The Rothamsted soil-carbon turnover model — discrete to continuous form

This paper examines the Rothamsted soil-carbon turnover model. This model and other soil carbon turnover models are increasingly being used in climate change and land use studies. The formulation of this model is as a discrete sums-of-exponentials. This discrete form may be converted to a continuous form which can be shown to be an asymptotic approximation of a simple linear first-order system of differential equations where the exponential decay rate constants in the sums-of-exponentials form approximate the first-order rate transfer coefficients in the differential equation form. There are many standard analytical results that can be obtained from this linear system of differential equations that could prove to be very useful in modelling soil-carbon turnover.