Phosphorus Module (54_phosphorus)


If activated, the phosphorus module can be used to estimate the major P-flows in the agricultural sector and to determine the dynmics of P-Pools in soils. It calculates also the costs connected to phosphorus fertilizers.



Name Description Unit A B
$sm\_years$ length of current time step years x
$vm\_prod\_reg$ regional aggregated production mio. ton DM x
$im\_attributes\_harvest$ attributes of harvested organs t DM WM Nr P K GJ per ton product x
$fm\_attributes\_residue\_ag$ Nutrient content of aboveground crop residues t nutrient per t DM x
$fm\_seed\_shr$ seed share relative to production dimensionless x
$vm\_prod\_res\_ag\_reg$ production of aboveground residues in each region mio. ton DM x
$vm\_res\_supply$ use of residues for different purposes dimensionless x
$vm\_area$ agricultural production area mio. ha x
$vm\_manure\_cropland$ Manure beingrecycled to croplands Tg nutrient x


Name Description Unit A B
$vm\_p\_fert\_costs$ costs for mineral fertilizers Mio USD x x

Interface plot

Figure 0: Information exchange among modules


(A) off (default)

Phosphorus fertilization costs set to 0:


no phosphorus, no limitations.

(B) normal_developer

The following P-flows are simulated by the module:
- P withdrawals by harvest: estimated as P content of crop harvest
- P withdrawals by harvest of aboveground residues: estimated as P content of AG residues (see 18_residues)
- P inputs by decaying recycled residues: estimated as P content of recycled residues (see 18_residues)
- P inputs by burned residues: estimated as P content of burned residues (see 18_residues), no combustion losses assumed
- P inputs by manure recycled to croplands: see 55_awms
- P inputs by fertilizers
- P inputs by release of plant-available P from the permanent P-Pool.
- P inputs by seed
- P inputs by weathering
- P losses by erosion
- P losses by leaching

Not represented are
- P withdrawals/inputs by belowground residues (no data available, and also not so important as belowground residues remain on field)
- P inputs by atmospheric deposition (just a minor issue)

Fertilizer costs are fertilizer consumption times price. The price comes from FAOSTAT import/export prices.
Alternatively, prices could also be used from Van Vuuren et al3 (2010).

Equation 2:

& vm\_p\_fert\_costs(i)\\
& =\\
& v54\_p\_fert\_reg(i) * f54\_p\_fert\_costs\_1995(i)\\

The model distinguishes implicitly (not explicitly) three pools: a dissolved (watersolved), a labile and a stable phosphorus (P) pool. All three pools exchange P.
Plants are endowed with a initial P amount through their seeds; all additional P they have to take up from the dissolved pool.

The model assumes smart farmers, whose main ambition is to always provide enough dissolved P to support plant growth, but also not to over-fertilize as this would waste valuable P. The dissolved P-pool is short-lived, but constantly replenished by the labile pool. The implicit aim of farmers is therefore to keep the labile pool at a level that provides enough dissolved P to support plant growth. We assume that plant uptake, dissolved and labile pool are proportional with an uptake-efficiency from the labile pool of 0.2 (Smil2 2000: 15%-25%, such that the target_labile_harvest_ratio is 1/0.2=5).

Crop harvest and residue harvest:
Harvested P is estimated based on crop-specific P contents of harvested organ and aboveground residues. These were aggregated with the spreadsheet
Data sources are Fritsch5(2007), FAO6(2004), Roy et al10 (2006), IFA et al11 (2007), Frederick et al12 (1986), USDA13 (2015), Chan and Lim14 (1980).
Belowground residues were not considered due to lack of data. See also module 18_residues.

Manure application to croplands:
Manure is estimated in the module 55_awms. So far no storage losses for P are assumed in AWMS, even though they may be considerable, for example in China (Liu et al1 2008).

Crop residues recycling:
We assume that all P in recycled and burned crop residues are returned to the labile pool. See module 18_residues.

Weathering is a rather minor and unimportant P source for managed lands. We assume it to be 1kg per ha, resulting in 1.5 Tg from weathering on the 1.5 Gha croplands, which is in a similar range as Smil2 (2000) assuming 2 Tg and Liu et al1 2008 assuming 1.6 Tg. Weathering enters the Labile Pool.

There is evidence that non-point source contribute a lot to aquatic sources.
Estimates range from 29-60% for major European rivers (Macleod9 2003).
Especially high leaching rates were reported for manure application (Macleod9 2003).
Also high soil P contributes to leaching (Macleod9 2003).
We therefore decided to apply a leaching factor to all inputs contributing to the labile pool.
Typical leaching rates in Europe are 3.5% (Liu et al1 2008). We assume that P inputs to the labile pool have to be 3.5% higher than P withdrawals from the labile pool.
Most inputs leach shortly after application (Hart7 2004), indicating that leaching should be subtracted before mineralization occurs.

