Juan Pineros Garcet

Metamodelling: Theory, concepts, and application to nitrate leaching

Nutrient fate and balance models for the root zone of agricultural crops are powerful instruments for the assessment of the impacts of agricultural management on nutrient leaching and groundwater quality. Deterministic nutrient balance models allow estimation of the space-time course of nutrients in terms of soil-crop typology, climatic boundary condition, and geo-hydrological boundary condition. However, due to computational time and parameterization constraints (the large number of parameters needed), the use of deterministic modelling in large scale applications or optimization studies is prohibited. As an alternative, metamodels can be constructed for specific applications from a limited number of deterministic simulations. Presently, no general mathematical definition of a metamodel is available. In this paper, a mathematical definition for a metamodel is developed. Next, a metamodelling analysis for the nitrogen leaching model WAVE is presented. Two metamodelling techniques, i.e., multidimensional kriging and neural network modelling, were compared on generated deterministic modelling results. For this application, multidimensional kriging, as compared to radial based neural network modelling, outperforms in terms of root mean square error, maximal error, and model efficiency.