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.

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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. That seasonal variation is the greatest and relatively constant north of the Arctic circle. There are similar but lesser seasonal variations in the Antarctic.

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. Much more data measured around the globe are published at the World Data Centre for Greenhouse Gases . The seasonal variations are caused by natural processes which are temperature dependant. Anthropogenic emissions are not temperature dependent. Therefore, evidence for an anthropogenic increase in atmospheric CO2, is more likely to be observed in long term changes with the seasonal variations factored out.

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 ice core 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 somewhere between -15 and -30, and that from inorganic origin has a value of 0 represented by the PDB standard, we can make a first estimate of the organic origin fraction by dividing the index by say -20. Actually, both fractions have ranges of values and there are inorganic fractionation processes that can produce values within the organic range. To get a better estimate of the average organic origin index value, regress the measured values of atmospheric concentration on the measured index values. The resulting concentration coefficient is an estimate of the average organic origin index value for the time period regressed. The ratio of the measured 13CO2 index to this value gives an estimate of the organic 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 Arctic data has both the highest background concentration values and the greatest seasonal variation. The seasonal variation is likely the results of the ever-changing unfrozen sink area (both ocean and land biosphere). We should be able to get a more accurate CO2 mass balance using these data from this primary sink area. Nearly all of the CO2 is coming from the south and is being delivered in the upper atmosphere.

So what do the Arctic data tell us? Take a look at what I have found at the two sources referenced above. The following plots are based on the monthly averaged data from all the land based measuring sites located north of 60N.

Fig 1. Arctic background CO2 concentrations as a function of time.

The above plot is point to point on averages of monthly averages of 18 sets of data. The average of all the two standard deviations is only 2.2 ppm. Any locational differences appear to be insignificant.

A similar analysis of 13CO2 index data yields the following plot.

Fig 2. Change in 13CO2 index in the Arctic as a function of time.

This plot is based on eight sets of flask data from the same region north of 60N. The observed variations in both plots appear to be mirror images as one should expect.

To reduce the error estimates and improve the signal to noise ratio, both sets of data were smoothed by calculating running three months averages. Since we want to determine the relative natural and anthropogenic contributions, and anthropogenic emissions are rates, we are more interested in accumulation rates rather than the amount accumulated as shown in the above plots. The total seasonal short-term rates were calculated as running two month differences (i.e. 6*(Mar. – Jan.). The long-term values are running twelve month differences (i.e. Jan. 2000 – Jan. 1999). Anthropogenic Emissions assumes uniform global distribution with no sink rate and is shown for comparison with the net measured rates.

Fig 3. Comparison of net short-term and long-term accumulation rates with anthropogenic emissions.

Fig. 4. Comparison of net long-term accumulation rates with anthropogenic emissions.

The seasonal variations (running 2 months) in all of these plots are orders of magnitude greater than the year to year variations (running twelve months). The two months net rates primarily reflect natural processes but may include anthropogenics that have cycled through the system.

The following are similar plots for the smoothed 13CO2 index values.

Fig. 5. Short and long-term rates of change in the 13CO2 index.

Fig. 6. Long term rates of change in the 13CO2 index.

Both sets of running two months differences fit a triangular wave form (cosine function with one harmonic) and an interaction with time term. The resulting R squares are greater than 0.99. Regressing the short-term CO2 accumulation rates on the 13 CO2 index rates and time times the index yields an index coefficient of -19.78 with 2 standard deviations (95% confidence limits) of 0.13. This is a best estimate of the organic fraction average 13 CO2 index mostly from natural sources. With this value I was able to calculate the organic and inorganic fractions of the natural annual cycles and estimate the relative contributions of each.

Fig. 7. Relative contribution to Arctic CO2 concentrations from organic and inorganic sources.

The long-term linear trends accumulation rates are 1.17 ppm/year for organics and 0.57 ppm/year for inorganics. The seasonal variation of the organics is greater than the inorganics and with an opposite phase.

The running 12 months difference data indicate much lower rates that change significantly from year to year. The contribution of anthropogenic emissions should be evident in these data but does not account for the variability.

Regressing the long-term CO2 accumulation rate on both the long-term rate of change in the 13CO2 index, anthropogenic emission rates, and their possible interaction yields the following results.

Table I. Results of regressing long-term CO2 accumulation rates on long-term 13CO2 index rate of change, anthropogenic emissions, and their interaction.

The following plot graphically presents these results for the anthropogenic contribution to the total long-term accumulation rate of atmospheric CO2.

Fig. 8. Relative contribution of anthropogenic CO2 to the long-term rate of accumulation in the Arctic.

I used the anthropogenic emission rate coefficient and related estimate of error to estimate the accumulation of anthropogenic CO2 in the atmosphere/surface system. The surface includes water, soil and biosphere that are affected by cycles with wave lengths of less than around 500 years. For example, the decay of forest litter has a cycle wave length of about 10 years. Phytoplankton decay is expected to cycle CO2 faster. The results are shown in the following plot.

Fig 9. Estimate of anthropogenic CO2 accumulation in the global atmosphere/surface system from Arctic atmosphere data.

Subtracting the anthropogenic accumulation from the total long-term accumulation (with seasonal variations factored out) gives the net natural long-term accumulation. the following plot shows the results for the Arctic.

Fig. 10. Estimated contributions to atmospheric CO2 concentrations in the Arctic.

Both anthropogenic and natural emissions have been rising, with anthropogenics rising faster than naturals. This relative rise rate is shown in the following plot.

Fig. 11. Relative contribution of anthropogenic emissions to the atmospheric accumulation of CO2 in the Arctic.

This plot indicates that lowering global anthropogenic emissions to 1990 levels would likely lower the accumulation in the Arctic by less than 5%.

