Contribution to the statistical study of the repartition and the modelization of dynamics of nitrate nitrogen in the soil

The nitrate nitrogen found in the soil has two origins first, an external source, the input from the nitrogenous fertilizers supply, a second, in situ, from the mineralization of organic nitrogen. This work consist of two parts: 1 - Statistical study on the repartitions of nitrate nitrogen the soil. A linear relationship has been found between the standard deviation and the mean of these repartitions equaling 0.3 with a correlation coefficient of 0.9. Thus the population of the concentration values of nitrate nitrogen is characterized by a variation coefficient of the order of 30 percent; such a value is very high. This great heterogeneity comes from the techniques used for spreading nitrogenous fertilizers, and the variable nature in space and time of the microbial activity. It is shown that the whole of the transfers should be considered as a proportion of the quantities present in the soil. The proposed model explains with respect to time, the existence of correlations between the present quantities at various depths and the dissymmetric evolutionary character towards the left side of the populations. 2 - Study of the dynamics of nitrate nitrogen in the soil. A method of calculation in kg.ha^-1 is first proposed for that remaining part of nitrogen. An emphasis is laid on the overestimation from systematic error on the passage from one numeric expression, concentration or intensive variable, to the other, quantity or extensive variable. A transformation coefficient, equivalent to a bulk density, is proposed; it depends on the moisture rate of the soil. The others terms in the manure balanced sheet are not precisely known. Only their net values are taken into consideration. The use of labelled nitrogen (¹⁵N) gives a better numeric understanding of the fate of mineral nitrogen in the soil-plant system. Many examples are given for wheat and for sugarbeet mostly: real and apparent coefficients of utilization, gross mineralization, gross immobilization, the lower risks in water table pollution under a crop. The input-output budget is balanced by making the assumption that the mineralized nitrogen and the nitrogen provided by fertilizers have the same fate. A compartmental model describing the dynamics of mineral nitrogen in bare or cultivated soil is proposed. The transfers, or exchangeable outflows, between the compartments i.e., the unknown quantities in the model are in number more than the equations. A solution to the system is given by an integral calculated by a hyperbolic hypothesis. This model is tested with the numerical data from an experiment carried out in pots with and without a crop. The gross mineralizations and immobilizations are calculated; their differences with corresponding net values are large. ¹⁵N permits to make the real extent of the microbial process conspicuous. Another study on the compartmental model is made with respect to time. The proposed solution is a direct consequence of the conclusions about heterogeneity of the repartition of mineral nitrogen. In conclusion, each of the two parts of this work leads to a presentation of a mathematical model. These two models, one statistical, analyzing the spatial effect, the other of the compartmental type, analyzing the dynamic effect, are independent of each other because of the mind proceeding at the start; but, they are complementary in terms of results. They do not exclude one another; they justify that the transfers of mineral nitrogen in the soil are proportional to the quantities present in the soil.