Consider 2m temperature remapping
So far, a special remapping procedure for the 2m temperature based on the static energy has been applied.
More specifically, the 2m temperature has first been transformed to the static energy. Then, the static energy gets remapped (first conservative remapping to coarse grid, if required, followed by bilinear interpolation onto the target grid) before it gets retransformed to the 2m temperature as the final step.
The surface topography (geopotential), required for the (re-)transformation, has undergone the same remapping procedure.
However, this procedure seems to produce the same result as the direct remapping of the 2m temperature (see plots below).
This would happen if all remapping steps constitute linear operation. Probably, this is also the case for the conservative remapping, so that the current procedure would be redundant.
Fig. 1: Result from the remapping procedure based on the static energy for the ERA5-dataset, 2016-07-01 04 UTC (10h forecast of the 2016-06-30 18 UTC run). Fig. 2: Same as Fig. 1, but for direct remapping of the 2m temperature.
An alternative, probably better approach, would be to use the high-resolved topography for the retransformation instead. This can be considered as a poor-man downscaling approach whose outcome might support the neural network in the downscaling task.