FuN-Balance: a fuzzy balance approach for the calculation of nitrate leaching with incorporation of data imprecision

The nitrogen-leaching model Fuzzy Nitrogen-Balance (FuN-Balance) presented in this paper was developed for the field-specific determination of nitrate concentrations of percolating water in agricultural catchments. The use of fuzzy numbers (uncertain numbers) allows one to estimate the accuracy of the modelʹs results even when the available data are not suitable for statistical analysis. Hence, the model is especially designed for situations where expert knowledge must be included and quantitative values about the accuracy of the results are required. The calculations of nitrate concentrations in percolating water were carried out in the 31 km2 catchment “Weißenstädter See” (Fichtelgebirge, Northern Bavaria). Fertilizer rates and plant uptake were estimated by the local department of agriculture. As the available data were insufficient for a statistical analysis, minimal, maximal and typical values were used to set up fuzzy numbers, which in turn were used to estimate the accuracy of the results. Additionally, the model takes into account the interdependence between different fuzzy variables. This accounts for the fact that uncertainties concerning input parameters are not independent of one another and leads to more reliable estimates of the expected range of results. The modelʹs results were compared with Nmin data obtained at more than 50 sites in the area studied. To make FuN-Balance a convenient tool for practical use, the developed FORTRAN code was integrated in a Visual Basic 6.0 user interface.