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.

Primary Energy: Renewable Fuels

Wind, solar, and biomass energy are modeled explicitly in the FeliX model. Investment in and development of these energy sources is calibrated to the results of IIASA's Global Energy Assessment (2012) for RCP 6.0. As shown below, future development of renewable energies--especially solar & biomass--shows strong dependence on population growth. In the case of biomass, this dependence has important consequences for land use change: specifically, forest degradation.

Annual primary energy supply (in EJ) generated from wind, solar, and biomass for the period [2000-2100]. The shaded ranges for each energy stream indicate the effects of high and low population estimates. Projections are consistent with IIASA's Global Energy Assessment for RCP 6.0.

Annual primary energy supply (in EJ) generated from wind, solar, and biomass for the period [2000-2100]. The shaded ranges for each energy stream indicate the effects of high and low population estimates. Projections are consistent with IIASA's Global Energy Assessment for RCP 6.0.


Primary Energy: Fossil Fuels

Historical rates of consumption of coal, oil, and gas are used in the FeliX model to project likely future demand. In the plot below, the model-generated market shares of coal, gas, and oil are plotted along with historical market share (defined as a fraction of primary energy supply) from the IEA publication Key World Energy Statistics 2013. This data is used to calibrate energy market parameters, including most importantly the price elasticity of demand (PED) for each fuel.

PEDs for natural gas and oil are calibrated to historical data, and are consistent with meta-analyses of long-term price elasticities of demand [1].

Over the course of the century, the market share of fossil fuels is projected to fall from nearly 100% of primary energy supply in 1999 to 56% in 2100. During this period, total annual primary energy supply also doubles, implying that absolute production levels stay roughly constant (coal) or peak and fall (oil & gas) over this period, as shown in the plots below.

A Note on Peak Oil: The BAU scenario of the FeliX model may overestimate fossil fuel reserves in order to avoid externalities like severe Peak Oil in projecting future development. The baseline is premised on the notion that global agriculture, energy, and development continue (muddle) along, more-or-less as they have been. A corollary of this assumption is that it is possible to just continue along, something that Peak Oil precludes. Similarly, specific and transformational technological developments such as fusion or a breakthrough GMO are, though possible, externalities which distract from consideration of the ultimate consequences of business-as-usual.

[1] Espey, M.: Gasoline demand revisited: an international meta-analysis of elasticities. Energy Economics 20, 273–295 (1998) 

Primary Energy: Supply

Total energy demand, shown below as the black dashed line, is based on per capita demand (tied to GDP) and scaled to BAU population projections. This coupling is calibrated to data from Key World Energy Statistics (2013), a product of the International Energy Agency, plotted below in grey. 

Total annual primary energy demand in EJ/year and supply in the BAU scenario. The colored numbers at right list the production from each source in 2100, while the grey numbers above the demand curve indicate supply as a&nbsp;fraction of demand. Historical data from the IEA is plotted in grey.

Total annual primary energy demand in EJ/year and supply in the BAU scenario. The colored numbers at right list the production from each source in 2100, while the grey numbers above the demand curve indicate supply as a fraction of demand. Historical data from the IEA is plotted in grey.

Seen above, total annual energy demand is predicted to grow nearly 90% by the end of the century. During this period, fossil fuels lose market share due to the expansion of renewables, with absolute production levels of oil and gas peaking around 2050 and 2060, respectively.

Each of the seven fuels integrated into the FeliX model is modeled independently, according to anticipated prices and return on investment (fossil fuels discussed here and renewables here). This information is used to calculate emissions from energy generation

Irrigation

Two water management systems are implemented for agricultural land: irrigation and rain-feeding. The percentage of total agricultural land under irrigation is a non-linear function of GDP per capita:

FeliX formula for irrigated area  σ ,&nbsp;expressed as&nbsp; a&nbsp;fraction of agricultural area.  σMIN  and&nbsp;  σMAX  represent lower and upper (a priori)&nbsp;limits on irrigated area, and are defined to be 0 and 1, respectively.  GDPpc  is global&nbsp;productivity per capita (variable),&nbsp;and  GDP†  is a reference value calibrated to 120,000 (US$2005 per capita).

FeliX formula for irrigated area σ, expressed as a fraction of agricultural area. σMIN and σMAX represent lower and upper (a priori) limits on irrigated area, and are defined to be 0 and 1, respectively. GDPpc is global productivity per capita (variable), and GDP† is a reference value calibrated to 120,000 (US$2005 per capita).

