Quantifying the Anthropogenic Contribution to the Global Background Level of Atmospheric CO2

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.

arctic co2

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.

 net arctic co2 accumulation

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

LT net Acc Rate co2

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.

long and short 13co2

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

lt rate of 12 co2 change

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.

organic and inorganic contributionsFig. 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.lt regress 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.

LT Anthro contribution

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.Anthro Accumulation

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.

relative contribution

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.

long-term global co2 roa

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.

LT 13CO2 roc

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.

regression 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.Global Nat and anthro rates

 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.SST relation

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.

net acc

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.

lower acc regression

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

upper 85% acc

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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121 Responses to Quantifying the Anthropogenic Contribution to the Global Background Level of Atmospheric CO2

  1. Brian H says:

    Now cross-correlate with ag productivity.

  2. Dear Fred,

    The basic problem with your calculation is a much common problem encountered when discussing the human contribution to the recent increase in the atmosphere.

    You are completely right that the fraction of human incuded CO2 is small compared to the total CO2 in the atmosphere, but still near 100% of the increase is caused by the human emissions…

    To explain that: the residence time you have calculated only shows how fast a molecule CO2 (whatever its origin) in the atmosphere is exchanged with a molecule of CO2 from one of the other reservoirs (oceans, vegetation,…). These exchanges are huge (about 150 GtC on total 800 GtC currently in the atmosphere), but that doesn’t change the total amount of the CO2 in the atmosphere. That only dilutes the fraction of human CO2, as much goes into the deep oceans at one side and human-free CO2 comes out at the other side, for the next hundreds of years.

    How much that dilutes, depends mainly of the total exchange flow between the deep oceans and the atmosphere, which can be calculated from the difference between what can be expected if all human CO2 still was in the atmosphere and what is observed. That gives an exchange flux of ~40 GtC/year:

    Where the difference in the early years probably is from vegetation, which is thought to have been a net source until ~1990.

    Thus the 13C/12C ratio simply is diluted by a natural throughput, but that says next to nothing about what the cause is of the increase, neither how fast any extra injection of CO2 into the atmosphere (whatever the source) is removed out of the atmosphere.

    The latter is much slower, as at the current 210 GtC (100 ppmv) increase above equilibrium, only 4 GtC is removed each year. That gives an “adjustment” e-fold time of about 53 years. Or a half life time of ~40 years. Quite a difference with the residence time…

    Humans emitted some 370 GtC since the start of the industrial revolution. The observed increase in the atmosphere is about 210 GtC (for 100 ppmv increase). That alone is sufficient as proof that human are responsible for the whole increase, but let’s give an example of the difference between the residence time and the adjustment time and the responding fate of human CO2 in the atmosphere: If we should have injected all human emissions since 1850 in the first year, how long does it take to get the fraction of human CO2 to near zero and how long would it take to reduce the extra CO2 back to equilibrium:

    Where FA is the fraction of human CO2 in the atmosphere, FL in the oceans surface, tCA total carbon in the atmosphere and nCA total natural carbon in the atmosphere.
    As you can see, after 50-60 years virtually no “human” carbon is left in the atmosphere, while still a lot of extra CO2 is over the old equilibrium. That extra still is 100% caused by the injection of human CO2, even if all human molecules are exchanged by natural CO2 molecules…

    Thus while your analyses of the fraction of human CO2 in the atmosphere is right, that doesn’t prove that humans aren’t the cause of the increase…

    • fhhaynie says:

      We agree that natural emission and sink rates are about 20 times greater than anthropogenic emissions and, that as the accumulation rises, the sink rate will increase. Where we disagree is I include a probability of a natural rise in emissions along with the rise in anthropogenic emissions while you only consider the anthropogenics in your mass balance. From historic proxie data we know that natural net accumulation rates have been changing along with changes in energy accumulation rates. There is no reason to expect that they are not continuing to change. If the natural net accumlation rate only changed by 5%, that change would be about equal to the anthropogenic rate. Try this exercise. Do your mass balance on Arctic CO2 data where the annual change in accumulation rate is the greatest. The accumulation rate is the slope of the CO2/time curve at a particular time. The Arctic Ocean is a big sink during the summer but the sink is stoppered with ice in the winter. There is a strong correlation between area of exposed ocean and net accumulation rate. Compare that with the Antarctic that is essentially neither source nor sink(the sink is the ocean around it that is not stoppered but shifted to the north as the ice freezes).

      • Dear Fred,

        I did consider all possibilities of natural and human releases:
        – if the increase in the atmosphere is larger than the human emissions, then both natural and human releases add to the increase in the atmosphere.
        – if the increase in the atmosphere is less that the human emissions, then the human emissions are the sole cause of the increase.
        – there is a decrease, then the natural sinks are larger than the natural sources + the human emissions.

        The problem is that you can’t have ánd a net increase in CO2 caused by natural flows ánd by the human emissions, as long as the net increase is less than the human emissions. In such case, the natural cycles show a deficit: more goes into sinks than is released by natural sources. Already 50 years long:

        If for some reason one or more natural inflows increased with an amount, even more than the contribution of the human emissions, that múst be compensated by an increase from a sink which removes the additional inflows, as long as the increase at the end of the year is less than the emissions. Thus all what happens is more circulation of the natural flows through the atmosphere causing a shorter residence time, but still no substantial contribution from natural flows to the total CO2 level in the atmosphere…

        The Arctic Ocean is a huge sink for CO2 in summer, but the mid-latitudes take over during winter, up to near the ice sheet border. See:
        CO2 levels are lowest in (especially NH) summer, but as the 13C/12C ratio shows, that is mostly due to growing new leaves in spring in the mid-latitudes…

        But that all doesn’t matter much, as that are seasonal changes, the trend is independent of the seasonal changes and follows the human emissions, not the ice sheet area (which is only decreasing in the past decades for the Arctic and growing in Antarctica):
        http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_2004.jpg and

      • fhhaynie says:

        Dear Ferdinand,

        Your statement – “if the increase in the atmosphere is less that the human emissions, then the human emissions are the sole cause of the increase.” is incorrect. the sink rate is proportional to the concentration which accumulates if the total emission rate (both natural and man made) is greater than the sink rate. To see how it works lets look at years 1963, 1985, and 2010.
        CO2ppm Accumulation rate Anthro emission rate sink rate natural emission rate Total emission rate
        1963 319 .65 .7 82.22 82.17 82.87
        1985 346 1 2 89.8 88.18 90.18
        2010 388 1.8 2.93 100 98 87 101.8

        Rates are ppm/year. The sink rate for 2010 is reasonably assumed to be around 100. The sink rates for the other two years are porportional. Note in order to maintain a mass balance, the natural emissions have been increasing. The 13CO2 index data indicate that about two-thirds of those natural emissions are from inorganic sources. Bart has been claiming that temperature changes account for all the accumulation which leaves no room in a mass balance for anthropogenics. That, also is incorrect.

      • Dear Fred,

        “Note in order to maintain a mass balance, the natural emissions have been increasing.”

        There is no need for that. To maintain a mass balance, it is sufficient that the natural sinks are increasing compared to the natural sources if the human emissions increase over the years, even if the bulk of the natural transfers remain the same.

        Take the oceans: temperature is the main driver of CO2 between the oceans and the atmosphere and back. An increase in CO2 ppmv in the atmosphere will reduce the pCO2 difference between the warm oceans in the Pacific equator and the atmosphere, thus reducing the transfer of CO2 from the oceans into the atmosphere. The opposite happens near the poles. Thus with increasing CO2 levels in the atmosphere, natural influxes are reduced and outfluxes increased. That makes that in every year since 1959 the sink rate increases, but in average only half of what humans emitted.

        There is no indication that the bulk of the carbon cycle has changed over the years. Temperature has its influence, mainly in year to year relative small changes in fluxes, but that largely levels off over the years.

