Carbon cycling

A schematic representation of the FeliX model carbon cycle is shown below. Emissions from the energy and LULUCF sectors cycle through the atmosphere into the land sink (biosphere and pedosphere) and ocean.

The formulas for calculating gross flux are shown at left in the diagram below and discussed in the most recent FeliX publication, "Pathways for balancing CO2 emissions and sinks."

The parameterization of the carbon cycle is validated against the Coupled Climate Carbon Cycle Model Intercomparison Project (C4MIP), as shown in the table below.

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Biosphere Carbon Balance

In addition to atmospheric and oceanic pools of carbon, the FeliX model tracks terrestrial carbon stocks in the biosphere and humus. Atmospheric carbon concentrations are linked logarithmically to the net primary productivity (NPP) of the biosphere, a measure of carbon uptake due to plant growth:

FeliX equation for net primary productivity  NPP(t)      [Pg  C/year]  , an expression of the annual biospheric uptake of atmospheric carbon.  NPP'  represents initial (ca. 1900) net primary productivity and is equal to  85.2 PgC/year . A dimensionless biostimulation coefficient  ε = 0.35 , describes the impact of atmospheric carbon on productivity, and  C(t)  and  C' = 590 GtC  represent present and preindustrial atmospheric gross carbon content, respectively. 

FeliX equation for net primary productivity NPP(t) [PgC/year], an expression of the annual biospheric uptake of atmospheric carbon. NPP' represents initial (ca. 1900) net primary productivity and is equal to 85.2 PgC/year. A dimensionless biostimulation coefficient ε = 0.35, describes the impact of atmospheric carbon on productivity, and C(t) and C' = 590 GtC represent present and preindustrial atmospheric gross carbon content, respectively. 

In the BAU scenario, the above equation evaluates to a gross uptake of roughly 90 PgC in 2010. This estimate is consistent with leading comprehensive assessments of global terrestrial NPP [1,2].

The biosphere also represents a source of carbon emissions. Annually, some 97% of the gross uptake of carbon is returned after a characteristic residence time (T = 10.6 years) to the atmosphere either directly or through an intermediate humus stage (T = 27.8 years).

As a result, terrestrial biomes represented a net sink of magnitude 2.2 PgC per year in 2010. This figure is in line with recent estimates, and is attributed almost entirely to forest productivity [2]. 

Emissions from land use and land use change are calculated separately, and range from 1.0-1.5 PgC per year, or 10% of total emissions in the BAU scenario.

[1] Haberl, H., et al.: Quantifying and mapping the human appropriation of net primary production in earth’s terrestrial ecosystems, vol. 104, pp. 12942–12945 (2007) 

[2] Pan, Y., et al.: A large and persistent carbon sink in the world’s forests. Science 333, 988–993 (2011) 

Oceans: Heat & Carbon Sinks

Oceanic heat content anomaly, a measure of heat uptake by ocean water (depth < 700m). Historical data from NOAA is also plotted. The inner (darker) and outer (lighter) shaded regions indicate the consequences of high and low population projections and non-CO2 greenhouse gas emissions pathways (RCPs 2.6 and 8.5), respectively. CLICK TO ENLARGE

Oceans are incorporated into the FeliX model as important sinks for both heat and carbon dioxide. Atmospheric-cum-oceanic systems are stratified by water depth (d) into 5 layers: 

  1. Mixed layer - atmosphere + air/water interface (water to depth of 100 m)
  2. Deep layer 1 - 100 m < d < 400 m
  3. Deep layer 2 - 400 m < d < 700 m
  4. Deep layer 3 - 700 m < d < 2000 m
  5. Deep layer 4 -  d > 2000 m

Each layer tends toward thermal and chemical equilibrium with the layers above and below it at a characteristic rate. The plot seen above right presents model results for oceanic heat content anomaly for depths less than 700m (the mixed layer and deep layers 1 and 2) in yottajoules (J x 10E24). The system is calibrated to historical data from NOAA [1], also shown in dark blue. The inner (darker) shaded region propagates the consequences of alternative population scenarios. The outer (lighter) shaded region depicts the consequences of alternative concentration pathways for non-CO2 greenhouse gases.

The plot below translates this anomaly into the temperature change in each ocean layer through 2100. This is calculated from the volume of each layer and the heat capacity of seawater. The inner (darker) and outer (lighter) shaded regions indicate the consequences of high and low population projections and non-CO2 greenhouse gas emissions (RCPs 2.6 and 8.5), respectively.

Oceanic temperature change in the BAU scenario, stratified by depth.&nbsp; The inner (darker) and outer (lighter) shaded regions indicate the consequences&nbsp;of high and low population projections and non-CO2 greenhouse gas emissions pathways&nbsp;  (RCPs 2.6 and 8.5), respectively.

Oceanic temperature change in the BAU scenario, stratified by depth. The inner (darker) and outer (lighter) shaded regions indicate the consequences of high and low population projections and non-CO2 greenhouse gas emissions pathways (RCPs 2.6 and 8.5), respectively.

Total annual transfer of carbon [Pg] from the atmosphere to all ocean layers. CLICK TO ENLARGE

Carbon dioxide released into the atmosphere propagates through the ocean layers in the same way. The plot at left projects total (net) annual transfer of carbon from the atmosphere to oceans, while the plot below calculates the resulting carbon concentration in each deep ocean layer. In both plots, shaded regions indicate uncertainties corresponding to the 80% confidence interval for population growth projections.

Rising oceanic carbon concentration in the BAU scenario, stratified by ocean layer depth. The shaded regions indicate uncertainty corresponding to the 80% confidence interval for population growth projections.

Rising oceanic carbon concentration in the BAU scenario, stratified by ocean layer depth. The shaded regions indicate uncertainty corresponding to the 80% confidence interval for population growth projections.


[1] Levitus S., J. I. Antonov, T. P. Boyer, R. A. Locarnini, H. E. Garcia, and A. V. Mishonov, 2009. Global ocean heat content 1955-2008 in light of recently revealed instrumentation problems. GRL, 36, L07608, doi:10.1029/2008GL037155. (link)