This study utilizes a model-generated dataset to evaluate the errors associated with the diagnosis of geopotential height using three approximate forms of the divergence equation (DE). The DE was solved on the original sigma-coordinate surfaces of the model because the objective is to isolate the error associated with use of particular forms of the DE and to exclude any error produced in the process of interpolating the data from observation points to the coordinate surface of the DE. Note that it is not uncommon practice with research or operational models to define balancing relationships, such as this DE, on the model-coordinate surfaces.
An inviscid, nonlinear, divergent DE produced rms geopotential height errors as large as 23 m and rms temperature errors of over 26°C in the lower planetary boundary layer (PBL), with minimal errors above 800 mb. Elimination of the isobaric divergence in the velocity field caused additional height errors of 5–6 m and temperature errors of 0.4°–1.2°C in the free troposphere. Use of a further-degraded DE without nonlinear terms caused height errors of 10–15 m in the upper troposphere with modestly increased temperature errors. Error fields at all levels had synoptic-scale features, with some meso-alpha structure. No spatial noise was apparent. Use of a temporal spectral filter to eliminate high-frequency modes from the model-generated data did not significantly influence the error associated with use of various forms of the DE.