The plot below traces the expansion of irrigation systems through 2100, explicitly displaying the percentage of agricultural land under irrigation (σ). This high-efficiency water management strategy is predicted to expand over 300% by the end of the century. Also shown is rain-fed area, which oscillates within a smaller range over the same period.

water_Agricultural_Water_Demand.png

For simplicity, average areal water consumption is primarily dependent on management system (binary) and secondarily linked to GDP per capita. Water use is not dependent on agricultural land subclassifications. Areal water demand is parameterized by GDP, growing with agricultural intensification according to the following equation:

FeliX formula for areal water demand (  
  
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   ω )  of irrigated ( I ) and rain-fed ( R ) land.&nbsp;Demand&nbsp;is scaled between&nbsp;  ω&nbsp; MIN (I,R) &nbsp;= (0.005, 0.005) and&nbsp;  ωMAX&nbsp;(    I,R)  = (0.05, 0.1), representing minimum and maximum water demand, respectively. &nbsp;  GDP†(I,R)  are  r  eference values&nbsp;calibrated to (4,000, 8,000)&nbsp;(US$2005 per capita).

FeliX formula for areal water demand (ω) of irrigated (I) and rain-fed (R) land. Demand is scaled between ω MIN (I,R) = (0.005, 0.005) and ωMAX (I,R) = (0.05, 0.1), representing minimum and maximum water demand, respectively.  GDP†(I,R) are reference values calibrated to (4,000, 8,000) (US$2005 per capita).

otal demand through 2100 is in the lower half of the plot above. Over this period, intensification and expansion lead to a 60% increase in total agricultural water demand.

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. 

Water & Agricultural Yields

One section of the FeliX model deals with water availability and usage, which carries consequences for agricultural yields and places exogenous limits on global (absolute) food production. The factor (γ) linking water availability to cropland yields is defined by the equation at right, where:

  • (Agricultural Water Withdrawal Fulfillment Factor) = 3.5 : a factor defining the strength of infrastructural limitations on agricultural water demand fulfillment.
  • σ (Maximum Water Withdrawal Rate: a variable function equivalent to Available Water Resources
  • θ (Agricultural Water Demand) : total agricultural water demand, based on extent of rainfed & irrigated land
SI_Agricultural_Water_Demand.png

In the above plot, annual Agricultural Water Demand is shown in green. Industrial and Domestic Water Demand (orange) are grouped together. Historical data from the UN International Hydrological Programme (IHP) is used to calibrate demand. The blue line represents IHP historical data on global annual supply, including withdrawals from surface and groundwater and non-conventional sources such as desalination [1].

Despite anticipated improvements in water use efficiency (due especially to irrigation), agricultural water demand grows 62% by 2100. Overall, water demand grows 75%, while supply is projected to grow only 54%. Unaddressed, this deficit limits the Maximum Water Withdrawal Rate for agricultural activities, with a double-digit negative impact on agricultural yields, as shown by the factors at the bottom of the plot.

[1] Shiklomanov, I.A., Rodda, J.C.: World water resources at the beginning of the twenty-first century. Technical report, International Hydrological Programme (IHP) of UNESCO (2003) 

Forests & Plantations

Forest land is an area of major interest, and an important factor in the evaluation of energy, agricultural, and climate change policies. The tension among agricultural, forest, and "other" lands is central to the FeliX model and has been discussed here.

Model results and FAO data on total forest area. At bottom, the expansion of managed forests and plantations (by 2 orders of magnitude)&nbsp;is shown in lime green. The demarcated regions around the&nbsp; Total Forest &nbsp;and  Managed Forest &nbsp;results indicate the consequences of high and low population scenarios.

Model results and FAO data on total forest area. At bottom, the expansion of managed forests and plantations (by 2 orders of magnitude) is shown in lime green. The demarcated regions around the Total Forest and Managed Forest results indicate the consequences of high and low population scenarios.

Shown above, total forest land is predicted to remain relatively stable at around 4 billion hectares through 2100. FAOSTAT historical data for the period [1990-2012] is also plotted. However, this general prediction belies several real threats to forest ecosystems and the valuable habitats they represent.

First, expansion of managed forests or plantations into formerly pristine areas replaces complex ecosystems with monocultures, with several important consequences: 

  1. Increased susceptibility to disease, climate change, drought, and invasive species
  2. Habitat destruction and biodiversity loss
  3. Potential soil degradation and carbon stock reduction

Secondly, through the current century, expansion of agricultural land is predicted to result in the destruction of nearly 700 million hectares of "other" natural habitats such as grasslands (discussed here). Though the model does not assign this burden to forests, they are vulnerable to being cleared for profit or even in the pursuit of food security. To wit, the high population scenario does predict both 10% deforestation and heightened demand for plantations by 2100.

