Introduction:
According to NASA, the earth has undergone numerous climate change cycles of glacial advance and retreat in the last 650,000 years. This natural climate change has been attributed to slight variations in Earth’s rotation and orbit that affect solar energy accumulation. However, today’s global warming trend has attracted much more concern than the natural cycles, because of its outlying high level of greenhouse gases, and the notion that humans have been contributing significantly to this trend since the Industrial Revolution. The evidence for rapid climate change includes the increased rate of the rising sea level, rise in global surface temperature, warming oceans, shrinking ice sheets, ocean acidification, glacial retreat, and extreme events including increased record temperatures and intense rainfall events.

Fig 1: NASA records atmospheric CO2 levels increasing above normal cyclic range after 1950. (1) More recently, analyses have been done that present data for the global carbon cycle and the effects of human greenhouse gas contribution. The carbon terms can be explained using the equation: Accumulation (of carbon in the system) = Input – Output + Generation. Input terms are sources of carbon (e.g. respiration of animals and plants), and output terms are sinks (e.g. respiration of trees or dissolution into the oceans). Plants use carbon to produce glucose, the vital sugar for supporting life, and eventually recycle the carbon atoms back into the atmosphere. Oceans are large sources/sinks for carbon, as they serve as a partition between the air and carbon that gets dissolved. Deep oceans are known to store enormous amounts of carbon, but for the sake of analysis they are thought to be separate from the system in focus. The generation term refers to the human greenhouse gas contribution. Burning fossil fuels for energy produces large amounts of greenhouse gas that may be accumulating in the atmosphere. According to NASA[2], the current carbon cycle values are:

In (GtC/yr)
Out
Generation
Accumulation
Oceans
97
100
6.5
2.5
Vegetation
119
120

These values are acceptable coming from NASA, and have also been verified by other sources[3] [4] with slight differences, although insignificant. The space program is able to accurately monitor atmospheric data using satellites that orbit Earth. They utilize “satellite measurements of surface winds and sea surface temperature, and future sea surface salinity measurements [2]” for CO2 flux estimations. Harvard University uses different strategies to achieve the same result. Using ice core carbon measurements [5], they can track the progression of CO2 trends throughout history. The accumulation of 2.5 Gigatonnes of CO2 per year seems small, but carbon dioxide tends to linger in the atmosphere for many years, so this accumulation will continue. The process appears to be a positive feedback loop, in that as the CO2 concentration increases so does the temperature, causing more CO2 to be released from oceans and frozen lands, further increasing the temperature and releasing even more carbon to be released of the atmosphere. The temperature rise and rate of CO2 release will increase in an exponential fashion. Some scientists believe the permafrost in northern frozen lands is at great risk of thawing and releasing enormous amounts of CO2:
Current research estimates that permafrost in the Northern Hemisphere holds 1,672 billion tons (Petagrams) of organic carbon. If just 10 percent of this permafrost were to thaw, it could release enough extra carbon dioxide to the atmosphere to raise temperatures an additional 0.7 degrees Celsius (1.3 degrees Fahrenheit) by 2100[6]. Also, as temperature increases, the solubility of carbon in the ocean decreases, so the effective absorption rate of the ocean will decrease. This will further contribute to the accumulation of carbon in the atmosphere.
In order to avoid complications in the carbon