Climate Diagnostics from Global Analyses: Conservation of Mass in ECMWF Analyses

The extent to which mass is conserved in European Centre for Medium Range Weather Forecasts (ECMWF) analyses archived on pressure surfaces is examined from two perspectives and with two different datasets. The data used come from the WMO archive of 7-level, twice daily initialized analyses and from the WCRP archive of 14-level, four-times daily uninitialized analyses. The first perspective, which considers the equation of continuity in pressure coordinates locally in three dimensions, reveals spurious residuals in the equation of up to 100% of the size of the divergence term, with largest errors of 60% to 100% in the tropics. In this case the horizontal velocity and vertical p-velodty (ω) fields are checked for consistency. Modest improvements occur when 14 versus 7 levels are used. The second perspective considers the vertical integral in which the surface pressure tendency should balance the total mass convergence into a column, and thus does not involve the omega fields. The latter reveals that the dominant residual is due to the failure to resolve the semidiurnal tide with only twice-daily data, so that a large-scale wavenumber 2 pattern with maxima in the tropics results as a residual. However, there are also many smaller scale and smaller amplitude features in the residual that cannot be explained simply. The residuals from the uninitialized analyses are much larger so that while four-times daily data removes much of the wavenumber 2 semidiurnal tide structure, the total residuals are just as large as with the twice-daily initialized data. Improvements in using 14 levels versus 7 are marginal for the vertical integral. The moisture budget, which is an important part of the overall mass budget, produces plausible estimates of vertically integrated evaporation minus precipitation, but needs to be validated. The primary source of the mass imbalance arises from the methods of postprocessing the variables onto pressure surfaces. Because sophisticated four-dimensional data assimilation now performs analyses of fields on model (sigma) surfaces, the postprocessing performs interpolations (using splines under tension) from model coordinates to pressure coordinates, with the result that the archived variables are really representative of individual levels rather than finite-sized layers. The implications are that residuals computed in other budgets, such as diabatic heating from the thermodynamic equation, will also include large errors, most of which will, however, be systematic. The effects of several common approximations in the treatment of the lower boundary on mass conservation are examined, and proper accounting for the full variations in both space and time of surface pressure on vertical mass integrals lead to the computation of kinematic orographic forcing from the analyses as a residual. The diagnosed lower boundary-induced vertical motions are weak and do not reveal the strong dipole patterns normally expected, which may indicate that the planetary waves are not adequately forced in the forecast model used in the four-dimensional data assimilation.