you first have to determine the scale of your biases. If they are local, the you can downscale model output and try correcting the biases locally using data. The interpolation scheme should avoid using cubic lagrangian for precipitation (you might end up with negative precipitation). if the biases are regional (as we found for air quality models in North America) then a regional bias correction is required (see the following reference for details of the method we have used):
Robichaud and Ménard, Atmos. Chem. Phys., 14, 1769–1800, 2014
at http://www.atmos-chem-phys.net/14/1769/2014/acp-14-1769-2014.html
You can download the gridded data series of grid points nearest to your observed stations. Then compare the series together and determine what are the differences in mean and standard deviation. Then you can apply these biases to your interpolated gridded data set.
You can have a look to the attached paper for a case study