On the use of random walk schemes in oil spill modelling

In oil spill models, vertical mixing due to turbulence is commonly modelled by random walk. If the eddy diffusivity varies with depth, failing to take the derivative of the diffusivity into account in the random walk scheme will lead to incorrect results. Depending on the diffusivity profile, the result may be either over- or underprediction of the amount of surfaced oil. The importance of using consistent random walk schemes has been known for decades in, e.g., the plankton modelling community. However, it appears not to be common knowledge in the oil spill community, with inconsistent random walk schemes appearing even in recent publications. We demonstrate and quantify the error due to inconsistent random walk, using a simplified oil spill model, and two different diffusivity profiles. In the two cases considered, a commonly used inconsistent scheme predicts respectively 54% and 202% the amount of surface oil, compared to a consistent scheme.