The tracer nudging method for correcting and preventing uneven tracer distributions in geodynamical models

Abstract. Tracers/markers/particles are commonly used in geodynamical models to track composition and sometimes temperature throughout the domain. A common problem is that over time, gaps in the tracer distribution can develop, often resulting in cells with no tracers as well as bunching of tracers. Here a correction method that perturbs or “nudges” the positions of tracers in such a way as to close gaps and eliminate bunching is presented. Test results show that this tracer nudging method is highly effective. Starting from an extremely heterogeneous tracer distribution with large regions of the domain devoid of tracers, it can produce an even distribution in only a few nudge iterations. In a time-stepping situation with a nudge every time-step, the amplitudes of the nudges are small yet sufficient to prevent gaps and bunches, allowing a low-order tracer advection method to be used while maintaining a tracer distribution that is more even than that obtained using higher-order advection methods alone. The nudge essentially corrects any non-conservation error inherent in an advection method. The computational cost is small because the method simply requires solving a Poisson equation.