      • fhhaynie says:

        Ferdinand, “There is no need for that” because your method of mass balance can not accept it. Again, thermodynamic only tells the direction of a process and not the rate. Year to year changes in temperature are not the driving force for fluxes, it is the within year temperature rate of change that is the driver. On land you can have a ten degree/day change. In the oceans it is slower but the surface water can warm more than 10 degrees as it crosses the equatorial pacific.

      • Dear Fred,

        There are several problems with your mass balance:

        – your sink/emission rates are calculated on the pCO2 difference in absolute values, that should be in ratio to the equilibrium value (~290 ppmv for the current temperature).
        – the local sink/release rates are quite different from the averages. For the warm Pacific, the pCO2 difference in 210 was 750 – 388 = 362 micoatm. In 1963 it was 750 – 319 = 431 microatm, if the seawater pCO2 remained the same. Thus an decrease of 83% instead of an increase. But the pCO2 of the warm oceans increased over time, thus the 750 microatm of 1963 might have been substantially lower (a DIC increase over time gives a higher pCO2). Nevertheless the output of the warm oceans decreased over time, together with the increase in the atmosphere.
        – the same, but opposite reasoning for the sink places. Where the uptake increased over time.

        Thus it is not that easy to calculate the change in sink/source rates. All we know for sure is the difference between these two: that is the difference between the anthro accumulation rate and the observed accumulation rate, minus what is absorbed by vegetation. The latter is currently around 0.6 ppmv/year.

        In summary, the difference between the sink/source flows over time are much smaller than you expect with decreasing inflows from and increasing outflows to the oceans.

      • fhhaynie says:

        Dear Ferdinand,

        Even the IPPC states that natural emission rates are about 20 times higher than anthropogenic rates, but they , like you, assume they change very little without the anthropogenic extra. Lets look at what is happening at the big sink (Arctic Ocean). I’ve looked at all the reported data at sites above 60 north. There are no significant differences between sites. They all share a common shape annual cycle that has the greatest amplitude. Combining all that data allowed me to calculate three month running averages and slopes with small error bars. The slopes in ppm/year are net accumulation rates. The difference between the maximum net accumulation rate and maximum net sink rate is around 100 ppm/year. Also noted was a slightly positive blip near zero when the Arctic is covered with ice. This rate is about what we observe in a year to year change. In the Arctic, the partial pressure of CO2 in the frigid water will be very low so any CO2 that reaches the surface will very likely be absorbed and during the spring melt will be consumed by those phytoplankton blooms.

      • “Thus an decrease of 83% instead of an increase.”

        Of course must be a decrease of 17%…

      • fhhaynie says:

        Dear Ferdinand,

        I thought you might wish to see these two plots.


      • Dear Fred,

        Thanks for the graphs…
        What they show is the up and downs over the seasons. Besides the amplitude (which seems much higher than I expected), the seasonal amplitudes are not of interest, only the net difference between uptake and release is of interest, and the evolution of the net difference over time.

        As you can deduce from that evolution, the sink rates seems to show more decrease than the source rates show increase, thus giving an increased net sink, but you better make a more accurate analyses with a 12-month running mean to remove the seasonal fluctuation. That will show you the real variability in sink rate of the Arctic, which in my opinion is smaller than you expect and certainly not in ratio to the change in absolute levels in the atmosphere, but in ratio to the local pCO2 difference over the same period…

      • fhhaynie says:


        The Arctic ocean, for all practical purposes, is never a source and always a sink. The area of that sink is decreased as ice forms. CO2 is still being delivered from the south in the upper atmosphere. In the winter as heat is radiated to space, there is an inversion (upper atmosphere warmer than the surface). Over ice, CO2 delivered to the surface is not absorbed and must be transported south to open water to be absorbed. All the while, the concentration in the upper atmosphere is decreasing because of a seasonal decrease in source emissions. At some point in time the net rate starts to decrease, well before the ice begins to melt. It continues to decrease until the concentrations being delivered to the upper atmosphere approaches the concentrations at the surface. Then a blip shows up in the curve that is about the same as the year to year rate of increase. This occurs when the ice is at its maximum. This is the area of the curve that interests you. So we have to somehow factor out the seasonal effect and then separate long-term natural effects from the anthro effects. First, we must get a handle on sink rate per unit area and its relation to concentration (flux). Subtract that from the net to get the combined source rate (what is being delivered from the upper atmosphere). It has to be greater than the sink rate because there is an annual accumulation. Then separate natural from anthropogenic. I don’t think your method of mass balance is able to do it. I can send you copies of my data spreadsheets if you want to try. There is no reason to assume that there is no natural year to year increase other than to make your model fit. I will be using my statistical methods with the above model.


    • bentabou says:

      “Anthropogenic emissions are not temperature dependent.” Really? In New England we burn a lot of oil in the winter and don’t need much air conditioning in the summer. Perhaps this cancels out globally, but our base level of CO2 would seem to need to vary seasonally to be accurate.

    • Coldish says:

      Dear Ferdinand, thank you for your calm and patient response to this old chestnut both here in 2012 and on Judith Curry’s site in 2015. I would have put this ‘thank you’ comment there, but am now excluded by Judith from commenting. I think her site could benefit from more of your contributions. Regards, Coldish.

      • Coldish,

        Some late reaction, I just added a few graphs here.
        It has been quite exhausting at Judith’s: over 2000 reactions in a few weeks…
        I was quite surprised by Judith’s comments, I thought she would see the main error in Fred’s reasoning: the often repeated confusion between residence time of an individual CO2 molecule (whatever the origin) and the time needed to reduce an extra shot of CO2 (whatever the source) back to equilibrium…

  3. fhhaynie says:

    By the way, you should notice that the Scripps data I used in the above original post had the seasonal variations factored out and is not limited to the Arctic and includes sources. I’m now using the Arctic because it is a simpler system and I hope to show you how a mass balance should work. As an engineer, you should be familiar with input/output flow models.

    • Fred,

      Some misunderstanding here, the graph you have send titled “Net accumulation rate of atmospheric CO2” was interpreted by me as the seasonal swings in the Arctic. But it gives a 21 point (months?) running average of the data? Makes not much sense to me, as you need to make a 12-month running average to know the net change in sink rate over time, which is what we are interested in…

      • fhhaynie says:

        I wasn’t trying to factor out the seasonal change with the 21 point running average and slope. The 21 points on monthly data from eleven stations gives me an average slope for between a two and three months time period. Fewer points for shorter periods produces greater error, while more points for longer periods tends to factor out the actual rates that I am trying to determine. What you are seeing are best estimates of slopes and not running averages of concentrations. I did calculate those as well and will be using them in my statistical analysis.

      • Fred,

        I am a little lost what the purpose is of your excersize…

        What the IPCC says and I think is right: there are lots of fluxes between the atmosphere and other reservoirs. These are huge, but in pre-industrial times, they were in a dynamic equilibrium. That equilibrium changes with temperature at about 4 ppmv/°C for short term temperature changes to 8 ppmv/°C for very long term changes.

        Thus the net result of a fixed temperature over millenia is a fixed CO2 level.

        Today we see a trend, of about 100 ppmv, slightly exponential, over the past 160 years. The variablity caused by temperature variability again is ~4 ppmv/°C around the trend. The trend itself is near 100% caused by the slightly exponential 210 ppmv human emissions over the same time span. A small contribution of a few ppmv comes from the increase in temperature of the oceans.

        So what is according to you the source of the increase and where does the human CO2 go?

      • Greg Goodman says:


        you may want to look at the artefacts and distortions introduced by running means.

        There’s a number of alternatives suggested ( with code ) that are a lot better.

        Triple running mean is easy to do but like gaussian does start to attenuate quite early. The best if you want to preserve longer period information is the lanczos filter. It has a flat part with no attenuation then a fairly quick transition band. For example you cut just about all 1y and less whilst preserving >2y with nearly not attenuation.

