Climate Changes

                                                          Introduction

Complex models of atmospheric carbon dioxide concentration, that involve more than four or five parameters, are relatively useless in either hind-casting or predicting regardless of how well they may fit available data. So it is better to work with a model that only involves a few known critical physical parameters.

I propose dividing the earth’s surface into four zones; an emission zone and a sink zone in each hemisphere: and analyzing only the vertical flow in each. The net flow direction in the emission zones is up because the surface temperature is warmer than the air above it. In the sink zones the net flow direction is down because the surface is colder than the air above it

                                                                  The Model

The emission zones are mostly over water between 45S and 45N.  The sink zones are the remaining earths surface that includes the polar regions. The net vertical flow of CO2 in the emission zones is up, while it is down in the sink zones. Carbon dioxide in the atmosphere travels via jet streams from the upper atmosphere at emission zones to the upper atmosphere above the polar sink zones. The cold open waters nearer the poles are the ultimate sinks that are hardly ever a source. The Antarctic is mostly covered with snow and ice so it is not much of a source. The year round open waters that surround the land are an ultimate sink for CO2.

The emission zones are anywhere thunderstorms can form. Basically, energy from the sun evaporates surface water at near the atmospheric dew-point temperature. Evaporation is an endothermic process. Carbon dioxide is not only emitted via Henry’s law, but also because the evaporating water directly releases it into the atmosphere into which it evaporates.  Water vapor is lighter than air and rises dragging both air and CO2 with it. As it all rises, it gets less dense with fewer molecular collisions, thus, resulting in lower atmospheric temperatures. Each collision is transferring energy between molecules.  At the bottom of clouds, the air temperature approaches the dew-point temperature, and water vapor begins to condense. Condensation is an exothermic process that warms the air making it lighter so it rises faster. The warmed air drags water droplets and CO2 with it as it rises faster. The flow rate increases with elevation and can become fast enough to hold up golf ball size hail stones. While all this turbulent movement is occurring, cold rain-drops are absorbing CO2.  That rain delivers most of emitted CO2 back to the surface where it is available to be re-admitted.

However, a relatively small but significant fraction of CO2 goes out the top of thunderclouds to be transported by jet streams to polar sink zones.  The water that freezes releases its absorbed CO2, contributing to the fraction that eventually reaches a sink zone. Water, ice,and CO2   in the top of clouds radiates IR   upward to space. The clouds below absorb their downward IR to then be radiated to space. Air is relatively transparent to IR so it retains much of the energy it has gained from collisions with water vapor and CO2 molecules, while it travels to a sink zone.  That energy transfer mechanism with collisions is reduced in the upper atmosphere where density is lower.

At the sink zones, the surface receives little to no energy from the sun and it continually radiates to space. The day/night day is a year long. The surface is cooler than the air above it and cools the air. The air sinks and warms with more collisions to then be cooled by the radiating surface.

                                                      Testing the Model

Scripps has been measuring atmospheric CO2 concentrations in the Pacific since 1957. These data are published on their website; Sampling Station Records. They recorded data from ten sites ranging from South Pole at 90S to Alert, Canada at 82.3N. NOAA started measuring CO2 concentrations in the seventies and publish the results on their website, Four of their measuring sites are located at four Scripp’s sites; South Pole, Samoa, Mauna Loa, and Point Barrow. They consider these as “baseline” sites and also record meteorological changes. Other sources of relevant data are available at  WDCGG (World Data Centre for Greenhous Gases), Climate Explorer: Starting point, and ESRL : PSD : Monthly Mean Time series

Atmospheric concentrations of CO2 consist of both natural and anthropogenic emissions. Most anthropogenic emissions result from burning fossil fuels. Natural emissions result primarily from warming and evaporation of water both from oceans and land. Included in natural emissions are breathing of animals, forest fires. and decaying of biological materials. There are many more sources of natural emissions than there are for anthropogenic emissions and natural emission rates are much greater than emission rates resulting from burning fossil fuels.

Both natural and fossil fuel burning emission rates are changing with time. We have estimates of fossil fuel burning rates and we have been monitoring atmospheric concentrations of CO2 for several years. These data can be used to give us a better estimate of how the ratio of natural to fossil fuel burning emission rates change with time.

The two regions on earth that are consistently sinks for atmospheric CO2 are those regions north of 45 degrees North and south of 45 degrees South (Arctic and Antarctic). While the air is flowing downward from the upper atmosphere in all of the area, it is only being absorbed by the cold, open waters that are not covered with ice. The evidence for this fact is demonstrated by comparing the seasonal changes in atmospheric concentrations of CO2 with seasonal changes in sea-ice concentrations.

