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Model description of Nutrients


The IMAGE-Global Nutrient Model (GNM) is a global distributed spatially explicit model using hydrology as the basis for describing nitrogen (N) and phosphorus (P) delivery to surface water and transport and in-stream retention in rivers, lakes, wetlands and reservoirs. IMAGE-GNM is coupled to the PCR-GLOBWB global hydrological model (Van Beek et al., 2011). In the IMAGE-GNM model, grid cells receive water with dissolved and suspended N and P from upstream grid cells; inside grid cells, N and P are delivered to water bodies via diffuse sources (surface runoff, shallow and deep groundwater, riparian zones; litterfall in floodplains; atmospheric deposition) and point sources (wastewater); N and P retention in a water body is calculated on the basis of the residence time of the water and nutrient uptake velocity; subsequently, water and nutrients are transported to downstream grid cells.


Urban wastewater contains N and P emitted by households and industries that are connected to a sewerage system, and households with sanitation but without a sewerage connection.

N discharges to surface water (EswN in kg per person per year) are calculated as follows (Van Drecht et al., 2009; Morée et al., 2013):

Formula 1: Human nutrient emissions


  • EhumN is human N emissions (kg per person per year),
  • D is the proportion of the total population connected to public sewerage systems (no dimension),
  • R N is the overall removal of N through wastewater treatment (no dimension).

Total P emissions to surface water are calculated in a similar way, but also include estimates of P emissions to surface water resulting from the use of P-based dishwasher and laundry detergents. Nutrient removal by wastewater treatment R is based on the relative contribution of four classes of treatment (none, primary, secondary and tertiary treatment). D is calculated from the proportion of households with improved sanitation. D and R by treatment class are scenario variables.

Soil nutrient budget

The soil budget approach (Bouwman et al., 2009; Bouwman et al., 2013c) considers all N and P inputs and outputs for IMAGE grid cells. N input terms in the budgets include application of synthetic N fertiliser (Nfert) and animal manure (Nman), biological N fixation (Nfix), and atmospheric N deposition (Ndep). Output terms include N withdrawal from the field through crop harvesting, hay and grass cutting, and grass consumed by grazing animals (Nwithdr).

The soil N budget (Nbudget) is calculated as follows:

Formula 2: The soil N budget.

The same approach is used for P, with input terms being animal manure and fertiliser. The soil nutrient budget does not include nutrient accumulation in soil organic matter for a positive budget (surplus), or nutrient depletion due to soil organic matter decomposition and mineralisation. With no accumulation, a surplus represents a potential loss to the environment. For N this includes NH3 volatilisation (see Component Emissions), denitrification, surface runoff and leaching. For P, this is surface runoff.

For spatial allocation of the nutrient input to IMAGE grid cells, grass and the crop groups in IMAGE (temperate cereals, rice, maize, tropical cereals, pulses, roots and tubers, oil crops, other crops, energy crops) and grass are aggregated to five broad groups. These groups are grass, wetland rice, leguminous crops, other upland crops and energy crops for both mixed and pastoral production systems (see Livestock systems).


Fertiliser use is based on nutrient use efficiency, representing crop production in kilograms of dry matter per kilogram of fertiliser N (NUE) and P (PUE). NUE and PUE vary between countries because of differences in crop mix, attainable yield potential, soil quality, amount and form of N and P application and management. In constructing scenarios on fertiliser use, data on the 1970–2005 period serve as a guide to distinguish countries with an input exceeding crop uptake (positive budget or surplus) from countries with a deficit. Generally, farmers in countries with a surplus are assumed to be increasingly efficient in fertiliser use (increasing NUE and PUE). In countries with nutrient deficits, an increase in crop yields is only possible with an increase in the nutrient input. Initially, this will lead to decreasing NUE and PUE, showing a decrease in soil nutrient depletion due to increased fertiliser use.


Total manure production is computed from animal stocks and N and P excretion rates (Figure Flowchart, middle). IMAGE uses constant N and P excretion rates per head for dairy and non-dairy cattle, buffaloes, sheep and goats, pigs, poultry, horses, asses, mules and camels. Constant excretion rates imply that the N and P excretion per unit of product decreases with increased milk and meat production per animal.

N and P in the manure for each animal category are spatially allocated to mixed and pastoral systems. In each country and system, the manure is distributed over three management systems: grazing; storage in animal housing and storage systems; and manure used outside the agricultural system for fuel or other purposes. The quantity of manure assigned to grazing is based on the proportion of grass in feed rations (Figure Flowchart, middle).

Stored animal manure available for cropland and grassland application includes all stored and collected manure, excluding ammonia volatilisation from animal houses and storage systems. In general, IMAGE assumes that 50% of available animal manure from storage systems is applied to arable land and the rest to grassland in industrialised countries. In most developing countries, 95% of the available manure is spread on croplands and 5% on grassland, thus accounting for the lower economic importance of grass compared to crops in these countries. In the European Union, maximum manure application rates are 170 to 250 kg N per ha , reflecting current regulations.

