# Evaluating the Effectiveness of Natural Carbon Sinks Through a Temperature-Dependent Model
## 2 Materials and Methods
### Separating Absorptions and Natural Emissions
#### 2.2.2 Estimating the Temperature Effect on Natural Emissions from Land Plants and Oceans  
As stated above, photosynthesis is the primary driver of the following processes of plant decay and soil respiration. In a recent article, it was confirmed that the Gross Primary Production (GPP) in absolute numbers is 5% larger than soil respiration [6]. In [32], the Net Primary Production (NPP) during the time interval from 1982 to 1999 was investigated. They found a yearly increase of 3.4 Gtc of NPP over 18 years. During this time, the temperature increased by 0.25 \({}^{\circ}\)C. This would imply a 13.6 Gtc increase of bound carbon per \({}^{\circ}\)C and year. According to the article, this was not only due to the increase of CO\({}_{2}\) fertilization but also, to a large degree, to the reduction of cloud cover over the Amazon rainforest and an increase in solar radiation, which directly influences photosynthetic processes more than CO\({}_{2}\) concentration and temperature. A later reported decline of yearly NPP by 0.55 Gtc in the years 2000-2009 [33] adjusts this exorbitantly high yearly number to 2.85 Gtc/0.5 \({}^{\circ}\)C = 5.7 Gtc/\({}^{\circ}\)C.  
According to [34], during the 19 years from 1989 to 2008, the natural emissions from soil respiration \(R_{S}\) have risen by 0.1 Gtc per year, i.e., 1.9 Gtc during the whole investigation period. During this time, the global temperature has risen by 0.3 \({}^{\circ}\)C see, e.g., Figure 4. Therefore, we have a temperature dependency of \(R_{S}\) per year:  
\[\frac{\Delta R_{S}}{\Delta T}=\frac{1.9}{0.3}\;\text{Gtc}/^{\circ}\text{C}=6.33 \;\text{Gtc}/^{\circ}\text{C}\]  
An \(R_{S}\) increase of 3.3 Gtc/\({}^{\circ}\)C per year is reported by [35]. According to [36], there is considerable uncertainty in the determination of the temperature sensitivity of soil respiration.  
Regarding the temperature dependence of the emissions from the oceans, we begin with the baseline of yearly emissions from oceans of 80-100 Gtc [1]. According to [37], the relative change in CO\({}_{2}\) partial pressure in seawater is 0.0423 per \({}^{\circ}\)C for a wide range of  
Figure 4: Monthly global sea surface temperature time series [12] and deseasonalized monthly global sea surface temperature data.  
temperatures from 2 \({}^{\circ}\)C to 28 \({}^{\circ}\)C. Therefore, the yearly increase in terms of absolute mass would be in the range between 80 GtC - 0.042/\({}^{\circ}\)C = 3.4 GtC/\({}^{\circ}\)C and 100 GtC - 0.042/\({}^{\circ}\)C = 4.2 GtC/\({}^{\circ}\)C. It is noteworthy that [PERSON] in the \"Conclusions\" of [9] agrees in principle with yearly rates ranging from 3 to 5 GtC/\({}^{\circ}\)C, but he restricts the validity of this process to just a few subsequent years, most likely as a consequence of his assumption that the temperature time derivative is the driving parameter, an assumption I do not share.  
Adding the collected evidence for temperature dependency of both soil respiration and ocean emissions results in a total range from 3.3 + 3.4 = 6.7 GtC/\({}^{\circ}\)C to 6.3 + 4.2 = 10.5 GtC/\({}^{\circ}\)C per year. This is based only on a few investigations, requiring further research. But it gives an indication of what we can realistically expect.