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The response of the Barnes objective analysis scheme is studied as a function of wavenumber or wavelength. The first- and second-pass theoretical response functions for continuous two-dimensional fields are derived using Fourier transforms. The results are compared with Barnes' (1973) responses for one-dimensional waves. The continuous theoretical response for one- and two-dimensional waves is compared with the response for discrete applications using uniformly spaced observations for the case where interpolation points and observation points are coincident and for the case where interpolation points are midway between observation points. The actual response of an idealized discrete application of the Barnes scheme is examined, confirming the results of the analysis of the discrete theoretical response.

The roles of adiabatic and diabatic forcings in the development of a cyclone are examined. The two types of height tendency equations (classical quasi-geostrophic and extended forms) employed to solve for height tendency are described. The extended equation, in which geostrophic wind is replaced with observed wind, the effects of diabatic heating are added, and three-dimensional varying static stability is permitted, is utilized to analyze the evolution of the January 9-11, 1975 cyclone event. The analysis reveals that vorticity advection has a primary effect on the movement and propagation of the wave system; the differential thermal advection has a secondary, but significant role in wave development; latent heating effects are minimal; and the vertical advection of static stability slows the propagation and development of the wave.