        Just try to avoid running means , they are a mess.

  4. ericgrimsrud says:

    Immediately upon reading your analysis of C isotopes, I had the same thought as expressed by Ferndinand. The C atom in a given CO2 molecule exists for only what, just a few years, before it is taking into a plant and then is spit our again as atmospheric CO2. Thus, the C isotope signature of atmospheric C quickly resembles that of all biolocial carbon. Yet, the excess C in the atmosphere (and the entire biological C cycle) caused by the addition of fossil fuel carbon to the biological C cycle persists for many centuries – until that excess C in the biological cycle is returned to the geological world (CaCO3 or coal, for example) and that takes a very long time.

    Since you and Ferdinand have extensively covered that ground, I will not add more here.

    But, if CO2 and the GHE are not major drivers of climate change, you must also account for the more distant past. Why, for example, was the world so hot about 50 Myrs ago and why was it in a snowball condition some 500 Myrs ago? Without the GH and albedo affects what do you have left to explain such extreme conditions ?

    Sincerely, Eric Grimsrud

    • fhhaynie says:

      Do you understand how Ferdinand has done his mass balance? Do you understand how I have done it? Your reply tends to indicate that you don’t. There are many natural cycles of varying length that Ferdinand’s method does not consider.He assumes that these natural cycles are too slow to be significant and adjusts his data to balance by saying the ocean is a net sink. If it were a net sink, there would be no accumulation. My method identifies some of the shorter length cycles that are statistically significant. The ice core data shows the longer wavelenth cycles very well but the time resolution is not good enough to show cycles with wavelengths less than about 500 years. There are several relatively short biological fractionation processes that could be causing the delay in the anthropogenic signal showing up in the atmosphere. One is the selective uptake by trees, and added decay of leaves several years later. The one I suspect is the uptake by phytoplakton in the Arctic with decay in the surface current that delivers it to the equator where it is readmitted to the atmosphere. Also,my method will do a better job of hind casting than will Ferdinand’s. His would project a constant low level of atmospheric CO2 prior to the industrial revolution.

      Note: Gavin Cawley (computer expert at UEA), recently published an article on the anthropogenic contribution based on Ferdinand’s method. I had a long e-mail conversation with him and he applies the same circular reasoning that Ferdinand does to come to the conclusion that all the accumulation is caused by burning of fossil fuel. I suggested he consult a chemical engineer about how to do a mass balance in a heterogenous flow system. He then mentioned Ferdinand. I suspect his paper will be cited in the next IPPC report.

  5. Crispin in Waterloo says:

    Greetings Gentlemen

    It was not the purpose of my visit here to discuss the sinks and sources however it is related to all the above. I came to discuss the annual cycle of CO2 in the Arctic taking into consideration the role played by water that annually freezes and melts. Perhaps this should be removed to a new thread however it is directly related to some of the issues above and I am flexible.

    Fred, I agree with some of your approach and I see what you mean when you describe the adjustments made because of what you described as circular reasoning. An element I felt was not fully described is the treatment of the oceans as a quantifiable sink. The ocean surfaces are treated as the border of some infinite ‘thing’. I was taken aback by the mention of a historic ‘equilibrium’ in the CO2 concentration. Given the size of the ocean sink and length of time in an overturning cycle i doubt that we know if or when an equilibrium condition had ever existed.

    I would draw the system thus: the atmosphere would be one sink, the oceans another, and the sources dotted around the system each with their mineral or parasitic larders attached. I don’t need to go beyond cartoon that to make my point: one of the elements in the system – the oceans – is gigantic with respect to the rest and is poorly characterised with respect to its regional CO2 content and temperature.

    The cycling of CO2 into and out of water and ice does not seem to be considered when examining the annual fluctuation in the Arctic. Why?

    I have invited another man from Waterloo, a practising hydrogeologist, to join us. Last night during the Super Bowl (which shows you how seriously we take the matter) we tried to put some numbers together to see if this was a subject worth pursuing and decided it was significant and therefore interesting.

    Simply put, at about 390 ppm(v) CO2 enters meltwater to a level of about 1128 g/ton and leaves (almost entirely) when that water is refrozen. The level absorbed is governed by the Henry Equation. None of this is news and should not need demonstration. The pH can be predicted from this law and if the Arctic ocean absorbs CO2 or does not depending on ice cover, the pH fluctuation would easily confirm it.

    The total mass of water involved in water/ice cycle in a NH winter (to which I would like to restrict my discussion) is quite large, involving all ground water that freezes (south to approx 40° N), all accumulated snow, lake and river ice, sea ice, muskeg, tundra and atmospheric ice/water (non-vapour) mass. Melting permafrost (if significant) constitutes a new and rapidly acting sink in summer. Glacial accumulation or melting is covered in the snow accumulation and melting.

    Snow and ice sublimation vapour are still counted as ‘ice’ until the vapour can condense above the freezing point which can take quite some time (whereupon it absorbs CO2). The net flow of water droplets into the Arctic would carry accumulated CO2 that is released locally when those droplets freeze. The latitude at which this takes place moves south as the winter progresses, then moves north again, annually.

    Our quest is to see how much of the annual variation in CO2 in the Arctic is caused by this water/ice cycle.

    • fhhaynie says:

      I agree that melt water will be a sink, but the outgassing of that melt water when it refreezes is small in comparison to the amount of CO2 that is being delivered to the Arctic from the South. Something else to consider is that the sea ice freezes from the top down so that any significant outgassing would immediatly be absorbed by the frigid sea water below the ice. I would like to restrict our mass balance to just the 18 million km^2 of ocean area (Arctic Ocean plus marginal seas). That way we don’t have to know the amount and rate of melting and freezing in other areas. Presently, I am working on the Arctic data and hope to present the results in a new post. Until then, we can continue to use this post to converse on the subject. The freezing and thawing of the Arctic sea ice certainly is an important factor in the annual fluctuations of CO2 and I think we have enough data to be able to quantify the effect.

  6. Crispin in Waterloo says:


    >I agree that melt water will be a sink, but the outgassing of that melt water when it refreezes is small in comparison to the amount of CO2 that is being delivered to the Arctic from the South.

    I know there are several assumptions about it but have not seen it quantified. It is also quite a bit less than the total emerging and sinking into the hydrosphere. It is the annual fluctuation that I am investigating – 6 ppm. The claims made for why it varies so much do not take into account the main source and sink which may be the ice/water cycle.

    >Something else to consider is that the sea ice freezes from the top down so that any significant outgassing would immediatly be absorbed by the frigid sea water below the ice. I would like to restrict our mass balance to just the 18 million km^2 of ocean area (Arctic Ocean plus marginal seas).

    This is freqiently cited as a reason it is not interesting nor large in quantity. However the nature of sea ice freezing is not at all like a freezing puddle of water and there is a large number of unknowns. If once frozen solid, and absent of cracks, the pH were to change significantly, that would be proof or partial proof that the sea water was absorbing additional CO2 from the ice as it continued to freeze. The assumption that ‘cold water sinks’ is untenable and I am not sure why it appears to have been accepted as a route away from the ice. If it were, then that CO2 would not re-emerge in the spring. The water is far from saturated so if it did sink, the ‘new water’ seen in spring would not be ‘outgassing’ CO2 in appreciable quantities. and it would only absorb what it normally absorbs at that temperature. The equations, you could say, are unbalanced and do not fit the narrative..

    >That way we don’t have to know the amount and rate of melting and freezing in other areas.

    Well, my point is that we always need to know the melting and freezing of the other areas if the far exceed the numbers in the areas we have imagined we know the numbers.

    >…The freezing and thawing of the Arctic sea ice certainly is an important factor in the annual fluctuations of CO2 and I think we have enough data to be able to quantify the effect.

