The issue is that the global data is at too low a resolution (x, y pixel size). Either work with a different data set, or reprocess your data. Reprocessing will not improve data accuracy - this is limited by the source, but you can improve the visual display of the data.
Convert your data from raster to point, and then use Interpolation tools (ie: kriging or idw) to create a new raster, but set the cell size to a much smaller value. The interpolation will smooth the transition between the points. You can also set the display of the resulting raster to "bilinear interpolation" to smooth it further.
Best Regards,
Jim