Implicit Filtering in Conjunction with Explicit Filtering

where S is a smoothing element; j i 1 -+ (j f I) Ax; Ax is a space increment. For S = b, the filter (1) removes thoroughly the 2Ax wave and damps all the longer waves. But for most meteorological purposes the smoothing of the longer waves is too strong. In order to prevent this undesired smoothing, Shapiro [2] constructed the n-element smoothing operator which consists of IZ basic operators in form (1) with the following essential properties: