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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Temperature Change

The climate sector of the FeliX model integrates the results of all other sectors and translates them into global average temperature change in the atmosphere and oceans.

Total radiative forcing [W/m*m] due to projected atmospheric concentrations of greenhouse gases. Historical data and RCP projections from IIASA's RCP database. [CLICK TO ENLARGE}

The model divides these systems into five separate reservoirs of heat and carbon (one atmospheric/upper ocean + four deep oceanic layers), each of which is in thermal contact with the reservoir layers above and below it. Each layer is characterized by a heat capacity (C, Wikipedia) and a heat transfer coefficient (h, Wikipedia), which determine the propagation of heat through the total system. These parameters are defined and discussed in the FeliX Model Report [pp. 84-92].

The radiative forcing due to CO2, N2O, CH4, and other greenhouse gases is calculated from the atmospheric concentration of each of these pollutants. Radiative forcing from carbon dioxide is based on endogenous predictions, while all others are set to RCP 4.5. Total atmospheric radiative forcing is shown above at right along with RCP projections and historical data from IIASA's RCP database.

The heat trapped by greenhouse gases is either transferred to deep ocean layers or results in global atmospheric temperature change. The plot below projects atmospheric temperature change relative to the global preindustrial average along with historical data from the NASA Goddard Institute for Space Studies (GISS) and the Hadley Center's Climactic Research Unit. For comparison, the range of warming associated with each RCP is shown at right. Historical data is used to calibrate the model, while RCP projections are used for scenario validation.

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)

Atmospheric Carbon Concentration

Net flux of carbon dioxide into the atmosphere results in rising atmospheric concentration, which is calculated endogenously in the FeliX model. Gross emissions are released during primary energy production; as a result of LULUC; and during to the natural decay of biomass and humus.

Carbon is withdrawn from the atmosphere in the following processes:

All of these fluxes are factored into the calculation of atmospheric carbon dioxide concentration, which is projected to rise monotonically through 2100. The BAU scenario result is shown below with RCP projections as well as the consequences of high and low population predictions (shaded red). Historical data, shown in grey, is taken from the CDIAC [1].

 Atmospheric concentration [ppm] in the BAU scenario and RCP projections.&nbsp;

Atmospheric concentration [ppm] in the BAU scenario and RCP projections. 

[1] Etheridge, D.M., Steele, L.P., Langenfelds, R.L., Francey, R.J., Barnola, J.-M., Morgan, V.I. 1998. Historical CO2 records from the Law Dome DE08, DE08-2, and DSS ice cores. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A