Error inhomogeneity in the computation of spherical mean displacement

The traditional method for computing the mean displacement in latitude–longitude coordinates is a spherical meridional–zonal resultant displacement method (MRDM), which regards the displacement as the resultant vector of the meridional and zonal displacement components. However, there are inhomogeneity and singularity in the computation error of the MRDM, especially at high latitudes. Using the NCEP/NCAR long-term monthly mean wind and idealized wind fields, the inhomogeneity in the MRDM was accessed by using a great circle displacement computing method (GCDM) for non-iterative cases. The MRDM and GCDM were also compared for iteration cases by taking the trajectories from a three-time level reference method as the real trajectories. In the horizontal direction, the GCDM assumes that an air particle moves along its locating great circle and that the magnitude of the displacement equals the arc length of the great circle. The inhomogeneity of the MRDM is evaluated in terms of the horizontal distance error from the products of wind speed, lapse time, and angle difference from the GCDM displacement orient. The non-iterative results show that the mean horizontal displacement computed through the MRDM has both computational and analytical errors. The displacement error of the MRDM depends on the wind speed, wind direction, and the departure latitude of the air particle. It increases with the wind speed and the departure latitude. The displacement magnitude error has a four-wave pattern and the displacement direction error has a two-wave feature in the definition range of the wind direction. The iterative result shows that the displacement magnitude error and angle error of the MRDM and GCDM with respect to the reference method increase with the lapse time and have similar distribution patterns. The mean magnitude error and the angle error of the MRDM are nearly twice as large as those of the GCDM.