Diagnosing Summertime Mesoscale Vertical Motion: Implications for Atmospheric Data Assimilation

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Abstract
Balance omega equations have recently been used to try to improve the characterization of balance in variational data assimilation schemes for numerical weather prediction (NWP). Results from Fisher and Fillion et al. indicate that a quasigeostrophic omega equation can be used adequately in the definition of the control variable to represent synoptic-scale balanced vertical motion. For high-resolution limited-area data assimilation and forecasting (1–10-km horizontal resolution), such a diagnostic equation for vertical motion needs to be revisited. Using a state-of-the-art NWP forecast model at 2.5-km horizontal resolution, these issues are examined. Starting from a complete diagnostic partial differential equation for omega, the rhs forcing terms were computed from model-generated fields. These include the streamfunction, temperature, and physical time tendencies of temperature in gridpoint space. To accurately compute one term of second-order importance (i.e., the ageostrophic vorticity tendency forcing term), a special procedure was used. With this procedure it is shown that Charney’s balance equation brings significant information in order to deduce the geostrophic time tendency term. Under these conditions, results show that for phenomena of length scales of 15–100 km over convective regions, a diagnostic equation can capture the major part of the model-generated vertical motion. The limitations of the digital filter initialization approach when used as in Fillion et al. with a cutoff period reduced to 1 h are also illustrated. The potential usefulness of this study for mesoscale atmospheric data assimilation is briefly discussed.

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