I'm new to climate science - starting to get familiar with the field by reading some published articles. Terminology is always hard when starting into a new domain.

In this paper, Dai - Increasing drought under global warming in observations and models, what does the author mean by the term "forcing," in relation to the PDSI?

Here is an example of usage:

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

Another example:

Figure 1a,b shows that the broad patterns of the linear trends from 1950 to 2010 in observed annual precipitation and calculated sc_PDSI_pm using observation-based forcing2

Here is the citation:

Dai, Aiguo. "Increasing drought under global warming in observations and models." Nature Climate Change 3, no. 1 (2013): 52-58.