First, separate annual variations from year-to-year changes. The atmospheric concentrations of CO2 at measuring sites in each polar sink zone uniformly change with time. This uniformity is the result of the air being well mixed over the whole regions. This fact is graphically illustrated in Figure 1 by the very close agreement within six sets of data reported by two organizations from four different latitudes. The reported ppm concentrations   have been converted to kg/m^2 at sea level by multiplying by 44/28.8/1000000*1013*10.197. This is the estimated amount of CO2 in a square meter vertical column.

Sea-ice concentration north of the Arctic circle (66.5N) is shown in Figure 2.

                    Figure 2. Sea-ice concentrations in the Arctic north of 66.5N.

            The obvious difference between Figures 1 and 2 is the non-linear  long-term increase in CO2 concentration. Since the sink rate from the regions atmosphere is being controlled by the fraction of open sea water which varies within a year, the observed long-term change represents the input at the top of the Arctic regions atmosphere. A thirteen month running average of the atmospheric concentration represents these values.The input at TOA  Arctic is what is being delivered from the output at TOA of emission zones. Scripps reported  seasonally adjusted monthly averages in column 10 are statistically the same as the 13 month running averages and they have calculated these values for multiple sites in both emission and sink zones. Figure 3. shows  how well the values in two poles apart sink zones agree with values in the emission zones based on 13 month running averages.

            So  subtracting the column 10 value from the column 9 value of the Point Barrow Scripps data separates out the within-year variation for that site. The results of a simple regression of these results on the sea-ice concentrations is presented in Table 1.

                                              REGRESSION RESULTS

          Constant                                                                               -0.3239

          Standard Error of Y coefficient                                               0.0304

          R Squared                                                                            0.8980

          Number of Observations                                                              485

          Degrees of Freedom                                                                  484

          Coefficient for Sea-ice concentration                                      0.5159

          Standard Error of Coefficient                                                 0.0072

           f Statistic                                                                                   4170

Table 1. Simple regression of within year variation on sea-ice concentration north of Arctic Circle north of 66.5N.

          The line in Figure 3 may be considered a “global  signature” for natural emissions rates. . The slopes are not emission rates because  the values are year-long averages of monthly emission rates. The year-to-year differences are more like a second derivative with time (kg/m^2/year^2). Further evidence for this is that in the emission zones the rates are positive(up) while in the sink zones they are negative(down). When the slopes in Figure 3 are equal to zero the average of rates up in the emission zones are equal to the averages of rates down in the sink zones. These rates can be compared to estimated global emissions of CO2 from burning of fossil fuels as shown in Figure 4.

          The blue line is the reported values of annual global anthropological emissions divided by the surface of the earth in square meters. This is like assuming they are instantly distributed uniformly across the globe without any of the many sinks acting on the amount in the atmosphere. The values in Figure 3 are two orders of magnitude greater than the values in Figure 4. Considering all the sinks (mostly cold rain) that are absorbing anthropological emissions. it is practically impossible for these relatively small amounts to be contributing to atmospheric concentrations of CO2.

                                                  CONCLUSIONS

          1. The sink rate in the polar regions is being controlled by the amount of area of cold ocean water that is not covered by ice. In the Arctic winter, most of the ocean is covered by ice and CO2 concentrations  rise until the ice begins to melt. As the ice melts, the concentrations decrease reaching an annual minimum in September. There is no year-to-year accumulation. In the Antarctic, cold waters surround the land and freezing ice covers a much smaller fraction of the surface in the Antarctic winter so there is less CO2 concentration buildup each year.

          2.Comparing Figures 3 and 4 is very strong evidence that it is practically impossible for burning of fossil fuels to be adding any significant amount to the global atmospheric concentration of CO2. Carbon dioxide levels will continue to rise as more ocean water is evaporated and more CO2 is released to TOA . Stopping all fossil fuel burning will not have an effect on this process.

          3.  Nature has a very effective “net zero” in cold rain and cold polar open waters. There is no year-to-year atmospheric accumulation of either natural or anthropological emissions.            .

Introduction

The quantity of natural emissions of CO2 into the atmosphere as used in existing models is no better than an educated guess. It is mistakenly assumed to be balanced out by natural sinks to show that burning fossil fuel emissions accumulate in the atmosphere. Thus, natural emissions are not included in the material balance used in the models. The reported residence times  or e-folds are actually fudge factors that allow model material balances to approximate observations.
Most of the natural flow of CO2 is from tropical and mid-latitude ocean sources to polar ocean sinks. Thus, material balances on these zones should give us better estimates of natural fluxes of CO2 in the atmosphere. The two main sink zones are 1, north of 45 degrees North and 2, south of 45 degrees South. The  source zones are  between 45 degrees South and 45 degrees North. The source zones are where the net vertical flux of air, moisture, and CO2 is up as a result of thunderstorms . The sink zones have vertical flows that are down because of  a perpetual inversion ( the surface is colder than the air above it).