To show that the Arctic is representative of the global distribution of atmospheric CO2, I similarly analyzed both the Mauna Loa and Antarctic (south of 60S) data. There are multiple data sets of CO2 and 13CO2 index for both locations.

The following plots compare the results with that obtained from the Arctic data.

Fig. 12. Global long-term rates of accumulation of CO2 for Mauna Loa and Antarctica compared with Arctic.

The trends are similar but the Arctic data is much more variable and the peaks appear to lag by a few months.

Fig. 13. Global long-term rate of change in the 13CO2 index for Mauna Loa and Antarctic compared with Arctic.

The same differences are observed in these results, but they are not as pronounced. Like the Arctic data, there is a strong relationship between the CO2 accumulation rate and the 13CO2 index for the Mauna Loa and Antarctic data. The latter should be a better global signature for atmospheric CO2 distribution and composition. I used the strong correlation ( R > 0.99 ) to calculate 13CO2 values back to 1957 (beginning of Scripps CO2 measurements). I then regressed the long-term CO2 values on anthropogenic emissions and an interaction term between anthropogenic emissions and the long-term rate of change in the 13CO2 values. The results are in the following table.

Table II. Results of regressing long-term CO2 accumulation rates at Mauna Loa and the Antarctic on anthropogenic emission rates and an interaction between anthropogenics and long-term rates of change in the 13CO2 index.

Comparing the results in Table II. with those in Table I. shows the correlation for Mauna Loa/Antarctic is better than for the Arctic. R is greater and the error terms are significantly less. The anthropogenic coefficient for Mauna Loa/Antarctic is less with less associated error, but well within the lower 95% confidence limit for the Arctic anthro coefficient. This coefficient is a better estimate of the fraction of anthropogenic emissions that is accumulating in the earth’s surface environment (water,soil, and biosphere). This coefficient was used to calculate the values for the following plot.

Fig. 14. Natural and anthropogenic emissions contributions to global long-term rates of accumulation of CO2 in the atmosphere. The natural contribution is the total long-term rate minus the anthropogenic emissions accumulation rate.

The natural component global signature looks like it was written by ENSO with matching variations and long-term change. I downloaded the NCDC v4 ERSST for the ENSO area (20S to 0 and 120E to 280E) from Climate Explorer, smoothed it with a 13 month running average, and regressing the long-term natural CO2 accumulation rates on these values and a cylical time function. The best fit is obtained with the CO2 accumulation rates lagging the SSTs by two months and a longer term lag associated with a 30.9 year wavelength cycle. The results are shown in the following plot.

Fig. 15. Relation between natural long-term CO2 accumulation rates and sea surface temperatures in the ENSO area (20S to 0 and 120E to 280E) cycles lagged.

The two months lag indicates temperature is controlling natural emissions of CO2 rather than CO2 concentrations controlling temperature. The mechanism is likely the processes of evaporation/condensation/absorption/convection/freezing that occurs in tropical thunderstorms. These clouds are pumping air containing water vapor and CO2 out their tops where the water freezes and releases CO2. Much of the cold water returns absorbed CO2 to the surface in rain. This cyclical process tends to fractionate the CO2 isotopes with more of the lighter isotopes going out the top. The concentration of the lighter fraction in the upper atmosphere should be a function of the number of cycles. By the time that upper atmospheric air reaches the Arctic, CO2 will have gone through many cycles, resulting in the highest concentrations of the lighter fraction. This effect is added to the biological fractionation effect that, also, is temperature dependant.

To place the relative contributions to global long-term accumulation of atmospheric CO2 in perspective, I used the rates to back calculate 95% confidence limits for both natural and anthropogenic components . The results are shown in the following two plots.

Figure 16. Global net accumulation of anthropogenic emissions and natural emissions of co2 in the atmosphere.

Figure 17. Global long-term relative anthropogenic emissions contribution to atmospheric CO2 accumulation.

Both natural and anthropogenic emissions have been increasing for over 50 years. Although anthropogenics represent a relatively small fraction of the total accumulation, that fraction has nearly tripled in the same time period. So what should we expect in the future and what effect would controlling anthropogenic emissions have on Global concentrations?

I did curve fitting on both the 95% limits of observed total long-term accumulation of CO2 and the estimated accumulation that is probably associated with anthropogenic emissions. I used a Fourier series type model for the total accumulation and an exponential model for anthropogenic emissions. The regression results for the total accumulation are given in tables III and IV.

Table III. Lower 95% limit for global long-term accumulation of atmospheric CO2.

Table IV. Upper 95% limit for global long-term accumulation of atmospheric CO2.

The anthropogenic emissions CO2 accumulation best fits:

Lower 95% Limit = exp(-42.851+.0231*t),and

Upper 95% Limit = exp(-42.486+0.023*t), where t is years.

Both fits have R squared values greater than 0.999.

These relationships can be used in “what if” calculations to project what we may probably expect in the future. For example, the following plot indicates that atmospheric concentrations will peak out around 450 ppm around 2060 if emission rates continued as trended.

Figure 18. Projected contributions of natural and anthropogenic emissions to the long-term global accumulation of CO2 in the atmosphere.

These should be rather good projections for areas around 15S latitude where seasonal variations are relatively insignificant. Seasonal variations at other latitudes are additive to these long-term projections.

I conclude that, the IPCC’s model assumptions that long-term natural net rate of accumulation is constant and anthropogenic emission rates are the only contributor to total long-term accumulation of atmospheric CO2, is false. It should be a simple matter for IPPC programmers to include these “what if” inputs in their models to see if they can produce more realistic projections. Also, they can enter lower anthropogenic emission rates to see how much (or how little) difference it makes in the value and time that atmospheric CO2 is expected to peak out. Economist could have a field day with cost/benefit modeling.

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