Crop yield and optimum nitrogen fertilization rates (Nopt) are often calculated ex post by specific functions of the nitrogen fertilization rate, but in doing this, uncertainties in terms of model choice, annual nitrogen response variations and parameter estimation are neglected. In the present study, Nopt, grain yields, net revenues and N balances were estimated for the three crops of an oilseed rape (OSR)–winter wheat–winter barley rotation. The effects of uncertainties were considered using three different statistical models, estimating an identical Nopt over the years and carrying out Monte-Carlo simulations where model parameters were varied according to their estimated standard errors. The statistical models used were the quadratic (Q) polynomial function, the linear response and plateau (LRP) function and the quadratic response and plateau (QRP) function.
The Q model tended to estimate the highest Nopt values for the three crops, followed by the QRP and the LRP model in an initial ex post analysis. The highest corresponding mean net revenues in the rotation were estimated by the LRP model, followed by the Q and QRP model; mean N balances increased in the order LRP, QRP and Q. In the comparison of the crops, OSR showed the highest N balances followed by wheat and barley. Considering the protein concentration in wheat, Nopt values estimated by the Q model were considerably higher than without the economic effects of grain quality.
In order to consider uncertainties in annual nitrogen response, an ex ante Nopt over the years was determined by maximizing the cumulated net revenues over all years in the rotation. Ex ante Nopt was higher as the mean of the ex post Nopt values for the QRP and LRP model. Average grain yields and net revenues were lower, N balances were higher. Running the Monte-Carlo simulations, ex post Nopt was obtained by 10 000 generated functions in each year and ex ante Nopt by 50 000 generated functions of years 1996, 1997, 1998, 1999 and 2002. This led to an increase in Nopt especially for the LRP model, while effects on the estimation of Nopt by the Q model were rather small. For the LRP model, corresponding mean net revenue decreased and mean N balance rose. In contrast, due to marginal changes in Nopt, the consideration of uncertainties in the estimations had only a small effect on net revenue and N balance in the Q model.
In general, all kinds of uncertainty tended to increase Nopt but this effect was much higher for the LRP model as compared to the Q model. This increase in Nopt was associated with decreasing net revenues and increasing N balances. Exceptionally in OSR using the Q model, however, the ex ante approaches considering uncertainty led to slightly lower Nopt values compared to the ex post value.