Vertical Flux in the Arctic Zone

The Main sink area in the Arctic zone (north of 45 degrees) is the open water of the Arctic ocean. In summer, when the sea ice melts, phytoplankton blooms enhance the cold water’s absorption ability. Most of the Arctic ocean is north of 70 North. When that area is mostly covered with sea ice, the main sink is effectively stoppered. Sea ice is not a sink.
CO2 is being delivered from the tropical source zone to the Arctic via upper atmosphere jet streams, The polar vortex winds keep the concentration well mixed over the Arctic zone. In this zone, an inversion exist most of the time so that the vertical flux is from the upper atmosphere to the surface. When it reaches the surface of the ice, it travels South until it reaches open water where it is readily absorbed.

The rate of change in concentration is an indicator of the CO2 flux. Time series concentration data are published at three websites. World Data Center for Greenhouse Gases (WDCGG), ESRL Global Monitoring Division, and Sampling Station Records | Scripps CO2 Program, Most of these data are recorded as monthly averages that do not include high values that are either errors or from local sources. Figure 1 shows how well the data from fifteen sites north of 45 degrees agree. Figure 1. CO2 data from fifteen sites north of 45 degrees.
Converting these ppm data to kilograms per square meter at one atmosphere gives us the results in Figure 2.

Figure 2. Arctic concentration data expressed as mass in a vertical column.

Also, a heavy carbon depletion index was measured at these sites. These data were treated similarly with the results in Figure 3.

Figure 3. Average of monthly values of 15 sets of heavy carbon depletion indexes

From after 1982 (when the index was first measured) Figure 3. is a mirror image of Figure 2. because they are mathematically and physically related. The C13/C12 ratio is an indexed fraction of the measured total. It is indexed to the actual ratio of inorganic source carbon which is given a value of zero. A mathematical expression of this relationship that can be used to estimate the relative mass fractions of organic and inorganic source carbon dioxides is:

(Total Mass)*(Measured Index) = (Organic Mass)*(Organic Index)

because the (Inorganic Mass) in the (Total Mass) is multiplied by the indexed value of zero. In the Arctic, all the values in this equation change seasonally and from year to year. The seasonal changes are directly related to the changes in the concentration of ice  covering the Arctic sink. Expressed mathematically:

Equation 1. TM*MI=a+b*Ice*TM+c*TM

where TM= Total Mass, MI= Measured Index, Ice = ice concentration North of 70 degrees, and a, b, and c are regression constants.

The indexed value of the organic source fraction at any one point in time is calculated as Ice*b + c. The results are presented as Figure 4.

Figure 4. Average index value for organic source CO2 in the Arctic.

The values are within a relatively narrow range between -13.6 (least depleted) and -14.2 (most depleted). The most depletion occurs when the ice concentration is at a maximum for each year and the least depletion occurs when there is the least ice concentration each year. The fact that the values vary with sink rate indicates that the atmospheric CO2 is being fractionated  as it is being delivered to the Arctic. The physical process is a combination of evaporation/condensation of water and absorbtion/extraction of CO2 in cloud water. The heavy isotope has a slightly lower vapor pressure than the lighter isotope so the concentration of the lighter isotope increases slightly in the atmosphere with each evaporation/condensation cycle of water in thunder storms. There are many of these cycles between the tropical source and the Arctic sink. The evidence of this behavior is observed when calculating the regression coefficients in equation 1 for different sets of data at different latitudes. The following table shows how significant this effect is on the b coefficient.

By contrast, the c regression coefficient does not vary significantly with latitude and thus, is the best estimate of the index value for the organic source CO2 being naturally released from the water wherever thunder storms are formed. The weighted average indexed value in the northern hemisphere is -13.301 with two standard deviations of only 0.053.

Knowing the indexed values, we can calculate the amounts of the organic and inorganic fractions and how they change with time. This is shown in Figure 5.

