Diagnostics for Imbalance on the Convective Scale

The analyses produced by a data assimilation system may be unbalanced, which is dynamically inconsistent with the forecasting model, leading to noisy forecasts and reduced skill. While there are effective procedures to reduce synoptic-scale imbalance, the situation on the convective scale is less clear because the flow on this scale is strongly divergent and nonhydrostatic. In this study, we compare three measures of imbalance relevant to convective-scale data assimilation: (i) surface pressure tendencies, (ii) vertical velocity variance in the vicinity of convective clouds, and (iii) departures from the vertical velocity prescribed by the weak temperature gradient (WTG) approximation. These are applied in a numerical weather prediction system, with three different data assimilation algorithms: 1) latent heat nudging (LHN), 2) local ensemble transform Kalman filter (LETKF), and 3) LETKF in combination with incremental analysis updates (IAUs). Results indicate that surface pressure tendency diagnoses a different type of imbalance than the vertical velocity variance and the WTG departure. The LETKF induces a spike in surface pressure tendencies, with a large-scale spatial pattern that is not clearly related to the precipitation pattern. This anomaly is notably reduced by the IAU. LHN does not generate a pronounced signal in the surface pressure but produces the most imbalance in the other two measures. The imbalances measured by the partitioned vertical velocity variance and WTG departures are similar and closely coupled to the convective precipitation. Between these two measures, the WTG departure has the advantage of being simpler and more economical to compute.