On the Relationship between Incremental Analysis Updating and Incremental Digital Filtering

Abstract Incremental analysis updating (IAU) refers to a method of smoothly inserting instantaneous analysis increments into a numerical model by spreading the increments over a time period. In this work, this method is shown to be identical to applying a digital filter to the time evolution of analysis increments [a method known as incremental digital filtering (IDF)] for the case of linear models with time-invariant coefficients. The equivalence of the two methods can be used to show that the constant weights typically employed in IAU applications result in too much damping of long waves. For weakly nonlinear models, the two methods will not produce identical filtered states even if the filter coefficients are the same. The implications of the similarities and differences of the two methods are discussed.