title: Improving the numerical stability of the MAGIC model.
abstract: MAGIC is one of the most widely used models for forecasting long-term acidification. The model's code, however, has been experiencing numerical instability, though this might not be widely known to the public users. The major instability comes from the analytical solution to two cubic equations for calculating SO4(2-) concentration and the exchangeable fraction of Al on the soils. The mathematical algorithm for calculating the concentration of SO4(2-) from a quadratic equation is also found unstable. This paper is aimed at improving the instability above through proved numerical algorithms.
authors.affiliation: Department of Environment Sciences and Engineering, Tsinghua University, Beijing 100084, China. dyx99g@mails.tsinghua.edu.cn
authors.forename: Y X
authors.initials: YX
authors.lastname: Deng
authors.forename: J N
authors.initials: JN
authors.lastname: Chen
authors.forename: X T
authors.initials: XT
authors.lastname: Hu
mesh_terms: D000327:Adsorption; D000465:Algorithms; D017607:Aluminum Compounds / Q000032:analysis / Q000737:chemistry; D005618:Fresh Water / Q000737:chemistry*; D006813:Humidity; D006863:Hydrogen-Ion Concentration; D007474:Ion Exchange; D008956:Models, Chemical; D012987:Soil / Q000032:analysis; D013431:Sulfates / Q000032:analysis / Q000737:chemistry; D014867:Water / Q000032:analysis
chemical_list: D017607:Aluminum Compounds; D012987:Soil; D013431:Sulfates; D014867:Water