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) 

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) 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.

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 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 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. 

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

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 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.

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).