Overview and application of the Mitscherlich equation and its extensions to estimate the soil nitrogen pool fraction associated with crop yield and nitrous oxide emission

Natural levels of soil nutrients are spatio-temporally variable and insufficient for agricultural purposes. Artificial fertilizers are applied to achieve greater crop growth rates and yield. Mitscherlich's equation and Boule's fertilizer units are described and illustrated in relation to crop yield then applied to estimate the nitrogen (N)-pool fraction in the soil that contributes to a component of greenhouse gas (GHG) emission, specifically the nitrous oxide (N₂O) flux. Mitscherlich (1909) proposed a diminishing returns model to extract information about soil N status for production responses. Mitscherlich's equation was generalized by Baule (1918) and modified by Bray (1945) to account for soil nutrient contributions for multiple fertilizers. These models are examined in this chapter. Their application results in the extraction of further information on soil nutrient variability and N₂O emission across various geo-positions (specific global locations). It is concluded that Mitscherlich's equation and Boule's fertilizer units are useful tools to investigate soil-fertilizer interaction and compare soil fertility and GHG emission.