The spectral balance equation

The formula for generating stream function coefficients in terms of height coefficients developed from the linear balance equation wherein the dependent variables are expanded in solid harmonics has been analyzed and results show that for non-zonal waves the kinetic energy derived increases with decreasing scale. A new set of basis functions has consequently been developed in which the geopotential field may be expanded to yield energetically consistent stream coefficients and simultaneously satisfy the balance condition. A relationship is determined whereby those stream coefficients may be determined from the height coefficients of a solid harmonic expansion and these coefficients are shown to be consistent with those previously derived for the zonal case.