The massive loss of soil matter through erosion events will mostly affect to stable P pool, as the largest amount of P is stored in the stable pool.
In a simplified way, we assume therefore that erosion depletes only the stable P pool.
As erosion events occur irregular and unexpectedly, we assume that farmers do not account for erosion P losses in their fertilization behavior.
Therefore, the subtraction of erosion losses from the stable pool is done after the optimization.
We estimate erosion based regional erosion rates.
For Sub-Saharan Africa, Latin America and India we assume 35 tons soil per ha lost to erosion, for the OECD 10 tons soil per ha, and for the rest 25 tons per ha (Liu et al1 2008).
The top 50cm of a ha cropland contain 0.5*100*100=5000qm, weighing 4000 tons (Liu et al1 2008).
This means that 0.25-0.875 percent of the stable P pool are lost to erosion.

Stable Pool to Labile pool:

Stable pool:
To estimate the stable pool initial condition, we make a spin-up from 1962 to 1995.
In 1960, we assume soils to be at natural state. We assume in the 4000 tons/ha topsoil an average P content of 0.5% according to Smil2 (2000) and Liu et al1(2008).
Additionally, we estimate organic carbon based on LPJ soil carbon estimates multiplied with a C : P ratio of 1:180. (C : N ratio of 15:1, N : P ratio 12:1)
We add inorganic fertilizers as reported by IFADATA8 (2011) for the period 1962 to 1995.
We subtract a share of the harvested crops; however, as feed and seed is recycled, we took regional demand shares used as food or material use to correct the net-harvest downward.
We did not consider crop residues, as most of them are directly recycled or recycled via manure back top cropland soils.
Finally we multiplied the erosion rates of 15-35 tons per ha with the 0.5% P content to get a rough estimate of erosion P losses in the past.
Resulting P-pools are about 1.66 (SAS) to 2.74 (EUR) tons P per ha.
Inorganic P is highest (about 3050 Tg globally), followed by organic P (about 500 Tg) and accumulated fertilizer (about 400 Tg). The largest withdrawals came for erosion (about 590 Tg) and harvested crops (about 110 Tg).
Relative to natural state, P pools decreased globally by about 10%, with highest increases in Europe and Pacific OECD and highest decreases in Africa and India (about-25%)

The constraints in the GAMScode look like follows:
The first constraint estimates the costs based on fertilizer consumption and fertilizer costs (costs were estimated based on export and import prices from FAOSTAT; an alternative source would be Van Vuuren et al3 (2010).

Equation 2:

& vm\_p\_fert\_costs(i) = v54\_p\_fert\_reg(i) * f54\_p\_fert\_costs\_1995(i)

The cropland soil constraint estimates the P fertilizer, required to provide a sufficient labile Pool for the desired production.

Equation 3:

& \sum_{kcr}(vm\_res\_supply(i,\text{"$recycle$"},kcr)*fm\_attributes\_residue\_ag(\text{"$p$"},kcr))\\
& + \sum_{kcr}( vm\_res\_supply(i,\text{"$burn$"},kcr)*fm\_attributes\_residue\_ag(\text{"$p$"},kcr))\\
& + vm\_manure\_cropland(i,\text{"$p$"})\\
& + v54\_p\_fert\_reg(i)\\
& + s54\_p\_weathering * \sum_{cell(i,j),kcr,w}(vm\_area(j,kcr,w))\\
& + p54\_p\_pool\_pre(t,i) * f54\_stable\_to\_labile\_share(i)\\
& =\\
& (1+(s54\_target\_labile\_harvest\_ratio-1) * s54\_labile\_to\_stable\_share)* \\
& \sum_{kcr}(\\
& vm\_prod\_reg(i,kcr)* im\_attributes\_harvest(\text{"$p$"},kcr)\\
& + vm\_prod\_res\_ag\_reg(i,kcr)*fm\_attributes\_residue\_ag(\text{"$p$"},kcr)\\
& - vm\_prod\_reg(i,kcr) * fm\_seed\_shr(i,kcr) * im\_attributes\_harvest(\text{"$p$"},kcr)\\
& ) * (1+s54\_p\_leaching\_share)\\

after optimization:

Equation 4:

& p54\_p\_pool(t,i) \\
& = \\
& p54\_p\_pool\_pre(t,i)+ \\
& sm\_years*( \\
& -(f54\_erosion(i)/s54\_topsoil) * p54\_p\_pool\_pre(t,i) \\
& - f54\_stable\_to\_labile\_share(i) * p54\_p\_pool\_pre(t,i) \\
& + (s54\_target\_labile\_harvest\_ratio-1) \\
& * s54\_labile\_to\_stable\_share \\
& * \sum_{kcr}( \\
& vm\_prod\_reg.l(i,kcr)* im\_attributes\_harvest(\text{"$p$"},kcr) \\
& + vm\_prod\_res\_ag\_reg.l(i,kcr)*fm\_attributes\_residue\_ag(\text{"$p$"},kcr) \\
& - vm\_prod\_reg.l(i,kcr) * fm\_seed\_shr(i,kcr) * im\_attributes\_harvest(\text{"$p$"},kcr) \\
& ))

Has not yet been published peer-reviewed.


