{"id":11573,"date":"2025-04-15T12:57:05","date_gmt":"2025-04-15T11:57:05","guid":{"rendered":"https:\/\/klima-fakten.net\/?p=11573"},"modified":"2025-04-22T21:28:48","modified_gmt":"2025-04-22T20:28:48","slug":"shares-of-anthropogenic-and-natural-emissions-in-the-increase-in-co2-concentration","status":"publish","type":"post","link":"https:\/\/klima-fakten.net\/?p=11573&lang=en","title":{"rendered":"Shares of anthropogenic and natural emissions in the increase in CO2 concentration"},"content":{"rendered":"
\"image_print\"<\/a><\/div>\n\n\n

The publication „Improvements and Extension of the Linear Carbon Sink Model“<\/a> shows that the global natural effective carbon sink depends on both the CO\"_2\" concentration and the global (sea surface) temperature anomaly. A brief derivation of these relationships is provided below. In contrast to the cited publication, this investigation uses monthly deseasonalized CO2<\/sub> concentration data<\/a> \"C_i\", monthly global sea surface temperature data<\/a> \"T_i\", and monthly emission data \"E_i\" from interpolated yearly emission data<\/a> at consecutive months \"i\" .<\/p>\n\n\n\n

The conservation of mass or the continuity equation imply that the monthly concentration growth
\"G_i=C_i-C_{i-1}\"
necessarily results from the sum of anthropogenic emissions \"E_i\" and natural emissions \"N_i\" , reduced by the monthly absorptions \"A_i\" :
<\/a>

(1) <\/span>   <\/span>\"\begin{equation*}G_i = E_i + N_i - A_i\end{equation*}\"<\/p>
By definition natural emissions here necessarily mean all CO2<\/sub> emissions except the anthropogenic emissions<\/a>.
The measurable sink effect \"S_i\" is the difference between anthropogenic emissions \"E_i\" and the concentration growth \"G_i\":
<\/a>

(2) <\/span>   <\/span>\"\begin{equation*}S_i = E_i - G_i\end{equation*}\"<\/p><\/p>\n\n\n\n

\"\"
Figure 1: Emissions, concentration growth and sink effect(sink effect is plotted downwards).<\/figcaption><\/figure>\n\n\n\n

It follows directly from equation 1  that the directly measurable sink effect \"S_i\" includes not only absorptions by the oceans and plants, but implicitly also natural emissions:
\"S_i = A_i - N_i\"
Therefore, the sink effect is not identical to the sum of all absorptions, but only the proportion of absorptions that have not been compensated by natural emissions during the current month.<\/p>\n\n\n\n

The work \u201c Improvements and Extension of the Linear Carbon Sink Model<\/a> \u201d shows that the global sink effect \"S_i\" is represented described by an extended model of CO\"_2\" concentration and global sea surface temperature \"T_i\":<\/a>
<\/a>

(3) <\/span>   <\/span>\"\begin{equation*} \hat{S}_i = a\cdot C_{i-1} +b\cdot T_{i-6} + c\end{equation*}\"<\/p>
As a matter of fact, the model fits best when there is a time lag of 6 months between temperature and sink effect.
The simple sink model described in the paper \u201cEmissions and CO 2<\/sub>  Concentration\u2014An Evidence Based Approach<\/a> \u201d, which depends only on the CO2<\/sub> oncentration, is used for comparison:
<\/a>

(4) <\/span>   <\/span>\"\begin{equation*} \hat{S}_i = a'\cdot C_{i-1} + c'\end{equation*}\"<\/p><\/p>\n\n\n\n

\"\"
Figure 2 Modeling of the sink effect with a simple sink model (orange) and an extended sink model (green)<\/figcaption><\/figure>\n\n\n\n

Figure 2 shows that the simple model reproduces the trend very well, but that the fluctuations can only be described by the extended model, i.e., by including dependence on the sea surface temperature. The parameters for the best fit of the extended model with yearly data are\u00a0\"a=0,045\", \"b=-3.2\" ppm\/\u00b0C, \"c=-14\" ppm.<\/p>\n\n\n\n

The increase in concentration can also be modeled using equations  2<\/a>, 3<\/a>, and 4<\/a> respectively:
<\/a>

(5) <\/span>   <\/span>\"\begin{equation*}\hat{G}_i = E_i - a\cdot C_{i-1} - b\cdot T_{i-1} - c\end{equation*}\"<\/p>
This is shown in Fig. 3. For comparison, the reconstruction with the simple sink model is shown here again (green curve).
<\/p>\n\n\n\n

\"\"
Fig. 3: Measured concentration increase (blue), reconstructed with simple sink model (orange), reconstructed with extended sink model (green).<\/figcaption><\/figure>\n\n\n\n

Reconstruction of concentration, differentiation of the influence of emissions and temperature<\/h4>\n\n\n\n

From the concentration growth, the course of the CO\"_2\" concentration can be reconstructed using the initial CO\"_2\" concentration , in this case the concentration in December 1958. According to equation 5, the concentration growth is controlled by the external state variables of anthropogenic emissions and temperature. Together with the determined parameter, the term results in the change in natural emissions due to the temperature anomaly . It is therefore interesting to first compare the magnitudes of both emission sources. The unit of measurement for emissions is GtC, which is calculated by multiplying the quantities otherwise measured in ppm by 2.123.<\/p>\n\n\n\n

Figure 4 shows anthropogenic emissions since 1959 and natural emissions based on the sea surface temperature anomaly scale. Before 1975, temperatures and thus natural emissions, are predominantly negative. This is due to the arbitrary choice of the zero point of the anomaly temperature scale.
<\/p>\n\n\n\n

\"\"
Figure 4: Anthropogenic emissions and temperature-induced natural emissions<\/figcaption><\/figure>\n\n\n\n

It is noticeable that anthropogenic emissions are on average about 4 GtC larger than the natural emissions. Overall, natural emissions are numerically much larger, since the constant term of about 30 GtC (14 ppm \\cdot 2.123 GtC\/ppm) also represents natural emissions. According to equation 14 in\u00a0Improvements and Extension of the Linear Carbon Sink Model,<\/a>\u00a0these constant natural emissions define\u00a0the equilibrium concentration at the temperature anomaly 0\u00b0C; with current figures, this equilibrium concentration is 315 ppm. This is not the pre-industrial state, which has a temperature anomaly of -0.48\u00b0C.\u00a0Fig. 5 shows three selected model scenarios. In addition to the actually measured concentration values, the reconstruction with the actual temperature and emission trends (orange) is shown. As expected, this remains very close to the measured data.<\/p>\n\n\n\n

\"\"
Figure 5: Measured concentration (blue), impact of three scenarios on the concentration. See text.<\/figcaption><\/figure>\n\n\n\n

In addition, two further scenarios are presented:<\/p>\n\n\n\n