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) 

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 , 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).

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. 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  r  eference values calibrated to (4,000, 8,000) (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] 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.

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) 

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).