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Three different trajectory schemes for oceanic and atmospheric generalcirculation models are compared in two different experiments. The theories ofthe trajectory schemes are presented showing the differential equations theysolve and why they are mass conserving. One scheme assumes that the velocityfields are stationary for set intervals of time between saved model outputsand solves the trajectory path from a differential equation only as afunction of space, i.e. <q>stepwise stationary</q>. The second scheme is aspecial case of the stepwise-stationary scheme, where velocities areassumed constant between general circulation model (GCM) outputs; it uses hence a <q>fixed GCM timestep</q>. The third scheme uses a continuous linear interpolation of the fieldsin time and solves the trajectory path from a differential equation as afunction of both space and time, i.e. a <q>time-dependent</q> scheme. The trajectoryschemes are tested <q>offline</q>, i.e. using the already integrated and storedvelocity fields from a GCM. The first comparison of the schemes usestrajectories calculated using the velocity fields from a high-resolutionocean general circulation model in the Agulhas region. The second comparisonuses trajectories calculated using the wind fields from an atmosphericreanalysis. The study shows that using the time-dependent scheme over thestepwise-stationary scheme greatly improves accuracy with only a smallincrease in computational time. It is also found that with decreasing timesteps the stepwise-stationary scheme becomes increasingly more accuratebut at increased computational cost. The time-dependent scheme istherefore preferred over the stepwise-stationary scheme. However, whenaveraging over large ensembles of trajectories, the two schemes arecomparable, as intrinsic variability dominates over numerical errors. Thefixed GCM time step scheme is found to be less accurate than thestepwise-stationary scheme, even when considering averages over largeensembles

Evaluation of oceanic and atmospheric trajectory schemes in the TRACMASS trajectory model v6.0