FITTING AMMONIA VOLATILIZATION DYNAMICS WITH A LOGISTIC EQUATION

To improve the interpretation of the results from NH3-volatilization e xperiments, the cumulative loss rates for different treatments were fi tted to a simple logistic equation. This equation is a function: Y = a (1 - e(-et))(i), with Y the cumulative N loss (%). The first derivativ e of this function represents the daily volatilization rate and is Y' = acie(-ct)(1 - e(-ct))(i-1). Important parameters such as the total c umulative loss (a), and the maximum (R(m)) and average (R(a)) volatili zation rates can easily be calculated. In the case of urea application s, an estimation can be made of the time it takes to hydrolyze all app lied urea (th). This parameter also corresponds to the lag phase of th e cumulative volatilization curve. Parameter i determines the position of the point of inflection of the curve. For values of i between 0 an d I, volatilization rates cannot be adequately calculated. This can be encountered if the initial volatilization rate is very high, e.g., af ter ammonium sulphate application upon calcareous soils. In this case, volatilization rates will be estimated by fitting the results to a mo dified logistic equation in which i = 1. This value of i is most commo n for NH4NO3 application. The best applicability of the logistic equat ion is with i values >1. These values are typical for the shape of cum ulative volatilization curves obtained on application of urea-containi ng fertilizers. Possible applications of the logistic equation are ill ustrated by some experimental results.