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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Carbon Dioxide Fertilization Effect

 FeliX equation for magnitude of fertilization effect (  γ ) of atmospheric carbon dioxide concentration on agricultural yields.   γmax = 0.1  (or 10%)   represents the maximum effect of atmospheric carbon .  Crat  represents the ratio of present to preindustrial atmospheric carbon   at each time step.

FeliX equation for magnitude of fertilization effect (γ) of atmospheric carbon dioxide concentration on agricultural yields. γmax = 0.1 (or 10%) represents the maximum effect of atmospheric carbon. Crat represents the ratio of present to preindustrial atmospheric carbon at each time step.

Rising atmospheric carbon dioxide concentrations have a moderate fertilizing effect on agricultural yields by increasing the availability of this essential input for photosynthesis and promoting water use efficiency [1].

In the equation at right, as the present/preindustrial ratio of atmospheric carbon rises monotonically from unity--doubling by 2100 in the BAU scenario--the magnitude of this effect also grows (up to 4% in BAU). With this (potentially) conservative estimate, the FeliX model reflects the loose consensus that carbon fertilization has or will have a net positive effect of magnitude less than 10%.

[1] Baldos, U.L.C., Hertel, T.W.: Global food security in 2050: the role of agricultural productivity and climate change. Aust. J. Agr. Resour. Ec. 58, 1–18 (2014) 

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) 

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

Gross Carbon Emissions

FeliX calculates associated gross emissions for each energy source directly from model predictions of primary energy demand and consumption. The plot below illustrates the contribution of each to total annual emissions, listing for convenience the specific values for 2010 and 2100. Overall, gross annual emissions are predicted to rise 66% between 2010 and 2100 in the BAU scenario.

 Gross annual emissions in Pg C from land use and land use change;&nbsp;and combustion of coal, oil, gas, and renewable energies (biomass).

Gross annual emissions in Pg C from land use and land use change; and combustion of coal, oil, gas, and renewable energies (biomass).

Historical data from the Carbon Dioxide Information Analysis Center (CDIAC) is shown for land use change, coal, oil, and gas in bold for the period [1900,2005]. This data is used to validate model projections, not for calibration.

The table at right lists emissions intensities for each of the carbon-emitting fuels represented in the model. These are consensus figures, and are not tuned to achieve agreement between IEA energy data and CDIAC emissions figures.

Gross emissions from renewable energies are equivalent to 107% of the carbon stored in harvested biomass (50% carbon by mass plus a penalty per unit weight for agricultural input, harvesting, and transport). Net emissions are significantly reduced due to prior uptake of atmospheric carbon in biomass increments.

Land Use Emissions

Emissions from land use & land use change (LULUC) contribute to total annual emissions in the FeliX model. LULUC emissions include agricultural inputs--especially fertilizers--as well as deforestation.

Agricultural emissions, shown below in brown, are predicted to rise steadily through 2100 due to the expansion of agricultural land as well as increased use of fertilizers. This parameter is calibrated in the model to historical data on agricultural emissions from the FAO.

 Carbon emissions [PgC/yr]&nbsp;from land use/land use change (LULUC) are represented by the shaded grey region. The specific contribution to LULUC emissions from agricultural land use (especially fertilizers) is calibrated to historical data from the FAO and shown in brown. The dark&nbsp;gray and brown shaded regions propagate&nbsp;the effects of high and low&nbsp;population estimates.

Carbon emissions [PgC/yr] from land use/land use change (LULUC) are represented by the shaded grey region. The specific contribution to LULUC emissions from agricultural land use (especially fertilizers) is calibrated to historical data from the FAO and shown in brown. The dark gray and brown shaded regions propagate the effects of high and low population estimates.

The second component of LULUC emissions is deforestation, which is determined endogenously in the model (is not calibrated to historical data). Deforestation is estimated to have contributed roughly 1 PgC in annual emissions for most of the period 1950-2000. For the next few decades, modest afforestation is predicted to partially offset agricultural emissions through the increase of forest carbon stocks.

Near the end of the century, however, competition for land is predicted to accelerate deforestation, resulting in a nearly-twofold increase in total LULUC emissions. This result is highly dependent on population estimates, as shown by the wide dark-grey shaded region.

Historical data from the CDIAC on total land use emissions is used as a check on model results.