    That is quite possible however it is only part of the answer. Suppose the ‘capped sea’ idea is completely correct. That means the rise in CO2 in the Arctic winter has only a small contribution from teh ocean. But the rise is 6ppm, a massive amount of CO2. We know the chemistry of ice and water and CO2. There are huge areas of snow and ice freezing across the NH in winter, and all that mass of freezing water/melting water changes the amount of CO2 in the atmosphere. Once the sea ice contribution is known there remains the question as to the contribution of the rest of the hydrosphere.

    The import of the investigation is what happens when Greenland (or any other large ice field) melts. By demonstrating the effect of the water/ice cycle we can predict with some accuracy the effect on atmospheric CO2 resulting from the (accumulating) permanent melting of existing ice fields. The effect is quite large. Where Greenland to melt, the absorption of CO2 would be on the order of 3.5·10^6 km^3 x .00128 = 4500 gigatons of CO2 causing plant growth chaos all over the world.

    Whether that effect will be seen can be deduced by analysing the water/ice cycle as it already exists. For example if 50% of the 6ppm fluctuation is caused by the cycle, it merits inclusion in all modelling exercises. So far I am convinced the accumulation of sea-raising meltwater is not modelled for CO2 absorption.

  7. fhhaynie says:

    >…The freezing and thawing of the Arctic sea ice certainly is an important factor in the annual fluctuations of CO2 and I think we have enough data to be able to quantify the effect.

    “That is quite possible however it is only part of the answer. Suppose the ‘capped sea’ idea is completely correct. That means the rise in CO2 in the Arctic winter has only a small contribution from teh ocean. But the rise is 6ppm, a massive amount of CO2. We know the chemistry of ice and water and CO2. There are huge areas of snow and ice freezing across the NH in winter, and all that mass of freezing water/melting water changes the amount of CO2 in the atmosphere. Once the sea ice contribution is known there remains the question as to the contribution of the rest of the hydrosphere.”

    That 6ppm rise is the result of closing the valve on the sink while CO2 is still being pumped into the Arctic from the South. The input rate can remain the same while the output rate (sink) is decreasing so that you have an increasing accumulation. Equilibrium is not involved in the Arctic. The input and output rates are much greater than the accumulation rate (positive or negative).

    Carbonic acid is a weak acid and creates a pH of around five in “clean rain” at atmospheric partial pressures. Sea water is loaded with basic ions (Ca, Mg, Na, etc) and has a pH of around eight. You may be able to observe a lowering of pH in relatively clean melt pools on glaciers, but I doubt that you will be able to see it in sea water or in soils.
    Have you been able to estimate the amount of “clean” melt water that is generated in a years time?

    The reason that sea water sinks in the Artic is because freezing on the surface concentrates the salts below the ice not that the ice cools it. The density change from concentration is much greater than a temperature density change.

  8. fhhaynie says:

    The annual melts should be about the same magnitude as annual precipitation.

  9. Crispin in Waterloo says:

    If a bog freezes each year, does all the water in it have to be replaced each year? I agree that all (virtually all) precipitation will be frozen and melt in Spring. That precipitation falls on wet ground. Really wet, in many places. I am pretty sure the volume of water in the bogs of Siberia is not replaced each year by precipitation but I am open to convincing.

    I was looking at the sea ice are tonight at http://ocean.dmi.dk/arctic/plots/icecover/icecover_current.png and there is a 2.5 m sq km difference between the 15% and 30% ice coverage. I think the idea that the sea ice caps the whole ocean needs a re-think. Certain some of it is capped, but how much? And if the coverage is only 75% ice cover does it still breath CO2 into the atmosphere as effectively as when it is 15% covered? Probably This seems to be a big gap in the proposal that the sea is basically sealed by ice. It is early February and there is still many millions of sq km that is not sealed at all.Every splash of a wave that goes over the top of a piece of ice and freezes in the sub-zero air gives its CO2 directly to the atmosphere – no cold sinking brine involved there. We need some real numbers on this. Did the CO2 rise at Point Barrow as the icea was starting to cover the oceanside, or immediately afterwards when a south wind blew in stores of CO2 from the South? That is a testable question. We already know that it drops rapidly when the ice melts in spring.

  10. fhhaynie says:

    Think about a melt pool on a Greenland glacier. It will be at zero degrees and is relatively pure. However, it is not very deep. The ice core data from Greenland can be dated by counting the melt rings. The snow that accumulates in the winter is not all melted each summer, only the top surface. When it refreezes, it traps the air in the uncompacted snow below it. That gas will diffuse through cracks until gravity compacts it at about 100 meters depth. Above 100 meters, the concentration of CO2 in the trapped air is close to a multi-decade average of the concentration in air above it. That is why I say that the annual melt should be around the same order of magnitude as precipitation rate (snow accumulation rate).
    Tundra is even more complicated to quantify. How deep is the permafrost? How much absorbed CO2 ends up trapped as methane clathrates? The quantity of outgassing when it refreezes will be very difficult to obtain.
    Let’s work on the less complicated ocean system where we actually have data.

    I am working with the reported ice area, not the extent. It is less affected by winds and better quantifies the “capping rate”. I will send you an Open Office spreadsheet that details how I am analyzing the data. I use similar statistical techniques to analyze other cyclical data such as atmospheric CO2 concentration. The Arctic Ocean and marginal seas cover about 18.1 million km^2. Last year, ice area reached a maximum in March at 13.29 million km^2 so there was 4.8 million km^2 of exposed sea water continuing to suck up as much CO2 as was delivered to the surface.

  11. Crispin in Waterloo says:

    How much of that 13.29m was 15% or 30% ice cover? It seems to me the figure looks like ‘covered in ice’ but the real figure is quite a bit less.You mention CO2 absorption by the water which we assume continues, but I am focussing with the release of CO2 from the ice (as a source) not the air.

    Re Greenland – lots of its annual precipitation falls as snow and remains as unmelted but is progressively compressed into ‘frozen water’ firn and it is not involved in the CO2 cycle until it melts one day in the far future as an iceberg (for example). The trapped CO2 in air bubbles is negligible compared with the expulsion of CO2 from the water that froze to make the snow. Were it not so, researchers would examine ice, not air bubbles.

    Re the permafrost: it is the water above the frost limit that is of interest – it cycles from water to ice each year.That is a source and sink for CO2. Agreed some is lost permanently. I am looking at the annual cycle for evidence that water/ice plays a quantifiable role in the magnitude of the annual change (6ppm or so). The depth of soil in the freezing-melting zone varies with location. In Ulaanbaatar it is about 3 metres though the city has permafrost starting at 6 metres.Further north, it is wetter and colder. Soil moisture is highly variable from South to North. Once into Siberia, it is really wet. The area involved in terms of soil moisture (excluding precipitation) is at least 20m sq km and the mass of water perhaps equal to that frozen in the sea ice – maybe it is twice the sea ice volume.

    Add to that precipitation at it looks at least a little like this:

    Sea ice mass 10^13 tons (?), ground water to 1.5m deep 4.5×10^13 tons plus precipitation of 6×10^12 (?). Total = 6×10^13 tons of ice. CO2 cycling in and out could be 80 GTons/season.

    • fhhaynie says:

      The 13.29 is all ice area. It is not the extent of ice which is associated with the % or concentration. It is roughly 15% less than the reported extent.
      Little precip falls as rain on glaciers in Greenland. The snow that falls has allready released it’s CO2 to the atmosphere before it reaches the surface, so there is none to release as it accumulates. The volume of melt water in pools on glaciers is relatively small compared to the volume change of sea ice in the Arctic. Some of that melt water falls through the cracks and serves as a lubricant for glaciers to slide on. CO2 in that water will not be returned to the atmosphere for a long time.

