FITTING AMMONIA VOLATILIZATION DYNAMICS WITH A LOGISTIC EQUATION

To improve the interpretation of the results from NH3-volatilization experiments, the cumulative loss rates for different treatments were fitted to a simple logistic equation. This equation is a function: Y = a(1 - e(-et))(i), with Y the cumulative N loss (%). The first derivative of this function represents the daily volatilization rate and is Y' = acie(-ct)(1 - e(-ct))(i-1). Important parameters such as the total cumulative loss (a), and the maximum (R(m)) and average (R(a)) volatilization rates can easily be calculated. In the case of urea applications, an estimation can be made of the time it takes to hydrolyze all applied urea (th). This parameter also corresponds to the lag phase of the cumulative volatilization curve. Parameter i determines the position of the point of inflection of the curve. For values of i between 0 and I, volatilization rates cannot be adequately calculated. This can be encountered if the initial volatilization rate is very high, e.g., after ammonium sulphate application upon calcareous soils. In this case, volatilization rates will be estimated by fitting the results to a modified logistic equation in which i = 1. This value of i is most common for NH4NO3 application. The best applicability of the logistic equation is with i values >1. These values are typical for the shape of cumulative volatilization curves obtained on application of urea-containing fertilizers. Possible applications of the logistic equation are illustrated by some experimental results.