__Review report for
IPCC WG1
Third Assessment Report (TAR) __

the report is available at:

**Chapter 3. The Carbon Cycle and Atmospheric
CO _{2}**

*by Jarl
Ahlbeck, D.Sc. (chem.eng),
*

*docent (env.science)
*

*Abo Akademi University (The Swedish
University of Finland) *

*Biskopsgatan 8, FIN-20500 Abo Finland
*

*email: jarl.ahlbeck@abo.fi *

**SUMMARY**

**In this review, I have concentrated on the
most important result for policy makers of TAR Chapter 3, the estimation
of future carbon dioxide concentration from emission scenarios by means
of two carbon cycle models as shown in Figure 3.14. **

**(**This figure is quite similar to the figure
published by IPCC 1996 (SAR) showing that the atmospheric concentration
of carbon dioxide will increase to 705 ppm the year 2100 as a result of
the emission scenario IS92a)

**A careful statistical analysis of avaliable
data for anthropogenic emissions and atmospheric carbon dioxide concentrations
for 1958-1998 indicates that the sink flow rate is primarily controlled
by the atmospheric concentration of carbon dioxide. If the statistically
obtained sink flow model is combined with a solution of the mass balance
differential equation using the emission scenario IS92a, a prediction of
580 ppm for the year 2100 is obtained. **

**The TAR estimate of about 700 ppm based on
IS92a for the year 2100 is thus at least 100 ppm too high. **

**INTRODUCTION**

The emission scenario IS92a is no prediction,
only a scenario, but the predictions based on IS92a are despite of that
widely used as basic predictions. The TAR estimate of about 700 ppm CO_{2}
in the atmosphere for the year 2100 is a result of an uncertain future
emissions inserted into uncertain carbon cycle models (*Chapter
3.7.3, page 25, line 47 *"*Two reduced-form
carbon cycle models have been used to derive CO _{2} - concentration
scenarios from emission scenarios"*

It is clear, that the value 700 ppm with no or little attention paid to the uncertainty will be used all over the world as a "scientific consensus" base for political decisions.

The fact that the standard deviation of the model
*parameters* alone cause a very large resulting standard deviation
in this prediction is not shown in *Figure 3.14.* But a more serious
fact is that the even small changes of the model *structure* would
decrease the estimated future concentration value to a great extent.

As today's concentration is 366 ppm (1998), the prediction implies an exponential growth of 0.64 %/yr, or a linear growth of 3.3 ppm/yr for the next century. An exponential regression analysis for Mauna Loa data 1958-1998 (recent 40 years) gives that the exponential increase rate has been 0.39 %/yr or a little more than half of the predicted percentage increase rate for the next century. For the period 1970-1998 (last 28 years), the Mauna Loa curve has not been exponential, it has been statistically linear, with an increase rate of 1.5 ppm/yr, or less than half of the predicted value for the future.

An exponential extrapolation from 1958-1998 Mauna Loa data (recent 40 years) gives a prediction of only 544 ppm for the year 2100. A linear extrapolation gives only 519 ppm.

The emission scenario IS92a suggests a rapidly
increasing global use of fossil fuels. The yearly emission rate should
increase almost linearily, about 0.115 GtC/yr^{2}. For the
period 1970-1998 the emissions have increased quite linearily too, by 0.085
GtC/yr^{2}. Since 1980, the increase rate of the yearly emission
rate has, however, been only about 0.06 GtC/yr^{2}. The reliability
of the IS92a scenario is therefore highly questionable.

