'Forcing' in PDSI Calculation
What does 'forcing' mean?

The PDSI is calculated from model output data. Models do not predict all relevant variables but some data need to be provided externally from the user. These externally provided data are denoted as "forcing" because they "force" the model to move in one direction (colloquially speaking). You might also call it "drive" a model -- but "to force" is the established expression in science.

In this case

In this particular case, the authors use observational data as input data for the model calculations. Therefore, the authors write


  The PDSI is calculated from a water-balance model forced with observed precipitation and temperature...


Other situations

One might force a model also with data from other models. A river run-off model might get input data from an atmospheric/meteorological model, which predicts precipitation and solar radiation at surface level. We could write


  The river run-off model ABC is forced by modeled precipitation and radiation of the XYZ meteorological model.