Volume 9 (2013) Pages 125-128
A non-negative filter is developed to avoid negative values that may be produced in the interpolation of a non-conservative semi-Lagrangian advection scheme of tracers. Non-negativity is realized by a variable transformation with a function using arcsine. One-dimensional advection tests show that the proposed filter eliminates negative values of the mixing ratio and reduces error, whereas other non-negative filters (e.g., the global hole filling method) increase error. The variable transformation with the arcsine function efficaciously reduces the error in the region where the mixing ratio is zero, with a small counter effect to non-zero values. The proposed filter is very simple, so that it can be used in multi-dimensional schemes without modification and can be combined with other filters, such as a mass fixer and a monotonic filter.