Numerical Simulation, An Art of Prediction, Volume 2 - Jean-François Sigrist

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in which a culture can potentially develop”.

      Performance data for soybeans, or any other crop, around the world can predict areas suitable for cultivation in other regions, whose climatology – and other factors, such as soil quality – are similar. Based on global data, the prediction is still limited to regions the size of a French department. The models also reveal the likely evolution trends of these areas with climate change.

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      Figure 1.13. Calculation of wheat crop yields in France and worldwide: the figure represents yield increases estimated by statistical methods, in different countries of the world and for the French departments. The unit is the ton of wheat per hectare cultivated and per year [MIC 13]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip.

      Fertilizers are organic substances, of plant or animal origin, or mineral substances (synthesized by the industrial fixation of atmospheric nitrogen) intended to provide plants with nutrient supplements. They contribute to improving their growth and increasing the yield and quality of production.

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      Figure 1.14. Fertilizers promote plant growth but their overintensive use has long-term harmful effects on the environment or may be dangerous for human health

      (source: www.123rf.com/)

      COMMENT ON FIGURE 1.14.– Often used in a mixture, fertilizers are mainly composed of three elements: nitrogen contributes to the vegetative development of all overground parts of the plant, phosphorus strengthens their resistance and participates in root development, and potassium promotes flowering and fruit development. They also provide plants with complementary elements (such as calcium or magnesium) and trace elements (such as iron, manganese, sodium or zinc), useful for plant life and development. Their use dates back to the early days of agriculture and, nowadays, the development of the chemical industry encourages their use, sometimes to an excessive extent.

      Their widespread use worldwide (Figure 1.15) supports the yields expected by some farmers, often at the expense of soil, water and air quality. Used in excessive quantities, fertilizers are responsible for the depletion, or even destruction, of ecosystems – inhibiting the ability of soils to regenerate naturally or permanently polluting groundwater reserves.

      Figure 1.15. Global use of nitrogen, potassium and phosphate fertilizers worldwide in 2014: major agricultural countries are making massive use of fertilizers. The quantities used are expressed in kilograms per hectare of cultivated land (source: Our World in Data/https://ourworldindata.org/fertilizer-and-pesticides). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip.

      Sophie Genermont, a researcher at INRA, has been working for more than 20 years on the development of a platform for simulating ammonia emissions resulting from the use of fertilizers [GEN 97, RAM 18], which contribute to the degradation of air quality:

      “Formed from organic nitrogen, ammonia is a pollutant of the air, and after deposition, of soils and water. About 95% of anthropogenic ammonia (present in the environment through human action) comes from agriculture.

      My work on the formation and volatilization of this compound is based on data measuring its concentrations in plants, water or soil. These are complemented by models of the physical, physico-chemical and biological processes at different scales”.

      Models are carried out for a plot, a small agricultural region, a country, or even, in the long term, a continent! They take into account the various factors that influence the migration of ammoniacal nitrogen in the environment – and exploit the data that make it possible to characterize it: meteorological, geological variables for the composition of surface soils, physical and chemical variables for the composition of fertilizers, statistics for the input practices carried out by farmers.

      “The simulations consist in solving equations modeling the physical, physicochemical and biological phenomena at work in soils, and at the interface between the soil and the atmosphere. Carried out on a plot scale, they give very fast results: a few seconds of calculation give an idea of the evolution of the phenomena that can actually be observed over a few weeks and this at an hourly time step!”

      Box 1.1. Physicochemical equations

      Many physical processes are modeled by equations that form the basis of the models used in the simulations of changes in chemical species concentrations. These include the laws established in the 19th Century by the French physicist Jean-Baptiste Biot (1774–1862), the French engineer Henry Darcy (1803–1858) and the German physiologist Adolf Fick (1829–1901). They relate the flow of a physical quantity to a variation of another quantity:

       – the law described by Fourier and formulated by Biot reflects the diffusion of heat. It is written as follows φ = –λ∇T and stipulates that the heat flux (φ) flows from hot areas to cold areas (∇T), all the more easily as the medium in question is conductive (λ);

       – Darcy’s law expresses the flow rate of an incompressible fluid filtering through a porous medium. It is written as follows φ = K∇H and indicates that the flow of a fluid between two points, made by its flow (φ), is all the easier as the medium is porous (K) and that the resistance to its flow, expressed by the hydraulic pressure losses (∇H), is low;

       – Fick’s law accounts for the diffusion of matter. It is written as follows φ = –ρD∇c and indicates that a chemical species spreads from areas where it is highly concentrated to areas where it is less concentrated. The mass flow of a component (φ) is inversely proportional to changes in its concentration (∇c) and depends on its density (ρ) and its propensity to spread (D).

      A set of simulations, aggregated for different plots and taking into account composition differences as well as meteorological factors, allows data to be reproduced on larger scales – typically a small agricultural region.

      “It is possible to scale up, for a country, with the same principle: by performing as many simulations as necessary

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