Name Description Unit A B
$ic54\_years$ time between previous and current time step years x
$s54\_labile\_to\_stable\_share$ share of labile pool changing to stable pool share x
$s54\_target\_labile\_harvest\_ratio$ labile pool to harvest ratio targeted by the farmer ratio x
$s54\_p\_weathering$ plant available P from weathering t per ha x
$s54\_p\_leaching\_share$ Nr losses to leaching as percentage of Nr withdrawal share x
$s54\_topsoil$ topsoil tons per ha x
$s54\_cp\_ratio\_organic\_soil$ carbon phosphorus ratio of organic soils ratio x
$s54\_p\_content\_organic\_soil$ p content of organic soils share x
$p54\_p\_pool(t,i)$ soil phosphorus pool Tg P x
$p54\_p\_pool\_pre(t,i)$ soil phosphorus pool Tg P x
$p54\_land\_pre(j)$ land under cropping in previous timestep Mha x
$v54\_p\_fert\_reg(i)$ inorganic fertilizer application Tg Nutrients x
$vm\_p\_fert\_costs(i)$ costs for mineral fertilizers Mio USD x x
$f54\_stable\_to\_labile\_share(i)$ share of phorphorus in stable pool changing into labile pool share x
$f54\_p_fert\_reg\_1995(i)$ input of inorganic industrial fertilizer in 1995 Mt Nutrient x
$f54\_p\_fert\_costs_1995(i)$ input of inorganic industrial fertilizer in 1995 Mt Nutrient x
$f54\_erosion(i)$ Topsoil loss per hectar Mt soil per Mha x
$f54\_stable\_pool\_spinup(i)$ Topsoil loss per hectar Mt soil per Mha x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)


Benjamin Bodirsky, Veikko Heintz

See Also

[[mo:Coding Etiquette]] 51_nitrogen 55_awms


1 Liu, Yi, Gara Villalba, Robert U. Ayres, and Hans Schroder. 2008. “Global Phosphorus Flows and Environmental Impacts from a Consumption Perspective.” Journal of Industrial Ecology 12 (2): 229–47. doi:10.1111/j.1530-9290.2008.00025.x.

2 Smil, Vaclav. 2000. “Phosphorus in the Environment: Natural Flows and Human Interferences.” Annual Review of Energy and the Environment 25 (1): 53–88.

3 Van Vuuren, D.P., A.F. Bouwman, and A.H.W. Beusen. 2010. “Phosphorus Demand for the 1970-2100 Period: A Scenario Analysis of Resource Depletion.” Global Environmental Change In Press, Corrected Proof. doi:10.1016/j.gloenvcha.2010.04.004.

4 Bouwman, A. F., K. K. Goldewijk, K. W. Van Der Hoek, A. H. W. Beusen, D. P. Van Vuuren, J. Willems, M. C. Rufino, and E. Stehfest. 2011. “Exploring Global Changes in Nitrogen and Phosphorus Cycles in Agriculture Induced by Livestock Production over the 1900--2050 Period.” Livestock and Global Change Special Feature of Proceedings of the National Academy of Sciences, 1–6. doi:10.1073/pnas.1012878108.

5 Fritsch, Friedhelm. 2007. Nährstoffgehalte in Düngemitteln Und Im Erntegut; Für Die Düngeplanung; Für Nährstoffvergleiche. Bad Kreuznach: Dienstleistungszentrum Ländlicher Raum Rheinhessen-Nahe-Hunsrück.

6 FAO. 2004. Scaling Soil Nutrient Balances. FAO Fertilizer and Plant Nutrition Bulletin. Rome: Food and Agriculture Organization of the United Nations.

7 Hart, Murray R., Bert F. Quin, and M. Nguyen. 2004. “Phosphorus Runoff from Agricultural Land and Direct Fertilizer Effects.” Journal of Environmental Quality 33 (6): 1954–72.

8 IFADATA. 2011. “Statistical Database of the International Fertilizer Association (IFA).”

9 Macleod, Christopher, and Phil Haygarth. 2003. “A Review of the Significance of Non-Point Source Agricultural Phosphorus to Surface Water.” Scope Newsletter 51: 1–10.

10 Roy, R.N., A. Finck, G.J. Blair, and H.L.S. Tandon. 2006. Plant Nutrition for Food Security. FAO FERTILIZER AND PLANT NUTRITION BULLETIN 16. FAO.

11 IFA. 2007. “Fertilizer Best Management Practices. General Principles, Strategy for Theor Adoption and Voluntary Initiatives vs Regulations.” HomePage/LIBRARY/.

12 Frederick, D.J., H.A. Magdwick, M.F. Jurgensen, and G.R. Oliver. 1986. “Seasonal Development of a Young Plantation of Eucalyptus Nitens.” New Zealand Journal of Forestry Science 16 (1): 78–86.

13 USDA. 2015. “Crop Nutrient Tool | USDA PLANTS.”

14 Chan, K.W., and K.C. Lim. 1980. “Use of the Oil Palm Waste Material for Increased Production.” In Soil Science and Agricultural Development in Malaysia, 213–43. Kuala Lumpur.