**INFORMATION ABOUT THE CARBON
DIOXIDE MODELS**

Detailed information including the source code
about the global carbon cycle computer programs used *is not given*
and the reliability of these models are therefore difficult to judge. But
the models are said to be based on nearly similar assumptions as the models
used in SAR. *(Page 5.,line 21 **"Simple
carbon cycle models as used in the SAR have* *been* *modified
..."**)* . I therefore analyze
a published model structure that has a similar structure as the model used
in SAR. This structure is clearly explained in the thesis *"Uncertainty
in Atmospheric CO _{2} Concentrations from a Parametric Uncertainty
Analysis of a Global Ocean Carbon Cycle Model"* by Gary Louis Holian, MIT,
september1998 at,

(http://web.mit.edu/globalchange/www/rpt39.html)

**BACKMIXED SURFACE AND EDDY DIFFUSION**

The mechanism for the ocean sink flow is modeled as a backmixed surface layer in equilibrium with the atmosphere combined with a diffusional mass transport of carbon from the surface to the deep ocean. The vertical eddy diffusion coefficient is obtained from measurements of the C-14 tracer from atomic bomb explosions and some other tracers. This structure of the model for the further transport of carbon from the surface to the deep ocean (Fick's second law of diffusion) makes the total absorption rate to some extent forced by the carbon concentration in the surface layer and hence by the atmospheric partial pressure of carbon dioxide. This dependence of the sink flow on the surface concentration is, however, not very strong because a concentration gradient is built up in the bulk according to the second order differential equation.

As the main part of the ocean sink according to the model thus goes to the backmixed ocean surface layer, a great part of the ocen sink flow is modeled according to a "constant airborne fraction" mechanism, or the sink flow rate in a constant multiplied by the emission rate and the atmospheric concentration has only little influence on the sink flow rate.

**OTHER DEEP OCEAN ABSORPTION MECHANISMS**

Numerous continuously and periodically changing circulation patterns such as ekman pumping and thermohaline circulation may, however, bring the backmixed surface water in other contact than by eddy diffusion with such bulk water that still has a pre-industrial carbon concentration. These processes may give a proportional dependence of the deep ocean sink flow rate on the equilibrium concentration of carbon in the surface layer and hence on the partial pressure of carbon dioxide in the atmosphere (Fick's first law of diffusion).

A possible modeling approach would be to use the fact that the amount of backmixed water is not constant, it is increasing. The introduction of an time dependent (increasing) equivalent amount of backmixed water would give a different model structure. 100 years into the future, or the 40 years 1958-1998 used in my analysis are enough long periods to cause a substantial error if the backmixed layer thickness is assumed to be constant.

But in the models, all effects other than the
eddy diffusion according to Fick's second law are normally corrected by
parameter adaption* *or by introducing a slightly larger value of
the eddy diffusion coefficient in the carbon cycle models than normally
used in ocean modeling. This is done because it is impossible to create
a absorption model structure that involves all complicated circulation
patterns. But this adaption cannot be very remarkable because the diffusion
coefficient is constrained by the experimental value obtained from C-14
and other tracers.

**THE MODEL STRUCTURE DETERMINES
THE PREDICTION**

Although the adaption gives more realistic theoretically calculated values of the recent ocean sink flow rate than without adaption it cannot, however, correct the fact that the model structure may be more or less flawed. The absorption rate is probably modeled too little sensitive for forcing by increased atmospheric carbon dioxide concentration. If, in reality, the influence of the atmospheric partial pressure on the ocean sink is greater than indicated by the model structure, the use of the model with the adapted (higher) parameter will unfortunately give a considerable overprediction of future carbon dioxide concentrations.

**STRANGE MODEL STRUCTURE FOR THE
BIOSPHERE**

However, the modeling of the ocean system may not be the main reason for the difference in predictions between a simple statistical approach and the big global models. The most important difference may be a result of unreliable modeling of the biosphere in these models.

In the thesis by Holian, the procedure for modeling the biosphere sink is described as follows:

- It was known that the total sink flow rate is 4 GtC/yr (1990)

- The ocean model gave an ocean sink flow rate of 2 GtC/yr and this value is constrained to a great extent by the experimental value of the deep ocean diffusion coefficient.

- As the ocean model is constrained, the only possibility was to state that the rest, 2 GtC/yr, or half of the total sink flow rate goes to the biosphere.

After this procedure, a complicated global biospheric model was run "the Terrestrial Ecosystem Model (TEM)" of the Marine Biological Laboratory at WHOI. This run came up with a biosphere fertilization sink of only 0.9 GtC/yr (for 1990), a value that, in fact, is dependent on the difference between today's atmospheric carbon dioxide concentration and the pre-industrial level.

