The four-dimensional data assimilation (FDDA) scheme included in MM5 is based on Newtonian relaxation or “nudging.” Nudging is a continuous form of FDDA where artificial (non-physical) forcing functions are added to the model's prognostic equations to nudge the solutions toward either a verifying analysis or toward observations. The artificial forcing terms are scaled by a nudging coefficient that is selected so that the nudging term will not dominate the prognostic equations. In general, the nudging terms tend to be an order of magnitude smaller than the dominant terms in the prognostic equations and represent the inverse of the e-folding time of the phenomena that the observations represent.

There are two types of nudging in MM5: analysis nudging and observation nudging (“obs nudging”). Analysis nudging gently forces the model solution toward gridded fields. Analysis nudging can make use of three-dimensional analyses and some surface analyses. Obs nudging gently forces the model solution toward individual observations, with the influence of the observations spread in space and time. Obs nudging is better suited for assimilating high frequency, asynoptic data that may not otherwise be included in an analysis. Nudging in MM5 is extensively discussed in Stauffer and Seaman [1990], Stauffer et al. [1991], and Stauffer and Seaman [1994].