The organic fraction changes rather rapidly with each freeze/thaw cycle but also increases from year to year at varying rates. The inorganic fraction remains rather constant. The annual cycle is the results of natural processes but the year to year increases could be assumed to be from increases in anthropogenic emissions. The natural emission rate changes can be estimated from the changes in the slopes of the curves (rate of change in concentration, delta c/delta t). The true rate  is dc/dt which can only be approximated with monthly average data. However, these data can be used to separate seasonal effects from year to year effects on flow rates. The seasonal effects are revealed with a two-month running difference. The year to year effects show up in a thirteen-month running difference.  These quantities are show in Figure 6.

The two-month difference is much greater than the year-to-year difference. It is caused by the natural process of freezing and thawing of the Arctic sea ice. Most of it balances out each year. However, there is a small year-to-year difference that is not balanced out. this is shown in Figure 7.

This figure most likely shows the rate of input of the organic CO2 into the upper atmosphere of the Arctic from tropical source waters. Analysis of similar data from NOAA’s four base-line observatories ( Pt. Barrow, Mauna Loa, Samoa, and South pole) reveal that this is a global observation. Figure 8. shows the results of this analysis.

Published global anthropogenic emission rates were converted to units of kg/m^2/year by dividing by the area of the earth. This essentially assumes that these emissions are immediately put in the stratosphere and uniformly distributed over the surface of the earth (extremely unlikely or impossible). These emissions are effected by the same processes as natural emissions (absorbed in clouds and returned to the surface in rain). The best estimate of this effect is the average of two standard deviations on the calculated average of natural emissions.  This value was calculated to be 0.057 kg/m^2/year and was subtracted from the unaffected anthropogenic emissions. These results are compared with natural emission rates of organic CO2 if Figure 9.

This figure graphically illustrates where the spurious correlation used as a mass balance by the IPCC was derived. It shows that natural emissions have been rising faster than sink rates over the long term at about the same rate as anthropogenic emissions. The IPPC assumes that net natural emissions over sink rates have not been rising. Over this period, the calculated average unaffected anthropogenic emission rate is more than twice the average net natural emission rate and that difference is assumed to be  accumulating in the atmosphere. The calculated average affected anthropogenic emission rate is less than zero which means there is no accumulation of either natural or anthropogenic CO2 from year to year.

The rise in the net natural flow rate from the tropics is associated with temperature changes primarily in the tropical pacific. Time series changes in meteorological data for different regions can be obtained at ESRL : PSD : Monthly Mean . The primary  source region selected is -22.5 to 22.5 latitude and 150 to 270 East longitude.  Tabulated  monthly average values for air temperature, SST, relative humidity, pressure, rain rate, precipitable water, and OLR are presented for years 1948 to present. Values from 1980 to the present were analyzed with multiple linear regression techniques to determine significant effects on the concentration and rate of change in concentration of organic source CO2. The CO2 data best fits a regression on dew point temperature (derived from air temperature and relative humidity) and the annual rate of change of precipitable water (running 13 months difference). The statistical significance is shown in the following table.

The b coefficient is for dew point temperature which is the temperature at which the surface of the ocean water evaporates and where it condenses at the bottom of clouds. The c coefficient is for the rate of change in precipitable water in a vertical square meter column. That rate of change is on the difference  between the evaporation rate and the condensation rate from year to year. These results are graphically illustrated in Figure 10.

The timing of the peaks in emissions in Figure 10. is evidence that natural emissions  of organic CO2 are related to ENSO changes in temperature that are controlling the evaporation and condensation of water. Those processes in clouds and thunderstorms are controlling the natural emissions of CO2 out of their tops.  Anthropogenic emissions are not affecting these changes.

The IPPC claims that the increasingly negative value of the index is the “smoking gun” that proves the negative effects. However, the data strongly indicates that  the negative increase is because the natural emissions  of organic source CO2 has been steadily increasing with a narrow index range around -13. The index values for anthropogenic emissions range from about -25 for solids such as coal to about -40 for natural gas.  If these emissions where contributing significantly to the average calculated organic source fraction, the value would be becoming more negative.  The data indicates, that in the Arctic, the index values have become slightly more positive rather than more negative.

This analysis indicates that the rising temperatures in the surface waters of the oceans have been increasing biological activity. This activity starts with phytoplankton blooms that are at the bottom of the food chain and ends in the large animals and fishes. This is a good thing because it means more food for a growing human population.

    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.

Revised 2/22/15.

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.

Welcome to my blog on climate change. I have been analyzing climate data for several years trying to determine how much the burning of fossil fuel contributes to observed environmental changes that we call climate. I will post the results of my analysis and hope that those of you that are qualified to do a “peer review” will point out any errors I may have made, and suggest improvements. You are welcome to replicate or improve on the techniques I use applying them to any  available data and submit it for publication. I stopped writing for publication over 20 years ago when I retired.