Probabilistic dynamics of soil nitrate: Coupling of ecohydrological and biogeochemical processes

In this paper we analyze the probabilistic dynamics resulting from a simplified model of soil moisture and nitrate mass in relatively arid environments, which accounts for relevant hydrologic and biogeochemical processes and for the random characters of rainfall. The soil nitrate balance includes uptake through transpiration, mineralization, nitrification, and denitrification. To allow an exact mathematical treatment, all nitrate fluxes are assumed to be linear functions of the state variables, namely, soil moisture and nitrate mass stored in soils. The range of applicability of the above simplification is investigated by means of numerical Monte Carlo simulations, showing that the linear approach is meaningful in relatively arid environments, where soil moisture contents are generally low. The moment-generating function of the joint probability distribution (pdf) of soil nitrate and water content is derived, thereby allowing a linkage between the main features of soil nitrate statistics and the underlying soil, vegetation, rainfall, and biogeochemical parameters. Exact expressions for the moments of the nitrate pdf and for the covariance of soil moisture and nitrate mass are derived. The pdf of the nitrate mass in storage within the soil is shown to be reasonably approximated by a gamma distribution in many cases of practical interest. Interestingly, nitrogen limitation for the ecosystem is shown to be directly related to low values of the product between the rate of rainfall arrivals and the characteristic time of nitrate removal.