      As for water in soil. When it absorbs CO2, it can react with basic ions or be eaton by microbes and be tied up as carbonates or carbohydrates. The plant growth during the summer ties up a good bit, probably for about 10 year before it decays. The freeze in the winter is top down so much of the potential release of CO2 is expected to be trapped between two ice layers. Again, the volume of water that freezes in soil during a cycle should be a good bit less than you have estimated. In any case, emissions from freezing surface water will be small compared to natural emissions from the equatorial oceans and other natural sources. Even the IPPC estimates thier rate is about 20 times anthropogenic emissions. However, they error in claiming that those natural emissions do not change significantly from year to year unless the “equilibrium” is upset by anthropogenics.

  12. Greg Goodman says:

    This may also be relevant. I’ve just derived what I think is a best estimation of Arctic melting period each year by filtering out some of the short term “whether” variability.

    This seems far more use than the usual obsession with one day per min in September.

      • Greg Goodman says:

        The dates of the annual minimum from that derivation are in the range year+0.68 to year+0.70

        The point of the minimum in cosine model I posted below is year+0.69 .

        This seems to be a good confirmation that it’s ice coverage that is the key player, rather than SLP ( Arctic oscillation ) or SST. Maybe a comparative plot would demonstrate that more conclusively.

        I admit that I was a bit sceptical of that idea when I first read it, but you seem to be bang on.

  13. Greg Goodman says:

    Fred, could you just clarify : what you are calling “daily” data from Scripps is their “dav” files which , while being individual daily readings are at anything between 1 and 2 week intervals.

    eg co2dav_Alert.csv

    could you also say what column you are using ?


    • Greg Goodman says:

      OK, I’ve got it. I’d mixed up some files.

      I suggest you try abs(cos(x)) for Alert CO2. That single function seems to produce less residuals that what you show. Maybe you could fit a second term to flatten the top a bit but the basis is a folded cosine. This is fairly intuitive with isolation and the variation in ice coverage. Also look at air temp it’s also slightly flattened cosine hump.

      Same would probably apply to Antarctic.

      • Greg Goodman says:

        ( abscos + cos + linear ) model fitted to Alert station data:

        Fitting detail below graph.

        Compare to MLO fitted cos + cos + lin , that I did a couple of year ago.

        Since MLO is quite triangular it lends itself to linear slope fitting the annual cycle , this gave rate of change of +14 and -19 ppmv / year .

        Down slope in Alert 59 ppmv / year

      • fhhaynie says:

        The original post analyzed the column 10 monthly data which have the annual cycles factored out (including higher frequency harmonics). The slopes in these plots are much less than the column 9 data with annual cycles.

      • fhhaynie says:

        Due to the orthagonal nature of sine and cosine functions, I am now doing regressions on paired cos(x) and sin(x). The resulting coefficients give you both the amplitude and frequency of a cycle. Harmonics are added if plots of residuals indicates their existance. It is like curve fitting with the major terms of a Fourier series. I use the square of the ratio of the coefficient to it’s standard error as an indicator of statistical significance and avoid over fitting by not including less significant terms. Also, I am now working with differences over different time periods (point to point slopes). You get rates of accumulation for different time scales while preserving the error function. I have found a global signiture of the CO2 data in the twelve month differences. There are no statistical differances between data from sites below 60 N. Sites above 60 N have cycles with similar frequencies but with greater amplitudes. The twelve month differences factor out the annual cycles. These signitures follow ENSO by about five months. Including anthropogenic emissions or time in the regression produces a better fit. Anthropogenic emissions and time are covarient so including both reduces the significances of both so it is difficult to determine what is natural and what is anthropogenic outside the ENSO temperature effect.

      • Greg Goodman says:

        paired cos(x) and sin(x) is exactly equivalent to fitting cos with a phase parameter. Instead of two amplitudes you have one amplitude and a phase, so same parameter count. It’s perhaps easier to see the amplitude of the signal directly this way since there is just one amplitude param.

        What do you mean by including “time” in the regression. If you mean including time itself as a regression variable this is equivalent to fitting a linear trend. There is clearly a roughly linear 2ppm/y rise. The aim seems to be to determine it’s origin so it does not seem useful to include both a linear trend and anthro in the regression variables.

        It would probably be more informative to look at rate of change. The actual atmospheric conc. is basically a cumulative integral. Integrals are a form low pass filter and smooth out a lot of detail.

        Here I compared d/dt(CO2) to SST

        Note I used the Lanczos filter there which preserves the most inter-annual signal (details in my earlier link to the article on running means)

        Your annual difference of monthly data is similar to this but presumably a lot noisier.

        ” You get rates of accumulation for different time scales while preserving the error function. ”

        Perhaps I misunderstood your description but this should produce a rate of change not an accumulation.

      • fhhaynie says:

        Early on I used a trial and error technique to fit cos with a phase parameter. The true amplitude of the cycle is revealed when the two terms and their amplitudes are added. Including time as a linier function with known cycles is a first step in an itterative process. For example, Fitting the annual cycle along with a linear trend will reveal longer cycles in the residuals. Those longer cycles can be fitted by trial and error regressing on cos(x) and sin(x) where x= 2*PI*t/w. W is wave length. The fist estimate of w is twice the time between peaks and valleys observed in the residuals. The linear function is not included in these subsequent regressions.

        The differences are divided by the time to give you a rate of accumulation (plus or minus). It is a rate of change. I think we are working toward the same goals using slightly different techniques.

      • Greg Goodman says:

        “The true amplitude of the cycle is revealed when the two terms and their amplitudes are added.”

        They are in quadrature so you need to sqrt the sum of squares. If you do that you should get exactly the same result as the amplitude of a fitted cos with a phase param.

        If you play around with trig identities the two forms can be seen to be identical

        BTW you might like to consider upping the WordPresss default limit of 1 for links in a comment. I notice if I include two links to graphs or something the comment gets held for moderation.

      • Greg Goodman says:

        I was curious as to what this 12mo diff of monthly data actually does to the data. My engineering mindset tends to make me regard processing like that as a filter ( which is indeed what it is ).

        So to see what it does I took the fourier transform. The result is “it’s worse than we thought”. TM.

        You may like to have a look, I’ve described it in more detail and plotted the frequency of this filter. My conclusion is, it would be better to filter out everything below 12mo.

        “These signitures follow ENSO by about five months. ”

        I don’t know how you have implements it, so I will just add a warming that the difference should be logged at the mid-point of the 12mo time interval, otherwise you will be introducing a 6mo phase shift. You should check this in relation to the 5 month lag you found.

  14. Greg Goodman says:

    There seems to be a correlation between dCO2 and SST globally on both annual and centennial scale but it does not account for more than about half the short term variability.

    You have shown a link to Arctic ice coverage. Ice coverage is also affected by SST, plus Henry’s Law dependency of d/dt (CO2) on SST.


    There’s a nest of interdependencies and covariability that is difficult to decypher but I think the latitudinal differences are interesting. That combined with the isotopic fraction may give us another angle on the attribution question.

  15. Greg Goodman says:


    Air Temps at Alert peak mid July and seem to have quite a different profile

    Do you have a source for daily SST. The best I have got is monthly averages of hadISST. It seems SST peaks in July too but the data is too course to be much use.

  16. fhhaynie says:

    We arn’t doing the same thing. I’m doing a running one year difference centered on the mid month. I.e.(Jan99-Jan98 centered on Jul 98 followed by Feb99-Feb98 centered on Aug 98 etc.) To determine the lag, normalize both sets over a common time period and plot both as a function of time. Shift one set by a month and regress. Keep shifting to maximize R^2.

    I don’t have a source for daily SST data.

  17. Greg Goodman says:

    Fine you are correct on the centring, just thought I’d mention it because a lot of people manage introduce a 6 mo lag when doing a running mean.

    No need to normalise, scaling won’t affect correlation.

    It can be worthwhile running the lags over a good range in both directions. This can help find mutual periodicities. Here’s an unrelated example of cross-correlation function.


    “We arn’t doing the same thing.”
    but the freq spectrum I posted does apply to a running one year difference as you describe. The mechanics of how it is calculated does not matter, the result will be the same as the convolution method and the filter response will be what I showed.

