• i3d
• InterpolationType

Interpolation type in i3d

The interpolation type is specified in the configuration file i3d.inp (line 3):

• 0 - only one nearest neighbor from the CLaMS grid is used (i.e. this interpolation does not cause any numerical diffusion)
• 1 - weighted interpolation over two triangles (i.e. 6 neighbors) the contribution of this 6 points depends on the horizontal distance within the upper and lower triangle as well as on the absolute vertical differences of these 6 points to the considered air parcel, i.e. APs with smallest $r$-values have the higher contribution where $r$ is defined as

  • $r = |\theta_{exp}-\theta|r_s, \quad r_s^{2=(x_{exp}-x)}2+(y_{exp}-y)^{2+(z_{exp}-z)}2$

  Here, index $exp$ denotes the coordinates of a given AP where the interpolation from the external (CLaMS) grid should be determined. $\theta_{exp}-\theta$ and $r_h$ are the distances in the $\theta$-space (absolute difference in $\zeta$-space) and on the unit sphere (i.e., points are on a unit sphere but the distance is defined in $R^3$), respectively.
• 2 - Interpolation type 0 and 1 (two output files per date are created)
• 3 - weighted interpolation over two triangles (i.e. 6 neighbors) the contribution of this 6 points depends on the horizontal distance within the upper and lower triangle as well as on the absolute vertical differences of these 6 points to the considered air parcel, i.e. APs with smallest $r$-values have the higher contribution where $r$ is defined as

  $r = \sqrt{(x_{exp}-x)^{2+(y_{exp}-y)}2+(z_{exp}-z)^{2+((theta_{exp}-theta)/delta_{theta}ratio)}2)}$