After that the rest, 1.1 GtC/yr, was simply considered
as a *constant* biospheric sink term (*a "residual flux
needed to balance the carbon*** budget"**). In other
words, a biospheric sink flow that is more than half of the inorganic
ocean sink was treated as constant term. The final dependence of the biospheric
sink on the atmospheric concentration was thus modeled as follows:

pre-industrial | 277 ppm | biosink (TEM) = 0 GtC/yr (balance) |

1990 | 352 ppm | biosink (TEM) = 0.9 GtC/yr |

future | 592 ppm | biosink (TEM) = 1.3GtC/yr |

After adding the constant term of 1.1 GtC/a, that
of course is zero for the pre - industrial situation (otherwise the biosphere
would deplete the atmosphere of carbon dioxide), the sensitivity for the
biosink flow rate on the atmospheric concentration is high or 0.026 GtC/yr/ppm
(**26 MtC/yr/ppm**) in the range from 277 to 352 ppm.

But in the range from 352 to 592 ppm the modeled
sensitivity seem to suddenly drop to 0.0054 GtC/yr/ppm (**1.25** **MtC/yr/ppm**),
or to only abt. 5 % of the original value ! Such a rapid decline of
the negative biospheric feedback is hardly possible.

One could also look upon the problem in a second
way: Why not assume that the TEM model is correct so that the real physical
value of the total biospheric sink 1990 was only 0.9 GtC/a. The whole rest,
3.1 GtC/a must then be absorbed by the oceans ! But now there
is a big problem: The adaption of the diffusion coefficient would now give
an extremely high value that is very far from that obtained by the C-14
tracer. *An oceanic sink flow rate of 3.1 GtC/yr for 1990 would indicate
that structure of the ocean model is erroneous*.

In fact, the hypothesis that the *structure*
of the ocean sink model is fundamentally wrong cannot be rejected. Some
recent reports (Hesshaimer *et al., Nature ***370**:201-203, 1994,
Broecker and Peng, *Global Biochem Cycles, ***8**:377-384, 1994)
indicate that there is a substantial controversy with respect to the size
of the radiocarbon pool in the ocean, the air-sea gas exchange rate and
the bomb-radiocarbon penetration depth. In fact, the ocean sink can not
only be greater than 2 GtC/yr, it can also be much smaller than 2 GtC/yr
also (for 1990), which means that the modeling of the biospheric sink becomes
even more important.

The modelers introduce a constant "balancing"
term in the biospheric sink model. This trick causes, if it is not physically
correct, a substantial overprediction of future carbon dioxide concentrations.
But there are certainly other possibilities, who will cause a completely
different model structure. Why not simply adapt a TEM-like model to give
a biosink flow rate 2 GtC/yr for 1990 so that the total biosink flow, 2
GtC/yr, is forced by the the deviation of the concentration from
the equilibrium state *(C-280 ppm)* ? This could have been done by
adapting the model parameters. With the sink flow rate to the biosphere
being more directly dependent on the atmospheric concentration, the predicted
value of the future concentration would decrease to a great extent.

Temperate and boral forests are very sensitive
to carbon fertilization, which means that more carbon dioxide in the atmosphere
causes increased uptake rate (Keller and Goldstein, *World Resources
Review, ***6**:63.87, 1994, Fan *et al*., *Science*, Oct
16, 1998). The introduction of a constant "balancing" term that
may cause an erroneous structure* *of the biospheric sink model and
thus an underprediction of the fertilization effect.

