How are real-world observations entered into a computing model, and how are such observations used by the model itself?
Before they can be used in a consistent way, real-world observations (in-situ, satellite, or from a moving platform) most likely have errors that need to be quality-corrected, or otherwise dealt with. In addition, the physical locations at which various real-world measurements are made most likely do not correspond precisely to the grid points defined within the mathematical model that is being computed. This calls for an extrapolation method between grid points. Additionally, if observations are not made at exactly the same time of day, then some form of time adjustment must be made to align the measurements to a common time point, say t0.
Data Assimilation deals with these and several other 'data input' issues:
The WCRP Observation and Assimilation Panel (WOAP)
CERFACS Ocean Data Assimilation Ocean data assimilation systems for seasonal predictions