ABSTRACl-"Least-squares" approximating polynomials are used to suppress bias and random errors in estimating vertical profiles of winds, divergence, and vertical motion. A quadratic polynomial is used to filter each wind profile. Profiles of divergence and vertical motion computed from a linear, a cross-product, and a quadratic two-dimensional (horizontal) approximating polynomial model and from the Bellamy technique are compared. The random-error variance component of the wind observations is estimated from the filtering polynomial prediction errors. In turn, the random-error variance component of the filtered wind, divergence, and vertical motion is determined from the wind observational error variance for the various models. 'In the presence of nonlinear variation in the horizontal wind field, the Bellamy modeling assumption of linear wind variation introduces biased divergence errors. The bias divergence errors will persist through a considerable portion of the troposphere as a result of the thermal wind relation and, in the vertical integration, will cause large 'kpurious" vertical motion estimates of w at the top of the profile. Divergencc estimates from both the cross-product and the quadratic approximating polynomial models of the horizontal wind field tend to be less biased in this situation and normally produce superior vertical motion profiles.