Biological N2 fixation

Data on biological N2 fixation by leguminous crops (pulses and soybeans) are obtained from the N in the harvested product (see nutrient withdrawal) following the approach of (Salvagiotti et al., 2008). Thus any change in the rate of biological N2 fixation by legumes is the result of yield changes for pulses and soybeans. In addition to leguminous crops, IMAGE uses an annual rate of biological N2 fixation of 5 kg N per ha for non-leguminous crops and grass, and 25 kg N per ha for wetland rice. N fixation rates in natural ecosystems were based on the low estimates for areal coverage by legumes (Cleveland et al., 1999) as described by Bouwman et al. (Bouwman et al., 2013a).

Atmospheric deposition

Deposition rates for historical and future years are calculated by scaling N deposition field for 2000 (obtained from atmospheric chemistry transport models), using emission inventories for the historical period and N gas emissions in the scenario considered. IMAGE does not include atmospheric P deposition.

Nutrient withdrawal

Withdrawal of N and P in harvested products is calculated from regional crop production in IMAGE and the N and P content for each crop, which is aggregated to the broad crop categories (wetland rice, leguminous crops, upland crops and energy crops). IMAGE also accounts for uptake by fodder crops. N withdrawal through grass consumption and harvest is assumed to amount to 60% of all N input (manure, fertiliser, deposition, N fixation), excluding NH3 volatilisation. P withdrawal through grazing or grass cutting is calculated as a proportion of 87.5% of fertiliser and manure P input. The rest is assumed to be lost through surface runoff. In calculating spatially nutrient withdrawal, a procedure is used to downscale regional crop production data from IMAGE to country estimates for nutrient withdrawal based on distributions in 2005.

Nutrient environmental fate

Nutrient losses from the plant-soil system to the soil-hydrology system are calculated from the soil nutrient budgets (Bouwman et al., 2013a). For N, the budget is corrected for ammonia volatilisation from grazing animals and from fertiliser and manure spreading (see Component Emissions). P not taken up by plants is generally bound to soil particles, with the only loss pathway being surface runoff. N is more mobile and is transported via surface runoff and through soil, groundwater and riparian zones to surface water.

Soil denitrification and leaching

Denitrification is calculated as a proportion of the soil N budget surplus based on the effect of temperature and residence time of water and nitrate in the root zone, and the effects of soil texture, soil drainage and soil organic carbon content. In a soil budget deficit, IMAGE assumes that denitrification does not occur. Leaching is the complement of the soil N budget.

Groundwater transport, surface runoff and denitrification

Two groundwater subsystems are distinguished. One is the shallow groundwater system representing interflow and surface runoff for the upper 5 m of the saturated zone, with short travel times for the water to enter local surface water at short distances or to infiltrate the deep groundwater system. The other is the deep system with a thickness of 50 m with generally long travel times draining to larger streams and rivers. Deep groundwater is assumed to be absent in areas of non-permeable, consolidated rocks or in the presence of surface water. Denitrification during groundwater transport is based on the travel time and the half-life of nitrate. The half-life depends on the lithological class (1 year for schists and shales containing pyrite, 2 years for alluvial material, and 5 years for all other lithological classes). Flows of water and nitrate from shallow groundwater to riparian zones are assumed to be absent in areas with surface water bodies, where the flow is assumed to bypass riparian zones flowing directly to streams or rivers.

Denitrification in riparian areas

The calculation of denitrification in riparian areas is similar to that in soils, but with two differences:

  1. a biologically active layer of 0.3 m thickness is assumed instead of 1 m for other soils;
  2. the approach includes the effect of pH on denitrification.

Nutrients from vegetation in floodplains

NPP from the LPJ model Carbon cycle and natural vegetation for wetlands and floodplains are used. Part of annual NPP is assumed to be deposited in the water during flooding, and where flooding is temporary, the litter from preceeding periods is assumed to be available for transport in the flood water. 50% of total NPP is assumed to end in the surface water.

Other direct sources of nutrients

Other sources include aquaculture, weathering and atmospheric deposition. Deposition is from the same data as used for the land nutriënt budgets. Aquaculture is taken from data from two recent studies (Bouwman et al., 2011; Bouwman et al., 2013c), and weathering. The calculation of P release from weathering is based on a recent study (Hartmann et al., 2014) which uses the lithological classes distinguished by (Dürr et al., 2005). The lithological classes are available on a 5 by 5 minute resolution, hence the weighted average P concentration within each 0.5 by 0.5 degree grid cell is calculated.

In-stream nutrient retention

The water that enters streams and rivers through surface runoff and discharges from groundwater and riparian zones is routed through stream and river channels, and passes through lakes, wetlands and reservoirs. The history of the construction of reservoirs during the 20th century is based on data from (Lehner et al., 2011). The nutrient retention in each of these systems is calculated on the basis of the nutrient spiralling ecological concept, which is based on residence time and temperature as described in (Beusen et al., 2014; Beusen et al., 2015).