    If you’re happy with that, fine but I’d recommend a 12 mo filter either before or after the differencing. That sort of distortion could produce some spurious results. This will not affect the 5 mo lag, it should make it clearer.

    If you are used to working in a spreadsheet you could try a three stage running mean using 12 mo , 9mo and 7mo windows respectively (the last two will centre nicely, the 12mo will give a 0.5mo lag)
    If you’re happy running commands, I can provide better solutions.

    I did find this monthly SST data and it seems to peak later, about the time of ice min. but it’s a lot lower than Alert.
    I’d like to find some real SST for Ellesmere Is. , at least one year of daily SST to check timing with the CO2 data.

    ” the function is cos(lat/a+b) ”
    What a and b values did you get from that?

    From the lack of any obvious lag and the degree of atmospheric mixing, I have difficulty seeing this as a build up. I think it has to be due to the larger annual flux.

    Gosta Pettersson’s ( swedish chemist ) says there is a small isotropic difference in absorption. It may be enough to explain this, I’ll have to check back on that.

    If it was vegetation cycle it would peak at a lower lat. then 82N, so I think it has to be to do with ocean interaction. I think this is an important effect you’ve highlighted.

  18. Greg Goodman says:

    You may find Gosta Pettersson’s papers interesting.

    Didn’t find the bit about dC13, I’ll check personal communications.

  19. fhhaynie says:

    I’m coming to similar conclusions with my present analysis techniques.

  20. Greg says:


    I found a faster decay and something longer than 14y, plus a decaying annual cycle that seems to be keyed into NH cycle.

  21. RickA says:

    Thank you for updating this analysis.

    460 ppm by 2060.

    Could you estimate when we will hit 560 ppm?

    I am interested in that number because that is a doubling of CO2 from 280 ppm.

    Thanks in advance.

    • fhhaynie says:

      My analysis suggests that even with continued anthropogenic emissions at increasing rates, 560 ppm will not be reached in this century.Natural emissions are expected to decrease at a faster rate after around 2060.

  22. curryja says:

    Reblogged this on Climate Etc. and commented:
    by Fred Haynie

  23. IPMeng says:

    I could not find a bio or CV on this page. Am I missing it?

    • fhhaynie says:

      I have not included a bio but maybe I should. I retired from research at the Atmospheric Sciences Research Laboratory in Early 1991. My primary responsibility at EPA was to supervise and do research on the effects of criteria pollutants on materials and to publish the results in Journals and congressionally mandated criteria documents. I have a masters degree from Auburn University, a masters degree in metallurgical engineering Ohio State, additional graduate work at Georgia Tech, University of Pennsylvania, and the University of Southern California. I have worked with and co-authored papers with atmospheric chemists, meterologist, economists, chemists, and statisticians. You can find some of my publications by Googling my name “Fred H. Haynie”. I had a side career as a naval aviator and have flown over a lot of ocean and retired as a Captain. I have a comfortable retirement and am not doing what I do to further my career or improve my reputation. Let the data show us the truth.

  24. blouis79 says:

    Science stands on the merits of the facts and analysis. Not on who said it.

    Fred, I am curious if you are able to clarify the correlation vs causation question on CO2 and temperature.

    Givwn that a climate is based on 30year time periods, what do the data look like if analysed in 30 year blocks? (apart from the obvious “we really don’t have enough data to make valid conclusions on climate with the availabel data)

    • fhhaynie says:

      There is nothing that requires you to work with 30 year periods and it can be missleading to do so. I am using a running year to year difference to separate out the annual variations which are at least 20 times greater than the year to year differences. The correlation seems rather evident in the statistical fit of the SST data. The causation is likely in the dynamic processes in tropical thunder clouds.

  25. Greg says:

    Fred, could I recommend using png rather than jpeg. Those graphs have some horrible compression artefacts that make them ugly and hard to read. 😉

    • fhhaynie says:

      Thanks, I’ll do that in the future, but I would prefer that some smart young PHD student do a critical review of all my work, make corrections of my errors, improve on it and publish.

  26. Greg says:


    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.

    I can confirm from teh Scripps Institute flask data from Alert , Canada that the annual cycle in 13CO2 is almost a perfect match for inverted total CO2 conc. with suitable scaling. (CO2* -.045)

    On the basis of what assumptions would this be ‘expected’?

  27. fhhaynie says:

    The regression coefficient -.045 is identical to -1/22….,which is not significantly different from the identity -.05=-1/20. The difference is error. It is like what you observe when you swap “independent” and “dependent” variables in a regression. Both are time dependent and the independent is assumed to be “fixed” with time but is not. With these large cyclic swings observed at Alert, slight shifts in timing of swings creates greater error in the resulting regression. A least squares calculation on the perpendicular to the slope would probably reduce the observed difference.
    The physical significance is -20 is what I expect to be the average 13CO2 index of the organic fraction observed all over the Arctic. There is a long-term change in that value with time. It gets more negative. Is it natural or anthropogenic is the question we are trying to answer.

    • Greg Goodman says:

      Thanks, I’m aware of the regression dilution problem. I’ve written an article on it and how it affects attempts to assess climate sensitivity ( it leads to exaggerated CS ) .

      Both the above ratios were determined by visual inspection of the residual to see when the annual signal was most effectively removed. The second value 0.050 or 20.0 was simple done taking a bit more care. It is 0.050 rather than 0.049 or 0.051.

      It is interesting that this is the same figure that you chose to represent the -15 to -30 range for “organic” CO2. But if that is a representative figure then this would imply that all the annual cycle is totally organic over the Arctic, which I think is very unlikely. A significant amount will be air/ocean exchange, with a lesser proportion being swept up from lower latitudes where more of the vegetation is and where the annual variation is notably smaller.

      Unless I’m missing your argument, I don’t see that adding up.

      There must be a value closer to -30 per mil being boosted by the typical atmospheric concentration of about -8 per mil

      The annual cycle in the Arctic seems to bear a strong resemblance to the variation in ice extent. Flattening out in the winter when much of area water is isolated from the air.

      This is rather different from the annual cycle at MLO which is claimed to be a globally representative..

      • fhhaynie says:

        There is little or no annual cycle at the site on Samoa (14.2S). The greatest amplitude is observed in the Arctic and closely follows the annual change in the area of ice. The frozen surface is not a sink but cold salty water with lots of phytoplankton is. The magnitude and shape of the cycle increase and change as you go north from Somoa but the around -20 value does not change significantly which suggests that an inorganic fractionation process is probably occuring as CO2 is being cycled between the ocean surface through the processes of condensation/absorpion/rain/freezing in clouds. These processes appear to concentrate the lighter CO2 as it is transported North. Evidence suggests the same behavior as it is transported South. However, the amplitude is smaller because there is little change in the open ocean sink area.

        Anthropogenic emissions have indexes of around -30 for petroleum and around -25 for coal. Decaying biologicals have values around -20. The fact that the index appears to be becoming more negative with time suggests anthropogenics are contributing.

      • fhhaynie says:

        For others who wish to comment on my blog, either click on my name or go to http://www.retired researcher.wordpress.com. Thanks again, Greg, for your comments on my blog.

  28. Greg Goodman says:

    “The greatest amplitude is observed in the Arctic and closely follows the annual change in the area of ice. ”

    It should be noted that the annual cycle in the german Black Forest is as large as in the Arctic and very similar in form. Whether this is because it is often ‘downwind’ of the Arctic, I don’t know but the latitude relationship, though true generally, is not always applicable.

    “The fact that the index appears to be becoming more negative with time suggests anthropogenics are contributing.”

    That is neither surprising nor in need of further evidence.

    Looking a MLO vs global SST we see that a simple linear relationship does not fit too well:
    There is a a region that could be considered linear within rather large non-linear ‘noise’. but this seems to breakdown at about 370 ppm where an almost flat linear relation would be found. This means either a very large sensitivity of CO2 to SST or SST being very insensitive to CO2. That can not be explained by simplistic GHG hypothesis.

