Reduced models for efficient simulation of spatially integrated outputs of one-dimensional substance transport models

We examined under what circumstances the results of a large number of runs of the one-dimensional, physics-based SOIL/SOILN nitrate transport model can be combined into a reduced (or meta) model. We considered the total flow of nitrate from a given area and investigated when and how hidden linear structures can be extracted from the underlying model. The presence of such structures can justify the use of spatially aggregated inputs to compute spatially aggregated outputs. Extensive Monte-Carlo simulations showed that some linear structures emerged when the outputs for a long period of time were summed. Other linear structures appeared as relationships between two different components of the model outputs. However, different cropping systems respond differently to changes in anthropogenic or meteorological forcings. Therefore, we derived a reduced model of long-term leaching of nitrogen from the root zone in an agricultural area by combining each combination of soil type and cropping system. Reduced models can help make process-oriented models more transparent, and they are particularly suitable for incorporation into decision support systems.