**A STATISTICAL APPROACH**

In order to update my recent statistical model, see "Absorption of Carbon Dioxide from the Atmosphere" for the sink flow, I added a column containing global radiosonde temperature data 1958-1998 (from balloons) for the surface to 100 mb to the original data matrix containing emission data and data for the atmospheric concentration, and performed a regression analysis for the model:

*F _{s} = b_{0} + b_{1}F_{em}
+ b_{2}C_{atm} + b_{3}* temp*

where *F _{s} *is the total sink (GtC/yr)

* F _{em
}*anthropogenic emissions, only fossil
fuels and cement

* temp
*= radiosonde temperature anomaly

The coefficients were estimated by nonlinear regressional
minimizing the residual sum of squares (SIMPLEX-search) between the observed
carbon dioxide concentration, *C _{i} *,

*C _{mod,i+1 }= C_{mod,i}(1-zb_{2})
+ F_{em,i}(z-zb_{1}) - zb_{0 }- zb_{3}*_{
}temp*

where *z = *0.471* *ppm/GtC

MIN S*(C _{mod,i }- C_{i} )^{2} *where

The updated non-linear regression results from the whole period 1958 - 1998 were:

*b _{0}*
= -12.311 GtC/yr
(old = -11.098)

*b _{1 }*=
0.063243 (dim.less) (old
= 0.0455)

*b _{2}*
= 0.04164 GtC/yr/ppm
(old = 0.03846)

*b _{3}*
= - 0.696 GtC/yr/

The residual sum of squares decreased from 12
to 10 ppm^{2} when the temperature was entered into the regression.
The residual standard deviation was only 0.5 ppm which means that the modelled
curve follows the Mauna Loa curve for the yearly mean values perfectly.

Although the influence of the temperature on the sink flow rate is smaller in this calculation (1958-1998) than in my previous calculation (see "The Carbon Dioxide Thermometer", 1979 - 1998 at the Daly website), it is still statistically significant and the sign is the same.

Inserting today's emission value of 6.5 GtC/yr (only fossil fuels and cement production, deforestation not included) and the atmospheric concentration is 366 ppm, we obtain by the model a sink flow of:

total sink flow rate = 3.34 GtC/yr

The model gives the partial pressure forced sink according to:

part.press. forced sink flow rate = 2.929 GtC/yr

which means that about 90 % of the sink flow is directly controlled by the partial pressure, and only 10 % is absorbed somewhere according to a "constant airborne fraction rule", or probably mixed into the backmixed ocean surface layer.

As a great part of the partial pressure forced
sink may be biospheric, *the modeling of the biospheric response of increased
carbon dioxide may almost completely control the reliability of the global
carbon dioxide models when the models are used for predictions.*

My statistical sink flow model gives a prediction of abt. 580 ppm as atmospheric carbon content for 2100 when the mass balance differential equation is completed by the updated model for the total sink flow rate, the differential equation is solved analytically, boundary values for 2000 are inserted, and emission data according to the scenario IS92a are inserted, and no change of temperature is assumed (see Equations (14) (15) and (16) in "Statistical Analysis of Atmospheric Concentration of Carbon Dioxide" on the Daly website).

The confidence interval for my prediction cannot be calculated exactly due to the intercorrelation between the independent variables, but it is probably about 40 ppm. The IS92a scenario would thus give a concentration for the year 2100 between 540 and 620 ppm.

According to thesis by Holian, when taking only the standard deviation of the parameters in the IPCC model into account, but keeping the model structure unchanged, the 95 % confidence interval gives for IS92a a concentration for the year 2100 between 612 and 798 ppm.

**CONCLUSIONS**

The emission scenario IS92a is exaggerated.

- Statistical analysis indicate that the total
sink flow rate is primarily controlled by the atmospheric concentration
with means that Nature shows strong self-damping effects (negative
feedbacks) that is not fully taken into account in the TAR prediction.
It is of course possible that these feedbacks would decline to some extent
with increased carbon dioxide concentration *(Executive summary, Page
4 lines 24 and 40)* but the decline rate seems to be overestimated to
a great extent in recent models. The reliability of the *structure*
of both the ocean models and the models for biospheric sink are questionable.

- The TAR prediction of the future atmospheric carbon dioxide concentration for 2100 by the scenario IS92a seems to be calculated more than 100 ppm too high.

- The yearly variations in the increase rate of
atmospheric carbon dioxide is, at least to some extent, a degassing/absorbing
effect of different temperatures. The explanation that it is an effect
of reduced terrestrial uptake during El Nino years *(Executive
Summary, Page 3, line* *43)* is not
supported by the statistical analysis.

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