Abstract The IAU (incremental analysis updating) process incorporates analysis increments into a model integration in a gradual manner. It does this by using analysis increments as constant forcings in a model's prognostic equations over a 6-h period centered on an analysis time. A linear analysis of the IAU procedure shows it to have the attractive properties of a low-pass time filter. The IAU process affects the response of the model to the analysis increments, and it leaves the model state unaffected where there were no data to assimilate. This result is contrasted with a simple dynamical relaxation (or “nudging”) scheme, which is shown, in this linear analysis, to have less desirable response characteristics, both from the analysis increments and from the background state of the model. The behavior of IAU in the context of the Goddard Earth Observing System (GEOS) Data Assimilation System is examined using a combination of large-scale diagnostics from month-long assimilations and detailed diagnostics ...