figures 7 and 10 are evidence that the input at TOA in the Arctic is coming from the tropical Pacific. The plots are similar to the average troposphere temperatures between 20S and 20N as shown in Figure 13.Figure 13. Average tropospheric temperature anomily between 20S and 20N.

The concentration of CO2 being pumped out the top of tropical thunder clouds is very likely a function of the temperature near the top before the water freezes. The following plot is from data at ESRL’s reannalysis website.Figure 14. ESRL reanalysis air temperature at 600mb between 20S and 20N.

Figures 7 and 10 are Representative of a global signature for natural emission rates. This is illustrated in Figure 15.Figure 15 Running twelve months difference in CO2 concentration at three Scripps monitoring sites.

Mauna Loa and Samoa are in the tropics and the flux is up from the surface. At the South Pole the flux is down. The fact that the signature are alike indicates the emission rates at areas in the tropics is being balanced by the sink rates at the poles. However, sink rates are not completely keeping up with emission rates and the net indicates a long term increase in emission rates.