    • fhhaynie says:

      That Black Forest site may be affected by local anthropogenic sources as well as polar winds. They may not be trying to show that their observations are “background” data as Scripps does. Other sites in Germany have high obsevations and Germany is still burning a lot of coal.

    • Greg and Fred,

      The main spring drop in CO2 and increase in δ13C are the NH extra-tropical forests which start to grow again after been dormant in winter. In fall leaves are shed off and start to decay, a process that goes on all winter, even under snow at -20°C. That is the reason that Schauinsland has the same summer-winter amplitude as Barrow or Alert.
      Winds of the Ferrel cells brings these CO2/δ13C level changes towards the polar sites.
      From the reverse CO2 and δ13C movements it is clear that the seasonal changes are caused by vegetation. If the seasonal changes were dominated by the oceans, the CO2 and δ13C changes would parallel each other (even including the isotopic fractionation at the ocean-atmosphere border and reverse):

      Tropical forests have a different “seasonal” regime, which is more ITCZ/monsoon/ENSO related which is more shown in year by year variability than in intra-year variability.

      • fhhaynie says:

        Yes, that is one explanation, and as you say, it may be the main one. The Arctic ocean is a big sink that changes it’s sink area as ice forms. That should be considered in explaining seasonal variability of CO2 in the Arctic. Both mechanisms are temperature dependent in that neither is a sink when they are frozen.

      • Greg says:

        Thanks Ferdi, so if I follow you there are persisent winds blowing form german forests towards Barrow and it is european forests that are the reason for the CO2 changes at Barrow, is that correct?

      • fhhaynie says:

        No, It is more likely the other way (Polar vortex) with the added input from German coal fired power plants.

      • Greg says:

        I don’t think Ferdinand’s comment is at all convincing, I just wanted him to confirm whether this was what he meant.

        Ferrel cells are a very simplistic idea and do not match what really happens. In any case they cycle between 30N adn 60N with westerly winds at the surface and would not take CO2 from german power plants to Barrow or Alert.

        Deep Rosby waves caused by the polar vortex do provide massive transport in both directions but still in an easterly direction when rising north. Any cold arctic air in Germany tends to come down from Russia via Scandinavia, not from N. America.

        The similarity in these two stations is very surprising and may contain important infromaiton if objectively analysed. Due to the atmospheric circulation patterns, I find it hard to see this as one area feeding the other to the point that they match. That tends to suggest independant causes leading to similar variability.

        Perhaps there is a strong vegetation driven change in the Arctic too. Except there the vegetation is aquatic: phytoplankton.

        Oddities like this merit closer attention because they can be more informative than when things do what we “expect”.

  29. Greg Goodman says:

    Samoa is interesting. It is in the western Pacific warm pool.

    As is generally true, it is rate of change of CO2 that correlated with SST, not a direct, in phase, relationship. It can also be seen that its dCO2 is closer to matching the global mean SST than the local one, reflecting the degree of CO2 being “well mixed”.


    • Greg Goodman says:

      There is a steady 2ppm/year rise, unrelated to SST behind the shorter inter-annual variations where dCO2 correlates with SST ( which suggests out-gassing ).

      I just found this plot which is a subset of the scatter plot above. The higher CO2 values really don’t support the idea of temperature being driven up by CO2.


      • Greg and Fred,

        While SST is the main driver, again it is vegetation which is dominant: again CO2 and δ13C are changing in reverse. With an El Niño, SST is high, but rain patterns change over the Amazon and some parts dry out, release more CO2 from decay and reduce their input + (natural) forest fires.
        Here the year by year variability of dCO2/dt and dδ13C/dt which are oppositely synchronized and both lag dT/dt at Mauna Loa:

      • Greg says:

        “While SST is the main driver, again it is vegetation which is dominant: ”

        So one thing is “main” and the other is “dominant”. You are making less and less sense recently Ferdi.

      • Greg says:

        Ferdi, what do you aim to show with this messy graph?

        If you want to show that dC13 matches CO2 at least invert one and overlay the data so that we don’t have to try and mentally invert it. It is impossible to see how well they match from your graph.

        Also it is obvious that the form of dT/dt does not match dCO2/dt although there is some similarity. This is because the inter-annual variability is dominated by temperature driven change where it is T(t) that correlates with dCO2/dt . That has be been thoroughly established by Allan MacRae, Ole Humlum and others ( me for example ). You are plotting orthogonal quantites hence the mismatch and the lag. The 9mo lag is a quarter cycle of the dominant short term variability which is about 3y.

        If you plot T(t) with dCO2/dt there is no phase lag.

        Using dT/dt is helpful to reduce the long term trend to a constant offset, this should then be compared to the second derivative of CO2.

        This clearly shows that *short term* variability in CO2 is driven by SST.

        Now if variation of δ13c is very similar to CO2 that means that it also correlates strongly with SST. If that points to anthopogenic emissions the link is not obvious. Maybe Fred has some ideas on that.

      • fhhaynie says:

        One possibility for the long-term more negative increase in the 13C index is decay of phytoplakton and seaweed in the surface waters of the tropics, the rate of decay being temperature dependent. The index value for that emitted CO2 is probably aroun -20.

    • Greg Goodman says:

      “There is little or no annual cycle at the site on Samoa (14.2S).”

      There is a clear annual cycle at Samoa, but since it is a tropical station, it is more like two separate 6mo bumps. The first, larger one peaks x.16 years the later one at x.60 years. ie Feb and July.

  30. fhhaynie says:

    Are those bumps synced with win the sun passes over that latitude? Possible additional evidence of temperature dependence.

    • Greg Goodman says:

      not quite that simply, sadly. There is a fair thermal lag from peak insolation to peak temperature since radiation produces a dT/dt not a T(t). In principal the temp would be 90deg out of phase with the insolation, ie three months later at higher latitudes. However there are negative feedbacks which shorten it a bit. NH solstice is 21st June temps peak about 2mo later.

      cf ice minimum is usually around 21 Sept.

      Since vegetation also responds to temp and insolation in the other sense, the timing of the peaks is going to depend up on a whole bunch of parameters and the timing of the peaks will not be that simple.

    • Greg Goodman says:

      There’s three replies there but no posts. Something stuck in moderation queue?

      • fhhaynie says:

        I think what is happening that your comments are being posted on my site and being reposted on Judith’s. I am probably responding to both with “ditto” last posted first.

  31. Eliza says:

    “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.” There no way the AGW establishment will let you publish this work.

    • fhhaynie says:

      It could be rewritten without including conclusions and presented simply as the most likely case, and be accepted by a journal. When Nature Climate Change first came out, they offered a years free subscription to individuals that had experience related to climate change. My years of research experience at EPA and my past publication record met thier qualifications so they sent me a subscription. I have been comfortably retired since 1991. I did some writing for publication after that but not much. I dropped my membership in three scientific organizations and did not attend any more conferences. I even declined updating a chapter in a handbook. The editor kindly did it for me. It was first published as Chapter 2 “Statistical Planning and Analysis” in 1971 in “Handbook on Corrosion Testing and Evaluation”. It was last published as Chapter 5 in “Corrosion Tests and Standards, Application and Interpretation” in 2005 (fourth time). At my age, I am not motivated to get back into the journal publication business. I would prefer some smart graduate student to take my ideas and techniques, improve on them, and start their own publishing career. I would gladly assist them in their journey.

  32. fhhaynie says:

    I’m presently doing an analysis of all the available data at Mauna Loa. There is a very strong relationship between CO2 and and the 12/13 C index. I will post my results when I complete the analysis.

    • Greg says:

      Are you using the daily data? This is much better than monthly means, though there are obviously some glitches and there are gaps since some days get taken out by QA controls.

      This are examples of daily CO2 from Scripps.

