ON THE FUNCTIONAL DEPENDENCE BETWEEN THE AGRICULTURAL YIELD AND THE FERTILIZATION WITH A SINGLE TYPE OF FERTILIZER PUBLISHED

Marius Boldea, Florin Sala, Isidora Radulov, Florin Crista, Adina Berbecea
It is common knowledge that applying fertilizers is of utmost importance for obtaining  higher yields and considerable profits. People are also aware of the risk of polluting the environment if the fertilizers are not applied properly. Therefore, knowing exactly what dosage is beneficial for each crop, in the particular conditions of each region, has represented the aim of research for many years. Thus, throughout the history of research in this field, mathematicians have worked together with agrochemists in interdisciplinary teams in order to get at better results. The main objective of the present paper is to prognose unifactorially the yields for any possible dosage of fertiliser. Knowing that the models we propose represent functional relations between productions and doses applied, we also know that the best prognosis will be generated by the most accurate determination of the constants which will intervene in the function expressions. Nitrogen ( ) - based fertiliser is known to be the most important chemical fertiliser; it is the most commonly used. Some factories produce fertilisers which contain nitrogen, phosphorus and potassium ( , , ) in pre-established proportions, which for the purpose of this study can be considered as being equivalent to a single type of fertiliser. Among the first important models which give the mathematical relation between agricultural yield and fertilisers is the Mitcherlich function. Admitting that yield increase  is proportional to the saturation superdeficit , the following differential equation results: ,                                                                              (1) the solution of which is ,                                                                          (2) in other words, the Mitcherlich function. In order to exemplify we apply the above-mentioned model on wheat experiences on Alex variety. The experiment was carried out at Timisoara Didactic Station between 2006 and 2009. The results are shown in Table 1. Constants ,  and  in relation (2) are determined through confrontation with experimental data, using the least squares method. When we represent grafically the Mitcherlich function and the experimental data, we get pictures 1-4. These graphics show that the experimental data are close to the theoretic curves, and this fact confirms the mathematical model taken into consideration.
fertilization; Mitscherlich; least squares; modeling
Presentation: oral

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