Thirdly (and relatedly), forest area predictions are heavily dependent on agricultural yields. If yields fail to keep up with population growth, rising food demand (especially animal products) will make cleared land (i.e. pasture) more valuable even than heavily-managed forests. 

Deforestation rates are used in the calculation of land use change emissions

 

Agricultural Yields

Agricultural productivity is modeled explicitly in FeliX in order to quantify the likely effect of several important factors on crop yields. These factors are:

Each factor is modeled on a global scale, a level of aggregation which obscures the disparate and often divergent local manifestations of each of these factors. Because it is not possible to derive rigorous analytical solutions with global applicability to these parameters, the model assigns each a net positive or negative effect of conservative magnitude. Follow links in the list above for more details on individual factors.

The table below lists the six independent, dimensionless productivity factors which parametrize agricultural yields in the model. INT, land management, and carbon fertilization are determined to boost productivities, while water availability (or lack thereof), pollution, and climate change effects threaten to reduce yields. The right-most column lists the product of all six factors, by which baseline productivity (calibrated to 1.2E6 kCal/ha/year) is scaled annually.

Agricultural yields are calculated as the product of six independently-derived scaling factors in the FeliX model. These include input-neutral technologies (INT), land management systems, water availability, ozone and black carbon pollution, carbon fertilization effects (C Fert), and climate change. The first seven columns show&nbsp;the temporal evolution of individual factors, while the final column calculates the final product, by which baseline productivity is scaled.

Agricultural yields are calculated as the product of six independently-derived scaling factors in the FeliX model. These include input-neutral technologies (INT), land management systems, water availability, ozone and black carbon pollution, carbon fertilization effects (C Fert), and climate change. The first seven columns show the temporal evolution of individual factors, while the final column calculates the final product, by which baseline productivity is scaled.

The figure below translates productivity factors into cropland yields, which represent an aggregate over all global regions as well as crop types. The columns at bottom depict the baseline population projection, while the grey bars display present and future cropland yield projections. Based on historical data, these projections from an independent analysis parametrize crop yields as a function of GPD [1]. They represent the range of likely productivity levels due to the spread of existing INTs and the development of additional yield-enhancing technologies.

The green curve&nbsp;represents&nbsp;global, aggregate cropland yields through 2100 in the FeliX model. The shaded region propagates the effects of high and low population estimates, which affect yields indirectly through&nbsp;water availability. The gray bars note econometric predictions of yield growth due to&nbsp;INT and land management (fertilizer use). At bottom,&nbsp;median population projections are also shown.&nbsp;

The green curve represents global, aggregate cropland yields through 2100 in the FeliX model. The shaded region propagates the effects of high and low population estimates, which affect yields indirectly through water availability. The gray bars note econometric predictions of yield growth due to INT and land management (fertilizer use). At bottom, median population projections are also shown. 

1. Herrero, M., Havlik, P., McIntire, J., Palazzo, A. and Valin, H. 2014. African Livestock Futures: Realizing the Potential of Livestock for Food Security, Poverty Reduction and the Environment in Sub-Saharan Africa. Office of the Special Representative of the UN Secretary General for Food Security and Nutrition and the United Nations System Influenza Coordination (UNSIC), Geneva, Switzerland, 118 p.

Agricultural Land

Land categorized as "agricultural" is subdivided into the following classes:

Schematic of Agricultural Land subdivisions in the model.       (Click to enlarge)

  • arable land
  • permanent crops
  • permanent meadows and pastures

Arable land and permanent crops can be used to produce food, feed, or energy crops, while permanent meadows and pastures are used only for feed production. The BAU scenario is calibrated to historical data available on FAOSTAT and shown in grey below.

Permanent pastures &amp;&nbsp;meadows (top) and arable land &amp; permanent crops&nbsp;(bottom)&nbsp;in the BAU scenario.&nbsp;

Permanent pastures & meadows (top) and arable land & permanent crops (bottom) in the BAU scenario. 

As shown in the plot above and here, the model predicts an end to the steady expansion of agricultural land seen in the second half of the last century: through 2050, growth in demand for vegetal and animal products is likely to be satisfied by agricultural intensification (discussed here).

After midcentury, however, the cumulative effects of fertilizer saturation, water scarcity, and ozone pollution may cause a stagnation in agricultural yields. As demand for food (in particular, animal products) continues to grow, agricultural land may begin to expand indefinitely after 2050 at the expense of natural habitats.

Land Use I

Land in the FeliX model is distributed among four mutually exclusive and collectively exhaustive categories: agricultural, forest, urban/industrial, and "other".

Agricultural, forest, and other land for the period&nbsp;1950-2100 shown with historical&nbsp;data available from the FAO.&nbsp;Annotations&nbsp;note the&nbsp;extent of each type of land in 2010 and 2100.&nbsp; Urban/industrial land represents an additional (static) 40 Mha.