      In general you will find the gaps are the same, ie if there’s d13CO2 there’s also a CO2 datum.

      • Greg says:

        Daily data for Alert, Canada. http://scrippsco2.ucsd.edu/data/alt

      • fhhaynie says:

        The “daily” raw data has some values that are not representitive of “background” but could be anthropogenic. Scripps excludes those “extreme” values in calculating their monthly averages. However, the correlation between CO2 and 13/12C index is stronger when they are included which suggest they have an anthropogenic origin. The NOAA/ESRL event data for Ochsenkopf, Germany gives a strong correlation indicating a considerable contribution from anthropogenics.

      • Greg says:

        No the daily data are also QA controlled. The monthly averages are simply monthly averages of the daily data, so the glitches get smoothed out.

        It is possible that QA does not remove everything that may be measurement error or a bad sample. I think they use 2sigma as the cut-off to test for fliers.

        If you cut out everything that is a bit off the line you are corrupting the data and imposing your expectations on what comes out. This has been the big problem of all climate data. “Homogenising” out anything that does not fit the agenda.

        I really don’t like monthly averages since there are climate effects on 14 and 28/29 day lengths due to lunar influences. It is a classic data processing error to subsample data without doing anti-alias filtering.

        A classic case was ERBE data where they have a huge 36 day cycle due to the satellite orbit ( which is itself and alias due to some particularly bad model assumptions of daily cloud cover ). When the data are resampled to “monthly” data they produce a significant alias at just over 6 months ( 198 days from memory).

        This alias was pointed out by Kevin Trenberth, on one of his better days, and ERBE no longer recommend using the monthly data.

        There is information in daily data that may be removed or worse, perverted in taking monthly averages.

        MLO is supposed to be an indication of ‘background’, the other stations are not. They are data for their respective stations. MLO is a special case since it is sited on active volcano.

      • Greg says:

        I’ve just done a quick analysis of the MLO and Alert daily data shown above.

        Very roughly the ratio of the long term rise ( fall ) between CO2 and d13C is about twice that of the scaling of the annual cycle.

        The annual cycles scale at about 20ppmv change in CO2 corresponding to about 20 permil change in d13C

        The long term scaling is about 45 at Alert and 55 at MLO.

        since the long term trend in CO2 is basically the same at the two sites, that means there is a significant difference in the long term change in d13C between the two sites. That should be informative.

        The “nzd” data for Baring Head, New Zealand are interesting too. Very little annual variation.

  33. Greg says:

    OOPS That should read: The annual cycles scale at about 20 ppmv change in CO2 corresponding to 1 permil change in d13C

  34. @fhHaynie
    There is an easier way to come to same conclusions as you did:
    just study minimum temperatures, [which supposedly should be going up if AGW were true]
    I had a sample of 54 weather stations
    a) equal amounts NH and SH
    b) balanced to zero on latitude
    c) 70/30 @sea /inland to eliminate certain cyclic weather influences

    Longitude does not matter, as long as you look at the average change in T/annum

    the 100% correlation suggests only nature at work here…..

  35. An interesting question to me would be: who put the heat off?

    it seems a man made ozonehole is less probable than a natural ozonehole?

  36. Greg says:

    That’s something I’ve been saying for a couple of years.


  37. Only very few of us have come to understand that there never was a man made ozone hole.
    it is just that above the oceans the chemical reactions [which is earth’s TOA defense system against harmful radiation hitting on us and flora and fauna]:
    N2 + O2 + (UV -C) => 2NO
    3O2 g + (UV-C) =.> 2O3 g

    might be perhaps a bit in competition with this reaction
    2[OH] + (UV-C) = > H2O2 g
    the latter reaction winning it above the oceans
    Unfortunately we do not measure H2O2 and that leaves everybody clueless.
    If you look at the spectrum of O3 and H2O2 you find striking similarities. They both have absorption in the UV-A and UV-B regions, meaning that [a little] less radiation of that type will hit earth, when there is more ozone and/or peroxide. The end result is a small shift in the chi square distribution of energy coming from the sun through the atmosphere.
    Therefore, the drop in the magnetic polar field strengths from the sun explains the current global cooling trend.

    The way to pick up this variation coming through the atmosphere is by looking at measurements of minima and maxima. I looked at 800000 of those, each, with the weather stations balanced by latitude and 70/30. I figured longitude does not matter as long as I look at the regressions of the change in T per annum. I am finding around 1996 -1997 where global incoming heat starting to decline. True enough, it seems from the Arosa ozone time series that ozone started its incline towards the end of the century.

    Earlier, I have shown you the actual global drop in minimum temps.
    I don’t have a picture for the drop in the rate of max. temp. in K/annum , the relationship there is:

    y=0.039ln (x) – 0.1112 (where y= years in the past)
    with r2 = 0.996
    valid for 1973 -2014

  38. Greg Goodman says:

    “True enough, it seems from the Arosa ozone time series that ozone started its incline towards the end of the century.”

    Ozone dropped mainly in two steps immediately following El Chichon and Mt P. That is what is reflected in the TLS graph and Is explained in more detail in the article beneath it.

  39. All volcanic activity, seen or unseen (below the oceans) can be heaped together with other events, like a shift in earth’s iron core, degree of mixing of water (moon pulls), extreme northern storms, etc, and this can affect the average temperature (“Means”); which is why the mean average temperature of earth is just not such a good proxy for anything at all.
    but as shown before, all that does not really affect minimum and maximum temperatures on earth.

    I challenge you to repeat my test, preferably chosing 50 other weather stations.

    • Greg says:

      So you’ve shown that there has been a slow down in global warming. That is pretty clear to everyone except Karl et al by this stage, though I doubt picking out four years from 40 is valid statistically.

      However, if you “heap” everything together you are throwing away the information that allows determination of the cause of variation and assumes, probably incorrectly, that everything will “average out”.

      This is fallacy upon which AGW was built: all variation is “noise” and all that is an attributatble signal is the correlation between a warming “trend” and rising CO2 ( which does not match the early 20th. c rise but we’ll try not to talk about that ! )

      It was the short term rise at the end of 20th c. that got everyone into a flap. Analysis of the detail you want to ignore suggests this was a secondary result of volcanic activity, which mainstream only sees as a cause of cooling.

  40. I am a bit confused
    Greg=also Greg Goodman?
    Just want to make sure

  41. @Greg
    You seem to misunderstand how I grouped the data, and therefore misinterpret my final results.
    By carrying out linear regressions (for each weather station, sampled as per my specified particular sampling procedure/ technique), I obtained the speed of warming/cooling from 1973, 1980, 1990 and 2000 in K/annum (i.e. the value before the x)
    I then averaged all results from those regressions for each station.
    By setting those results out again against time I get acceleration /deceleration in K/annum2
    Low and behold, in both the study of minima and maxima I get perfect curves. It is just like someone [God, or if you donot believe in God: nature] is throwing a ball and by setting the speed of the ball in m/s you find the deceleration in m/s2 due to gravitation?

    Now what do the curves tell me?
    For one thing: there is only global warming or global cooling. There is no pause. It is either cooling or warming. There was only a very short pause for a small time space when the curve cuts the zero line, i.e. this is where the speed of warming / cooling is zero
    Looking at the minima graph, this happened about 19 years ago, counting from 2014.
    If you solve the equation I obtained for maxima namely
    y=0.039ln (x) – 0.1112 (where y= years in the past)
    with r2 = 0.996
    valid for 1973 -2014
    you should get 17.3
    So, looking at maxima the energy coming in started to come down after 1997, regardless of what happens to the mean temp. of earth.

    Now, an interesting question is of course: how do I explain those 2 curves, looking at what happens on the sun?

  42. Henry said
    (where y= years in the past)

    Henry says
    sorry, I got my wires crossed
    y is the speed of warming/cooling
    x is years in the past (valid for at least 1973 -2014)

    so when y=0, x = 17.3

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