The three dimensional structure of the atmospheric energy budget: methodology and evaluation

Studies of the vertically-integrated energy and moisture budgets of the atmosphere are expanded to three dimensions. The vertical integrals of the moisture, energy and heat budget equations computed analytically act as a very strong constraint on any local computational results of the vertical structure. This paper focuses on the methodology and difficulties in closing the budgets and satisfying constraints, given the need to use a pressure coordinate because model coordinates all differ. Vertical interpolation destroys delicate mass balances and can lead to inconsistencies, such as from how geopotential or vertical motion is computed. Using the advective rather than flux form of the equations greatly reduces the contamination from these effects. Results are documented for January 1989 using European Centre for Medium Range Weather Forecasts reanalysis (ERA-40) data. The moistening, diabatic heating and total energy forcing of the atmosphere are computed as a residual from the analyses using the moisture, dry energy (dry static energy plus kinetic energy) and total atmospheric (moist static plus kinetic) energy equations. The components from the monthly averaged flow and transients, as a function of layer in the atmosphere, and as quasi-horizontal and vertical fluxes of dry static, latent and kinetic energy are examined. Results show the moistening of the atmosphere at the surface, its release as latent heat in precipitation and transformation into dry static energy, and thus net radiative cooling as a function of height and location. The vertically integrated forcings computed from the model parameterizations are compared with available observations and budget-derived values, and large ERA-40 model biases are revealed in radiation and precipitation. The energy and moisture budget-derived quantities are more realistic, although results depend on the quality of the analyses which are not constructed to conserve mass, moisture or energy, owing to analysis increments.