## page was renamed from I3d/InterpolationType
## page was renamed from I3dInterpolationType
## page was renamed from Interpolation type
#format inline_latex

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

 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. $\Delta{\theta}ratio$ is the aspect ratio (horizontal/vertical resolution) of the simulation. In July 2010 i3d was updated to ensure interpolation between the values of $\theta_{exp}$

 * 2 - Interpolation type 0 and 1 (two output files per date are created)
 
The earlier definition 1 of the weight is not supported  after July 2010 (but could be re-created from CVS):
 *  former type 1 - weighted interpolation over two triangles (i.e. 6 neighbors). The contribution of these 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 

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