Agricultural, forest, and other land for the period 1950-2100 shown with historical data available from the FAO. Annotations note the extent of each type of land in 2010 and 2100. Urban/industrial land represents an additional (static) 40 Mha.

Each category is calibrated to FAOSTAT data on a global level (available for 1961-2010 for agricultural and 1990-2012 for forest and other land). Though not on a geographically explicit basis, land can be repurposed--most notably, due to changes in demand for agricultural land.

Between 2010 and 2100, growth in global population and per capita GDP leads to a 17% expansion in agricultural land (a collective label for arable land, permanent crops, and permanent meadows & pastures). This expansion is driven by both supply- and demand-side factors. 

Schematic diagram of land use in the model.                   (Click to enlarge)

Because land is a finite resource, transitions are zero-sum (modulo discrepancies due to rounding above). In the BAU scenario, agricultural land expands at the cost of natural habitats included in forests and "other" land (i.e. grassland). Though this burden appears to fall entirely on the latter category, the general category of "forest" includes in this case both natural and managed plots, masking a significant threat of deforestation or degradation (a trend which will discussed in another entry).

Global GDP

Along with population, global economic productivity (GDP) factors into most sectors of the FeliX model on absolute and per capita bases. Global GPD is shown below for the period 1950 through 2100 along with SSP projections.

Global GDP in bilions of US dollars (2005): historical data from the GGDC is shown in grey, and the projections associated with SSPs 1-5 are shown in dotted lines. The shaded red region indicates the absolute shift in GDP due to high and low population estimates.

Summary Statistics for gross world product (GWP) fit to historical data on absolute and per capita bases. &nbsp; (Click to enlarge)

Summary Statistics for gross world product (GWP) fit to historical data on absolute and per capita bases.   (Click to enlarge)

The red solid line in the plot represents the FeliX BAU prediction, which is calibrated to historical data from the Maddison Project, a database developed and maintained by the Groningen Growth and Development Centre at the University of Groningen in the Netherlands. SSP projections, shown in dotted lines, are used for validation of the model results.

The BAU scenario uses the central value for population growth (10.6 billion in 2100), while the red shaded region shows the sensitivity of GDP to the 80% confidence interval (CI) for fertility rates (discussed in a previous post). On an absolute basis, GDP is correlated with population (more precisely, the number of able-bodied adults comprising the global workforce), and the outer bounds of the population 80% CI translate to ±9% effect on GDP.

GDP is shown below on a per capita basis in order to isolate the predicted additional contribution of global development to economic growth:

Per capita GDP in&nbsp;US$(2005) for the period 1900-2100.

Per capita GDP in US$(2005) for the period 1900-2100.

Historical data again comes from the GGDC, and the SSP projections are again displayed in dotted lines. This plot shows a much smaller dependence on population estimates, indicating that global development on a per capita basis is largely independent of fertility rates in the FeliX model.

Population I

The population sector of the model drives the evolution of every other parameter of the model, and is in turn affected by other sectors via their aggregate effects on birth rates and life expectancies.

The world population is divided by age into three categories: 0 to 14 years, 15 through 64 years, and 65 plus years. The global workforce is assumed to be 75% of the middle-aged group. Population development is affected by factors including GDP, education, food security, and environmental factors including pollution levels, water quality, and biodiversity. The FeliX global population projection, shown below in red, is calibrated to historical data from the FAO (shown including FAO extrapolations to future population in grey).  

Global population in the BAU scenario of the FeliX model from 1950-2100. The model is calibrated to historical data from FAOSTAT, shown in grey. For comparison, the range of predictions as parameterized by the Shared Socioeconomic Pathways (SSP 1-5) are also shown through 2100.

Summary Statistics (Click to enlarge)

In the BAU scenario, the world population is expected to peak just above 10.6 billion people near the end of this century. For comparison, all five SSP projections are also shown through 2100. The specific factors informing the FeliX population projections will be detailed in a subsequent post.

Population growth in this model is validated by comparison to figures from the World Population Prospects: The 2012 Revision, and the associated Science paper "World population stabilization unlikely this century", both publications of the UN Department of Economic and Social Affairs (UNDESA). This research identifies a median expectation of 10.9 billion, adding:

There is an 80% probability that world population, now 7.2 billion people,                                      will increase to between 9.6 billion and 12.3 billion in 2100.

Because global population numbers are central to every other sector in the FeliX model, we use the high and low projections from UNDESA probabilistic projections (representing the 80% confidence interval) to examine the sensitivity of other figures of merit to the full range of likely fertility rates.