Automatic fuzzy-rule assessment and its application to the modelling of nitrogen leaching for large regions
Diffuse nutrient emissions from agricultural land is one of the major sources of pollution for ground water, rivers and coastal waters. The quantification of pollutant loads requires mathematical modelling of water and nutrient cycles. The deterministic simulation of nitrogen dynamics, represented by complicated highly non-linear processes, requires the application of detailed models with many parameters and large associated data bases. The operation of those models within integrated assessment tools or decision support systems for large regions is often not feasible. Fuzzy rule based modelling provides a fast, transparent and parameter parsimonious alternative. Besides, it allows regionalisation and integration of results from different models and measurements at a higher generalised level and enables explicit consideration of expert knowledge. In this paper an algorithm for the assessment of fuzzy rules for fuzzy modelling using simulated annealing is presented. The fuzzy rule system is applied to simulate nitrogen leaching for selected agricultural soils within the 23687 km2 Saale River Basin. The fuzzy rules are defined and calibrated using results from simulation experiments carried out with the deterministic modelling system SWIM. Monthly aggregated time series of simulated water balance components (e.g. percolation and evapotranspiration), fertilization amounts, resulting nitrogen leaching and crop parameters are used for the derivation of the fuzzy rules. The 30-year simulation period was divided into 20 years for training and 10 years for validation, with the latter taken from the middle part of the period. Three specific fuzzy rule systems were created from the simulation experiments, one for each selected soil profile. Each rule system includes 15 rules as well as one prescribed rules from expert knowledge and 7 input variables. The performance of the fuzzy rule system is satisfactory for the assessment of nitrate leaching on annual to long term time steps. The approach allows rapid scenario analysis for large regions and has the potential to become part of decision support systems for generalised integrated assessment of water and nutrients in macroscale regions.
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