To study forth-order compact schemes in numerical atmospheric or oceanic models, a general method is proposed for dispersion relation of hydrostatic linear baroclinic adjustment equations with differential or difference schemes, at horizontal length of 100 km, 10 km and I kin, respectively. Non-staggered grids (N grids), Lorenz grids (L grids), Charney-Phillips grids (CP grids), Lorenz time staggered grids (LTS grids) and Charney-Phillips time staggered grids (CPTS grids) in a second-order centered scheme and a forth-order compact scheme are compared. The forth-order compact scheme reduces errors of frequency, horizontal and vertical component of group velocity on N grids, CP grids and CPTS grids obviously, but increases errors of horizontal and vertical component of group velocity on LTS grids.